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

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

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

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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

Hayek's the Sensory Order and Gadamer's Phenomenological Hermeneutics

This article reinterprets Hayek's cognitive psychology from the standpoint of the categories employed by phenomenological hermeneutics, and notably by Gadamer. Both Hayek and Gadamer agree on the idea that consciousness is the outcome of a process of interpretation that depends on a 'shifting horizon' – a hermeneutical horizon that is the product of history and that is subject to a constant evolution over time. By comparing Hayek's anti-objectivistic psychology with Gadamer's view, it is possible to clarify and enrich Hayek's distributed knowledge paradigm as well as his criticism of the mechanistic and deterministic theories of action

Agent-Based Simulation as an Implementation of Methodological Individualism

This paper investigates the relationship between methodological individualism (MI) and Agent-Based Simulation (ABS). We discuss and analyze a thesis defended by philosophers Caterina Marchionni and Petri Ylikoski (2013). The thesis maintains that, since MI is often considered to be a reductionist approach, it is confusing and meaningless to assume that ABS, which is a non-reductionist and emergentist explanatory model, is committed to MI. We reject this thesis arguing that, from a philosophical standpoint, addressing the problem of the consistency between MI and ABS from a strictly utilitarian perspective is unsatisfactory. We analyze this problem in more substantial terms, i.e. focusing on its more theoretical and conceptual aspects. Moreover, we maintain that ABS explanations must be regarded as individualist explanations and provide a set of logical and historical arguments against the widespread interpretation of MI in terms of reductionism