Hyperbolic planforms in relation to visual edges and textures perception

We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g. optical imaging, and opens the door to the design of experiments to test these hypotheses. We study the specific problem of visual edges and textures perception and suggest that these features may be represented at the population level in the visual cortex as a specific second-order tensor, the structure tensor, perhaps within a hypercolumn. We then extend the classical ring model to this case and show that its natural framework is the non-Euclidean hyperbolic geometry. This brings in the beautiful structure of its group of isometries and certain of its subgroups which have a direct interpretation in terms of the organization of the neural populations that are assumed to encode the structure tensor. By studying the bifurcations of the solutions of the structure tensor equations, the analog of the classical Wilson and Cowan equations, under the assumption of invariance with respect to the action of these subgroups, we predict the appearance of characteristic patterns. These patterns can be described by what we call hyperbolic or H-planforms that are reminiscent of Euclidean planar waves and of the planforms that were used in [1, 2] to account for some visual hallucinations. If these patterns could be observed through brain imaging techniques they would reveal the built-in or acquired invariance of the neural organization to the action of the corresponding subgroups.Comment: 34 pages, 11 figures, 2 table

Topological Aspects of Epistemology and Metaphysics

The aim of this paper is to show that (elementary) topology may be useful for dealing with problems of epistemology and metaphysics. More precisely, I want to show that the introduction of topological structures may elucidate the role of the spatial structures (in a broad sense) that underly logic and cognition. In some detail I’ll deal with “Cassirer’s problem” that may be characterized as an early forrunner of Goodman’s “grue-bleen” problem. On a larger scale, topology turns out to be useful in elaborating the approach of conceptual spaces that in the last twenty years or so has found quite a few applications in cognitive science, psychology, and linguistics. In particular, topology may help distinguish “natural” from “not-so-natural” concepts. This classical problem that up to now has withstood all efforts to solve (or dissolve) it by purely logical methods. Finally, in order to show that a topological perspective may also offer a fresh look on classical metaphysical problems, it is shown that Leibniz’s famous principle of the identity of indiscernibles is closely related to some well-known topological separation axioms. More precisely, the topological perspective gives rise in a natural way to some novel variations of Leibniz’s principle

Soft Image Segmentation: On the Clustering of Irregular, Weighted, Multivariate Marked Networks

The contribution exposes and illustrates a general, flexible formalism, together with an associated iterative procedure, aimed at determining soft memberships of marked nodes in a weighted network. Gathering together spatial entities which are both spatially close and similar regarding their features is an issue relevant in image segmentation, spatial clustering, and data analysis in general. Unoriented weighted networks are specified by an ``exchange matrix", determining the probability to select a pair of neighbors. We present a family of membership-dependent free energies, whose local minimization specifies soft clusterings. The free energy additively combines a mutual information, as well as various energy terms, concave or convex in the memberships: within-group inertia, generalized cuts (extending weighted Ncut and modularity), and membership discontinuities (generalizing Dirichlet forms). The framework is closely related to discrete Markov models, random walks, label propagation and spatial autocorrelation (Moran's I), and can express the Mumford-Shah approach. Four small datasets illustrate the theory

Psychoneural Isomorphism: From Metaphysics to Robustness

At the beginning of the 20th century, Gestalt psychologists put forward the concept of psychoneural isomorphism, which was meant to replace Fechner’s obscure notion of psychophysical parallelism and provide a heuristics that may facilitate the search for the neural correlates of the mind. However, the concept has generated much confusion in the debate, and today its role is still unclear. In this contribution, I will attempt a little conceptual spadework in clarifying the concept of psychoneural isomorphism, focusing exclusively on conscious visual perceptual experience and its neural correlates. Firstly, I will outline the history of our concept, and its alleged metaphysical and epistemic roles. Then, I will clarify the nature of isomorphism and rule out its metaphysical role. Finally, I will review some epistemic roles of our concept, zooming in on the work of Jean Petitot, and suggest that it does not play a relevant heuristic role. I conclude suggesting that psychoneural isomorphism might be an indicator of robustness for certain mathematical descriptions of perceptual content

A chemosensory GPCR as a potential target to control the Root-Knot Nematode Meloidogyne incognita parasitism in plants.

Made available in DSpace on 2019-10-24T18:15:24Z (GMT). No. of bitstreams: 1 molecules2403798.pdf: 19607038 bytes, checksum: 72043c875bb4164ff917bd5eeeed827d (MD5) Previous issue date: 2019bitstream/item/203619/1/molecules-24-03798.pd