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

- XSummer - Transcendental Functions and Symbolic Summation in Form

Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their generalizations appear as building blocks, originating for example from the expansion of generalized hypergeometric functions around integer values of the parameters. In this Letter we discuss the implementation of several algorithms to solve these sums by algebraic means, using the computer algebra system Form.Comment: 21 pages, 1 figure, Late

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

Low energy expansion of the four-particle genus-one amplitude in type II superstring theory

A diagrammatic expansion of coefficients in the low-momentum expansion of the genus-one four-particle amplitude in type II superstring theory is developed. This is applied to determine coefficients up to order s^6R^4 (where s is a Mandelstam invariant and R^4 the linearized super-curvature), and partial results are obtained beyond that order. This involves integrating powers of the scalar propagator on a toroidal world-sheet, as well as integrating over the modulus of the torus. At any given order in s the coefficients of these terms are given by rational numbers multiplying multiple zeta values (or Euler--Zagier sums) that, up to the order studied here, reduce to products of Riemann zeta values. We are careful to disentangle the analytic pieces from logarithmic threshold terms, which involves a discussion of the conditions imposed by unitarity. We further consider the compactification of the amplitude on a circle of radius r, which results in a plethora of terms that are power-behaved in r. These coefficients provide boundary `data' that must be matched by any non-perturbative expression for the low-energy expansion of the four-graviton amplitude. The paper includes an appendix by Don Zagier.Comment: JHEP style. 6 eps figures. 50 page

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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Are Hermeneutics and the Austrian Approach Compatible? A Clarifying Analysis

This paper investigates the merging of the Austrian Approach and Hermeneutics under a new light. It defends a middle ground between the standpoint of the Austrian hermeneutists and that of their critics. The latter, especially Rothbard, considered hermeneutics to be incompatible with Austrian School because they confused hermeneutics with what Mises calls "polylogism", i.e. with cognitive nihilism. Their view was incorrect, but their criticism of the Austrian hermeneutists was not completely unfounded. Austrian hermeneutists did not clearly separate what they called hermeneutics from the postmodernist epistemologies of authors such as Derrida, Kuhn, and Rorty. This article demonstrates that hermeneutics as intended by Gadamer, its greatest theorist, has nothing to do with postmodernism. It is a fallibilist theory of the objective truth in the sense of Popper. So it is compatible both with the Austrians' antipolylogism and their methodological individualism

Effect of genotypic, meteorological and agronomic factors on the gluten index of winter durum wheat

The determination of the gluten index is a widely used method for analysing the gluten strength of bread wheat and spring durum wheat genotypes. The present work was carried out to study the effect of the genotype, meteorological factors (temperature, precipitation and number of days with Tmax ≥ 30 °C) and agronomic treatments (N fertilisation and plant protection) on the gluten index of winter durum wheat varieties and breeding lines. The results indicated that the gluten index had little dependence on the environment, being determined to the greatest extent by the genotype. Compared with varieties having weak gluten, those with a strong gluten matrix responded less sensitively to changes in environmental conditions. Among the meteorological factors, high temperature at the end of the grain-filling period caused the greatest reduction in the mean gluten index of three varieties (R 2 = 0.462), while the fertiliser was found to be a significant factor affecting the gluten strength of winter durum wheat varieties. Using selection based on the gluten index, the gluten strength of winter durum wheat lines can be improved sufficiently to make them competitive with high quality spring varieties