Archive ouverte UNIGE | last documents for author 'Gregor Chliamovitch'https://archive-ouverte.unige.ch/Latest objects deposited in the Archive ouverte UNIGE for author 'Gregor Chliamovitch'engAssessing complexity in cellular automata using information theoryhttps://archive-ouverte.unige.ch/unige:137995https://archive-ouverte.unige.ch/unige:137995We discuss two ways in which information theory can be used to assess complexity in a system of interacting agents. In the first part, we adopt a global viewpoint and propose a characterization of complexity based on successive maximum entropy estimations of the probability density describing the system, thereby quantifying the respective role played by low and high orders of interaction. In the second part we reconsider the question from a local perspective, focussing on the statistical dependencies between neighbouring agents. These tools are tried on simple cellular automata in order to put them in perspective with other notions of complexity usually employed for such systems. We show that these approaches are hardly comparable, despite some overlap in simple cases. However this allows to interpret complexity in terms of interactions at work in a system (instead of making reference to any particular realization of this dynamics), and to shed some light on the role of initial conditions in complex systems. Clustering of the 88 non-equivalent Elementary Cellular Automata according to their position in the space of information processing features. Rules are coloured according to their Wolfram class. ECA in class I are shown in black, class II in red, chaotic automata (class III) in green and automata displaying complex behaviour (class IV) in blue. In spite of some important important differences, information features and Wolfram class are seen to overlap to a certain extent.Fri, 26 Jun 2020 12:18:44 +0200Kinetic Theory beyond the Stosszahlansatzhttps://archive-ouverte.unige.ch/unige:135931https://archive-ouverte.unige.ch/unige:135931In a recent paper (Chliamovitch, et al., 2015), we suggested using the principle of maximum entropy to generalize Boltzmann’s Stosszahlansatz to higher-order distribution functions. This conceptual shift of focus allowed us to derive an analog of the Boltzmann equation for the two-particle distribution function. While we only briefly mentioned there the possibility of a hydrodynamical treatment, we complete here a crucial step towards this program. We discuss bilocal collisional invariants, from which we deduce the two-particle stationary distribution. This allows for the existence of equilibrium states in which the momenta of particles are correlated, as well as for the existence of a fourth conserved quantity besides mass, momentum and kinetic energy.Mon, 18 May 2020 15:28:53 +0200Multi-scale representation of high frequency market liquidityhttps://archive-ouverte.unige.ch/unige:135927https://archive-ouverte.unige.ch/unige:135927We introduce an event based framework mapping financial data onto a state based discretisation of time series. The mapping is intrinsically multi-scale and naturally accommodates itself with tick-by-tick data. Within this framework, we define an information theoretic quantity that characterises the unlikeliness of price trajectories and, akin to a liquidity measure, detects and predicts stress in financial markets. In particular, we show empirical examples within the foreign exchange market where the new measure not only quantifies liquidity but also seems to act as an early warning signal.Mon, 18 May 2020 15:20:28 +0200Information theory and maximum entropy principles in non-equilibrium statistical physicshttps://archive-ouverte.unige.ch/unige:96244https://archive-ouverte.unige.ch/unige:96244Complexity is often envisaged as the impossibility of reconstructing the whole of a system from the knowledge of its parts. When a probabilistic description is in order, a mathematically rigorous way to formalize this intuition is to rely on the principle of maximum entropy as a tool to infer probability distributions from structural or observational constraints. This thesis aims at evaluating this heuristic criterion in three different contexts. First, we consider the case where the transition matrix generating a discrete and finite Markov process has to be rebuilt from observed autocorrelation, with an emphasis on short historical samples. Second, we examine how maximum entropy methods and information theory can be linked to complexity as usually expressed in the particular context of cellular automata. The last part reconsiders key assumptions underlying kinetic theory of gases from the perspective of information theory, aiming in particular at generalizing Boltzmann's molecular chaos hypothesis.Wed, 23 Aug 2017 09:11:01 +0200