arXiv subjects

R. Vilela Mendes

Publications and source records attributed to R. Vilela Mendes.

At least 91 records · Page 5Linked to original sources

arXiv2001

Using Immunology Principles for Anomaly Detection in Electrical Systems

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. Applications are being developed for electromechanical drives and network power transformers. Experimental results illustrate an application to fault detection in squirrel-cage electric motors.

nlin.AO↗

arXiv2001

Non-commutative space-time and the uncertainty principle

The full algebra of relativistic quantum mechanics (Lorentz plus Heisenberg) is unstable. Stabilization by deformation leads to a new deformation parameter $ε\ell ^{2}$, $\ell $ being a length and $ε$ a $\pm$ 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 following from gravity and string theory.

quant-ph↗

arXiv2001

Quantum computation by quantum-like systems

Using a quantumlike description for light propagation in nonhomogeneous optical fibers, quantum information processing can be implemented by optical means. Quantum-like bits (qulbits) are associated to light modes in the optical fiber and quantum gates to segments of the fiber providing an unitary transformation of the mode structure along a space direction. Simulation of nonlinear quantum effects is also discussed.

quant-ph↗

arXiv2001

A process-reconstruction analysis of market fluctuations

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 other topics are also discussed, in particular the asymptotic stationarity of the processes and the behavior of statistical indicators of level (1) and (2). We end up with some remarks concerning the nature of the market fluctuation process.

cond-mat.stat-mech↗

arXiv2001

Tomograms and other transforms. A unified view

A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the symplectic and affine groups is treated in some detail. Special emphasis is given to the properties of the scale-time and scale-frequency tomograms. Tomograms are interpreted as a tool to sample the signal space by a family of curves or as the matrix element of a projector.

math-ph↗

arXiv2000

Structure-generating mechanisms in agent-based models

The emergence of dynamical structures in multi-agent systems is analysed. Three different mechanisms are identified, namely: (1) sensitive-dependence and convex coupling, (2) sensitive-dependence and extremal dynamics and (3) interaction through a collectively generated field. The dynamical origin of the emergent structures is traced back either to a modification, by interaction, of the Lyapunov spectrum or to multistable dynamics.

nlin.AO↗

arXiv2000

Function and form in networks of interacting agents

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 methods. For sufficiently large networks, very different structures may indeed be obtained for the same functionality. Clustering, characteristic path length and hierarchy are structural differences, which in turn have implications on the robustness and adaptability of the networks. In networks, as opposed to simple graphs, the connections between the agents are not necessarily symmetric and may have positive or negative signs. New characteristic coefficients are introduced to characterize this richer connectivity structure.

nlin.AO↗

arXiv2000

Gauge strata and particle generations

Phenomenological evidence suggests the existence of non-trivial background fields in the QCD vacuum. On the other hand SU(3) gauge theory possessses three different classes of both non-generic and non-trivial strata that may be used as classical backgrounds. It is suggested that this three-fold multiplicity of non-trivial vacua may be related to the existence of particle generations, which would then find an explanation in the framework of the standard model.

hep-th↗

arXiv2000

Language identification of controlled systems: Modelling, control and anomaly detection

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 grammars. A learning algorithm is proposed for on-line generation of the grammar productions, this formulation being then used for modelling, control and anomaly detection. Practical applications are described for electromechanical drives. Grammatical interpolation techniques yield accurate results and the pattern detection capabilities of the language-based formulation makes it a promising technique for the early detection of anomalies or faulty behaviour.

cs.CL↗

arXiv2000

From synchronization to multistability in two coupled quadratic maps

The phenomenology of a system of two coupled quadratic maps is studied both analytically and numerically. Conditions for synchronization are given and the bifurcations of periodic orbits from this regime are identified. In addition, we show that an arbitrarily large number of distinct stable periodic orbits may be obtained when the maps parameter is at the Feigenbaum period-doubling accumulation point. An estimate is given for the coupling strength needed to obtain any given number of stable orbits.

nlin.CD↗

arXiv2000

Lyapunov exponent in quantum mechanics. A phase-space approach

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 classical and quantum notions is very clear. Then we also obtain the corresponding expressions in Hilbert space. Some examples are worked out. Classical and quantum exponents are seen to coincide for local and non-local time-dependent quadratic potentials. For non-quadratic potentials classical and quantum exponents are different and some insight is obtained on the taming effect of quantum mechanics on classical chaos. A detailed analysis is made for the standard map. Providing an unambiguous extension of the notion of Lyapunov exponent to quantum mechnics, the method that is developed is also computationally efficient in obtaining analytical results for the Lyapunov exponent, both classical and quantum.

quant-ph↗

arXiv1999

Geometry, stochastic calculus and quantum fields in a non-commutative space-time

The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic quantum mechanics algebra is also unstable. Its stabilization requires the non-commutativity of the space-time coordinates and the existence of a fundamental length constant. The new relativistic quantum mechanics algebra has important consequences on the geometry of space-time, on quantum stochastic calculus and on the construction of quantum fields. Some of these effects are studied in this paper.

math-ph↗

arXiv1999

Multistability in dynamical systems

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 unstable invariant sets. A short review of the existent results is presented, as well as two new results concerning the existence of a large number of stable periodic orbits in a perturbed marginally stable dissipative map and an infinite number of such orbits in two coupled quadratic maps working on the Feigenbaum accumulation point.

chao-dyn↗

arXiv1999

On some dynamical problems related to boundary layer turbulence

A number of simplified dynamical problems is studied in an attempt to clarify some of the mechanisms leading to turbulence and the existing proposals to control this transition. A simplified set of boundary layer equations displays a solution that corresponds to the rolls and streaks instability and exhibits its streamwise localized nature. The effect of random phases as a device to control the transfer of energy to the small scales is studied both for the shell and the boundary layer models. In spite of the simplified nature of the models, they also provide some insight on the prospects for active turbulence control by external body forces.

physics.flu-dyn↗

arXiv1999

Characterizing self-organization and coevolution by ergodic invariants

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 nearest-neighbor coupling, a generalized Bak-Sneppen model and a continuous minority model.

adap-org↗

arXiv1998

Clustering and synchronization with positive Lyapunov exponents

Clustering and correlation effects are frequently observed in chaotic systems in situations where, because of the positivity of the Lyapunov exponents, no dimension reduction is to be expected. In this paper, using a globally coupled network of Bernoulli units, one finds a general mechanism by which strong correlations and slow structures are obtained at the synchronization edge. A structure index is defined, which diverges at the transition points. Some conclusions are drawn concerning the construction of an ergodic theory of self-organization.

adap-org↗

arXiv1998

Neural networks and logical reasoning systems. A translation table

A correspondence is established between the elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the hardware and dynamical operations of neural networks. The correspondence is framed as a general translation dictionary which, hopefully, will allow to go back and forth between symbolic and network formulations, a desirable step in learning-oriented systems and multicomputer networks. In the framework of Horn clause logics it is found that atomic propositions with n arguments correspond to nodes with n-th order synapses, rules to synaptic intensity constraints, forward chaining to synaptic dynamics and queries either to simple node activation or to a query tensor dynamics.

cond-mat.dis-nn↗

arXiv1998

Dynamics of networks and applications

A survey is made of several aspects of the dynamics of networks, with special emphasis on unsupervised learning processes, non-Gaussian data analysis and pattern recognition in networks with complex nodes.

cond-mat.dis-nn↗