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.
The paper challenges the assumption, common amongst philosophers, that the reality described in the fundamental theories of microphysics is all the reality we have. It will be argued that this assumption is in fact incompatible with the nature of such theories. It will be shown further that the macro-world of three-dimensional bodies and of such qualitative… (More)
Preamble Physical reality is all the reality we have, and so physical theory in the standard sense is all the ontology we need. This, at least, was an assumption taken almost universally for granted by the advocates of exact philosophy for much of the present century. Every event, it was held, is a physical event, and all structure in reality is physical… (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)