http://popups.lib.uliege.be/1373-5411/index.php?id=335 Publications of Auteurs Philippe Sabatier fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=987 Living systems, in certain circumstances, try to predict future situations, and by that, begin to adapt in advance. The behaviour of adaptation of the sportsman, or of the predator, that begins before the properly told effort, show us remarkable anticipatory characteristics. It is impossible to understand the anticipatory behaviour, and the autonomous actions, of the individuals without having recourse to a dual control. We must distinguished a direct control, each element of the action is felt, and a dual control, only the aim of the target is consciously present (attended to), the other elements of the action are relegated to the periphery of the attention. The living being deals with its external middle to establish its internal coherence, but it takes this into account only to distinguish itself by the action. The relationship/separation between the living being and its environment leans both on an internal action (to adapt it), and on an external action (to adapt its middle). The importance of the dual action for the living being, holds in the fact that it exists by the means of its self-constituent activity, "connected to" and "distinct of' a no-self. We use a dynamic structure involving catastrophe theory, to model anticipative process. The dynamics of the predation, a good example of anticipating system, can be described by an attraction of the predator with regard to the prey. René Thom showed how to use the cusp catastrophe to model predation. The predation activity can be defined by a potential. This structure takes in account the duality of the living being, the substance which is a material organisation, and the goal, which is a relational abstraction. In this paper, a new interpretation of the catastrophe theory is given in the framework of hyperincursion: a hyperincursive system is an extension of recursive systems in which the state of the system is computed from a function of itself. A Hyperincursive Cusp Function can be modelled by a Heaviside Cusp Function. A Hyperincursive Boolean Table can be built and a hyperincursive algebraic linear function can model a cusp which represents an elementary flip-flop one bit memory. A recursive process defines the successive states from its initial conditions and a hyperincursive process defines the successive states from the path chosen in the control parameters space. The recursive process is related to an internal observer and the hyperincursive process is related to an extemal observer. Wed, 03 Jul 2024 16:00:21 +0200 Tue, 08 Oct 2024 14:41:07 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=987 http://popups.lib.uliege.be/1373-5411/index.php?id=613 The spread of an epidemic can be studied on a discrete space into small cells arranged into a ds-dimensional regular lattice [Durett & Levin, 1994]. Each sites are occupied by healthy individuals may be infected by neighbours, after which they recover completely, they recover and are subsequently immune, or they die. Such a model is a generalisation of the differential equation approach. It corresponds to a modification of the directed percolation problem, useful to describe a large number of disordered systems in physics and chemistry. A critical concentration separate a phase where the epidemic dies out after a finite number of time steps, from a phase where the epidemic can continue forever. In the simplest models, we assume that the vicinity, in which the infection process takes place, is a small domain surrounding the healthy individual considered. This vicinity is made up of the first layers of M = 3ds-1 cells surrounding the central cell considered (Moore neighbourhood). The purpose of this article is to generalise the dimension of the substrate by introducing a fractal distribution of the sites. For each distribution of infected individuals in this vicinity, there is a certain probability ξ of infection. Due to the self-similarity, the infection quantities are significantly modified on fractal substrate. The fractal distribution of the sites can be related to the spatial distribution of the epidemic vector [Meltzer, 1991]. Vector distribution is a matter of suitable habitat, which is a sum of a wide range of environmental factors (humidity, soil moisture, ground temperature, parasitic-host population density, etc..). The distribution of the sites can be also related to the genetic distribution of the susceptibility of the host population. In a herd, the laws of inheritance form a discrete and recursive system which mixes and distributes the genes of susceptibility. We can propose an aggregation model of relatives around an individual, which is based on the direct inheritance. Fri, 28 Jun 2024 14:53:50 +0200 Fri, 28 Jun 2024 14:53:58 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=613 http://popups.lib.uliege.be/1373-5411/index.php?id=370 Working on the pre-attentive stage of perception by the human visual system (HVS), we propose both a modelling of chromatic perception (l) by means of 4 attactors associated to a mathematical symbolism induced by branching theory, and some structures for the shapes -or coloured shapes- processing. This research involved by the computer graphics and neurophysiology results about recognition of optical signal processing circuits have necessitated to reinvest the visual chain : object (emitter or re-emitter), light information vehicle, the colour receiver, the processors of the SVH. The local physico-mathematical formula set very developed about propagation, has brought solutions for monochromatic waves and for obstacle with smooth edge reveal neither various curvatures (2) nor a fortiori the texture of reemitting object U(3). A resort to a formula-set about interaction matter radiation, extended to a systemic approach,give an algorithmic stage to take account the spatial character (2) and (3). Taking account on one side this scalar conjecture about visual information, and on another side a retinal functional specialisation, we propose a modelling of C occluding edge detection of 3D-object. C except in isolated points by envelop method. The elaboration of a valuation table of morphemes associating the mathematical characteristics of curves with their pregnance treat the more cognitive stage of processing associating edge and colour. Some pictures illustrate the abilities of curves family to suggest 3D-shape. The chromaticity of delimited areas strengthen, or rather create, psycho-affective suggests associated to logos. Wed, 26 Jun 2024 12:17:09 +0200 Fri, 28 Jun 2024 16:58:54 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=370 http://popups.lib.uliege.be/1373-5411/index.php?id=324 In epidemiology (or in biology of populations), an usual process consists in building up local parametrized models, which analysis permits to derive some noteworthy states by weighting speeds of dynamics. The potential existence of complex structures with several chaotic evolution schemes leads to a macroscopical approach by means of non linear dynamic systems. Provided that one calculates different types of means according to some protocols which can be only based on the underlying micro-structures, a way of resolving by the use of multiple scales is efficient. The direct micro bottom-up processing, by means of distribution functions, leads to some relations which are very interesting for physics of collisions, but it doesn't permit to satisfy macroscopic scale constraints, even after successive integrations. We quote pressure as an example. Fri, 21 Jun 2024 14:48:29 +0200 Fri, 21 Jun 2024 14:48:38 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=324