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)
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.
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)
1 Introduction: " converting chemical information into a geometrical form "
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)