Topological and geometrical structures in neurosciences
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Topology and geometry in neuroscience
chairs of the sessions
Topics
This session will focus on the advances on Algebraic Topology and Geometrical methods in neurosciences (see [1-105] bellow, among many others). The field is currently knowing an impressive development coming both:_ from theoretical neuroscience and machine learning fields, like Graph Neural Networks [30-42], Bayesian geometrical inference [27-29], Message Passing, probability and cohomology [92-95], Information Topology [53-54,62-66,96-105] or Networks [83-85,90-91], higher order n-body statistical interactions [67,74,94-95,99,101]
_ from topological data analysis applications to real neural recordings, ranging from subcellular [43,51] genetic or omic expressions [81,101], spiking dynamic and neural coding [1-25,45-47,50-52,79], to cortical areas fMRI, EEG [26,67-72,76-80,84-89], linguistic [54-61] and consciousness [48,53,102].
Bibliographical references: (to be completed)
Carina Curto, Nora Youngs and Vladimir Itskov and colleagues:
[1] C. Curto, N. Youngs. Neural ring homomorphisms and maps between neural codes. Submitted. arXiv.org preprint.
[2] C. Curto, J. Geneson, K. Morrison. Fixed points of competitive threshold-linear networks. Neural Computation, in press, 2019. arXiv.org preprint.
[3] C. Curto, A. Veliz-Cuba, N. Youngs. Analysis of combinatorial neural codes: an algebraic approach. Book chapter in Algebraic and Combinatorial Computational Biology. R. Robeva, M. Macaulay (Eds), 2018.
[4] C. Curto, V. Itskov. Combinatorial neural codes. Handbook of Discrete and Combinatorial Mathematics, Second Edition, edited by Kenneth H. Rosen, CRC Press, 2018. pdf
[5] C. Curto, E. Gross, J. Jeffries, K. Morrison, M. Omar, Z. Rosen, A. Shiu, N. Youngs. What makes a neural code convex? SIAM J. Appl. Algebra Geometry, vol. 1, pp. 222-238, 2017. pdf, SIAGA link, and arXiv.org preprint
[6] C. Curto. What can topology tells us about the neural code? Bulletin of the AMS, vol. 54, no. 1, pp. 63-78, 2017. pdf, Bulletin link.
[7] C. Curto, K. Morrison. Pattern completion in symmetric threshold-linear networks. Neural Computation, Vol 28, pp. 2825-2852, 2016. pdf, arXiv.org preprint.
[8] C. Giusti, E. Pastalkova, C. Curto, V. Itskov. Clique topology reveals intrinsic geometric structure in neural correlations. PNAS, vol. 112, no. 44, pp. 13455-13460, 2015. pdf, PNAS link.
[9] C. Curto, A. Degeratu, V. Itskov. Encoding binary neural codes in networks of threshold-linear neurons. Neural Computation, Vol 25, pp. 2858-2903, 2013. pdf, arXiv.org preprint.
[10] K. Morrison, C. Curto. Predicting neural network dynamics via graphical analysis. Book chapter in Algebraic and Combinatorial Computational Biology. R. Robeva, M. Macaulay (Eds), 2018. arXiv.org preprint,
[11] 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. arXiv.org preprint.
[12] C. Curto, V. Itskov, K. Morrison, Z. Roth, J.L. Walker. Combinatorial neural codes from a mathematical coding theory perspective. Neural Computation, Vol 25(7):1891-1925, 2013. arXiv.org preprint.
[13] C. Curto, A. Degeratu, V. Itskov. Flexible memory networks. Bulletin of Mathematical Biology, Vol 74(3):590-614, 2012. arXiv.org preprint.
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[17] C. Curto, V. Itskov. Cell groups reveal structure of stimulus space. PLoS Computational Biology, Vol. 4(10): e1000205, 2008.
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Sunghyon Kyeong and colleagues:
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Jonathan Pillow and colleagues:
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[45] E. Mullier, J. Vohryzek, A. Griffa, Y. Alemàn-Gómez, C. Hacker, K. Hess, and P. Hagmann, Functional brain dynamics are shaped by connectome n-simplicial organization, (2020) submitted.
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[48] A. Doerig, A. Schurger, K. Hess, and M. H. Herzog, The unfolding argument: why IIT and other causal structure theories of consciousness are empirically untestable, Consciousness and Cognition 72 (2019) 49-59.
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