2,319 research outputs found
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
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
On U_q(SU(2))-symmetric Driven Diffusion
We study analytically a model where particles with a hard-core repulsion
diffuse on a finite one-dimensional lattice with space-dependent, asymmetric
hopping rates. The system dynamics are given by the
\mbox{U[SU(2)]}-symmetric Hamiltonian of a generalized anisotropic
Heisenberg antiferromagnet. Exploiting this symmetry we derive exact
expressions for various correlation functions. We discuss the density profile
and the two-point function and compute the correlation length as well
as the correlation time . The dynamics of the density and the
correlations are shown to be governed by the energy gaps of a one-particle
system. For large systems and depend only on the asymmetry. For
small asymmetry one finds indicating a dynamical exponent
as for symmetric diffusion.Comment: 10 pages, LATE
Synchronization and Redundancy: Implications for Robustness of Neural Learning and Decision Making
Learning and decision making in the brain are key processes critical to
survival, and yet are processes implemented by non-ideal biological building
blocks which can impose significant error. We explore quantitatively how the
brain might cope with this inherent source of error by taking advantage of two
ubiquitous mechanisms, redundancy and synchronization. In particular we
consider a neural process whose goal is to learn a decision function by
implementing a nonlinear gradient dynamics. The dynamics, however, are assumed
to be corrupted by perturbations modeling the error which might be incurred due
to limitations of the biology, intrinsic neuronal noise, and imperfect
measurements. We show that error, and the associated uncertainty surrounding a
learned solution, can be controlled in large part by trading off
synchronization strength among multiple redundant neural systems against the
noise amplitude. The impact of the coupling between such redundant systems is
quantified by the spectrum of the network Laplacian, and we discuss the role of
network topology in synchronization and in reducing the effect of noise. A
range of situations in which the mechanisms we model arise in brain science are
discussed, and we draw attention to experimental evidence suggesting that
cortical circuits capable of implementing the computations of interest here can
be found on several scales. Finally, simulations comparing theoretical bounds
to the relevant empirical quantities show that the theoretical estimates we
derive can be tight.Comment: Preprint, accepted for publication in Neural Computatio
On generalized cluster algorithms for frustrated spin models
Standard Monte Carlo cluster algorithms have proven to be very effective for
many different spin models, however they fail for frustrated spin systems.
Recently a generalized cluster algorithm was introduced that works extremely
well for the fully frustrated Ising model on a square lattice, by placing bonds
between sites based on information from plaquettes rather than links of the
lattice. Here we study some properties of this algorithm and some variants of
it. We introduce a practical methodology for constructing a generalized cluster
algorithm for a given spin model, and investigate apply this method to some
other frustrated Ising models. We find that such algorithms work well for
simple fully frustrated Ising models in two dimensions, but appear to work
poorly or not at all for more complex models such as spin glasses.Comment: 34 pages in RevTeX. No figures included. A compressed postscript file
for the paper with figures can be obtained via anonymous ftp to
minerva.npac.syr.edu in users/paulc/papers/SCCS-527.ps.Z. Syracuse University
NPAC technical report SCCS-52
Breaking quantum linearity: constraints from human perception and cosmological implications
Resolving the tension between quantum superpositions and the uniqueness of
the classical world is a major open problem. One possibility, which is
extensively explored both theoretically and experimentally, is that quantum
linearity breaks above a given scale. Theoretically, this possibility is
predicted by collapse models. They provide quantitative information on where
violations of the superposition principle become manifest. Here we show that
the lower bound on the collapse parameter lambda, coming from the analysis of
the human visual process, is ~ 7 +/- 2 orders of magnitude stronger than the
original bound, in agreement with more recent analysis. This implies that the
collapse becomes effective with systems containing ~ 10^4 - 10^5 nucleons, and
thus falls within the range of testability with present-day technology. We also
compare the spectrum of the collapsing field with those of known cosmological
fields, showing that a typical cosmological random field can yield an efficient
wave function collapse.Comment: 13 pages, LaTeX, 3 figure
A quantitative theory of current-induced step bunching on Si(111)
We use a one-dimensional step model to study quantitatively the growth of
step bunches on Si(111) surfaces induced by a direct heating current.
Parameters in the model are fixed from experimental measurements near 900 deg C
under the assumption that there is local mass transport through surface
diffusion and that step motion is limited by the attachment rate of adatoms to
step edges. The direct heating current is treated as an external driving force
acting on each adatom. Numerical calculations show both qualitative and
quantitative agreement with experiment. A force in the step down direction will
destabilize the uniform step train towards step bunching. The average size of
the step bunches grows with electromigration time as t^beta, with beta = 0.5,
in agreement with experiment and with an analytical treatment of the steady
states. The model is extended to include the effect of direct hopping of
adatoms between different terraces. Monte-Carlo simulations of a solid-on-solid
model, using physically motivated assumptions about the dynamics of surface
diffusion and attachment at step edges, are carried out to study two
dimensional features that are left out of the present step model and to test
its validity. These simulations give much better agreement with experiment than
previous work. We find a new step bending instability when the driving force is
along the step edge direction. This instability causes the formation of step
bunches and antisteps that is similar to that observed in experiment.Comment: 11 pages, 7 figure
General Framework for phase synchronization through localized sets
We present an approach which enables to identify phase synchronization in
coupled chaotic oscillators without having to explicitly measure the phase. We
show that if one defines a typical event in one oscillator and then observes
another one whenever this event occurs, these observations give rise to a
localized set. Our result provides a general and easy way to identify PS, which
can also be used to oscillators that possess multiple time scales. We
illustrate our approach in networks of chemically coupled neurons. We show that
clusters of phase synchronous neurons may emerge before the onset of phase
synchronization in the whole network, producing a suitable environment for
information exchanging. Furthermore, we show the relation between the localized
sets and the amount of information that coupled chaotic oscillator can
exchange
Genetic control of cellular morphogenesis in Müller glia.
Cell shape is critical for the proper function of every cell in every tissue in the body. This is especially true for the highly morphologically diverse neural and glia cells of the central nervous system. The molecular processes by which these, or indeed any, cells gain their particular cell-specific morphology remain largely unexplored. To identify the genes involved in the morphogenesis of the principal glial cell type in the vertebrate retina, the Müller glia (MG), we used genomic and CRISPR based strategies in zebrafish (Danio rerio). We identified 41 genes involved in various aspects of MG cell morphogenesis and revealed a striking concordance between the sequential steps of anatomical feature addition and the expression of cohorts of functionally related genes that regulate these steps. We noted that the many of the genes preferentially expressed in zebrafish MG showed conservation in glia across species suggesting evolutionarily conserved glial developmental pathways.The work was supported by a Marie Curie Individual Fellowship (MSCA-IF-2015-707668) to MCP, a JG Graves Medical Research Fellowship and Wellcome Trust Seed Award (210152/Z/18/Z) to RBM and an Investigator Award from the Wellcome Trust (SIA 100329/Z/12/Z) to WAH
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