2013-14: LDHD: Topological Data Analysis: February 3-7, 2014

Workshop Information

February 3, 2014 - 9:00am - February 7, 2014 - 1:00pm

This workshop was held at SAMSI.

Topological Data Analysis began a little more than 20 years ago with the introduction of persistence by Edelsbrunner, Lestcher and Zomorodian. Since that time the field has grown significantly. Many strong theorems, numerous algorithms, and pieces of software have been created in that period. More recently, the field has considered stochastic modeling and analysis, which has resulted in interactions with Statistics, Probability, and Computer Science. This workshop focused on the interaction of Statistics and Probability with this new area of Applied Mathematics. The goals were to familiarize people in both areas with techniques from the other and to understand what future directions are the most promising.

Topics included:

  • Statistics and persistent homology
  • Topological data analysis and inference in dynamical systems and time series
  • Topological data analysis and shape statistics
  • Topological data analysis and network models
  • Probability models for random topology objects
  • Statistical applications of Hodge theory

Schedule
Participant List
Speaker Title and Abstracts
Poster Titles

Schedule

Monday, February 3, 2014
at SAMSI, Room 150

8:30-8:55 a.m. Registration
8:55-9:00 Welcome
9:00-9:40 Frederic Chazal, INRIA
Stability and Convergence Properties of Persistence Diagrams in Topological Data Analysis
9:40-10:00 Break
10:00-10:40 Yusu Wang, Ohio State University
Data Sparsification in Inferring Topology of Manifolds
10:40-11:00 Break
11:00-11:40 Peter Bubenik, Cleveland State University
Statistical Topological Data Analysis using Persistence Landscapes
11:40-1:00 Lunch (provided at SAMSI)
1:00-1:40 Megan Owen, Lehman College (CUNY)
Mean and Variance of Metric Trees
1:40-2:00 Break
2:00-2:40 Andrew Nobel, University of North Carolina
Some Uniformity Results for Dynamical Systems
2:40-3:00 Break
3:00-3:40 Larry Wasserman, Carnegie Mellon University
Statistical Inference for Functional Summaries of Persistent Homology
3:40-4:00 Break
4:00-5:00 Discussion

Tuesday, February 4, 2014
at SAMSI, Room 150

9:00-9:40 a.m. Yuliy Baryshnikov, University of Illinois
What is the Dimension of the Internet?
9:40-10:00 Break
10:00-10:40 Katharine Turner, University of Chicago
Can Topological Summary Statistics be Sufficient?
10:40-11:00 Break
11:00-11:40 Giseon Heo, University of Alberta
Topological and Statistical Data Analysis
11:40-1:00 Lunch (provided at SAMSI)
1:00-1:40 Facundo Memoli, Ohio State University
Curvature Sets over Persistence Diagrams
1:40-2:00 Break
2:00-2:40 Paul Bendich, Duke University
Persistent Local Homology: Theory, Algorithms, Applications, New Directions
2:40-3:00 Break
3:00-3:40 Lek-Heng Lim, University of Chicago
Hodge Theory in Data Analysis
3:40-4:00 Break
4:00-5:00 Discussion
5:00-6:30 Poster Session and Reception

SAMSI will provide poster presentation boards and tape. The board dimensions are 4 ft. wide by 3 ft. high. They are tri-fold with each side being 1 ft. wide and the center 2 ft. wide. Please make sure your poster fits the board. The boards can accommodate up to 16 pages of paper measuring 8.5 inches by 11 inches.

Wednesday, February 5, 2014
at SAMSI, Room 150

9:00-9:40 a.m. Fabrizio Lecci, Carnegie Mellon University
Statistical Inference for Persistence Diagrams
9:40-10:00 Break
10:00-10:40 Elizabeth Munch, Institute for Mathematics and its Applications
Categorification of Reeb Graphs
10:40-11:00 Break
11:00-11:40 J.S. Marron, University of North Carolina
OODA of Tree-Structured Data Objects
11:40-12:00 Discussion
12:00 Box Lunch (provided at SAMSI) - Free Afternoon

Thursday, February 6, 2014
at SAMSI, Room 150

9:00-9:40 a.m. Jose Perea, Duke University
Persistent Homology of Time-delay Embeddings
9:40-10:00 Break
10:00-10:40 Jessi Cisewski, Carnegie Mellon University
Persistent Homology of the Intergalactic Medium via the Lyman-alpha Forest
10:40-11:00 Break
11:00-11:40 Bei Wang, University of Utah
Geometric Inference on Kernel Density Estimates
11:40-1:00 Lunch (provided at SAMSI)
1:00-1:40 Brittany Fasy, Tulane University
Local Homology Based Distance Between Maps
1:40-2:00 Break
2:00-2:40 Harish Chintakunta, North Carolina State University
Distributed Homology using Harmonics
2:40-3:00 Break
3:00-3:40 Vic Patrangenaru, Florida State University
Neighborhood Hypothesis Testing for Mean Contour Shapes of Corpus Callosum Mid Sections
3:40-4:00 Break
4:00-5:00 Discussion

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Friday, February 7, 2014
at SAMSI, Room 150

9:00-9:40 a.m. Omer Bobrowski, Duke University
Phase Transitions in Random Čech Complexes
9:40-10:00 Break
10:00-10:40 Jennifer Gamble, North Carolina State University
Quantifying Coverage in Dynamic Sensor Networks with Zigzag Persistent Homology
10:40-11:00 Break
11:00-11:40 Peter Kim, University of Guelph
Pyrosequencing and Computational Topology: A tale of two homologies
11:40-12:00 Discussion
12:00 Lunch (provided at SAMSI)
Adjourn
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