21,022 research outputs found
Large System Analysis of the Energy Consumption Distribution in Multi-User MIMO Systems with Mobility
In this work, we consider the downlink of a single-cell multi-user MIMO
system in which the base station (BS) makes use of antennas to communicate
with single-antenna user equipments (UEs). The UEs move around in the cell
according to a random walk mobility model. We aim at determining the energy
consumption distribution when different linear precoding techniques are used at
the BS to guarantee target rates within a finite time interval . The
analysis is conducted in the asymptotic regime where and grow large
with fixed ratio under the assumption of perfect channel state information
(CSI). Both recent and standard results from large system analysis are used to
provide concise formulae for the asymptotic transmit powers and beamforming
vectors for all considered schemes. These results are eventually used to
provide a deterministic approximation of the energy consumption and to study
its fluctuations around this value in the form of a central limit theorem.
Closed-form expressions for the asymptotic means and variances are given.
Numerical results are used to validate the accuracy of the theoretical analysis
and to make comparisons. We show how the results can be used to approximate the
probability that a battery-powered BS runs out of energy and also to design the
cell radius for minimizing the energy consumption per unit area. The imperfect
CSI case is also briefly considered.Comment: 8 figures, 2 tables, to appear on IEEE Transactions on Wireless
Communication
Is the Voter Model a model for voters?
The voter model has been studied extensively as a paradigmatic opinion
dynamics' model. However, its ability for modeling real opinion dynamics has
not been addressed. We introduce a noisy voter model (accounting for social
influence) with agents' recurrent mobility (as a proxy for social context),
where the spatial and population diversity are taken as inputs to the model. We
show that the dynamics can be described as a noisy diffusive process that
contains the proper anysotropic coupling topology given by population and
mobility heterogeneity. The model captures statistical features of the US
presidential elections as the stationary vote-share fluctuations across
counties, and the long-range spatial correlations that decay logarithmically
with the distance. Furthermore, it recovers the behavior of these properties
when a real-space renormalization is performed by coarse-graining the
geographical scale from county level through congressional districts and up to
states. Finally, we analyze the role of the mobility range and the randomness
in decision making which are consistent with the empirical observations.Comment: 13 pages, 13 figure
Random walks with imperfect trapping in the decoupled-ring approximation
We investigate random walks on a lattice with imperfect traps. In one
dimension, we perturbatively compute the survival probability by reducing the
problem to a particle diffusing on a closed ring containing just one single
trap. Numerical simulations reveal this solution, which is exact in the limit
of perfect traps, to be remarkably robust with respect to a significant
lowering of the trapping probability. We demonstrate that for randomly
distributed traps, the long-time asymptotics of our result recovers the known
stretched exponential decay. We also study an anisotropic three-dimensional
version of our model, where for sufficiently large transverse diffusion the
system is described by the mean-field kinetics. We discuss possible
applications of some of our findings to the decay of excitons in semiconducting
organic polymer materials, and emphasize the crucial influence of the spatial
trap distribution on the kinetics.Comment: 10 page
Modeling two-language competition dynamics
During the last decade, much attention has been paid to language competition
in the complex systems community, that is, how the fractions of speakers of
several competing languages evolve in time. In this paper we review recent
advances in this direction and focus on three aspects. First we consider the
shift from two-state models to three state models that include the possibility
of bilingual individuals. The understanding of the role played by bilingualism
is essential in sociolinguistics. In particular, the question addressed is
whether bilingualism facilitates the coexistence of languages. Second, we will
analyze the effect of social interaction networks and physical barriers.
Finally, we will show how to analyze the issue of bilingualism from a game
theoretical perspective.Comment: 15 pages, 5 figures; published in the Special Issue of Advances in
Complex Systems "Language Dynamics
Reduced order modeling of fluid flows: Machine learning, Kolmogorov barrier, closure modeling, and partitioning
In this paper, we put forth a long short-term memory (LSTM) nudging framework
for the enhancement of reduced order models (ROMs) of fluid flows utilizing
noisy measurements. We build on the fact that in a realistic application, there
are uncertainties in initial conditions, boundary conditions, model parameters,
and/or field measurements. Moreover, conventional nonlinear ROMs based on
Galerkin projection (GROMs) suffer from imperfection and solution instabilities
due to the modal truncation, especially for advection-dominated flows with slow
decay in the Kolmogorov width. In the presented LSTM-Nudge approach, we fuse
forecasts from a combination of imperfect GROM and uncertain state estimates,
with sparse Eulerian sensor measurements to provide more reliable predictions
in a dynamical data assimilation framework. We illustrate the idea with the
viscous Burgers problem, as a benchmark test bed with quadratic nonlinearity
and Laplacian dissipation. We investigate the effects of measurements noise and
state estimate uncertainty on the performance of the LSTM-Nudge behavior. We
also demonstrate that it can sufficiently handle different levels of temporal
and spatial measurement sparsity. This first step in our assessment of the
proposed model shows that the LSTM nudging could represent a viable realtime
predictive tool in emerging digital twin systems
Weak ergodicity breaking induced by global memory effects
We study the phenomenon of weak ergodicity breaking for a class of globally
correlated random walk dynamics defined over a finite set of states. The
persistence in a given state or the transition to another one depends on the
whole previous temporal history of the system. A set of waiting time
distributions, associated to each state, set the random times between
consecutive steps. Their mean value is finite for all states. The probability
density of time-averaged observables is obtained for different memory
mechanisms. This statistical object explicitly shows departures between time
and ensemble averages. While the mean residence time in each state may result
divergent, we demonstrate that this condition is in general not necessary for
breaking ergodicity. Hence, global memory effects are an alternative mechanism
able to induce this property. Analytical and numerical calculations support
these results.Comment: 11 pages, 3 figure
Chimera states: Effects of different coupling topologies
Collective behavior among coupled dynamical units can emerge in various forms
as a result of different coupling topologies as well as different types of
coupling functions. Chimera states have recently received ample attention as a
fascinating manifestation of collective behavior, in particular describing a
symmetry breaking spatiotemporal pattern where synchronized and desynchronized
states coexist in a network of coupled oscillators. In this perspective, we
review the emergence of different chimera states, focusing on the effects of
different coupling topologies that describe the interaction network connecting
the oscillators. We cover chimera states that emerge in local, nonlocal and
global coupling topologies, as well as in modular, temporal and multilayer
networks. We also provide an outline of challenges and directions for future
research.Comment: 7 two-column pages, 4 figures; Perspective accepted for publication
in EP
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