PDF III: Medium: Collaborative Research:
Topological Data Analysis for Large Network Visualization

Award Number and Duration

NSF IIS 1513616: September 1, 2015 to August 31, 2019 plus 1-year NCE

NSF IIS 1513651: September 1, 2015 to August 31, 2019

NSF IIS 1650224, 1853956 (REU Supplement)

Point of Contact

Bei Wang
Assistant Professor
School of Computing and Scientific Computing and Imaging Institute
University of Utah
beiwang AT sci.utah.edu
http://www.sci.utah.edu/~beiwang

PI and Co-PIs

Bei Wang (PI)
Assistant Professor
School of Computing and Scientific Computing and Imaging Institute
University of Utah
beiwang AT sci.utah.edu
http://www.sci.utah.edu/~beiwang

Carlos Scheidegger (Co-PI)
Assistant Professor
Department of Computer Science
University of Arizona
cscheid AT email.arizona.edu
https://cscheid.net/

Paul Rosen (Co-PI)
Assistant Professor
Computer Science and Engineering
University of South Florida
prosen AT usf.edu
http://www.cspaul.com/wordpress/

Overview

This project leverages topological methods to develop a new class of data analysis and visualization techniques to understand the structure of networks. Networks are often used in modeling social, biological and technological systems, and capturing relationships among individuals, businesses, and genomic entities. Understanding such large, complex data sources is highly relevant and important in application areas including brain connectomics, epidemiology, law enforcement, public policy and marketing. The proposed research will be evaluated over multiple data sources, including but not limited to large social, communication and brain network datasets. Furthermore, the new approaches developed in this project will be integrated into growing data analysis curricula, shared through developing workshops, and used as topics to continue attracting underrepresented groups into STEM fields and computer science specifically.

The scientific challenges this project addresses are two-fold: how to use topology to extract features from the data; and how to design effective visualizations to communicate these features to domain experts and decision makers. Topological techniques central to this project provide a strong theoretical basis for simplifying and summarizing complex data while still preserving critical underlying structures. They also provide a basis for task-oriented designs that allow us to control the volume of data to be displayed in visualizations, so users can develop faithful mental models of the data, facilitating information discovery. This project focuses on two research agendas. First, it proposes a rich body of topological summarization techniques to extract and preserve important topological features within large-scale graph-structured networks, and to obtain compact and hierarchical representations that are suitable for visual exploration. The feature extracting process captures complex interactions in the system, describes features at all scales, is robust with respect to noise, and has efficient computation. Second, this project proposes designing visualizations that encode the extracted topological structures explicitly, focusing on investigating techniques to fully exploit their properties in the visual metaphors to be developed. This project web site provides additional information and will include access to developed tools and test data sets.

Honors and Awards

Best Paper Award, Rene Corbet, Ulderico Fugacci, Michael Kerber, Claudia Landi, Bei Wang. Shape Modeling International (SMI), 2019.

Honorable Mention in the Computing Research Association (CRA) Outstanding Undergraduate Researchers, Yiliang Shi (Undergraduate RA), 2018.

GEM fellowship award, William Garnes (REU, Undergraduate RA), 2018.

Best Paper Award, Primoz Skraba, Paul Rosen, Bei Wang, Guoning Chen, Harsh Bhatia, Valerio Pascucci. IEEE Pacific Visualization (PacificVis), 2016.

Publications

Papers marked with * use alphabetic ordering of authors.
Students are underlined.
Year 4 (2018 - 2019)
PDF A Kernel for Multi-Parameter Persistent Homology.
René Corbet, Ulderico Fugacci, Michael Kerber, Claudia Landi, Bei Wang.
Shape Modeling International (SMI), 2019.
Computers & Graphics: X, 2(100005), 2019.
arXiv Version: arXiv:1809.10231.
Best Paper Award at SMI 2019!

Persistent Homology Guided Force-Directed Graph Layouts.
Ashley Suh, Mustafa Hajij, Bei Wang, Carlos Scheidegger, Paul Rosen.
IEEE Transactions on Visualization and Computer Graphics (InfoVis 2019), accepted, 2019.
arXiv Version: arXiv:1712.05548.
A Structural Average of Labeled Merge Trees for Uncertainty Visualization.
Lin Yan, Yusu Wang, Elizabeth Munch, Ellen Gasparovic, Bei Wang.
IEEE Transactions on Visualization and Computer Graphics (SciVis 2019), accepted, 2019.

PDF Revisiting Abnormalities in Brain Network Architecture Underlying Autism Using Topology-Inspired Statistical Inference.
Sourabh Palande, Vipin Jose, Brandon Zielinski, Jeffrey Anderson, P. Thomas Fletcher and Bei Wang.
International Workshop on Connectomics in NeuroImaging (CNI) at MICCAI, 2017.
Brain Connectivity, 9(1):13-21, 2019
PDF Robust Extraction and Simplification of 2D Symmetric Tensor Field Topology.
Jochen Jankowai, Bei Wang, Ingrid Hotz.
Eurographics Conference on Visualization (EuroVis), 2019.
Computer Graphics Forum (CGF), 38(3), pages 337-349, 2019.

PDF Mesh Learning Using Persistent Homology on the Laplacian Eigenfunctions.
Yunhao Zhang, Haowen Liu, Paul Rosen, Mustafa Hajij.
International Geometry Summit Poster, 2019.

PDF Homology-Preserving Dimensionality Reduction via Manifold Landmarking and Tearing.
Lin Yan, Yaodong Zhao, Paul Rosen, Carlos Scheidegger, Bei Wang.
IEEE Symposium on Visualization in Data Science (VDS), 2018.
arXiv Version: arXiv:1806.08460
PDF TopoLines: Topological Smoothing for Line Charts.
Ashley Suh, Christopher Salgado, Mustafa Hajij, Paul Rosen.
IEEE Visualization Conference Poster, 2018.

PDF Using Topological Data Analysis to Infer the Quality in Point Cloud-based 3D Printed Objects.
Paul Rosen, Mustafa Hajij, Junyi Tu, Tanvirul Arafin, Les Piegl.
Computer Aided Design & Applications,16(3), pages 519-527, 2019.
PDF DimReader: Axis Lines That Explain Non-Linear Projections.
Rebecca Faust, David Glickenstein, Carlos Scheidegger.
IEEE Transactions on Visualization and Computer Graphics (InfoVis 2018), 25(1), pages 481-490, 2019.
ArXiv Version: ArXiv:1710.00992
Year 3 (2017 - 2018)
PDF A Complete Characterization of the 1-DimensionalIntrinsic Čech Persistence Diagrams for Metric Graphs.
Ellen Gasparovic, Maria Gommel, Emilie Purvine, Radmila Sazdanovic, Bei Wang, Yusu Wang and Lori Ziegelmeier.
Association for Women in Mathematics Series: Research in Computational Topology
Editors: Erin Chambers, Brittany Terese Fasy, Lori Ziegelmeier. 2018.
arXiv Version: arXiv:1512.04108.
DOI: 10.1007/978-3-319-89593-2
PDF Visual Exploration of Semantic Relationships in Neural Word Embeddings.
Shusen Liu, Peer-Timo Bremer, Jayaraman J. Thiagarajan, Vivek Srikumar, Bei Wang, Yarden Livnat and Valerio Pascucci.
IEEE Transactions on Visualization and Computer Graphics (InfoVis 2017), 24(1), pages 553-562, 2018.
DOI: 10.1109/TVCG.2017.2745141
PDF A Vector Field Design Approach to Animated Transitions.
Yong Wang, Daniel Archambault, Carlos E. Scheidegger, Huamin Qu.
IEEE Transactions on Visualization and Computer Graphics, 24(9), pages 2487-2500, 2018.
DOI: 10.1109/TVCG.2017.2750689
PDF Discrete Stratified Morse Theory: A User's Guide.
Kevin Knudson and Bei Wang.
International Symposium on Computational Geometry (SOCG), 2018.
arXiv Version: arXiv:1801.03183.
PDF Sheaf-Theoretic Stratification Learning.
Adam Brown and Bei Wang.
International Symposium on Computational Geometry (SOCG), 2018.
arXiv Version: arXiv:1712.07734.
PDF Vietoris-Rips and Čech Complexes of Metric Gluings.
Michal Adamaszek, Henry Adams, Ellen Gasparovic, Maria Gommel, Emilie Purvine, Radmila Sazdanovic, Bei Wang, Yusu Wang and Lori Ziegelmeier.
International Symposium on Computational Geometry (SOCG), 2018.
arXiv Version: arXiv:1712.06224.
PDF Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology.
Mustafa Hajij, Bei Wang, Carlos Scheidegger, Paul Rosen.
IEEE Pacific Visualization Symposium (PacificVis), 2018.
arXiv Version: arXiv:1707.06683.
DOI: 10.1109/PacificVis.2018.00024
PDF The Shape of an Image: A Study of Mapper on Images.
Alejandro Robles, Mustafa Hajij, Paul Rosen.
13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications, 2018.
arXiv Version: arXiv:1710.09008.
PDF Visualizing Sensor Network Coverage with Location Uncertainty.
Tim Sodergren, Jessica Hair, Jeff M. Phillips and Bei Wang.
IEEE Symposium on Visualization in Data Science (VDS), 2017.
ArXiv Version: ArXiv:1710.06925
PDF Open Problems in Computational Topology.
Brittany Terese Fasy and Bei Wang (with contributions by members of the WinCompTop community).
SIGACT NEWS Open Problems Column, Edited by Bill Gasarch, 48(3), 2017.
Online Version: SIGACT NEWS open problems column.
PDF Topology, Computation and Data Analysis (Dagstuhl Seminar 17292)
Editors: Hamish Carr, Michael Kerber, and Bei Wang.
Report from Dagstuhl Seminar, 2018.
Online Version: Topology, Computation and Data Analysis (Dagstuhl Seminar 17292).
Year 2 (2016 - 2017)
PDF Visualizing High-Dimensional Data: Advances in the Past Decade.
Shusen Liu, Dan Maljovec, Bei Wang, Peer-Timo Bremer and Valerio Pascucci
IEEE Transactions on Visualization and Computer Graphics (TVCG), 23(3), pages 1249-1268, 2017.
Survey Website (Maintained by Shusen Liu).
PDF Gaussian Cubes: Real-Time Modeling for Visual Exploration of Large Multidimensional Datasets.
Zhe Wang, Nivan Ferreira, Youhao Wei, Aarthy Sankari Bhaskar and Carlos Scheidegger.
IEEE Transactions on Visualization and Computer Graphics (TVCG), 23(1), pages 681-690, 2017.
PDF DSPCP: A Data Scalable Approach for Identifying Relationships in Parallel Coordinates.
Hoa Nguyen and Paul Rosen.
IEEE Transactions on Visualization and Computer Graphics (TVCG), 2017.
PDF Grassmannian Atlas: A General Framework for Exploring Linear Projections of High-Dimensional Data.
Shusen Liu, Peer-Timo Bremer, Jayaraman J. Thiagarajan, Bei Wang, Brian Summa and Valerio Pascucci.
Computer Graphics Forum (CGF), 35(3), pages 1-10, 2016.
PDF Exploring the Evolution of Pressure-Perturbations to Understand Atmospheric Phenomena.
Wathsala Widanagamaachchi, Alexander Jacques, Bei Wang, Erik Crosman, Peer-Timo Bremer, Valerio Pascucci and John Horel.
IEEE Pacific Visualization Symposium (PacificVis), 2017.

PDF A Hybrid Solution to Calculating Augmented Join Trees of 2D Scalar Fields in Parallel.
Paul Rosen, Junyi Tu and Les Piegl.
CAD Conference and Exhibition (Accepted, Extended Abstract), 2017.
PDF Visual Exploration of Multiway Dependencies in Multivariate Data.
Hoa Nguyen, Paul Rosen and Bei Wang.
ACM SIGGRAPH ASIA Symposium on Visualization, 2016.

PDF Gaussian Cubes: Real-Time Modeling for Visual Exploration of Large Multidimensional Datasets.
Zhe Wang, Nivan Ferreira, Youhao Wei, Aarthy Sankari Bhaskar and Carlos Scheidegger.
IEEE Visualization Conference (VIS), 2016.
PDF Grassmannian Atlas: A General Framework for Exploring Linear Projections of High-Dimensional Data.
Shusen Liu, Peer-Timo Bremer, Jayaraman J. Thiagarajan, Bei Wang, Brian Summa and Valerio Pascucci.
Eurographics Conference on Visualization (EuroVis), 2016.
Year 1 (2015 - 2016)
PDF Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion.
Primoz Skraba, Paul Rosen, Bei Wang, Guoning Chen, Harsh Bhatia and Valerio Pascucci.
IEEE Transactions on Visualization and Computer Graphics (TVCG), 22(6), pages 1683-1693, 2016.
Supplemental Video. Vortex Video.
PDF Kernel Partial Least Squares Regression for Relating Functional Brain Network Topology to Clinical Measures of Behavior.
Eleanor Wong, Sourabh Palande, Bei Wang, Brandon Zielinski, Jeffrey Anderson and P. Thomas Fletcher.
International Symposium on Biomedical Imaging (ISBI), 2016.
Poster presentations at ISBI by Eleanor Wong and at TGDA@OSU by Sourabh Palande.
PDF Convergence between Categorical Representations of Reeb Space and Mapper.
Elizabeth Munch and Bei Wang*.
International Symposium on Computational Geometry (SOCG), 2016.
arXiv Version: arXiv:1512.04108. Invited Talk at TGDA@OSU.
PDF Exploring Persistent Local Homology in Topological Data Analysis.
Brittany T. Fasy and Bei Wang*.
Special session on Topological Methods in Data Science and Analysis,
IEEE International Conference on Acoustics, Speech and Signal Process (ICASSP), 2016.
PDF Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion.
Primoz Skraba, Paul Rosen, Bei Wang, Guoning Chen, Harsh Bhatia and Valerio Pascucci.
IEEE Pacific Visualization (PacificVis), 2016. Best Paper Award!
Supplemental Video. Vortex Video.

Manuscripts

Visualizing Interdependent Power-Water Infrastructure Networks: Tasks, Challenges and Opportunities.
Han Han, Konstantinos Oikonomou, Nithin Chalapathi, Masood Parvania, Bei Wang.
Under review, 2019.

PDF TopoLines: Topological Smoothing for Line Charts.
Ashley Suh, Christopher Salgado, Mustafa Hajij, Paul Rosen.
Under review, 2019.

PDF The Relationship Between the Intrinsic Cech and Persistence Distortion Distances for Metric Graphs.
Ellen Gasparovic, Maria Gommel, Emilie Purvine, Radmila Sazdanovic, Bei Wang, Yusu Wang, Lori Ziegelmeier.
Under review, 2019.
arXiv Version: arXiv:1812.05282.
PDF Local Versus Global Distances for Zigzag Persistence Modules.
Ellen Gasparovic, Maria Gommel, Emilie Purvine, Radmila Sazdanovic, Bei Wang, Yusu Wang, Lori Ziegelmeier.
Under review, 2019.
arXiv Version: arXiv:1903.08298.
PDF MOG: Mapper on Graphs for Relationship Preserving Clustering.
Mustafa Hajij, Bei Wang, Paul Rosen.
In revision, 2018.
arXiv Version: arXiv:1804.11242.
PDF Towards Spectral Sparsification of Simplicial Complexes Based on Generalized Effective Resistance.
Braxton Osting, Sourabh Palande and Bei Wang.
Under review, 2018.
arXiv Version: arXiv:1708.08436.
PDF Distributed Mapper.
Mustafa Hajij, Basem Assiri, Paul Rosen.
Under review, 2018.
arXiv Version: arXiv:1712.03660.

Software Downloads

MOG: Mapper on Graphs.
MOG is designed for relationship preserving clustering of large graphs for graph visualization.

Under construction.
TopoLines: Topological Smoothing for Line Charts.
TopoLines is a method for smoothing line charts by leveraging techniques from topological data analysis.

Under construction.
TopoCubes: Interactive Exploration of Persistence Homology of Large Datasets.
TopoCubes extend state-of-the-art in-memory data cubes to support real-time interactive visualization of topological data analysis on large datasets.

Under construction.
PHFDL: Persistent Homology Guided Force-Directed Graph Layouts.
https://github.com/USFDataVisualization/PersistentHomologyOnGraphs


PHFDL implements persistent homology guided force-directed graph layouts.

Under construction.
AMT: Interactive Visualization of Labeled Merge Trees and Their 1-Center
https://github.com/tdavislab/amt

AMT is under active development. Please excuse its appearance (e.g. documentations) while its under construction.

Presentations, Educational Development and Broader Impacts

Year 4 (2018 - 2019)

Paul Rosen Invited Talk: Interacting with Data Using Geometry and Topology, at Early Career in Visualization Summer Camp, Nashville TN, June, 2019.

Carlos Scheidegger Invited Talk: Topological Data Analysis: the promise behind the hype (or the hype behind the promise?), at Yale University Biostatistics Seminar, April 2019.

Paul Rosen Invited Talk: MOG: Mapper on Graphs, at Dagstuhl Seminar 19212: Topology, Computation and Data Analysis, May 19 - 24, 2019.

Bei Wang and Bala Krishnamoorthy Workshop Organization: 8th Annual Minisymposium on Computational Topology during the Computational Geometry Week, June 18-21, 2019.

Bei Wang Workshop Organization: Dagstuhl Seminar: Topology, Computation and Data Analysis, May 19 - 24, 2019.

Bei Wang Invited Talk: A Structural Average of Labeled Merge Trees for Uncertainty Visualization, at Dagstuhl Seminar 19212: Topology, Computation and Data Analysis, May 19 - 24, 2019.

Bei Wang Invited Talk: An Introduction to Discrete Stratified Morse Theory, at JMM AMS-AWM Special Session on Women in Applied and Computational Topology, Jan. 26 , 2019.

Bei Wang Invited Talk: Mapper on Graphs and Visual Detection of Structural Changes in Time-Varying Graphs, at VISA Research, Dec. 12 , 2018.

Bei Wang Conference Talk: Homology-Preserving Dimensionality Reduction via Manifold Landmarking and Tearing, at Symposium on Visualization in Data Science (VDS) at IEEE VIS, Oct. 22 , 2018.

Bei Wang Invited Talk: Topological Perspectives On Stratification Learning, at ICERM TRIPODS Summer Bootcamp: Topology and Machine Learning, Aug. 6-10, 2018.

Year 3 (2017 - 2018)

Bei Wang Conference Talk: Discrete Stratified Morse Theory: A User's Guide, at 34th International Symposium on Computational Geometry (SOCG), June 11-14, 2018.

Bei Wang Invited Talk: Stratification Learning with Computational Topology: Overview, Challenges, and Opportunities, at CG Week 3rd Workshop on Geometry and Machine Learning, June 11, 2018.

Bei Wang Invited Talk: Stratification Learning with Computational Topology, at IMA Workshop Bridging Statistics and Sheaves , May 21 - 25, 2018.

Bei Wang Invited Talk:Topological Data Analysis In a Nutshell, at NII Shonan Meeting Seminar 122 Analysing Large Collections of Time Series, Feburary 12-15, 2018.

Sourabh Palande Oral presentation: Revisiting Abnormalities in Brain Network Architecture Underlying Autism Using Topology-Inspired Statistical Inference, at International Workshop on Connectomics in NeuroImaging (CNI) at MICCAI , September 14, 2017.

Bei Wang Seminar Organizer for Dagstuhl Seminar: Topology, Computation and Data Analysis, July 16 - 21, 2017. Co-Organizers: Hamish Carr, Michael Kerber.

Paul Rosen Conference Talk: Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology, Pacific Visualization, April 10-13, 2018.

Paul Rosen Conference Talk: The shape of an image: A study of mapper on images, 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications, January 27-29, 2018.

Paul Rosen Conference Talk: DSPCP: A Data Scalable Approach for Identifying Relationships in Parallel Coordinates, IEEE SciVis, Oct. 1-6, 2018.  

Paul Rosen Conference Talk: A Hybrid Solution to Calculating Augmented Join Trees of 2D Scalar Fields In Parallel, CAD Conference and Exhibition, Aug. 10-12, 2017.

Carlos Scheidegger Invited talk: What's in that t-SNE plot? The tangent map help explain non-linear dimensionality reduction techniques, the UA-TRIPODS conference, Tucson, AZ, May 25th, 2018.

Year 2 (2016 - 2017)

Bei Wang Invited Talk: Relating Functional Brain Network Topology to Clinical Measures of Behavior in Autism, at BIRS Workshop Topological Methods in Brain Network Analysis, May 7-12, 2017.

Bei Wang Invited Talk: Towards Spectral Sparsification of Simplicial Complexes based on Generalized Effective Resistance, at AWM (Association for Women in Mathematics) Research Symposium, Special Session: Applications of Topology and Geometry, University of California Los Angeles (UCLA), April 8-9, 2017.

Bei Wang Dagstuhl Seminar Talk: Towards Spectral Sparsification of Simplicial Complexes based on Generalized Effective Resistance, at Dagstuhl Seminar on Computational Geometry, April 23-28, 2017.

Bei Wang Invited Talks: Topological Thinking in Visualization and Structural Inference of Point Clouds, at Topological Data Analysis and Related Topics (TDART), Advanced Institute for Material Science (AIMR), Tohoku University, Japan, Feburary 8-10, 2017.

Bei Wang Tutorial Organizer and Speaker: Recent Advancements of Feature-based Flow Visualization and Analysis, at at IEEE Visualization Conference, Baltimore, Maryland. October 23-28, 2016.

Bei Wang Workshop Organizer and Speaker, at International Workshop on Topological Data Analysis in Biomedicine (TDA-Bio), part of the 7th ACM Conference on Bioinformatics, Computational Biology, and Health Informatics (ACM-BCB), Oct 2, 2016.

Zhe Wang Conference Talk: Gaussian Cubes: Real-Time Modeling for Visual Exploration of Large Multidimensional Datasets, at IEEE Visualization Conference, Baltimore, Maryland. October 27, 2016.

Year 1 (2015 - 2016)

Bei Wang Lecturer: at Hi-GEAR (Girls Engineering Abilities Realized) Camp, part of Engineering Summer Camps at the University of Utah, June 13-17, 2016. Hi-GEAR is designed to expose young women (currently in 9th-12th grade) to a variety of engineering and computer science careers with hands-on experiential learning and collaborative team projects.

Bei Wang Conference Talk at 32nd International Symposium on Computational Geometry (SoCG 2016), Boston, USA. June 14-18, 2016. Conference Webpage.

Bei Wang Invited Talk at Topology, Geometry, and Data Analysis Conference at Ohio State University, Columbus, Ohio. May 16 to 20, 2016. Conference Webpage.

Sourabh Palande Poster presentation at Topology, Geometry, and Data Analysis Conference at Ohio State University, Columbus, Ohio. May 16, 2016.

Bei Wang Distinguished Lecture Understanding the Shape of Data with Topological Data Analysis and Visualization, from Vector Fields to Brain Networks, Norrköping Visualization Center, Linköping University Norrköping Campus, Sweden, May 4th, 2016.

Bei Wang Conference Talk at The 9th IEEE Pacific Visualization Symposium, Taipei, Taiwan. April 19 to 22, 2016. Conference Webpage.

Students and Postdocs

Current Students

Sourabh Palande (Graduate RA, 2015 - Present)
School of Computing and Scientific Computing and Imaging Institute
University of Utah
sourabh AT sci.utah.edu
https://www.sci.utah.edu/people/sourabh.html

Lin Yan (Graduate RA, 2017 - Present)
School of Computing and Scientific Computing and Imaging Institute
University of Utah
linyan AT sci.utah.edu
http://www.sci.utah.edu/people/linyan.html

Nithin Chalapathi (REU, Undergraduate RA, 2019 - Present)
School of Computing and Scientific Computing and Imaging Institute
University of Utah
nithin.ch10 AT gmail.com
http://www.sci.utah.edu/people/nithin.html

Ghulam Quadri (Graduate RA, PhD, 2018 - Present)
Computer Science & Engineering Department
University of South Florida
ghulamjilani AT mail.usf.edu
http://jiquadcs.com/

Tanmay Kotha (Graduate RA, MS, 2018 - Present)
Computer Science & Engineering Department
University of South Florida
tanmay AT mail.usf.edu

Chukwubuikem Ume-Ugwa (REU, Undergraduate RA, BS, 2018 - Present)
Computer Engineering and Chemical Engineering
University of South Florida
cumeugwa AT mail.usf.edu

Past Students and PostDoc

Junyi Tu (Graduate RA, 2016 - 2018)
Department of Mathematics and Statistics
University of South Florida
junyi AT mail.usf.edu

Mustafa Hajij (Postdoc, 2016 - 2018)
Department of Mathematics & Statistics
University of South Florida
mhajij AT usf.edu
Assistant Professor @ College of Charleston

Adam Brown (Graduate RA, 2017 - 2019, Graduated Spring 2019)
Department of Mathematics
University of Utah
abrown AT math.utah.edu
PostDoc @ IST Austria

Yaodong Zhao (Graduate RA, 2017 - 2019, Graduated Spring 2019)
School of Computing and Scientific Computing and Imaging Institute
University of Utah
yaodong.zhao AT utah.edu
First job @ LeanTaaS

Yiliang Shi (Undergraduate RA, 2017 - 2018, Graduated Spring 2018)
School of Computing and Scientific Computing and Imaging Institute
University of Utah
Honorable Mention in the Computing Research Association (CRA) Outstanding Undergraduate Researchers, 2018.
CRA Outstanding Undergraduate Researchers award program recognizes undergraduate students in North American colleges and universities who show outstanding research potential in an area of computing research.
Graduate school @ Columbia University, PhD.

William Garnes (REU, Undergraduate RA, 2016 - 2017, Graduated Spring 2018)
School of Computing and Scientific Computing and Imaging Institute
University of Utah
wagarnes AT sci.utah.edu
College of Engineering Scholarship, 2017 - 2018
GEM fellowship award, 2018
GEM is a network of leading corporations and institutions dedicated to enable qualified students from underrepresented communities to pursue graduate education in science and engineering.
Graduate school @Clemson University, MS.

Ashley Suh (Undergraduate RA, 2017 - 2018, Graduated Spring 2018)
Computer Science and Engineering
University of South Florida
asuh AT mail.usf.edu
Graduate School @ Tufts University, PhD.

Tim Sodergren (Graduate RA, 2016 - 2017)
School of Computing and Scientific Computing and Imaging Institute
University of Utah
tsodergren AT sci.utah.edu

Matthew Howa (REU, Undergraduate RA, 2016 - 2017)
School of Computing and Scientific Computing and Imaging Institute
University of Utah
mahowa AT sci.utah.edu

Todd Harry Reeb (Graduate RA, Summer 2016)
Department of Mathematics
University of Utah
reeb AT math.utah.edu

Jackson Pawson (Undergraduate RA, 2015 - 2016, Graduated Spring 2016)
Computer Science and Engineering
University of South Florida
jacksonpawson AT gmail.com

Collaborators

Tom Fletcher
Braxton Osting
Elizabeth Munch
Brandon Zielinski
Jeff Anderson

Acknowledgement

This material is based upon work supported or partially supported by the National Science Foundation under Grant No.1513616 and 1513651, project titled "III: Medium: Collaborative Research: Topological Data Analysis for Large Network Visualization."

Any opinions, findings, and conclusions or recommendations expressed in this project are those of author(s) and do not necessarily reflect the views of the National Science Foundation.

Web page last update: July 12, 2019.