Françoise Fogelman-Soulié

DECREASING ENERGY FUNCTIONS AS A TOOL FOR STUDYING THRESHOLD NETWORKS

Block sequential iterations of threshold networks are studied through the use of a monotonic operator, analogous to the spin glass energy. This allows to characterize the dynamics: transient and fixed points. We then extend this method to networks of generalized majority functions and spin glasses.

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.

RANDOM BOOLEAN NETWORKS

Random boolean networks are defined and used as models of systems composed of many interacting components. Computer simulations showing the organization of these networks in subnets, as well as a temporal organization in limit cycles are reported. The influence of the different boolean laws on this organization is investigated and results concerning the stability of the organization against “surgery” and external noise are presented.

Specific roles of the different Boolean mappings in random networks

Random Boolean networks have striking properties of self-organization. In this paper we propose an algorithm based on the different roles of Boolean mappings and on the connection structure to analyze the organization of the network. For a few cases— transfer mappings, AND/OR, equivalence/XOR—rigorous results are obtained about the dynamics of homogeneous networks. Conclusions are then drawn concerning the non-homogeneous networks.

Emergence of classification procedures in automata networks as a model for functional self-organization

Networks of automata are general models for self-organizing properties of living systems. We study their ability to recognize binary sequences. This property is found to be generic over a large class of networks, is efficient as compared to standard methods and is extendable to hierarchical classification. The mechanism of recognition is explicited.

A case study in a recommender system based on purchase data

Collaborative filtering has been extensively studied in the context of ratings prediction. However, industrial recommender systems often aim at predicting a few items of immediate interest to the user, typically products that (s)he is likely to buy in the near future. In a collaborative filtering setting, the prediction may be based on the users purchase history rather than rating information, which may be unreliable or unavailable. In this paper, we present an experimental evaluation of various collaborative filtering algorithms on a real-world dataset of purchase history from customers in a store of a French home improvement and building supplies chain. These experiments are part of the development of a prototype recommender system for salespeople in the store. We show how different settings for training and applying the models, as well as the introduction of domain knowledge may dramatically influence both the absolute and the relative performances of the different algorithms. To the best of our knowledge, the influence of these parameters on the quality of the predictions of recommender systems has rarely been reported in the literature.

A Social Formalism and Survey for Recommender Systems

This paper presents a general formalism for Recommender Systems based on Social Network Analysis. After introducing the classical categories of recommender systems, we present our Social Filtering formalism and show that it extends association rules, classical Collaborative Filtering and Social Recommendation, while providing additional possibilities. This allows us to survey the literature and illustrate the versatility of our approach on various publicly available datasets, comparing our results with the literature.

Parallel and sequential computation on Boolean networks

Abstract A model of large assemblies of computing elements is provided by the concept of boolean network F :{0, 1} n → {0, 1} n . Then we compare different regimes of this system, namely, parallel and sequential computations within the framework of discrete iterations. It is shown that, although the asymptotic behavior of the network—as characterized by the limit cycles of the iterations—may differ from one sort of regime to another, it may, however, be largely predicted as for its spatial structure. We show that for all iterations some elements never change state in any limit cycle: they form the stable core. We introduce the notion of forcing domain of a boolean network, provide an algorithm to build it and show that it is a good approximation to the stable core. This, thus, provides a spatial characterization of the limit cycles of the different iterations. A theoretical bound on the transient length is provided through the entropy of the network.

Frustration and stability in random boolean networks

Abstract Discrete iterations of boolean mappings are known to yield to limit cycles [3, 8]. These limit cycles share a common stable part: the stable core which never oscillate along the different limit cycles. We show that non-frustrated circuits (defined as an extension of [7, 10]) are part of this core. We then characterize non-frustration — thus stability — in terms of the discrete derivative as introduced in [6, 11, 12].

Monetization and Services on a Real Online Social Network Using Social Network Analysis

Large social networks provide many services to their users for free. To be able to do so, these sites need to monetize their audience, in order to increase the level of services offered to their users and develop their business. Monetization of a social network platform comes not only from efficient advertising features but also from all features which would contribute in increasing the audience. In this paper, we focus on 3 monetization axes: community management, personalized advertising, and recommendation. We propose for each of these axes several features we can implement using social network analysis. These features were tested on the data of a real French social blog platform Skyrock.com, the second largest social network in France.