Gérard Weisbuch

Mixing beliefs among interacting agents

We present a model of opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. High thresholds yield convergence of opinions towards an average opinion, whereas low thresholds result in several opinion clusters: members of the same cluster share the same opinion but are no longer influenced by members of other clusters.

Meet, discuss, and segregate!

We present a model of opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. High thresholds yield convergence of opinions toward an average opinion, whereas low thresholds result in several opinion clusters. The model is further generalized to network interactions, threshold heterogeneity, adaptive thresholds, and binary strings of opinions.

Disordered systems and biological organization

The NATO workshop on Disordered Systems and Biological Organization was attended, in march 1985, by 65 scientists representing a large variety of fields: Mathematics, Computer Science, Physics and Biology. It was the purpose of this interdisciplinary workshop to shed light on the conceptual connections existing between fields of research apparently as different as: automata theory, combinatorial optimization, spin glasses and modeling of biological systems, all of them concerned with the global organization of complex systems, locally interconnected. Common to many contributions to this volume is the underlying analogy between biological systems and spin glasses: they share the same properties of stability and diversity. This is the case for instance of primary sequences of biopo Iymers I ike proteins and nucleic acids considered as the result of mutation-selection processes [P. W. Anderson, 1983] or of evolving biological species [G. Weisbuch, 1984]. Some of the most striking aspects of our cognitive apparatus, involved In learning and recognttlon [J. Hopfield, 19821, can also be described in terms of stability and diversity in a suitable configuration space. These interpretations and preoccupations merge with those of theoretical biologists like S. Kauffman [1969] (genetic networks) and of mathematicians of automata theory: the dynamics of networks of automata can be interpreted in terms of organization of a system in multiple possible attractors. The present introduction outlInes the relationships between the contributions presented at the workshop and brIefly discusses each paper in its particular scientific context.

Social percolation models

We here relate the occurrence of extreme market shares, close to either 0 or 100%, in the media industry to a percolation phenomenon across the social network of customers. We further discuss the possibility of observing self-organized criticality when customers and cinema producers adjust their preferences and the quality of the produced films according to previous experience. Comprehensive computer simulations on square lattices do indeed exhibit self-organized criticality towards the usual percolation threshold and related scaling behaviour.

Bounded confidence and social networks

Abstract.In the so-called bounded confidence model proposed by Deffuant et al, agents can influence each other’s opinion provided that the opinions are already sufficiently close enough. We discuss here the influence of possible social network topologies on the dynamics of this model.

Localized memories in idiotypic networks

The present paper investigates conditions under which immunological memory can be maintained by stimulatory idiotypic network interactions. The paper was motivated by the work of (De Boer & Hogeweg, 1989b, Bull. math. Biol. 51, 381-408.) which claimed that idiotypic memory is not possible because of percolation within the network. Here we reinvestigate the issue of percolation using both the previous model and a simpler one (Weisbuch, 1990, J. theor. Biol. 143, 507-522.) that allows analytic analysis. We focus on network topologies in which each Ab1 is connected to several Ab2s, which in turn are connected to several Ab3s. It is demonstrated that, for a considerable range of parameters, both models account for the existence of localized memory-states in which only the Ab1 and the Ab2 clones are activated and the clones of the Ab3 level remain virgin. The existence of localized memory-states seems to contradict the previous percolation result. This discrepancy will be shown to depend on the system dynamics. By simulation we explore the parameter regimes for which one finds percolation and those for which localized memory-states exists. We show that the conditions required for attaining the localized memory-state are considerably more stringent than those required for its existence and local stability. We conclude that both localized memory and percolation are possible in stimulatory idiotypic networks.

Dynamical Phase Transitions in 3-Dimensional Spin Glasses

We study the time evolution of the distance between two configurations submitted to the same thermal noise for the 3d ± J Ising spin glass. We observe three temperature regimes: a high-temperature regime where the distances vanishes in the long-time limit. An intermediate-temperature regime where the distance has a nonzero limit independent of the initial distance. A low-temperature regime where the distance in the long time limit seems to depend upon the initial distance. For the sake of comparison, we have repeated our simulations for the ferromagnetic case.

Interacting Agents and Continuous Opinions Dynamics

We present a model of opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. High thresholds yield convergence of opinions towards an average opinion, whereas low thresholds result in several opinion clusters. The model is further generalised to threshold heterogeneity, adaptive thresholds and binary strings of opinions.

Theoretical and experimental insights into immunology

Immunology is largely a science of observation and experimentation, and these approaches have lead to great increases in our knowledge of the genes, molecules and cells of the immune system. This book is an up-to-date discussion of the current state of modelling and theoretical work in immunology, of the impact of theory on experiment, and of future directions for theoretical research. Among the topics discussed are the function and evolution of the immune system, computer modelling of the humoral immune response and of idiotypic networks and idiotypic mimicry, T-cell memory, cryptic peptides, new views and models of AIDS and autoimmunity, and the shaping of the immune repertoire by early presented antigens and self-immunoglobulin.

Decision making dynamics in corporate boards

Members of boards of directors of large corporations who also serve together on an outside board, form the so-called interlock graph of the board and are assumed to have a strong influence on each others’ opinion. We here study how the size and the topology of the interlock graph affect the probability that the board approves a strategy proposed by the Chief Executive Officer. We propose a measure of the impact of the interlock on the decision making, which is found to be a good predictor of the decision dynamics outcome. We present two models of decision making dynamics, and we apply them to the data of the boards of the largest US corporations in 1999.