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A four-node network consisting of a negative circuit controlling a positive one is studied. It models some of the features of the p53 gene network. Using piecewise linear dynamics with thresholds, the allowed dynamical classes are fully characterized and coded. The biologically relevant situations are identified and conclusions drawn concerning the… (More)

- R. Vilela Mendes
- 1999

In addition to the emergent complexity of patterns that appears when many agents come in interaction, it is also useful to characterize the dynamical processes that lead to their self-organization. A set of ergodic invariants is identified for this purpose, which is computed in several examples, namely a Bernoulli network with either global or… (More)

Small-world (SW) networks have been identified in many different fields. Topological coefficients like the clustering coefficient and the characteristic path length have been used in the past for a qualitative characterization of these networks. Here a dynamical approach is used to characterize the small-world phenomenon. Using the β−model, a coupled map… (More)

—The immune system is a cognitive system of complexity comparable to the brain and its computational algorithms suggest new solutions to engineering problems or new ways of looking at these problems. Using immunological principles, a two-(or three-) module algorithm is developed which is capable of launching a specific response to an anomalous situation for… (More)

—Formal language techniques have been used in the past to study autonomous dynamical systems. However, for controlled systems, new features are needed to distinguish between information generated by the system and input control. We show how the modeling framework for controlled dynamical systems leads naturally to a formulation in terms of context-dependent… (More)

In this paper we introduce and briefly discuss some of the basic results of large-deviation theory. We propose that large-deviation analysis be used as a tool complementary to the usual intermittency analysis because, as we show, systems exhibiting similar factorial moment behaviour may be quite different from the point of view of large-deviation… (More)

The main problem we address in this paper is whether function determines form when a society of agents organizes itself for some purpose or whether the organizing method is more important than the functionality in determining the structure of the ensemble. As an example, we use a neural network that learns the same function by two different learning… (More)

Networks have been studied mainly by statistical methods which emphasize their topological structure. Here, one collects some mathematical tools and results which might be useful to study both the dynamics of agents living on the network and the networks themselves as evolving dynamical systems. They include decomposition of differential dynamics, ergodic… (More)

- R. Vilela Mendes
- 2002

Using a metric related to the returns correlation, a method is proposed to reconstruct an economic space from the market data. A reduced subspace, associated to the systematic structure of the market , is identified and its dimension related to the number of terms in factor models. Example were worked out involving sets of companies from the DJIA and S&P500… (More)

Formal language techniques have been used in the past to study autonomous dynamical systems. However, for controlled systems, new features are needed to distinguish between information generated by the system and input control. We show how the modelling framework for controlled dynamical systems leads naturally to a formulation in terms of context-dependent… (More)