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Vers une neurogéométrie. Fibrations corticales, structures de contact et contours subjectifs modaux L'accès aux archives de la revue « Mathématiques et sciences humaines » Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques RÉSUMÉ-Ce travail propose certains modèles variationnels pour les processus corticaux(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)
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 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)
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)
Book synopsis 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(More)
III (1974): Uber die kausale Struktur des rea/en Welt. What follows is a defence of what is at root a correspondence theory of truth for sentences with empirical content. Two extreme positions can be distinguished in regard to what it is in reality to which such sentences correspond. 2 At the one extreme is the position of those, such as Davidson, who(More)
SUMMARY — Snow is white iff…. Predication and perception. The paper tackles the problem of the links between the formal (logical) syntax and semantics of perceptive judgements and their perceptive (geometrical) content. In the most elementary situations, the perceptive content is reducible to a qualitative filling-in of spatial domains (objects' extensions)(More)