Lecture series for mathematicians (and interested neuroscientists): Topology of the brain

Thời gian: 09:00 đến 10:00 ngày 17/12/2019, 09:00 đến 10:00 ngày 18/12/2019, 09:00 đến 10:00 ngày 19/12/2019,

Địa điểm: C2-714, VIASM

Báo cáo viên: Prof. Kathryn Hess, École polytechnique fédérale de Lausanne, France

Lecture series for mathematicians (and interested neuroscientists)

Lecture 1:

- Date: December 17, 2019

- Time: 9:00-10:00 

- Title:  How to grow synthetic digital neurons 

- Abstract: The generation of digital morphologies that reproduce the anatomical and electrical characteristics of biological neurons is a vital step towards the reconstruction and simulation of physiologically realistic brain networks, as neuronal morphologies “shape" the dynamical properties of the brain. The principles that define how neurons take shape are still largely unknown, however.

In this talk I will describe a topology-based generative model of neurons that implicitly captures correlations of features within a growing shape, without the need for manual identification of dependencies between features. Our algorithm is based on a topological descriptor of branching morphologies, which I will describe in detail, that reliably categorizes neurons into morphologically distinct groups, in combination with a small set of morphometrics.  We validated our method on both morphological and electrical properties of biological neurons.

This is joint work with a team of scientists from the Blue Brain Project, led by Lida Kanari.

Lecture 2:

- Date: December 18, 2019

- Time: 9:00-10:00 

- Title: Topological exploration of neuronal network dynamics 

- Abstract: One of the paramount challenges in neuroscience is to understand the dynamics of networks of interconnected neurons. In this talk I will describe a novel approach to classifying network dynamics that employs tools from topological data analysis. The efficacy of our method was established by studying simulated activity in three small artificial neural networks in which we varied certain “biological” parameters, giving rise to dynamics that could be classified into four regimes, and showing that a machine learning classifier trained on features extracted from persistent homology could accurately predict the regime of the network it was trained on and also generalize to other networks not presented during training. I will also discuss the application of these methods to networks of actual neurons. This is joint work with Jean-Baptiste Bardin and Gard Spreemann. 


Lecture 3:

- Date: December 19, 2019

- Time: 9:00-10:00 

- Title: Topological analysis of networks 

- Abstract:   Over the past decade or so, graph theory has proved to be extremely useful for analyzing network structure and function, for networks arising in brain imaging, power grids, social networks, and more.  More recently, the tools of algebraic topology have been successfully applied to characterizing and quantifying network structure and function, particularly in networks of neurons and brain regions. 

In this talk I will present both the general framework for such topological analyses and a number of proof-of-concept case studies, illustrating the utility of these methods.


About Prof. Kathryn Hess, École polytechnique fédérale de Lausanne, Switzerland

Webpage: https://hessbellwald-lab.epfl.ch/hessbellwald/


Kathryn Hess is a professor of mathematics at École Polytechnique Fédérale de Lausanne (EPFL) and is known for her work on homotopy theory, category theory, and algebraic topology, both pure and applied. In particular, she applies the methods of algebraic topology to better understanding neuroscience, cancer biology, and materials science. She is a fellow of the American Mathematical Society. 

Hess has worked and written extensively on topics in algebraic topology including homotopy theory, model categories and algebraic K-theory. She has also used the methods of algebraic topology and category theory to investigate homotopical generalizations of descent theory and Hopf–Galois extensions. In particular, she has studied generalizations of these structures for ring spectra and differential graded algebras. 

She has more recently used algebraic topology to understand structures in neuroscience and materials science. 

Hess received the Polysphere d'Or Teaching Award for her teaching at EPFL in 2013. In 2017, she was named a fellow of the American Mathematical Society for "contributions to homotopy theory, applications of topology to the analysis of biological data, and service to the mathematical community". In 2017, she received an award as a distinguished speaker of the European Mathematical Society.


List of articles on these subjects: 

  1. M. W. Reimann, M. Nolte, M. Scolamiero, K. Turner, R. Perin, G. Chindemi, P. Dlotko, R. Levi, K. Hess, and H. Markram, Cliques of neurons bound into cavities provide a missing link between structure and function, Front. Comput. Neurosci., 12 June 2017, doi: 10.3389/fncom.2017.00048.

Cliques of neurons bound into cavities provide a missing link between structure and function 

  1. L. Kanari, P. Dlotko, M. Scolamiero, R. Levi,  J. C. Shillcock, K. Hess, and H. Markram, A topological representation of branching morphologies, Neuroinformatics (2017) doi: 10.1007/s12021-017-9341-1.

 A topological representation of branching neuronal morphologies 

  1. J.-B. Bardin, G. Spreemann, K. Hess, Topological exploration of artificial neuronal network dynamics, Network Neuroscience (2019) https://doi.org/10.1162/netn\_a\_00080.

Topological exploration of artificial neuronal network dynamics 

  1. L. Kanari, S. Ramaswamy, Y. Shi, S. Morand, J. Meystre, R. Perin, M. Abdellah, Y. Wang, K. Hess, and H. Markram, Objective classification of neocortical pyramidal cells, Cerebral Cortex (2019) bhy339, https://doi.org/10.1093/cercor/bhy339.

Objective morphological classification of neocortical pyramidal cells 


Few videos that may be of interest as well, ordered from least to most mathematical: 

The very short, very vague introduction to our work, filmed by the EPFL: https://youtu.be/ZQTqvv6HHHY 

A TEDx talk I gave a couple of years ago: https://youtu.be/uQKrCKy3h1E 

A series of excellent videos produced by PBS on our work:

https://youtu.be/M0M3srBoTkY, https://youtu.be/rlI1KOo1gp4, https://youtu.be/akgU8nRNIp0 

A talk I gave to an audience of applied topologists two years ago: https://youtu.be/vD27zKxoio0