C. Vidal – författare

This book deals with combinatorial aspects of epistasis, a notion that existed for years in genetics and appeared in the ?eld of evolutionary algorithms in the early 1990s. Even thoughthe?rst chapterputsepistasisintheperspective ofevolutionary algorithms and arti?cial intelligence, and applications occasionally pop up in other chapters, thisbookisessentiallyaboutmathematics, aboutcombinatorialtechniques to compute in an e?cient and mathematically elegant way what will be de?ned as normalized epistasis. Some of the material in this book ?nds its origin in the PhD theses of Hugo Van Hove [97] and Dominique Suys [95]. The sixth chapter also contains material that appeared in the dissertation of Luk Schoofs [84]. Together with that of M. Teresa Iglesias [36], these dissertations form the backbone of a decade of mathematical ventures in the world of epistasis. The authors wish to acknowledge support from the Flemish Fund of Scienti?c - search (FWO-Vlaanderen) and of the Xunta de Galicia.They also wish to explicitly mentiontheintellectualandmoralsupporttheyreceivedthroughoutthepreparation of this work from their family and their colleagues Emilio Villanueva, Jose Mar'a Barja and Arnold Beckelheimer, as well as our local T T Xpert Jan Adriaenssens.

This volume gathers most of the lectures and communications presented at the meeting t held in Bordeaux from the 27th to the 29 h of September and entitled "Far from equi­ librium : instabilities and structures". This meeting is part of a series of seve­ ral other interdisciplinary conferences such as Elmau 1972, London 1974, Dortmund 1976, Elmau 1977, Tokyo 1978. The old science classification scheme proposed by Auguste Comte tends to be eve­ ry day a bit more blurred out: one gives here, if needed, one additional illustra­ tion of this trend. The three key words "far from equilibrium", "instabilities" and "structures" best illustrate the new concepts which emerge from the description of the dynamics of various systems relevant to many different research areas. Laser emission, chemical reactions, fluid motions, exhibit very particular phenomena when, under appropriate external action,they occur far from equilibrium. These proceedings include the experimental description of such phenomena as well as theoretical at­ tempts in understanding them. Most of the topics investigated here belong to the domains of physics and chemistry but one should be careful not to underestimate the underlying potential biological interest. If the study of simple systems (e. g. , described by a few variables) has been qui­ te successful for several centuries, the recent bearing of our attention on complex systems constitutes a genuine epistemological breakthrough bridging the gap which used to exist between the sciences and the humanism.

This volume gathers most of the lectures and communications presented at the meeting t held in Bordeaux from the 27th to the 29 h of September and entitled "Far from equi­ librium : instabilities and structures". This meeting is part of a series of seve­ ral other interdisciplinary conferences such as Elmau 1972, London 1974, Dortmund 1976, Elmau 1977, Tokyo 1978. The old science classification scheme proposed by Auguste Comte tends to be eve­ ry day a bit more blurred out: one gives here, if needed, one additional illustra­ tion of this trend. The three key words "far from equilibrium", "instabilities" and "structures" best illustrate the new concepts which emerge from the description of the dynamics of various systems relevant to many different research areas. Laser emission, chemical reactions, fluid motions, exhibit very particular phenomena when, under appropriate external action,they occur far from equilibrium. These proceedings include the experimental description of such phenomena as well as theoretical at­ tempts in understanding them. Most of the topics investigated here belong to the domains of physics and chemistry but one should be careful not to underestimate the underlying potential biological interest. If the study of simple systems (e. g. , described by a few variables) has been qui­ te successful for several centuries, the recent bearing of our attention on complex systems constitutes a genuine epistemological breakthrough bridging the gap which used to exist between the sciences and the humanism.

Markedly apart from elementary particle physics, another current has been building up and cont i nuous ly growi ng within contemporary phys i cs for severa 1 decades, and even expanding into many other disciplines, especially chemistry, biology and, quite recently, economics. Several reasons account for this: presumably the most impor- tant one lies in the fact that, whatever the specific problem, model or material concerned, the same basic mathematical features are always involved. In this way, a general phenomenology has emerged which, unlike thermodynamics, is no longer depen- dent upon the details or specifics: what largely prevails is the nonlinear charac- ter of the underlying dynamics. Perhaps we are witnessing the emergence of a "non- linear physics" - in a way similar to the birth of "quantum physics" in the twen- ties - a physics which deals with the general behaviour of systems, whatever they are or may be.Over the past fifteen years, chemical systems evolving sufficiently far from equilibrium have proved to be particularly well fitted to experimental research on nonlinear behaviour: oscillation, multistability, birhythmicity, chaotic evolution, spatial self-organization and hysteresis are displayed by chemical reactions whose number is growing each year. In this volume are collected the lectures, communica- tions and posters (abstracts) presented at an international meeting entitled: "Non-Equilibrium Dynamics in Chemical Systems", held in Bordeaux (France), Septem- ber 3 rd-lth, 1984.

An international conference. titled Nonlinear Phenomena in Chemical Dynamics was held in Bordeaux on September 7-11, 1981. The present volume contains the text of lectures and abstracts of posters presented during the meeting. This conference is part of a series of scientific multidisciplinary meetings in which chemistry is involved at various levels. Amongst the most recent ones let us mention Aachen 1979, Bielefeld 1979, New York 1979, Elmau 1981. In addition, this meeting is a direct extension of the first one that took place in Bordeaux in 1978 on the topic "Far from equilibrium: instabilities and structures," at the conclusions of which we could write (cf. Far fram Equilibrium, Springer Series in Synergetics, Vol. 3): "The three key words, far fram equilibriUm, instabilities and structuPes, best illustrate the new concepts which emerge from the description of the dynamics of various systems relevant to many different research areas. " The present proceedings show how much these remarks have remained true, even though substantial progress has been achieved during the three last years. To get a ,deeper experimental knowledge of open reacting systems, to model and simulate reaction-diffusion systems, to develop the mathematical theory of dynamical sys­ tems, these are the main direction~ in current investigations.

An international conference. titled Nonlinear Phenomena in Chemical Dynamics was held in Bordeaux on September 7-11, 1981. The present volume contains the text of lectures and abstracts of posters presented during the meeting. This conference is part of a series of scientific multidisciplinary meetings in which chemistry is involved at various levels. Amongst the most recent ones let us mention Aachen 1979, Bielefeld 1979, New York 1979, Elmau 1981. In addition, this meeting is a direct extension of the first one that took place in Bordeaux in 1978 on the topic "Far from equilibrium: instabilities and structures," at the conclusions of which we could write (cf. Far fram Equilibrium, Springer Series in Synergetics, Vol. 3): "The three key words, far fram equilibriUm, instabilities and structuPes, best illustrate the new concepts which emerge from the description of the dynamics of various systems relevant to many different research areas. " The present proceedings show how much these remarks have remained true, even though substantial progress has been achieved during the three last years. To get a ,deeper experimental knowledge of open reacting systems, to model and simulate reaction-diffusion systems, to develop the mathematical theory of dynamical sys­ tems, these are the main direction~ in current investigations.