17,225 research outputs found
Effective complexity of stationary process realizations
The concept of effective complexity of an object as the minimal description
length of its regularities has been initiated by Gell-Mann and Lloyd. The
regularities are modeled by means of ensembles, that is probability
distributions on finite binary strings. In our previous paper we propose a
definition of effective complexity in precise terms of algorithmic information
theory. Here we investigate the effective complexity of binary strings
generated by stationary, in general not computable, processes. We show that
under not too strong conditions long typical process realizations are
effectively simple. Our results become most transparent in the context of
coarse effective complexity which is a modification of the original notion of
effective complexity that uses less parameters in its definition. A similar
modification of the related concept of sophistication has been suggested by
Antunes and Fortnow.Comment: 14 pages, no figure
Extreme Quantum Advantage for Rare-Event Sampling
We introduce a quantum algorithm for efficient biased sampling of the rare
events generated by classical memoryful stochastic processes. We show that this
quantum algorithm gives an extreme advantage over known classical biased
sampling algorithms in terms of the memory resources required. The quantum
memory advantage ranges from polynomial to exponential and when sampling the
rare equilibrium configurations of spin systems the quantum advantage diverges.Comment: 11 pages, 9 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/eqafbs.ht
Half-tapering strategy for conditional simulation with large datasets
Gaussian conditional realizations are routinely used for risk assessment and
planning in a variety of Earth sciences applications. Conditional realizations
can be obtained by first creating unconditional realizations that are then
post-conditioned by kriging. Many efficient algorithms are available for the
first step, so the bottleneck resides in the second step. Instead of doing the
conditional simulations with the desired covariance (F approach) or with a
tapered covariance (T approach), we propose to use the taper covariance only in
the conditioning step (Half-Taper or HT approach). This enables to speed up the
computations and to reduce memory requirements for the conditioning step but
also to keep the right short scale variations in the realizations. A criterion
based on mean square error of the simulation is derived to help anticipate the
similarity of HT to F. Moreover, an index is used to predict the sparsity of
the kriging matrix for the conditioning step. Some guides for the choice of the
taper function are discussed. The distributions of a series of 1D, 2D and 3D
scalar response functions are compared for F, T and HT approaches. The
distributions obtained indicate a much better similarity to F with HT than with
T.Comment: 39 pages, 2 Tables and 11 Figure
Vector opinion dynamics in a model for social influence
We present numerical simulations of a model of social influence, where the
opinion of each agent is represented by a binary vector. Agents adjust their
opinions as a result of random encounters, whenever the difference between
opinions is below a given threshold. Evolution leads to a steady state, which
highly depends on the threshold and a convergence parameter of the model. We
analyze the transition between clustered and homogeneous steady states. Results
of the cases of complete mixing and small-world networks are compared.Comment: Latex file, 14 pages and 11 figures, Accepted in Physica
Sum Spectral Efficiency Maximization in Massive MIMO Systems: Benefits from Deep Learning
This paper investigates the joint data and pilot power optimization for
maximum sum spectral efficiency (SE) in multi-cell Massive MIMO systems, which
is a non-convex problem. We first propose a new optimization algorithm,
inspired by the weighted minimum mean square error (MMSE) approach, to obtain a
stationary point in polynomial time. We then use this algorithm together with
deep learning to train a convolutional neural network to perform the joint data
and pilot power control in sub-millisecond runtime, making it suitable for
online optimization in real multi-cell Massive MIMO systems. The numerical
result demonstrates that the solution obtained by the neural network is
less than the stationary point for four-cell systems, while the sum SE loss is
in a nine-cell system.Comment: 4 figures, 1 table. Accepted by ICC 2019. arXiv admin note: text
overlap with arXiv:1901.0362
Effect of risk perception on epidemic spreading in temporal networks
Many progresses in the understanding of epidemic spreading models have been
obtained thanks to numerous modeling efforts and analytical and numerical
studies, considering host populations with very different structures and
properties, including complex and temporal interaction networks. Moreover, a
number of recent studies have started to go beyond the assumption of an absence
of coupling between the spread of a disease and the structure of the contacts
on which it unfolds. Models including awareness of the spread have been
proposed, to mimic possible precautionary measures taken by individuals that
decrease their risk of infection, but have mostly considered static networks.
Here, we adapt such a framework to the more realistic case of temporal networks
of interactions between individuals. We study the resulting model by analytical
and numerical means on both simple models of temporal networks and empirical
time-resolved contact data. Analytical results show that the epidemic threshold
is not affected by the awareness but that the prevalence can be significantly
decreased. Numerical studies highlight however the presence of very strong
finite-size effects, in particular for the more realistic synthetic temporal
networks, resulting in a significant shift of the effective epidemic threshold
in the presence of risk awareness. For empirical contact networks, the
awareness mechanism leads as well to a shift in the effective threshold and to
a strong reduction of the epidemic prevalence
Fluctuation-Dissipation relations in Driven Granular Gases
We study the dynamics of a 2d driven inelastic gas, by means of Direct
Simulation Monte Carlo (DSMC) techniques, i.e. under the assumption of
Molecular Chaos. Under the effect of a uniform stochastic driving in the form
of a white noise plus a friction term, the gas is kept in a non-equilibrium
Steady State characterized by fractal density correlations and non-Gaussian
distributions of velocities; the mean squared velocity, that is the so-called
{\em granular temperature}, is lower than the bath temperature. We observe that
a modified form of the Kubo relation, which relates the autocorrelation and the
linear response for the dynamics of a system {\em at equilibrium}, still holds
for the off-equilibrium, though stationary, dynamics of the systems under
investigation. Interestingly, the only needed modification to the equilibrium
Kubo relation is the replacement of the equilibrium temperature with an
effective temperature, which results equal to the global granular temperature.
We present two independent numerical experiment, i.e. two different observables
are studied: (a) the staggered density current, whose response to an impulsive
shear is proportional to its autocorrelation in the unperturbed system and (b)
the response of a tracer to a small constant force, switched on at time ,
which is proportional to the mean-square displacement in the unperturbed
system. Both measures confirm the validity of Kubo's formula, provided that the
granular temperature is used as the proportionality factor between response and
autocorrelation, at least for not too large inelasticities.Comment: 11 pages, 7 figures, submitted for publicatio
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