This page contains references and materials related to the lectures of Carina Curto and Vladimir Itskov for the third school in topological data analysis, Mexico City, Jan 22-28, 2017: Tercera Escuela de Analisis Topologico de Datos.

Problems
Exercises on convex codes and order complexes

Software
Download CliqueTop-Jan2017 (.zip file, less than 1MB). This includes a script, clique_top_script_27jan2017.m, that computes clique topology for a symmetric matrix and plots the resulting Betti curves.

Get the latest version of the CliqueTop software on GitHub.

References
1. C. Curto. What can topology tells us about the neural code? Bulletin of the AMS, vol. 54, no. 1, pp. 63-78, 2017. Bulletin of the AMS link

2. C. Giusti, E. Pastalkova, C. Curto*, V. Itskov* (*equal last authors). Clique topology reveals intrinsic geometric structure in neural correlations. PNAS, vol. 112, no. 44, pp. 13455-13460, 2015. PNAS link

3. C. Curto, E. Gross, J. Jeffries, K. Morrison, M. Omar, Z. Rosen, A. Shiu, N. Youngs. What makes a neural code convex? SIAGA, in press, 2017. arXiv.org preprint

4. J. Cruz, C. Giusti, V. Itskov, B. Kronholm. On open and closed convex codes. 2016. arXiv.org preprint

5. C. Curto, V. Itskov, A. Veliz-Cuba, N. Youngs. The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes. Bulletin of Mathematical Biology, Volume 75, Issue 9, pp. 1571-1611, 2013. PDF

6. C. Giusti, V. Itskov. A no-go theorem for one-layer feedforward networks. Neural Computation, 26 (11):2527-2540, 2014. PDF

7. C. Curto*, V. Itskov*. Cell groups reveal structure of stimulus space. PLoS Computational Biology, Vol. 4(10): e1000205, 2008. PLoS link

Graduate School at Penn State
Math PhD Program