http://popups.lib.uliege.be/1373-5411/index.php?id=158 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=920 In real condition, elements form sets whose delimitation is vague, thus defining fuzzy sets in Zadeh's acception or fluids sets according to Gentilhomme's definition. Any system characterized by uncontrollability and disorder in which the least changed in its status at a certain moment rapidly leads to important changes in the status measured at a later moment can be defined as a chaotic system. The interdisciplinary study of chaotic system has become a science of complexity or the science of the chaos. Science has always searched the order in a chaotic universe and the science of the chaos uses a geometry named fractal; fractals are defined as a form at which fractal dimension surpassed its topologic dimension or as any form at which the parts have as many details as the whole or as forms which are strictly self-similar and not statistically self-similar. The notion of information necessary involves the notion of order and the notion of order involves the rationality of system as through the relation information shows how rationally organized the elements of the system are and what rational functionality they fulfill within the order which defines the system. By introducing the concept of structural-diachronic cell associate whit the elementary amount of information (the bit) the paper interprets the concept of information in a fractal manner of maximal generality, in the sense that any fraction of the bit is a bit in itself, the structural-diachronic cells being strictly self similar. The fractal interpretation of the concept of information is the theoretical support of the Basis of Universal Knowledge Similar to the human brain. Mon, 01 Jul 2024 14:07:58 +0200 Tue, 08 Oct 2024 14:38:05 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=920 http://popups.lib.uliege.be/1373-5411/index.php?id=1193 A method to sort out temporal correlations in financial data within the Detrended Fluctuation Analysis (DFA) statistical method is used. Both linear and cubic detrendings are considered. Our findings are surprisingly similar to those for DNA sequences which appeared as a mosaic of coding and non-coding patches. Fri, 05 Jul 2024 15:46:35 +0200 Fri, 05 Jul 2024 15:46:45 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=1193 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=156 This paper shows that different algorithmic methods can generate self-symmetrical Sierpinski fractals. A first category deals with a hyperincursive generator based on a composition rule applied to a defined path in the frame. A second category of algorithms is based on a recursive generator obeying certain symmetries. This paper will consider generalised Sierpinski fractals generated by modulo 2 and modulo 3. Even and odd modulo give rise to very different properties of symmetry. Tue, 18 Jun 2024 16:40:48 +0200 Tue, 18 Jun 2024 16:41:02 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=156