Recent advances in mathematical neuroscience: cortically inspired models for vision and synaptic plasticity

Thursday, June 17 at 02:15am (PDT)
Thursday, June 17 at 10:15am (BST)
Thursday, June 17 06:15pm (KST)

SMB2021 SMB2021 Follow Monday (Tuesday) during the "MS17" time block.
Note: this minisymposia has multiple sessions. The second session is MS05-NEUR (click here).

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Luca Calatroni (Laboratoire I3S, CNRS, UCA & Inria Sophia Antipolis Méditerranée, France), Mathieu Desroches (MathNeuro Project-Team, Inria Sophia Antipolis Méditerranée & Université Côté d’Azur, France), Valentina Franceschi (Dipartimento di Matematica, Università degli Studidi Padova, Italy), Dario Prandi (Université Paris-Saclay, CNRS, CentraleSupélec, L2S, France)


The purpose of this symposium is to gather together experts working in the field of mathematical neuroscience, with a focus on those working on cortical inspired models for vision and synaptic plasticity. In particular the speakers will present recent results on variational and differential approaches to the understanding of the primary visual cortex as well as more recent models based on neural networks and predictive coding.

Marcelo Bertalmío

(Spanish National Research Council (CSIC), Spain)
"Evidence for the intrinsically nonlinear nature of receptive fields in vision"
The responses of visual neurons, as well as visual perception phenomena in general, are highly nonlinear functions of the visual input, while most vision models are grounded on the notion of a linear receptive field (RF). The linear RF has a number of inherent problems: it changes with the input, it presupposes a set of basis functions for the visual system, and it conflicts with recent studies on dendritic computations. Here we propose to model the RF in a nonlinear manner, introducing the intrinsically nonlinear receptive field (INRF). Apart from being more physiologically plausible and embodying the efficient representation principle, the INRF has a key property of wide-ranging implications: for several vision science phenomena where a linear RF must vary with the input in order to predict responses, the INRF can remain constant under different stimuli. We also prove that Artificial Neural Networks with INRF modules instead of linear filters have a remarkably improved performance and better emulate basic human perception.

Emre Baspinar

(CNRS/NeuroPSI, France)
"A biologically-inspired model for Poggendorff type illusions"
In this talk, we will see a new biologically-inspired sub-Riemannian model employing Wilson-Cowan type mean field equations described in the model geometry proposed in [1], and in a similar fashion as in [2]. The model is applied to reproducing orientation-dependent Poggendorff- type illusions. The novelty of the model is that it embeds sub-Riemannian diffusion into the neuronal interaction term appearing in the mean field equations. This tunes the neuronal interactions in agreement with the functional architecture of the visual cortex. [1] G. Citti and A. Sarti, “A cortical based model of perceptual completion in the roto-translation space,” Journal of Mathematical Imaging and Vision, vol. 24, no. 3, pp. 307–326, 2006. [2] M. Bertalmío, L. Calatroni, V. Franceschi, B. Franceschiello, and D. Prandi, “Cortical-inspired Wilson–Cowan type equations for orientation-dependent contrast perception modelling,” Journal of Mathematical Imaging and Vi- sion, pp. 1–19, 2020.

Rasa Gulbinaite

(Netherlands Institute for Neuroscience, The Netherlands)
"Resonance frequencies in the visual cortex and illusory perception"
Sensory cortices stimulated by rhythmic sounds, lights, or touch will respond in a rhythmic manner at frequencies identical or harmonically related to the stimulus. These responses are maximal when a certain cortical circuit is driven at or close to the frequencies it generates naturally. The resonance frequencies are also tightly linked to the system's response to a single impulse (impulse response function). Using examples from human EEG studies and widefield glutamate imaging in mice, I will demonstrate that resonance phenomena are preserved across species and across spatial scales of neural activity; and illustrate how stimulation at resonance frequencies can create illusory percepts.

Ludovic Sacchelli

(LAGEPP, Université Claude Bernard Lyon 1 (UCBL), France)
"Cortical-inspired sound processing: hearing with the visual cortex"
We propose a mathematical model of sound reconstruction based on a functional architecture of the auditory cortex (A1). The model is inspired by the geometrical modeling of vision, where variational information in the perceived image plays a major role. Sound processing in A1 occurs in the time frequency domain, where sound signals can be understood as images where times plays a fundamental role. In order to respect these symmetries, the inclusion of variational information in sounds translates to a lift from the time frequency domain to the Heisenberg group. In that space, sound signals undergo reconstruction via adapted Wilson-Cowan integro-differential equations that we illustrate with preliminary numerical experiments.

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Virtual conference of the Society for Mathematical Biology, 2021.