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- 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)

- V I Man 'ko, R Vilela Mendes
- 2000

Using the symplectic tomography map, both for the probability distributions in classical phase space and for the Wigner functions of its quantum counterpart, we discuss a notion of Lyapunov exponent for quantum dynamics. Because the marginal distributions, obtained by the tomography map, are always well defined probabilities, the correspondence between… (More)

- R Vilela Mendes
- 1999

In neuroscience, optics and condensed matter there is ample physical evidence for multistable dynamical systems, that is, systems with a large number of attractors. The known mathematical mechanisms that lead to multiple attractors are homoclinic tangencies and stabilization , by small perturbations or by coupling, of systems possessing a large number of… (More)

- Carlos Aguirre, João F. Martins, Rui Vilela Mendes
- I. J. Bifurcation and Chaos
- 2006

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)

Accurate control of quantum evolution is an essential requirement for quantum state engineering, laser chemistry, quantum information and quantum computing. Conditions of controllability for systems with a finite number of energy levels have been extensively studied. By contrast, results for controllability in infinite dimensions have been mostly negative,… (More)

- R. Vilela Mendes
- 2004

A deterministic version of the Bak-Sneppen model is studied. The role of the Lyapunov spectrum in the onset of scale-free behavior is established and avalanches are interpreted as return times to a zero-measure set. The problem of accurate determination of the scaling exponents near the critical barrier is addressed using a characteristic function approach.… (More)

- Paulo J. Costa Branco, J. A. Dente, Rui Vilela Mendes
- IEEE Trans. Industrial Electronics
- 2003

—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)

- R. Vilela Mendes, R. Limaand, T. Araújo
- 2001

The statistical properties of a stochastic process may be described (1)by the expectation values of the observables, (2)by the probability distribution functions or (3)by probability measures on path space. Here an analysis of level (3) is carried out for market fluctuation processes. Gibbs measures and chains with complete connections are considered. Some… (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 full algebra of relativistic quantum mechanics (Lorentz plus Heisenberg) is unstable. Stabilization by deformation leads to a new deformation parameter εℓ 2 , ℓ being a length and ε a ± sign. The implications of the deformed algebras for the uncertainty principle and the density of states are worked out and compared with the results of past analysis… (More)