Schedule for: 17w5043 - Topological Methods in Brain Network Analysis

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

In this tutorial talk I will give an overview, aimed at neuroscientists, of some of the standard techniques in topological data analysis. I'll then present several examples illustrating the variety of ways in which these methods have been used to shed light on neuroscience data sets. These examples range from multi-neuron recordings in cortex and hippocampus to functional networks in fMRI. Finally, I'll discuss how topology may help us to understand olfaction and the space of smells.

Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

This presentation gives an introduction to the R package TDA, which provides some tools for Topological Data Analysis. The salient topological features of data can be quantified with persistent homology. The R package TDA provide an R interface for the efficient algorithms of the C++ libraries GUDHI, Dionysus, and PHAT. Specifically, The R package TDA includes functions for computing the persistent homology of the Rips complex, alpha complex, and alpha shape complex, and a function for the persistent homology of sublevel sets (or superlevel sets) of arbitrary functions evaluated over a grid of points. The R package TDA also provides a function for computing the confidence band that determines the significance of the features in the resulting persistence diagrams.

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

https://project.inria.fr/gudhi/ http://link.springer.com/chapter/10.1007/978-3-662-44199-2_28

http://gregoryhenselman.org/eirene/ http://www.math.upenn.edu/~ghrist/preprints/Eirene.pdf

https://github.com/DIPHA/dipha http://www.geometrie.tugraz.at/kerber/kerber_papers/bkr-dcph.pdf https://bitbucket.org/phat-code/phat http://www.geometrie.tugraz.at/kerber/kerber_papers/phat_jsc.pdf

Non-linear rank of a matrix M is the minimal possible rank of a matrix obtained by applying arbitrary monotone-increasing functions to each row of M. The problem of finding the non-linear rank often arises in neuroscience context.  In this talk I will explain how the topology of hyperplane arrangements is closely related to the problem of finding the non-linear rank.  I will then present an algebraic approach and computational results for estimating the nonlinear rank.

Inference of feedforward vs feedback connectivity. I will describe efforts to disentangle the influence of these kinds of connectivities on oscillatory dynamics and the cancellation of redundant inputs.

Metric graphs are special types of metric spaces used to model and represent simple, ubiquitous, geometric relations in data such as biological networks, social networks, and road networks. In this talk we focus on using persistence to obtain qualitative-quantitative summaries of metric graphs. We analyze the information contained in these persistence- based summaries of graphs, and compare their discriminative powers. This is joint work with Ellen Gasparovic, Maria Gommel, Emilie Purvine, Bei Wang, Yusu Wang, and Lori Ziegelmeier. 

We describe a novel method for analyzing the relationship between functional brain networks and behavioral phenotypes in autism using kernel partial least squares regression and topological data analysis. This is joint work with Eleanor Wong, Sourabh Palande, Brandon Zielinski, Jeffrey Anderson and P. Thomas Fletcher.

A stable multi-scale kernel is presented that allows to use persistent homology in the context of machine learning

The statistical inference on persistent homology incurs computation on a grid of points, which is computationally infeasible if the dimension is high. This work tries to mitigate computations by building a valid confidence set for the persistent homology of a density filtration on Rips complex.

We've heard about a huge variety of tools this week. Now is the time to circle back, at a higher level of abstraction, and summarize what tools are available, and what types of questions they are suitable for answering.

5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon.