Jean Petitot

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We present a geometrical model of the functional architecture of the primary visual cortex (V1) and, more precisely, of its pinwheel structure. The problem is to understand from within how the internal "imminent" geometry of the visual cortex can produce the "transcendent" geometry of the external space. We use first the concept of blowing up to model V1 as(More)
We propose to model the functional architecture of the primary visual cortex V1 as a principal fiber bundle where the two-dimensional retinal plane is the base manifold and the secondary variables of orientation and scale constitute the vertical fibers over each point as a rotation–dilation group. The total space is endowed with a natural symplectic(More)
Some papers of this special issue concern recent results on mathematical models of segmentation. As they are rather technical we propose here a pedagogical introduction for the non-mathematical reader. We briefly present the variational model of image segmentation proposed by David Mumford and we summarize some fundamental results of De Giorgi's school.
Large sets of elements interacting locally and producing specific architectures reliably form a category that transcends the usual dividing line between biological and engineered systems. We propose to call them morphogenetically architected complex systems (MACS). While taking the emergence of properties seriously, the notion of MACS enables at the same(More)
We propose a novel dynamical system approach to cognitive linguistics based on cellular automata and spiking neural networks. How can the same relationship 'in' apply to containers as different as 'box', 'tree' or 'bowl'? Our objective is to categorize the infinite diversity of schematic visual scenes into a small set of grammatical elements and elucidate(More)
We present a geometrical model of the functional architecture of the primary visual cortex. In particular we describe the geometric structure of connections found both in neurophysiological and psychophysical experiments, modeling both co-axial and trans-axial excitatory connections. The model shows what could be the deep structure for both boundary and(More)
With Francisco Varela’s death, one of the most beautiful minds I ever met has gone to heaven. The inspired way he succeeded in synthesizing cognitive neurosciences, dynamical models of global brain activity and the phenomenological dimension of consciousness was truly amazing and wonderful. His scientific production was constitutive of a spiritual vocation.(More)
This book – written in collaboration with René Doursat, director of the Complex Systems Institute, Paris – adds a new dimension to Cognitive Grammars. It provides a rigorous, operational mathematical foundation, which draws from topology, geometry and dynamical systems to model iconic «image-schemas» and «conceptual archetypes». It defends the thesis that(More)