From ba72d47d8d8ed897b857ac6f2ecee086be7ee70c Mon Sep 17 00:00:00 2001
From: Liz Munch <muncheli@msu.edu>
Date: Mon, 27 Jan 2025 15:44:25 -0500
Subject: [PATCH 01/25] Testing figure referencing

---
 paper/figures/CombineGraphExample.png | Bin 0 -> 230017 bytes
 paper/figures/CombineGraphExample.svg |  61 ++++++++++++++++++++++++++
 paper/paper.md                        |  14 ++++--
 3 files changed, 71 insertions(+), 4 deletions(-)
 create mode 100644 paper/figures/CombineGraphExample.png
 create mode 100644 paper/figures/CombineGraphExample.svg

diff --git a/paper/figures/CombineGraphExample.png b/paper/figures/CombineGraphExample.png
new file mode 100644
index 0000000000000000000000000000000000000000..1d65f93111e1d33dc81ca202a83ececa4358ca05
GIT binary patch
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diff --git a/paper/paper.md b/paper/paper.md
index 241a1a9..9358da7 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -42,13 +42,19 @@ The *ECT* package for Python presented here provides a fast and well-documented
 
 # The ECT
 
-**TODO: Get permission for the Matisse example image**
 
-We start by defining the Euler Characteristic Transform, and direct the reader to [@Munch2025] for a full survey article on the subject. 
+We start by defining the Euler Characteristic Transform. 
+This construction came to the attention of the TDA community beginning with a proof of injectivity of the representation for simplicial complexes embedded in dimension up to 3 by Turner *et al.* [@Turner2014]. 
+Subsequently, using the machinery of Euler calculus @Schapira1995, this theorem was extended concurrently by [@Ghrist2018] and [@Curry2022] to nice enough subsets in any ambient dimension.
+We direct the reader to [@Munch2025] for a full survey article on the subject. 
 
-To start, we assume our input is an undirected graph $G$ with an embedding in 2D given by a map on the vertices $f: V(G) \to \mathbb{R}^2$. A graph can be constructed as follows. 
+To start, we assume our input is an undirected graph $G$ with an embedding in 2D given by a map on the vertices $f: V(G) \to \mathbb{R}^2$. A graph can be constructed as seen in \autoref{fig:example_graph}. 
+
+![(Left and middle) An example of an embedded graph with two choices of function $f_\omega$ drawn as the coloring on the nodes. (Right) The ECT matrix of the graph shown.\label{fig:example_graph}](figures/CombineGraphExample.png)
+
+
+![Testing scaling](figures/CombineGraphExample.png){ width=20% }
 
-![An example of an embedded graph](figures/example_graph.png)
 
 For a choice of direction $\theta \in [0,2\pi]$, we can induce a function on the vertex set. 
 Thinking of  this as $\omega \in \mathbb{S}^1$ by defining the unit vector $\omega = (\cos(\theta), \sin(\theta))$, the function $g_\omega$ is defined on the vertices of $G$ by taking the dot product of the embedding coordinates with the unit vector, specifically

From c0aa827dbcd176f9c4509251fe9e2358c97d6a1c Mon Sep 17 00:00:00 2001
From: Liz Munch <muncheli@msu.edu>
Date: Mon, 27 Jan 2025 15:56:45 -0500
Subject: [PATCH 02/25] Adding content and updating bib

---
 paper/figures/CombineGraphExample.png | Bin 230017 -> 232232 bytes
 paper/figures/CombineGraphExample.svg |  48 +-
 paper/paper.bib                       | 609 ++++++++++++++++++++++++++
 paper/paper.md                        |  19 +-
 4 files changed, 642 insertions(+), 34 deletions(-)

diff --git a/paper/figures/CombineGraphExample.png b/paper/figures/CombineGraphExample.png
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+         id="image1-9"
+         x="329.52328"
+         y="-103.12798" /></g></g></svg>
diff --git a/paper/paper.bib b/paper/paper.bib
index c8d3ac1..3145636 100644
--- a/paper/paper.bib
+++ b/paper/paper.bib
@@ -608,4 +608,613 @@ @Article{Munch2025
   publisher     = {Taylor \& Francis},
 }
 
+@Article{Turner2014,
+  author       = {K. Turner and S. Mukherjee and D. M. Boyer},
+  journal      = {Information and Inference},
+  title        = {Persistent homology transform for modeling shapes and surfaces},
+  year         = {2014},
+  month        = {Dec},
+  number       = {4},
+  pages        = {310--344},
+  volume       = {3},
+  comment      = {Requested copy from the MSU Library, 3/22/18},
+  creationdate = {2018-03-22T00:00:00},
+  doi          = {10.1093/imaiai/iau011},
+  file         = {:Persistence/Turner2014a_Published.pdf:PDF;:Persistence/Turner2014a.pdf:PDF;:Persistence/Turner2014a_ErikSlides.pdf:PDF},
+  priority     = {prio1},
+  publisher    = {Oxford University Press ({OUP})},
+  readstatus   = {read},
+}
+
+@InCollection{Schapira1995,
+  author    = {P. Schapira},
+  booktitle = {Applied Algebra, Algebraic Algorithms and Error-Correcting Codes},
+  publisher = {Springer Berlin Heidelberg},
+  title     = {Tomography of constructible functions},
+  year      = {1995},
+  pages     = {427--435},
+  doi       = {10.1007/3-540-60114-7_33},
+  file      = {:DirectionalTransform/Schapira1995.pdf:PDF},
+}
+
+@Article{Baryshnikov2011,
+  author    = {Yuliy Baryshnikov and Robert Ghrist and David Lipsky},
+  journal   = {Inverse Problems},
+  title     = {Inversion of {E}uler integral transforms with applications to sensor data},
+  year      = {2011},
+  month     = {nov},
+  number    = {12},
+  pages     = {124001},
+  volume    = {27},
+  doi       = {10.1088/0266-5611/27/12/124001},
+  file      = {:DirectionalTransform/Baryshnikov2011.pdf:PDF},
+  publisher = {{IOP} Publishing},
+}
+
+@Article{Curry2012,
+  author        = {Curry, Justin and Ghrist, Robert and Robinson, Michael},
+  title         = {{E}uler Calculus with Applications to Signals and Sensing},
+  year          = {2012},
+  month         = feb,
+  abstract      = {This article surveys the Euler calculus - an integral calculus based on Euler characteristic - and its applications to data, sensing, networks, and imaging.},
+  archiveprefix = {arXiv},
+  copyright     = {arXiv.org perpetual, non-exclusive license},
+  doi           = {10.48550/ARXIV.1202.0275},
+  eprint        = {1202.0275},
+  file          = {:Curry2012 - Euler Calculus with Applications to Signals and Sensing.pdf:PDF:http\://arxiv.org/pdf/1202.0275v1;:DirectionalTransform/Curry2012a.pdf:PDF},
+  keywords      = {Algebraic Topology (math.AT), FOS: Mathematics, 65R10, 58C35},
+  primaryclass  = {math.AT},
+  publisher     = {arXiv},
+}
+
+@InCollection{Heiss2017,
+  author    = {Teresa Heiss and Hubert Wagner},
+  booktitle = {Computer Analysis of Images and Patterns},
+  publisher = {Springer International Publishing},
+  title     = {Streaming Algorithm for {E}uler Characteristic Curves of Multidimensional Images},
+  year      = {2017},
+  pages     = {397--409},
+  doi       = {10.1007/978-3-319-64689-3_32},
+  file      = {:DirectionalTransform/Heiss2017.pdf:PDF},
+}
+
+@Article{Fasy2018,
+  author        = {Brittany Terese Fasy and Samuel Micka and David L. Millman and Anna Schenfisch and Lucia Williams},
+  journal       = {arXiv:1811.11337},
+  title         = {Challenges in Reconstructing Shapes from {E}uler Characteristic Curves},
+  year          = {2018},
+  month         = nov,
+  abstract      = {Shape recognition and classification is a problem with a wide variety of applications. Several recent works have demonstrated that topological descriptors can be used as summaries of shapes and utilized to compute distances. In this abstract, we explore the use of a finite number of Euler Characteristic Curves (ECC) to reconstruct plane graphs. We highlight difficulties that occur when attempting to adopt approaches for reconstruction with persistence diagrams to reconstruction with ECCs. Furthermore, we highlight specific arrangements of vertices that create problems for reconstruction and present several observations about how they affect the ECC-based reconstruction. Finally, we show that plane graphs without degree two vertices can be reconstructed using a finite number of ECCs.},
+  archiveprefix = {arXiv},
+  creationdate  = {2018-12-04T00:00:00},
+  eprint        = {http://arxiv.org/abs/1811.11337v1},
+  file          = {:Fasy2018 - Challenges in Reconstructing Shapes from Euler Characteristic Curves.pdf:PDF:http\://arxiv.org/pdf/1811.11337v1;:DirectionalTransform/Fasy2018b.pdf:PDF},
+  keywords      = {cs.CG},
+  primaryclass  = {cs.CG},
+}
+
+@Article{Ghrist2018,
+  author    = {Robert Ghrist and Rachel Levanger and Huy Mai},
+  journal   = {Journal of Applied and Computational Topology},
+  title     = {Persistent homology and {E}uler integral transforms},
+  year      = {2018},
+  month     = {aug},
+  number    = {1-2},
+  pages     = {55--60},
+  volume    = {2},
+  doi       = {10.1007/s41468-018-0017-1},
+  file      = {:DirectionalTransform/Ghrist2018_Article_PersistentHomologyAndEulerInte.pdf:PDF},
+  publisher = {Springer Science and Business Media {LLC}},
+}
+
+@PhdThesis{Betthauser2018,
+  author   = {Betthauser,Leo M.},
+  title    = {Topological Reconstruction of Grayscale Images},
+  year     = {2018},
+  note     = {Copyright - Copyright ProQuest Dissertations Publishing 2018; Last updated - 2023-03-08},
+  abstract = {Topological data analysis (TDA) is a powerful tool to solve classification problems using the underlying shape of data. Furthermore, TDA is useful in shape reconstruction of compact manifolds embedded in two and three dimensional Euclidean space. Unfortunately, these reconstructions can be computationally taxing. Many in the field are searching for solutions which are more computationally efficient and theoretical guarantees for the minimal amount of information for reconstructions within a given tolerance of error.Our approach is to study TDA on voxel data to offer both a computationally and memory efficient solution in practice. Assuming a lattice structure for our cubical geometric realization we are able to prove a sharp upper bound for all dimensions of 2d for the number of persistence diagrams generated from sublevel set filtrations required to reconstruct grayscale digital images. By improving topological reconstructions, the authors believe that TDA may become a pragmatic tool to apply to computerized tomography images for both storage and potentially classification for automated diagnosis of particular diseases such as melanoma.},
+  file     = {:DirectionalTransform/Betthauser2018.pdf:PDF},
+  isbn     = {9798837539299},
+  journal  = {ProQuest Dissertations and Theses},
+  keywords = {Topological data analysis; Shape reconstruction of compact manifolds; Classification problems; Voxel data; Mathematics; Applied mathematics; Computer science; Bioinformatics; Information science; 0364:Applied Mathematics; 0723:Information science; 0405:Mathematics; 0715:Bioinformatics; 0984:Computer science},
+  language = {English},
+  pages    = {74},
+  url      = {http://ezproxy.msu.edu/login?url=https://www.proquest.com/dissertations-theses/topological-reconstruction-grayscale-images/docview/2691763884/se-2},
+}
+
+@Article{Crawford2019,
+  author    = {Lorin Crawford and Anthea Monod and Andrew X. Chen and Sayan Mukherjee and Ra{\'{u}}l Rabad{\'{a}}n},
+  journal   = {Journal of the American Statistical Association},
+  title     = {Predicting Clinical Outcomes in Glioblastoma: An Application of Topological and Functional Data Analysis},
+  year      = {2019},
+  month     = {Oct},
+  number    = {531},
+  pages     = {1139--1150},
+  volume    = {115},
+  doi       = {10.1080/01621459.2019.1671198},
+  file      = {:DirectionalTransform/Crawford2019.pdf:PDF},
+  publisher = {Informa {UK} Limited},
+}
+
+@Article{Fasy2019,
+  author        = {Fasy, Brittany Terese and Micka, Samuel and Millman, David L. and Schenfisch, Anna and Williams, Lucia},
+  journal       = {arXiv:1912.12759},
+  title         = {A Faithful Discretization of the Augmented Persistent Homology Transform},
+  year          = {2019},
+  month         = {Dec},
+  abstract      = {The persistent homology transform (PHT) represents a shape with a multiset of persistence diagrams parameterized by the sphere of directions in the ambient space. In this work, we describe a finite set of diagrams that discretize the PHT such that it faithfully represents the underlying shape. We provide a discretization that is exponential in the dimension of the shape (making it Furthermore, we provide an output-sensitive algorithm; that is, the algorithm reports the discretization in time proportional to the size of the discretization. Finally, our approach relies only on knowing the heights and dimensions of topological events, meaning that it can be adapted to provide discretizations of other dimension-returning topological transforms, including the Betti curve transform.},
+  archiveprefix = {arXiv},
+  copyright     = {arXiv.org perpetual, non-exclusive license},
+  doi           = {10.48550/ARXIV.1912.12759},
+  eprint        = {1912.12759},
+  file          = {:Fasy2019 - A Faithful Discretization of the Augmented Persistent Homology Transform.pdf:PDF:http\://arxiv.org/pdf/1912.12759v4;:DirectionalTransform/Fasy2019.pdf:PDF},
+  keywords      = {Computational Geometry (cs.CG), FOS: Computer and information sciences},
+  primaryclass  = {cs.CG},
+  publisher     = {arXiv},
+}
+
+@InProceedings{Jiang2020,
+  author    = {Jiang, Qitong and Kurtek, Sebastian and Needham, Tom},
+  booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops},
+  title     = {The Weighted {E}uler Curve Transform for Shape and Image Analysis},
+  year      = {2020},
+  month     = {June},
+  file      = {:DirectionalTransform/Jiang2020.pdf:PDF},
+}
+
+@PhdThesis{Micka2020,
+  author   = {Micka,Samuel A.},
+  title    = {Searching and Reconstruction: Algorithms with Topological Descriptors},
+  year     = {2020},
+  abstract = {Topological data analysis and, more specifically, persistent homology have received significant attention as a method of describing the shape of complex data. Persistent homology measures the persistence (i.e., "relative size'') of topological features such as connected components, holes, voids, etc. as a space is filtered. The persistence is often plotted in what is referred to as a persistence diagram. Persistence diagrams encode both topological and geometric information about shapes. Moreover, certain parameterized sets of persistence diagrams are sufficient for representing particular classes of shapes. In other words, a set of persistence diagrams can be substituted for the shape. Shape representation using persistence diagrams has shown promise in several learning and classification tasks on shape data. However, choosing a sufficient parameterized set of persistence diagrams is challenging. Previous solutions utilize exhaustive sampling approaches based on assumptions on the geometry of the shape and algebraic results. We consider the inverse problem of "reconstructing'' the shape, using (augmented) persistence diagrams. Developing algorithms for reconstruction provides an alternative method of finding descriptors for representation that is optimized to minimize the number of diagrams and time complexity. In this work, we provide deterministic algorithms for reconstructing simplicial complexes in R^d and discuss challenges in reconstruction using other topological descriptors.Shape reconstruction, and several other areas of research utilizing the persistence diagram, are predisposed to generating large numbers of diagrams. As such, developing efficient methods for searching in the space of persistence diagrams is also of great importance. We consider the bottleneck distance in the space of persistence diagrams. The bottleneck distance is used often in practice for comparing one diagram to another. However, the cost of computing the bottleneck distance can grow prohibitive for large sets of diagrams using a brute-force approach. We offer a data structure and algorithm for identifying the approximate nearest neighbor (and approximate k-nearest neighbors) in the space of persistence diagrams in less time than the brute-force approach for large sets of diagrams.},
+  file     = {:DirectionalTransform/Micka2020-MickaThesis.pdf:PDF},
+  isbn     = {9798643180715},
+  journal  = {ProQuest Dissertations and Theses},
+  keywords = {Algorithms; Bottleneck distance; Montana State University; Nearest neighbor; Persistence diagram search; Shape reconstruction; Computer science; 0984:Computer science},
+  language = {English},
+  pages    = {169},
+  url      = {http://ezproxy.msu.edu/login?url=https://www.proquest.com/dissertations-theses/searching-reconstruction-algorithms-with/docview/2404677419/se-2},
+}
+
+@Article{Belton2020,
+  author    = {Robin Lynne Belton and Brittany Terese Fasy and Rostik Mertz and Samuel Micka and David L. Millman and Daniel Salinas and Anna Schenfisch and Jordan Schupbach and Lucia Williams},
+  journal   = {Computational Geometry},
+  title     = {Reconstructing embedded graphs from persistence diagrams},
+  year      = {2020},
+  month     = {Oct},
+  pages     = {101658},
+  volume    = {90},
+  abstract  = {The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space. Recent work has shown that well-chosen (finite) sets of PDs can differentiate between geometric simplicial complexes, providing a method for representing complex shapes using a finite set of descriptors. A related inverse problem is the following: given a set of PDs (or an oracle we can query for persistence diagrams), what is underlying geometric simplicial complex? In this paper, we present an algorithm for reconstructing embedded graphs in $\mathbb{R}^d$ (plane graphs in $\mathbb{R}^2$) with $n$ vertices from $n^2 - n + d + 1$ directional (augmented) PDs. Additionally, we empirically validate the correctness and time-complexity of our algorithm in $\mathbb{R}^2$ on randomly generated plane graphs using our implementation, and explain the numerical limitations of implementing our algorithm.},
+  doi       = {10.1016/j.comgeo.2020.101658},
+  file      = {:DirectionalTransform/Belton2019a.pdf:PDF;:Belton2020 - Reconstructing Embedded Graphs from Persistence Diagrams.pdf:PDF:http\://arxiv.org/pdf/1912.08913v2;:DirectionalTransform/Belton2020.pdf:PDF},
+  publisher = {Elsevier {BV}},
+}
+
+@Article{Amezquita2021,
+  author    = {Erik J Am{\'{e}}zquita and Michelle Y Quigley and Tim Ophelders and Jacob B Landis and Daniel Koenig and Elizabeth Munch and Daniel H Chitwood},
+  journal   = {in silico Plants},
+  title     = {Measuring hidden phenotype: quantifying the shape of barley seeds using the {E}uler characteristic transform},
+  year      = {2021},
+  month     = {Dec},
+  number    = {1},
+  volume    = {4},
+  doi       = {10.1093/insilicoplants/diab033},
+  editor    = {Tsu-Wei Chen and Stephen P Long},
+  file      = {:DirectionalTransform/Amezquita2021a.pdf:PDF},
+  publisher = {Oxford University Press ({OUP})},
+}
+
+@Article{Wang2021,
+  author    = {Bruce Wang and Timothy Sudijono and Henry Kirveslahti and Tingran Gao and Douglas M. Boyer and Sayan Mukherjee and Lorin Crawford},
+  journal   = {The Annals of Applied Statistics},
+  title     = {A statistical pipeline for identifying physical features that differentiate classes of 3D shapes},
+  year      = {2021},
+  month     = {jun},
+  number    = {2},
+  volume    = {15},
+  doi       = {10.1214/20-aoas1430},
+  file      = {:DirectionalTransform/Wang2021a.pdf:PDF},
+  publisher = {Institute of Mathematical Statistics},
+}
+
+@Article{Johnson2021,
+  author        = {Johnson, Megan and Jung, Jae-Hun},
+  journal       = {Journal of the Korean Society for Industrial and Applied Mathematics},
+  title         = {Instability of the Betti Sequence for Persistent Homology and a Stabilized Version of the Betti Sequence},
+  year          = {2021},
+  number        = {4},
+  volume        = {25},
+  abstract      = {Topological Data Analysis (TDA), a relatively new field of data analysis, has proved very useful in a variety of applications. The main persistence tool from TDA is persistent homology in which data structure is examined at many scales. Representations of persistent homology include persistence barcodes and persistence diagrams, both of which are not straightforward to reconcile with traditional machine learning algorithms as they are sets of intervals or multisets. The problem of faithfully representing barcodes and persistent diagrams has been pursued along two main avenues: kernel methods and vectorizations. One vectorization is the Betti sequence, or Betti curve, derived from the persistence barcode. While the Betti sequence has been used in classification problems in various applications, to our knowledge, the stability of the sequence has never before been discussed. In this paper we show that the Betti sequence is unstable under the 1-Wasserstein metric with regards to small perturbations in the barcode from which it is calculated. In addition, we propose a novel stabilized version of the Betti sequence based on the Gaussian smoothing seen in the Stable Persistence Bag of Words for persistent homology. We then introduce the normalized cumulative Betti sequence and provide numerical examples that support the main statement of the paper.},
+  archiveprefix = {arXiv},
+  comment       = {Published website is rather sketchy},
+  copyright     = {Creative Commons Attribution 4.0 International},
+  doi           = {10.12941/jksiam.2021.25.296},
+  eprint        = {2109.09218},
+  file          = {:Johnson2021 - Instability of the Betti Sequence for Persistent Homology and a Stabilized Version of the Betti Sequence.pdf:PDF:http\://arxiv.org/pdf/2109.09218v1;:DirectionalTransform/Johnson2021.pdf:PDF},
+  keywords      = {Algebraic Topology (math.AT), Computational Geometry (cs.CG), Numerical Analysis (math.NA), FOS: Mathematics, FOS: Computer and information sciences, 54-08},
+  primaryclass  = {math.AT},
+  publisher     = {arXiv},
+}
+
+@Article{Curry2022,
+  author        = {Justin Curry and Sayan Mukherjee and Katharine Turner},
+  journal       = {Transactions of the American Mathematical Society, Series B},
+  title         = {How Many Directions Determine a Shape and other Sufficiency Results for Two Topological Transforms},
+  year          = {2022},
+  month         = {Oct},
+  number        = {32},
+  pages         = {1006--1043},
+  volume        = {9},
+  abstract      = {In this paper we consider two topological transforms based on Euler calculus: the persistent homology transform (PHT) and the Euler characteristic transform (ECT). Both of these transforms are of interest for their mathematical properties as well as their applications to science and engineering, because they provide a way of summarizing shapes in a topological, yet quantitative, way. Both transforms take a shape, viewed as a tame subset M of R^d, and associates to each direction v in S^{d-1} a shape summary obtained by scanning M in the direction v. These shape summaries are either persistence diagrams or piecewise constant integer valued functions called Euler curves. By using an inversion theorem of Schapira, we show that both transforms are injective on the space of shapes---each shape has a unique transform. By making use of a stratified space structure on the sphere, induced by hyperplane divisions, we prove additional uniqueness results in terms of distributions on the space of Euler curves. Finally, our main result provides the first (to our knowledge) finite bound required to specify any shape in certain uncountable families of shapes, bounded below by curvature. This result is perhaps best appreciated in terms of shattering number or the perspective that any point in these particular moduli spaces of shapes is indexed using a tree of finite depth.},
+  archiveprefix = {arXiv},
+  date          = {2018-05-24},
+  doi           = {10.1090/btran/122},
+  eprint        = {1805.09782v1},
+  file          = {:Persistence/PersHomTransform/Curry2018.pdf:PDF;:Curry2022 - How Many Directions Determine a Shape and Other Sufficiency Results for Two Topological Transforms.pdf:PDF:http\://arxiv.org/pdf/1805.09782v1;:DirectionalTransform/Curry2018-arxiv-v2.pdf:PDF},
+  keywords      = {math.AT, math.ST, stat.TH},
+  primaryclass  = {math.AT},
+  publisher     = {American Mathematical Society ({AMS})},
+}
+
+@Article{Tang2022,
+  author    = {Wai Shing Tang and Gabriel Monteiro da Silva and Henry Kirveslahti and Erin Skeens and Bibo Feng and Timothy Sudijono and Kevin K. Yang and Sayan Mukherjee and Brenda Rubenstein and Lorin Crawford},
+  journal   = {{PLOS} Computational Biology},
+  title     = {A topological data analytic approach for discovering biophysical signatures in protein dynamics},
+  year      = {2022},
+  month     = {may},
+  number    = {5},
+  pages     = {e1010045},
+  volume    = {18},
+  doi       = {10.1371/journal.pcbi.1010045},
+  editor    = {Petras J Kundrotas},
+  file      = {:DirectionalTransform/Tang2022.pdf:PDF},
+  publisher = {Public Library of Science ({PLoS})},
+}
+
+@Article{Meng2022,
+  author        = {Meng, Kun and Wang, Jinyu and Crawford, Lorin and Eloyan, Ani},
+  journal       = {arXiv:2204.12699},
+  title         = {Randomness and Statistical Inference of Shapes via the Smooth {E}uler Characteristic Transform},
+  year          = {2022},
+  month         = {Apr},
+  abstract      = {In this paper, we provide the foundations for deriving the distributional properties of the smooth Euler characteristic transform. Motivated by functional data analysis, we propose two algorithms for testing hypotheses on random shapes based on these foundations. Simulation studies are provided to support our mathematical derivations and show the performance of our hypothesis testing framework. We apply our proposed algorithms to analyze a data set of mandibular molars from four genera of primates to test for shape differences and interpret the corresponding results from the morphology viewpoint. Our discussions connect the following fields: algebraic and computational topology, probability theory and stochastic processes, Sobolev spaces and functional analysis, statistical inference, morphology, and medical imaging.},
+  archiveprefix = {arXiv},
+  copyright     = {arXiv.org perpetual, non-exclusive license},
+  doi           = {10.48550/ARXIV.2204.12699},
+  eprint        = {2204.12699},
+  file          = {:Meng2022 - Randomness and Statistical Inference of Shapes Via the Smooth Euler Characteristic Transform.pdf:PDF:http\://arxiv.org/pdf/2204.12699v2;:DirectionalTransform/Meng2022.pdf:PDF},
+  keywords      = {Methodology (stat.ME), FOS: Computer and information sciences},
+  primaryclass  = {stat.ME},
+  publisher     = {arXiv},
+}
+
+@Article{Turner2022,
+  author        = {Turner, Katharine and Robins, Vanessa and Morgan, James},
+  journal       = {arXiv:2208.14583},
+  title         = {The Extended Persistent Homology Transform of manifolds with boundary},
+  year          = {2022},
+  month         = aug,
+  abstract      = {The Extended Persistent Homology Transform (XPHT) is a topological transform which takes as input a shape embedded in Euclidean space, and to each unit vector assigns the extended persistence module of the height function over that shape with respect to that direction. We can define a distance between two shapes by integrating over the sphere the distance between their respective extended persistence modules. By using extended persistence we get finite distances between shapes even when they have different Betti numbers. We use Morse theory to show that the extended persistence of a height function over a manifold with boundary can be deduced from the extended persistence for that height function restricted to the boundary, alongside labels on the critical points as positive or negative critical. We study the application of the XPHT to binary images; outlining an algorithm for efficient calculation of the XPHT exploiting relationships between the PHT of the boundary curves to the extended persistence of the foreground.},
+  archiveprefix = {arXiv},
+  copyright     = {Creative Commons Attribution 4.0 International},
+  doi           = {10.48550/ARXIV.2208.14583},
+  eprint        = {2208.14583},
+  file          = {:Turner2022 - The Extended Persistent Homology Transform of Manifolds with Boundary.pdf:PDF:http\://arxiv.org/pdf/2208.14583v1;:DirectionalTransform/Turner2022.pdf:PDF},
+  keywords      = {Algebraic Topology (math.AT), FOS: Mathematics, 55N31},
+  primaryclass  = {math.AT},
+  publisher     = {arXiv},
+}
+
+@Article{Dlotko2022,
+  author        = {Dłotko, Paweł and Gurnari, Davide},
+  journal       = {arXiv:2212.01666},
+  title         = {{E}uler Characteristic Curves and Profiles: a stable shape invariant for big data problems},
+  year          = {2022},
+  month         = {Dec},
+  abstract      = {Tools of Topological Data Analysis provide stable summaries encapsulating the shape of the considered data. Persistent homology, the most standard and well studied data summary, suffers a number of limitations; its computations are hard to distribute, it is hard to generalize to multifiltrations and is computationally prohibitive for big data-sets. In this paper we study the concept of Euler Characteristics Curves, for one parameter filtrations and Euler Characteristic Profiles, for multi-parameter filtrations. While being a weaker invariant in one dimension, we show that Euler Characteristic based approaches do not possess some handicaps of persistent homology; we show efficient algorithms to compute them in a distributed way, their generalization to multifiltrations and practical applicability for big data problems. In addition we show that the Euler Curves and Profiles enjoys certain type of stability which makes them robust tool in data analysis. Lastly, to show their practical applicability, multiple use-cases are considered.},
+  archiveprefix = {arXiv},
+  copyright     = {arXiv.org perpetual, non-exclusive license},
+  doi           = {10.48550/ARXIV.2212.01666},
+  eprint        = {2212.01666},
+  file          = {:Dlotko2022 - Euler Characteristic Curves and Profiles_ a Stable Shape Invariant for Big Data Problems.pdf:PDF:http\://arxiv.org/pdf/2212.01666v1;:DirectionalTransform/Dlotko2022.pdf:PDF},
+  keywords      = {Algebraic Topology (math.AT), Computational Geometry (cs.CG), Machine Learning (cs.LG), FOS: Mathematics, FOS: Computer and information sciences},
+  primaryclass  = {math.AT},
+  publisher     = {arXiv},
+}
+
+@Article{Wang2022,
+  author        = {Wang, Fan and Wagner, Hubert and Chen, Chao},
+  journal       = {arXiv:2203.09087},
+  title         = {GPU Computation of the {E}uler Characteristic Curve for Imaging Data},
+  year          = {2022},
+  month         = mar,
+  abstract      = {Persistent homology is perhaps the most popular and useful tool offered by topological data analysis, with point-cloud data being the most common setup. Its older cousin, the Euler characteristic curve (ECC) is less expressive, but far easier to compute. It is particularly suitable for analyzing imaging data, and is commonly used in fields ranging from astrophysics to biomedical image analysis. These fields are embracing GPU computations to handle increasingly large datasets. We therefore propose an optimized GPU implementation of ECC computation for 2D and 3D grayscale images. The goal of this paper is twofold. First, we offer a practical tool, illustrating its performance with thorough experimentation, but also explain its inherent shortcomings. Second, this simple algorithm serves as a perfect backdrop for highlighting basic GPU programming techniques that make our implementation so efficient, and some common pitfalls we avoided. This is intended as a step towards a wider usage of GPU programming in computational geometry and topology software. We find this is particularly important as geometric and topological tools are used in conjunction with modern, GPU-accelerated machine learning frameworks.},
+  archiveprefix = {arXiv},
+  copyright     = {Creative Commons Attribution Non Commercial No Derivatives 4.0 International},
+  doi           = {10.48550/ARXIV.2203.09087},
+  eprint        = {2203.09087},
+  file          = {:Wang2022 - GPU Computation of the Euler Characteristic Curve for Imaging Data.pdf:PDF:http\://arxiv.org/pdf/2203.09087v2;:DirectionalTransform/Wang2022.pdf:PDF},
+  keywords      = {Computational Geometry (cs.CG), FOS: Computer and information sciences},
+  primaryclass  = {cs.CG},
+  publisher     = {arXiv},
+}
+
+@Article{Perez2022,
+  author        = {Perez, Daniel},
+  title         = {{E}uler and {B}etti curves are stable under Wasserstein deformations of distributions of stochastic processes},
+  year          = {2022},
+  month         = nov,
+  abstract      = {Euler and Betti curves of stochastic processes defined on a $d$-dimensional compact Riemannian manifold which are almost surely in a Sobolev space $W^{n,s}(X,\mathbb{R})$ (with $d<n$) are stable under perturbations of the distributions of said processes in a Wasserstein metric. Moreover, Wasserstein stability is shown to hold for all $p>\frac{d}{n}$ for persistence diagrams stemming from functions in $W^{n,s}(X,\mathbb{R})$.},
+  archiveprefix = {arXiv},
+  copyright     = {Creative Commons Attribution 4.0 International},
+  doi           = {10.48550/ARXIV.2211.12384},
+  eprint        = {2211.12384},
+  file          = {:Perez2022 - Euler and Betti Curves Are Stable under Wasserstein Deformations of Distributions of Stochastic Processes.pdf:PDF:http\://arxiv.org/pdf/2211.12384v1;:DirectionalTransform/Perez2022.pdf:PDF},
+  keywords      = {Probability (math.PR), Algebraic Topology (math.AT), FOS: Mathematics, 60G60, 62M40, 55N31},
+  primaryclass  = {math.PR},
+  publisher     = {arXiv},
+}
+
+@Article{Marsh2023,
+  author        = {Marsh, Lewis and Beers, David},
+  journal       = {arXiv:2303.13200},
+  title         = {Stability and Inference of the {E}uler Characteristic Transform},
+  year          = {2023},
+  month         = mar,
+  abstract      = {The Euler characteristic transform (ECT) is a signature from topological data analysis (TDA) which summarises shapes embedded in Euclidean space. Compared with other TDA methods, the ECT is fast to compute and it is a sufficient statistic for a broad class of shapes. However, small perturbations of a shape can lead to large distortions in its ECT. In this paper, we propose a new metric on compact one-dimensional shapes and prove that the ECT is stable with respect to this metric. Crucially, our result uses curvature, rather than the size of a triangulation of an underlying shape, to control stability. We further construct a computationally tractable statistical estimator of the ECT based on the theory of Gaussian processes. We use our stability result to prove that our estimator is consistent on shapes perturbed by independent ambient noise; i.e., the estimator converges to the true ECT as the sample size increases.},
+  archiveprefix = {arXiv},
+  copyright     = {Creative Commons Attribution 4.0 International},
+  doi           = {10.48550/ARXIV.2303.13200},
+  eprint        = {2303.13200},
+  file          = {:Marsh2023 - Stability and Inference of the Euler Characteristic Transform.pdf:PDF:http\://arxiv.org/pdf/2303.13200v1;:DirectionalTransform/Marsh2023.pdf:PDF},
+  keywords      = {Statistics Theory (math.ST), Algebraic Topology (math.AT), FOS: Mathematics},
+  primaryclass  = {math.ST},
+  publisher     = {arXiv},
+}
+
+@Article{Paik2023,
+  author        = {Paik, Taejin},
+  journal       = {arXiv:2302.13565},
+  title         = {Invariant Representations of Embedded Simplicial Complexes},
+  year          = {2023},
+  month         = feb,
+  abstract      = {Analyzing embedded simplicial complexes, such as triangular meshes and graphs, is an important problem in many fields. We propose a new approach for analyzing embedded simplicial complexes in a subdivision-invariant and isometry-invariant way using only topological and geometric information. Our approach is based on creating and analyzing sufficient statistics and uses a graph neural network. We demonstrate the effectiveness of our approach using a synthetic mesh data set.},
+  archiveprefix = {arXiv},
+  copyright     = {Creative Commons Attribution 4.0 International},
+  doi           = {10.48550/ARXIV.2302.13565},
+  eprint        = {2302.13565},
+  file          = {:Paik2023 - Invariant Representations of Embedded Simplicial Complexes.pdf:PDF:http\://arxiv.org/pdf/2302.13565v1;:DirectionalTransform/Paik2023.pdf:PDF},
+  keywords      = {Machine Learning (cs.LG), Artificial Intelligence (cs.AI), Computational Geometry (cs.CG), Algebraic Topology (math.AT), FOS: Computer and information sciences, FOS: Mathematics, I.2.6; I.5.1; I.5.2, 68T07, 55N31},
+  primaryclass  = {cs.LG},
+  publisher     = {arXiv},
+}
+
+@Article{Fasy2022,
+  author        = {Fasy, Brittany Terese and Patel, Amit},
+  title         = {Persistent Homology Transform Cosheaf},
+  year          = {2022},
+  month         = aug,
+  abstract      = {We employ the recent discovery of functoriality for persistent homology to recast the Persistent Homology Transform of a geometric complex as a cosheaf of combinatorial persistence diagrams. Detailed examples are provided. We hope the recasting of the PH transform as a cellular cosheaf will allow for the adoption of existing methods from category theory and (co)sheaf theory to the study of shapes.},
+  archiveprefix = {arXiv},
+  copyright     = {Creative Commons Attribution 4.0 International},
+  doi           = {10.48550/ARXIV.2208.05243},
+  eprint        = {2208.05243},
+  file          = {:Fasy2022 - Persistent Homology Transform Cosheaf.pdf:PDF:http\://arxiv.org/pdf/2208.05243v1},
+  keywords      = {Algebraic Topology (math.AT), Computational Geometry (cs.CG), Category Theory (math.CT), FOS: Mathematics, FOS: Computer and information sciences},
+  primaryclass  = {math.AT},
+  publisher     = {arXiv},
+}
+
+@Article{Amezquita2020,
+  author            = {Erik J. Am{\'{e}}zquita and Michelle Y. Quigley and Tim Ophelders and Elizabeth Munch and Daniel H. Chitwood},
+  journal           = {Developmental Dynamics},
+  title             = {The shape of things to come: Topological data analysis and biology, from molecules to organisms},
+  year              = {2020},
+  month             = {Apr},
+  authorwithsymbols = {Erik J. Am{\'{e}}zquita$^\dagger$ and Michelle Y. Quigley and Tim Ophelders and Elizabeth Munch and Daniel H. Chitwood},
+  comment           = {CCF-1907591, CMMI-1800466;},
+  creationdate      = {2020-06-28T00:00:00},
+  doi               = {10.1002/dvdy.175},
+  image             = {Amezquita2020_PlantScans.png},
+  keywords          = {journal},
+  publisher         = {Wiley},
+}
+
+@Book{Friedman2018,
+  author    = {Michael Friedman},
+  publisher = {Springer International Publishing},
+  title     = {A History of Folding in Mathematics},
+  year      = {2018},
+  doi       = {10.1007/978-3-319-72487-4},
+}
+
+@Article{Euler1758,
+  author  = {Euler, Leonhard},
+  journal = {Euler Archive - All Works},
+  title   = {Elementa doctrinae solidorum},
+  year    = {1758},
+  file    = {:DirectionalTransform/Euler1758.pdf:PDF},
+}
+
+@Book{Dries1998,
+  author    = {L. P. D. van den Dries},
+  publisher = {Cambridge University Press},
+  title     = {Tame Topology and {O}-minimal Structures},
+  year      = {1998},
+  month     = {may},
+  doi       = {10.1017/cbo9780511525919},
+}
+
+@Article{White2020,
+  author    = {Alexander E. White and Rebecca B. Dikow and Makinnon Baugh and Abigail Jenkins and Paul B. Frandsen},
+  journal   = {Applications in Plant Sciences},
+  title     = {Generating segmentation masks of herbarium specimens and a data set for training segmentation models using deep learning},
+  year      = {2020},
+  month     = {jun},
+  number    = {6},
+  volume    = {8},
+  doi       = {10.1002/aps3.11352},
+  publisher = {Wiley},
+}
+
+@Book{Gower2004,
+  author    = {John C Gower and Garmt B Dijksterhuis},
+  publisher = {Oxford University Press},
+  title     = {Procrustes Problems},
+  year      = {2004},
+  month     = {jan},
+  doi       = {10.1093/acprof:oso/9780198510581.001.0001},
+}
+
+@Article{Marsh2022,
+  author        = {Marsh, Lewis and Zhou, Felix Y. and Qin, Xiao and Lu, Xin and Byrne, Helen M. and Harrington, Heather A.},
+  journal       = {arXiv:2212.10883},
+  title         = {Detecting Temporal shape changes with the {E}uler Characteristic Transform},
+  year          = {2022},
+  month         = {Dec},
+  abstract      = {Organoids are multi-cellular structures which are cultured in vitro from stem cells to resemble specific organs (e.g., brain, liver) in their three-dimensional composition. Dynamic changes in the shape and composition of these model systems can be used to understand the effect of mutations and treatments in health and disease. In this paper, we propose a new technique in the field of topological data analysis for DEtecting Temporal shape changes with the Euler Characteristic Transform (DETECT). DETECT is a rotationally invariant signature of dynamically changing shapes. We demonstrate our method on a data set of segmented videos of mouse small intestine organoid experiments and show that it outperforms classical shape descriptors. We verify our method on a synthetic organoid data set and illustrate how it generalises to 3D. We conclude that DETECT offers rigorous quantification of organoids and opens up computationally scalable methods for distinguishing different growth regimes and assessing treatment effects.},
+  archiveprefix = {arXiv},
+  copyright     = {Creative Commons Attribution 4.0 International},
+  doi           = {10.48550/ARXIV.2212.10883},
+  eprint        = {2212.10883},
+  file          = {:Marsh2022 - Detecting Temporal Shape Changes with the Euler Characteristic Transform.pdf:PDF:http\://arxiv.org/pdf/2212.10883v2;:TOREVIEW/TRMA/TRMA-2022-011_Proof_hi.pdf:PDF},
+  keywords      = {Quantitative Methods (q-bio.QM), Algebraic Topology (math.AT), Tissues and Organs (q-bio.TO), FOS: Biological sciences, FOS: Mathematics},
+  primaryclass  = {q-bio.QM},
+  publisher     = {arXiv},
+}
+
+@Article{Roy2020,
+  author    = {A. Roy and R. A. I. Haque and A. J. Mitra and M. Dutta Choudhury and S. Tarafdar and T. Dutta},
+  journal   = {Physics of Fluids},
+  title     = {Understanding flow features in drying droplets via {E}uler characteristic surfaces{\textemdash}A topological tool},
+  year      = {2020},
+  month     = {Dec},
+  number    = {12},
+  pages     = {123310},
+  volume    = {32},
+  doi       = {10.1063/5.0026807},
+  publisher = {{AIP} Publishing},
+}
+
+@Article{Fasy2022a,
+  author        = {Fasy, Brittany Terese and Micka, Samuel and Millman, David L. and Schenfisch, Anna and Williams, Lucia},
+  title         = {Efficient Graph Reconstruction and Representation Using Augmented Persistence Diagrams},
+  year          = {2022},
+  month         = {Dec},
+  abstract      = {Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of persistence diagrams, parameterized by directions in the ambient space. A recent advance in understanding the PHT used the framework of reconstruction in order to find finite a set of directions to faithfully represent the shape, a result that is of both theoretical and practical interest. In this paper, we improve upon this result and present an improved algorithm for graph -- and, more generally one-skeleton -- reconstruction. The improvement comes in reconstructing the edges, where we use a radial binary (multi-)search. The binary search employed takes advantage of the fact that the edges can be ordered radially with respect to a reference plane, a feature unique to graphs.},
+  archiveprefix = {arXiv},
+  copyright     = {Creative Commons Attribution 4.0 International},
+  doi           = {10.48550/ARXIV.2212.13206},
+  eprint        = {2212.13206},
+  file          = {:Fasy2022a - Efficient Graph Reconstruction and Representation Using Augmented Persistence Diagrams.pdf:PDF:http\://arxiv.org/pdf/2212.13206v1;:DirectionalTransform/Fasy2022.pdf:PDF},
+  keywords      = {Computational Geometry (cs.CG), FOS: Computer and information sciences},
+  primaryclass  = {cs.CG},
+  publisher     = {arXiv},
+}
+
+@InCollection{Cates2017,
+  author    = {Joshua Cates and Shireen Elhabian and Ross Whitaker},
+  booktitle = {Statistical Shape and Deformation Analysis},
+  publisher = {Elsevier},
+  title     = {{ShapeWorks}},
+  year      = {2017},
+  pages     = {257--298},
+  doi       = {10.1016/b978-0-12-810493-4.00012-2},
+}
+
+@Article{Dupuis1998,
+  author    = {Paul Dupuis and Ulf Grenander and Michael I. Miller},
+  journal   = {Quarterly of Applied Mathematics},
+  title     = {Variational problems on flows of diffeomorphisms for image matching},
+  year      = {1998},
+  number    = {3},
+  pages     = {587--600},
+  volume    = {56},
+  doi       = {10.1090/qam/1632326},
+  publisher = {American Mathematical Society ({AMS})},
+}
+
+@Article{Gao2019,
+  author    = {Tingran Gao and Shahar Z. Kovalsky and Ingrid Daubechies},
+  journal   = {{SIAM} Journal on Mathematics of Data Science},
+  title     = {Gaussian Process Landmarking on Manifolds},
+  year      = {2019},
+  month     = {jan},
+  number    = {1},
+  pages     = {208--236},
+  volume    = {1},
+  doi       = {10.1137/18m1184035},
+  publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})},
+}
+
+@Article{Boyer2011,
+  author    = {Doug M. Boyer and Yaron Lipman and Elizabeth St. Clair and Jesus Puente and Biren A. Patel and Thomas Funkhouser and Jukka Jernvall and Ingrid Daubechies},
+  journal   = {Proceedings of the National Academy of Sciences},
+  title     = {Algorithms to automatically quantify the geometric similarity of anatomical surfaces},
+  year      = {2011},
+  month     = {Oct},
+  number    = {45},
+  pages     = {18221--18226},
+  volume    = {108},
+  doi       = {10.1073/pnas.1112822108},
+  publisher = {Proceedings of the National Academy of Sciences},
+}
+
+@Article{Wang2023,
+  author  = {Elena Wang and Elizabeth Munch and Erin Chambers},
+  journal = {In progress},
+  title   = {A Distance for Geometric Graphs via the Labeled Merge Tree Interleaving Distance},
+  year    = {2023},
+}
+
+@Article{Beltramo2022,
+  author    = {Gabriele Beltramo and Primoz Skraba and Rayna Andreeva and Rik Sarkar and Ylenia Giarratano and Miguel O. Bernabeu},
+  journal   = {Foundations of Data Science},
+  title     = {{E}uler characteristic surfaces},
+  year      = {2022},
+  number    = {4},
+  pages     = {505--536},
+  volume    = {4},
+  doi       = {10.3934/fods.2021027},
+  file      = {:DirectionalTransform/Beltramo2022.pdf:PDF},
+  publisher = {American Institute of Mathematical Sciences ({AIMS})},
+}
+
+@InProceedings{Nadimpalli2023,
+  author        = {Nadimpalli, Kalyan Varma and Chattopadhyay, Amit and Rieck, Bastian},
+  booktitle     = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops},
+  title         = {Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images From Single 2D Slices},
+  year          = {2023},
+  month         = {June},
+  pages         = {571-579},
+  publisher     = {arXiv},
+  abstract      = {The computer vision task of reconstructing 3D images, i.e., shapes, from their single 2D image slices is extremely challenging, more so in the regime of limited data. Deep learning models typically optimize geometric loss functions, which may lead to poor reconstructions as they ignore the structural properties of the shape. To tackle this, we propose a novel topological loss function based on the Euler Characteristic Transform. This loss can be used as an inductive bias to aid the optimization of any neural network toward better reconstructions in the regime of limited data. We show the effectiveness of the proposed loss function by incorporating it into SHAPR, a state-of-the-art shape reconstruction model, and test it on two benchmark datasets, viz., Red Blood Cells and Nuclei datasets. We also show a favourable property, namely injectivity and discuss the stability of the topological loss function based on the Euler Characteristic Transform.},
+  archiveprefix = {arXiv},
+  copyright     = {Creative Commons Attribution Non Commercial Share Alike 4.0 International},
+  doi           = {10.48550/ARXIV.2303.05286},
+  eprint        = {2303.05286},
+  file          = {:http\://arxiv.org/pdf/2303.05286v1:PDF;:DirectionalTransform/Nadimpalli2023.pdf:PDF},
+  journal       = {arXiv:2303.05286},
+  keywords      = {Machine Learning (cs.LG), Quantitative Methods (q-bio.QM), FOS: Computer and information sciences, FOS: Biological sciences},
+  primaryclass  = {cs.LG},
+}
+
+@Article{Kirveslahti2023,
+  author        = {Kirveslahti, Henry and Mukherjee, Sayan},
+  journal       = {Journal of Applied and Computational Topology},
+  title         = {Representing fields without correspondences: the lifted {E}uler characteristic transform},
+  year          = {2023},
+  issn          = {2367-1734},
+  month         = aug,
+  abstract      = {Topological transforms have been very useful in statistical analysis of shapes or surfaces without restrictions that the shapes are diffeomorphic and requiring the estimation of correspondence maps. In this paper we introduce two topological transforms that generalize from shapes to fields, $f:\mathbf{R}^3 \rightarrow \mathbf{R}$. Both transforms take a field and associate to each direction $v\in S^{d-1}$ a summary obtained by scanning the field in the direction $v$. The transforms we introduce are of interest for both applications as well as their theoretical properties. The topological transforms for shapes are based on an Euler calculus on sets. A key insight in this paper is that via a lifting argument one can develop an Euler calculus on real valued functions from the standard Euler calculus on sets, this idea is at the heart of the two transforms we introduce. We prove the transforms are injective maps. We show for particular moduli spaces of functions we can upper bound the number of directions needed determine any particular function.},
+  archiveprefix = {arXiv},
+  copyright     = {arXiv.org perpetual, non-exclusive license},
+  doi           = {10.48550/ARXIV.2111.04788},
+  eprint        = {2111.04788},
+  file          = {:http\://arxiv.org/pdf/2111.04788v4:PDF;:DirectionalTransform/Kirveslahti2021.pdf:PDF},
+  keywords      = {Algebraic Topology (math.AT), FOS: Mathematics, 62R40, 52C45 (Primary) 68U05 (Secondary)},
+  primaryclass  = {math.AT},
+  publisher     = {Springer Science and Business Media LLC},
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}
diff --git a/paper/paper.md b/paper/paper.md
index 9358da7..70debee 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -50,10 +50,9 @@ We direct the reader to [@Munch2025] for a full survey article on the subject.
 
 To start, we assume our input is an undirected graph $G$ with an embedding in 2D given by a map on the vertices $f: V(G) \to \mathbb{R}^2$. A graph can be constructed as seen in \autoref{fig:example_graph}. 
 
-![(Left and middle) An example of an embedded graph with two choices of function $f_\omega$ drawn as the coloring on the nodes. (Right) The ECT matrix of the graph shown.\label{fig:example_graph}](figures/CombineGraphExample.png)
 
 
-![Testing scaling](figures/CombineGraphExample.png){ width=20% }
+<!-- ![Testing scaling](figures/CombineGraphExample.png){ width=20% } -->
 
 
 For a choice of direction $\theta \in [0,2\pi]$, we can induce a function on the vertex set. 
@@ -62,11 +61,7 @@ $$
 g_\omega(v) = \langle f(v), \omega\rangle.
 $$
 <!-- This is done in the code using the `g_omega` method as shown.  -->
-
-Some examples are shown below. 
-
-![Example 1](figures/example_graph_pi_over_2.png)
-![Example 2](figures/example_graph_pi_over_2.png)
+Some examples are shown in \autoref{fig:example_graph}. 
 
 Now we can set up the ECT for the embedded graph. The ECT is defined as 
 $$
@@ -79,14 +74,14 @@ Perhaps a better way of looking at this same function for visualization purposes
 $$
 \begin{matrix}
 \text{ECT}(G): & \mathbb{S}^1 \times \mathbb{R} & \to &  \mathbb{Z}\\
-& (\omega,a) & \mapsto & \chi(g_\omega^{-1}(-\infty,a]) 
+& (\omega,a) & \mapsto & \chi(g_\omega^{-1}(-\infty,a]).
 \end{matrix}
 $$
-After discretizing, the example embedded graph has an ECT matrix as shown below. 
-![Example ECT](figures/example_ect.png)
+After discretizing, the example embedded graph has an ECT matrix as shown in the bottom row of \autoref{fig:example_graph}.
+The main functionality of the `ECT` package is to be able to compute the ECT matrix for graphs embedded in $\mathbb{R}^d$ for $d \in \{2,3\}$.
+
+![(Top row) An example of an embedded graph with two choices of function $f_\omega$ drawn as the coloring on the nodes. (Bottom) The ECT matrix of the graph shown.\label{fig:example_graph}](figures/CombineGraphExample.png)
 
-The main functionality of the package is to be able to compute the ECT matrix for graphs embedded in $\mathbb{R}^d$ for $d \in \{2,3\}$.
-Additional functionality is given for embedded CW complexes, such as the example shown below.  
 
 ## Extension to higher dimensional embedding
 

From 00cd4cf6178cd84c57beaffb9b5fdd3324d91954 Mon Sep 17 00:00:00 2001
From: Liz Munch <muncheli@msu.edu>
Date: Tue, 28 Jan 2025 15:43:31 -0500
Subject: [PATCH 03/25] Added refs

---
 paper/paper.bib | 24 ++++++++++++++++++++++++
 paper/paper.md  |  6 +++++-
 2 files changed, 29 insertions(+), 1 deletion(-)

diff --git a/paper/paper.bib b/paper/paper.bib
index 3145636..655739d 100644
--- a/paper/paper.bib
+++ b/paper/paper.bib
@@ -1217,4 +1217,28 @@ @Article{Kirveslahti2023
   publisher     = {Springer Science and Business Media LLC},
 }
 
+@InCollection{Diaconis2013,
+  author       = {Persi Diaconis and Susan Holmes and Mehrdad Shahshahani},
+  booktitle    = {Advances in Modern Statistical Theory and Applications: A Festschrift in honor of Morris L. Eaton},
+  publisher    = {Institute of Mathematical Statistics},
+  title        = {Sampling from a Manifold},
+  year         = {2013},
+  pages        = {102--125},
+  creationdate = {2017-11-03T00:00:00},
+  doi          = {10.1214/12-imscoll1006},
+  file         = {:Diaconis2013.pdf:PDF},
+}
+
+@Book{Mardia1999,
+  author    = {Mardia, Kanti V. and Jupp, Peter E.},
+  publisher = {Wiley},
+  title     = {Directional Statistics},
+  year      = {1999},
+  isbn      = {9780470316979},
+  month     = jan,
+  doi       = {10.1002/9780470316979},
+  issn      = {1940-6347},
+  journal   = {Wiley Series in Probability and Statistics},
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}
diff --git a/paper/paper.md b/paper/paper.md
index 70debee..c717002 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -85,7 +85,11 @@ The main functionality of the `ECT` package is to be able to compute the ECT mat
 
 ## Extension to higher dimensional embedding
 
-**TODO: If we're going to have 3D stuff implemented, we need the version for that descibed.**
+In theory, the ECT can be defined for a space embedded in $\R^d$ for any $d$. 
+In practice, for applications geared toward encoding shapes seen in the physical world, this is largely limited to the cases $d=2$ or $d=3$. 
+Still, issues arise in applications in the case of $d=3$ where the choice for discretizing the directions chosen on the sphere $\mathbb{S}^2$ is not canonical like the case of $d=2$ and the circle $\mathbb{S}^1$ [@Mardia1999]. 
+
+
 
 ## Extension to higher dimensional cells
 

From ed2fe5b22501323b949d52331729339b8a1fa2e6 Mon Sep 17 00:00:00 2001
From: Liz Munch <muncheli@msu.edu>
Date: Thu, 30 Jan 2025 13:34:45 -0500
Subject: [PATCH 04/25] Compile pretty please!

---
 paper/paper.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/paper/paper.md b/paper/paper.md
index c717002..f6b77a0 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -85,7 +85,7 @@ The main functionality of the `ECT` package is to be able to compute the ECT mat
 
 ## Extension to higher dimensional embedding
 
-In theory, the ECT can be defined for a space embedded in $\R^d$ for any $d$. 
+In theory, the ECT can be defined for a space embedded in $\mathbb{R}^d$ for any $d$. 
 In practice, for applications geared toward encoding shapes seen in the physical world, this is largely limited to the cases $d=2$ or $d=3$. 
 Still, issues arise in applications in the case of $d=3$ where the choice for discretizing the directions chosen on the sphere $\mathbb{S}^2$ is not canonical like the case of $d=2$ and the circle $\mathbb{S}^1$ [@Mardia1999]. 
 

From 014471081cf7e9e9cc64a402ef078dbbd60348f0 Mon Sep 17 00:00:00 2001
From: Liz Munch <muncheli@msu.edu>
Date: Fri, 7 Mar 2025 11:28:39 -0500
Subject: [PATCH 05/25] Minor edits

---
 paper/paper.md | 10 ++++++++--
 1 file changed, 8 insertions(+), 2 deletions(-)

diff --git a/paper/paper.md b/paper/paper.md
index f6b77a0..0137d0e 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -88,12 +88,18 @@ The main functionality of the `ECT` package is to be able to compute the ECT mat
 In theory, the ECT can be defined for a space embedded in $\mathbb{R}^d$ for any $d$. 
 In practice, for applications geared toward encoding shapes seen in the physical world, this is largely limited to the cases $d=2$ or $d=3$. 
 Still, issues arise in applications in the case of $d=3$ where the choice for discretizing the directions chosen on the sphere $\mathbb{S}^2$ is not canonical like the case of $d=2$ and the circle $\mathbb{S}^1$ [@Mardia1999]. 
-
-
+To this end we have implemented **Make sure this is true** the 3D ECT for graph inputs. 
+In order to handle issues with choices of direction discretiziations, we have implemented multiple options for sampling, **Which ones? **
+- Uniform in $\theta$ and $\rho$? 
+- Whatever other sampling methods I can find in that directions book. 
+- From wikipedia: 
+  - [Kent distribution](https://en.wikipedia.org/wiki/Kent_distribution) 
+  - [von Mises-Fisher](https://en.wikipedia.org/wiki/Von_Mises%E2%80%93Fisher_distribution#Matrix_Von_Mises-Fisher)
 
 ## Extension to higher dimensional cells
 
 **TODO: add in stuff about the CW complex inputs**
+- CW Complexes might be too broad a term. Perhaps "[polygon mesh](https://en.wikipedia.org/wiki/Polygon_mesh)" is better. 
 
 ## Distances 
 

From ea07bc3d873a0b1fe404761f4d94ba51e3d0f998 Mon Sep 17 00:00:00 2001
From: yemeen <yemeen.ayub.14@cnu.edu>
Date: Fri, 29 Aug 2025 19:30:46 -0400
Subject: [PATCH 06/25] clean up old sections and add start of SON

---
 paper/paper.md | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/paper/paper.md b/paper/paper.md
index 0137d0e..13080ac 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -56,7 +56,7 @@ To start, we assume our input is an undirected graph $G$ with an embedding in 2D
 
 
 For a choice of direction $\theta \in [0,2\pi]$, we can induce a function on the vertex set. 
-Thinking of  this as $\omega \in \mathbb{S}^1$ by defining the unit vector $\omega = (\cos(\theta), \sin(\theta))$, the function $g_\omega$ is defined on the vertices of $G$ by taking the dot product of the embedding coordinates with the unit vector, specifically
+Thinking of this as $\omega \in \mathbb{S}^1$ by defining the unit vector $\omega = (\cos(\theta), \sin(\theta))$, the function $g_\omega$ is defined on the vertices of $G$ by taking the dot product of the embedding coordinates with the unit vector, specifically
 $$
 g_\omega(v) = \langle f(v), \omega\rangle.
 $$
@@ -96,7 +96,7 @@ In order to handle issues with choices of direction discretiziations, we have im
   - [Kent distribution](https://en.wikipedia.org/wiki/Kent_distribution) 
   - [von Mises-Fisher](https://en.wikipedia.org/wiki/Von_Mises%E2%80%93Fisher_distribution#Matrix_Von_Mises-Fisher)
 
-## Extension to higher dimensional cells
+
 
 **TODO: add in stuff about the CW complex inputs**
 - CW Complexes might be too broad a term. Perhaps "[polygon mesh](https://en.wikipedia.org/wiki/Polygon_mesh)" is better. 
@@ -109,11 +109,11 @@ Additional code is included for computing distances between the resulting ECT ma
 
 ## Generalized versions of ECT
 
-SECT, DECT, whatever else? 
+The ECT package provides implementations for both the Smooth Euler Characteristic Transform and the Differentiable Euler Characteristic Transform. This allows for users to quickly examine their dataset under the lense of various topological transforms to find what best suits their problem.
 
-# Statement of need
+# Statement of Need
 
-**TODO: Are there any existing ECT packages?**
+Despite the ECT's mathematical elegances, there has been a notable absense of efficient, user-friendly Python implementations that can handle the computational demands of modern research datasets. The ECT package addressed this by leveraging Numba's just-in-time compilation to achieve significant speedups over naive Python implementations, making it practical to compute ECTs for large-scale datasets. This performance is then complimented by the many utility functions for visualizing and comparing different Euler Characteristic Tranforms such as the ECT, SECT, and the DECT.
 
 Yemeen is going to find any needed references.
 

From fec9095b5c151054c90b3f62f68e99d17919dbd7 Mon Sep 17 00:00:00 2001
From: yemeen <yemeen.ayub.14@cnu.edu>
Date: Thu, 18 Sep 2025 19:56:38 -0400
Subject: [PATCH 07/25] shorten for 1k word length

---
 paper/paper.md | 15 +++++----------
 1 file changed, 5 insertions(+), 10 deletions(-)

diff --git a/paper/paper.md b/paper/paper.md
index 13080ac..8037b4c 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -34,19 +34,14 @@ bibliography: paper.bib
 
 # Summary
 
-The field of Topological Data Analysis encodes the shape of data in quantifiable representations of the information, sometimes called "topological signatures" or "topological summaries". 
-The goal is to ensure that these summaries are robust enough to be useable in the face of noise, while having access to fast enough algorithms to make them useful in practice. 
-Often, these two goals are at odds with each other since the more complex the representation in order to retain as much information as possible generally results in larger computation time.  
-The Euler Characteristic Transform (ECT) is a construction which is rapidly gaining popularity in Topological Data Analysis settings due to its ability to be both at once: robust to the input providing a provably complete representation of an input embedded shape, while being much faster to compute than its commonly used cousin, the Persistent Homology Transform. 
-The *ECT* package for Python presented here provides a fast and well-documented implementation of the ECT for graphs embedded in 2 or 3 dimensions. This new package is particularly timely since access to easy-to-use code will make the ECT accessible to more practitioners and domain scientists interested in using it for applications. ***TODO Assuming we actually have this up to 3d***
 
-# The ECT
+The field of Topological Data Analysis encodes the shape of data in quantifiable representations of the information, sometimes called "topological signatures" or "topological summaries". The goal is to ensure that these summaries are robust to noise and useful in practice. In many methods, richer representations bring higher computation cost, creating a tension between robustness and speed. The Euler Characteristic Transform (ECT) has gained popularity because it strikes this balance by providing a stable topological summary, yet is typically much faster to compute than its widely used cousin, the Persistent Homology Transform.
 
+The ect Python package offers a fast and well documented implementation of ECT forinputs in any embedding dimension and with a wide range of complex types. With a few lines of code, users can generate ECT features by sampling directions, computing Euler characteristic curves, and vectorizing them for downstream tasks such as classification or regression. The package includes practical options for direction sampling, normalization, and visualizing various versions of the ECT. These options allow for smooth integration into other scientific package such as Numpy, Scipy, and PyTorch. By lowering the barrier to computing the ECT on embedded complexes, ect makes these topological summaries accessible to a wider range of practioners and domain scientists.
 
-We start by defining the Euler Characteristic Transform. 
-This construction came to the attention of the TDA community beginning with a proof of injectivity of the representation for simplicial complexes embedded in dimension up to 3 by Turner *et al.* [@Turner2014]. 
-Subsequently, using the machinery of Euler calculus @Schapira1995, this theorem was extended concurrently by [@Ghrist2018] and [@Curry2022] to nice enough subsets in any ambient dimension.
-We direct the reader to [@Munch2025] for a full survey article on the subject. 
+## The Euler Characteristic Transform
+
+We give a high level introduction of the ECT here. We direct the reader to [@Munch2025] for a full survey article on the subject. 
 
 To start, we assume our input is an undirected graph $G$ with an embedding in 2D given by a map on the vertices $f: V(G) \to \mathbb{R}^2$. A graph can be constructed as seen in \autoref{fig:example_graph}. 
 

From e91a3f79bf379e7049e543e32921189191827bf7 Mon Sep 17 00:00:00 2001
From: Liz Munch <muncheli@msu.edu>
Date: Wed, 1 Oct 2025 11:21:31 -0400
Subject: [PATCH 08/25] Edited intro, pushing to make sure the compiler is
 happy

---
 paper/paper.bib | 24 ++++++++++++++++++++++++
 paper/paper.md  |  5 ++---
 2 files changed, 26 insertions(+), 3 deletions(-)

diff --git a/paper/paper.bib b/paper/paper.bib
index 655739d..97a5a73 100644
--- a/paper/paper.bib
+++ b/paper/paper.bib
@@ -1241,4 +1241,28 @@ @Book{Mardia1999
   journal   = {Wiley Series in Probability and Statistics},
 }
 
+@Article{Wasserman2018,
+  author       = {Larry Wasserman},
+  journal      = {Annual Review of Statistics and Its Application},
+  title        = {Topological Data Analysis},
+  year         = {2018},
+  month        = {mar},
+  number       = {1},
+  pages        = {501--532},
+  volume       = {5},
+  creationdate = {2018-04-12T00:00:00},
+  doi          = {10.1146/annurev-statistics-031017-100045},
+  file         = {:Persistence/PersistenceSurveys/Wasserman2018.pdf:PDF},
+  keywords     = {survey, statistics, persistence},
+  priority     = {prio1},
+  publisher    = {Annual Reviews},
+}
+
+@Book{Ghrist2014,
+  title    = {Elementary Applied Topology},
+  year     = {2014},
+  author   = {Robert Ghrist},
+  keywords = {textbook, survey},
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}
diff --git a/paper/paper.md b/paper/paper.md
index 8037b4c..3c481c8 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -34,10 +34,9 @@ bibliography: paper.bib
 
 # Summary
 
+The field of Topological Data Analysis [@Dey2021,@Wasserman2018,@Ghrist2014,@Munch2017] encodes the shape of data in quantifiable representations of the information, sometimes called "topological signatures" or "topological summaries". The goal is to ensure that these summaries are robust to noise and useful in practice. In many methods, richer representations bring higher computation cost, creating a tension between robustness and speed. The Euler Characteristic Transform (ECT) [@Turner2014,@Munch2025] has gained popularity for encoding the information of embedded shapes in $\R^d$---such as graphs, simplicial complexes, and meshes--because it strikes this balance by providing a complete topological summary, yet is typically much faster to compute than its widely used cousin, the Persistent Homology Transform [@Turner2014].
 
-The field of Topological Data Analysis encodes the shape of data in quantifiable representations of the information, sometimes called "topological signatures" or "topological summaries". The goal is to ensure that these summaries are robust to noise and useful in practice. In many methods, richer representations bring higher computation cost, creating a tension between robustness and speed. The Euler Characteristic Transform (ECT) has gained popularity because it strikes this balance by providing a stable topological summary, yet is typically much faster to compute than its widely used cousin, the Persistent Homology Transform.
-
-The ect Python package offers a fast and well documented implementation of ECT forinputs in any embedding dimension and with a wide range of complex types. With a few lines of code, users can generate ECT features by sampling directions, computing Euler characteristic curves, and vectorizing them for downstream tasks such as classification or regression. The package includes practical options for direction sampling, normalization, and visualizing various versions of the ECT. These options allow for smooth integration into other scientific package such as Numpy, Scipy, and PyTorch. By lowering the barrier to computing the ECT on embedded complexes, ect makes these topological summaries accessible to a wider range of practioners and domain scientists.
+The `ect` Python package offers a fast and well-documented implementation of ECT for inputs in any embedding dimension and with a wide range of complex types. With a few lines of code, users can generate ECT features by sampling directions, computing Euler characteristic curves, and vectorizing them for downstream tasks such as classification or regression. The package includes practical options for direction sampling, normalization, and visualizing various versions of the ECT. These options allow for smooth integration into other scientific package such as `Numpy`, `Scipy`, and `PyTorch`. By lowering the barrier to computing the ECT on embedded complexes, `ect` makes these topological summaries accessible to a wider range of practitioners and domain scientists.
 
 ## The Euler Characteristic Transform
 

From 2a3e62c3401b44e897c57af0e9e158ea682e98c8 Mon Sep 17 00:00:00 2001
From: Liz Munch <muncheli@msu.edu>
Date: Wed, 1 Oct 2025 12:15:14 -0400
Subject: [PATCH 09/25] Put the figures back from an old commit

---
 paper/figures/Matisse_MDS.png              | Bin 0 -> 157243 bytes
 paper/figures/example_ect.png              | Bin 0 -> 63230 bytes
 paper/figures/example_graph.png            | Bin 0 -> 37355 bytes
 paper/figures/example_graph_7pi_over_4.png | Bin 0 -> 66193 bytes
 paper/figures/example_graph_pi_over_2.png  | Bin 0 -> 58525 bytes
 paper/generating_figures.ipynb             | 351 +++++++++++++++++++++
 paper/paper.md                             |   4 +-
 7 files changed, 353 insertions(+), 2 deletions(-)
 create mode 100644 paper/figures/Matisse_MDS.png
 create mode 100644 paper/figures/example_ect.png
 create mode 100644 paper/figures/example_graph.png
 create mode 100644 paper/figures/example_graph_7pi_over_4.png
 create mode 100644 paper/figures/example_graph_pi_over_2.png
 create mode 100644 paper/generating_figures.ipynb

diff --git a/paper/figures/Matisse_MDS.png b/paper/figures/Matisse_MDS.png
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diff --git a/paper/generating_figures.ipynb b/paper/generating_figures.ipynb
new file mode 100644
index 0000000..9c97f89
--- /dev/null
+++ b/paper/generating_figures.ipynb
@@ -0,0 +1,351 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "ImportError",
+     "evalue": "cannot import name 'create_example_graph' from 'ect' (/Users/lizliz/Library/CloudStorage/Dropbox/Math/Code/ect/.conda-ect-3-11/lib/python3.11/site-packages/ect/__init__.py)",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
+      "\u001b[31mImportError\u001b[39m                               Traceback (most recent call last)",
+      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[1]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mect\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mimport\u001b[39;00m ECT, EmbeddedGraph, EmbeddedCW,create_example_graph\n\u001b[32m      3\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mmatplotlib\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mpyplot\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mplt\u001b[39;00m\n\u001b[32m      4\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mnumpy\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mnp\u001b[39;00m\n",
+      "\u001b[31mImportError\u001b[39m: cannot import name 'create_example_graph' from 'ect' (/Users/lizliz/Library/CloudStorage/Dropbox/Math/Code/ect/.conda-ect-3-11/lib/python3.11/site-packages/ect/__init__.py)"
+     ]
+    }
+   ],
+   "source": [
+    "from ect import ECT, EmbeddedGraph, EmbeddedCW,create_example_graph\n",
+    "\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "import networkx as nx"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0D_pers_Sandbox.ipynb             \u001b[34mgithub_collaboration\u001b[m\u001b[m/\n",
+      "\u001b[34mDionysus\u001b[m\u001b[m/                         gudhi_library_2.3.0.zip\n",
+      "\u001b[34mDionysusExamples\u001b[m\u001b[m/                 \u001b[34mhera\u001b[m\u001b[m/\n",
+      "\u001b[34mEirene0_3_5\u001b[m\u001b[m/                      \u001b[34mhtml\u001b[m\u001b[m/\n",
+      "Eirene0_3_5.zip                   julia-0.5.2-linux-x86_64.tar.gz\n",
+      "Goldfarb.txt                      \u001b[34mjulia-f4c6c9d4bb\u001b[m\u001b[m/\n",
+      "GoldfarbOutput_0.txt              \u001b[34mmapper\u001b[m\u001b[m/\n",
+      "GoldfarbOutput_1.txt              mapperOld.zip\n",
+      "GoldfarbOutput_2.txt              \u001b[34mmatlab\u001b[m\u001b[m/\n",
+      "GoldfarbOutput_betti.txt          \u001b[34mnbconvert\u001b[m\u001b[m/\n",
+      "\u001b[34mHungarian\u001b[m\u001b[m/                        \u001b[34mnbsphinx\u001b[m\u001b[m/\n",
+      "\u001b[34mJohnSuite\u001b[m\u001b[m/                        \u001b[34mnips2017\u001b[m\u001b[m/\n",
+      "\u001b[34mNPEET\u001b[m\u001b[m/                            perseusRipsEx.txt\n",
+      "\u001b[34mNumbaWorkshop_Jan2018\u001b[m\u001b[m/            \u001b[34mpypersistence\u001b[m\u001b[m/\n",
+      "\u001b[34mPersDistances\u001b[m\u001b[m/                    \u001b[34mpypersistence-git\u001b[m\u001b[m/\n",
+      "\u001b[34mPerseus\u001b[m\u001b[m/                          \u001b[34mpypersistence-old\u001b[m\u001b[m/\n",
+      "\u001b[34mProgramming\u001b[m\u001b[m/                      \u001b[34mrecon\u001b[m\u001b[m/\n",
+      "\u001b[34mSUMOExamples\u001b[m\u001b[m/                     \u001b[34mrecon-examples\u001b[m\u001b[m/\n",
+      "\u001b[34manimationExample\u001b[m\u001b[m/                 \u001b[34mripser\u001b[m\u001b[m/\n",
+      "\u001b[34mcat-list.github.io\u001b[m\u001b[m/               ripsex_0.txt\n",
+      "\u001b[34mceREEBerus\u001b[m\u001b[m/                       ripsex_betti.txt\n",
+      "\u001b[34mcechmate\u001b[m\u001b[m/                         \u001b[34mrivet\u001b[m\u001b[m/\n",
+      "\u001b[34mdoctrees\u001b[m\u001b[m/                         rivetInstallErrors.txt\n",
+      "\u001b[34mect\u001b[m\u001b[m/                              \u001b[34mteaspoon\u001b[m\u001b[m/\n",
+      "\u001b[34mect-on-images\u001b[m\u001b[m/                    \u001b[34mteaspoon-Old\u001b[m\u001b[m/\n",
+      "\u001b[34mfzz\u001b[m\u001b[m/                              teaspoon-wass-dist-sandbox.ipynb\n",
+      "\u001b[34mgeom_bottleneck\u001b[m\u001b[m/\n"
+     ]
+    }
+   ],
+   "source": [
+    "ls .."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Construct an example graph \n",
+    "# Note that this is the same graph that is returned by:\n",
+    "# G = create_example_graph()\n",
+    "\n",
+    "G = EmbeddedGraph()\n",
+    "\n",
+    "G.add_node('A', 1, 2)\n",
+    "G.add_node('B', 3, 4)\n",
+    "G.add_node('C', 5, 7)\n",
+    "G.add_node('D', 3, 6)\n",
+    "G.add_node('E', 4, 3)\n",
+    "G.add_node('F', 4, 5)\n",
+    "\n",
+    "G.add_edge('A', 'B')\n",
+    "G.add_edge('B', 'C')\n",
+    "G.add_edge('B', 'D')\n",
+    "G.add_edge('B', 'E')\n",
+    "G.add_edge('C', 'D')\n",
+    "G.add_edge('E', 'F')\n",
+    "\n",
+    "G.set_centered_coordinates()\n",
+    "\n",
+    "G.plot()\n",
+    "plt.savefig('paper/figures/example_graph.png', bbox_inches='tight', dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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btmxBr169MGHCBLRv3x5FRUXIyMjAxo0bUVRUhIsXL6JJkya48847kZKSgtDQUGzcuBF79+7FO++8U2e7+/fvjzfeeAM5OTlmQTVgwAAsXLgQzZs3R5MmTeo8TmpqKgDgxRdfxD333AN/f3+zgLFHVFQUhg4dikWLFsHPzw+dO3fGxo0bkZ6eDuDK9S9ZlrF48WKsWLECwOUBBX5+foiPj4dWq3VoSjRX/fzGxMRg5MiReO+99xAcHIyIiAjMnTsXjRs3xrx582rd15nXwFasWIHq6upab14+ePBgjbDKy8tDcHAwLly4gAYNGuDEiRM4cuQIPvjgA9M2UVFRGDlyZI3jGXtcSu+RG7hzCKStfvvtNzFhwgTRvHlzERAQIMLCwkS/fv3EvHnzREVFhWm7jIwMMWTIEBEaGiqCg4PFoEGDxM6dO82OpTS82tp9jcOQCwsLa7SxtmH0126vtO2mTZtE165dRUBAgGjRooX48MMPxdSpU0VgYGCdXx9bzmPN5zTatm2bSE1NFQEBASI5OVksWLDAdK6r5efni4kTJ4rExETh7+8v4uLixA033CAWLVokhBBCr9eLZ599VqSkpIiwsDAREhIiUlJSLA5/vlZJSYnQarUiLCxMVFdXm9b/97//FQDE3//+9xr7WPo+v/7666Jx48ZCo9GY3rfl66ckPz9fjBw5UoSHh4v4+Hjx5JNPim+++UYAED///LMQ4vJQ++DgYFFVVSWEEOKuu+4SS5cuFUIIsX79ehEVFVXn18HSMHohHP/5tVZRUZG4/fbbRUhIiIiNjRWTJ08WJSUldh/PHr179xYxMTFmPwtX0+v1ws/PT7zwwgtm68ePHy90Op24/fbbhRBXhsobvye14TB6zyIJodKVfXKakSNH4tChQ4rXosizTZo0CStWrMDZs2fh5+eHb7/9Fk8//TSys7NRVVWFxo0b49NPP8WQIUPw4osvIisry9Q7I9cYPnw4QkND8fnnn7u7KWQjrygh1ieXLl0yGx12/PhxrFmzxuLoPvIMer0eAQEBZteutm/fjoULF2LatGnw87v8T61BgwbIy8tDXl4e/vvf/yIqKgqHDx9GcnIyFi1ahFWrVrnrI9RbAwcOtOraKXke9sA8THx8PMaOHYvk5GScOnUKH3zwAfR6Pfbt26d4PxZ5hm+//RavvfYa7rzzTjRo0AAZGRn4+OOP0bVrV2zbts30R0lVVRXuvfderF+/HkOHDsULL7yAm2++GVqtFjNmzKh1GiwiMscA8zDjxo3Dli1bkJeXB51Ohz59+uDNN9+0OE8geYYdO3bgueeew+HDh1FeXo7mzZvjrrvuwvTp0/kIDiKVMMCIiMgrqToX4gcffIDOnTsjPDwc4eHh6NOnj1PvaSIiovpL1R7Yd999B61Wi1atWkEIgaVLl2LWrFnYt2+f4nyERERE1nJ5CTEyMhKzZs3C+PHj69xWlmWcOXMGYWFhqkz/Q0RkLyEELl68iISEBKueW2aviooKVFZWOnycgIAABAYGOqFFnsNlw+gNBgO++OILlJWVWZzPUK/Xm00plJubi/bt27uqiURENsvJybFqBhh7VFRUIKlZKPIKDA4fKy4uDidOnPCpEFM9wA4cOIA+ffqgoqICoaGh+OabbyyGUlpaWo1nKQGXf0DUnIeQiMhWJSUlSExMtOpZhfaqrKxEXoEBJ9KbITzM/l5eyUUZSamnUFlZ6VMBpnoJsbKyEqdPn0ZxcTG+/PJLfPjhh9i2bZtiiF3bAzP+gBQXFzPAiMijlJSUICIiQtXfT8ZznP8tyeEAa9T6hM/9LlW9BxYQEGB6IGNqair27t2L9957DwsXLqyxrU6ng06nU7tJRERexSBkGBzoahiE7LzGeBCXTyUly7JVj84gIqLLZAjIsD/BHNnXk6kaYNOnT8ewYcPQtGlTXLx4EcuXL8fWrVvNniVFRES1kyHDkT6UY3t7LlUDrKCgAKNHj8bZs2cRERGBzp0744cffsCNN96o5mmJiKgeUDXAPvroIzUPT0RULxiEgMGB8XaO7OvJ+DgVIiIPx2tgylSdC5GIiEgt7IEREXk4GQIG9sBqYIAREXk4lhCVsYRIREReiT0wIiIPx1GIyhhgREQeTv5rcWR/X8QSIhEReSX2wIiIPJzBwVGIjuzryRhgREQeziDg4Gz0zmuLJ2GAERF5OF4DU8YAIyKvdrGsAht/PIoDR3Nx6LczKCwqg5BlBOr80bJ5NNq1iseAXq3QoXU8JElyd3PJiRhgROSV/rxQhg8/+wlrtxxCVbUBGkmCQb5SK6uq1mPfoT/w69EzWL5yL1o0i8KDd/fD9b1bubHV9pEhwQD7w1d2YF9PxgAjIq+zeecxvP3BepRfqoT8V2hZutfJYLhcQPv99Dm8+PYqDOrTGlMfGYwG4cEua6+jZHF5cWR/X8Rh9ETkVZZ++TNenv0dysr1pvCyhjHftu0+jgnPLUNeYYlKLSRXYYARkddY8d0v+M/yHQCuBJKtZFmg4FwJJr+0AhdKyp3YOvUY/iohOrL4IpYQicgr/PZ7PuYv3VbrNpdKzyH3+FZcKDiOyooSaDRaBIfHIapxCmKTekOr9QcAGGSB/HMlePc/m/Da1BGuaL5DHA0hBhgRkZtUG2S8/t6aWrcpyjuCY3s+haTxQ0zTVASHxUGIapScP4mTB1ej/GI+Wna907S9LAts/ukYbujX1isHdhADjIi8wM5fsnEi57zF9yvKinBs7zLoghqiY/9HEBAYbnovPrkfLrU7hz/zjtTYT5IkLF6xEwN6tfToIfaykCALB0YhOrCvJ+M1MCLyeF+uzoBGY/mXcO7xLZCr9WjZbZRZeBkFhUYhoWX/GuuFEMg+VYjDx/Oc2l5n4zUwZQwwIvJoZeV67DuYU+uIw6KzRxAYEonwRs1tPr5Wq8H23ccdaCG5C0uIROTRfjtRUOtUtNVVFaisKEZkfAe7jm8wyDhy/Kx9jXMRAzQwONDfMDixLZ6EAUZEHu33U4WQJMvD5g3VFQAArZ/O7nNknSy0e19XEA5eAxO8BkZE5Hrll6qg0Vj+VaX1CwQAGKr1dp+jQl9l976u4OprYNu3b8eIESOQkJAASZKwcuXKWrffunUrJEmqseTlqXttkQFGRB5Nq5Ugarlr2c8/EAGB4Sgvsf+XZW0BWR+VlZUhJSUF8+fPt2m/Y8eO4ezZs6YlJiZGpRZexhIiEXm0mKjwOqeMahjXDvknd6Pk/Em7BnJENwq1s3WuYRAaGIQD18BsnLVk2LBhGDZsmM3niYmJQYMGDWzez178s4OIPFqb5Ng6t2ncaiA02gBk7fsSlRUXa7x/qfQczmT9qLivViOhQ+t4h9upJhkSZGgcWC6XEEtKSswWvd7+squSLl26ID4+HjfeeCN++uknpx5bCQOMiDxa47gGCA8NrHWboNAotO5xH/Rl57Fv4yz8/usq5J3cjbO/78RvvyzHvk2zUX4xX3FfWRbo1LaxGk33OImJiYiIiDAtaWlpTjlufHw8FixYgK+++gpfffUVEhMTMXDgQGRkZDjl+JawhEhEHk2jkdC3WwLWbc8GahmM0Ci+A7rcMAW5x7eh6Owh5J3YBY3GD8Hh8UjqOAKxzXsp7ucf4IfB17VVqfXO4ay5EHNychAefuVGb53O/pGbV2vTpg3atGljet23b19kZ2djzpw5+PTTT51yDiUMMCLyWIcOHcLrr7+OVd+tR7ebptU53VNQaLTZfId10WgkDB/UASHBzvlFrhbHr4FdvggWHh5uFmBq6tmzJ3bs2KHqOVhCJCKPc+jQIdxzzz3o1KkTfv75Z/xr7lsYc2dvOHO6QkkCQoN1eOjefs47KJlkZmYiPl7da4vsgRGRxzD2uD7//HM0bdoUCxcuxJgxYxAQEICqKgN27P0dp/44D4MTHjEsBPD84zd5xZOZLw/icGAyXxv3LS0tRVZWlun1iRMnkJmZicjISDRt2hTTp09Hbm4uPvnkEwDA3LlzkZSUhA4dOqCiogIffvghNm/ejPXr19vdZmswwIjI7WoLLiN/fy1mz7gDj0xfhqI/yxwOsUce6I/re7d2tOkuITs4lZRc62RcNf3yyy8YNGiQ6fWUKVMAAGPGjMGSJUtw9uxZnD592vR+ZWUlpk6ditzcXAQHB6Nz587YuHGj2THUIIna7hB0s5KSEkRERKC4uNhldVsicp1rg+vFF1+sEVzXKjh3EU+8/D/knC22+REoGo0ECcDkcYNw583dHGq7K34/Gc/xxf62CA7T2n2c8osGjEo56nO/S9kDIyKXs6bHZUlUZAjOHFqO0qpYRCT0BIA6b3TWaCTIskBSYiO89OTNaNk82imfw1WcNYjD1zDAiMhlHAkuo/nz5+PH7duwZcsWtOvYDd+u/xUrf9iP4ouXAFzpZclCQIjLA+9TOzbFHTd3Q59uSdBqvW/smvGGZPv3Z4AREdnFGcEFANnZ2Zg2bRomTpyIgQMHAgAm3HcdHrq3H87kF+NoVh4Kzl+EwSAjOCgALZpHo1XzGAQH2XYeT2MQEgwOzCjvyL6ejAFGRKpxVnABgCzLePDBBxEbG4t//vOfZu9JkoTGcQ3QOK6Bk1pO3oABRkRO58zgMpo/fz62b9+OLVu2IDTUsyffdTbHH2jJEiIRUa3UCC5AuXRYn8hCA9mBQRyyjw7i8L6rmUTkca6dOWPhwoX47bffMGHCBIfDq7bSIdVv7IERkd3U6nFdrT6XDo1YQlTGACMim7kiuACWDo1kODaSUHZeUzwKS4hEZDU1S4XXYumQ6sIeGBHVyVU9rquxdHiF4zcy+2ZfhQFGRBa5I7gAlg6v5fhUUr4ZYL75qYjIIa4sFV6LpUOyFntgRGTirh7X1Vg6rMnVzwPzFgwwIvKI4AJYOrSEJURlDDCiesxTggtg6bA2jt8H5psBpuqnSktLQ48ePRAWFoaYmBiMHDkSx44dU/OURGQFd17jssRYOly8eDFLh2QVVQNs27ZtmDhxIn7++Wds2LABVVVVuOmmm1BWVqbmaYnIAk8MLoClw7rIQnJ48UWqlhDXrVtn9nrJkiWIiYlBeno6BgwYoOapiegqnlQqvBZLh3WTHSwh8j4wJyguLgYAREZGKr6v1+uh1+tNr0tKSlzSLiJf5cnBZcRRh2Qvl8WyLMt46qmn0K9fP3Ts2FFxm7S0NERERJiWxMREVzWPyKd4aqnwWiwdWsf4OBVHFl/ksk81ceJEHDx4EJ999pnFbaZPn47i4mLTkpOT46rmEfkEbwkugKVDWxggObz4IpeUECdNmoTvv/8e27dvR5MmTSxup9PpoNPpXNEkIp/iDaXCa7F0SI5SNcCEEJg8eTK++eYbbN26FUlJSWqejqje8cbgAlg6tJXjT2T2zRKiqgE2ceJELF++HKtWrUJYWBjy8vIAABEREQgKClLz1EQ+zVuDC2Dp0B4GwKEyoMF5TfEoqgbYBx98AAA1/sL6+OOPMXbsWDVPTeSTvDm4jFg6JGdRvYRIRI7zheACWDq0F0uIyjgXIpEH85XgAlg6dAQn81XGACPyQL4UXEYsHdpPOPg4FeGjw+h9M5aJvJQ33cdlC5YOSQ3sgRF5AF/scRmxdOg4lhCVMcCI3MiXg8uIpUPHOTqjvK/ORu+bsUzk4Xy1VHgtlg5JTeyBEblQfehxGbF06Dx8IrMyBhiRC9Sn4DJi6dB5WEJU5puxTOQh6kup8FosHZIrsAdGpIL62OMyYunQ+WRoHHqqMp/ITER1qs/BZcTSofMZhASDA2VAR/b1ZAww8lllJeX46Zs9OLr7OI7uzcKfeRcgBBARFYbW3VugTY+WuO72nmgQHeHwuRhcl7F0SK7EACOfc+5MEZb/4yusX7oV+kuV0PprYai68kCJ82eKcOrwH1j38Wa8P/kjDLy7Lx546U40aZ1g87kYXFewdKgeDuJQxgAjnyGEwMb/bse8SR9Cf6kScrUMAGbhZWSoNpj+u3XFT9j2xS6Mf/M+3PbkcGi12jrPxeCqiaVD9QgHZ6MXPjoTh29+Kqp3hBD44OkleHvM+7hUWmEKL2sYqmVUV1Zj4TOf4PW73kVVZZXFbevrqMK6sHSoLgMkhxdfxAAjn/Cf5z7FN/9ac/mFA4+h27lqL/75wL8gy+YByOCyjKVDcheWEMnr7V6dji/e+a7G+jPiJA7jF9NrDTTwQwBCEYEoxCEBzeEn+ZvtI2SB7V/+jJQFG3DL40NYKrQCS4fqk4Vj17FkH322MAOMvFrphTLMHv8BJI0EYeFfaTLaIwghEBDQowJ/ohC/YT9O4zhSRF+ESQ1q7PPB1CX4dO1ifLX6CwZXLVg6dA0+kVkZA4y82pr/bETxuRKL4QUAUYhDuBRpep2EtigSBcjET9iPnegjhkArmQ/cqNRX4uS2QgZXLVg6JHdjgJHXkmUZK99fW2t4WRIpxSBJtEM2DiIPp9AYyWbva6BBrJyI++95gOFlAUuHriM7+ERmR/b1ZL7Zr6R64XjGCRTmnLd7/3g0BQCcR77i+/rySvzyQ6bdx/dlLB26lnEmDkcWX8QAI6/12y/ZkBz4dxkoBcMP/riEMsX3tf5aHE//3f4T+CiWDslTsIRIXuv3/Seh8dMq3qhsLS38UI1qxfcM1QYc33fC7mP7KpYOXY+DOJQxwMhrlRaX23X962oGVCMAOuU3BVD6Z6lDx/c1LB26hwwHp5LiNTAiz6LVOvbjWyHKUY0qBMFyL0Lj4Dl8CUuH5GnYAyOv1Si+ISSNBNhZQTyL05ePg1jF9zVaDaKaNLK3eT6HpUP3EQ6OQhQ+2gNjgJHXatkt2e7rX0WiACdwBEEIQdxfoxGVtE5tYW/zfApLh+7F2eiVsT5CXqtd71ZWbXcOeTgrTuGMOImT4igyxI/IwHYEQIcU9K1xE7ORbJCtPocvY+nQ/YyDOBxZbLF9+3aMGDECCQkJkCQJK1eurHOfrVu3olu3btDpdGjZsiWWLFli34e1AQOMvFZc8xh0vr59ndepfsdhHMJeHEEGTiMLgEBrpKA3bkSoZPlhlrHNo9Gpfzsnt9r7GEuHixcvZumwnigrK0NKSgrmz59v1fYnTpzAzTffjEGDBiEzMxNPPfUUHnroIfzwww+qtpMlRPJqIycPx6/bDiu+lyA1RwKa23VcSZIwctIwaDT1+288lg49g6tLiMOGDcOwYcOs3n7BggVISkrCO++8AwBo164dduzYgTlz5mDIkCE2ndsW9ftfJ3m9fiN7oNOAdtD6Oe9HWaPVIKFlHG55XL1/eN6ApUPPYZxKypEFAEpKSswWvV7vlPbt2rULgwcPNls3ZMgQ7Nq1yynHt4QBRl5No9Hg2Y8nws/f7/KIRCcQssDzn0xGQGD9ngORpUPfk5iYiIiICNOSlpbmlOPm5eUhNtZ8NG9sbCxKSkpw6dIlp5xDCUuI5PXik2Ix8+tn8dKINMiAwzc3T/nwMbTrVb8Hb7B06FmcVULMyclBeHi4ab1OZ+Emfi/BHhj5hB5DuuAf37+AwGCdXeVErZ8Gfv5aPLdkEoaOG6RCC70HS4eexxhgjiwAEB4ebrY4K8Di4uKQn28+KXZ+fj7Cw8MRFBTklHMoYYCRz+h+Uwo+OjwXXf+vEwBYFWTGEYwtUppjQeZs3Dj6elXb6A1YOiRb9enTB5s2bTJbt2HDBvTp00fV87KESD4lukkjvLn2RezbdADf/vsH7Px2L4QsoNFqIElAVVUV/Pz8IBsulxk7X98et04cij63dIdWq3w/WH3C0qFncvUoxNLSUmRlZZlenzhxApmZmYiMjETTpk0xffp05Obm4pNPPgEAPProo3j//ffx3HPP4cEHH8TmzZvx+eefY/Xq1Xa32RoMMPI5kiSh2+DO6Da4My7+WYrjGSdwPP13/HboOD795FM8/PBD6H9zP7ROTUbD2Abubq7HYOnQc7k6wH755RcMGnSllD5lyhQAwJgxY7BkyRKcPXsWp0+fNr2flJSE1atX4+mnn8Z7772HJk2a4MMPP1R1CD0ASEIIx654q6ikpAQREREoLi42u/BIZI+MjAykpqYiPT0d3bp1c3dzPM68efPwxBNPYMuWLex9WcEVv5+M57hxzSPwD7F/VGxVWSU2DF/oc79L2QMjIpYOPZyAY49E8dheioMYYET1HEuHno+T+SpjgBHVc3xMiudjgCnjMHqieoylQ/Jm7IER1VMsHXoP9sCUMcCI6imWDr0HA0wZS4hE9RBLh+QL2AMjqmdYOvQ+QkgQDvSiHNnXkzHAiOoZlg69z9XP9LJ3f1/EEiJRPcLSIfkS9sCI6gmWDr0XB3EoY4AR1RMsHXovXgNTxhIiUT3A0iH5IlUDbPv27RgxYgQSEhIgSRJWrlyp5umISAFLh97PWU9k9jWqBlhZWRlSUlIwf/58NU9DRLXgE5a9n7GE6Mjii1S9BjZs2DAMGzbM6u31ej30er3pdUlJiRrNIqo3WDr0DcLBXpSvBphHXQNLS0tDRESEaUlMTHR3k4i8FkuH5Os8KsCmT5+O4uJi05KTk+PuJhF5LZYOfYcAIIQDi7s/gEo8ahi9TqeDTqdzdzOIvB5Lh75FhgSJM3HU4FE9MCJyHEuHVF94VA+MiBzHG5Z9D29kVqZqgJWWliIrK8v0+sSJE8jMzERkZCSaNm2q5qmJ6iWWDn2TLCRInEqqBlUD7JdffsGgQYNMr6dMmQIAGDNmDJYsWaLmqYnqHZYOqb5RNcAGDhwIIXx1/AuRZ2Hp0HcZRxM6sr8v4jUwIh/A0qFv4zUwZRyFSOTlWDqk+oo9MCIvx9Kh72MPTBkDjMiLsXRYP3AUojIGGJGXYumw/uAgDmUMMCIvxdIh1XcMMCIvxNJh/XK5B+bINTAnNsaDMMCIvAxLh/UPB3EoY4AReRmWDokuY4AReRGWDusnAcee6eWjFUQGGJG3sKZ0KAuB3X/kIOPsWRwsyEdeaSkMQkaELhAdYmLQOTYOA5o1R2hAgItbT45gCVEZA4zIS9RWOqyorsKn+/dj6f59OHPxIjTS5V9Y8lVX73fn/oFqWUagnx/ubN8BD6d2R5PwCJd+BiJnYoAReYHaSofpZ85g6vq1yCkugfirWCQrDDurlmUAQEV1Nf534Fd8ceggXuh/Pe7vnGIKPPJQrCEq4lyIRB6uttLhioMHcNcXnyG35Ep4WcMgBPQGA2Zu3YzJa75HpcHg7GaTM/1VQrR3gY+WEBlgRB7OWDpcvHixWenwi0MHMX3TBghcDiR7rcs6jifXrobhrx4aeR7jTByOLL6IAUbkwSyVDo+dO4cXN290yjkEgB+ys7Akc59TjkfkKrwGRuShLJUOq2UZU9evrfVhsRd378G5/61QfC/ihkGIHPG3Guvf/ulHDEpKRnLDho43npyKoxCVMcCIPJSlUYfrs7NwuLDQqmM0GDYU/o0izdb5x8UpbisLgfl7fsY7Q4bZ32hSh6PXsRhgROQqtY06/CRzHzSSpDjS8FrB7dpC1zTRqnMahMB3vx3DiwMGIjIoyJ5mE7kUr4EReZjaRh0WlJViz5lcq8LLHgZZxvrs46ocm+zHQRzK2AMj8jC13bB8ID/fpmPJFZdgKC01W6etZf5ErUaDX/PzcU9Hm05DauN9YIoYYEQepK65Dg8XFkIrSVYPm8/798Ia65LmvmNx+2pZxv68PKvbS+RODDAiD2HNXIcXKiqgsSHAGt15O/yjo21qx4WKSzZtT+rjKERlDDAiD2HNY1JsnfFJ17Sp1YM4rpzDN3/ZeT0fLQM6goM4iDyAtY9JaRQUrNoADqOo4GBVj0/kLOyBEbmZLU9Y7hgT49C0UXXx02jQJS5eteOTfVhCVMYAI3IzW56w3Ck2FhLUqyZVyzK6WLjRmdyIoxAVsYRI5Ea2PmG5QWAQ/i8pGVqVrlMF+fnhxuSWqhybHCE5YfE9DDAiN7GldHi10SldVCkjaiUJozp0RAif1kxegiVEIjexpXR4teuaNkP/ps2wM+e0xSAL69UTYb16Wn1MCUCwvz8m9uhl9T7kQiwhKmIPjMgNbC0dXk2SJPxz8E3Q+fk5rTAkALw26AZEh4Q46YjkVMIJix3mz5+P5s2bIzAwEL169cKePXssbrtkyRJIkmS2BAYG2ndiKzHAiFzM3tLh1eLDwvDBzSOgkSSnhNj4rqm4pU1bJxyJfMWKFSswZcoUzJw5ExkZGUhJScGQIUNQUFBgcZ/w8HCcPXvWtJw6dUrVNjLAiFzM0hOWbdW/WXN8dOttCND62TWoQ/PXPo9274EX+g/gDcyezPg4FUcWG7377ruYMGECxo0bh/bt22PBggUIDg7G4sWLLe4jSRLi4uJMS2xsrCOfuk4MMCIXcqR0qGRAs+ZY//cxSE1oDOBKKNXGOCatUVAQPr71NjzXrz/Dy8M5azb6kpISs0Wv1yuer7KyEunp6Rg8eLBpnUajweDBg7Fr1y6L7SwtLUWzZs2QmJiIW2+9FYcOHXLq1+FaDDAiF3FG6VBJYkQElt8xCv++eQR6Nm5sWu+n0UADQMgytFeVGhuHhWN6/+uxcfQ4XN88yWntIM+XmJiIiIgI05KWlqa43blz52AwGGr0oGJjY5FnYbLnNm3aYPHixVi1ahX++9//QpZl9O3bF3/88YfTP4cRRyESuYi9ow6toZEkDG3ZCkNbtkJuSQky887iQEE+jubkYM2atbhjxN8woF17dIyJRYeYGKt6auRBnDQKMScnB+Hh4abVOp3OoWZdrU+fPujTp4/pdd++fdGuXTssXLgQr7/+utPOczUGGJELOLt0WJvG4eFoHB6Om1u3QUZGBpbe9wAmPD0F3Tp1VvW8pCI7r2OZ7Y/LgyyuDjBLoqKioNVqkX/N8+fy8/MRZ+VMLf7+/ujatSuysrJsb6+VWEIkUplapUMitQQEBCA1NRWbNm0yrZNlGZs2bTLrZdXGYDDgwIEDiI9Xb25N9sCIVKZm6ZDqB0lcXhzZ31ZTpkzBmDFj0L17d/Ts2RNz585FWVkZxo0bBwAYPXo0GjdubLqO9tprr6F3795o2bIlLly4gFmzZuHUqVN46KGH7G94HRhgRCpyZemQfJgbZuK4++67UVhYiJdffhl5eXno0qUL1q1bZxrYcfr0aWg0V4p4f/75JyZMmIC8vDw0bNgQqamp2LlzJ9q3b+9Aw2vHACNSCUuH5DROugZmq0mTJmHSpEmK723dutXs9Zw5czBnzhy7zmMvBhiRSlg6JFIXA4xIBSwdklNxMl9FDDAiJ2PpkJyOAaaIAUbkZCwdErkGA4zIiVg6JFWwB6aIAUbkJCwdkmrcNArR0zHAiJyEpUMi12KAETkBS4ekJnfMxOENGGBEDmLpkFTHa2CKXDKZ7/z589G8eXMEBgaiV69e2LNnjytOS+QSznrCMhHZRvUAW7FiBaZMmYKZM2ciIyMDKSkpGDJkCAoKCtQ+NZHqWDokch/VA+zdd9/FhAkTMG7cOLRv3x4LFixAcHAwFi9eXGNbvV5f45HXRJ6KpUNyFQlXroPZtbj7A6hE1QCrrKxEeno6Bg8efOWEGg0GDx6MXbt21dg+LS3N7HHXiYmJajaPyCEsHZLLGIfRO7L4IFUD7Ny5czAYDKbp941iY2ORl5dXY/vp06ejuLjYtOTk5KjZPCK7sXRI5H4eNQpRp9NBp9O5uxlEtWLpkFyOoxAVqRpgUVFR0Gq1yM/PN1ufn5+PuLg4NU9NpBresEwuxwBTpGoJMSAgAKmpqdi0aZNpnSzL2LRpE/r06aPmqYlUwdIhkedQvYQ4ZcoUjBkzBt27d0fPnj0xd+5clJWVYdy4cWqfmsipWDokd+FMHMpUD7C7774bhYWFePnll5GXl4cuXbpg3bp1NQZ2EHk6lg7JbVhCVOSSQRyTJk3CpEmTXHEqIlWwdEjkeTxqFCKRJ2LpkNyOPTBFDDCiOrB0SO7Ga2DKXDKZL5G3YumQyHOxB0ZkAUuH5DH4RGZFDDAiC1g6JI/Ba2CKGGBEClg6JE/Ca2DKeA2M6BosHRJ5B/bAiK7B0iF5HJYQFTHAiK7C0iF5JAdLiL4aYCwhEv2FpUMi78IeGPksIQSOnCtEZt5ZHCosQPaZM4gZPxbzfzuCAVqgc0wcUuLioZEuDzFm6ZA8FkuIihhg5HP01dX46sghLNm/D1lF5yEB0Go0qJZlBHfqgO2F+dhakAcBICEsDKM7d0XvkDCWDslzMcAUMcDIp/yan4ep69ci+88iGG/dFACqZRkAIEkSDOLKv+YzFy/irZ+2Q3PpEmJ7pLJ0SORFeA2MfMaKQwdw++fLcfLCnwCs/6NTAKjW6YDbb8VHh36FED765yp5LeN9YI4svog9MPIJnx86gOmb1tu9v6S5/Lfce7t3QRYCT/fu56ymEZFK2AMjr3eoIB8vbN7gtOPN2/MzNp/43WnHIyJ1sAdGXq3SYMCU9WthaarSi7v34tzyFWbrNKEhCIiLQ8QNAxHcvl2NfTSQ8PzGddj49wcRERioQquJbMRBHIrYAyOvturYERwvOm82MENJg+FDEP3AvYh64F40uGEQDKWlyF/4EcoPHq6xrQyBPysqsDgzXa1mE9mE18CUMcDIawkhsCQzAxqL/a8rgtu1RWiPVIT1SEXE/w1E/JMTAa0WpRn7FLeXhcCyA/tRZTA4u9lE9hEOLD6KAUZeK/vPIhw5VwjZjn+hmqAgSP7+psEbSoouXcLOnNOONJGIVMQAI6+1Pz/P6m3lSxUwlJbBUFqKyrN5OP/5VxB6PUK7p1rcRytJNp2DSDWO9L58uBfGQRzktQ4V5MPvrxk26pL374VmryU/P0TddxeC2ra2uI8sgIMF+Q63k8hRfB6YMgYYea2iikuQrbzpuNGdt8E/JhoAYLhYitJf0nHuf19AowtESEonxX0EBM6VlzmtvUTkXAww8lq2TJiha9YUuqaJptch3brgzKw5OP/lNwju0A6Sn/I/BR/9w5W8DYfRK+I1MPJakUFBppnkbSVpNAhs1RKGkhJUFZ5T3gZAo6BgB1pI5BwcRq+MAUZeq310jFXXvywR8uUh8rJer/i+RpLQMSbW7uMTkbpYQiSv1Tk2zu59hcGAS0d/A7RaBMQph5RBCIfOQeQ0LCEqYoCR12od2QgtIxshu+h8nf8+y48cRVV+AQDAUFqK0vR9qC48h4jB/weNhemiInQ69Ets6uRWE9mBAaaIAUZeS5IkjOvSDS9aMZHvhTU/XNnP3w/+MTFoNOp2hPXro7i9VpJwX6cU6CwM7iAi9+O/TvJqt7dtj0Xpe/FHSbHifIhhvXogrFcPm44pAQgN0GF8V8s3ORO5Eu8DU8ZBHOTVdH5+mDNkuNX3g1lDAHjzhhsRyRGI5Ck4E4ciBhh5vS5x8bhBG+C047Utu4ShLVo57XhEDmOAKWKAkddbsGAB/jPpCXQ4VwQJsOveMOMeXQzA2hdewowZMyCc2KsjIufjNTDyagsWLMBjjz2GJ554AnNf/Qf2nsnF1PVrceZiidV/dGokCRE6HdJuuAk3tWiFd2TgmWeeAQD84x//gGTnzdJEzsJrYMoYYOS1zMJr7lxIkoSejZtg/QNjsezAfizdvw+5F0ugkSRIgGmQx9WvI4OC8ECnLhiT0hUNg4IAAFOnTgXAECMPwmH0ihhg5JWUwssoyN8fD3Xrjge7piL9bC725+XhUGEBCsvKIEMgMjAIHWJi0CkmDr0aN4G/Vlvj+AwxImD+/PmYNWsW8vLykJKSgnnz5qFnz54Wt//iiy/w0ksv4eTJk2jVqhXeeustDB8+XLX2McDI69QWXlfTSBJ6JDRBj4Qmdp2HIUaewh0lxBUrVmDKlClYsGABevXqhblz52LIkCE4duwYYmJiamy/c+dO3HvvvUhLS8Pf/vY3LF++HCNHjkRGRgY6duxof+NrwUEc5FWsDS9nmTp1KmbPno0333yTAzvIfdwwCvHdd9/FhAkTMG7cOLRv3x4LFixAcHAwFi9erLj9e++9h6FDh+LZZ59Fu3bt8Prrr6Nbt254//33bT+5ldgDI6/h6vAyYk+MfEVJSYnZa51OB51OV2O7yspKpKenY/r06aZ1Go0GgwcPxq5duxSPvWvXLkyZMsVs3ZAhQ7By5UrHG24BA4y8grvCy4ghRm7lpEEciYmJZqtnzpyJV155pcbm586dg8FgQGys+UTXsbGxOHr0qOIp8vLyFLfPy8uzv911YICRx3N3eBkxxMhdJFy5V9He/QEgJycH4eHhpvVKvS9vwgAjj+Yp4WXEECNvFh4ebhZglkRFRUGr1SI/P99sfX5+PuLilB8xFBcXZ9P2zsBBHOSxPC28jDiwg1zOxYM4AgICkJqaik2bNpnWybKMTZs2oU8f5Sc49OnTx2x7ANiwYYPF7Z2BPTDySJ4aXkbsiZEruWMY/ZQpUzBmzBh0794dPXv2xNy5c1FWVoZx48YBAEaPHo3GjRsjLS0NAPDkk0/i+uuvxzvvvIObb74Zn332GX755RcsWrTI/obXgQFGHsfTw8uIIUYu44aZOO6++24UFhbi5ZdfRl5eHrp06YJ169aZBmqcPn0aGs2VIl7fvn2xfPlyzJgxAy+88AJatWqFlStXqnYPGMAAIw/jLeFlxBAjXzZp0iRMmjRJ8b2tW7fWWDdq1CiMGjVK5VZdwQAjj+Ft4WXEECOX4KXWGhhg5BG8NbyMGGKkJs5Gr4wBRm7n7eFlxBAjci0GGLmVr4SXEUOMVMHHqShSLcDeeOMNrF69GpmZmQgICMCFCxfUOhV5KV8LLyOGGDkbS4jKVAuwyspKjBo1Cn369MFHH32k1mnIS/lqeBkxxIjUp1qAvfrqqwCAJUuWqHUK8lK+Hl5GDDFyGpYQFXnUNTC9Xg+9Xm96fe3U/+T96kt4GTHEyBlYQlTmUQGWlpZm6rmR76lv4WXEECNSh02T+U6bNg2SJNW6WHpWjDWmT5+O4uJi05KTk2P3sciz1NfwMuIEwOQQNzyR2RvY1AObOnUqxo4dW+s2ycnJdjfG0tNBybvV9/AyYk+M7MZrYIpsCrDo6GhER0er1RbyQQwvcwwxsgevgSlT7RrY6dOnUVRUhNOnT8NgMCAzMxMA0LJlS4SGhqp1WvIgDC9lDDEi51AtwF5++WUsXbrU9Lpr164AgC1btmDgwIFqnZY8BMOrdgwxsglLiIpUC7AlS5bwHrB6iuFlHYYYWUsSApIDA38c2deTedQwevJ+DC/bMMSI7McAI6dheNmHIUZ1YglREQOMnILh5RiGGNWGoxCVMcDIYQwv52CIEdmGAUYOYXg5F0OMFLGEqIgBRnZjeKmDIUbXYglRGQOM7MLwUhdDjKhuDDCyGcPLNRhiZMISoiIGGNmE4eVaDDECWEK0hAFGVmN4uQdDjNgDU8YAI6swvNzLlhAThvNA1a9A9SE0iTiMBbNiEB++DOLSH4B/R0CbxO8f+QQGGNWJ4eUZagsxIQRQ+RNE+aeAfisu/8mtRWQwMObucPj5rYEo/u7ygbQtgZDRQNCtkKQg138QsouvlgEdwQCjWjG8PItSiEEugCieAVRuA6DFlXqRARoJCPCXABiuHMSQDVHyMlC6AGgwC1JAD1d+BLKHEJcXR/b3QQwwsojh5ZmuDrHmCYUYf+deQFT89a7B8o4mf/0yk/Mgiu4HQp8EQh7n95e8DgOMFDG8PNvUqVPROOYMbr3+W8gGCRqNPUeRAQCi9D1AVEMKe9KpbSTn4ShEZXb92JNvY3h5PmEoxF03bYW/n8bO8LpG2XyIih+ccCBShXDC4oMYYGSG4eX5hBAQJS8BohwajfJvpiUrSqCNP25x+Tn90jV7SBDFL0HIRep/ACInYQmRTBheXqJyN6DfbNWmrz4bieZN/Wusb9k84Jo1AhAXIUoXQAp/wQmNJGeS5MuLI/v7IgYYAWB4eRNR/l9cHm1Y94CNof8Xgu5dAq08sgG49AVE2NMcXu9peCOzIpYQieHlRYRcAug3wrrRhvacoAyo2KTOsYmcjD2weo7h5WWqDsI4etAaxRdlnDtvHnaSBDSK1FrYww+iKhNS0N/sbyM5HUchKmOA1WMMLy9UfRiXCyfWhdhNd+XWWKfTSSg/2dLSCYCq/XY3j1TCG5kVMcDqKYaXdxKGAtgSYO+nRaNVsvmADa2lzpeRodCutpF62ANTxgCrhxhe9UePLoE2DOIw8tEha+RzGGD1DMPLu0maMAi1h5RpItQ9PtmOoxAVMcDqEYaXD/BrB9VGIF4+AeDfScXjkz1YQlTGYfT1BMPLR/h3VPkEBkgMMPIS7IHVAwwv3yFp4yD8u1x+YKUV16rWbS7D0azKGuv79ghCcrOaM3QAGkB3o8PtJCfjKERFDDAfx/DyPVLwaIjiKVZtO3OW8tyGH82NVQgwLRA4FJI2ysEWkrOxhKiMAebDGF4+KnAIUNYSqD4BS9fDxt4djrF3h9t4YAlSyOMON4/IVXgNzEcxvHyXJPlDipgNZw8tk0KfgOTfyqnHJCfh41QUMcB8EMPL90n+7SGFv+Sko2mAgAFAyENOOh45m7GE6MjiixhgPobhVX9IwfdDCnvxr1cO/FMO6A+p4fuQJF5RIO/Cn1gfwvCqf6SQMYBfK4ji5wG5ENbPoqEFIEEKmwIEj2V4eTpZXF4c2d8HsQfmIxhe9Zek6wspai0Q8jigifxr7eWAMud35b+BIyBFfQcp5CGGlzfgNTBF/Mn1AQwvkjShkMKegAh9DNDvgKjaB1QdAAx5AGRAEw74d4Tk1xEI/D9ImobubjLZQIKDw+id1hLPwgDzcgwvupok+QOBgyAFDnJ3U4hUxwDzYgwvonqCM3EoYoB5KYYXUf3BmTiUcRCHF2J4EZGnKCoqwv3334/w8HA0aNAA48ePR2lpaa37DBw4EJIkmS2PPvqozedmD8zLMLyI6iEPfh7Y/fffj7Nnz2LDhg2oqqrCuHHj8PDDD2P58uW17jdhwgS89tprptfBwcE2n5sB5kUYXkT1kyQEJAeuYzmyb22OHDmCdevWYe/evejevTsAYN68eRg+fDhmz56NhIQEi/sGBwcjLi7OofOzhOglGF5E5KiSkhKzRa/XO3S8Xbt2oUGDBqbwAoDBgwdDo9Fg9+7dte67bNkyREVFoWPHjpg+fTrKy8ttPj97YF6A4UVUz8mwfpIVS/sDSExMNFs9c+ZMvPLKK3YfNi8vDzExMWbr/Pz8EBkZiby8PIv73XfffWjWrBkSEhLw66+/4vnnn8exY8fw9ddf23R+BpiHY3gRkbNKiDk5OQgPv/KYHZ1Op7j9tGnT8NZbb9V6zCNHjtjdnocfftj0/506dUJ8fDxuuOEGZGdno0WLFlYfhwHmwRheRORM4eHhZgFmydSpUzF27Nhat0lOTkZcXBwKCgrM1ldXV6OoqMim61u9evUCAGRlZTHAfAHDi4hMXDwKMTo6GtHR0XVu16dPH1y4cAHp6elITU0FAGzevBmyLJtCyRqZmZkAgPj4eJvayUEcHojhRURmjDNxOLKooF27dhg6dCgmTJiAPXv24KeffsKkSZNwzz33mEYg5ubmom3bttizZw8AIDs7G6+//jrS09Nx8uRJfPvttxg9ejQGDBiAzp0723R+9sA8DMOLiK7lyTNxLFu2DJMmTcINN9wAjUaDO+64A//6179M71dVVeHYsWOmUYYBAQHYuHEj5s6di7KyMiQmJuKOO+7AjBkzbD43A8yDMLyIyNtERkbWetNy8+bNIa7qASYmJmLbtm1OObdqJcSTJ09i/PjxSEpKQlBQEFq0aIGZM2eisrJSrVN6NYYXEVnkoSVEd1OtB3b06FHIsoyFCxeiZcuWOHjwICZMmICysjLMnj1brdN6JYYXEdVGki8vjuzvi1QLsKFDh2Lo0KGm18nJyTh27Bg++OADBthVGF5ERPZx6TWw4uJiREZGWnxfr9ebTW1SUlLiima5DcOLiKzC54Epctkw+qysLMybNw+PPPKIxW3S0tIQERFhWq6d9sSXMLyIyGrCCYsPsjnApk2bVuM5LtcuR48eNdsnNzcXQ4cOxahRozBhwgSLx54+fTqKi4tNS05Oju2fyAswvIiIHGdzCdHaKUaMzpw5g0GDBqFv375YtGhRrfvpdDqLc3P5CoYXEdnKUx+n4m42B5i1U4wAl3tegwYNQmpqKj7++GNoNPV74g+GFxHZhdfAFKk2iCM3NxcDBw5Es2bNMHv2bBQWFprec/QhZt6I4UVE5FyqBdiGDRuQlZWFrKwsNGnSxOw94aN/DVjC8CIihwg49jwwH/2Vq1pNb+zYsRBCKC71CcOLiBxlvAbmyOKLOBeiihheROQUAg5eA3NaSzxK/R5VoSKGFxGRutgDUwHDi4iciqMQFTHAnIzhRUROJwNw5FeJj07myxKiEzG8iIhchz0wJ2F4EZFaOBOHMgaYEzC8iEhVvAamiCVEBzG8iIjcgz0wBzC8iMgl2ANTxACzE8OLiFyGAaao3gZYib4CBwsKcLiwABcr9ZAgITokBB2jY9A2Kho6P8tfGoYXEZH71asAM8gytp48gU9+3Ycdp09BANBIEjR/BZBBliEABGi1uLVNWzzQuSs6xcSaHYPhRUQux/vAFNWbAMsuOo+p69fi14J8aCXJNDWYLATka7rXlQYDvj5yGF8cPoTb2rbHywMGISIwkOFFRG7BYfTK6kWAfXXkEKZvWm+aCd9gxTfTuM23x45g+6mTGF4l47WJkxheROR6vAamyOcD7LODv+KFzRvs3t8gBIoulWOpvhKjn30Gc996m+FFROQBfDrA9p75Ay86EF5GAoAmwB8HWjbHnxWXEBkU7HjjiIisJQtAcqAXJftmD8xnb2S+VFWFqT+srbO3VPLjTzjx5DM48+57tR9QknBRr8fMrZud2EoiIisYS4iOLD7IZwPso33pOFN6scYAjWuVpu+DX2RD6E/loKrwXK3bGoTA6uPHsCf3D2c2lYiI7OCTAVYty/jk1311hlfV+fPQnziJyJG3QBMagtJfMuo8tlaSsHT/Pmc1lYjICo72vtgD8xrbT53EufLyOrcr/WUfNMFBCO7QDiEpnVGaXneAGYTAD9nHcaHikjOaSkRUN5YQFflkgGWcPQM/Td0frSw9A8GdO0Hy80NoaldUF56D/tTpOveThcCB/HxnNJWIiOzkkwF2oCAPBrn2W8/1OX+gKr8Aod26AAB0yUnQNohAaXrd5UGtJOHXAgYYEbmILBxffJBPBtgfJSV1VnxLf8mANiwMga1aAgAkSUJI1y4oy8iEqCP8JElCQVmpk1pLRFQHITu++CCfDLC6Bm8IWUZZRiYCW7VA9fkiVBWeQ1XhOQQ2awrDxYu49NvxOs9RXUfIERGRunzyRuZwna7W9yt+y4KhpARlGZkoy8is8X7ZLxkIbtum1mOEBQQ40kQiIutxKilFPhlgHaJjcKSwENUWus2l6RnQhIYiatRtNd4r238QZb8eRKPKKmgC/BX3r5ZltI2KcWqbiYgskh0cCu+j18B8MsA6xcbhs0MHFN+TK6tQtv8AQrqkIKRLSo33tRERKMvYh/KDh0wDPBTPEcMAIyIXYQ9MkU9eA7shKdn0jK9rlR88BKHXI7hTe8X3dc2aQhMagjIL94RJAJIbNERyw0hnNZeIiOzgkwEWExKKoS1aQasQYmXpGZD8/RDUprXivpJGg+D27VB+5BgMZWWK24zp0o0z0hOR6wg4eCOzuz+AOnyyhAgAE3v0wrrsmqMJYyc8WOe+0fffg+j776mxXiNJiA4Owe1tlXtvRESqYAlRkU/2wACgXXQMJvXo7dBTuK8lC4HZNw1FCEcgEhG5nc8GGAA83qMXeiQ0sXg9zFaPde+JfonNnHIsIiKrybLjiw/y6QAL0Grx4S23ITU+we6emHG/B7uk4pk+1zmraURE1uNkvop8OsAAIDQgAJ+MvBOPpPaEBCgO7LBEK0kI9vfH7BuH4sX+13PgBhGRB/HZQRxX0/n54bl+/TGkRUvM+Xknfjx90hRG1047pZUkyELAX6vFyDbt8HTvfogNDXVHs4mILuMgDkX1IsCMUuLisWTkHcgpLsaarGM4kJ+P/fl5uKjXQ6OREBUUjC7x8egal4CbW7VGuC7Q3U0mIuJMHBbUqwAzSoyIwCOpPd3dDCIickC9DDAiIm8ihAzhwCNRHNnXkzHAiIg8nXDwoZS8BkZERG4hHLwG5qMB5vPD6ImIyDexB0ZE5OlkGZAcuI7Fa2BEROQWLCEqYgmRiIi8EgOMiMjDCVl2eFHLG2+8gb59+yI4OBgNGjSw7vMIgZdffhnx8fEICgrC4MGDcfx4zcdf1YUBRkTk6Tx4Mt/KykqMGjUKjz32mNX7vP322/jXv/6FBQsWYPfu3QgJCcGQIUNQUVFh07l5DYyIqJ4oKSkxe63T6aDT6Rw65quvvgoAWLJkiVXbCyEwd+5czJgxA7feeisA4JNPPkFsbCxWrlyJe+6p+TBhS9gDIyLydLJwfAGQmJiIiIgI05KWlubyj3LixAnk5eVh8ODBpnURERHo1asXdu3aZdOx2AMjIvJ0QgBwZBj95QDLyclBeHi4abWjvS975OXlAQBiY2PN1sfGxpresxZ7YERE9UR4eLjZYinApk2bBkmSal2OHj3q4tbXpGoP7JZbbkFmZiYKCgrQsGFDDB48GG+99RYSEhLUPC0RkU8RsoCQ7B+IIWwcxDF16lSMHTu21m2Sk5PtaktcXBwAID8/H/Hx8ab1+fn56NKli03HUjXABg0ahBdeeAHx8fHIzc3FM888gzvvvBM7d+5U87RERL5FyHCshGjbvtHR0YiOjrb/fLVISkpCXFwcNm3aZAqskpIS7N6926aRjIDKAfb000+b/r9Zs2aYNm0aRo4ciaqqKvj7+6t5aiIin+HqHpgtTp8+jaKiIpw+fRoGgwGZmZkAgJYtWyL0r6fZt23bFmlpabjtttsgSRKeeuop/OMf/0CrVq2QlJSEl156CQkJCRg5cqRN53bZII6ioiIsW7YMffv2tRheer0eer3e9PraIZ9ERORZXn75ZSxdutT0umvXrgCALVu2YODAgQCAY8eOobi42LTNc889h7KyMjz88MO4cOECrrvuOqxbtw6BgYE2nVsSakYzgOeffx7vv/8+ysvL0bt3b3z//fdo1KiR4ravvPKK6Z6Cq107coaIyN1KSkqQmJiICxcuICIiQrVzRERE4DoMhx/sr1pVowo7sAbFxcW+9btU2Oj55583zippcTly5Ihp+8LCQnHs2DGxfv160a9fPzF8+HAhy7LisSsqKkRxcbFpOXz4cJ3n4sKFCxd3Ljk5Obb+GrXapUuXRFxcnFPaGRcXJy5duqRaW93B5h5YYWEhzp8/X+s2ycnJCAgIqLH+jz/+QGJiInbu3Ik+ffrUeS5ZlnHmzBmEhYVBkiRbmmkT419S9amnx8/Mz+yrXPWZhRC4ePEiEhISoNGod0dSRUUFKisrHT5OQECAzSU6T2fzNTBHRqfIf00oefV1rtpoNBo0adLErnPZw3hvRH3Cz1w/8DOrQ63S4dUCAwN9LnicRbVBHLt378bevXtx3XXXoWHDhsjOzsZLL72EFi1aWNX7IiIiqo1q/d7g4GB8/fXXuOGGG9CmTRuMHz8enTt3xrZt29wyfQkREfkW1XpgnTp1wubNm9U6vFPpdDrMnDmzXgUrP3P9wM9Mvkz1YfRERERq4GS+RETklRhgRETklRhgRETklRhgRETklRhgRETklRhgVzl58iTGjx+PpKQkBAUFoUWLFpg5c6ZTpnHxZG+88Qb69u2L4OBgNGjQwN3NUc38+fPRvHlzBAYGolevXtizZ4+7m6Sa7du3Y8SIEUhISIAkSVi5cqW7m6S6tLQ09OjRA2FhYYiJicHIkSNx7NgxdzeLVMQAu8rRo0chyzIWLlyIQ4cOYc6cOViwYAFeeOEFdzdNVZWVlRg1apTND5PzJitWrMCUKVMwc+ZMZGRkICUlBUOGDEFBQYG7m6aKsrIypKSkYP78+e5uists27YNEydOxM8//4wNGzagqqoKN910E8rKytzdNFIJ7wOrw6xZs/DBBx/g999/d3dTVLdkyRI89dRTuHDhgrub4nS9evVCjx498P777wO4PC9nYmIiJk+ejGnTprm5deqSJAnffPONzQ8L9HaFhYWIiYnBtm3bMGDAAHc3h1TAHlgdiouLERkZ6e5mkAMqKyuRnp6OwYMHm9ZpNBoMHjwYu3btcmPLSE3GByjy36/vYoDVIisrC/PmzcMjjzzi7qaQA86dOweDwYDY2Fiz9bGxscjLy3NTq0hNsizjqaeeQr9+/dCxY0d3N4dUUi8CbNq0aZAkqdbl6NGjZvvk5uZi6NChGDVqFCZMmOCmltvPns9M5CsmTpyIgwcP4rPPPnN3U0hFqk3m60mmTp2KsWPH1rpNcnKy6f/PnDmDQYMGoW/fvli0aJHKrVOHrZ/Zl0VFRUGr1SI/P99sfX5+PuLi4tzUKlLLpEmT8P3332P79u0ufZ4guV69CDBbHsKZm5uLQYMGITU1FR9//LGqT1pVkyMPHvU1AQEBSE1NxaZNm0wDGWRZxqZNmzBp0iT3No6cRgiByZMn45tvvsHWrVuRlJTk7iaRyupFgFkrNzcXAwcORLNmzTB79mwUFhaa3vPlv9RPnz6NoqIinD59GgaDAZmZmQCAli1bIjQ01L2Nc5IpU6ZgzJgx6N69O3r27Im5c+eirKwM48aNc3fTVFFaWoqsrCzT6xMnTiAzMxORkZFo2rSpG1umnokTJ2L58uVYtWoVwsLCTNc3IyIiEBQU5ObWkSoEmXz88ccCgOLiy8aMGaP4mbds2eLupjnVvHnzRNOmTUVAQIDo2bOn+Pnnn93dJNVs2bJF8Xs6ZswYdzdNNZb+7X788cfubhqphPeBERGRV/LOCzxERFTvMcCIiMgrMcCIiMgrMcCIiMgrMcCIiMgrMcCIiMgrMcCIiMgrMcCIiMgrMcCIiMgrMcCIiMgrMcCIiMgr/T9gDLBVFZHcvAAAAABJRU5ErkJggg==",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "G.plot(color_nodes_theta=7*np.pi/4)\n",
+    "plt.title('Coloring nodes with $g_\\omega$ for  $\\\\theta = 7\\pi/4$')\n",
+    "plt.savefig('paper/figures/example_graph_7pi_over_4.png', bbox_inches='tight', dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "FileNotFoundError",
+     "evalue": "[Errno 2] No such file or directory: '../paper/figures/example_graph_pi_over_2.png'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mFileNotFoundError\u001b[0m                         Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[11], line 3\u001b[0m\n\u001b[1;32m      1\u001b[0m G\u001b[38;5;241m.\u001b[39mplot(color_nodes_theta\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m2\u001b[39m\u001b[38;5;241m*\u001b[39mnp\u001b[38;5;241m.\u001b[39mpi\u001b[38;5;241m/\u001b[39m\u001b[38;5;241m4\u001b[39m)\n\u001b[1;32m      2\u001b[0m plt\u001b[38;5;241m.\u001b[39mtitle(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mColoring nodes with $g_\u001b[39m\u001b[38;5;124m\\\u001b[39m\u001b[38;5;124momega$ for  $\u001b[39m\u001b[38;5;130;01m\\\\\u001b[39;00m\u001b[38;5;124mtheta = \u001b[39m\u001b[38;5;124m\\\u001b[39m\u001b[38;5;124mpi/2$\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m----> 3\u001b[0m plt\u001b[38;5;241m.\u001b[39msavefig(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m../paper/figures/example_graph_pi_over_2.png\u001b[39m\u001b[38;5;124m'\u001b[39m, bbox_inches\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mtight\u001b[39m\u001b[38;5;124m'\u001b[39m, dpi\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m300\u001b[39m)\n",
+      "File \u001b[0;32m/opt/anaconda3/lib/python3.11/site-packages/matplotlib/pyplot.py:1228\u001b[0m, in \u001b[0;36msavefig\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m   1225\u001b[0m fig \u001b[38;5;241m=\u001b[39m gcf()\n\u001b[1;32m   1226\u001b[0m \u001b[38;5;66;03m# savefig default implementation has no return, so mypy is unhappy\u001b[39;00m\n\u001b[1;32m   1227\u001b[0m \u001b[38;5;66;03m# presumably this is here because subclasses can return?\u001b[39;00m\n\u001b[0;32m-> 1228\u001b[0m res \u001b[38;5;241m=\u001b[39m fig\u001b[38;5;241m.\u001b[39msavefig(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)  \u001b[38;5;66;03m# type: ignore[func-returns-value]\u001b[39;00m\n\u001b[1;32m   1229\u001b[0m fig\u001b[38;5;241m.\u001b[39mcanvas\u001b[38;5;241m.\u001b[39mdraw_idle()  \u001b[38;5;66;03m# Need this if 'transparent=True', to reset colors.\u001b[39;00m\n\u001b[1;32m   1230\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m res\n",
+      "File \u001b[0;32m/opt/anaconda3/lib/python3.11/site-packages/matplotlib/figure.py:3395\u001b[0m, in \u001b[0;36mFigure.savefig\u001b[0;34m(self, fname, transparent, **kwargs)\u001b[0m\n\u001b[1;32m   3393\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m ax \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39maxes:\n\u001b[1;32m   3394\u001b[0m         _recursively_make_axes_transparent(stack, ax)\n\u001b[0;32m-> 3395\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcanvas\u001b[38;5;241m.\u001b[39mprint_figure(fname, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n",
+      "File \u001b[0;32m/opt/anaconda3/lib/python3.11/site-packages/matplotlib/backend_bases.py:2204\u001b[0m, in \u001b[0;36mFigureCanvasBase.print_figure\u001b[0;34m(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)\u001b[0m\n\u001b[1;32m   2200\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m   2201\u001b[0m     \u001b[38;5;66;03m# _get_renderer may change the figure dpi (as vector formats\u001b[39;00m\n\u001b[1;32m   2202\u001b[0m     \u001b[38;5;66;03m# force the figure dpi to 72), so we need to set it again here.\u001b[39;00m\n\u001b[1;32m   2203\u001b[0m     \u001b[38;5;28;01mwith\u001b[39;00m cbook\u001b[38;5;241m.\u001b[39m_setattr_cm(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfigure, dpi\u001b[38;5;241m=\u001b[39mdpi):\n\u001b[0;32m-> 2204\u001b[0m         result \u001b[38;5;241m=\u001b[39m print_method(\n\u001b[1;32m   2205\u001b[0m             filename,\n\u001b[1;32m   2206\u001b[0m             facecolor\u001b[38;5;241m=\u001b[39mfacecolor,\n\u001b[1;32m   2207\u001b[0m             edgecolor\u001b[38;5;241m=\u001b[39medgecolor,\n\u001b[1;32m   2208\u001b[0m             orientation\u001b[38;5;241m=\u001b[39morientation,\n\u001b[1;32m   2209\u001b[0m             bbox_inches_restore\u001b[38;5;241m=\u001b[39m_bbox_inches_restore,\n\u001b[1;32m   2210\u001b[0m             \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m   2211\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m   2212\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m bbox_inches \u001b[38;5;129;01mand\u001b[39;00m restore_bbox:\n",
+      "File \u001b[0;32m/opt/anaconda3/lib/python3.11/site-packages/matplotlib/backend_bases.py:2054\u001b[0m, in \u001b[0;36mFigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m   2050\u001b[0m     optional_kws \u001b[38;5;241m=\u001b[39m {  \u001b[38;5;66;03m# Passed by print_figure for other renderers.\u001b[39;00m\n\u001b[1;32m   2051\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mdpi\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mfacecolor\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124medgecolor\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124morientation\u001b[39m\u001b[38;5;124m\"\u001b[39m,\n\u001b[1;32m   2052\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mbbox_inches_restore\u001b[39m\u001b[38;5;124m\"\u001b[39m}\n\u001b[1;32m   2053\u001b[0m     skip \u001b[38;5;241m=\u001b[39m optional_kws \u001b[38;5;241m-\u001b[39m {\u001b[38;5;241m*\u001b[39minspect\u001b[38;5;241m.\u001b[39msignature(meth)\u001b[38;5;241m.\u001b[39mparameters}\n\u001b[0;32m-> 2054\u001b[0m     print_method \u001b[38;5;241m=\u001b[39m functools\u001b[38;5;241m.\u001b[39mwraps(meth)(\u001b[38;5;28;01mlambda\u001b[39;00m \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs: meth(\n\u001b[1;32m   2055\u001b[0m         \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m{k: v \u001b[38;5;28;01mfor\u001b[39;00m k, v \u001b[38;5;129;01min\u001b[39;00m kwargs\u001b[38;5;241m.\u001b[39mitems() \u001b[38;5;28;01mif\u001b[39;00m k \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;129;01min\u001b[39;00m skip}))\n\u001b[1;32m   2056\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:  \u001b[38;5;66;03m# Let third-parties do as they see fit.\u001b[39;00m\n\u001b[1;32m   2057\u001b[0m     print_method \u001b[38;5;241m=\u001b[39m meth\n",
+      "File \u001b[0;32m/opt/anaconda3/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:496\u001b[0m, in \u001b[0;36mFigureCanvasAgg.print_png\u001b[0;34m(self, filename_or_obj, metadata, pil_kwargs)\u001b[0m\n\u001b[1;32m    449\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mprint_png\u001b[39m(\u001b[38;5;28mself\u001b[39m, filename_or_obj, \u001b[38;5;241m*\u001b[39m, metadata\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, pil_kwargs\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m    450\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m    451\u001b[0m \u001b[38;5;124;03m    Write the figure to a PNG file.\u001b[39;00m\n\u001b[1;32m    452\u001b[0m \n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    494\u001b[0m \u001b[38;5;124;03m        *metadata*, including the default 'Software' key.\u001b[39;00m\n\u001b[1;32m    495\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m--> 496\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_print_pil(filename_or_obj, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mpng\u001b[39m\u001b[38;5;124m\"\u001b[39m, pil_kwargs, metadata)\n",
+      "File \u001b[0;32m/opt/anaconda3/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445\u001b[0m, in \u001b[0;36mFigureCanvasAgg._print_pil\u001b[0;34m(self, filename_or_obj, fmt, pil_kwargs, metadata)\u001b[0m\n\u001b[1;32m    440\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m    441\u001b[0m \u001b[38;5;124;03mDraw the canvas, then save it using `.image.imsave` (to which\u001b[39;00m\n\u001b[1;32m    442\u001b[0m \u001b[38;5;124;03m*pil_kwargs* and *metadata* are forwarded).\u001b[39;00m\n\u001b[1;32m    443\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m    444\u001b[0m FigureCanvasAgg\u001b[38;5;241m.\u001b[39mdraw(\u001b[38;5;28mself\u001b[39m)\n\u001b[0;32m--> 445\u001b[0m mpl\u001b[38;5;241m.\u001b[39mimage\u001b[38;5;241m.\u001b[39mimsave(\n\u001b[1;32m    446\u001b[0m     filename_or_obj, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuffer_rgba(), \u001b[38;5;28mformat\u001b[39m\u001b[38;5;241m=\u001b[39mfmt, origin\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mupper\u001b[39m\u001b[38;5;124m\"\u001b[39m,\n\u001b[1;32m    447\u001b[0m     dpi\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfigure\u001b[38;5;241m.\u001b[39mdpi, metadata\u001b[38;5;241m=\u001b[39mmetadata, pil_kwargs\u001b[38;5;241m=\u001b[39mpil_kwargs)\n",
+      "File \u001b[0;32m/opt/anaconda3/lib/python3.11/site-packages/matplotlib/image.py:1676\u001b[0m, in \u001b[0;36mimsave\u001b[0;34m(fname, arr, vmin, vmax, cmap, format, origin, dpi, metadata, pil_kwargs)\u001b[0m\n\u001b[1;32m   1674\u001b[0m pil_kwargs\u001b[38;5;241m.\u001b[39msetdefault(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mformat\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;28mformat\u001b[39m)\n\u001b[1;32m   1675\u001b[0m pil_kwargs\u001b[38;5;241m.\u001b[39msetdefault(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mdpi\u001b[39m\u001b[38;5;124m\"\u001b[39m, (dpi, dpi))\n\u001b[0;32m-> 1676\u001b[0m image\u001b[38;5;241m.\u001b[39msave(fname, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mpil_kwargs)\n",
+      "File \u001b[0;32m/opt/anaconda3/lib/python3.11/site-packages/PIL/Image.py:2436\u001b[0m, in \u001b[0;36mImage.save\u001b[0;34m(self, fp, format, **params)\u001b[0m\n\u001b[1;32m   2434\u001b[0m         fp \u001b[38;5;241m=\u001b[39m builtins\u001b[38;5;241m.\u001b[39mopen(filename, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mr+b\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m   2435\u001b[0m     \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m-> 2436\u001b[0m         fp \u001b[38;5;241m=\u001b[39m builtins\u001b[38;5;241m.\u001b[39mopen(filename, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mw+b\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m   2438\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m   2439\u001b[0m     save_handler(\u001b[38;5;28mself\u001b[39m, fp, filename)\n",
+      "\u001b[0;31mFileNotFoundError\u001b[0m: [Errno 2] No such file or directory: '../paper/figures/example_graph_pi_over_2.png'"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "G.plot(color_nodes_theta=2*np.pi/4)\n",
+    "plt.title('Coloring nodes with $g_\\omega$ for  $\\\\theta = \\pi/2$')\n",
+    "plt.savefig('../paper/figures/example_graph_pi_over_2.png', bbox_inches='tight', dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
+       "       2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
+       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
+       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
+       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "myect = ECT(num_dirs = 100, num_thresh=100)\n",
+    "myect.set_bounding_radius(1.2 * G.get_bounding_radius())\n",
+    "\n",
+    "myect.calculateECC(G, np.pi/2,bound_radius=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "myect.plotECC(G, -np.pi/2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "myect.calculateECT(G)\n",
+    "\n",
+    "M = myect.get_ECT()\n",
+    "\n",
+    "# We can use the built in command to plot the matrix. Unlike the plotECC function, this command does not calculate the ECT when called so it must have been run earlier. An equivalent command is myect.plotECT()\n",
+    "myect.plot('ECT')\n",
+    "\n",
+    "plt.savefig('paper/figures/example_ect.png', bbox_inches='tight', dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## CW Complex version"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "TypeError",
+     "evalue": "loop of ufunc does not support argument 0 of type Axes which has no callable cos method",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
+      "\u001b[0;31mAttributeError\u001b[0m: 'Axes' object has no attribute 'cos'",
+      "\nThe above exception was the direct cause of the following exception:\n",
+      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[16], line 13\u001b[0m\n\u001b[1;32m     10\u001b[0m K\u001b[38;5;241m.\u001b[39madd_face([\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mA\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mB\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mC\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mD\u001b[39m\u001b[38;5;124m'\u001b[39m])\n\u001b[1;32m     12\u001b[0m \u001b[38;5;66;03m# K.set_centered_coordinates()\u001b[39;00m\n\u001b[0;32m---> 13\u001b[0m K\u001b[38;5;241m.\u001b[39mplot()\n",
+      "File \u001b[0;32m~/Library/CloudStorage/Dropbox/Math/Code/ect/ect/ect/embed_cw.py:174\u001b[0m, in \u001b[0;36mEmbeddedCW.plot\u001b[0;34m(self, bounding_circle, color_nodes_theta, ax, **kwargs)\u001b[0m\n\u001b[1;32m    171\u001b[0m     fig \u001b[38;5;241m=\u001b[39m ax\u001b[38;5;241m.\u001b[39mget_figure()\n\u001b[1;32m    173\u001b[0m ax \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mplot_faces(\u001b[38;5;241m0\u001b[39m, facecolor\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlightblue\u001b[39m\u001b[38;5;124m'\u001b[39m, ax\u001b[38;5;241m=\u001b[39max)\n\u001b[0;32m--> 174\u001b[0m ax \u001b[38;5;241m=\u001b[39m \u001b[38;5;28msuper\u001b[39m()\u001b[38;5;241m.\u001b[39mplot(bounding_circle, color_nodes_theta, ax)\n\u001b[1;32m    175\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m ax\n",
+      "File \u001b[0;32m~/Library/CloudStorage/Dropbox/Math/Code/ect/ect/ect/embed_graph.py:482\u001b[0m, in \u001b[0;36mEmbeddedGraph.plot\u001b[0;34m(self, bounding_circle, bounding_center_type, color_nodes_theta, ax, with_labels, **kwargs)\u001b[0m\n\u001b[1;32m    480\u001b[0m     nx\u001b[38;5;241m.\u001b[39mdraw(\u001b[38;5;28mself\u001b[39m, pos, with_labels\u001b[38;5;241m=\u001b[39mwith_labels, ax\u001b[38;5;241m=\u001b[39max, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m    481\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m--> 482\u001b[0m     g \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mg_omega(color_nodes_theta)\n\u001b[1;32m    483\u001b[0m     color_map \u001b[38;5;241m=\u001b[39m [g[v] \u001b[38;5;28;01mfor\u001b[39;00m v \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mnodes]\n\u001b[1;32m    484\u001b[0m     \u001b[38;5;66;03m# Some weird plotting to make the colorbar work.\u001b[39;00m\n",
+      "File \u001b[0;32m~/Library/CloudStorage/Dropbox/Math/Code/ect/ect/ect/embed_graph.py:347\u001b[0m, in \u001b[0;36mEmbeddedGraph.g_omega\u001b[0;34m(self, theta)\u001b[0m\n\u001b[1;32m    332\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mg_omega\u001b[39m(\u001b[38;5;28mself\u001b[39m, theta):\n\u001b[1;32m    333\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m    334\u001b[0m \u001b[38;5;124;03m    Function to compute the function :math:`g_\\omega(v)` for all vertices :math:`v` in the graph in the direction of :math:`\\\\theta \\in [0,2\\pi]` . This function is defined by :math:`g_\\omega(v) = \\langle \\\\texttt{pos}(v), \\omega \\\\rangle` .\u001b[39;00m\n\u001b[1;32m    335\u001b[0m \n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    344\u001b[0m \n\u001b[1;32m    345\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m--> 347\u001b[0m     omega \u001b[38;5;241m=\u001b[39m (np\u001b[38;5;241m.\u001b[39mcos(theta), np\u001b[38;5;241m.\u001b[39msin(theta))\n\u001b[1;32m    349\u001b[0m     g \u001b[38;5;241m=\u001b[39m {}\n\u001b[1;32m    350\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m v \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mnodes:\n",
+      "\u001b[0;31mTypeError\u001b[0m: loop of ufunc does not support argument 0 of type Axes which has no callable cos method"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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RACApMQIAJCVGAICkxAgAkJQYAQCSEiMAQFJiBABISowAAEmJEQAgKTECACQlRgCApMQIAJCUGAEAkhIjAEBSYgQASEqMAABJiREAICkxAgAkJUYAgKTECACQlBgBAJISIwBAUmIEAEhKjAAASYkRACApMQIAJCVGAICkxAgAkJQYAQCSEiMAQFJiBABISowAAEmJEQAgKTECACQlRgCApMQIAJCUGAEAkhIjAEBSYgQASEqMAABJiREAICkxAgAkJUYAgKTECACQlBgBAJISIwBAUmIEAEhKjAAASY0rRjo6OqK+vj4qKiqioaEhdu/efcq1mzZtiquuuipmzJgRM2bMiKampndcDwCcWQqOka1bt0Zra2u0tbXF3r17Y+7cudHc3Byvv/76qOt37doVN9xwQ/zsZz+Lrq6uqKuri09/+tPxu9/97j0PDwAUv5Isy7JCTmhoaIhPfvKT8eCDD0ZExNDQUNTV1cVXvvKVWLly5buePzg4GDNmzIgHH3wwlixZMqbnzOfzUVVVFX19fVFZWVnIuO9q24HXTuv1AKDYfP7C2gm57lhfvwu6MzIwMBB79uyJpqamty9QWhpNTU3R1dU1pmu88cYb8eabb8YHP/jBU645fvx45PP5EQ8AYGoqKEaOHj0ag4ODUV1dPeJ4dXV19PT0jOkad9xxR8yePXtE0Pyl9vb2qKqqGn7U1dUVMiYAUEQm9dM069atiy1btsQTTzwRFRUVp1y3atWq6OvrG34cPnx4EqcEACbTtEIWz5w5M8rKyqK3t3fE8d7e3qipqXnHc++///5Yt25d/PSnP43LLrvsHdfmcrnI5XKFjAYAFKmC7oyUl5fH/Pnzo7Ozc/jY0NBQdHZ2RmNj4ynPu+++++Lee++NnTt3xoIFC8Y/LQAw5RR0ZyQiorW1NZYuXRoLFiyIhQsXxoYNG6K/vz+WLVsWERFLliyJOXPmRHt7e0RE/Pu//3usWbMmHnvssaivrx9+b8kHPvCB+MAHPnAavxQAoBgVHCMtLS1x5MiRWLNmTfT09MS8efNi586dw29qPXToUJSWvn3D5dvf/nYMDAzEP/zDP4y4TltbW3zta197b9MDAEWv4N8zkoLfMwIAE6eofs8IAMDpJkYAgKTECACQlBgBAJISIwBAUmIEAEhKjAAASYkRACApMQIAJCVGAICkxAgAkJQYAQCSEiMAQFJiBABISowAAEmJEQAgKTECACQlRgCApMQIAJCUGAEAkhIjAEBSYgQASEqMAABJiREAICkxAgAkJUYAgKTECACQlBgBAJISIwBAUmIEAEhKjAAASYkRACApMQIAJCVGAICkxAgAkJQYAQCSEiMAQFJiBABISowAAEmJEQAgKTECACQlRgCApMQIAJCUGAEAkhIjAEBSYgQASEqMAABJiREAICkxAgAkJUYAgKTECACQlBgBAJISIwBAUmIEAEhKjAAASYkRACCpccVIR0dH1NfXR0VFRTQ0NMTu3bvfcf2PfvSjuOiii6KioiIuvfTS2LFjx7iGBQCmnoJjZOvWrdHa2hptbW2xd+/emDt3bjQ3N8frr78+6vpnn302brjhhrjpppti3759cf3118f1118fv/rVr97z8ABA8SvJsiwr5ISGhob45Cc/GQ8++GBERAwNDUVdXV185StfiZUrV560vqWlJfr7++MnP/nJ8LG//du/jXnz5sXGjRvH9Jz5fD6qqqqir68vKisrCxn3XW078NppvR4AFJvPX1g7Idcd6+t3QXdGBgYGYs+ePdHU1PT2BUpLo6mpKbq6ukY9p6ura8T6iIjm5uZTro+IOH78eOTz+REPAGBqmlbI4qNHj8bg4GBUV1ePOF5dXR0vvPDCqOf09PSMur6np+eUz9Pe3h733HNPIaON20TVIAAwNu/LT9OsWrUq+vr6hh+HDx9OPRIAMEEKujMyc+bMKCsri97e3hHHe3t7o6amZtRzampqClofEZHL5SKXyxUyGgBQpAq6M1JeXh7z58+Pzs7O4WNDQ0PR2dkZjY2No57T2Ng4Yn1ExNNPP33K9QDAmaWgOyMREa2trbF06dJYsGBBLFy4MDZs2BD9/f2xbNmyiIhYsmRJzJkzJ9rb2yMi4vbbb4+rr746Hnjggbjuuutiy5Yt8ctf/jIefvjh0/uVAABFqeAYaWlpiSNHjsSaNWuip6cn5s2bFzt37hx+k+qhQ4eitPTtGy5XXHFFPPbYY3HXXXfFnXfeGR/96EfjySefjEsuueT0fRUAQNEq+PeMpDCRv2cEAJgYE/J7RgAATjcxAgAkJUYAgKTECACQlBgBAJISIwBAUmIEAEhKjAAASYkRACCpgn8dfApv/ZLYfD6feBIAYKzeet1+t1/2XhQxcuzYsYiIqKurSzwJAFCoY8eORVVV1Sn/eVH8bZqhoaF49dVXY/r06VFSUnLarpvP56Ouri4OHz7sb95MIPs8eez15LDPk8M+T46J3Ocsy+LYsWMxe/bsEX9E9y8VxZ2R0tLS+NCHPjRh16+srPSNPgns8+Sx15PDPk8O+zw5Jmqf3+mOyFu8gRUASEqMAABJndExksvloq2tLXK5XOpRpjT7PHns9eSwz5PDPk+O98M+F8UbWAGAqeuMvjMCAKQnRgCApMQIAJCUGAEAkpryMdLR0RH19fVRUVERDQ0NsXv37ndc/6Mf/SguuuiiqKioiEsvvTR27NgxSZMWt0L2edOmTXHVVVfFjBkzYsaMGdHU1PSu/7/wtkK/p9+yZcuWKCkpieuvv35iB5wiCt3nP/zhD7F8+fKora2NXC4XF1xwgX9/jEGh+7xhw4a48MIL4+yzz466urpYsWJF/OlPf5qkaYvTz3/+81i0aFHMnj07SkpK4sknn3zXc3bt2hWf+MQnIpfLxUc+8pF49NFHJ3bIbArbsmVLVl5enm3evDn79a9/nd1yyy3Zueeem/X29o66/he/+EVWVlaW3Xfffdnzzz+f3XXXXdlZZ52VPffcc5M8eXEpdJ9vvPHGrKOjI9u3b1+2f//+7B//8R+zqqqq7H/+538mefLiU+hev+Xll1/O5syZk1111VXZ5z73uckZtogVus/Hjx/PFixYkF177bXZM888k7388svZrl27su7u7kmevLgUus/f//73s1wul33/+9/PXn755eypp57KamtrsxUrVkzy5MVlx44d2erVq7Nt27ZlEZE98cQT77j+4MGD2TnnnJO1trZmzz//fPatb30rKysry3bu3DlhM07pGFm4cGG2fPny4f89ODiYzZ49O2tvbx91/Re+8IXsuuuuG3GsoaEh+6d/+qcJnbPYFbrPf+nEiRPZ9OnTs+9973sTNeKUMZ69PnHiRHbFFVdk3/nOd7KlS5eKkTEodJ+//e1vZ+edd142MDAwWSNOCYXu8/Lly7O/+7u/G3GstbU1u/LKKyd0zqlkLDHy1a9+Nfv4xz8+4lhLS0vW3Nw8YXNN2R/TDAwMxJ49e6KpqWn4WGlpaTQ1NUVXV9eo53R1dY1YHxHR3Nx8yvWMb5//0htvvBFvvvlmfPCDH5yoMaeE8e7117/+9Zg1a1bcdNNNkzFm0RvPPv/4xz+OxsbGWL58eVRXV8cll1wSa9eujcHBwckau+iMZ5+vuOKK2LNnz/CPcg4ePBg7duyIa6+9dlJmPlOkeC0sij+UNx5Hjx6NwcHBqK6uHnG8uro6XnjhhVHP6enpGXV9T0/PhM1Z7Mazz3/pjjvuiNmzZ5/0zc9I49nrZ555Jh555JHo7u6ehAmnhvHs88GDB+O//uu/4otf/GLs2LEjXnrppfjyl78cb775ZrS1tU3G2EVnPPt84403xtGjR+NTn/pUZFkWJ06ciNtuuy3uvPPOyRj5jHGq18J8Ph9//OMf4+yzzz7tzzll74xQHNatWxdbtmyJJ554IioqKlKPM6UcO3YsFi9eHJs2bYqZM2emHmdKGxoailmzZsXDDz8c8+fPj5aWlli9enVs3Lgx9WhTyq5du2Lt2rXx0EMPxd69e2Pbtm2xffv2uPfee1OPxns0Ze+MzJw5M8rKyqK3t3fE8d7e3qipqRn1nJqamoLWM759fsv9998f69ati5/+9Kdx2WWXTeSYU0Khe/2b3/wmXnnllVi0aNHwsaGhoYiImDZtWhw4cCDOP//8iR26CI3ne7q2tjbOOuusKCsrGz528cUXR09PTwwMDER5efmEzlyMxrPPd999dyxevDhuvvnmiIi49NJLo7+/P2699dZYvXp1lJb67+vT4VSvhZWVlRNyVyRiCt8ZKS8vj/nz50dnZ+fwsaGhoejs7IzGxsZRz2lsbByxPiLi6aefPuV6xrfPERH33Xdf3HvvvbFz585YsGDBZIxa9Ard64suuiiee+656O7uHn589rOfjWuuuSa6u7ujrq5uMscvGuP5nr7yyivjpZdeGo69iIgXX3wxamtrhcgpjGef33jjjZOC460AzPyZtdMmyWvhhL019n1gy5YtWS6Xyx599NHs+eefz2699dbs3HPPzXp6erIsy7LFixdnK1euHF7/i1/8Ips2bVp2//33Z/v378/a2tp8tHcMCt3ndevWZeXl5dnjjz+evfbaa8OPY8eOpfoSikahe/2XfJpmbArd50OHDmXTp0/P/vmf/zk7cOBA9pOf/CSbNWtW9o1vfCPVl1AUCt3ntra2bPr06dkPfvCD7ODBg9l//ud/Zueff372hS98IdWXUBSOHTuW7du3L9u3b18WEdn69euzffv2Zb/97W+zLMuylStXZosXLx5e/9ZHe//t3/4t279/f9bR0eGjve/Vt771reyv//qvs/Ly8mzhwoXZf//3fw//s6uvvjpbunTpiPU//OEPswsuuCArLy/PPv7xj2fbt2+f5ImLUyH7/Dd/8zdZRJz0aGtrm/zBi1Ch39P/PzEydoXu87PPPps1NDRkuVwuO++887JvfvOb2YkTJyZ56uJTyD6/+eab2de+9rXs/PPPzyoqKrK6urrsy1/+cva///u/kz94EfnZz3426r9z39rbpUuXZldfffVJ58ybNy8rLy/PzjvvvOy73/3uhM5YkmXubQEA6UzZ94wAAMVBjAAASYkRACApMQIAJCVGAICkxAgAkJQYAQCSEiMAQFJiBABISowAAEmJEQAgKTECACT1/wCLuVSMYdNdGAAAAABJRU5ErkJggg==",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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QDOECACRDuAAAyRAuAEAyhAsAkAzhAgAkQ7gAAMkQLgBAMoQLAJAM4QIAJEO4AADJEC4AQDKECwCQDOECACRDuAAAyRAuAEAyhAsAkAzhAgAkQ7gAAMkQLgBAMoQLAJAM4QIAJEO4AADJEC4AQDKECwCQDOECACRDuAAAyRAuAEAyhAsAkAzhAgAkQ7gAAMkQLgBAMoQLAJAM4QIAJEO4AADJEC4AQDKECwCQDOECACRDuAAAyRAuAEAyhAsAkAzhAgAkQ7gAAMkQLgBAMoQLAJAM4QIAJEO4AADJEC4AQDKECwCQjCGFS1NTU1RVVUVJSUlUV1fH9u3bjzp3w4YNcdFFF8XkyZNj8uTJUVtb+6bzAQCOJu9w2bRpU9TX10dDQ0Ps3LkzZs6cGXV1dfHSSy8NOn/btm1x+eWXx+9///toaWmJysrK+NSnPhV/+9vf3vbmAYCJpSDLsiyfBdXV1XH++efHunXrIiKir68vKisr4/rrr4/ly5e/5fre3t6YPHlyrFu3LhYtWjTonO7u7uju7u7/c2dnZ1RWVkZHR0eUlpbms10AYIx0dnZGWVnZsP78zusZl56entixY0fU1tb+9w4KC6O2tjZaWlqO6T5effXVeP311+Md73jHUec0NjZGWVlZ/62ysjKfbQIA41Re4XLgwIHo7e2N8vLyAePl5eXR1tZ2TPdx4403xvTp0wfEz/9asWJFdHR09N/279+fzzYBgHFq0mhebM2aNbFx48bYtm1blJSUHHVeLpeLXC43ijsDAFKQV7hMmTIlioqKor29fcB4e3t7VFRUvOnaO+64I9asWRO//e1v49xzz81/pwDAhJfXS0XFxcUxe/bsaG5u7h/r6+uL5ubmqKmpOeq622+/PW677bbYunVrzJkzZ+i7BQAmtLxfKqqvr4/FixfHnDlzYu7cubF27dro6uqKJUuWRETEokWLYsaMGdHY2BgREd/97ndj1apV8bOf/Syqqqr63wtz8sknx8knnzyMDwUAGO/yDpcFCxbEyy+/HKtWrYq2traYNWtWbN26tf8Nu/v27YvCwv8+kfPDH/4wenp64rOf/eyA+2loaIhvfvObb2/3AMCEkvf3uIyFkfgcOAAwssb8e1wAAMaScAEAkiFcAIBkCBcAIBnCBQBIhnABAJIhXACAZAgXACAZwgUASIZwAQCSIVwAgGQIFwAgGcIFAEiGcAEAkiFcAIBkCBcAIBnCBQBIhnABAJIhXACAZAgXACAZwgUASIZwAQCSIVwAgGQIFwAgGcIFAEiGcAEAkiFcAIBkCBcAIBnCBQBIhnABAJIhXACAZAgXACAZwgUASIZwAQCSIVwAgGQIFwAgGcIFAEiGcAEAkiFcAIBkCBcAIBnCBQBIhnABAJIhXACAZAgXACAZwgUASIZwAQCSIVwAgGQIFwAgGcIFAEiGcAEAkiFcAIBkCBcAIBnCBQBIhnABAJIhXACAZAgXACAZwgUASIZwAQCSIVwAgGQIFwAgGcIFAEiGcAEAkiFcAIBkDClcmpqaoqqqKkpKSqK6ujq2b9/+pvMfeOCBOOuss6KkpCTOOeec2LJly5A2CwBMbHmHy6ZNm6K+vj4aGhpi586dMXPmzKirq4uXXnpp0PmPP/54XH755XHllVfGrl27Yv78+TF//vx46qmn3vbmAYCJpSDLsiyfBdXV1XH++efHunXrIiKir68vKisr4/rrr4/ly5cfMX/BggXR1dUVv/71r/vHPvrRj8asWbNi/fr1g16ju7s7uru7+//c0dERp512Wuzfvz9KS0vz2S4AMEY6OzujsrIyDh48GGVlZcNyn5PymdzT0xM7duyIFStW9I8VFhZGbW1ttLS0DLqmpaUl6uvrB4zV1dXFL3/5y6Nep7GxMW699dYjxisrK/PZLgBwHPjHP/4xNuFy4MCB6O3tjfLy8gHj5eXlsWfPnkHXtLW1DTq/ra3tqNdZsWLFgNg5ePBgvOc974l9+/YN2wNnaN6oZ89+jT1ncfxwFscX53H8eOMVk3e84x3Ddp95hctoyeVykcvljhgvKyvzD+FxorS01FkcJ5zF8cNZHF+cx/GjsHD4PsSc1z1NmTIlioqKor29fcB4e3t7VFRUDLqmoqIir/kAAEeTV7gUFxfH7Nmzo7m5uX+sr68vmpubo6amZtA1NTU1A+ZHRDz66KNHnQ8AcDR5v1RUX18fixcvjjlz5sTcuXNj7dq10dXVFUuWLImIiEWLFsWMGTOisbExIiJuuOGGuPjii+POO++Myy67LDZu3BhPPPFE3HPPPcd8zVwuFw0NDYO+fMTochbHD2dx/HAWxxfncfwYibPI++PQERHr1q2L733ve9HW1hazZs2K73//+1FdXR0RER//+Mejqqoq7r///v75DzzwQNx8883x4osvxvvf//64/fbb49JLLx22BwEATAxDChcAgLHgdxUBAMkQLgBAMoQLAJAM4QIAJOO4CZempqaoqqqKkpKSqK6uju3bt7/p/AceeCDOOuusKCkpiXPOOSe2bNkySjsd//I5iw0bNsRFF10UkydPjsmTJ0dtbe1bnh3HLt+/F2/YuHFjFBQUxPz580d2gxNIvmdx8ODBWLp0aUybNi1yuVyceeaZ/j01TPI9i7Vr18YHPvCBOPHEE6OysjKWLVsWr7322ijtdvz6wx/+EPPmzYvp06dHQUHBm/4Owjds27YtPvKRj0Qul4v3ve99Az6BfMyy48DGjRuz4uLi7L777sv+/Oc/Z1dffXV26qmnZu3t7YPO/+Mf/5gVFRVlt99+e/b0009nN998c3bCCSdkTz755CjvfPzJ9yyuuOKKrKmpKdu1a1e2e/fu7Itf/GJWVlaW/fWvfx3lnY8/+Z7FG1544YVsxowZ2UUXXZR95jOfGZ3NjnP5nkV3d3c2Z86c7NJLL80ee+yx7IUXXsi2bduWtba2jvLOx598z+KnP/1plsvlsp/+9KfZCy+8kD3yyCPZtGnTsmXLlo3yzsefLVu2ZCtXrsweeuihLCKyhx9++E3n7927NzvppJOy+vr67Omnn85+8IMfZEVFRdnWrVvzuu5xES5z587Nli5d2v/n3t7ebPr06VljY+Og8z/3uc9ll1122YCx6urq7Etf+tKI7nMiyPcs/tfhw4ezU045JfvJT34yUlucMIZyFocPH84uuOCC7Ec/+lG2ePFi4TJM8j2LH/7wh9npp5+e9fT0jNYWJ4x8z2Lp0qXZJz7xiQFj9fX12YUXXjii+5xojiVcvvGNb2Qf/vCHB4wtWLAgq6ury+taY/5SUU9PT+zYsSNqa2v7xwoLC6O2tjZaWloGXdPS0jJgfkREXV3dUedzbIZyFv/r1Vdfjddff31YfxPoRDTUs/jWt74VU6dOjSuvvHI0tjkhDOUsfvWrX0VNTU0sXbo0ysvL4+yzz47Vq1dHb2/vaG17XBrKWVxwwQWxY8eO/peT9u7dG1u2bPElqGNguH52j/lvhz5w4ED09vZGeXn5gPHy8vLYs2fPoGva2toGnd/W1jZi+5wIhnIW/+vGG2+M6dOnH/EPJ/kZylk89thjce+990Zra+so7HDiGMpZ7N27N373u9/FF77whdiyZUs899xz8eUvfzlef/31aGhoGI1tj0tDOYsrrrgiDhw4EB/72Mciy7I4fPhwXHvttXHTTTeNxpb5f472s7uzszP+/e9/x4knnnhM9zPmz7gwfqxZsyY2btwYDz/8cJSUlIz1diaUQ4cOxcKFC2PDhg0xZcqUsd7OhNfX1xdTp06Ne+65J2bPnh0LFiyIlStXxvr168d6axPOtm3bYvXq1XH33XfHzp0746GHHorNmzfHbbfdNtZbY4jG/BmXKVOmRFFRUbS3tw8Yb29vj4qKikHXVFRU5DWfYzOUs3jDHXfcEWvWrInf/va3ce65547kNieEfM/i+eefjxdffDHmzZvXP9bX1xcREZMmTYpnnnkmzjjjjJHd9Dg1lL8X06ZNixNOOCGKior6xz74wQ9GW1tb9PT0RHFx8YjuebwaylnccsstsXDhwrjqqqsiIuKcc86Jrq6uuOaaa2LlypVRWOi/30fL0X52l5aWHvOzLRHHwTMuxcXFMXv27Ghubu4f6+vri+bm5qipqRl0TU1NzYD5ERGPPvroUedzbIZyFhERt99+e9x2222xdevWmDNnzmhsddzL9yzOOuusePLJJ6O1tbX/9ulPfzouueSSaG1tjcrKytHc/rgylL8XF154YTz33HP98RgR8eyzz8a0adNEy9swlLN49dVXj4iTN4Iy86v6RtWw/ezO733DI2Pjxo1ZLpfL7r///uzpp5/OrrnmmuzUU0/N2trasizLsoULF2bLly/vn//HP/4xmzRpUnbHHXdku3fvzhoaGnwcepjkexZr1qzJiouLswcffDD7+9//3n87dOjQWD2EcSPfs/hfPlU0fPI9i3379mWnnHJK9pWvfCV75plnsl//+tfZ1KlTs29/+9tj9RDGjXzPoqGhITvllFOyn//859nevXuz3/zmN9kZZ5yRfe5znxurhzBuHDp0KNu1a1e2a9euLCKyu+66K9u1a1f2l7/8JcuyLFu+fHm2cOHC/vlvfBz661//erZ79+6sqakp3Y9DZ1mW/eAHP8hOO+20rLi4OJs7d272pz/9qf9/u/jii7PFixcPmP+LX/wiO/PMM7Pi4uLswx/+cLZ58+ZR3vH4lc9ZvOc978ki4ohbQ0PD6G98HMr378X/J1yGV75n8fjjj2fV1dVZLpfLTj/99Ow73/lOdvjw4VHe9fiUz1m8/vrr2Te/+c3sjDPOyEpKSrLKysrsy1/+cvbPf/5z9Dc+zvz+978f9N//b/z/v3jx4uziiy8+Ys2sWbOy4uLi7PTTT89+/OMf533dgizzXBkAkIYxf48LAMCxEi4AQDKECwCQDOECACRDuAAAyRAuAEAyhAsAkAzhAgAkQ7gAAMkQLgBAMoQLAJCM/wM9kKRvAVrZIAAAAABJRU5ErkJggg==",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "K = EmbeddedCW()\n",
+    "\n",
+    "K.add_node('A', 0,0)\n",
+    "K.add_node('B', 1,0)\n",
+    "K.add_node('C', 1,1)\n",
+    "K.add_node('D', 0,1)\n",
+    "\n",
+    "K.add_edges_from((('A', 'B'), ('B', 'C'), ('C', 'D'), ('D', 'A')))\n",
+    "\n",
+    "K.add_face(['A', 'B', 'C', 'D'])\n",
+    "\n",
+    "# K.set_centered_coordinates()\n",
+    "K.plot()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": ".conda-ect-3-11",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/paper/paper.md b/paper/paper.md
index 3c481c8..42ec258 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -40,9 +40,9 @@ The `ect` Python package offers a fast and well-documented implementation of ECT
 
 ## The Euler Characteristic Transform
 
-We give a high level introduction of the ECT here. We direct the reader to [@Munch2025] for a full survey article on the subject. 
+We give a high level introduction of the ECT here as defined in [@Turner2014], and direct the reader to [@Munch2025] for a full survey article specifically on the subject. Further, note that the code is built to handle embedded cell complexes of arbitrary dimension, but for ease of introduction, we explain the basics using embedded graphs.
 
-To start, we assume our input is an undirected graph $G$ with an embedding in 2D given by a map on the vertices $f: V(G) \to \mathbb{R}^2$. A graph can be constructed as seen in \autoref{fig:example_graph}. 
+To start, we assume our input is an undirected graph $G$ with a straight-line embedding in 2D given by a map on the vertices $f: V(G) \to \mathbb{R}^2$. A graph can be constructed as seen in \autoref{fig:example_graph}.
 
 
 

From 55525ff1588bbb1043c339dc7c771efe6d420857 Mon Sep 17 00:00:00 2001
From: yemeen <yemeen.ayub.14@cnu.edu>
Date: Wed, 1 Oct 2025 12:20:06 -0400
Subject: [PATCH 10/25] test workflow

---
 paper/paper.md | 6 ------
 1 file changed, 6 deletions(-)

diff --git a/paper/paper.md b/paper/paper.md
index 42ec258..b06fcbe 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -109,12 +109,6 @@ The ECT package provides implementations for both the Smooth Euler Characteristi
 
 Despite the ECT's mathematical elegances, there has been a notable absense of efficient, user-friendly Python implementations that can handle the computational demands of modern research datasets. The ECT package addressed this by leveraging Numba's just-in-time compilation to achieve significant speedups over naive Python implementations, making it practical to compute ECTs for large-scale datasets. This performance is then complimented by the many utility functions for visualizing and comparing different Euler Characteristic Tranforms such as the ECT, SECT, and the DECT.
 
-Yemeen is going to find any needed references.
-
-- DECT 
-- Demeter 
-- 
-
 # Representative Publications Using ECT
 
 Have we actually used it yet? 

From b91a8bba1a30b9e806689da3e095511eeb62ce70 Mon Sep 17 00:00:00 2001
From: yemeen <yemeen.ayub.14@cnu.edu>
Date: Wed, 1 Oct 2025 12:25:37 -0400
Subject: [PATCH 11/25] Add workflow to compile paper draft and upload PDF

---
 .github/workflows/compile-paper.yml | 23 +++++++++++++++++++++++
 1 file changed, 23 insertions(+)
 create mode 100644 .github/workflows/compile-paper.yml

diff --git a/.github/workflows/compile-paper.yml b/.github/workflows/compile-paper.yml
new file mode 100644
index 0000000..05d0598
--- /dev/null
+++ b/.github/workflows/compile-paper.yml
@@ -0,0 +1,23 @@
+on: [push, workflow_dispatch]
+
+jobs:
+  paper:
+    runs-on: ubuntu-latest
+    name: Paper Draft
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+      - name: Build draft PDF
+        uses: openjournals/openjournals-draft-action@master
+        with:
+          journal: joss
+          # This should be the path to the paper within your repo.
+          paper-path: paper/paper.md
+      - name: Upload
+        uses: actions/upload-artifact@v4
+        with:
+          name: paper
+          # This is the output path where Pandoc will write the compiled
+          # PDF. Note, this should be the same directory as the input
+          # paper.md
+          path: paper/paper.pdf

From ff6699ef9489e2a2f4c90d90b0c9c36b5a6a0d17 Mon Sep 17 00:00:00 2001
From: Liz Munch <muncheli@msu.edu>
Date: Wed, 1 Oct 2025 12:56:17 -0400
Subject: [PATCH 12/25] Testing compiler

---
 .gitignore                                |   2 +
 Extra_Notebooks/Figs_For_JOSS_Paper.ipynb |   0
 paper/figures/example_graph.png           | Bin 37355 -> 66832 bytes
 paper/figures/example_graph_pi_over_2.png | Bin 58525 -> 101125 bytes
 paper/generating_figures.ipynb            | 159 ++++++++++------------
 5 files changed, 75 insertions(+), 86 deletions(-)
 create mode 100644 Extra_Notebooks/Figs_For_JOSS_Paper.ipynb

diff --git a/.gitignore b/.gitignore
index 6a058df..60a4a1d 100644
--- a/.gitignore
+++ b/.gitignore
@@ -8,6 +8,8 @@ benchmarks/results/*
 src/ect/embed_graph.py
 src/ect/embed_cw.py
 
+.conda*
+
 # Byte-compiled / optimized / DLL files
 __pycache__/
 *.py[cod]
diff --git a/Extra_Notebooks/Figs_For_JOSS_Paper.ipynb b/Extra_Notebooks/Figs_For_JOSS_Paper.ipynb
new file mode 100644
index 0000000..e69de29
diff --git a/paper/figures/example_graph.png b/paper/figures/example_graph.png
index 2700c01982dbdba2c967afba44ce32ac03898f9d..e48a994301376ee4a26ba43464a8687b505ae1a8 100644
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diff --git a/paper/generating_figures.ipynb b/paper/generating_figures.ipynb
index 9c97f89..84b033b 100644
--- a/paper/generating_figures.ipynb
+++ b/paper/generating_figures.ipynb
@@ -4,21 +4,9 @@
    "cell_type": "code",
    "execution_count": 1,
    "metadata": {},
-   "outputs": [
-    {
-     "ename": "ImportError",
-     "evalue": "cannot import name 'create_example_graph' from 'ect' (/Users/lizliz/Library/CloudStorage/Dropbox/Math/Code/ect/.conda-ect-3-11/lib/python3.11/site-packages/ect/__init__.py)",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
-      "\u001b[31mImportError\u001b[39m                               Traceback (most recent call last)",
-      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[1]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mect\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mimport\u001b[39;00m ECT, EmbeddedGraph, EmbeddedCW,create_example_graph\n\u001b[32m      3\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mmatplotlib\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mpyplot\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mplt\u001b[39;00m\n\u001b[32m      4\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mnumpy\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mnp\u001b[39;00m\n",
-      "\u001b[31mImportError\u001b[39m: cannot import name 'create_example_graph' from 'ect' (/Users/lizliz/Library/CloudStorage/Dropbox/Math/Code/ect/.conda-ect-3-11/lib/python3.11/site-packages/ect/__init__.py)"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
-    "from ect import ECT, EmbeddedGraph, EmbeddedCW,create_example_graph\n",
+    "from ect import ECT, EmbeddedComplex #, EmbeddedGraph, EmbeddedCW #,create_example_graph\n",
     "\n",
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -27,40 +15,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0D_pers_Sandbox.ipynb             \u001b[34mgithub_collaboration\u001b[m\u001b[m/\n",
-      "\u001b[34mDionysus\u001b[m\u001b[m/                         gudhi_library_2.3.0.zip\n",
-      "\u001b[34mDionysusExamples\u001b[m\u001b[m/                 \u001b[34mhera\u001b[m\u001b[m/\n",
-      "\u001b[34mEirene0_3_5\u001b[m\u001b[m/                      \u001b[34mhtml\u001b[m\u001b[m/\n",
-      "Eirene0_3_5.zip                   julia-0.5.2-linux-x86_64.tar.gz\n",
-      "Goldfarb.txt                      \u001b[34mjulia-f4c6c9d4bb\u001b[m\u001b[m/\n",
-      "GoldfarbOutput_0.txt              \u001b[34mmapper\u001b[m\u001b[m/\n",
-      "GoldfarbOutput_1.txt              mapperOld.zip\n",
-      "GoldfarbOutput_2.txt              \u001b[34mmatlab\u001b[m\u001b[m/\n",
-      "GoldfarbOutput_betti.txt          \u001b[34mnbconvert\u001b[m\u001b[m/\n",
-      "\u001b[34mHungarian\u001b[m\u001b[m/                        \u001b[34mnbsphinx\u001b[m\u001b[m/\n",
-      "\u001b[34mJohnSuite\u001b[m\u001b[m/                        \u001b[34mnips2017\u001b[m\u001b[m/\n",
-      "\u001b[34mNPEET\u001b[m\u001b[m/                            perseusRipsEx.txt\n",
-      "\u001b[34mNumbaWorkshop_Jan2018\u001b[m\u001b[m/            \u001b[34mpypersistence\u001b[m\u001b[m/\n",
-      "\u001b[34mPersDistances\u001b[m\u001b[m/                    \u001b[34mpypersistence-git\u001b[m\u001b[m/\n",
-      "\u001b[34mPerseus\u001b[m\u001b[m/                          \u001b[34mpypersistence-old\u001b[m\u001b[m/\n",
-      "\u001b[34mProgramming\u001b[m\u001b[m/                      \u001b[34mrecon\u001b[m\u001b[m/\n",
-      "\u001b[34mSUMOExamples\u001b[m\u001b[m/                     \u001b[34mrecon-examples\u001b[m\u001b[m/\n",
-      "\u001b[34manimationExample\u001b[m\u001b[m/                 \u001b[34mripser\u001b[m\u001b[m/\n",
-      "\u001b[34mcat-list.github.io\u001b[m\u001b[m/               ripsex_0.txt\n",
-      "\u001b[34mceREEBerus\u001b[m\u001b[m/                       ripsex_betti.txt\n",
-      "\u001b[34mcechmate\u001b[m\u001b[m/                         \u001b[34mrivet\u001b[m\u001b[m/\n",
-      "\u001b[34mdoctrees\u001b[m\u001b[m/                         rivetInstallErrors.txt\n",
-      "\u001b[34mect\u001b[m\u001b[m/                              \u001b[34mteaspoon\u001b[m\u001b[m/\n",
-      "\u001b[34mect-on-images\u001b[m\u001b[m/                    \u001b[34mteaspoon-Old\u001b[m\u001b[m/\n",
-      "\u001b[34mfzz\u001b[m\u001b[m/                              teaspoon-wass-dist-sandbox.ipynb\n",
-      "\u001b[34mgeom_bottleneck\u001b[m\u001b[m/\n"
+      "\u001b[34mExtra_Notebooks\u001b[m\u001b[m/ \u001b[34mbuild\u001b[m\u001b[m/           \u001b[34mect\u001b[m\u001b[m/             pyproject.toml\n",
+      "LICENSE          \u001b[34mdata\u001b[m\u001b[m/            \u001b[34mect.egg-info\u001b[m\u001b[m/    \u001b[34msrc\u001b[m\u001b[m/\n",
+      "Makefile         \u001b[34mdist\u001b[m\u001b[m/            \u001b[34mlogo\u001b[m\u001b[m/            \u001b[34mtests\u001b[m\u001b[m/\n",
+      "README.md        \u001b[34mdoc_source\u001b[m\u001b[m/      make.bat\n",
+      "\u001b[34mbenchmarks\u001b[m\u001b[m/      \u001b[34mdocs\u001b[m\u001b[m/            \u001b[34mpaper\u001b[m\u001b[m/\n"
      ]
     }
    ],
@@ -70,12 +36,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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",
+      "image/png": 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DNLvfXMPV3eyCNEGkfS0mqwnMe3b7WGBfRLP7zTVc3dtdkCaI9PwWk9VEz549iRui2f3mGo5ut6QJIj2/xWQ1gdlt3Abmi2b3m6tR3W5KE0R6fovJaoKb2QDR7H5zNdrXbkoT2HpaLWdkiilfzW42VyN97bY0ga2n1XIGy+xwg7tmDuYaqq/dmCaI9PwWk9UEKqtzexDEVXNqaiobcw3V125ME0R6fovJagIfPG7YUTMW7dxYtJmKd+6kmto6iouPp9aWFurYIYVyhw+nmyaMp9zcXFNt4851586dVFJSwsZcg/W1W9MEkZ7fYrKawNpCbjvJnKR57br19NTSZZQxIJtyxoyjW2+8lZK9BpPX19ZS6b49VLD0OaooXUD3zJpJeVMmG2rbOy2QmJioDJaLuQbqazenCSI9v8VkNcGxzKMdNGOBvRmz51ByRh+a+avl1D7F/ywdGO6QnJHq1VBXSxtWLKXfvfYaLX96ScBKS/5yrliSBIuDcjHXQH3t5jRBpOe3mKwmpCJV7CktLaVbbruD8uY+TIMuvdzwfjDiKbPn08HP/kYTJ+fRmpdfpKysLEMPtGCydrl7t6qv3Z4m8CBVuGxYe5LbXH4rNeMOFgY7bdFiyugTeLHOYMCYsf/NP7ydijasU1MoQz3QwgB1t5qKkb7mkCaI9PwWk9VE9+7diRtWakaKAHewZg3WA/ZHOz/4j1tpzHXfCvlAi2M/e+vmkCaItK/FZDWBE4/bwHyrNOMhF3Kw4aQIgoF2umRl0+49e+j6b3876AMtjv3s0R0fH88iTRBpX8e12uFpRZDbc6xse/r0aercubPV4Qg25drrvxP0IdeMb4+kdklJ1K59snrI1W/w12nSj/NpSM6IgG1iu9/M+RF9+N67rB5oGQVpgmeffVYZD9IEeXl5xI0zBv0pPqZRMQJT8LhhhWaMg8UwrUAG62Hek8vpiY1bqfBPH9DoST+gx+++jf7x15KA26O9Pl+/WI2DDQbHfgZbt25lkyaItK/FZDXBbeaTVZox0QDjYMPhyhu+Rzfcchu98dvlQbfLHTNOtR8Mjv2M0QSffPIJmzRBpH0tJquJqqoq4oYVmkt27aKBFw8Ne7+vX55Dh/d/HnSbAUOGqpliweDWz57RBJj95PbRBNHqazFZTSBXww0rNJ+rqQ2ZKvCHkUcRmLCA9oPBrZ89owkAlzRBpH1tS5MtLCxUV8gRIwI/mLA7dXV1xA0rNKMWgRn2795F/b42JOL2OfWz96SDa6+9lk2aINK+tqXJ5ufn0969e2nHjh3kVDC8hRtWaEaxl3D55O0/0purX6Qb77w74va59LPvpIPs7GziRrzJvpZxsppA4RBuWKE5tWMHVezFu/iLP56YO6NtCFff7K/RT595ib5+RU7QfdAu2g8Gl372nXRg45Gf2jDb1zzOEAuoxQfUhqX/3KY5Z9gwVU0LhV4CsXzbP5+EhwvaRTlE7v3srzYBDNftuqPV1zy+61hAWloaccMKzagHW7J1i5a2i7duUe1z7udAtQncrtsfZjWLyWosWMINKzSj4HZF6QGVBogmSBVUHjpAOTk5rPs5UG0Ct+v2h1nNYrKa4Dif3SrNKLhdtGJpVNssWlFI986axbqfg5UwdLPuQJjVLCarCY7TLa3SjBUN6ivKVD3YaIB2GqvKacrk77Pt51AlDN2qOxgyrdZmZGZmEjes1IwVDdY++XOqKDsSUTsVRw6rdtAe534OVcLQrbqDYVazmKwmUMyZG1ZqxpIxq19aRSsX/nOFAzNgv5WPPaBWRkhPT2fbz0ZWOnCj7lCY1SxDuDTRrVs34obVmgcMGECb1q9VBbxLevSmiT/ONzTlFg/NNj1fqFIEWBHBqMHaQXO0MbrSgdt0G8GsZjFZTZw7d87yNa84asYd7bo1q1Uh7yXzZ1J61iBVTQvFXvytVothWlWHDqqHZ0ZysHbUHE2MrnTgNt1GMKtZTFYTSUlJxA07acbDMLxQb/aNzX+gV1avpC+PHFG1CLqmpVGn1I5qosFP8/8r5DAtp2iOlHAWRHSTbqOY1SwmK7gajKPFq7GxkQoKCtTvHnroIZYmEQxOCyLGGnnwpYmGhgbihmh2LuEuiOgW3eFgVrOYrCY4rkkmmt2fJnCT7nAxq1lMVhMnTpwgbohmPmkCp+s2g1nNYrKakMHaPHC65nDTBG7RbQaZjGAzjh49StwQze5PE7hBt1nMahaT1YQU0OCBUzVHOprAqbojQQrE2AwpoMEDp2o2myZwuu5IkAIxNiOcqZluQTS7P03gZN2RYlazmKwmTp8+TdwQzXwmHThNdzQwq1lMVhMpKSnEDdHs/jSBU3VHA7OaxWQ10WJiqWqnI5rdnyZwou5oYVazmKwmmpqaiBuimU9tAqfojiZmNWs12ffee48mTpxIvXv3pri4ONXJXMDXMW6IZvenCZymO5qY1azVZGtqauiKK66gwsJC4sapU6eIG6LZ/WkCJ+mONmY1ay11iCtmNK6aTiQjI4O4IZr5lDC0u24dmNUcb7dSYmfOnLng5VRkDSQe2F1ztNMETtGtA7OabWWyKKrcpUuXtle/fv3U7+vr69W8YTzd88y6wL8oxIwTCMtC4Fb+5MmTVFdXp94MJKm9tz1//rz6fW1trdquurpapTOOHz+u/ua9La7+OB7aQuUdjI87e/YsVVZWqguB97a4Q8C/+D3+7rk4tG/fXu1vNG7E5S9u/OwbN/bzFzeOEypuT7y+cWM7bI/9AsWN4+G4OD7i8I3bg7+4oRP7QTf0B4q7qqqq7T30F7dnn2Bxo/9848a2KNSNYTiIxRO373voiRttGYkbzxpwfvqLG7H4ixtt+caNr/T+4sb7jfMU73eocxZteMd98OBB2rVrFyUkJNC1116r0gTe77dv3Ph/qM8a4kbbeB+jHfcJr3MWx/L3WUNsvp81I3FHwyO8z29P3EaIa0XkMQAn44YNG2jSpEkBt8Gb510YF28gjBZvvNPqV6IjuM3vtrNmXSsj2FUzTODZZ59VBoMUwdSpU6Pavl1168RXM/wJN4Oh/MlWy8/g7g8vNyA5Kx7YVbN3muB73/seG906cUVO1k3g6wY3RLN7RxM4QbduzGrWeieLPMj+/fvbfv7iiy9Ujgjrl/fv35/cTGpqKnFDNNtrNAHSBLoWRLSb7lhgVrPWO9lPP/2Uhg8frl5g3rx56v+PPvoouR3kALkhmt2fJrCr7lhgVrPWO9nRo0erK6ogCO5IEwjhIzlZTUTr6bWTEM3uTxPYTXcsMatZTFZjPpobotn9aQK76Y4lZjWLyWoCD/e4IZr5pAnsoDvWmNUsJqsJ3FVwQzS7P01gF91WYFazmKwmuM2GAaLZ/WkCu+i2Almt1mbIap48sFKzlaMJpK+NIyariV69ehE3RLP70wQepK+NIyarCclZ8cAqzValCTxIXxtHTFYTaWlpxA3RzGfSgfS1ccRkNYGaldwQze5PE3iQvjaOmKwm4uP5vbWi2f1pAg/S18bh907FCFSj54Zodn+awIP0tXFsVbTbbV8tOnXqRJwQzfZIExQXF9PGos1UvHMn1dTWUVx8PLW2tFDHDimUO3w43TRhPOXm5kYUj/S1ccRkNSEPBngQK81G0gRr162np5Yuo4wB2ZQzZhzdeuOtlNyhQ9vf62trqXTfHipY+hxVlC6ge2bNpLwpk03FI31tHDFZTWChN26zYkSzNWkCxDBj9hxKzuhDM3+1nNqn/NtYvYHhDskZqV4NdbW0YcVS+t1rr9Hyp5dQjx49wopJ+to4kpPVBLcTEIjm2KcJSktLaeLkPBp18500Zfb8gAbrC7bD9tgP+x86dCisuKSvjSMmqwmZdsgD3ZqDpQlwZ3XLbXfQtEWLadCll5tqH/th/5t/eLtaWtso0tfGEZPVRGZmJnFDNMc2TYAUQd7chymjT9+IjoP90Q7aM4r0tXHEZDVx7Ngx4oZojl2aAA+5kIM1ewfrC9pJSs9U7RpB+to48uBLE1LUmAe6NIcaTYBRBHjIFYwZ3x5J7ZKSKCk5Wf2cPfQKmvU/vwq4/cQf59NT82cYGnEgfW0cMVmNS1Uk/+vk5oJojk2aAONgMUzLyEOueU8up4EXDzV0XLTXIyubSkpKKCcnJ+i20tfGkXSBJmShOR5EW7ORSQeYaIBxsDrIHTNOtR8K6WvjiMkKgo0wMumgZNcuw3enT8ydQfdPGqNeH7+1JeT2A4YMVTPFhOgh6QJNNDY2EjdEc2xqE5yrqTU8HjacdIFnwgLaD4X0tcPvZAsLC9XXpBEjRpBTSU1NJW6I5tjUJkAtAp0YaV/62uEmm5+fT3v37qUdO3aQUzl58iRxQzTHpoQhir3oxEj70tcON1k3IGsg8SAamsMtYZjasYMq9qIDtIv2QyF9bRwxWU3gg8MN0RyblQ5yhg1T1bRCsXzbJ2HlYwHaRTnEUEhfG0dMVhNSQIMHkWo2s9IB6sGWbA09UsAMxVu3qPZDIX1tHDFZTUgBDR5EotnsSgcouF1RekCVK4x2qqDy0IGQExGA9LVxxGQ1EW59TjcgmmO3ICIKbhetWErRpGhFId07a5ahbaWvjSMmq4lTp04RN0Rz7BZERH2B+ooyOvjZ3ygaoJ3GqnKaMvn7hraXvjaOmKwmUlJSiBuiObYLImJFg7VP/pwqyo5QJFQcOazaQXtGkb42jpisJvB1kBuiWX+awPfr6+qXVtHKhfNN39Fiv5WPPUBrXn6R0tPTDe8nfW0cmVariRbNA8btiGjWnybwZcCAAbRp/VpVcLukR29VrtDIlFs8NNv0fKFKERRtWBeWwQLpa+OIyWpCvk7xIBzN0UoT+LujXbdmtSq4vWT+TErPGqSqaaHYi7/VajFMq+rQQfXwzGgO1hfpa+OIyWpMknM7EUVzbNIEwR6G4YV6s29s/gO9snolfXnkiKpF0DUtjTqldlQTDX6a/1+GhmkFQ/raOGKymsjIyCBuiObYpQlCjaPFC1WjCgoK1O8eeuihqNaAlb42jjz40oSsgcQDI5p1pQmsRPraOGKympBphzwIpTkWaQIrkL42jpisJmTaIQ9CaY5lmiCWSF8bR0xWE5Kz4kEwzW5ME3iQvjaOmKwmpKgxb81uTRN4kL42jpisJmR5Dt6a3Zom8CB9bRwxWU3IQnN8Nbs5TeBB+to4YrKCEEXcniYQwkdMVhPRHPjtFESz+9MEHqSvjSMmq4lz584RN7hr5pAm8MC9r8NBTFYT3bp1I25w1swtTcC5r8NFTFYT+MrIDc6auaQJPHDua1uabGFhoap7mZycTN/85jfpk08+Ibcj0w75aOaUJuDe17Y02TVr1tC8efNo4cKFVFJSQldccQV997vfdf2VUKYd8uDw4cOs0gSc+7rMrtNqn3jiCbrrrrvozjvvVCfg8uXL1Veq3/72t+RmevXqRdzgqPkf//gHqzQB577uZVJzvO7BuyggPGbMmH8fMD5e/fzhhx9+ZfuGhgY6c+bMBS+n4vY7dX9w04w0we7du1mlCbj2tW1zslVVVeqpa8+ePS/4PX72V5sRBYa7dOnS9urXr5/6fX19PR09elStseO5Zce/MHEIx9AKVC3H3OK6ujrVdlNT0wXbnj9/Xv2+trZWbVddXU01NTV0/Phx9TfvbREzjoe2Tpw4QadPn6azZ89SZWWluhB4b4uvifgXv8ffPRcHxIr9jcaNuPzFjZ9948Z+/uLGcULF7YnXN25sh+2xX6C4cTwcF8dHHL5xo58CxQ2d2A+6oT9Q3DhnPO+hv7g9+wSLG/3nGze2xThHVLZHLJ64fd9DT9xoK1jcnjRBQkKC+oaG4iG+cSMWf3GjLd+4Ydj+4sb7jfMU73eocxZt+MaNqaCIEX/zfb/RX97vN/4f6rOGuD1LY0c77hNe5yyO5e+zhth8P2tG4o6GR3if3564jRDXisg1AdFIFn/wwQc0atSott//5Cc/UU9jP/744wu2x5uHlwe8gTBavPGdO3cmJ4ETpnv37sQJO2uO9ioB27Zto/fff18N6/nRj35ky7tYnSsj2LmvdeGrGf6Em8FQ/qR1+RmsgImrKK4E3uBnf/mN9u3bq5cbSEzkt7IPF83eowmuueYaWxqsbrj0dTQ0a00X4MqJtYbefvvttt/hdh4/e9/ZuhHknrnBQbPvpIPBgwcTRzj0dbQ0a3+nMHzrueeeo1WrVtHf//53mjlzpspzYLSBm0HehxscNPtOOuCg2R8cddeZ1Kz9nv/mm29WSepHH31UJZWHDRtGf/zjH7/yMMxtIFfDDbdr9jfpgOPXZg59HU3NMbnnnz17Nh06dEg91MLDLsz6cjt44skNN2sOVJvAzZqDwVF3lUnN/BIrMUKmHbqLQLUJ3Kw5GBx197HrtFquyLRD9xCsNoFbNYeCo+4yu06r5Urv3r2JG27UHKqEoRs1G4Gj7t4mNYvJasLobBA34UbNoUoYulGzETjqLjepWUxWE9xmw7hRs5EShm7TbBSOurub1CwmqwknF7cxi5s0G13pwE2aw4Gj7jMmNYvJasIt04O5aja60oGbNIcDR93tTWoWkxUEHziudCDoQ0xWYwUkbrhBc7gLIrpBsxk46m40qVlMVhOo48kNN2gOd0FEN2g2A0fdqSY1i8lqAkV/ueF0zWbSBE7XbBaOuk+a1CwmqwlZA8ndaQI3aI4Ejrp7mdTMs4RQjO6KuM3vtqNmrDG3sWgz7SguoSNlZRQXH0/b/vwBpXbsQLnDh9NNE8armsfhpgnsrDkWcNRdblKzmKwmuJ2AdtO8dt16emrpMsoYkE05Y8bRbTfeSskdOrT9vb62lkr37aGCpc/R0f3zKatvbxry9a+HPZrATppjCUfdfUxqFpPVWEyC24loB82oXTxj9hxKzuhDM3+1nNqn/NtYvYHhDskZqV4NdbX0+8InaOu722nWrFmO02wFHHWXmdQsJquJHj16EDes1lxaWkq33HYH5c19mAZdernh/WDEP5z/CB387G80cXIerXn5RcrKynKEZqvgqLuHSc3y4EsTnmWTOWGlZtzBwmCnLVoclsF6g/2w/80/vN1wgWaO/cxV9ymTmsVkNYEHKNywUjNSBLiDzejTN6J2sD/aQXtG4NjPXHV3MKlZTFYTTU1NxA2rNOMhF3KwZu9gfUE7SemZqt1QcOxnrrqbTGqWnKwmsPQ5N6zSjFEEeMgViBnfHkntkpIoKTmZzjc20sCLh9LM/158wWgDXyb+OJ+emj+D8qZMDnpsjv3MVXeLSc1yJ6uJlJQU4oYVmjEOFsO0Ao0i8DDvyeX0q9e30q+L3qXac2fpnQ1rgm6P9npkZVNJSUnQ7Tj2M1fdKSY1i8lq4vTp08QNKzRjogHGwRql6XwjNdTVUWrn0Ms7544Zp9oPBsd+5qr7tEnNYrKaSE9PJ25Yoblk1y719T8UT8ydQfdPGkPTrxlG8fHxdNW4G0PuM2DIUCreuTPoNhz7mavudJOaxWQ1cfz4ceKGFZrP1dSGTBV4pwtWfriHevTpSy8tfjzkPsjZov1gcOxnrrqPm9RsS5MtLCxUBTpGjBhBToXbbBirNKMWQTgkJCbSlTeMp51/ficq7XPsZ666+5jUbEuTzc/Pp71799KOHTvIqci69LGh1cQT3z0f/Zn6DMyOSvsc+5mr7jKTmmUIlyYyMjKIG1ZoRjUtFHsJNhzLk5PFEC6UNOzRuy/d/dj/hmwb7aL9YHDsZ666M0xqFpPVxIkTJ9jV3LRCc86wYaqaFgq9BGL5tk9MtY12UQ4xGBz7mavuEyY12zJd4AY6d+5M3LBCM+rBlmzdoqXt4q1bVPvB4NjPXHV3NqlZTFYT9fX1xA0rNKPgdkXpAVWuMJogVVB56ADl5OQE345hP3PVXW9Ss5isJuLi4ogbVmm+Z9ZMKlqxNKptFq0opHsN1Jbl2M9cdceZ1Cwmq4mkpCTihlWaUV+g9thhOrDnb1FpD3VlG6vKacrk74fclmM/c9WdZFKzmKwmzp07R9ywSnNtbS1dNXIEPb/wAaooOxJRWxVHDtOKxx6k//2f/za0Pcd+5qr7nEnNYrKa6NatG3HDCs0w2BdffFH9O+XGCbTiZ3PVnagZsN9v5v0Xjb3+Otq0aRNVV1eH3IdjP3PV3c2kZjFZTWDlU27EWrPHYDHdEYsfzps3j/7w+gb6cM0LtHbJLw0/DMN22P6j11bSlo2vU3Z2Np05c4ZWrlwZ0mg59jNX3RUmNce1YqF5m4ITvUuXLqr6DcchI4Jxg502bdoFBTxQcHvJsuWUnjVIVdNCsRd/q9VimFbVoYPq4ZknB3v27FlatWqVGheJ8w5td+3alZxGY2MjFRQUqP8/9NBDLPOodvAnMVlNyGqe1hmsb73ZNzb/QVXTQrEX1CLAVFnM5MJEA4yD9TdMy6jR2rmfdZqsnXXrwlezUX+SGV+a4DYbJlaawzFYzzhavMKlU6dOdMcdd7QZLVIH/oyWYz9z1d3LpGbJyWpCSsFZb7CR4jHa7t27B8zRcuxnrrqPu6nUoRtwYg7PzppjbbBGjZZjP3PV3dWkZjFZjabADV2arTJYI0bLsZ+56q41qVlMVhOJifzS3To0W22woYyWYz8DjroTTWoWk9UE1pHiRrQ128Vggxktx5lPQM5v4/B7p2KEVClyl8EGMto33njD0MwwtyHnt3HEZDXhtHG9dtJsV4P1Z7Se4V3cjFbOb+OIyWqiqqqKuBENzXY3WF+jzczMNDwF103I+W0cMVlNcJsNEw3NTjFYb6P9wQ9+EHQcrVuR89s4YrKakNU83W2wHmCuoSYsuBE5v40jJquJ3r17EzfManaqwXo0G5kZ5jbk/DaOmKwmjh49Stwwo9nJBuutmZvRyvltA5N9/PHH6aqrrqIOHTpQWloaccNJRmGVZqcbLPCOl5PROq2frNQcr7PM2tSpU2nmzJnEEXzIuBGOZjcYrD/NXIxWzm8bmOyiRYto7ty5dNlllxFH2rdvT9wwqtktBhtIMwejlfPbOJKTFWKKmww2GByMVnCgyTY0NKgT0vvlVJAu4UYozW402GCa3Wy0cn5rMtkFCxZQXFxc0Ne+ffvILFgqA8s5eF79+vVrmzOMJ3stLS1tY9XwL0RjcTMU6Th16hSdPHmS6urq6NixY9TU1HTBtufPn1e/xwcd2+Fkr6mpUR94/M172+bmZnU8tIVpk1heAsuRVFZWqguB97ZYvQf/4vf4u+figJ+xv9G4EZe/uPGzb9zYz1/cOE6ouD3x+saN7bA99gsUN46H4+L4iMM3brQRKG78/5VXXlE/w3zGjx+vDNY3bsyq8byH/uL2tB8sbvSfv7jR375x+76HnrjRFrZD/0Av+gv95vt+4284P/3FjVhSU1Np7NixymhRYAQXmYMHD34l7vLy8pBxhzpn0YZv3Dh+QkKC+pvveeIbN/4f6rOGuNE2jh/tuL3PWRzL32cNsfl+1ozEHQ2P8D6/PXEbIaw1viAMb0QwBg0adMFaQrh633fffUpgKPDm4eUBbyCM1olrfKHDuY0lDKTZjXew4fazFYsz6lzjS85v0rPGV48ePdRLZ2LZLQl1WQPJ/QYbTj8bXTPMKcj5bYOc7Jdffkm7du1S/+LWGv/Hi0v9TaNfJdys2e0GG24/uylHK+e3DUz20UcfpeHDh9PChQuVseL/eH366afEAe4FNDgYrJl+dovRcj+/bWGyOHmQ7vV9jR49mjjAuYAGF4M1289uMFrO57ejh3C5CZ25aztr5mSwkfSz042W6/ltBjFZTRgZTeE2MPyFk8FG2s9ONlqO5/cpk5rFZDWBwjicwB3sm2++ycpgo9HPTjVabud3JJrFZDWBgc5c8KQIYA6cDDZa/exEo+V0fkeqWUxWE5h5wgHvHCyu9JwMNpr97DSj5XJ+R0OzmKwmkpOTye34PuSaNGkSK4ONdj87yWg5nN/R0iwmqwknF7cxgr9RBImJYU0gdAXR7menGK3bz29H1JPljpvv6AIN03Kz5kDo0OwEo5W+No6YrCZgQG4k2DhYt2oOhi7Ndjda6WvjiMlqwo3TDkNNNHCj5lDo1Gxno5W+No6YrCbcNu3QyEwut2k2gm7NdjVa6WvjiMlqomfPnuQWjE6VdZNmo8RCsx2NVvraOGEV7Y41Rovi2nWKqRtqboZTi8AtmsMhlpqNFv4uLi6mjUWbaUdxCR0pK6O4+HjqmpZGqR07UO7w4XTThPGUm5sbUSzS12TYn8RkNZqT06cehlvsxQ2awyXWmoMZ7dp16+mppcsoY0A25YwZRwOGDKVkr9jqa2updN8eKtm6hSpKD9A9s2ZS3pTJpuKQviYxWavBGkHdunUjp2KmmpbTNZvBCs2+RjthwgRa8MjPKDmjD02YPovap4Q2v4a6WipasZTqK8po+dNLwq4wJX1Nhv1JcrKawKKSTsVsuUInazaLFZq9c7SHDh2iG6dMpVE330lTZs83ZLAA22F77Ddxcp5qJxykr40jJquJdu3akROJpB6sUzVHglWaPSv+vvnOu3Tvr5+jQZdebqod7Ddt0WK6+Ye3q1VfjSJ9bRwxWU1gKWGnEWnBbSdqjhQrNc9f8BBNX/gLyujTN6J2sH/e3Idpxuw5hveRvjaOmKwmnJavisaKBk7THA2s0oyHXMjBmr2D9QXtJKVnqnaNIH1tHDFZTVRUVJBTiNaSMU7SHC2s0oxRBHjIFYwZ3x5Jc8ZeQ/dPGtP2OvT53wNuP/HH+fTUsmWGji99bRx+ZZNihFOmHUZzTS6naI4mVmjGOFgM0zLykGvek8tp4MVDDbWL9npkZVNJSQnl5OQE3Vb62jhyJ8t42mG0Fz10guZoY4VmTDTAOFgd5I4Zp9oPhfS1ceROVhOZmZlkZ3SsKmt3zTqwQnPJrl106023Gtr2ibkzKMmr2PTPV2+i9skpAbfHBIZXX1sVsl3pa+OIyWqcgte7d2+yI7qW7bazZl1YoflcTa3h8bDhpAsAZoih/VBIXzs8XVBYWEiXXHIJjRgxgpyKvznlbjZYO2vWiRWaUYvA6valrx1usvn5+bR3717asWMHORWYGSeD9bTPDSs0t2pexNBI+9LXxpF0gSbstt6VboO1o+ZYYIVmVNNCsRfv4i9Gc7LTFiyiy668OuD2aBfth0L62jj83qkYEa/5K53dDNZummOFFZpzhg1T1bSG5IwMut3ybZ+E3TbaRTnEUEhfG4ffOxUj6uvriZPB2klzLLFCM+rBolyhDoq3blHth0L62jhispqwQ2nGWBqsXTTHGis0o+A26sGiXGE0Qaqg8tCBkBMRgPS1ccRkNRFORSM3GKwdNFuBVZpRcBv1YKNJ0YpCundW8Km6HqSvjSMmqwkrxxBaYbCA27hJKzVjRQMU3D742d+i0h7aaawqpymTv29oe+lr44jJauLo0aOsDNZKzVZipWasaLD2yZ9TRdmRiNqpOHJYtYP2jCJ9bRwxWU1YcaW30mCB3N3EFiwZs/qlVbRy4XzTd7TYb+VjD9Cal18M61yRvjaOmKwmYn2lt9pggdzdxJ4BAwbQpvVr6cM1L9DaJb80/DAM22H7j15bSUUb1lFWVpajdFuBWc2ykKImGhoaqH379mwMNtaa7YKdNKPg9pJlyyk9a5CqphVotVoM06o6dFA9PDOag7Wz7ljhq1lWq7WYysrKsFcAdbLBxlKznbCjZtSbfWPzH6h4505V7AW1CDBVFjO5MNEA42CNDNNymm7d+Go26k8y40sTyV5TGTkYbKw02w07asY4Wry46daNWc2Sk9VEi+YiHnYz2FhotiMcNXPV3WJSs5isJpqamlgZrG7NdoWjZq66m0xqFpPVRAcDFZLcZLA6NdsZjpq56u5gUrOYrCaqq6tZGawuzXaHo2auuqtNahaT1USvXr2i2p7dDVaHZifAUTNX3b1MahaT1UR5eTkrg422ZqfAUTNX3eUmNcs4WZvjFIMVBG6cMehPcieriWisS+80g42GZqfBUTNX3WUmNYvJaiIjI4OVwUZDsxPhqJmr7gyTmsVkNXHy5ElWBhupZqfCUTNX3SdNahaT1QTMkZPBRqLZyXDUzFV3R5OaxWQ1cf78eVYGa1az0+Gomavu8yY1azPZ0tJSmj59Og0cOJBSUlIoOzubFi5cSI2NjcSBcAdtON1ggY0HqmiDo2auultNatZWhWvfvn2qoMIzzzxDgwcPpj179tBdd91FNTU1tHjxYnI74VTscYPBAqnMxAeOupNNatZmsmPHjlUvD4MGDaLPP/+cli1bxsJkMYbOyFxntxhsOJrdBEfNXHWfMak5pjlZDNrt1q0bccCIUbrJYIGTYzcLR81cdaeb1Bwzk92/fz8tWbKE7r777qDLO+Bq4f1yKjBOTgZrRLMb4aiZq+7jJjWHbbILFiyguLi4oC/kY31nSiB1MHXqVJWXDURBQYGapuZ59evXT/2+vr5eLWKGHK9n1gX+xUO0iooKOnfuHJ06dUqNY6urq6Njx46p2o/e2+LJIH4Pc8N2qKiD/DDeOPzNe9vm5mZ1PLR14sQJdQd+9uxZtfwELgTe2yIZjn/xe/zdc3HAWkDY31/caG/16tUqBtzZT548WX0N8Rc3fvaNG3r9xY3jhIrbE69v3NgO22O/QHHjeDgujo84EA/i8sTt3d++caN/sB/6C/0WKO6qqqq299Bf3J59gsWN/vMXN/rbN27f99ATN9oyEjfOd5yf/uJGLP7iRlu+cWNefKi4Q52zaMM7bhwj2PvtGzf+H+qzhjbRNh5mRzvuE17nLI7l77OG2Hw/a0bijoZHeJ/fnri11C6AOLwZwUD+NSkpSf0fwkePHk1XXnklrVy5kuLjA/s63jy8POANhNE6sXYBOqJPnz4s7mBDaXYzHDVz1V3mo9kWCykiqOuuu06tN/Tyyy9TQkICmwIxuEomJiayMdhAmt0OR81cdTf5aLa8QAwMFnew/fv3V6MJcAeMW3G8OICvMJwM1p9mDnDUzFV3lUnN2i5Fb731lnrYhVffvn3ZDWT2vrJxMFjgtG8b0YCjZq66O5vUrO1OFkYCM/X34gAS8ZwM1lszJzhq5qq73qRmqV2gCTzg42SwINhDTbfCUTNX3fEmNfPKXMcQDPnAMC0uBgu4PQjhqpmr7kSTmvldjmIA7mA3bdrEymA9urnBUTNX3bUmNfO7HGnGkyLAk0hOBgvS0tKIGxw1c9WdZlKz3MlGEe8cLIyVk8ECDNPjBkfNXHVXmtQsJhslfB9y5eXlsTJYwG0GEFfNXHX3MalZTDYK+BtF4D09mAuygikfOOouM6lZcrIREmiYFgpVcCMzM5O4wVEzV92ZJjXLnWwEBBsHy2X6sDeimQ8cdR8zqVlM1iShJhp07dqVuCGa+cBRd1eTmsVkTWBkJhfqUHJDNPOBo+4ak5rFZMPE6FRZTz1dTohmPnDUnWRSM9sHX8XFxbSxaDMV79xJNbV1FBcfT60tLdSxQwrlDh9ON00Yr+rgesOtFoEgCJHDzmTXrltPTy1dRhkDsilnzDi69cZbKdlrBcr62loq3beHCpY+RxWlC+ieWTMpb8rksA2W4xAu0cwHjrobTGrWujJCpERzZQTM1pgxew4lZ/ShCdNnUfuU0Ev7NtTVUtGKpVR77DBdNXKEMlqjd7DoEKzzxQnRzAeOuht8NFu+MoKdKC0tpYmT82jUzXfSlNnzDRkswHbY/qpbptPzq15Si7IZTRFI5XgecNTMVXeVSc2uv5PFHSwMdtqixZTR58IVGsKhouwIrfjZXNqy8XVDJou3FSuZckI084Gj7lYfzXIn+y+QIsib+3BEBguw/833/0y1ZwSs0ssN0cwHjrqPmtQc7/aHXMjBDrr08qi0h3aS0jNVu6GQAho84KiZq+4+UiDmq2AUAR5yBaPu3Dm6NWcwFf50nqE2J/44n55atizkdlJAgwccNXPVXWZSc7ybx8FimFaoh1x/2bKRBl1yOX381haqMzCjA+31yMqmkpKSoNtxHD8rmvnAUXe6Sc2uNVlMNMA42FC8vXY1Tborny75xjeV4Rohd8w41X4wkBTnhmjmA0fdZ0xqdq3JluzaRQMvHhp0m8P7/0FVx47SsGtG0/V5/0Hb1v7OUNsDhgxVM8WCkZycTNwQzXzgqDvZpGbXmuy5mtqQqYK31/6ORt+URwkJCZRz7fV0vOwwHTnw/0K2jRliaD8YHOvJimY+cNTdYlKzLafVFhYWqldzc7PpNlCLIBhN58/T9jfWUmJiO3q/aIP6XWNdHb299lW648GFkbff1ETcEM184Ki7yaRmW5psfn6+enkG+5oBxV6CsWPbn6hnvyz63zVFbb/DXeyjt0+hW+c9TInt2kXUfgeveghcEM184Ki7g0nNrk0XpHbsoIq9BOLtdb+jayd8/4Lf9c3+GnXr2Ys+feetoG2jXbQfjOrqauKGaOYDR93VJjXb8k42GuQMG6aqaQ3JGen37488+7Lf3y9e/6eQbaNdlEMMRs+ePYkbopkPHHX3NKnZtXeyqAdbsnWLlraLt25R7QdD1kDiAUfNXHUfkzW+LgQFtytKD6hyhdEEqYLKQwcoJycn6HYy7ZAHHDVz1d1HptV+FRTcRj3YaFK0opDunRV8qi6QaYc84KiZq+4ymVb7VbCiQX1FGR387G9RaQ/tNFaV05TJFz4w80dGRgZxQzTzgaPuDJOaXW2yYPnTS2jtkz9X9WAjoeLIYdUO2jPCyZMniRuimQ8cdZ80qdn1JtujRw9a/dIqWrlwvuk7Wuy38rEHaM3LLxouEpGamkrcEM184Kg71aRm15ssGDBgAG1av5Y+XPMCrV3yS8MPw7Adtv/otZVUtGEdZWVlGT4mlqrhhmjmA0fdjSY1u3acrL872nVrVquC20vmz6T0rEGqmhaKvfhbrRbDtKoOHVQPz4zkYH2x8ao+2hDNfOCou9WkZtev8RWs3uwbm/+gqmmh2AtqEWCqLGZyYaIBxsGGGqYVDKxsy23qoWjmA0fdtT6ajfoTmztZf+No8dIFOoDbSSia+cBR9xmTmlnkZK2ge/fuxA3RzAeOurub1Cwmq4mKigrihmjmA0fdFSY1s83JCoIgxMKf5E5WEzLtkAccNXPVXSbTau2FlILjAUfNXHX3lFKH9qKqqoq4IZr5wFF3lUnNYrKaMLtsjpMRzXzgqLuLSc1ispqoq6sjbohmPnDUXWdSs5isJuJDrGbrRkQzHzjqjjepmd87FSMSE/lNphPNfOCoO9GkZjFZjfOcuSGa+cBRd61JzWKymkhLSyNuiGY+cNSdZlKzmKwmKisriRuimQ8cdVea1KzVZG+88Ubq378/JScnU2ZmJt1222109OhR4oCs5skDjpq56u5jx9Vqr7vuOnrttdfo888/p3Xr1tGBAwcoLy+POCDTDnnAUTNX3WUmNce0QMwbb7xBkyZNooaGBmrXrp2rC8S0tLSwG+YimvnAUXeLj2bbFYjBSo+vvPIKXXXVVQENFuaLwL1fTuXYsWPEDdHMB466j5nUrH2w24MPPkhPP/20Gv5w5ZVXUlFRUcBtCwoKaNGiRX4TzuXl5apAA4T27t1b5XaxciyuIikpKdTU1KSuNPg/zBkFdlH/0bMt1viC0Xfq1Inq6+spLi6OkpKSqKamhrp27aqO4dkWx8G+eJqIWR4JCQnqCoaLAPY/ceJE27bINSM2HO/s2bOqTYB2jx8/TqdOnTIUN/LW2N83bqz1juN5x42LFN5P37h79eqljhksbk+8vnG3b99exdHc3Kzi8hc33sPq6mpVHf78+fNqzSPvuDG3Gyt6+osbcWCcIeLC1R/b+osbujwXYSxc5xu3Z59gcePYaM837o4dO6o2vePu1q3bBe+hJ27cmSDWUHFjW/wd/e0bN843bOMbN85PHN87bpwPiDNY3CDYOYufEaMnbvQ/3vtA7zfa8I4bfYpj4ZiBzlnEjZjRLtqIdtwJ/zpn0T76wPezhpjQZ96fNSNxR8MjvM9vHOfgwYPq+CGTAa1h8uCDD6LFoK+///3vbdtXVla2fv75561/+tOfWq+++urW733ve60tLS1+266vr289ffp022vv3r0hjyUveclLXmTh6/Dhw0E9M+ycLK46uLoEY9CgQW1XGW+OHDlC/fr1ow8++IBGjRoV8li46uCqgSsLripmGDFiBO3YsYNiCa6S0Hn48GFLcsmiOTZw1Gy17hE20gzrxB017oSD5afDThfglhovM8A0Ab6+GgGB9+3blyIBXz+semiG41pxbNEcWzhqtkp3gs00G6nMpS0n+/HHH6srzjXXXKPyGRi+9bOf/Yyys7MN3cVGi/z8fOKGaOaBaHYG2oZw7d69m+69917661//qhLHSFqPHTuWHnnkEdcPZHby0DOziGYemrnqPhOBZm13spdddhlt27aNOIIn3gsXLlT/ckE084Gj7vYRaLb1arWCIAhOh9eUDUEQhBgjJisIgqARMVlBEASNiMkKgiBoRExWM6WlpTR9+nQaOHCgmjONccJ4SumZ0+1WHn/8cVUMCHUO3FpFv7CwkAYMGKDm83/zm9+kTz75hNzMe++9RxMnTlQznDAD8/XXXyc3U1BQoGaYYcYpalqggiDKtoaLmKxm9u3bp2a6PfPMM/TZZ5/Rk08+ScuXL6eHH36Y3AwuIlOnTqWZM2eSG1mzZg3NmzdPXTBLSkroiiuuoO9+97uq4IhbwXh36MTFhQPbt29Xkx8++ugjeuutt1QhmhtuuEG9D2ERboEYIXL+7//+r3XgwIGtHHjhhRdau3Tp0uo2Ro4c2Zqfn9/2c3Nzc2vv3r1bCwoKWjkA69iwYUMrJyoqKpTu7du3h7Wf3MlaAGaNoFyb4Ny79OLiYhozZswFdTbw84cffmhpbILezy0I97MrJhtj9u/fT0uWLKG7777b6lAEk6CuKGqqoqaoN55apoL7aGlpofvuu4+uvvpqGjp0aFj7ismaZMGCBSr5H+yFfKzvGkGo34Bc5V133UUcNAuCG0Buds+ePbR69Wr7rYzgVu6//36aNm1ayLq6HlAXFwtL4on7s88+Sxw0uxVU20fJPawG4A1+xqoDgruYPXu2WtEFoyvMlF4VkzVJOHV1cQcLg83NzaUXXnjBsQvQRVJL2E2gID368u2331bDejxfJ/EzPpCCO2htbaU5c+bQhg0b6N1331XDMM0gJqsZGOzo0aMpKyuLFi9erFaW8ODmu54vv/xSrZeEf5G/3LVrl/r94MGD1TpJTgfDt+644w76xje+QSNHjqRf//rXamjPnXfeSW7l3Llz6pmChy+++EL1Kx4E9e/fn9yYInj11Vdp48aNaqysJ9+OkocY824YbeMdhLYhTIHWBnIzd9xxh1/N77zzTqtbWLJkSWv//v1bk5KS1JCujz76qNXNoO/89Sn62o1QgM8tPtPhIKUOBUEQNOLM5KAgCIJDEJMVBEHQiJisIAiCRsRkBUEQNCImKwiCoBExWUEQBI2IyQqCIGhETFYQBEEjYrKCIAgaEZMVBEHQiJisIAiCRsRkBUEQSB//H0IwzndqeOCzAAAAAElFTkSuQmCC",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -89,14 +55,14 @@
     "# Note that this is the same graph that is returned by:\n",
     "# G = create_example_graph()\n",
     "\n",
-    "G = EmbeddedGraph()\n",
+    "G = EmbeddedComplex()\n",
     "\n",
-    "G.add_node('A', 1, 2)\n",
-    "G.add_node('B', 3, 4)\n",
-    "G.add_node('C', 5, 7)\n",
-    "G.add_node('D', 3, 6)\n",
-    "G.add_node('E', 4, 3)\n",
-    "G.add_node('F', 4, 5)\n",
+    "G.add_node('A', (1, 2))\n",
+    "G.add_node('B', (3, 4))\n",
+    "G.add_node('C', (5, 7))\n",
+    "G.add_node('D', (3, 6))\n",
+    "G.add_node('E', (4, 3))\n",
+    "G.add_node('F', (4, 5))\n",
     "\n",
     "G.add_edge('A', 'B')\n",
     "G.add_edge('B', 'C')\n",
@@ -105,20 +71,39 @@
     "G.add_edge('C', 'D')\n",
     "G.add_edge('E', 'F')\n",
     "\n",
-    "G.set_centered_coordinates()\n",
+    "G.center_coordinates()\n",
     "\n",
     "G.plot()\n",
-    "plt.savefig('paper/figures/example_graph.png', bbox_inches='tight', dpi=300)"
+    "plt.savefig('figures/example_graph.png', bbox_inches='tight', dpi=300)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
+    {
+     "ename": "FileNotFoundError",
+     "evalue": "[Errno 2] No such file or directory: 'paper/figures/example_graph_7pi_over_4.png'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
+      "\u001b[31mFileNotFoundError\u001b[39m                         Traceback (most recent call last)",
+      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[4]\u001b[39m\u001b[32m, line 3\u001b[39m\n\u001b[32m      1\u001b[39m G.plot(color_nodes_theta=\u001b[32m7\u001b[39m*np.pi/\u001b[32m4\u001b[39m)\n\u001b[32m      2\u001b[39m plt.title(\u001b[33m'\u001b[39m\u001b[33mColoring nodes with $g_\u001b[39m\u001b[33m\\\u001b[39m\u001b[33momega$ for  $\u001b[39m\u001b[38;5;130;01m\\\\\u001b[39;00m\u001b[33mtheta = 7\u001b[39m\u001b[33m\\\u001b[39m\u001b[33mpi/4$\u001b[39m\u001b[33m'\u001b[39m)\n\u001b[32m----> \u001b[39m\u001b[32m3\u001b[39m \u001b[43mplt\u001b[49m\u001b[43m.\u001b[49m\u001b[43msavefig\u001b[49m\u001b[43m(\u001b[49m\u001b[33;43m'\u001b[39;49m\u001b[33;43mpaper/figures/example_graph_7pi_over_4.png\u001b[39;49m\u001b[33;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mbbox_inches\u001b[49m\u001b[43m=\u001b[49m\u001b[33;43m'\u001b[39;49m\u001b[33;43mtight\u001b[39;49m\u001b[33;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdpi\u001b[49m\u001b[43m=\u001b[49m\u001b[32;43m300\u001b[39;49m\u001b[43m)\u001b[49m\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Library/CloudStorage/Dropbox/Math/Code/ect/.conda-ect-3-11/lib/python3.11/site-packages/matplotlib/pyplot.py:1251\u001b[39m, in \u001b[36msavefig\u001b[39m\u001b[34m(*args, **kwargs)\u001b[39m\n\u001b[32m   1248\u001b[39m fig = gcf()\n\u001b[32m   1249\u001b[39m \u001b[38;5;66;03m# savefig default implementation has no return, so mypy is unhappy\u001b[39;00m\n\u001b[32m   1250\u001b[39m \u001b[38;5;66;03m# presumably this is here because subclasses can return?\u001b[39;00m\n\u001b[32m-> \u001b[39m\u001b[32m1251\u001b[39m res = \u001b[43mfig\u001b[49m\u001b[43m.\u001b[49m\u001b[43msavefig\u001b[49m\u001b[43m(\u001b[49m\u001b[43m*\u001b[49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m  \u001b[38;5;66;03m# type: ignore[func-returns-value]\u001b[39;00m\n\u001b[32m   1252\u001b[39m fig.canvas.draw_idle()  \u001b[38;5;66;03m# Need this if 'transparent=True', to reset colors.\u001b[39;00m\n\u001b[32m   1253\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m res\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Library/CloudStorage/Dropbox/Math/Code/ect/.conda-ect-3-11/lib/python3.11/site-packages/matplotlib/figure.py:3490\u001b[39m, in \u001b[36mFigure.savefig\u001b[39m\u001b[34m(self, fname, transparent, **kwargs)\u001b[39m\n\u001b[32m   3488\u001b[39m     \u001b[38;5;28;01mfor\u001b[39;00m ax \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m.axes:\n\u001b[32m   3489\u001b[39m         _recursively_make_axes_transparent(stack, ax)\n\u001b[32m-> \u001b[39m\u001b[32m3490\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43mcanvas\u001b[49m\u001b[43m.\u001b[49m\u001b[43mprint_figure\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfname\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Library/CloudStorage/Dropbox/Math/Code/ect/.conda-ect-3-11/lib/python3.11/site-packages/matplotlib/backend_bases.py:2186\u001b[39m, in \u001b[36mFigureCanvasBase.print_figure\u001b[39m\u001b[34m(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)\u001b[39m\n\u001b[32m   2182\u001b[39m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[32m   2183\u001b[39m     \u001b[38;5;66;03m# _get_renderer may change the figure dpi (as vector formats\u001b[39;00m\n\u001b[32m   2184\u001b[39m     \u001b[38;5;66;03m# force the figure dpi to 72), so we need to set it again here.\u001b[39;00m\n\u001b[32m   2185\u001b[39m     \u001b[38;5;28;01mwith\u001b[39;00m cbook._setattr_cm(\u001b[38;5;28mself\u001b[39m.figure, dpi=dpi):\n\u001b[32m-> \u001b[39m\u001b[32m2186\u001b[39m         result = \u001b[43mprint_method\u001b[49m\u001b[43m(\u001b[49m\n\u001b[32m   2187\u001b[39m \u001b[43m            \u001b[49m\u001b[43mfilename\u001b[49m\u001b[43m,\u001b[49m\n\u001b[32m   2188\u001b[39m \u001b[43m            \u001b[49m\u001b[43mfacecolor\u001b[49m\u001b[43m=\u001b[49m\u001b[43mfacecolor\u001b[49m\u001b[43m,\u001b[49m\n\u001b[32m   2189\u001b[39m \u001b[43m            \u001b[49m\u001b[43medgecolor\u001b[49m\u001b[43m=\u001b[49m\u001b[43medgecolor\u001b[49m\u001b[43m,\u001b[49m\n\u001b[32m   2190\u001b[39m \u001b[43m            \u001b[49m\u001b[43morientation\u001b[49m\u001b[43m=\u001b[49m\u001b[43morientation\u001b[49m\u001b[43m,\u001b[49m\n\u001b[32m   2191\u001b[39m \u001b[43m            \u001b[49m\u001b[43mbbox_inches_restore\u001b[49m\u001b[43m=\u001b[49m\u001b[43m_bbox_inches_restore\u001b[49m\u001b[43m,\u001b[49m\n\u001b[32m   2192\u001b[39m \u001b[43m            \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m   2193\u001b[39m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[32m   2194\u001b[39m     \u001b[38;5;28;01mif\u001b[39;00m bbox_inches \u001b[38;5;129;01mand\u001b[39;00m restore_bbox:\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Library/CloudStorage/Dropbox/Math/Code/ect/.conda-ect-3-11/lib/python3.11/site-packages/matplotlib/backend_bases.py:2042\u001b[39m, in \u001b[36mFigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>\u001b[39m\u001b[34m(*args, **kwargs)\u001b[39m\n\u001b[32m   2038\u001b[39m     optional_kws = {  \u001b[38;5;66;03m# Passed by print_figure for other renderers.\u001b[39;00m\n\u001b[32m   2039\u001b[39m         \u001b[33m\"\u001b[39m\u001b[33mdpi\u001b[39m\u001b[33m\"\u001b[39m, \u001b[33m\"\u001b[39m\u001b[33mfacecolor\u001b[39m\u001b[33m\"\u001b[39m, \u001b[33m\"\u001b[39m\u001b[33medgecolor\u001b[39m\u001b[33m\"\u001b[39m, \u001b[33m\"\u001b[39m\u001b[33morientation\u001b[39m\u001b[33m\"\u001b[39m,\n\u001b[32m   2040\u001b[39m         \u001b[33m\"\u001b[39m\u001b[33mbbox_inches_restore\u001b[39m\u001b[33m\"\u001b[39m}\n\u001b[32m   2041\u001b[39m     skip = optional_kws - {*inspect.signature(meth).parameters}\n\u001b[32m-> \u001b[39m\u001b[32m2042\u001b[39m     print_method = functools.wraps(meth)(\u001b[38;5;28;01mlambda\u001b[39;00m *args, **kwargs: \u001b[43mmeth\u001b[49m\u001b[43m(\u001b[49m\n\u001b[32m   2043\u001b[39m \u001b[43m        \u001b[49m\u001b[43m*\u001b[49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43m{\u001b[49m\u001b[43mk\u001b[49m\u001b[43m:\u001b[49m\u001b[43m \u001b[49m\u001b[43mv\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mfor\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mk\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mv\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01min\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m.\u001b[49m\u001b[43mitems\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mk\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01mnot\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;129;43;01min\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mskip\u001b[49m\u001b[43m}\u001b[49m\u001b[43m)\u001b[49m)\n\u001b[32m   2044\u001b[39m \u001b[38;5;28;01melse\u001b[39;00m:  \u001b[38;5;66;03m# Let third-parties do as they see fit.\u001b[39;00m\n\u001b[32m   2045\u001b[39m     print_method = meth\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Library/CloudStorage/Dropbox/Math/Code/ect/.conda-ect-3-11/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:481\u001b[39m, in \u001b[36mFigureCanvasAgg.print_png\u001b[39m\u001b[34m(self, filename_or_obj, metadata, pil_kwargs)\u001b[39m\n\u001b[32m    434\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mprint_png\u001b[39m(\u001b[38;5;28mself\u001b[39m, filename_or_obj, *, metadata=\u001b[38;5;28;01mNone\u001b[39;00m, pil_kwargs=\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[32m    435\u001b[39m \u001b[38;5;250m    \u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    436\u001b[39m \u001b[33;03m    Write the figure to a PNG file.\u001b[39;00m\n\u001b[32m    437\u001b[39m \n\u001b[32m   (...)\u001b[39m\u001b[32m    479\u001b[39m \u001b[33;03m        *metadata*, including the default 'Software' key.\u001b[39;00m\n\u001b[32m    480\u001b[39m \u001b[33;03m    \"\"\"\u001b[39;00m\n\u001b[32m--> \u001b[39m\u001b[32m481\u001b[39m     \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_print_pil\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfilename_or_obj\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[33;43m\"\u001b[39;49m\u001b[33;43mpng\u001b[39;49m\u001b[33;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mpil_kwargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmetadata\u001b[49m\u001b[43m)\u001b[49m\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Library/CloudStorage/Dropbox/Math/Code/ect/.conda-ect-3-11/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:430\u001b[39m, in \u001b[36mFigureCanvasAgg._print_pil\u001b[39m\u001b[34m(self, filename_or_obj, fmt, pil_kwargs, metadata)\u001b[39m\n\u001b[32m    425\u001b[39m \u001b[38;5;250m\u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    426\u001b[39m \u001b[33;03mDraw the canvas, then save it using `.image.imsave` (to which\u001b[39;00m\n\u001b[32m    427\u001b[39m \u001b[33;03m*pil_kwargs* and *metadata* are forwarded).\u001b[39;00m\n\u001b[32m    428\u001b[39m \u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m    429\u001b[39m FigureCanvasAgg.draw(\u001b[38;5;28mself\u001b[39m)\n\u001b[32m--> \u001b[39m\u001b[32m430\u001b[39m \u001b[43mmpl\u001b[49m\u001b[43m.\u001b[49m\u001b[43mimage\u001b[49m\u001b[43m.\u001b[49m\u001b[43mimsave\u001b[49m\u001b[43m(\u001b[49m\n\u001b[32m    431\u001b[39m \u001b[43m    \u001b[49m\u001b[43mfilename_or_obj\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43mbuffer_rgba\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mformat\u001b[39;49m\u001b[43m=\u001b[49m\u001b[43mfmt\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43morigin\u001b[49m\u001b[43m=\u001b[49m\u001b[33;43m\"\u001b[39;49m\u001b[33;43mupper\u001b[39;49m\u001b[33;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[32m    432\u001b[39m \u001b[43m    \u001b[49m\u001b[43mdpi\u001b[49m\u001b[43m=\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43mfigure\u001b[49m\u001b[43m.\u001b[49m\u001b[43mdpi\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmetadata\u001b[49m\u001b[43m=\u001b[49m\u001b[43mmetadata\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mpil_kwargs\u001b[49m\u001b[43m=\u001b[49m\u001b[43mpil_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Library/CloudStorage/Dropbox/Math/Code/ect/.conda-ect-3-11/lib/python3.11/site-packages/matplotlib/image.py:1657\u001b[39m, in \u001b[36mimsave\u001b[39m\u001b[34m(fname, arr, vmin, vmax, cmap, format, origin, dpi, metadata, pil_kwargs)\u001b[39m\n\u001b[32m   1655\u001b[39m pil_kwargs.setdefault(\u001b[33m\"\u001b[39m\u001b[33mformat\u001b[39m\u001b[33m\"\u001b[39m, \u001b[38;5;28mformat\u001b[39m)\n\u001b[32m   1656\u001b[39m pil_kwargs.setdefault(\u001b[33m\"\u001b[39m\u001b[33mdpi\u001b[39m\u001b[33m\"\u001b[39m, (dpi, dpi))\n\u001b[32m-> \u001b[39m\u001b[32m1657\u001b[39m \u001b[43mimage\u001b[49m\u001b[43m.\u001b[49m\u001b[43msave\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfname\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43mpil_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
+      "\u001b[36mFile \u001b[39m\u001b[32m~/Library/CloudStorage/Dropbox/Math/Code/ect/.conda-ect-3-11/lib/python3.11/site-packages/PIL/Image.py:2583\u001b[39m, in \u001b[36mImage.save\u001b[39m\u001b[34m(self, fp, format, **params)\u001b[39m\n\u001b[32m   2581\u001b[39m         fp = builtins.open(filename, \u001b[33m\"\u001b[39m\u001b[33mr+b\u001b[39m\u001b[33m\"\u001b[39m)\n\u001b[32m   2582\u001b[39m     \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[32m-> \u001b[39m\u001b[32m2583\u001b[39m         fp = \u001b[43mbuiltins\u001b[49m\u001b[43m.\u001b[49m\u001b[43mopen\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfilename\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[33;43m\"\u001b[39;49m\u001b[33;43mw+b\u001b[39;49m\u001b[33;43m\"\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[32m   2584\u001b[39m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[32m   2585\u001b[39m     fp = cast(IO[\u001b[38;5;28mbytes\u001b[39m], fp)\n",
+      "\u001b[31mFileNotFoundError\u001b[39m: [Errno 2] No such file or directory: 'paper/figures/example_graph_7pi_over_4.png'"
+     ]
+    },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 2 Axes>"
       ]
@@ -135,31 +120,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
-    {
-     "ename": "FileNotFoundError",
-     "evalue": "[Errno 2] No such file or directory: '../paper/figures/example_graph_pi_over_2.png'",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mFileNotFoundError\u001b[0m                         Traceback (most recent call last)",
-      "Cell \u001b[0;32mIn[11], line 3\u001b[0m\n\u001b[1;32m      1\u001b[0m G\u001b[38;5;241m.\u001b[39mplot(color_nodes_theta\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m2\u001b[39m\u001b[38;5;241m*\u001b[39mnp\u001b[38;5;241m.\u001b[39mpi\u001b[38;5;241m/\u001b[39m\u001b[38;5;241m4\u001b[39m)\n\u001b[1;32m      2\u001b[0m plt\u001b[38;5;241m.\u001b[39mtitle(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mColoring nodes with $g_\u001b[39m\u001b[38;5;124m\\\u001b[39m\u001b[38;5;124momega$ for  $\u001b[39m\u001b[38;5;130;01m\\\\\u001b[39;00m\u001b[38;5;124mtheta = \u001b[39m\u001b[38;5;124m\\\u001b[39m\u001b[38;5;124mpi/2$\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m----> 3\u001b[0m plt\u001b[38;5;241m.\u001b[39msavefig(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m../paper/figures/example_graph_pi_over_2.png\u001b[39m\u001b[38;5;124m'\u001b[39m, bbox_inches\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mtight\u001b[39m\u001b[38;5;124m'\u001b[39m, dpi\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m300\u001b[39m)\n",
-      "File \u001b[0;32m/opt/anaconda3/lib/python3.11/site-packages/matplotlib/pyplot.py:1228\u001b[0m, in \u001b[0;36msavefig\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m   1225\u001b[0m fig \u001b[38;5;241m=\u001b[39m gcf()\n\u001b[1;32m   1226\u001b[0m \u001b[38;5;66;03m# savefig default implementation has no return, so mypy is unhappy\u001b[39;00m\n\u001b[1;32m   1227\u001b[0m \u001b[38;5;66;03m# presumably this is here because subclasses can return?\u001b[39;00m\n\u001b[0;32m-> 1228\u001b[0m res \u001b[38;5;241m=\u001b[39m fig\u001b[38;5;241m.\u001b[39msavefig(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)  \u001b[38;5;66;03m# type: ignore[func-returns-value]\u001b[39;00m\n\u001b[1;32m   1229\u001b[0m fig\u001b[38;5;241m.\u001b[39mcanvas\u001b[38;5;241m.\u001b[39mdraw_idle()  \u001b[38;5;66;03m# Need this if 'transparent=True', to reset colors.\u001b[39;00m\n\u001b[1;32m   1230\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m res\n",
-      "File \u001b[0;32m/opt/anaconda3/lib/python3.11/site-packages/matplotlib/figure.py:3395\u001b[0m, in \u001b[0;36mFigure.savefig\u001b[0;34m(self, fname, transparent, **kwargs)\u001b[0m\n\u001b[1;32m   3393\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m ax \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39maxes:\n\u001b[1;32m   3394\u001b[0m         _recursively_make_axes_transparent(stack, ax)\n\u001b[0;32m-> 3395\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcanvas\u001b[38;5;241m.\u001b[39mprint_figure(fname, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n",
-      "File \u001b[0;32m/opt/anaconda3/lib/python3.11/site-packages/matplotlib/backend_bases.py:2204\u001b[0m, in \u001b[0;36mFigureCanvasBase.print_figure\u001b[0;34m(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)\u001b[0m\n\u001b[1;32m   2200\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m   2201\u001b[0m     \u001b[38;5;66;03m# _get_renderer may change the figure dpi (as vector formats\u001b[39;00m\n\u001b[1;32m   2202\u001b[0m     \u001b[38;5;66;03m# force the figure dpi to 72), so we need to set it again here.\u001b[39;00m\n\u001b[1;32m   2203\u001b[0m     \u001b[38;5;28;01mwith\u001b[39;00m cbook\u001b[38;5;241m.\u001b[39m_setattr_cm(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfigure, dpi\u001b[38;5;241m=\u001b[39mdpi):\n\u001b[0;32m-> 2204\u001b[0m         result \u001b[38;5;241m=\u001b[39m print_method(\n\u001b[1;32m   2205\u001b[0m             filename,\n\u001b[1;32m   2206\u001b[0m             facecolor\u001b[38;5;241m=\u001b[39mfacecolor,\n\u001b[1;32m   2207\u001b[0m             edgecolor\u001b[38;5;241m=\u001b[39medgecolor,\n\u001b[1;32m   2208\u001b[0m             orientation\u001b[38;5;241m=\u001b[39morientation,\n\u001b[1;32m   2209\u001b[0m             bbox_inches_restore\u001b[38;5;241m=\u001b[39m_bbox_inches_restore,\n\u001b[1;32m   2210\u001b[0m             \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m   2211\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m   2212\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m bbox_inches \u001b[38;5;129;01mand\u001b[39;00m restore_bbox:\n",
-      "File \u001b[0;32m/opt/anaconda3/lib/python3.11/site-packages/matplotlib/backend_bases.py:2054\u001b[0m, in \u001b[0;36mFigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m   2050\u001b[0m     optional_kws \u001b[38;5;241m=\u001b[39m {  \u001b[38;5;66;03m# Passed by print_figure for other renderers.\u001b[39;00m\n\u001b[1;32m   2051\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mdpi\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mfacecolor\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124medgecolor\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124morientation\u001b[39m\u001b[38;5;124m\"\u001b[39m,\n\u001b[1;32m   2052\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mbbox_inches_restore\u001b[39m\u001b[38;5;124m\"\u001b[39m}\n\u001b[1;32m   2053\u001b[0m     skip \u001b[38;5;241m=\u001b[39m optional_kws \u001b[38;5;241m-\u001b[39m {\u001b[38;5;241m*\u001b[39minspect\u001b[38;5;241m.\u001b[39msignature(meth)\u001b[38;5;241m.\u001b[39mparameters}\n\u001b[0;32m-> 2054\u001b[0m     print_method \u001b[38;5;241m=\u001b[39m functools\u001b[38;5;241m.\u001b[39mwraps(meth)(\u001b[38;5;28;01mlambda\u001b[39;00m \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs: meth(\n\u001b[1;32m   2055\u001b[0m         \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m{k: v \u001b[38;5;28;01mfor\u001b[39;00m k, v \u001b[38;5;129;01min\u001b[39;00m kwargs\u001b[38;5;241m.\u001b[39mitems() \u001b[38;5;28;01mif\u001b[39;00m k \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;129;01min\u001b[39;00m skip}))\n\u001b[1;32m   2056\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:  \u001b[38;5;66;03m# Let third-parties do as they see fit.\u001b[39;00m\n\u001b[1;32m   2057\u001b[0m     print_method \u001b[38;5;241m=\u001b[39m meth\n",
-      "File \u001b[0;32m/opt/anaconda3/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:496\u001b[0m, in \u001b[0;36mFigureCanvasAgg.print_png\u001b[0;34m(self, filename_or_obj, metadata, pil_kwargs)\u001b[0m\n\u001b[1;32m    449\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mprint_png\u001b[39m(\u001b[38;5;28mself\u001b[39m, filename_or_obj, \u001b[38;5;241m*\u001b[39m, metadata\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, pil_kwargs\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m    450\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m    451\u001b[0m \u001b[38;5;124;03m    Write the figure to a PNG file.\u001b[39;00m\n\u001b[1;32m    452\u001b[0m \n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    494\u001b[0m \u001b[38;5;124;03m        *metadata*, including the default 'Software' key.\u001b[39;00m\n\u001b[1;32m    495\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m--> 496\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_print_pil(filename_or_obj, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mpng\u001b[39m\u001b[38;5;124m\"\u001b[39m, pil_kwargs, metadata)\n",
-      "File \u001b[0;32m/opt/anaconda3/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445\u001b[0m, in \u001b[0;36mFigureCanvasAgg._print_pil\u001b[0;34m(self, filename_or_obj, fmt, pil_kwargs, metadata)\u001b[0m\n\u001b[1;32m    440\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m    441\u001b[0m \u001b[38;5;124;03mDraw the canvas, then save it using `.image.imsave` (to which\u001b[39;00m\n\u001b[1;32m    442\u001b[0m \u001b[38;5;124;03m*pil_kwargs* and *metadata* are forwarded).\u001b[39;00m\n\u001b[1;32m    443\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m    444\u001b[0m FigureCanvasAgg\u001b[38;5;241m.\u001b[39mdraw(\u001b[38;5;28mself\u001b[39m)\n\u001b[0;32m--> 445\u001b[0m mpl\u001b[38;5;241m.\u001b[39mimage\u001b[38;5;241m.\u001b[39mimsave(\n\u001b[1;32m    446\u001b[0m     filename_or_obj, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuffer_rgba(), \u001b[38;5;28mformat\u001b[39m\u001b[38;5;241m=\u001b[39mfmt, origin\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mupper\u001b[39m\u001b[38;5;124m\"\u001b[39m,\n\u001b[1;32m    447\u001b[0m     dpi\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfigure\u001b[38;5;241m.\u001b[39mdpi, metadata\u001b[38;5;241m=\u001b[39mmetadata, pil_kwargs\u001b[38;5;241m=\u001b[39mpil_kwargs)\n",
-      "File \u001b[0;32m/opt/anaconda3/lib/python3.11/site-packages/matplotlib/image.py:1676\u001b[0m, in \u001b[0;36mimsave\u001b[0;34m(fname, arr, vmin, vmax, cmap, format, origin, dpi, metadata, pil_kwargs)\u001b[0m\n\u001b[1;32m   1674\u001b[0m pil_kwargs\u001b[38;5;241m.\u001b[39msetdefault(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mformat\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;28mformat\u001b[39m)\n\u001b[1;32m   1675\u001b[0m pil_kwargs\u001b[38;5;241m.\u001b[39msetdefault(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mdpi\u001b[39m\u001b[38;5;124m\"\u001b[39m, (dpi, dpi))\n\u001b[0;32m-> 1676\u001b[0m image\u001b[38;5;241m.\u001b[39msave(fname, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mpil_kwargs)\n",
-      "File \u001b[0;32m/opt/anaconda3/lib/python3.11/site-packages/PIL/Image.py:2436\u001b[0m, in \u001b[0;36mImage.save\u001b[0;34m(self, fp, format, **params)\u001b[0m\n\u001b[1;32m   2434\u001b[0m         fp \u001b[38;5;241m=\u001b[39m builtins\u001b[38;5;241m.\u001b[39mopen(filename, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mr+b\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m   2435\u001b[0m     \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m-> 2436\u001b[0m         fp \u001b[38;5;241m=\u001b[39m builtins\u001b[38;5;241m.\u001b[39mopen(filename, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mw+b\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m   2438\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m   2439\u001b[0m     save_handler(\u001b[38;5;28mself\u001b[39m, fp, filename)\n",
-      "\u001b[0;31mFileNotFoundError\u001b[0m: [Errno 2] No such file or directory: '../paper/figures/example_graph_pi_over_2.png'"
-     ]
-    },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 2 Axes>"
       ]
@@ -171,34 +137,55 @@
    "source": [
     "G.plot(color_nodes_theta=2*np.pi/4)\n",
     "plt.title('Coloring nodes with $g_\\omega$ for  $\\\\theta = \\pi/2$')\n",
-    "plt.savefig('../paper/figures/example_graph_pi_over_2.png', bbox_inches='tight', dpi=300)"
+    "plt.savefig('figures/example_graph_pi_over_2.png', bbox_inches='tight', dpi=300)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "np.float64(3.2015621187164243)"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "G.get_bounding_radius()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
-       "       2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
-       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
-       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
-       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])"
+       "ECTResult([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,\n",
+       "            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
+       "            2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
+       "            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
+       "            1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]],\n",
+       "          dtype=int32)"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "myect = ECT(num_dirs = 100, num_thresh=100)\n",
-    "myect.set_bounding_radius(1.2 * G.get_bounding_radius())\n",
+    "myect.bound_radius = 1.2 * G.get_bounding_radius()\n",
     "\n",
-    "myect.calculateECC(G, np.pi/2,bound_radius=True)"
+    "myect.calculate(G, np.pi/2)"
    ]
   },
   {

From 3d3f6b45a4487d5d53d7acc6aad0605ba2751ec8 Mon Sep 17 00:00:00 2001
From: yemeen <yemeen.ayub.14@cnu.edu>
Date: Wed, 1 Oct 2025 13:33:57 -0400
Subject: [PATCH 13/25] add filtration figure

---
 paper/paper.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/paper/paper.md b/paper/paper.md
index b06fcbe..7449129 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -34,7 +34,7 @@ bibliography: paper.bib
 
 # Summary
 
-The field of Topological Data Analysis [@Dey2021,@Wasserman2018,@Ghrist2014,@Munch2017] encodes the shape of data in quantifiable representations of the information, sometimes called "topological signatures" or "topological summaries". The goal is to ensure that these summaries are robust to noise and useful in practice. In many methods, richer representations bring higher computation cost, creating a tension between robustness and speed. The Euler Characteristic Transform (ECT) [@Turner2014,@Munch2025] has gained popularity for encoding the information of embedded shapes in $\R^d$---such as graphs, simplicial complexes, and meshes--because it strikes this balance by providing a complete topological summary, yet is typically much faster to compute than its widely used cousin, the Persistent Homology Transform [@Turner2014].
+The field of Topological Data Analysis [@Dey2021,@Wasserman2018,@Ghrist2014,@Munch2017] encodes the shape of data in quantifiable representations of the information, sometimes called "topological signatures" or "topological summaries". The goal is to ensure that these summaries are robust to noise and useful in practice. In many methods, richer representations bring higher computation cost, creating a tension between robustness and speed. The Euler Characteristic Transform (ECT) [@Turner2014,@Munch2025] has gained popularity for encoding the information of embedded shapes in $\mathbb{R}^d$---such as graphs, simplicial complexes, and meshes--because it strikes this balance by providing a complete topological summary, yet is typically much faster to compute than its widely used cousin, the Persistent Homology Transform [@Turner2014].
 
 The `ect` Python package offers a fast and well-documented implementation of ECT for inputs in any embedding dimension and with a wide range of complex types. With a few lines of code, users can generate ECT features by sampling directions, computing Euler characteristic curves, and vectorizing them for downstream tasks such as classification or regression. The package includes practical options for direction sampling, normalization, and visualizing various versions of the ECT. These options allow for smooth integration into other scientific package such as `Numpy`, `Scipy`, and `PyTorch`. By lowering the barrier to computing the ECT on embedded complexes, `ect` makes these topological summaries accessible to a wider range of practitioners and domain scientists.
 
@@ -45,6 +45,7 @@ We give a high level introduction of the ECT here as defined in [@Turner2014], a
 To start, we assume our input is an undirected graph $G$ with a straight-line embedding in 2D given by a map on the vertices $f: V(G) \to \mathbb{R}^2$. A graph can be constructed as seen in \autoref{fig:example_graph}.
 
 
+![A filtration of a graph showing the sublevel sets of $g_\omega$ for a fixed direction $\omega$. The vertices and edges are added to the filtration as the height increases.\label{fig:filtration}](figures/filtration.png)
 
 <!-- ![Testing scaling](figures/CombineGraphExample.png){ width=20% } -->
 

From dd90c0dde5eda647f2c6432e9227a6265a310926 Mon Sep 17 00:00:00 2001
From: yemeen <yemeen.ayub.14@cnu.edu>
Date: Wed, 1 Oct 2025 14:13:58 -0400
Subject: [PATCH 14/25] add filtration figure

---
 paper/figures/filtration.png | Bin 0 -> 21357 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 paper/figures/filtration.png

diff --git a/paper/figures/filtration.png b/paper/figures/filtration.png
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From 288bab4925f987ea1d18c05d885095e7e27b91d4 Mon Sep 17 00:00:00 2001
From: Liz Munch <muncheli@msu.edu>
Date: Wed, 1 Oct 2025 14:17:58 -0400
Subject: [PATCH 15/25] Trying to fix the citation issues

---
 .gitignore     | 1 +
 paper/paper.md | 2 +-
 2 files changed, 2 insertions(+), 1 deletion(-)

diff --git a/.gitignore b/.gitignore
index 60a4a1d..b670a00 100644
--- a/.gitignore
+++ b/.gitignore
@@ -9,6 +9,7 @@ src/ect/embed_graph.py
 src/ect/embed_cw.py
 
 .conda*
+.vscode/*
 
 # Byte-compiled / optimized / DLL files
 __pycache__/
diff --git a/paper/paper.md b/paper/paper.md
index 7449129..d3e78bb 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -34,7 +34,7 @@ bibliography: paper.bib
 
 # Summary
 
-The field of Topological Data Analysis [@Dey2021,@Wasserman2018,@Ghrist2014,@Munch2017] encodes the shape of data in quantifiable representations of the information, sometimes called "topological signatures" or "topological summaries". The goal is to ensure that these summaries are robust to noise and useful in practice. In many methods, richer representations bring higher computation cost, creating a tension between robustness and speed. The Euler Characteristic Transform (ECT) [@Turner2014,@Munch2025] has gained popularity for encoding the information of embedded shapes in $\mathbb{R}^d$---such as graphs, simplicial complexes, and meshes--because it strikes this balance by providing a complete topological summary, yet is typically much faster to compute than its widely used cousin, the Persistent Homology Transform [@Turner2014].
+The field of Topological Data Analysis [@Dey2021;@Wasserman2018;@Ghrist2014;@Munch2017] encodes the shape of data in quantifiable representations of the information, sometimes called "topological signatures" or "topological summaries". The goal is to ensure that these summaries are robust to noise and useful in practice. In many methods, richer representations bring higher computation cost, creating a tension between robustness and speed. The Euler Characteristic Transform (ECT) [@Turner2014;@Munch2025] has gained popularity for encoding the information of embedded shapes in $\mathbb{R}^d$---such as graphs, simplicial complexes, and meshes--because it strikes this balance by providing a complete topological summary, yet is typically much faster to compute than its widely used cousin, the Persistent Homology Transform [@Turner2014].
 
 The `ect` Python package offers a fast and well-documented implementation of ECT for inputs in any embedding dimension and with a wide range of complex types. With a few lines of code, users can generate ECT features by sampling directions, computing Euler characteristic curves, and vectorizing them for downstream tasks such as classification or regression. The package includes practical options for direction sampling, normalization, and visualizing various versions of the ECT. These options allow for smooth integration into other scientific package such as `Numpy`, `Scipy`, and `PyTorch`. By lowering the barrier to computing the ECT on embedded complexes, `ect` makes these topological summaries accessible to a wider range of practitioners and domain scientists.
 

From 48ad99bdd13fcdfd0a50c6aa80f9f73dc58a8fc6 Mon Sep 17 00:00:00 2001
From: Liz Munch <muncheli@msu.edu>
Date: Wed, 1 Oct 2025 15:05:31 -0400
Subject: [PATCH 16/25] Made heavy pass through the paper, still needs some
 refs and the like.

---
 paper/paper.bib | 13 +++++++++++
 paper/paper.md  | 59 +++++++++++++++++++------------------------------
 2 files changed, 36 insertions(+), 36 deletions(-)

diff --git a/paper/paper.bib b/paper/paper.bib
index 97a5a73..29b1cea 100644
--- a/paper/paper.bib
+++ b/paper/paper.bib
@@ -1265,4 +1265,17 @@ @Book{Ghrist2014
   keywords = {textbook, survey},
 }
 
+@Book{Goodman2018,
+  editor    = {Jacob E. Goodman and Joseph O'Rourke and Csaba D. Tóth},
+  publisher = {CRC Press},
+  title     = {Handbook of discrete and computational geometry},
+  year      = {2018},
+  address   = {Boca Raton},
+  edition   = {Third edition},
+  isbn      = {9781351645911},
+  series    = {Discrete mathematics and its applications},
+  pagetotal = {11928},
+  ppn_gvk   = {1007357088},
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}
diff --git a/paper/paper.md b/paper/paper.md
index d3e78bb..8e655a1 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -1,5 +1,5 @@
 ---
-title: 'ECT: A Python Package for the Euler Characteristic Transform'
+title: '`ect`: A Python Package for the Euler Characteristic Transform'
 tags:
   - Python
   - Topological Data Analysis
@@ -40,32 +40,19 @@ The `ect` Python package offers a fast and well-documented implementation of ECT
 
 ## The Euler Characteristic Transform
 
-We give a high level introduction of the ECT here as defined in [@Turner2014], and direct the reader to [@Munch2025] for a full survey article specifically on the subject. Further, note that the code is built to handle embedded cell complexes of arbitrary dimension, but for ease of introduction, we explain the basics using embedded graphs.
+The Euler characteristic is a standard construction from algebraic topology (See e.g. [@Hatcher]). 
+In its simplest form, for a given polyhedron $K$, it is defined as the alternating sum $\chi(K) = v_K-e_K+f_K$ where $v_K$, $e_K$, and $f_K$ stand for the counts of the numbers of vertices, edges, and faces in $K$, respectively.
+The Euler Characteristic Transform (ECT) extends this idea to encode the changing Euler characteristic for sublevelsets of an input space in different directions.
+We give a high level introduction of the ECT here as defined in [@Turner2014], and direct the reader to [@Munch2025] for a full survey article specifically on the subject. 
+<!-- Further, note that the code is built to handle embedded cell complexes of arbitrary dimension, but for ease of introduction, we explain the basics using embedded graphs. -->
 
-To start, we assume our input is an undirected graph $G$ with a straight-line embedding in 2D given by a map on the vertices $f: V(G) \to \mathbb{R}^2$. A graph can be constructed as seen in \autoref{fig:example_graph}.
+To start, we have input `ect.EmbeddedComplex`, which is a polyhedral complex $K$ (See [@Goodman2018] Ch. 17.4) which is a collection of convex polytopes in $\mathbb{R}^n$ closed under the face relation. While we note the code can handle shapes in any dimension, we will give an exposition focusing on the case of a straight-line graph embedding like the example given in \autoref{fig:example_graph} embedded in $\mathbb{R}^2$.
 
-
-![A filtration of a graph showing the sublevel sets of $g_\omega$ for a fixed direction $\omega$. The vertices and edges are added to the filtration as the height increases.\label{fig:filtration}](figures/filtration.png)
-
-<!-- ![Testing scaling](figures/CombineGraphExample.png){ width=20% } -->
-
-
-For a choice of direction $\theta \in [0,2\pi]$, we can induce a function on the vertex set. 
-Thinking of this as $\omega \in \mathbb{S}^1$ by defining the unit vector $\omega = (\cos(\theta), \sin(\theta))$, the function $g_\omega$ is defined on the vertices of $G$ by taking the dot product of the embedding coordinates with the unit vector, specifically
-$$
+For a choice of direction $\omega \in \mathbb{S}^{n-1}$, we induce a function on the vertex set given by $
 g_\omega(v) = \langle f(v), \omega\rangle.
-$$
-<!-- This is done in the code using the `g_omega` method as shown.  -->
-Some examples are shown in \autoref{fig:example_graph}. 
-
-Now we can set up the ECT for the embedded graph. The ECT is defined as 
-$$
-\begin{matrix}
-\text{ECT}(G): & \mathbb{S}^1 & \to & \text{Func}(\mathbb{R}, \mathbb{Z})\\
-& \omega & \mapsto & \{ a \mapsto \chi(g_\omega^{-1}(-\infty,a]) \}
-\end{matrix}
-$$
-Perhaps a better way of looking at this same function for visualization purposes is to treat this function as defined on a cylinder,
+$, the dot product of the embedding coordinates of the vertex with the unit vector $\omega \in \mathbb{R}^n$. 
+Some examples are shown for the embedded graph in \autoref{fig:example_graph}. 
+The ECT for the embedded graph is given by
 $$
 \begin{matrix}
 \text{ECT}(G): & \mathbb{S}^1 \times \mathbb{R} & \to &  \mathbb{Z}\\
@@ -73,12 +60,12 @@ $$
 \end{matrix}
 $$
 After discretizing, the example embedded graph has an ECT matrix as shown in the bottom row of \autoref{fig:example_graph}.
-The main functionality of the `ECT` package is to be able to compute the ECT matrix for graphs embedded in $\mathbb{R}^d$ for $d \in \{2,3\}$.
 
 ![(Top row) An example of an embedded graph with two choices of function $f_\omega$ drawn as the coloring on the nodes. (Bottom) The ECT matrix of the graph shown.\label{fig:example_graph}](figures/CombineGraphExample.png)
 
+<!-- ![A filtration of a graph showing the sublevel sets of $g_\omega$ for a fixed direction $\omega$. The vertices and edges are added to the filtration as the height increases.\label{fig:filtration}](figures/filtration.png) -->
 
-## Extension to higher dimensional embedding
+<!-- ## Extension to higher dimensional embedding
 
 In theory, the ECT can be defined for a space embedded in $\mathbb{R}^d$ for any $d$. 
 In practice, for applications geared toward encoding shapes seen in the physical world, this is largely limited to the cases $d=2$ or $d=3$. 
@@ -94,25 +81,25 @@ In order to handle issues with choices of direction discretiziations, we have im
 
 
 **TODO: add in stuff about the CW complex inputs**
-- CW Complexes might be too broad a term. Perhaps "[polygon mesh](https://en.wikipedia.org/wiki/Polygon_mesh)" is better. 
-
-## Distances 
+- CW Complexes might be too broad a term. Perhaps "[polygon mesh](https://en.wikipedia.org/wiki/Polygon_mesh)" is better.  -->
 
-Additional code is included for computing distances between the resulting ECT matrices. 
+## Capabilities of the `ect` package 
 
-![MDS of Matisse](figures/Matisse_MDS.png)
+The main functionality of the `ect` package is to compute the ECT using the class `ect.ect.ECT`, including for higher dimensional structures than described in the previous section.
+This can be modified to accept different choices of subsets of directions of the sphere $\mathbb{S}^{n-1}$, including uniform and random sampling methods.
+Variants of the ECT are also implemented including the Smooth Euler Characteristic Transform (SECT) [ADD CITATION]; and the Differentiable Euler Characteristic Transform (DECT) [ADD CITATION]. 
+The ECT output is also capable of easily returning distances between transforms, generally defined as the $L_p$ distance between two functions $ECT(K_1), ECT(K_2):\mathbb{S}^{n-1} \times \mathbb{R} \to \mathbb{Z}$.
 
-## Generalized versions of ECT
+<!-- ![MDS of Matisse](figures/Matisse_MDS.png) -->
 
-The ECT package provides implementations for both the Smooth Euler Characteristic Transform and the Differentiable Euler Characteristic Transform. This allows for users to quickly examine their dataset under the lense of various topological transforms to find what best suits their problem.
 
 # Statement of Need
 
-Despite the ECT's mathematical elegances, there has been a notable absense of efficient, user-friendly Python implementations that can handle the computational demands of modern research datasets. The ECT package addressed this by leveraging Numba's just-in-time compilation to achieve significant speedups over naive Python implementations, making it practical to compute ECTs for large-scale datasets. This performance is then complimented by the many utility functions for visualizing and comparing different Euler Characteristic Tranforms such as the ECT, SECT, and the DECT.
+Despite the ECT's mathematical elegances, there has been a notable absence of efficient, user-friendly, continuously maintained Python implementations that can handle the computational demands of modern research datasets. The ECT package addressed this by leveraging Numba's just-in-time compilation to achieve significant speedups over naive Python implementations, making it practical to compute ECTs for large-scale datasets. This performance is then complimented by the many utility functions for visualizing and comparing different Euler Characteristic Tranforms such as the ECT, SECT, and the DECT.
 
-# Representative Publications Using ECT
+<!-- # Representative Publications Using ECT
 
-Have we actually used it yet? 
+Have we actually used it yet?  -->
 
 # Acknowledgements
 

From 445adb57f3dc11af7acedbfb1d5cd9edcdeceae8 Mon Sep 17 00:00:00 2001
From: Liz Munch <muncheli@msu.edu>
Date: Wed, 1 Oct 2025 15:08:22 -0400
Subject: [PATCH 17/25] Bleeping Latex.

---
 paper/paper.md | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/paper/paper.md b/paper/paper.md
index 8e655a1..0b9f345 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -48,9 +48,7 @@ We give a high level introduction of the ECT here as defined in [@Turner2014], a
 
 To start, we have input `ect.EmbeddedComplex`, which is a polyhedral complex $K$ (See [@Goodman2018] Ch. 17.4) which is a collection of convex polytopes in $\mathbb{R}^n$ closed under the face relation. While we note the code can handle shapes in any dimension, we will give an exposition focusing on the case of a straight-line graph embedding like the example given in \autoref{fig:example_graph} embedded in $\mathbb{R}^2$.
 
-For a choice of direction $\omega \in \mathbb{S}^{n-1}$, we induce a function on the vertex set given by $
-g_\omega(v) = \langle f(v), \omega\rangle.
-$, the dot product of the embedding coordinates of the vertex with the unit vector $\omega \in \mathbb{R}^n$. 
+For a choice of direction $\omega \in \mathbb{S}^{n-1}$, we induce a function on the vertex set given by $g_\omega(v) = \langle f(v), \omega\rangle$, the dot product of the embedding coordinates of the vertex with the unit vector $\omega \in \mathbb{R}^n$. 
 Some examples are shown for the embedded graph in \autoref{fig:example_graph}. 
 The ECT for the embedded graph is given by
 $$

From d513c625923cfa07d11a2b6f8fde6b3270d83455 Mon Sep 17 00:00:00 2001
From: Liz Munch <muncheli@msu.edu>
Date: Wed, 1 Oct 2025 15:22:01 -0400
Subject: [PATCH 18/25] Added a few more citations

---
 paper/paper.bib | 38 ++++++++++++++++++++++++++++++++++++++
 paper/paper.md  |  8 ++++----
 2 files changed, 42 insertions(+), 4 deletions(-)

diff --git a/paper/paper.bib b/paper/paper.bib
index 29b1cea..ca13fa7 100644
--- a/paper/paper.bib
+++ b/paper/paper.bib
@@ -1278,4 +1278,42 @@ @Book{Goodman2018
   ppn_gvk   = {1007357088},
 }
 
+@Article{Meng2024,
+  author    = {Meng, Kun and Wang, Jinyu and Crawford, Lorin and Eloyan, Ani},
+  journal   = {Journal of the American Statistical Association},
+  title     = {Randomness of Shapes and Statistical Inference on Shapes via the Smooth Euler Characteristic Transform},
+  year      = {2024},
+  issn      = {1537-274X},
+  month     = may,
+  number    = {549},
+  pages     = {498--510},
+  volume    = {120},
+  doi       = {10.1080/01621459.2024.2353947},
+  publisher = {Informa UK Limited},
+}
+
+@InProceedings{Roell2024,
+  author    = {Ernst R{\"o}ell and Bastian Rieck},
+  booktitle = {The Twelfth International Conference on Learning Representations},
+  title     = {Differentiable Euler Characteristic Transforms for Shape Classification},
+  year      = {2024},
+  url       = {https://openreview.net/forum?id=MO632iPq3I},
+}
+
+@Article{Rieck2024,
+  author        = {Rieck, Bastian},
+  title         = {Topology meets Machine Learning: An Introduction using the Euler Characteristic Transform},
+  year          = {2024},
+  month         = oct,
+  abstract      = {This overview article makes the case for how topological concepts can enrich research in machine learning. Using the Euler Characteristic Transform (ECT), a geometrical-topological invariant, as a running example, I present different use cases that result in more efficient models for analyzing point clouds, graphs, and meshes. Moreover, I outline a vision for how topological concepts could be used in the future, comprising (1) the learning of functions on topological spaces, (2) the building of hybrid models that imbue neural networks with knowledge about the topological information in data, and (3) the analysis of qualitative properties of neural networks. With current research already addressing some of these aspects, this article thus serves as an introduction and invitation to this nascent area of research.},
+  archiveprefix = {arXiv},
+  copyright     = {arXiv.org perpetual, non-exclusive license},
+  doi           = {10.48550/ARXIV.2410.17760},
+  eprint        = {2410.17760},
+  file          = {:Rieck2024 - Topology Meets Machine Learning_ an Introduction Using the Euler Characteristic Transform.pdf:PDF:http\://arxiv.org/pdf/2410.17760v1;:TOREVIEW/Notices/241007-Rieck-v1.pdf:PDF},
+  keywords      = {Machine Learning (cs.LG), Algebraic Topology (math.AT), FOS: Computer and information sciences, FOS: Mathematics, 55N31, 62R40, 68T09},
+  primaryclass  = {cs.LG},
+  publisher     = {arXiv},
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}
diff --git a/paper/paper.md b/paper/paper.md
index 0b9f345..a58f40a 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -34,7 +34,7 @@ bibliography: paper.bib
 
 # Summary
 
-The field of Topological Data Analysis [@Dey2021;@Wasserman2018;@Ghrist2014;@Munch2017] encodes the shape of data in quantifiable representations of the information, sometimes called "topological signatures" or "topological summaries". The goal is to ensure that these summaries are robust to noise and useful in practice. In many methods, richer representations bring higher computation cost, creating a tension between robustness and speed. The Euler Characteristic Transform (ECT) [@Turner2014;@Munch2025] has gained popularity for encoding the information of embedded shapes in $\mathbb{R}^d$---such as graphs, simplicial complexes, and meshes--because it strikes this balance by providing a complete topological summary, yet is typically much faster to compute than its widely used cousin, the Persistent Homology Transform [@Turner2014].
+The field of Topological Data Analysis [@Dey2021;@Wasserman2018;@Ghrist2014;@Munch2017] encodes the shape of data in quantifiable representations of the information, sometimes called "topological signatures" or "topological summaries". The goal is to ensure that these summaries are robust to noise and useful in practice. In many methods, richer representations bring higher computation cost, creating a tension between robustness and speed. The Euler Characteristic Transform (ECT) [@Turner2014;@Munch2025;@Rieck2024] has gained popularity for encoding the information of embedded shapes in $\mathbb{R}^d$---such as graphs, simplicial complexes, and meshes--because it strikes this balance by providing a complete topological summary, yet is typically much faster to compute than its widely used cousin, the Persistent Homology Transform [@Turner2014].
 
 The `ect` Python package offers a fast and well-documented implementation of ECT for inputs in any embedding dimension and with a wide range of complex types. With a few lines of code, users can generate ECT features by sampling directions, computing Euler characteristic curves, and vectorizing them for downstream tasks such as classification or regression. The package includes practical options for direction sampling, normalization, and visualizing various versions of the ECT. These options allow for smooth integration into other scientific package such as `Numpy`, `Scipy`, and `PyTorch`. By lowering the barrier to computing the ECT on embedded complexes, `ect` makes these topological summaries accessible to a wider range of practitioners and domain scientists.
 
@@ -43,7 +43,7 @@ The `ect` Python package offers a fast and well-documented implementation of ECT
 The Euler characteristic is a standard construction from algebraic topology (See e.g. [@Hatcher]). 
 In its simplest form, for a given polyhedron $K$, it is defined as the alternating sum $\chi(K) = v_K-e_K+f_K$ where $v_K$, $e_K$, and $f_K$ stand for the counts of the numbers of vertices, edges, and faces in $K$, respectively.
 The Euler Characteristic Transform (ECT) extends this idea to encode the changing Euler characteristic for sublevelsets of an input space in different directions.
-We give a high level introduction of the ECT here as defined in [@Turner2014], and direct the reader to [@Munch2025] for a full survey article specifically on the subject. 
+We give a high level introduction of the ECT here as defined in [@Turner2014], and direct the reader to [@Munch2025;@Rieck2024] for full survey articles specifically on the subject. 
 <!-- Further, note that the code is built to handle embedded cell complexes of arbitrary dimension, but for ease of introduction, we explain the basics using embedded graphs. -->
 
 To start, we have input `ect.EmbeddedComplex`, which is a polyhedral complex $K$ (See [@Goodman2018] Ch. 17.4) which is a collection of convex polytopes in $\mathbb{R}^n$ closed under the face relation. While we note the code can handle shapes in any dimension, we will give an exposition focusing on the case of a straight-line graph embedding like the example given in \autoref{fig:example_graph} embedded in $\mathbb{R}^2$.
@@ -85,7 +85,7 @@ In order to handle issues with choices of direction discretiziations, we have im
 
 The main functionality of the `ect` package is to compute the ECT using the class `ect.ect.ECT`, including for higher dimensional structures than described in the previous section.
 This can be modified to accept different choices of subsets of directions of the sphere $\mathbb{S}^{n-1}$, including uniform and random sampling methods.
-Variants of the ECT are also implemented including the Smooth Euler Characteristic Transform (SECT) [ADD CITATION]; and the Differentiable Euler Characteristic Transform (DECT) [ADD CITATION]. 
+Variants of the ECT are also implemented including the Smooth Euler Characteristic Transform (SECT) [@Crawford2019;@Meng2022]; and the Differentiable Euler Characteristic Transform (DECT) [@Roell2024]. 
 The ECT output is also capable of easily returning distances between transforms, generally defined as the $L_p$ distance between two functions $ECT(K_1), ECT(K_2):\mathbb{S}^{n-1} \times \mathbb{R} \to \mathbb{Z}$.
 
 <!-- ![MDS of Matisse](figures/Matisse_MDS.png) -->
@@ -93,7 +93,7 @@ The ECT output is also capable of easily returning distances between transforms,
 
 # Statement of Need
 
-Despite the ECT's mathematical elegances, there has been a notable absence of efficient, user-friendly, continuously maintained Python implementations that can handle the computational demands of modern research datasets. The ECT package addressed this by leveraging Numba's just-in-time compilation to achieve significant speedups over naive Python implementations, making it practical to compute ECTs for large-scale datasets. This performance is then complimented by the many utility functions for visualizing and comparing different Euler Characteristic Tranforms such as the ECT, SECT, and the DECT.
+Despite the ECT's mathematical power, there has been a notable absence of efficient, user-friendly, continuously maintained Python implementations that can handle the computational demands of modern research datasets. The ECT package addressed this by leveraging Numba's just-in-time compilation to achieve significant speedups over naive Python implementations, making it practical to compute ECTs for large-scale datasets. This performance is then complimented by the many utility functions for visualizing and comparing different Euler Characteristic Tranforms such as the ECT, SECT, and the DECT.
 
 <!-- # Representative Publications Using ECT
 

From 0e6792b4ceab1404bfb3f126a3faf980c53998c4 Mon Sep 17 00:00:00 2001
From: yemeen <yemeen.ayub.14@cnu.edu>
Date: Thu, 2 Oct 2025 14:42:20 -0400
Subject: [PATCH 19/25] add orcid, fix dash, add grant number

---
 paper/paper.md | 18 +++++++-----------
 1 file changed, 7 insertions(+), 11 deletions(-)

diff --git a/paper/paper.md b/paper/paper.md
index a58f40a..a68a422 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -11,13 +11,13 @@ authors:
     orcid: 0000-0002-9459-9493
   - name: Yemeen Ayub
     affiliation: 1
-    orcid: 0000-0000-0000-0000
-  - name: Dan Chitwood 
+    orcid: 0009-0009-6667-0991
+  - name: Daniel H. Chitwood 
     affiliation: 1
-    orcid: 0000-0000-0000-0000
+    orcid: 0000-0003-4875-1447
   - name: Sarah McGuire
     affiliation: 2
-    orcid: 0000-0000-0000-0000
+    orcid: 0000-0003-4020-0536
 affiliations:
  - name: Michigan State University, East Lansing, MI, USA
    index: 1
@@ -34,7 +34,7 @@ bibliography: paper.bib
 
 # Summary
 
-The field of Topological Data Analysis [@Dey2021;@Wasserman2018;@Ghrist2014;@Munch2017] encodes the shape of data in quantifiable representations of the information, sometimes called "topological signatures" or "topological summaries". The goal is to ensure that these summaries are robust to noise and useful in practice. In many methods, richer representations bring higher computation cost, creating a tension between robustness and speed. The Euler Characteristic Transform (ECT) [@Turner2014;@Munch2025;@Rieck2024] has gained popularity for encoding the information of embedded shapes in $\mathbb{R}^d$---such as graphs, simplicial complexes, and meshes--because it strikes this balance by providing a complete topological summary, yet is typically much faster to compute than its widely used cousin, the Persistent Homology Transform [@Turner2014].
+The field of Topological Data Analysis [@Dey2021;@Wasserman2018;@Ghrist2014;@Munch2017] encodes the shape of data in quantifiable representations of the information, sometimes called "topological signatures" or "topological summaries". The goal is to ensure that these summaries are robust to noise and useful in practice. In many methods, richer representations bring higher computation cost, creating a tension between robustness and speed. The Euler Characteristic Transform (ECT) [@Turner2014;@Munch2025;@Rieck2024] has gained popularity for encoding the information of embedded shapes in $\mathbb{R}^d$--such as graphs, simplicial complexes, and meshes--because it strikes this balance by providing a complete topological summary, yet is typically much faster to compute than its widely used cousin, the Persistent Homology Transform [@Turner2014].
 
 The `ect` Python package offers a fast and well-documented implementation of ECT for inputs in any embedding dimension and with a wide range of complex types. With a few lines of code, users can generate ECT features by sampling directions, computing Euler characteristic curves, and vectorizing them for downstream tasks such as classification or regression. The package includes practical options for direction sampling, normalization, and visualizing various versions of the ECT. These options allow for smooth integration into other scientific package such as `Numpy`, `Scipy`, and `PyTorch`. By lowering the barrier to computing the ECT on embedded complexes, `ect` makes these topological summaries accessible to a wider range of practitioners and domain scientists.
 
@@ -42,7 +42,7 @@ The `ect` Python package offers a fast and well-documented implementation of ECT
 
 The Euler characteristic is a standard construction from algebraic topology (See e.g. [@Hatcher]). 
 In its simplest form, for a given polyhedron $K$, it is defined as the alternating sum $\chi(K) = v_K-e_K+f_K$ where $v_K$, $e_K$, and $f_K$ stand for the counts of the numbers of vertices, edges, and faces in $K$, respectively.
-The Euler Characteristic Transform (ECT) extends this idea to encode the changing Euler characteristic for sublevelsets of an input space in different directions.
+The ECT extends this idea to encode the changing Euler characteristic for sublevel sets of an input space in different directions.
 We give a high level introduction of the ECT here as defined in [@Turner2014], and direct the reader to [@Munch2025;@Rieck2024] for full survey articles specifically on the subject. 
 <!-- Further, note that the code is built to handle embedded cell complexes of arbitrary dimension, but for ease of introduction, we explain the basics using embedded graphs. -->
 
@@ -78,8 +78,6 @@ In order to handle issues with choices of direction discretiziations, we have im
 
 
 
-**TODO: add in stuff about the CW complex inputs**
-- CW Complexes might be too broad a term. Perhaps "[polygon mesh](https://en.wikipedia.org/wiki/Polygon_mesh)" is better.  -->
 
 ## Capabilities of the `ect` package 
 
@@ -95,9 +93,7 @@ The ECT output is also capable of easily returning distances between transforms,
 
 Despite the ECT's mathematical power, there has been a notable absence of efficient, user-friendly, continuously maintained Python implementations that can handle the computational demands of modern research datasets. The ECT package addressed this by leveraging Numba's just-in-time compilation to achieve significant speedups over naive Python implementations, making it practical to compute ECTs for large-scale datasets. This performance is then complimented by the many utility functions for visualizing and comparing different Euler Characteristic Tranforms such as the ECT, SECT, and the DECT.
 
-<!-- # Representative Publications Using ECT
 
-Have we actually used it yet?  -->
 
 # Acknowledgements
 
@@ -105,6 +101,6 @@ This material is based in part upon work supported in part by the National Scien
 CCF-1907591,
 CCF-2106578,
 and CCF-2142713.
-**Get the rest?**
+This work was also supported by US National Science Foundation Plant Genome Research Program awards (IOS-2310355, IOS-2310356, and IOS-2310357).
 
 # References

From 1f6cae59b453f81b564d95b16b0c98f53e2dfaa5 Mon Sep 17 00:00:00 2001
From: yemeen <yemeen.ayub.14@cnu.edu>
Date: Thu, 2 Oct 2025 16:09:53 -0400
Subject: [PATCH 20/25] fix wording

---
 paper/paper.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/paper/paper.md b/paper/paper.md
index a68a422..1ccca7e 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -91,7 +91,7 @@ The ECT output is also capable of easily returning distances between transforms,
 
 # Statement of Need
 
-Despite the ECT's mathematical power, there has been a notable absence of efficient, user-friendly, continuously maintained Python implementations that can handle the computational demands of modern research datasets. The ECT package addressed this by leveraging Numba's just-in-time compilation to achieve significant speedups over naive Python implementations, making it practical to compute ECTs for large-scale datasets. This performance is then complimented by the many utility functions for visualizing and comparing different Euler Characteristic Tranforms such as the ECT, SECT, and the DECT.
+Despite the ECT's mathematical power, there has been a notable absence of efficient, user-friendly, continuously maintained Python packages that can handle the computational demands of modern research datasets. The ECT package addressed this by leveraging Numba's just-in-time compilation to achieve significant speedups over naive Python implementations, making it practical to compute ECTs for large-scale datasets. This performance is then complimented by the many utility functions for visualizing and comparing different Euler Characteristic Tranforms such as the ECT, SECT, and the DECT.
 
 
 

From dac7783ecd7674cf07b8dcb93a7d62b5e49588c8 Mon Sep 17 00:00:00 2001
From: yemeen <yemeen.ayub.14@cnu.edu>
Date: Thu, 2 Oct 2025 21:00:32 -0400
Subject: [PATCH 21/25] change order

---
 paper/paper.md | 15 ++++++++-------
 1 file changed, 8 insertions(+), 7 deletions(-)

diff --git a/paper/paper.md b/paper/paper.md
index 1ccca7e..6ebfc89 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -5,25 +5,26 @@ tags:
   - Topological Data Analysis
   - Euler Characteristic 
 authors:
-  - name: Elizabeth Munch
-    corresponding: true # (This is how to denote the corresponding author)
-    affiliation: 1
-    orcid: 0000-0002-9459-9493
   - name: Yemeen Ayub
+  - corresponding: true
     affiliation: 1
     orcid: 0009-0009-6667-0991
-  - name: Daniel H. Chitwood 
+  - name: Elizabeth Munch
     affiliation: 1
-    orcid: 0000-0003-4875-1447
+    orcid: 0000-0002-9459-9493
   - name: Sarah McGuire
     affiliation: 2
     orcid: 0000-0003-4020-0536
+  - name: Daniel H. Chitwood 
+    affiliation: 1
+    orcid: 0000-0003-4875-1447
+
 affiliations:
  - name: Michigan State University, East Lansing, MI, USA
    index: 1
  - name: Pacific Northwest National Lab (PNNL), USA
    index: 2
-date: Jan 2025
+date: Oct 2025
 bibliography: paper.bib
 
 # Optional fields if submitting to a AAS journal too, see this blog post:

From 4fee3594d50a6174584971cf3f81c04cea84735f Mon Sep 17 00:00:00 2001
From: yemeen <yemeen.ayub.14@cnu.edu>
Date: Thu, 2 Oct 2025 21:05:10 -0400
Subject: [PATCH 22/25] fix title

---
 paper/paper.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/paper/paper.md b/paper/paper.md
index 6ebfc89..f4810bd 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -1,5 +1,5 @@
 ---
-title: '`ect`: A Python Package for the Euler Characteristic Transform'
+title: 'ect: A Python Package for the Euler Characteristic Transform'
 tags:
   - Python
   - Topological Data Analysis

From 7ce88dc2cd484bfc3a024570d7a0d8de7fe7dd56 Mon Sep 17 00:00:00 2001
From: yemeen <yemeen.ayub.14@cnu.edu>
Date: Fri, 3 Oct 2025 11:36:28 -0400
Subject: [PATCH 23/25] Update corresponding author format in paper metadata

---
 paper/paper.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/paper/paper.md b/paper/paper.md
index f4810bd..ae0cef2 100644
--- a/paper/paper.md
+++ b/paper/paper.md
@@ -6,7 +6,7 @@ tags:
   - Euler Characteristic 
 authors:
   - name: Yemeen Ayub
-  - corresponding: true
+    corresponding: true
     affiliation: 1
     orcid: 0009-0009-6667-0991
   - name: Elizabeth Munch

From 7b23ee3c3e9942a2d944cfac993a6ffdadc5a78c Mon Sep 17 00:00:00 2001
From: yemeen <yemeen.ayub.14@cnu.edu>
Date: Fri, 3 Oct 2025 11:52:55 -0400
Subject: [PATCH 24/25] prune bib

---
 paper/paper.bib | 1212 ++---------------------------------------------
 1 file changed, 33 insertions(+), 1179 deletions(-)

diff --git a/paper/paper.bib b/paper/paper.bib
index ca13fa7..58a78cb 100644
--- a/paper/paper.bib
+++ b/paper/paper.bib
@@ -1,582 +1,24 @@
-@article{Pearson:2017,
-  	url = {http://adsabs.harvard.edu/abs/2017arXiv170304627P},
-  	Archiveprefix = {arXiv},
-  	Author = {{Pearson}, S. and {Price-Whelan}, A.~M. and {Johnston}, K.~V.},
-  	Eprint = {1703.04627},
-  	Journal = {ArXiv e-prints},
-  	Keywords = {Astrophysics - Astrophysics of Galaxies},
-  	Month = mar,
-  	Title = {{Gaps in Globular Cluster Streams: Pal 5 and the Galactic Bar}},
-  	Year = 2017
-}
-
-@book{Binney:2008,
-  	url = {http://adsabs.harvard.edu/abs/2008gady.book.....B},
-  	Author = {{Binney}, J. and {Tremaine}, S.},
-  	Booktitle = {Galactic Dynamics: Second Edition, by James Binney and Scott Tremaine.~ISBN 978-0-691-13026-2 (HB).~Published by Princeton University Press, Princeton, NJ USA, 2008.},
-  	Publisher = {Princeton University Press},
-  	Title = {{Galactic Dynamics: Second Edition}},
-  	Year = 2008
-}
-
-@article{gaia,
-    author = {{Gaia Collaboration}},
-    title = "{The Gaia mission}",
-    journal = {Astronomy and Astrophysics},
-    archivePrefix = "arXiv",
-    eprint = {1609.04153},
-    primaryClass = "astro-ph.IM",
-    keywords = {space vehicles: instruments, Galaxy: structure, astrometry, parallaxes, proper motions, telescopes},
-    year = 2016,
-    month = nov,
-    volume = 595,
-    doi = {10.1051/0004-6361/201629272},
-    url = {http://adsabs.harvard.edu/abs/2016A%26A...595A...1G},
-}
-
-@article{astropy,
-    author = {{Astropy Collaboration}},
-    title = "{Astropy: A community Python package for astronomy}",
-    journal = {Astronomy and Astrophysics},
-    archivePrefix = "arXiv",
-    eprint = {1307.6212},
-    primaryClass = "astro-ph.IM",
-    keywords = {methods: data analysis, methods: miscellaneous, virtual observatory tools},
-    year = 2013,
-    month = oct,
-    volume = 558,
-    doi = {10.1051/0004-6361/201322068},
-    url = {http://adsabs.harvard.edu/abs/2013A%26A...558A..33A}
-}
-
-@misc{fidgit,
-  author = {A. M. Smith and K. Thaney and M. Hahnel},
-  title = {Fidgit: An ungodly union of GitHub and Figshare},
-  year = {2020},
-  publisher = {GitHub},
-  journal = {GitHub repository},
-  url = {https://github.com/arfon/fidgit}
-}
-
-@MastersThesis{Yi2022,
-  author = {Yi, Wenbo},
-  school = {University of Oslo},
-  title  = {When Hearts Beat as One – Cardiac Dynamics and Synchrony in String Quartet Performances},
-  year   = {2022},
-  url    = {https://www.duo.uio.no/handle/10852/96059},
-}
-
-@Article{Gilpin2021,
-  author        = {Gilpin, William},
-  journal       = {NeurIPS (Neural Information Processing Systems) 2021},
-  title         = {Chaos as an interpretable benchmark for forecasting and data-driven modelling},
-  year          = {2021},
-  month         = oct,
-  abstract      = {The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying attractor. Chaotic systems thus pose a unique challenge to modern statistical learning techniques, while retaining quantifiable mathematical properties that make them controllable and interpretable as benchmarks. Here, we present a growing database currently comprising 131 known chaotic dynamical systems spanning fields such as astrophysics, climatology, and biochemistry. Each system is paired with precomputed multivariate and univariate time series. Our dataset has comparable scale to existing static time series databases; however, our systems can be re-integrated to produce additional datasets of arbitrary length and granularity. Our dataset is annotated with known mathematical properties of each system, and we perform feature analysis to broadly categorize the diverse dynamics present across the collection. Chaotic systems inherently challenge forecasting models, and across extensive benchmarks we correlate forecasting performance with the degree of chaos present. We also exploit the unique generative properties of our dataset in several proof-of-concept experiments: surrogate transfer learning to improve time series classification, importance sampling to accelerate model training, and benchmarking symbolic regression algorithms.},
-  archiveprefix = {arXiv},
-  comment       = {Cited old tsp paper},
-  copyright     = {arXiv.org perpetual, non-exclusive license},
-  doi           = {10.48550/ARXIV.2110.05266},
-  eprint        = {2110.05266},
-  file          = {:Gilpin2021 - Chaos As an Interpretable Benchmark for Forecasting and Data Driven Modelling.pdf:PDF},
-  keywords      = {Machine Learning (cs.LG), Signal Processing (eess.SP), Chaotic Dynamics (nlin.CD), FOS: Computer and information sciences, FOS: Electrical engineering, electronic engineering, information engineering, FOS: Physical sciences},
-  primaryclass  = {cs.LG},
-  publisher     = {arXiv},
-}
-
- 
-@Article{Myers2023,
-  author    = {Myers, Audun D. and Muñoz, David and Khasawneh, Firas A and Munch, Elizabeth},
-  journal   = {EPJ Data Science},
-  title     = {Temporal network analysis using zigzag persistence},
-  year      = {2023},
-  issn      = {2193-1127},
-  month     = mar,
-  number    = {1},
-  volume    = {12},
-  doi       = {10.1140/epjds/s13688-023-00379-5},
-  publisher = {Springer Science and Business Media LLC},
-}
-
- 
-@Article{Myers2023a,
-  author    = {Myers, Audun D. and Chumley, Max M. and Khasawneh, Firas A. and Munch, Elizabeth},
-  journal   = {Physical Review E},
-  title     = {Persistent homology of coarse-grained state-space networks},
-  year      = {2023},
-  issn      = {2470-0053},
-  month     = mar,
-  number    = {3},
-  pages     = {034303},
-  volume    = {107},
-  doi       = {10.1103/physreve.107.034303},
-  publisher = {American Physical Society (APS)},
-}
-
- 
-@Article{Guezel2022,
-  author    = {Güzel, İsmail and Munch, Elizabeth and Khasawneh, Firas A.},
-  journal   = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
-  title     = {Detecting bifurcations in dynamical systems with CROCKER plots},
-  year      = {2022},
-  issn      = {1089-7682},
-  month     = sep,
-  number    = {9},
-  volume    = {32},
-  doi       = {10.1063/5.0102421},
-  publisher = {AIP Publishing},
-}
-
- 
-@Article{Myers2023c,
-  author    = {Myers, Audun D. and Khasawneh, Firas A. and Munch, Elizabeth},
-  journal   = {SIAM Journal on Applied Dynamical Systems},
-  title     = {Persistence of Weighted Ordinal Partition Networks for Dynamic State Detection},
-  year      = {2023},
-  issn      = {1536-0040},
-  month     = feb,
-  number    = {1},
-  pages     = {65--89},
-  volume    = {22},
-  doi       = {10.1137/22m1476848},
-  publisher = {Society for Industrial & Applied Mathematics (SIAM)},
-}
-
-@Article{Jones2023,
-  author        = {Jones, Benjamin and Wei, Guowei},
-  title         = {Persistent Directed Flag Laplacian},
-  year          = {2023},
-  month         = dec,
-  abstract      = {Topological data analysis (TDA) has had enormous success in science and engineering in the past decade. Persistent topological Laplacians (PTLs) overcome some limitations of persistent homology, a key technique in TDA, and provide substantial insight to the behavior of various geometric and topological objects. This work extends PTLs to directed flag complexes, which are an exciting generalization to flag complexes, also known as clique complexes, that arise naturally in many situations. We introduce the directed flag Laplacian and show that the proposed persistent directed flag Laplacian (PDFL) is a distinct way of analyzing these flag complexes. Example calculations are provided to demonstrate the potential of the proposed PDFL in real world applications.},
-  archiveprefix = {arXiv},
-  copyright     = {Creative Commons Attribution 4.0 International},
-  doi           = {10.48550/ARXIV.2312.02099},
-  eprint        = {2312.02099},
-  file          = {:Jones2023 - Persistent Directed Flag Laplacian.pdf:PDF},
-  keywords      = {Algebraic Topology (math.AT), FOS: Mathematics},
-  primaryclass  = {math.AT},
-  publisher     = {arXiv},
-}
-
- 
-@Article{Tanweer2024_FODS,
-  author    = {Tanweer, Sunia and Khasawneh, Firas A. and Munch, Elizabeth},
-  journal   = {Foundations of Data Science},
-  title     = {Robust crossings detection in noisy signals using topological signal processing},
-  year      = {2024},
-  issn      = {2639-8001},
-  number    = {2},
-  pages     = {154--171},
-  volume    = {6},
-  doi       = {10.3934/fods.2024006},
-  publisher = {American Institute of Mathematical Sciences (AIMS)},
-}
-
-@PhdThesis{Collins2022,
-  author   = {Collins,Joseph R.},
-  title    = {Topological Time-Series Classification},
-  year     = {2022},
-  note     = {Copyright - Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works; Last updated - 2023-08-04},
-  abstract = {We establish a strong connection between Topological Data Analysis (TDA)and the field of time-series classification. This is accomplished via two novel contributions. The first is a method for extracting topological information from a timeseries in a manner which circumvents the expensive computation normally required. The second is an adaption of an existing topological summary to create an efficient topological time-series pooling operator. Taken together, these insights enable anew classifier, TopRocket (Topological Random Convolutional Kernel Transform).Using standard comparison methods, TopRocket ranks second among all univariate time-series classifiers. Further, TopRocket is the best performing scalable classifier. As a final contribution, we provide the fastest available implementation of the algorithm for computing time-series sublevel set persistence. This provides a foundation for further investigation of TDA for time-series classification.This work lies at the intersection of TDA and machine learning, where success is dependent on efficiently extracting topological information from data and using that information with downstream models. For this purpose, we develop an efficient, data-based, topological summary, the Betti pooling operator. We rigorously demonstrate the utility of TopRocket by evaluating its performance against the University of California Riverside (UCR) Time Series Archive, a widely used benchmark collection of data sets. TopRocket is the first TDA-based classifier to obtain state-of-the art results on any similarly competitive problem. We strongly believe that TDA will play a central role in the future of machine learning.},
-  isbn     = {9798802715796},
-  journal  = {ProQuest Dissertations and Theses},
-  keywords = {Machine learning; Time-series classification; Topological data analysis; Computer science; 0984:Computer science},
-  language = {English},
-  pages    = {105},
-  url      = {https://ezproxy.msu.edu/login?url=https://www.proquest.com/dissertations-theses/topological-time-series-classification/docview/2671576993/se-2},
-}
-
-@PhdThesis{Tymochko2022,
-  author   = {Tymochko,Sarah},
-  title    = {Topological Approaches for Quantifying the Shape of Time Series Data},
-  year     = {2022},
-  note     = {Copyright - Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works; Last updated - 2024-02-16},
-  abstract = {Topological data analysis (TDA) is field that started only two decades ago and has already shown promise both in theory and in applications. The goal of TDA is to quantify the shape of data in a manner that is concise and robust using concepts from algebraic topology. Persistent homology, arguably the most popular tool from TDA, studies the shape of a filtered space by watching how its homology changes. The output of persistent homology is a persistence diagram, which encodes information about the changing homology. Persistent homology has shown success in various application areas; one ever growing area of study in this field is time series analysis. Nonlinear time series analysis is a research field in and of itself that aims to capture structure in time series data, however, it lacks theoretically justified tools to analyze the resulting structure. Persistent homology comes with a solid theoretical framework, is robust to noise, and quantifies the same type of structure as appears in time series data. Thus combining tools from time series analysis and TDA provides a new approach to analyze and quantify behavior in time series data. One field where time series are prevalent is dynamical systems, since a time series arises from a projection of a solution to a system. Specifically, given a time series, Takens' theorem can be leveraged to embed the time series as a point cloud in a higher dimensional space, where this point cloud is a sampling of the full state space. Then for each time series, persistent homology can be computed on the embedding. The result is a persistence diagram for each time series. The question then becomes how do we analyze this collection of persistence diagrams to learn something about the original time series data? Many people have developed methods to answer this question, through methods such as machine learning or statistics. This dissertation provides several new methods leveraging tools from both TDA and nonlinear time series analysis to study time varying data.},
-  isbn     = {979-8-209-98467-2},
-  journal  = {ProQuest Dissertations and Theses},
-  keywords = {Applied topology; Signal processing; Time series analysis; Topological data analysis; Applied mathematics; Mathematics; 0364:Applied Mathematics; 0405:Mathematics},
-  language = {English},
-  pages    = {123},
-  url      = {https://ezproxy.msu.edu/login?url=https://www.proquest.com/dissertations-theses/topological-approaches-quantifying-shape-time/docview/2649015601/se-2},
-}
-
-@Article{Elchesen2022,
-  author        = {Elchesen, Alex and Hartsock, Iryna and Perea, Jose A. and Rask, Tatum},
-  title         = {Learning on Persistence Diagrams as Radon Measures},
-  year          = {2022},
-  month         = dec,
-  abstract      = {Persistence diagrams are common descriptors of the topological structure of data appearing in various classification and regression tasks. They can be generalized to Radon measures supported on the birth-death plane and endowed with an optimal transport distance. Examples of such measures are expectations of probability distributions on the space of persistence diagrams. In this paper, we develop methods for approximating continuous functions on the space of Radon measures supported on the birth-death plane, as well as their utilization in supervised learning tasks. Indeed, we show that any continuous function defined on a compact subset of the space of such measures (e.g., a classifier or regressor) can be approximated arbitrarily well by polynomial combinations of features computed using a continuous compactly supported function on the birth-death plane (a template). We provide insights into the structure of relatively compact subsets of the space of Radon measures, and test our approximation methodology on various data sets and supervised learning tasks.},
-  archiveprefix = {arXiv},
-  copyright     = {arXiv.org perpetual, non-exclusive license},
-  doi           = {10.48550/ARXIV.2212.08295},
-  eprint        = {2212.08295},
-  file          = {:Elchesen2022 - Learning on Persistence Diagrams As Radon Measures.pdf:PDF:http\://arxiv.org/pdf/2212.08295v1},
-  keywords      = {Computational Geometry (cs.CG), Machine Learning (cs.LG), Algebraic Topology (math.AT), FOS: Computer and information sciences, FOS: Mathematics, 55N31},
-  primaryclass  = {cs.CG},
-  publisher     = {arXiv},
-}
-
-@Article{Chumley2023,
-  author    = {Chumley, Max M. and Yesilli, Melih C. and Chen, Jisheng and Khasawneh, Firas A. and Guo, Yang},
-  journal   = {Precision Engineering},
-  title     = {Pattern characterization using topological data analysis: Application to piezo vibration striking treatment},
-  year      = {2023},
-  issn      = {0141-6359},
-  month     = sep,
-  pages     = {42--57},
-  volume    = {83},
-  doi       = {10.1016/j.precisioneng.2023.05.005},
-  publisher = {Elsevier BV},
-}
-
-@InProceedings{Tymochko2019,
-  author    = {Tymochko, Sarah and Munch, Elizabeth and Khasawneh, Firas A.},
-  booktitle = {2019 18th IEEE International Conference On Machine Learning And Applications (ICMLA)},
-  title     = {Adaptive Partitioning for Template Functions on Persistence Diagrams},
-  year      = {2019},
-  month     = dec,
-  publisher = {IEEE},
-  doi       = {10.1109/icmla.2019.00202},
-}
-
-@Article{Myers2022,
-  author    = {Myers, Audun D. and Khasawneh, Firas A. and Fasy, Brittany T.},
-  journal   = {Foundations of Data Science},
-  title     = {ANAPT: Additive noise analysis for persistence thresholding},
-  year      = {2022},
-  issn      = {2639-8001},
-  number    = {2},
-  pages     = {243},
-  volume    = {4},
-  doi       = {10.3934/fods.2022005},
-  publisher = {American Institute of Mathematical Sciences (AIMS)},
-}
-
-@Article{Perea2022,
-  author    = {Perea, Jose A. and Munch, Elizabeth and Khasawneh, Firas A.},
-  journal   = {Foundations of Computational Mathematics},
-  title     = {Approximating Continuous Functions on Persistence Diagrams Using Template Functions},
-  year      = {2022},
-  issn      = {1615-3383},
-  month     = jun,
-  number    = {4},
-  pages     = {1215--1272},
-  volume    = {23},
-  doi       = {10.1007/s10208-022-09567-7},
-  publisher = {Springer Science and Business Media LLC},
-}
-
-@Article{Bauer2021,
-  author   = {Bauer, Ulrich},
-  journal  = {J. Appl. Comput. Topol.},
-  title    = {Ripser: efficient computation of {V}ietoris-{R}ips persistence barcodes},
-  year     = {2021},
-  issn     = {2367-1726},
-  number   = {3},
-  pages    = {391--423},
-  volume   = {5},
-  doi      = {10.1007/s41468-021-00071-5},
-  fjournal = {Journal of Applied and Computational Topology},
-  mrclass  = {55N31 (55-04)},
-  mrnumber = {4298669},
-  url      = {https://doi.org/10.1007/s41468-021-00071-5},
-}
-
-@Misc{Saul2019,
-  author = {Nathaniel Saul and Chris Tralie},
-  title  = {Scikit-TDA: Topological Data Analysis for Python},
-  year   = {2019},
-  doi    = {10.5281/zenodo.2533369},
-  url    = {https://doi.org/10.5281/zenodo.2533369},
-}
-
-@Article{Otter2017,
-  author       = {Nina Otter and Mason A Porter and Ulrike Tillmann and Peter Grindrod and Heather A Harrington},
-  journal      = {{EPJ} Data Science},
-  title        = {A roadmap for the computation of persistent homology},
-  year         = {2017},
-  month        = {aug},
-  number       = {1},
-  volume       = {6},
-  creationdate = {2017-11-01T00:00:00},
-  doi          = {10.1140/epjds/s13688-017-0109-5},
-  file         = {:Persistence/Computation/Otter2017.pdf:PDF},
-  publisher    = {Springer Nature},
-}
-
-@Other{Boissonnat2016,
-  author       = {Jean-Daniel Boissonnat and Marc Glisse and Miroslav Kramar and Cl\'ement Maria and Vincent Rouvreau},
-  creationdate = {2018-04-12T00:00:00},
-  file         = {Bauer2016a.pdf:Bauer2016a.pdf:PDF},
-  howpublished = {\url{http://gudhi.gforge.inria.fr/}},
-  readstatus   = {read},
-  title        = {{GUDHI}: Geometry Understanding in Higher Dimensions},
-  url          = {http://gudhi.gforge.inria.fr/},
-  year         = {2016},
-}
-
-@Misc{Tauzin2020,
-  author        = {Guillaume Tauzin and Umberto Lupo and Lewis Tunstall and Julian Burella Pérez and Matteo Caorsi and Anibal Medina-Mardones and Alberto Dassatti and Kathryn Hess},
-  title         = {giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration},
-  year          = {2020},
-  archiveprefix = {arXiv},
-  eprint        = {2004.02551},
-  primaryclass  = {cs.LG},
-}
-
-@Other{Morozov2019,
-  author       = {Dmitriy Morozov},
-  groups       = {Persistence - Theory},
-  howpublished = {\url{http://www.mrzv.org/software/dionysus2/}},
-  title        = {Dionysus2},
-  year         = {2019},
-}
-
-@Article{Fasy2014,
-  author        = {Brittany Terese Fasy and Jisu Kim and Fabrizio Lecci and Clément Maria},
-  title         = {Introduction to the R package TDA},
-  year          = {2014},
-  month         = nov,
-  abstract      = {We present a short tutorial and introduction to using the R package TDA, which provides some tools for Topological Data Analysis. In particular, it includes implementations of functions that, given some data, provide topological information about the underlying space, such as the distance function, the distance to a measure, the kNN density estimator, the kernel density estimator, and the kernel distance. The salient topological features of the sublevel sets (or superlevel sets) of these functions can be quantified with persistent homology. We provide an R interface for the efficient algorithms of the C++ libraries GUDHI, Dionysus and PHAT, including a function for the persistent homology of the Rips filtration, and one for the persistent homology of sublevel sets (or superlevel sets) of arbitrary functions evaluated over a grid of points. The significance of the features in the resulting persistence diagrams can be analyzed with functions that implement recently developed statistical methods. The R package TDA also includes the implementation of an algorithm for density clustering, which allows us to identify the spatial organization of the probability mass associated to a density function and visualize it by means of a dendrogram, the cluster tree.},
-  archiveprefix = {arXiv},
-  creationdate  = {2019-11-11T00:00:00},
-  eprint        = {http://arxiv.org/abs/1411.1830v2},
-  file          = {:Fasy2014 - Introduction to the R Package TDA.pdf:PDF:http\://arxiv.org/pdf/1411.1830v2},
-  keywords      = {cs.MS, cs.CG, stat.CO},
-  primaryclass  = {cs.MS},
-}
-
-@InProceedings{BinMasood2019,
-  author    = {Bin Masood, Talha and Budin, Joseph and Falk, Martin and Favelier, Guillaume and Garth, Christoph and Gueunet, Charles and Guillou, Pierre and Hofmann, Lutz and Hristov, Petar and Kamakshidasan, Adhitya and Kappe, Christopher and Klacansky, Pavol and Laurin, Patrick and Levine, Joshua and Lukasczyk, Jonas and Sakurai, Daisuke and Soler, Maxime and Steneteg, Peter and Tierny, Julien and Usher, Will and Vidal, Jules and Wozniak, Michal},
-  booktitle = {{TopoInVis}},
-  title     = {{An Overview of the Topology ToolKit}},
-  year      = {2019},
-}
-
-@Book{Dey2021,
+@book{Dey2021,
   author    = {Dey, Tamal K. and Wang, Yusu},
   publisher = {Cambridge University Press},
   title     = {Computational Topology for Data Analysis},
   year      = {2021},
-  file      = {:MathTextbooks/DeyWang-CTDAbook.pdf:PDF},
-}
-
-@Article{Bubenik2015,
-  author       = {Peter Bubenik},
-  journal      = {Journal of Machine Learning Research},
-  title        = {Statistical Topological Data Analysis using Persistence Landscapes},
-  year         = {2015},
-  pages        = {77-102},
-  volume       = {16},
-  creationdate = {2018-08-04T00:00:00},
-  file         = {Bubenik2015.pdf:Persistence/StatsAndPersistence/Bubenik2015.pdf:PDF},
-  keywords     = {relevant featurization},
-  url          = {http://jmlr.org/papers/v16/bubenik15a.html},
+  file      = {:MathTextbooks/DeyWang-CTDAbook.pdf:PDF}
 }
 
-@Article{Adams2017,
-  author       = {Henry Adams and Tegan Emerson and Michael Kirby and Rachel Neville and Chris Peterson and Patrick Shipman and Sofya Chepushtanova and Eric Hanson and Francis Motta and Lori Ziegelmeier},
-  journal      = {Journal of Machine Learning Research},
-  title        = {Persistence Images: A Stable Vector Representation of Persistent Homology},
+@article{Munch2017,
+  author       = {Elizabeth Munch},
+  journal      = {Journal of Learning Analytics},
+  title        = {A User's Guide to Topological Data Analysis},
   year         = {2017},
-  number       = {8},
-  pages        = {1-35},
-  volume       = {18},
-  creationdate = {2018-08-04T00:00:00},
-  file         = {:MachineLearning/Adams2017.pdf:PDF},
-  keywords     = {featurization},
-  url          = {http://jmlr.org/papers/v18/16-337.html},
-}
-
-@Article{Adcock2016,
-  author       = {Aaron Adcock and Erik Carlsson and Gunnar Carlsson},
-  journal      = {Homology, Homotopy and Applications},
-  title        = {The Ring of Algebraic Functions on Persistence Bar Codes},
-  year         = {2016},
-  number       = {1},
-  pages        = {381-402},
-  volume       = {18},
-  creationdate = {2018-08-04T00:00:00},
-  doi          = {10.4310/HHA.2016.v18.n1.a21},
-  file         = {Adcock2012.pdf:Persistence/Adcock2012.pdf:PDF;:Persistence/StatsAndPersistence/Machine Learning/Adcock201_HHA_Version.pdf:PDF},
-  groups       = {Applications of Persistence},
-  keywords     = {featurization},
-  quality      = {1},
-  ranking      = {rank5},
-  readstatus   = {read},
-}
-
-@Article{Dey2022,
-  doi = {10.48550/arxiv.2204.11080},
-  url = {https://arxiv.org/abs/2204.11080},
-  author = {Dey,  Tamal K. and Hou,  Tao},
-  keywords = {Computational Geometry (cs.CG),  Algebraic Topology (math.AT),  FOS: Computer and information sciences,  FOS: Computer and information sciences,  FOS: Mathematics,  FOS: Mathematics},
-  title = {Fast Computation of Zigzag Persistence},
-  publisher = {arXiv},
-  year = {2022},
-  copyright = {arXiv.org perpetual,  non-exclusive license}
-}
-
-@Article{Munch2017,
-  author         = {Elizabeth Munch},
-  journal        = {Journal of Learning Analytics},
-  title          = {A User's Guide to Topological Data Analysis},
-  year           = {2017},
-  number         = {2},
-  volume         = {4},
-  abstract       = {Topological data analysis (TDA) is a collection of powerful tools that can quantify shape and structure in data in order to answer questions from the data's domain. This is done by representing some aspect of the structure of the data in a simplified topological signature. In this article, we introduce two of the most commonly used topological signatures. First, the persistence diagram represents loops and holes in the space by considering connectivity of the data points for a continuum of values rather than a single fixed value. The second topological signature, the mapper graph, returns a 1-dimensional structure representing the shape of the data, and is particularly good for exploration and visualization of the data. While these techniques are based on very sophisticated mathematics, the current ubiquity of available software means that these tools are more accessible than ever to be applied to data by researchers in education and learning, as well as all domain scientists.},
-  creationdate   = {2018-05-30T00:00:00},
-  doi            = {10.18608/jla.2017.42.6},
-}
-
-@Article{Wang2016,
-  author    = {Wang, Minggang and Tian, Lixin},
-  journal   = {Physica A: Statistical Mechanics and its Applications},
-  title     = {From time series to complex networks: The phase space coarse graining},
-  year      = {2016},
-  issn      = {0378-4371},
-  month     = nov,
-  pages     = {456--468},
-  volume    = {461},
-  doi       = {10.1016/j.physa.2016.06.028},
-  publisher = {Elsevier BV},
-}
-
-@Article{Tanweer2024_NODY,
-  author    = {Tanweer, Sunia and Khasawneh, Firas A. and Munch, Elizabeth and Tempelman, Joshua R.},
-  journal   = {Nonlinear Dynamics},
-  title     = {A topological framework for identifying phenomenological bifurcations in stochastic dynamical systems},
-  year      = {2024},
-  issn      = {1573-269X},
-  month     = feb,
-  number    = {6},
-  pages     = {4687–4703},
-  volume    = {112},
-  doi       = {10.1007/s11071-024-09289-1},
-  publisher = {Springer Science and Business Media LLC},
-  url       = {http://dx.doi.org/10.1007/s11071-024-09289-1},
-}
-
-@Article{Tanweer2024_PREM,
-  author    = {Tanweer, Sunia and Khasawneh, Firas A.},
-  journal   = {Probabilistic Engineering Mechanics},
-  title     = {Topological detection of phenomenological bifurcations with unreliable kernel density estimates},
-  year      = {2024},
-  issn      = {0266-8920},
-  month     = apr,
-  pages     = {103634},
-  volume    = {76},
-  doi       = {10.1016/j.probengmech.2024.103634},
-  publisher = {Elsevier BV},
-  url       = {http://dx.doi.org/10.1016/j.probengmech.2024.103634},
-}
-
-@Conference{Myers2020,
-  author    = {Myers, Audun D. and Melih Yesilli and Sarah Tymochko and Firas Khasawneh and Elizabeth Munch},
-  booktitle = {Topological Data Analysis and Beyond Workshop at NeurIPS 2020},
-  title     = {Teaspoon: A comprehensive python package for topological signal processing},
-  year      = {2020},
-  image     = {teaspoon.png},
-  keywords  = {conference},
-  url       = {https://openreview.net/pdf?id=qUoVqrIcy2P},
-}
-
-@Article{CrawleyBoevey2015,
-  author    = {Crawley-Boevey, William},
-  journal   = {Journal of Algebra and Its Applications},
-  title     = {Decomposition of pointwise finite-dimensional persistence modules},
-  year      = {2015},
-  issn      = {1793-6829},
-  month     = mar,
-  number    = {05},
-  pages     = {1550066},
-  volume    = {14},
-  doi       = {10.1142/s0219498815500668},
-  publisher = {World Scientific Pub Co Pte Lt},
-}
-
-@InProceedings{Myers2023b,
-  author    = {Myers, Audun D. and Kvinge, Henry and Emerson, Tegan},
-  booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops},
-  title     = {TopFusion: Using Topological Feature Space for Fusion and Imputation in Multi-Modal Data},
-  year      = {2023},
-  month     = {June},
-  pages     = {600-609},
-  doi       = {10.1109/cvprw59228.2023.00067}
-}
-
-@Article{Chevyrev2018,
-  author={Chevyrev, Ilya and Nanda, Vidit and Oberhauser, Harald},
-  journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, 
-  title={Persistence Paths and Signature Features in Topological Data Analysis}, 
-  year={2020},
-  volume={42},
-  number={1},
-  pages={192-202},
-  keywords={Bars;Extraterrestrial measurements;Algebra;Data analysis;Kernel;Topological data analysis;barcodes;signature features;kernel learning},
-  doi={10.1109/TPAMI.2018.2885516}}
-
-
-@InProceedings{Reininghaus2015,
-  author={Reininghaus, Jan and Huber, Stefan and Bauer, Ulrich and Kwitt, Roland},
-  booktitle={2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)}, 
-  title={A stable multi-scale kernel for topological machine learning}, 
-  year={2015},
-  volume={},
-  number={},
-  pages={4741-4748},
-  keywords={Yttrium},
-  doi={10.1109/CVPR.2015.7299106}}
-
-@Article{McCullough2015,
-  author    = {McCullough, Michael and Small, Michael and Stemler, Thomas and Iu, Herbert Ho-Ching},
-  title     = {Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems},
-  journal   = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
-  year      = {2015},
-  volume    = {25},
-  number    = {5},
-  pages     = {053101},
-  doi       = {10.1063/1.4919075},
-  file      = {:Dynamics/McCullough2015.pdf:PDF;McCullough2015-arxiv.pdf:Dynamics/TSA/McCullough2015-arxiv.pdf:PDF},
-  publisher = {AIP Publishing},
-}
-
-
-@article{myers2024delay,
-  title={Delay parameter selection in permutation entropy using topological data analysis},
-  author={Myers, Audun D and Chumley, Max M and Khasawneh, Firas A},
-  journal={La Matematica},
-  pages={1--34},
-  year={2024},
-  publisher={Springer},
-  doi = {10.1007/s44007-024-00110-4}
+  number       = {2},
+  volume       = {4},
+  abstract     = {Topological data analysis (TDA) is a collection of powerful tools that can quantify shape and structure in data in order to answer questions from the data's domain. This is done by representing some aspect of the structure of the data in a simplified topological signature. In this article, we introduce two of the most commonly used topological signatures. First, the persistence diagram represents loops and holes in the space by considering connectivity of the data points for a continuum of values rather than a single fixed value. The second topological signature, the mapper graph, returns a 1-dimensional structure representing the shape of the data, and is particularly good for exploration and visualization of the data. While these techniques are based on very sophisticated mathematics, the current ubiquity of available software means that these tools are more accessible than ever to be applied to data by researchers in education and learning, as well as all domain scientists.},
+  creationdate = {2018-05-30T00:00:00},
+  doi          = {10.18608/jla.2017.42.6}
 }
 
-@article{chelidze2017reliable,
-  title={Reliable estimation of minimum embedding dimension through statistical analysis of nearest neighbors},
-  author={Chelidze, David},
-  journal={Journal of Computational and Nonlinear Dynamics},
-  volume={12},
-  number={5},
-  pages={051024},
-  year={2017},
-  publisher={American Society of Mechanical Engineers},
-  doi = {10.1115/1.4036814}
-}
-
-@article{cao1997practical,
-  title={Practical method for determining the minimum embedding dimension of a scalar time series},
-  author={Cao, Liangyue},
-  journal={Physica D: Nonlinear Phenomena},
-  volume={110},
-  number={1-2},
-  pages={43--50},
-  year={1997},
-  publisher={Elsevier},
-  doi = {10.1016/s0167-2789(97)00118-8}
-}
-
-@Book{Hatcher,
+@book{Hatcher,
   author       = {Allen Hatcher},
   publisher    = {Cambridge University Press},
   title        = {Algebraic Topology},
@@ -584,10 +26,10 @@ @Book{Hatcher
   creationdate = {2011-05-23T00:00:00},
   file         = {Hatcher - algebraic topology.pdf:MathTextbooks/Hatcher - algebraic topology.pdf:PDF},
   groups       = {Classic Textbooks},
-  owner        = {liz},
+  owner        = {liz}
 }
 
-@Article{Munch2025,
+@article{Munch2025,
   author        = {Munch, Elizabeth},
   journal       = {The American Mathematical Monthly},
   title         = {An Invitation to the Euler Characteristic Transform},
@@ -605,10 +47,10 @@ @Article{Munch2025
   image         = {Munch2023.png},
   keywords      = {Computational Geometry (cs.CG),FOS: Computer and information sciences,journal},
   primaryclass  = {cs.CG},
-  publisher     = {Taylor \& Francis},
+  publisher     = {Taylor \& Francis}
 }
 
-@Article{Turner2014,
+@article{Turner2014,
   author       = {K. Turner and S. Mukherjee and D. M. Boyer},
   journal      = {Information and Inference},
   title        = {Persistent homology transform for modeling shapes and surfaces},
@@ -623,106 +65,10 @@ @Article{Turner2014
   file         = {:Persistence/Turner2014a_Published.pdf:PDF;:Persistence/Turner2014a.pdf:PDF;:Persistence/Turner2014a_ErikSlides.pdf:PDF},
   priority     = {prio1},
   publisher    = {Oxford University Press ({OUP})},
-  readstatus   = {read},
-}
-
-@InCollection{Schapira1995,
-  author    = {P. Schapira},
-  booktitle = {Applied Algebra, Algebraic Algorithms and Error-Correcting Codes},
-  publisher = {Springer Berlin Heidelberg},
-  title     = {Tomography of constructible functions},
-  year      = {1995},
-  pages     = {427--435},
-  doi       = {10.1007/3-540-60114-7_33},
-  file      = {:DirectionalTransform/Schapira1995.pdf:PDF},
-}
-
-@Article{Baryshnikov2011,
-  author    = {Yuliy Baryshnikov and Robert Ghrist and David Lipsky},
-  journal   = {Inverse Problems},
-  title     = {Inversion of {E}uler integral transforms with applications to sensor data},
-  year      = {2011},
-  month     = {nov},
-  number    = {12},
-  pages     = {124001},
-  volume    = {27},
-  doi       = {10.1088/0266-5611/27/12/124001},
-  file      = {:DirectionalTransform/Baryshnikov2011.pdf:PDF},
-  publisher = {{IOP} Publishing},
+  readstatus   = {read}
 }
 
-@Article{Curry2012,
-  author        = {Curry, Justin and Ghrist, Robert and Robinson, Michael},
-  title         = {{E}uler Calculus with Applications to Signals and Sensing},
-  year          = {2012},
-  month         = feb,
-  abstract      = {This article surveys the Euler calculus - an integral calculus based on Euler characteristic - and its applications to data, sensing, networks, and imaging.},
-  archiveprefix = {arXiv},
-  copyright     = {arXiv.org perpetual, non-exclusive license},
-  doi           = {10.48550/ARXIV.1202.0275},
-  eprint        = {1202.0275},
-  file          = {:Curry2012 - Euler Calculus with Applications to Signals and Sensing.pdf:PDF:http\://arxiv.org/pdf/1202.0275v1;:DirectionalTransform/Curry2012a.pdf:PDF},
-  keywords      = {Algebraic Topology (math.AT), FOS: Mathematics, 65R10, 58C35},
-  primaryclass  = {math.AT},
-  publisher     = {arXiv},
-}
-
-@InCollection{Heiss2017,
-  author    = {Teresa Heiss and Hubert Wagner},
-  booktitle = {Computer Analysis of Images and Patterns},
-  publisher = {Springer International Publishing},
-  title     = {Streaming Algorithm for {E}uler Characteristic Curves of Multidimensional Images},
-  year      = {2017},
-  pages     = {397--409},
-  doi       = {10.1007/978-3-319-64689-3_32},
-  file      = {:DirectionalTransform/Heiss2017.pdf:PDF},
-}
-
-@Article{Fasy2018,
-  author        = {Brittany Terese Fasy and Samuel Micka and David L. Millman and Anna Schenfisch and Lucia Williams},
-  journal       = {arXiv:1811.11337},
-  title         = {Challenges in Reconstructing Shapes from {E}uler Characteristic Curves},
-  year          = {2018},
-  month         = nov,
-  abstract      = {Shape recognition and classification is a problem with a wide variety of applications. Several recent works have demonstrated that topological descriptors can be used as summaries of shapes and utilized to compute distances. In this abstract, we explore the use of a finite number of Euler Characteristic Curves (ECC) to reconstruct plane graphs. We highlight difficulties that occur when attempting to adopt approaches for reconstruction with persistence diagrams to reconstruction with ECCs. Furthermore, we highlight specific arrangements of vertices that create problems for reconstruction and present several observations about how they affect the ECC-based reconstruction. Finally, we show that plane graphs without degree two vertices can be reconstructed using a finite number of ECCs.},
-  archiveprefix = {arXiv},
-  creationdate  = {2018-12-04T00:00:00},
-  eprint        = {http://arxiv.org/abs/1811.11337v1},
-  file          = {:Fasy2018 - Challenges in Reconstructing Shapes from Euler Characteristic Curves.pdf:PDF:http\://arxiv.org/pdf/1811.11337v1;:DirectionalTransform/Fasy2018b.pdf:PDF},
-  keywords      = {cs.CG},
-  primaryclass  = {cs.CG},
-}
-
-@Article{Ghrist2018,
-  author    = {Robert Ghrist and Rachel Levanger and Huy Mai},
-  journal   = {Journal of Applied and Computational Topology},
-  title     = {Persistent homology and {E}uler integral transforms},
-  year      = {2018},
-  month     = {aug},
-  number    = {1-2},
-  pages     = {55--60},
-  volume    = {2},
-  doi       = {10.1007/s41468-018-0017-1},
-  file      = {:DirectionalTransform/Ghrist2018_Article_PersistentHomologyAndEulerInte.pdf:PDF},
-  publisher = {Springer Science and Business Media {LLC}},
-}
-
-@PhdThesis{Betthauser2018,
-  author   = {Betthauser,Leo M.},
-  title    = {Topological Reconstruction of Grayscale Images},
-  year     = {2018},
-  note     = {Copyright - Copyright ProQuest Dissertations Publishing 2018; Last updated - 2023-03-08},
-  abstract = {Topological data analysis (TDA) is a powerful tool to solve classification problems using the underlying shape of data. Furthermore, TDA is useful in shape reconstruction of compact manifolds embedded in two and three dimensional Euclidean space. Unfortunately, these reconstructions can be computationally taxing. Many in the field are searching for solutions which are more computationally efficient and theoretical guarantees for the minimal amount of information for reconstructions within a given tolerance of error.Our approach is to study TDA on voxel data to offer both a computationally and memory efficient solution in practice. Assuming a lattice structure for our cubical geometric realization we are able to prove a sharp upper bound for all dimensions of 2d for the number of persistence diagrams generated from sublevel set filtrations required to reconstruct grayscale digital images. By improving topological reconstructions, the authors believe that TDA may become a pragmatic tool to apply to computerized tomography images for both storage and potentially classification for automated diagnosis of particular diseases such as melanoma.},
-  file     = {:DirectionalTransform/Betthauser2018.pdf:PDF},
-  isbn     = {9798837539299},
-  journal  = {ProQuest Dissertations and Theses},
-  keywords = {Topological data analysis; Shape reconstruction of compact manifolds; Classification problems; Voxel data; Mathematics; Applied mathematics; Computer science; Bioinformatics; Information science; 0364:Applied Mathematics; 0723:Information science; 0405:Mathematics; 0715:Bioinformatics; 0984:Computer science},
-  language = {English},
-  pages    = {74},
-  url      = {http://ezproxy.msu.edu/login?url=https://www.proquest.com/dissertations-theses/topological-reconstruction-grayscale-images/docview/2691763884/se-2},
-}
-
-@Article{Crawford2019,
+@article{Crawford2019,
   author    = {Lorin Crawford and Anthea Monod and Andrew X. Chen and Sayan Mukherjee and Ra{\'{u}}l Rabad{\'{a}}n},
   journal   = {Journal of the American Statistical Association},
   title     = {Predicting Clinical Outcomes in Glioblastoma: An Application of Topological and Functional Data Analysis},
@@ -733,145 +79,10 @@ @Article{Crawford2019
   volume    = {115},
   doi       = {10.1080/01621459.2019.1671198},
   file      = {:DirectionalTransform/Crawford2019.pdf:PDF},
-  publisher = {Informa {UK} Limited},
-}
-
-@Article{Fasy2019,
-  author        = {Fasy, Brittany Terese and Micka, Samuel and Millman, David L. and Schenfisch, Anna and Williams, Lucia},
-  journal       = {arXiv:1912.12759},
-  title         = {A Faithful Discretization of the Augmented Persistent Homology Transform},
-  year          = {2019},
-  month         = {Dec},
-  abstract      = {The persistent homology transform (PHT) represents a shape with a multiset of persistence diagrams parameterized by the sphere of directions in the ambient space. In this work, we describe a finite set of diagrams that discretize the PHT such that it faithfully represents the underlying shape. We provide a discretization that is exponential in the dimension of the shape (making it Furthermore, we provide an output-sensitive algorithm; that is, the algorithm reports the discretization in time proportional to the size of the discretization. Finally, our approach relies only on knowing the heights and dimensions of topological events, meaning that it can be adapted to provide discretizations of other dimension-returning topological transforms, including the Betti curve transform.},
-  archiveprefix = {arXiv},
-  copyright     = {arXiv.org perpetual, non-exclusive license},
-  doi           = {10.48550/ARXIV.1912.12759},
-  eprint        = {1912.12759},
-  file          = {:Fasy2019 - A Faithful Discretization of the Augmented Persistent Homology Transform.pdf:PDF:http\://arxiv.org/pdf/1912.12759v4;:DirectionalTransform/Fasy2019.pdf:PDF},
-  keywords      = {Computational Geometry (cs.CG), FOS: Computer and information sciences},
-  primaryclass  = {cs.CG},
-  publisher     = {arXiv},
-}
-
-@InProceedings{Jiang2020,
-  author    = {Jiang, Qitong and Kurtek, Sebastian and Needham, Tom},
-  booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops},
-  title     = {The Weighted {E}uler Curve Transform for Shape and Image Analysis},
-  year      = {2020},
-  month     = {June},
-  file      = {:DirectionalTransform/Jiang2020.pdf:PDF},
-}
-
-@PhdThesis{Micka2020,
-  author   = {Micka,Samuel A.},
-  title    = {Searching and Reconstruction: Algorithms with Topological Descriptors},
-  year     = {2020},
-  abstract = {Topological data analysis and, more specifically, persistent homology have received significant attention as a method of describing the shape of complex data. Persistent homology measures the persistence (i.e., "relative size'') of topological features such as connected components, holes, voids, etc. as a space is filtered. The persistence is often plotted in what is referred to as a persistence diagram. Persistence diagrams encode both topological and geometric information about shapes. Moreover, certain parameterized sets of persistence diagrams are sufficient for representing particular classes of shapes. In other words, a set of persistence diagrams can be substituted for the shape. Shape representation using persistence diagrams has shown promise in several learning and classification tasks on shape data. However, choosing a sufficient parameterized set of persistence diagrams is challenging. Previous solutions utilize exhaustive sampling approaches based on assumptions on the geometry of the shape and algebraic results. We consider the inverse problem of "reconstructing'' the shape, using (augmented) persistence diagrams. Developing algorithms for reconstruction provides an alternative method of finding descriptors for representation that is optimized to minimize the number of diagrams and time complexity. In this work, we provide deterministic algorithms for reconstructing simplicial complexes in R^d and discuss challenges in reconstruction using other topological descriptors.Shape reconstruction, and several other areas of research utilizing the persistence diagram, are predisposed to generating large numbers of diagrams. As such, developing efficient methods for searching in the space of persistence diagrams is also of great importance. We consider the bottleneck distance in the space of persistence diagrams. The bottleneck distance is used often in practice for comparing one diagram to another. However, the cost of computing the bottleneck distance can grow prohibitive for large sets of diagrams using a brute-force approach. We offer a data structure and algorithm for identifying the approximate nearest neighbor (and approximate k-nearest neighbors) in the space of persistence diagrams in less time than the brute-force approach for large sets of diagrams.},
-  file     = {:DirectionalTransform/Micka2020-MickaThesis.pdf:PDF},
-  isbn     = {9798643180715},
-  journal  = {ProQuest Dissertations and Theses},
-  keywords = {Algorithms; Bottleneck distance; Montana State University; Nearest neighbor; Persistence diagram search; Shape reconstruction; Computer science; 0984:Computer science},
-  language = {English},
-  pages    = {169},
-  url      = {http://ezproxy.msu.edu/login?url=https://www.proquest.com/dissertations-theses/searching-reconstruction-algorithms-with/docview/2404677419/se-2},
-}
-
-@Article{Belton2020,
-  author    = {Robin Lynne Belton and Brittany Terese Fasy and Rostik Mertz and Samuel Micka and David L. Millman and Daniel Salinas and Anna Schenfisch and Jordan Schupbach and Lucia Williams},
-  journal   = {Computational Geometry},
-  title     = {Reconstructing embedded graphs from persistence diagrams},
-  year      = {2020},
-  month     = {Oct},
-  pages     = {101658},
-  volume    = {90},
-  abstract  = {The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space. Recent work has shown that well-chosen (finite) sets of PDs can differentiate between geometric simplicial complexes, providing a method for representing complex shapes using a finite set of descriptors. A related inverse problem is the following: given a set of PDs (or an oracle we can query for persistence diagrams), what is underlying geometric simplicial complex? In this paper, we present an algorithm for reconstructing embedded graphs in $\mathbb{R}^d$ (plane graphs in $\mathbb{R}^2$) with $n$ vertices from $n^2 - n + d + 1$ directional (augmented) PDs. Additionally, we empirically validate the correctness and time-complexity of our algorithm in $\mathbb{R}^2$ on randomly generated plane graphs using our implementation, and explain the numerical limitations of implementing our algorithm.},
-  doi       = {10.1016/j.comgeo.2020.101658},
-  file      = {:DirectionalTransform/Belton2019a.pdf:PDF;:Belton2020 - Reconstructing Embedded Graphs from Persistence Diagrams.pdf:PDF:http\://arxiv.org/pdf/1912.08913v2;:DirectionalTransform/Belton2020.pdf:PDF},
-  publisher = {Elsevier {BV}},
-}
-
-@Article{Amezquita2021,
-  author    = {Erik J Am{\'{e}}zquita and Michelle Y Quigley and Tim Ophelders and Jacob B Landis and Daniel Koenig and Elizabeth Munch and Daniel H Chitwood},
-  journal   = {in silico Plants},
-  title     = {Measuring hidden phenotype: quantifying the shape of barley seeds using the {E}uler characteristic transform},
-  year      = {2021},
-  month     = {Dec},
-  number    = {1},
-  volume    = {4},
-  doi       = {10.1093/insilicoplants/diab033},
-  editor    = {Tsu-Wei Chen and Stephen P Long},
-  file      = {:DirectionalTransform/Amezquita2021a.pdf:PDF},
-  publisher = {Oxford University Press ({OUP})},
-}
-
-@Article{Wang2021,
-  author    = {Bruce Wang and Timothy Sudijono and Henry Kirveslahti and Tingran Gao and Douglas M. Boyer and Sayan Mukherjee and Lorin Crawford},
-  journal   = {The Annals of Applied Statistics},
-  title     = {A statistical pipeline for identifying physical features that differentiate classes of 3D shapes},
-  year      = {2021},
-  month     = {jun},
-  number    = {2},
-  volume    = {15},
-  doi       = {10.1214/20-aoas1430},
-  file      = {:DirectionalTransform/Wang2021a.pdf:PDF},
-  publisher = {Institute of Mathematical Statistics},
-}
-
-@Article{Johnson2021,
-  author        = {Johnson, Megan and Jung, Jae-Hun},
-  journal       = {Journal of the Korean Society for Industrial and Applied Mathematics},
-  title         = {Instability of the Betti Sequence for Persistent Homology and a Stabilized Version of the Betti Sequence},
-  year          = {2021},
-  number        = {4},
-  volume        = {25},
-  abstract      = {Topological Data Analysis (TDA), a relatively new field of data analysis, has proved very useful in a variety of applications. The main persistence tool from TDA is persistent homology in which data structure is examined at many scales. Representations of persistent homology include persistence barcodes and persistence diagrams, both of which are not straightforward to reconcile with traditional machine learning algorithms as they are sets of intervals or multisets. The problem of faithfully representing barcodes and persistent diagrams has been pursued along two main avenues: kernel methods and vectorizations. One vectorization is the Betti sequence, or Betti curve, derived from the persistence barcode. While the Betti sequence has been used in classification problems in various applications, to our knowledge, the stability of the sequence has never before been discussed. In this paper we show that the Betti sequence is unstable under the 1-Wasserstein metric with regards to small perturbations in the barcode from which it is calculated. In addition, we propose a novel stabilized version of the Betti sequence based on the Gaussian smoothing seen in the Stable Persistence Bag of Words for persistent homology. We then introduce the normalized cumulative Betti sequence and provide numerical examples that support the main statement of the paper.},
-  archiveprefix = {arXiv},
-  comment       = {Published website is rather sketchy},
-  copyright     = {Creative Commons Attribution 4.0 International},
-  doi           = {10.12941/jksiam.2021.25.296},
-  eprint        = {2109.09218},
-  file          = {:Johnson2021 - Instability of the Betti Sequence for Persistent Homology and a Stabilized Version of the Betti Sequence.pdf:PDF:http\://arxiv.org/pdf/2109.09218v1;:DirectionalTransform/Johnson2021.pdf:PDF},
-  keywords      = {Algebraic Topology (math.AT), Computational Geometry (cs.CG), Numerical Analysis (math.NA), FOS: Mathematics, FOS: Computer and information sciences, 54-08},
-  primaryclass  = {math.AT},
-  publisher     = {arXiv},
-}
-
-@Article{Curry2022,
-  author        = {Justin Curry and Sayan Mukherjee and Katharine Turner},
-  journal       = {Transactions of the American Mathematical Society, Series B},
-  title         = {How Many Directions Determine a Shape and other Sufficiency Results for Two Topological Transforms},
-  year          = {2022},
-  month         = {Oct},
-  number        = {32},
-  pages         = {1006--1043},
-  volume        = {9},
-  abstract      = {In this paper we consider two topological transforms based on Euler calculus: the persistent homology transform (PHT) and the Euler characteristic transform (ECT). Both of these transforms are of interest for their mathematical properties as well as their applications to science and engineering, because they provide a way of summarizing shapes in a topological, yet quantitative, way. Both transforms take a shape, viewed as a tame subset M of R^d, and associates to each direction v in S^{d-1} a shape summary obtained by scanning M in the direction v. These shape summaries are either persistence diagrams or piecewise constant integer valued functions called Euler curves. By using an inversion theorem of Schapira, we show that both transforms are injective on the space of shapes---each shape has a unique transform. By making use of a stratified space structure on the sphere, induced by hyperplane divisions, we prove additional uniqueness results in terms of distributions on the space of Euler curves. Finally, our main result provides the first (to our knowledge) finite bound required to specify any shape in certain uncountable families of shapes, bounded below by curvature. This result is perhaps best appreciated in terms of shattering number or the perspective that any point in these particular moduli spaces of shapes is indexed using a tree of finite depth.},
-  archiveprefix = {arXiv},
-  date          = {2018-05-24},
-  doi           = {10.1090/btran/122},
-  eprint        = {1805.09782v1},
-  file          = {:Persistence/PersHomTransform/Curry2018.pdf:PDF;:Curry2022 - How Many Directions Determine a Shape and Other Sufficiency Results for Two Topological Transforms.pdf:PDF:http\://arxiv.org/pdf/1805.09782v1;:DirectionalTransform/Curry2018-arxiv-v2.pdf:PDF},
-  keywords      = {math.AT, math.ST, stat.TH},
-  primaryclass  = {math.AT},
-  publisher     = {American Mathematical Society ({AMS})},
-}
-
-@Article{Tang2022,
-  author    = {Wai Shing Tang and Gabriel Monteiro da Silva and Henry Kirveslahti and Erin Skeens and Bibo Feng and Timothy Sudijono and Kevin K. Yang and Sayan Mukherjee and Brenda Rubenstein and Lorin Crawford},
-  journal   = {{PLOS} Computational Biology},
-  title     = {A topological data analytic approach for discovering biophysical signatures in protein dynamics},
-  year      = {2022},
-  month     = {may},
-  number    = {5},
-  pages     = {e1010045},
-  volume    = {18},
-  doi       = {10.1371/journal.pcbi.1010045},
-  editor    = {Petras J Kundrotas},
-  file      = {:DirectionalTransform/Tang2022.pdf:PDF},
-  publisher = {Public Library of Science ({PLoS})},
+  publisher = {Informa {UK} Limited}
 }
 
-@Article{Meng2022,
+@article{Meng2022,
   author        = {Meng, Kun and Wang, Jinyu and Crawford, Lorin and Eloyan, Ani},
   journal       = {arXiv:2204.12699},
   title         = {Randomness and Statistical Inference of Shapes via the Smooth {E}uler Characteristic Transform},
@@ -885,351 +96,10 @@ @Article{Meng2022
   file          = {:Meng2022 - Randomness and Statistical Inference of Shapes Via the Smooth Euler Characteristic Transform.pdf:PDF:http\://arxiv.org/pdf/2204.12699v2;:DirectionalTransform/Meng2022.pdf:PDF},
   keywords      = {Methodology (stat.ME), FOS: Computer and information sciences},
   primaryclass  = {stat.ME},
-  publisher     = {arXiv},
-}
-
-@Article{Turner2022,
-  author        = {Turner, Katharine and Robins, Vanessa and Morgan, James},
-  journal       = {arXiv:2208.14583},
-  title         = {The Extended Persistent Homology Transform of manifolds with boundary},
-  year          = {2022},
-  month         = aug,
-  abstract      = {The Extended Persistent Homology Transform (XPHT) is a topological transform which takes as input a shape embedded in Euclidean space, and to each unit vector assigns the extended persistence module of the height function over that shape with respect to that direction. We can define a distance between two shapes by integrating over the sphere the distance between their respective extended persistence modules. By using extended persistence we get finite distances between shapes even when they have different Betti numbers. We use Morse theory to show that the extended persistence of a height function over a manifold with boundary can be deduced from the extended persistence for that height function restricted to the boundary, alongside labels on the critical points as positive or negative critical. We study the application of the XPHT to binary images; outlining an algorithm for efficient calculation of the XPHT exploiting relationships between the PHT of the boundary curves to the extended persistence of the foreground.},
-  archiveprefix = {arXiv},
-  copyright     = {Creative Commons Attribution 4.0 International},
-  doi           = {10.48550/ARXIV.2208.14583},
-  eprint        = {2208.14583},
-  file          = {:Turner2022 - The Extended Persistent Homology Transform of Manifolds with Boundary.pdf:PDF:http\://arxiv.org/pdf/2208.14583v1;:DirectionalTransform/Turner2022.pdf:PDF},
-  keywords      = {Algebraic Topology (math.AT), FOS: Mathematics, 55N31},
-  primaryclass  = {math.AT},
-  publisher     = {arXiv},
-}
-
-@Article{Dlotko2022,
-  author        = {Dłotko, Paweł and Gurnari, Davide},
-  journal       = {arXiv:2212.01666},
-  title         = {{E}uler Characteristic Curves and Profiles: a stable shape invariant for big data problems},
-  year          = {2022},
-  month         = {Dec},
-  abstract      = {Tools of Topological Data Analysis provide stable summaries encapsulating the shape of the considered data. Persistent homology, the most standard and well studied data summary, suffers a number of limitations; its computations are hard to distribute, it is hard to generalize to multifiltrations and is computationally prohibitive for big data-sets. In this paper we study the concept of Euler Characteristics Curves, for one parameter filtrations and Euler Characteristic Profiles, for multi-parameter filtrations. While being a weaker invariant in one dimension, we show that Euler Characteristic based approaches do not possess some handicaps of persistent homology; we show efficient algorithms to compute them in a distributed way, their generalization to multifiltrations and practical applicability for big data problems. In addition we show that the Euler Curves and Profiles enjoys certain type of stability which makes them robust tool in data analysis. Lastly, to show their practical applicability, multiple use-cases are considered.},
-  archiveprefix = {arXiv},
-  copyright     = {arXiv.org perpetual, non-exclusive license},
-  doi           = {10.48550/ARXIV.2212.01666},
-  eprint        = {2212.01666},
-  file          = {:Dlotko2022 - Euler Characteristic Curves and Profiles_ a Stable Shape Invariant for Big Data Problems.pdf:PDF:http\://arxiv.org/pdf/2212.01666v1;:DirectionalTransform/Dlotko2022.pdf:PDF},
-  keywords      = {Algebraic Topology (math.AT), Computational Geometry (cs.CG), Machine Learning (cs.LG), FOS: Mathematics, FOS: Computer and information sciences},
-  primaryclass  = {math.AT},
-  publisher     = {arXiv},
-}
-
-@Article{Wang2022,
-  author        = {Wang, Fan and Wagner, Hubert and Chen, Chao},
-  journal       = {arXiv:2203.09087},
-  title         = {GPU Computation of the {E}uler Characteristic Curve for Imaging Data},
-  year          = {2022},
-  month         = mar,
-  abstract      = {Persistent homology is perhaps the most popular and useful tool offered by topological data analysis, with point-cloud data being the most common setup. Its older cousin, the Euler characteristic curve (ECC) is less expressive, but far easier to compute. It is particularly suitable for analyzing imaging data, and is commonly used in fields ranging from astrophysics to biomedical image analysis. These fields are embracing GPU computations to handle increasingly large datasets. We therefore propose an optimized GPU implementation of ECC computation for 2D and 3D grayscale images. The goal of this paper is twofold. First, we offer a practical tool, illustrating its performance with thorough experimentation, but also explain its inherent shortcomings. Second, this simple algorithm serves as a perfect backdrop for highlighting basic GPU programming techniques that make our implementation so efficient, and some common pitfalls we avoided. This is intended as a step towards a wider usage of GPU programming in computational geometry and topology software. We find this is particularly important as geometric and topological tools are used in conjunction with modern, GPU-accelerated machine learning frameworks.},
-  archiveprefix = {arXiv},
-  copyright     = {Creative Commons Attribution Non Commercial No Derivatives 4.0 International},
-  doi           = {10.48550/ARXIV.2203.09087},
-  eprint        = {2203.09087},
-  file          = {:Wang2022 - GPU Computation of the Euler Characteristic Curve for Imaging Data.pdf:PDF:http\://arxiv.org/pdf/2203.09087v2;:DirectionalTransform/Wang2022.pdf:PDF},
-  keywords      = {Computational Geometry (cs.CG), FOS: Computer and information sciences},
-  primaryclass  = {cs.CG},
-  publisher     = {arXiv},
-}
-
-@Article{Perez2022,
-  author        = {Perez, Daniel},
-  title         = {{E}uler and {B}etti curves are stable under Wasserstein deformations of distributions of stochastic processes},
-  year          = {2022},
-  month         = nov,
-  abstract      = {Euler and Betti curves of stochastic processes defined on a $d$-dimensional compact Riemannian manifold which are almost surely in a Sobolev space $W^{n,s}(X,\mathbb{R})$ (with $d<n$) are stable under perturbations of the distributions of said processes in a Wasserstein metric. Moreover, Wasserstein stability is shown to hold for all $p>\frac{d}{n}$ for persistence diagrams stemming from functions in $W^{n,s}(X,\mathbb{R})$.},
-  archiveprefix = {arXiv},
-  copyright     = {Creative Commons Attribution 4.0 International},
-  doi           = {10.48550/ARXIV.2211.12384},
-  eprint        = {2211.12384},
-  file          = {:Perez2022 - Euler and Betti Curves Are Stable under Wasserstein Deformations of Distributions of Stochastic Processes.pdf:PDF:http\://arxiv.org/pdf/2211.12384v1;:DirectionalTransform/Perez2022.pdf:PDF},
-  keywords      = {Probability (math.PR), Algebraic Topology (math.AT), FOS: Mathematics, 60G60, 62M40, 55N31},
-  primaryclass  = {math.PR},
-  publisher     = {arXiv},
-}
-
-@Article{Marsh2023,
-  author        = {Marsh, Lewis and Beers, David},
-  journal       = {arXiv:2303.13200},
-  title         = {Stability and Inference of the {E}uler Characteristic Transform},
-  year          = {2023},
-  month         = mar,
-  abstract      = {The Euler characteristic transform (ECT) is a signature from topological data analysis (TDA) which summarises shapes embedded in Euclidean space. Compared with other TDA methods, the ECT is fast to compute and it is a sufficient statistic for a broad class of shapes. However, small perturbations of a shape can lead to large distortions in its ECT. In this paper, we propose a new metric on compact one-dimensional shapes and prove that the ECT is stable with respect to this metric. Crucially, our result uses curvature, rather than the size of a triangulation of an underlying shape, to control stability. We further construct a computationally tractable statistical estimator of the ECT based on the theory of Gaussian processes. We use our stability result to prove that our estimator is consistent on shapes perturbed by independent ambient noise; i.e., the estimator converges to the true ECT as the sample size increases.},
-  archiveprefix = {arXiv},
-  copyright     = {Creative Commons Attribution 4.0 International},
-  doi           = {10.48550/ARXIV.2303.13200},
-  eprint        = {2303.13200},
-  file          = {:Marsh2023 - Stability and Inference of the Euler Characteristic Transform.pdf:PDF:http\://arxiv.org/pdf/2303.13200v1;:DirectionalTransform/Marsh2023.pdf:PDF},
-  keywords      = {Statistics Theory (math.ST), Algebraic Topology (math.AT), FOS: Mathematics},
-  primaryclass  = {math.ST},
-  publisher     = {arXiv},
-}
-
-@Article{Paik2023,
-  author        = {Paik, Taejin},
-  journal       = {arXiv:2302.13565},
-  title         = {Invariant Representations of Embedded Simplicial Complexes},
-  year          = {2023},
-  month         = feb,
-  abstract      = {Analyzing embedded simplicial complexes, such as triangular meshes and graphs, is an important problem in many fields. We propose a new approach for analyzing embedded simplicial complexes in a subdivision-invariant and isometry-invariant way using only topological and geometric information. Our approach is based on creating and analyzing sufficient statistics and uses a graph neural network. We demonstrate the effectiveness of our approach using a synthetic mesh data set.},
-  archiveprefix = {arXiv},
-  copyright     = {Creative Commons Attribution 4.0 International},
-  doi           = {10.48550/ARXIV.2302.13565},
-  eprint        = {2302.13565},
-  file          = {:Paik2023 - Invariant Representations of Embedded Simplicial Complexes.pdf:PDF:http\://arxiv.org/pdf/2302.13565v1;:DirectionalTransform/Paik2023.pdf:PDF},
-  keywords      = {Machine Learning (cs.LG), Artificial Intelligence (cs.AI), Computational Geometry (cs.CG), Algebraic Topology (math.AT), FOS: Computer and information sciences, FOS: Mathematics, I.2.6; I.5.1; I.5.2, 68T07, 55N31},
-  primaryclass  = {cs.LG},
-  publisher     = {arXiv},
+  publisher     = {arXiv}
 }
 
-@Article{Fasy2022,
-  author        = {Fasy, Brittany Terese and Patel, Amit},
-  title         = {Persistent Homology Transform Cosheaf},
-  year          = {2022},
-  month         = aug,
-  abstract      = {We employ the recent discovery of functoriality for persistent homology to recast the Persistent Homology Transform of a geometric complex as a cosheaf of combinatorial persistence diagrams. Detailed examples are provided. We hope the recasting of the PH transform as a cellular cosheaf will allow for the adoption of existing methods from category theory and (co)sheaf theory to the study of shapes.},
-  archiveprefix = {arXiv},
-  copyright     = {Creative Commons Attribution 4.0 International},
-  doi           = {10.48550/ARXIV.2208.05243},
-  eprint        = {2208.05243},
-  file          = {:Fasy2022 - Persistent Homology Transform Cosheaf.pdf:PDF:http\://arxiv.org/pdf/2208.05243v1},
-  keywords      = {Algebraic Topology (math.AT), Computational Geometry (cs.CG), Category Theory (math.CT), FOS: Mathematics, FOS: Computer and information sciences},
-  primaryclass  = {math.AT},
-  publisher     = {arXiv},
-}
-
-@Article{Amezquita2020,
-  author            = {Erik J. Am{\'{e}}zquita and Michelle Y. Quigley and Tim Ophelders and Elizabeth Munch and Daniel H. Chitwood},
-  journal           = {Developmental Dynamics},
-  title             = {The shape of things to come: Topological data analysis and biology, from molecules to organisms},
-  year              = {2020},
-  month             = {Apr},
-  authorwithsymbols = {Erik J. Am{\'{e}}zquita$^\dagger$ and Michelle Y. Quigley and Tim Ophelders and Elizabeth Munch and Daniel H. Chitwood},
-  comment           = {CCF-1907591, CMMI-1800466;},
-  creationdate      = {2020-06-28T00:00:00},
-  doi               = {10.1002/dvdy.175},
-  image             = {Amezquita2020_PlantScans.png},
-  keywords          = {journal},
-  publisher         = {Wiley},
-}
-
-@Book{Friedman2018,
-  author    = {Michael Friedman},
-  publisher = {Springer International Publishing},
-  title     = {A History of Folding in Mathematics},
-  year      = {2018},
-  doi       = {10.1007/978-3-319-72487-4},
-}
-
-@Article{Euler1758,
-  author  = {Euler, Leonhard},
-  journal = {Euler Archive - All Works},
-  title   = {Elementa doctrinae solidorum},
-  year    = {1758},
-  file    = {:DirectionalTransform/Euler1758.pdf:PDF},
-}
-
-@Book{Dries1998,
-  author    = {L. P. D. van den Dries},
-  publisher = {Cambridge University Press},
-  title     = {Tame Topology and {O}-minimal Structures},
-  year      = {1998},
-  month     = {may},
-  doi       = {10.1017/cbo9780511525919},
-}
-
-@Article{White2020,
-  author    = {Alexander E. White and Rebecca B. Dikow and Makinnon Baugh and Abigail Jenkins and Paul B. Frandsen},
-  journal   = {Applications in Plant Sciences},
-  title     = {Generating segmentation masks of herbarium specimens and a data set for training segmentation models using deep learning},
-  year      = {2020},
-  month     = {jun},
-  number    = {6},
-  volume    = {8},
-  doi       = {10.1002/aps3.11352},
-  publisher = {Wiley},
-}
-
-@Book{Gower2004,
-  author    = {John C Gower and Garmt B Dijksterhuis},
-  publisher = {Oxford University Press},
-  title     = {Procrustes Problems},
-  year      = {2004},
-  month     = {jan},
-  doi       = {10.1093/acprof:oso/9780198510581.001.0001},
-}
-
-@Article{Marsh2022,
-  author        = {Marsh, Lewis and Zhou, Felix Y. and Qin, Xiao and Lu, Xin and Byrne, Helen M. and Harrington, Heather A.},
-  journal       = {arXiv:2212.10883},
-  title         = {Detecting Temporal shape changes with the {E}uler Characteristic Transform},
-  year          = {2022},
-  month         = {Dec},
-  abstract      = {Organoids are multi-cellular structures which are cultured in vitro from stem cells to resemble specific organs (e.g., brain, liver) in their three-dimensional composition. Dynamic changes in the shape and composition of these model systems can be used to understand the effect of mutations and treatments in health and disease. In this paper, we propose a new technique in the field of topological data analysis for DEtecting Temporal shape changes with the Euler Characteristic Transform (DETECT). DETECT is a rotationally invariant signature of dynamically changing shapes. We demonstrate our method on a data set of segmented videos of mouse small intestine organoid experiments and show that it outperforms classical shape descriptors. We verify our method on a synthetic organoid data set and illustrate how it generalises to 3D. We conclude that DETECT offers rigorous quantification of organoids and opens up computationally scalable methods for distinguishing different growth regimes and assessing treatment effects.},
-  archiveprefix = {arXiv},
-  copyright     = {Creative Commons Attribution 4.0 International},
-  doi           = {10.48550/ARXIV.2212.10883},
-  eprint        = {2212.10883},
-  file          = {:Marsh2022 - Detecting Temporal Shape Changes with the Euler Characteristic Transform.pdf:PDF:http\://arxiv.org/pdf/2212.10883v2;:TOREVIEW/TRMA/TRMA-2022-011_Proof_hi.pdf:PDF},
-  keywords      = {Quantitative Methods (q-bio.QM), Algebraic Topology (math.AT), Tissues and Organs (q-bio.TO), FOS: Biological sciences, FOS: Mathematics},
-  primaryclass  = {q-bio.QM},
-  publisher     = {arXiv},
-}
-
-@Article{Roy2020,
-  author    = {A. Roy and R. A. I. Haque and A. J. Mitra and M. Dutta Choudhury and S. Tarafdar and T. Dutta},
-  journal   = {Physics of Fluids},
-  title     = {Understanding flow features in drying droplets via {E}uler characteristic surfaces{\textemdash}A topological tool},
-  year      = {2020},
-  month     = {Dec},
-  number    = {12},
-  pages     = {123310},
-  volume    = {32},
-  doi       = {10.1063/5.0026807},
-  publisher = {{AIP} Publishing},
-}
-
-@Article{Fasy2022a,
-  author        = {Fasy, Brittany Terese and Micka, Samuel and Millman, David L. and Schenfisch, Anna and Williams, Lucia},
-  title         = {Efficient Graph Reconstruction and Representation Using Augmented Persistence Diagrams},
-  year          = {2022},
-  month         = {Dec},
-  abstract      = {Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of persistence diagrams, parameterized by directions in the ambient space. A recent advance in understanding the PHT used the framework of reconstruction in order to find finite a set of directions to faithfully represent the shape, a result that is of both theoretical and practical interest. In this paper, we improve upon this result and present an improved algorithm for graph -- and, more generally one-skeleton -- reconstruction. The improvement comes in reconstructing the edges, where we use a radial binary (multi-)search. The binary search employed takes advantage of the fact that the edges can be ordered radially with respect to a reference plane, a feature unique to graphs.},
-  archiveprefix = {arXiv},
-  copyright     = {Creative Commons Attribution 4.0 International},
-  doi           = {10.48550/ARXIV.2212.13206},
-  eprint        = {2212.13206},
-  file          = {:Fasy2022a - Efficient Graph Reconstruction and Representation Using Augmented Persistence Diagrams.pdf:PDF:http\://arxiv.org/pdf/2212.13206v1;:DirectionalTransform/Fasy2022.pdf:PDF},
-  keywords      = {Computational Geometry (cs.CG), FOS: Computer and information sciences},
-  primaryclass  = {cs.CG},
-  publisher     = {arXiv},
-}
-
-@InCollection{Cates2017,
-  author    = {Joshua Cates and Shireen Elhabian and Ross Whitaker},
-  booktitle = {Statistical Shape and Deformation Analysis},
-  publisher = {Elsevier},
-  title     = {{ShapeWorks}},
-  year      = {2017},
-  pages     = {257--298},
-  doi       = {10.1016/b978-0-12-810493-4.00012-2},
-}
-
-@Article{Dupuis1998,
-  author    = {Paul Dupuis and Ulf Grenander and Michael I. Miller},
-  journal   = {Quarterly of Applied Mathematics},
-  title     = {Variational problems on flows of diffeomorphisms for image matching},
-  year      = {1998},
-  number    = {3},
-  pages     = {587--600},
-  volume    = {56},
-  doi       = {10.1090/qam/1632326},
-  publisher = {American Mathematical Society ({AMS})},
-}
-
-@Article{Gao2019,
-  author    = {Tingran Gao and Shahar Z. Kovalsky and Ingrid Daubechies},
-  journal   = {{SIAM} Journal on Mathematics of Data Science},
-  title     = {Gaussian Process Landmarking on Manifolds},
-  year      = {2019},
-  month     = {jan},
-  number    = {1},
-  pages     = {208--236},
-  volume    = {1},
-  doi       = {10.1137/18m1184035},
-  publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})},
-}
-
-@Article{Boyer2011,
-  author    = {Doug M. Boyer and Yaron Lipman and Elizabeth St. Clair and Jesus Puente and Biren A. Patel and Thomas Funkhouser and Jukka Jernvall and Ingrid Daubechies},
-  journal   = {Proceedings of the National Academy of Sciences},
-  title     = {Algorithms to automatically quantify the geometric similarity of anatomical surfaces},
-  year      = {2011},
-  month     = {Oct},
-  number    = {45},
-  pages     = {18221--18226},
-  volume    = {108},
-  doi       = {10.1073/pnas.1112822108},
-  publisher = {Proceedings of the National Academy of Sciences},
-}
-
-@Article{Wang2023,
-  author  = {Elena Wang and Elizabeth Munch and Erin Chambers},
-  journal = {In progress},
-  title   = {A Distance for Geometric Graphs via the Labeled Merge Tree Interleaving Distance},
-  year    = {2023},
-}
-
-@Article{Beltramo2022,
-  author    = {Gabriele Beltramo and Primoz Skraba and Rayna Andreeva and Rik Sarkar and Ylenia Giarratano and Miguel O. Bernabeu},
-  journal   = {Foundations of Data Science},
-  title     = {{E}uler characteristic surfaces},
-  year      = {2022},
-  number    = {4},
-  pages     = {505--536},
-  volume    = {4},
-  doi       = {10.3934/fods.2021027},
-  file      = {:DirectionalTransform/Beltramo2022.pdf:PDF},
-  publisher = {American Institute of Mathematical Sciences ({AIMS})},
-}
-
-@InProceedings{Nadimpalli2023,
-  author        = {Nadimpalli, Kalyan Varma and Chattopadhyay, Amit and Rieck, Bastian},
-  booktitle     = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops},
-  title         = {Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images From Single 2D Slices},
-  year          = {2023},
-  month         = {June},
-  pages         = {571-579},
-  publisher     = {arXiv},
-  abstract      = {The computer vision task of reconstructing 3D images, i.e., shapes, from their single 2D image slices is extremely challenging, more so in the regime of limited data. Deep learning models typically optimize geometric loss functions, which may lead to poor reconstructions as they ignore the structural properties of the shape. To tackle this, we propose a novel topological loss function based on the Euler Characteristic Transform. This loss can be used as an inductive bias to aid the optimization of any neural network toward better reconstructions in the regime of limited data. We show the effectiveness of the proposed loss function by incorporating it into SHAPR, a state-of-the-art shape reconstruction model, and test it on two benchmark datasets, viz., Red Blood Cells and Nuclei datasets. We also show a favourable property, namely injectivity and discuss the stability of the topological loss function based on the Euler Characteristic Transform.},
-  archiveprefix = {arXiv},
-  copyright     = {Creative Commons Attribution Non Commercial Share Alike 4.0 International},
-  doi           = {10.48550/ARXIV.2303.05286},
-  eprint        = {2303.05286},
-  file          = {:http\://arxiv.org/pdf/2303.05286v1:PDF;:DirectionalTransform/Nadimpalli2023.pdf:PDF},
-  journal       = {arXiv:2303.05286},
-  keywords      = {Machine Learning (cs.LG), Quantitative Methods (q-bio.QM), FOS: Computer and information sciences, FOS: Biological sciences},
-  primaryclass  = {cs.LG},
-}
-
-@Article{Kirveslahti2023,
-  author        = {Kirveslahti, Henry and Mukherjee, Sayan},
-  journal       = {Journal of Applied and Computational Topology},
-  title         = {Representing fields without correspondences: the lifted {E}uler characteristic transform},
-  year          = {2023},
-  issn          = {2367-1734},
-  month         = aug,
-  abstract      = {Topological transforms have been very useful in statistical analysis of shapes or surfaces without restrictions that the shapes are diffeomorphic and requiring the estimation of correspondence maps. In this paper we introduce two topological transforms that generalize from shapes to fields, $f:\mathbf{R}^3 \rightarrow \mathbf{R}$. Both transforms take a field and associate to each direction $v\in S^{d-1}$ a summary obtained by scanning the field in the direction $v$. The transforms we introduce are of interest for both applications as well as their theoretical properties. The topological transforms for shapes are based on an Euler calculus on sets. A key insight in this paper is that via a lifting argument one can develop an Euler calculus on real valued functions from the standard Euler calculus on sets, this idea is at the heart of the two transforms we introduce. We prove the transforms are injective maps. We show for particular moduli spaces of functions we can upper bound the number of directions needed determine any particular function.},
-  archiveprefix = {arXiv},
-  copyright     = {arXiv.org perpetual, non-exclusive license},
-  doi           = {10.48550/ARXIV.2111.04788},
-  eprint        = {2111.04788},
-  file          = {:http\://arxiv.org/pdf/2111.04788v4:PDF;:DirectionalTransform/Kirveslahti2021.pdf:PDF},
-  keywords      = {Algebraic Topology (math.AT), FOS: Mathematics, 62R40, 52C45 (Primary) 68U05 (Secondary)},
-  primaryclass  = {math.AT},
-  publisher     = {Springer Science and Business Media LLC},
-}
-
-@InCollection{Diaconis2013,
-  author       = {Persi Diaconis and Susan Holmes and Mehrdad Shahshahani},
-  booktitle    = {Advances in Modern Statistical Theory and Applications: A Festschrift in honor of Morris L. Eaton},
-  publisher    = {Institute of Mathematical Statistics},
-  title        = {Sampling from a Manifold},
-  year         = {2013},
-  pages        = {102--125},
-  creationdate = {2017-11-03T00:00:00},
-  doi          = {10.1214/12-imscoll1006},
-  file         = {:Diaconis2013.pdf:PDF},
-}
-
-@Book{Mardia1999,
+@book{Mardia1999,
   author    = {Mardia, Kanti V. and Jupp, Peter E.},
   publisher = {Wiley},
   title     = {Directional Statistics},
@@ -1238,10 +108,10 @@ @Book{Mardia1999
   month     = jan,
   doi       = {10.1002/9780470316979},
   issn      = {1940-6347},
-  journal   = {Wiley Series in Probability and Statistics},
+  journal   = {Wiley Series in Probability and Statistics}
 }
 
-@Article{Wasserman2018,
+@article{Wasserman2018,
   author       = {Larry Wasserman},
   journal      = {Annual Review of Statistics and Its Application},
   title        = {Topological Data Analysis},
@@ -1255,17 +125,17 @@ @Article{Wasserman2018
   file         = {:Persistence/PersistenceSurveys/Wasserman2018.pdf:PDF},
   keywords     = {survey, statistics, persistence},
   priority     = {prio1},
-  publisher    = {Annual Reviews},
+  publisher    = {Annual Reviews}
 }
 
-@Book{Ghrist2014,
+@book{Ghrist2014,
   title    = {Elementary Applied Topology},
   year     = {2014},
   author   = {Robert Ghrist},
-  keywords = {textbook, survey},
+  keywords = {textbook, survey}
 }
 
-@Book{Goodman2018,
+@book{Goodman2018,
   editor    = {Jacob E. Goodman and Joseph O'Rourke and Csaba D. Tóth},
   publisher = {CRC Press},
   title     = {Handbook of discrete and computational geometry},
@@ -1275,32 +145,18 @@ @Book{Goodman2018
   isbn      = {9781351645911},
   series    = {Discrete mathematics and its applications},
   pagetotal = {11928},
-  ppn_gvk   = {1007357088},
+  ppn_gvk   = {1007357088}
 }
 
-@Article{Meng2024,
-  author    = {Meng, Kun and Wang, Jinyu and Crawford, Lorin and Eloyan, Ani},
-  journal   = {Journal of the American Statistical Association},
-  title     = {Randomness of Shapes and Statistical Inference on Shapes via the Smooth Euler Characteristic Transform},
-  year      = {2024},
-  issn      = {1537-274X},
-  month     = may,
-  number    = {549},
-  pages     = {498--510},
-  volume    = {120},
-  doi       = {10.1080/01621459.2024.2353947},
-  publisher = {Informa UK Limited},
-}
-
-@InProceedings{Roell2024,
+@inproceedings{Roell2024,
   author    = {Ernst R{\"o}ell and Bastian Rieck},
   booktitle = {The Twelfth International Conference on Learning Representations},
   title     = {Differentiable Euler Characteristic Transforms for Shape Classification},
   year      = {2024},
-  url       = {https://openreview.net/forum?id=MO632iPq3I},
+  url       = {https://openreview.net/forum?id=MO632iPq3I}
 }
 
-@Article{Rieck2024,
+@article{Rieck2024,
   author        = {Rieck, Bastian},
   title         = {Topology meets Machine Learning: An Introduction using the Euler Characteristic Transform},
   year          = {2024},
@@ -1313,7 +169,5 @@ @Article{Rieck2024
   file          = {:Rieck2024 - Topology Meets Machine Learning_ an Introduction Using the Euler Characteristic Transform.pdf:PDF:http\://arxiv.org/pdf/2410.17760v1;:TOREVIEW/Notices/241007-Rieck-v1.pdf:PDF},
   keywords      = {Machine Learning (cs.LG), Algebraic Topology (math.AT), FOS: Computer and information sciences, FOS: Mathematics, 55N31, 62R40, 68T09},
   primaryclass  = {cs.LG},
-  publisher     = {arXiv},
+  publisher     = {arXiv}
 }
-
-@Comment{jabref-meta: databaseType:bibtex;}

From 6364cf4f2617def05af7814ddac5c981982dfb45 Mon Sep 17 00:00:00 2001
From: yemeen <yemeen.ayub.14@cnu.edu>
Date: Sat, 22 Nov 2025 17:15:59 -0500
Subject: [PATCH 25/25] update readme to reflect new changes

---
 README.md | 42 +++++++++++++++++++++++++++++++++---------
 1 file changed, 33 insertions(+), 9 deletions(-)

diff --git a/README.md b/README.md
index a896676..7e2e497 100644
--- a/README.md
+++ b/README.md
@@ -1,10 +1,16 @@
 # `ect`: A python package for computing the Euler Characteristic Transform
 
-Python computation tools for computing the Euler Characteristic Transform of embedded graphs. 
+Python computation tools for computing the Euler Characteristic Transform of embedded complexes. 
 
 ## Description
 
-Right now, the content includes stuff for doing ECT on graphs embedded in 2D. Eventually the goal is to get voxel versions, higher dimensional simplicial complexes, etc in here.
+The package provides fast tools for computing the Euler Characteristic Transform (ECT) on embedded cell complexes in any ambient dimension. You build a complex (vertices, edges, and optional higher‑dimensional cells), choose a set of directions and thresholds, and compute either the exact ECT or its smoothed/differentiable variants. Results come back as NumPy arrays with metadata, plotting helpers, and distance utilities, making it straightforward to visualize transforms and compare shapes. The core is implemented with NumPy and Numba, with optional validation of geometric and structural constraints when constructing complexes.
+
+- `EmbeddedComplex`: convert point clouds into complexes with vertices, edges, and higher‑dimensional cells with embedded coordinates.
+- `ECT`, `SECT`, `DECT` : ECT calculations along with the smooth and differentiable variants over sampled directions and transforms.
+- `Directions`: uniform, random, or custom directions (angles in 2D; vectors in any dimension)
+- Results as `ECTResult`: behaves like a NumPy array, with plotting and distance helpers
+- Optional geometric/structural validation when building complexes
 
 For more information on the ECT, see:
 
@@ -17,16 +23,12 @@ For more information on the ECT, see:
 - The documentation is available at: [munchlab.github.io/ect](https://munchlab.github.io/ect/)
 - A tutorial jupyter notebook can be found [here](https://munchlab.github.io/ect/notebooks/Tutorial-ECT_for_embedded_graphs.html)
 
-### Dependencies
-
-- `networkx`
-- `numpy`
-- `matplotlib`
-- `numba`
 
 ### Installing
 
-The package can be installed using pip:
+Requires Python 3.10+.
+
+Install from PyPI:
 
 ```{bash}
 pip install ect
@@ -40,6 +42,28 @@ cd ect
 pip install .
 ```
 
+### Quickstart
+
+Compute an ECT for a simple embedded triangle and plot it.
+
+```python
+from ect import ECT, EmbeddedComplex
+
+G = EmbeddedComplex()
+G.add_node("a", [0.0, 0.0])
+G.add_node("b", [1.0, 0.0])
+G.add_node("c", [0.5, 0.8])
+G.add_edge("a", "b")
+G.add_edge("b", "c")
+G.add_edge("c", "a")
+
+ect = ECT(num_dirs=32, num_thresh=128)
+result = ect.calculate(G)
+result.plot()
+```
+
+
+
 ## Authors
 
 This code was written by [Liz Munch](https://elizabethmunch.com/) along with her research group and collaborators. People who have contributed to `ect` include: