Over the last decade topological analysis has been established as a new tool for analysis of spiking data.
Today’s guest has been a pioneer in adapting this mathematical technique for use in our field and explains concepts and example applications.
We also also talk about so-called threshold-linear network model, a generalization of Hopfield networks exhibiting a much richer dynamics, where Carina has done some exciting mathematical explorations.
Links to papers/books mentioned in the podcast:
- Curto and Itskov: “Cell Groups Reveal Structure of Stimulus Space”, PLoS Computational Biology, 2008
- Giusti et al: “Clique topology reveals intrinsic geometric structure in neural correlations”, PNAS, 2015
- Zhou et al: “Hyberbolic geometry of the olfactory space”, Science Advances, 2018
- Chaudhuri et al: “The intrinsic attractor manifold and population dynamics of a canonical cognitive circuit across waking and sleep”, Nature Neuroscience, 2019
- Gardner et al: “Toroidal topology of population activity in grid cells”, Nature, 2022
- Curto et al: “Fixed points of competitive threshold-linear networks”, Neural Computation, 2019
- Curto et al: “Stable fixed points of combinatorial threshold-linear networks”, Adv Appl Math, 2024
The podcast was recorded on January 2nd, 2024 and lasts 2 hours and 14 minutes.
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