Streaming of the Second NeuroMat Workshop, New Frontiers in NeuroMathematics

Seven videos of the Second NeuroMat Workshop, New Frontiers in NeuroMathematics, that occurred from November 22 to 25, at the University of São Paulo. Streaming was made available by USP. Videos in English.

A brain soccer derby

An interesting way of thinking on brain functioning --and research in this area-- is to compare neurons to soccer fans in a stadium. Scientists would be observers "outside" the stadium, trying to make sense of what goes on "on the field." Antonio Galves, Mente e Cérebro, 01/2017. (In Portuguese.)

Contrast response functions in the visual wulst of the alert burrowing owl: a single-unit study

Vieira P.G., de Sousa J.P. and Baron J.

The neuronal representation of luminance contrast has not been thoroughly studied in birds. Here we present a detailed quantitative analysis of the contrast response of 120 individual neurons recorded from the visual wulst of awake burrowing owls (Athene cunicularia). Stimuli were sine-wave gratings presented within the cell classical receptive field and optimized in terms of eye preference, direction of drift, and spatiotemporal frequency. As contrast intensity was increased from zero to near 100%, most cells exhibited a monotonic response profile with a compressive, at times saturating, nonlinearity at higher contrasts. However, contrast response functions were found to have a highly variable shape across cells. With the view to capture a systematic trend in the data, we assessed the performance of four plausible models (linear, power, logarithmic, and hyperbolic ratio) using classical goodness-of-fit measures and more rigorous statistical tools for multimodel inferences based on the Akaike information criterion. From this analysis, we conclude that a high degree of model uncertainty is present in our data, meaning that no single descriptor is able on its own to capture the heterogeneous nature of single-unit contrast responses in the wulst. We further show that the generalizability of the hyperbolic ratio model established, for example, in the primary visual cortex of cats and monkeys is not tenable in the owl wulst mainly because most neurons in this area have a much wider dynamic range that starts at low contrast. The challenge for future research will be to understand the functional implications of these findings.

Continuity properties of a factor of Markov chains

Walter A. F. de Carvalho, Sandro Gallo and Nancy L. Garcia

Starting from a Markov chain with a finite or a countable infinite alphabet, we consider the chain obtained when all but one symbol are indistinguishable for the practitioner. We study conditions on the transition matrix of the Markov chain ensuring that the image chain has continuous or discontinuous transition probabilities with respect to the past.

Stochastic Ising model with plastic interactions

Eugene Pechersky, Guillem Via and Anatoly Yambartsev

We propose a new model based on the Ising model with the aim to study synaptic plasticity phenomena in neural networks. It is today well established in biology that the synapses or connections between certain types of neurons are strengthened when the neurons are co-active, a form of the so called synaptic plasticity. Such mechanism is believed to mediate the formation and maintenance of memories. The proposed model describes some features from that phenomenon. Together with the spin-flip dynamics, in our model the coupling constants are also subject to stochastic dynamics, so that they interact with each other. The evolution of the system is described by a continuous-time Markov jump process.




The Research, Innovation and Dissemination Center for Neuromathematics is hosted by the University of São Paulo and funded by FAPESP (São Paulo Research Foundation).


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