2,070 research outputs found
Variable-Length Intrinsic Randomness Allowing Positive Value of the Average Variational Distance
This paper considers the problem of variable-length intrinsic randomness. We
propose the average variational distance as the performance criterion from the
viewpoint of a dual relationship with the problem formulation of
variable-length resolvability. Previous study has derived the general formula
of the -variable-length resolvability. We derive the general formula
of the -variable-length intrinsic randomness. Namely, we characterize
the supremum of the mean length under the constraint that the value of the
average variational distance is smaller than or equal to a constant .
Our result clarifies a dual relationship between the general formula of
-variable-length resolvability and that of -variable-length
intrinsic randomness. We also derive a lower bound of the quantity
characterizing our general formula
Random-singlet phase in disordered two-dimensional quantum magnets
We study effects of disorder (randomness) in a 2D square-lattice S=1/2 quantum spin system, the J-Q model with a 6-spin interaction Q supplementing the Heisenberg exchange J. In the absence of disorder the system hosts antiferromagnetic (AFM) and columnar valence-bond-solid (VBS) ground states. The VBS breaks Z4 symmetry, and in the presence of arbitrarily weak disorder it forms domains. Using QMC simulations, we demonstrate two kinds of such disordered VBS states. Upon dilution, a removed site leaves a localized spin in the opposite sublattice. These spins form AFM order. For random interactions, we find a different state, with no order but algebraically decaying mean correlations. We identify localized spinons at the nexus of domain walls between different VBS patterns. These spinons form correlated groups with the same number of spinons and antispinons. Within such a group, there is a strong tendency to singlet formation, because of spinon-spinon interactions mediated by the domain walls. Thus, no long-range AFM order forms. We propose that this state is a 2D analog of the well-known 1D random singlet (RS) state, though the dynamic exponent z in 2D is finite. By studying the T-dependent magnetic susceptibility, we find that z varies, from z=2 at the AFM--RS phase boundary and larger in the RS phase The RS state discovered here in a system without geometric frustration should correspond to the same fixed point as the RS state recently proposed for frustrated systems, and the ability to study it without Monte Carlo sign problems opens up opportunities for further detailed characterization of its static and dynamic properties. We also discuss experimental evidence of the RS phase in the quasi-two-dimensional square-lattice random-exchange quantum magnets Sr2CuTe1−xWxO6.Accepted manuscrip
Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets
We study effects of disorder (randomness) in a 2D square-lattice
quantum spin system, the - model with a 6-spin interaction
supplementing the Heisenberg exchange . In the absence of disorder the
system hosts antiferromagnetic (AFM) and columnar valence-bond-solid (VBS)
ground states. The VBS breaks symmetry, and in the presence of
arbitrarily weak disorder it forms domains. Using QMC simulations, we
demonstrate two kinds of such disordered VBS states. Upon dilution, a removed
site leaves a localized spin in the opposite sublattice. These spins form AFM
order. For random interactions, we find a different state, with no order but
algebraically decaying mean correlations. We identify localized spinons at the
nexus of domain walls between different VBS patterns. These spinons form
correlated groups with the same number of spinons and antispinons. Within such
a group, there is a strong tendency to singlet formation, because of
spinon-spinon interactions mediated by the domain walls. Thus, no long-range
AFM order forms. We propose that this state is a 2D analog of the well-known 1D
random singlet (RS) state, though the dynamic exponent in 2D is finite. By
studying the T-dependent magnetic susceptibility, we find that varies, from
at the AFM--RS phase boundary and larger in the RS phase The RS state
discovered here in a system without geometric frustration should correspond to
the same fixed point as the RS state recently proposed for frustrated systems,
and the ability to study it without Monte Carlo sign problems opens up
opportunities for further detailed characterization of its static and dynamic
properties. We also discuss experimental evidence of the RS phase in the
quasi-two-dimensional square-lattice random-exchange quantum magnets
SrCuTeWO.Comment: 31 pages, 29 figures; substantial additions in v2; additional
analysis in v
Synchronization in complex networks
Synchronization processes in populations of locally interacting elements are
in the focus of intense research in physical, biological, chemical,
technological and social systems. The many efforts devoted to understand
synchronization phenomena in natural systems take now advantage of the recent
theory of complex networks. In this review, we report the advances in the
comprehension of synchronization phenomena when oscillating elements are
constrained to interact in a complex network topology. We also overview the new
emergent features coming out from the interplay between the structure and the
function of the underlying pattern of connections. Extensive numerical work as
well as analytical approaches to the problem are presented. Finally, we review
several applications of synchronization in complex networks to different
disciplines: biological systems and neuroscience, engineering and computer
science, and economy and social sciences.Comment: Final version published in Physics Reports. More information
available at http://synchronets.googlepages.com
Refining self-propelled particle models for collective behaviour
Swarming, schooling, flocking and herding are all names given to the wide variety of collective behaviours exhibited by groups of animals, bacteria and even individual cells. More generally, the term swarming describes the behaviour of an aggregate of agents (not necessarily biological) of similar size and shape which exhibit some emergent property such as directed migration or group cohesion. In this paper we review various individual-based models of collective behaviour and discuss their merits and drawbacks. We further analyse some one-dimensional models in the context of locust swarming. In specific models, in both one and two dimensions, we demonstrate how varying the parameters relating to how much attention individuals pay to their neighbours can dramatically change the behaviour of the group. We also introduce leader individuals to these models with the ability to guide the swarm to a greater or lesser degree as we vary the parameters of the model. We consider evolutionary scenarios for models with leaders in which individuals are allowed to evolve the degree of influence neighbouring individuals have on their subsequent motion
Multiscale Bayesian State Space Model for Granger Causality Analysis of Brain Signal
Modelling time-varying and frequency-specific relationships between two brain
signals is becoming an essential methodological tool to answer heoretical
questions in experimental neuroscience. In this article, we propose to estimate
a frequency Granger causality statistic that may vary in time in order to
evaluate the functional connections between two brain regions during a task. We
use for that purpose an adaptive Kalman filter type of estimator of a linear
Gaussian vector autoregressive model with coefficients evolving over time. The
estimation procedure is achieved through variational Bayesian approximation and
is extended for multiple trials. This Bayesian State Space (BSS) model provides
a dynamical Granger-causality statistic that is quite natural. We propose to
extend the BSS model to include the \`{a} trous Haar decomposition. This
wavelet-based forecasting method is based on a multiscale resolution
decomposition of the signal using the redundant \`{a} trous wavelet transform
and allows us to capture short- and long-range dependencies between signals.
Equally importantly it allows us to derive the desired dynamical and
frequency-specific Granger-causality statistic. The application of these models
to intracranial local field potential data recorded during a psychological
experimental task shows the complex frequency based cross-talk between amygdala
and medial orbito-frontal cortex.
Keywords: \`{a} trous Haar wavelets; Multiple trials; Neuroscience data;
Nonstationarity; Time-frequency; Variational methods
The published version of this article is
Cekic, S., Grandjean, D., Renaud, O. (2018). Multiscale Bayesian state-space
model for Granger causality analysis of brain signal. Journal of Applied
Statistics. https://doi.org/10.1080/02664763.2018.145581
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