14,008 research outputs found
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 degrees of freedom and 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:
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