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Updated: Aug 17, 2026

Extracting Visual Evoked Potentials from EEG Data Recorded During fMRI-guided Transcranial Magnetic Stimulation
Published on: May 12, 2014
From neural oscillations to variational problems in the visual cortex
Alessandro Sarti1, Giovanna Citti, Maria Manfredini
1Dipartimento di Elettronica, Informatica e Sistemistica, Universitá degli Studi di Bologna, Viale Risorgimento 2, Bologna IT-40136, Italy. asarti@deis.unibo.it
Abstract:
Aim of this study is to provide a formal link between connectionist neural models and variational psycophysical ones. We show that the solution of phase difference equation of weakly connected neural oscillators gamma-converges as the dimension of the grid tends to 0, to the gradient flow relative to the Mumford-Shah functional in a Riemannian space. The Riemannian metric is directly induced by the pattern of neural connections. Next, we embed the energy functional in the specific geometry of the functional space of the primary visual cortex, that is described in terms of a subRiemannian Heisenberg space. Namely, we introduce the Mumford-Shah functional with the Heisenberg metric and discuss the applicability of our main gamma-convergence result to subRiemannian spaces.
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