Quantum Uncertainty in Doubly Special Relativity

The modification of the quantum mechanical commutators in a relativistic theory with an invariant length scale (DSR) is identified. Two examples are discussed where a classical behavior is approached in one case when the energy approaches the inverse of the invariant length which appears as a cutoff in the energy and in the second case when the mass is much larger than the inverse of the invariant length.Comment: 4 pages, no figure

Characterization of Local Configuration Controllability for a Class of Mechanical Systems

We investigate local configuration controllability for mechanical control systems within the affine connection formalism. Extending the work by Lewis for the single-input case, we are able to characterize local configuration controllability for systems with $n$ degrees of freedom and $n-1$ input forces.Comment: 20 pages, no figure

Constraints from Neutrino Decay on Superluminal Velocities

The splitting of neutrinos, a viable reaction for superluminal neutrinos, is shown to have phenomenologically relevant consequences if one accepts the recent OPERA results for the velocity of neutrinos. Neutrino splitting can be used to put strong constraints on the energy dependence of the velocity of propagation of neutrinos in a general analysis of modifications of relativistic kinematics and to propose observable effects due to the departures from special relativity in neutrino physics

Departures from special relativity beyond effective field theories

The possibility to have a deviation from relativistic quantum field theory requiring to go beyond effective field theories is discussed. A few recent attempts to go in this direction both at the theoretical and phenomenological levels are briefly reviewed.Comment: 8 pages, in honor of Adriano Di Giacomo on his 70th birthday, contribution to the Festschrif

Fine-tuning problems in quantum field theory and Lorentz invariance: A scalar-fermion model with a physical momentum cutoff

We study the consistency of having Lorentz invariance as a low energy approximation within the quantum field theory framework. A model with a scalar and a fermion field is used to show how a Lorentz invariance violating high momentum scale, a physical cutoff rendering the quantum field theory finite, can be made compatible with a suppression of Lorentz invariance violations at low momenta. The fine tuning required to get this suppression and to have a light scalar particle in the spectrum is determined at one loop.Comment: Revised version; minor changes. The main content of the paper is not altere

Chaotic hopping between attractors in neural networks

We present a neurobiologically--inspired stochastic cellular automaton whose state jumps with time between the attractors corresponding to a series of stored patterns. The jumping varies from regular to chaotic as the model parameters are modified. The resulting irregular behavior, which mimics the state of attention in which a systems shows a great adaptability to changing stimulus, is a consequence in the model of short--time presynaptic noise which induces synaptic depression. We discuss results from both a mean--field analysis and Monte Carlo simulations.Comment: 12 pages, 5 figure

Control of neural chaos by synaptic noise

We studied neural automata -or neurobiologically inspired cellular automata- which exhibits chaotic itinerancy among the different stored patterns or memories. This is a consequence of activity-dependent synaptic fluctuations, which continuously destabilize the attractor and induce irregular hopping to other possible attractors. The nature of the resulting irregularity depends on the dynamic details, namely, on the intensity of the synaptic noise and on the number of sites of the network that are synchronously updated at each time step. Varying these details, different regimes occur from regular to chaotic. In the absence of external agents, the chaotic behavior may turn regular after tuning the noise intensity. It is argued that a similar mechanism might be at the origin of the self-control of chaos in natural systems.Comment: 6 pages, 3 figures. To appear in Biosystems, 200

Complex Networks: Time-Dependent Connections and Silent Nodes

We studied, both analytically and numerically, complex excitable networks, in which connections are time dependent and some of the nodes remain silent at each time step. More specifically, (a) there is a heterogenous distribution of connection weights and, depending on the current degree of order, some connections are reinforced/weakened with strength Phi on short-time scales, and (b) only a fraction rho of nodes are simultaneously active. The resulting dynamics has attractors which, for a range of Phi values and rho exceeding a threshold, become unstable, the instability depending critically on the value of rho. We observe that (i) the activity describes a trajectory in which the close neighborhood of some of the attractors is constantly visited, (ii) the number of attractors visited increases with rho, and (iii) the trajectory may change from regular to chaotic and vice versa as rho is, even slightly modified. Furthermore, (iv) time series show a power-law spectra under conditions in which the attractors' space is most efficiently explored. We argue on the possible qualitative relevance of this phenomenology to networks in several natural contexts.Comment: 12 pages, 7 figure

Instability of attractors in autoassociative networks with bioinspired fast synaptic noise

We studied autoassociative networks in which synapses are noisy on a time scale much shorter that the one for the neuron dynamics. In our model a presynaptic noise causes postsynaptic depression as recently observed in neurobiological systems. This results in a nonequilibrium condition in which the network sensitivity to an external stimulus is enhanced. In particular, the fixed points are qualitatively modified, and the system may easily scape from the attractors. As a result, in addition to pattern recognition, the model is useful for class identification and categorization.Comment: 6 pages, 2 figure

On the approximation of the probability density function of the randomized heat equation

In this paper we study the randomized heat equation with homogeneous boundary conditions. The diffusion coeffcient is assumed to be a random variable and the initial condition is treated as a stochastic process. The solution of this randomized partial differential equation problem is a stochastic process, which is given by a random series obtained via the classical method of separation of variables. Any stochastic process is determined by its finite-dimensional joint distributions. In this paper, the goal is to obtain approximations to the probability density function of the solution (the first finite-dimensional distributions) under mild conditions. Since the solution is expressed as a random series, we perform approximations of its probability density function. We use two approaches: broadly speaking, first, dealing with the random Fourier coefficients of the random series, and second, taking advantage of the Karhunen-Loeve expansion of the initial condition stochastic process. Finally, several numerical examples illustrating the potentiality of our findings with regard to both approaches are presented.Comment: Pages: 35; Figures: 31 Tables: