3,563 research outputs found
Dual Monte Carlo and Cluster Algorithms
We discuss the development of cluster algorithms from the viewpoint of
probability theory and not from the usual viewpoint of a particular model. By
using the perspective of probability theory, we detail the nature of a cluster
algorithm, make explicit the assumptions embodied in all clusters of which we
are aware, and define the construction of free cluster algorithms. We also
illustrate these procedures by rederiving the Swendsen-Wang algorithm,
presenting the details of the loop algorithm for a worldline simulation of a
quantum 1/2 model, and proposing a free cluster version of the
Swendsen-Wang replica method for the random Ising model. How the principle of
maximum entropy might be used to aid the construction of cluster algorithms is
also discussed.Comment: 25 pages, 4 figures, to appear in Phys.Rev.
Delay-induced multiple stochastic resonances on scale-free neuronal networks
We study the effects of periodic subthreshold pacemaker activity and
time-delayed coupling on stochastic resonance over scale-free neuronal
networks. As the two extreme options, we introduce the pacemaker respectively
to the neuron with the highest degree and to one of the neurons with the lowest
degree within the network, but we also consider the case when all neurons are
exposed to the periodic forcing. In the absence of delay, we show that an
intermediate intensity of noise is able to optimally assist the pacemaker in
imposing its rhythm on the whole ensemble, irrespective to its placing, thus
providing evidences for stochastic resonance on the scale-free neuronal
networks. Interestingly thereby, if the forcing in form of a periodic pulse
train is introduced to all neurons forming the network, the stochastic
resonance decreases as compared to the case when only a single neuron is paced.
Moreover, we show that finite delays in coupling can significantly affect the
stochastic resonance on scale-free neuronal networks. In particular,
appropriately tuned delays can induce multiple stochastic resonances
independently of the placing of the pacemaker, but they can also altogether
destroy stochastic resonance. Delay-induced multiple stochastic resonances
manifest as well-expressed maxima of the correlation measure, appearing at
every multiple of the pacemaker period. We argue that fine-tuned delays and
locally active pacemakers are vital for assuring optimal conditions for
stochastic resonance on complex neuronal networks.Comment: 7 two-column pages, 5 figures; accepted for publication in Chao
Cluster update and recognition
We present a fast and robust cluster update algorithm that is especially
efficient in implementing the task of image segmentation using the method of
superparamagnetic clustering. We apply it to a Potts model with spin
interactions that are are defined by gray-scale differences within the image.
Motivated by biological systems, we introduce the concept of neural inhibition
to the Potts model realization of the segmentation problem. Including the
inhibition term in the Hamiltonian results in enhanced contrast and thereby
significantly improves segmentation quality. As a second benefit we can - after
equilibration - directly identify the image segments as the clusters formed by
the clustering algorithm. To construct a new spin configuration the algorithm
performs the standard steps of (1) forming clusters and of (2) updating the
spins in a cluster simultaneously. As opposed to standard algorithms, however,
we share the interaction energy between the two steps. Thus the update
probabilities are not independent of the interaction energies. As a
consequence, we observe an acceleration of the relaxation by a factor of 10
compared to the Swendson and Wang procedure.Comment: 4 pages, 2 figure
A Complex Network Approach to Topographical Connections
The neuronal networks in the mammals cortex are characterized by the
coexistence of hierarchy, modularity, short and long range interactions,
spatial correlations, and topographical connections. Particularly interesting,
the latter type of organization implies special demands on the evolutionary and
ontogenetic systems in order to achieve precise maps preserving spatial
adjacencies, even at the expense of isometry. Although object of intensive
biological research, the elucidation of the main anatomic-functional purposes
of the ubiquitous topographical connections in the mammals brain remains an
elusive issue. The present work reports on how recent results from complex
network formalism can be used to quantify and model the effect of topographical
connections between neuronal cells over a number of relevant network properties
such as connectivity, adjacency, and information broadcasting. While the
topographical mapping between two cortical modules are achieved by connecting
nearest cells from each module, three kinds of network models are adopted for
implementing intracortical connections (ICC), including random,
preferential-attachment, and short-range networks. It is shown that, though
spatially uniform and simple, topographical connections between modules can
lead to major changes in the network properties, fostering more effective
intercommunication between the involved neuronal cells and modules. The
possible implications of such effects on cortical operation are discussed.Comment: 5 pages, 5 figure
Cluster Algorithm for a Solid-On-Solid Model with Constraints
We adapt the VMR (valleys-to-mountains reflections) algorithm, originally
devised by us for simulations of SOS models, to the BCSOS model. It is the
first time that a cluster algorithm is used for a model with constraints. The
performance of this new algorithm is studied in detail in both phases of the
model, including a finite size scaling analysis of the autocorrelations.Comment: 10 pages, 3 figures appended as ps-file
Dynamic behaviors in directed networks
Motivated by the abundance of directed synaptic couplings in a real
biological neuronal network, we investigate the synchronization behavior of the
Hodgkin-Huxley model in a directed network. We start from the standard model of
the Watts-Strogatz undirected network and then change undirected edges to
directed arcs with a given probability, still preserving the connectivity of
the network. A generalized clustering coefficient for directed networks is
defined and used to investigate the interplay between the synchronization
behavior and underlying structural properties of directed networks. We observe
that the directedness of complex networks plays an important role in emerging
dynamical behaviors, which is also confirmed by a numerical study of the
sociological game theoretic voter model on directed networks
Loop algorithms for quantum simulations of fermion models on lattices
Two cluster algorithms, based on constructing and flipping loops, are
presented for worldline quantum Monte Carlo simulations of fermions and are
tested on the one-dimensional repulsive Hubbard model. We call these algorithms
the loop-flip and loop-exchange algorithms. For these two algorithms and the
standard worldline algorithm, we calculated the autocorrelation times for
various physical quantities and found that the ordinary worldline algorithm,
which uses only local moves, suffers from very long correlation times that
makes not only the estimate of the error difficult but also the estimate of the
average values themselves difficult. These difficulties are especially severe
in the low-temperature, large- regime. In contrast, we find that new
algorithms, when used alone or in combinations with themselves and the standard
algorithm, can have significantly smaller autocorrelation times, in some cases
being smaller by three orders of magnitude. The new algorithms, which use
non-local moves, are discussed from the point of view of a general prescription
for developing cluster algorithms. The loop-flip algorithm is also shown to be
ergodic and to belong to the grand canonical ensemble. Extensions to other
models and higher dimensions is briefly discussed.Comment: 36 pages, RevTex ver.
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