3,575 research outputs found
Exact Simulation of Non-stationary Reflected Brownian Motion
This paper develops the first method for the exact simulation of reflected
Brownian motion (RBM) with non-stationary drift and infinitesimal variance. The
running time of generating exact samples of non-stationary RBM at any time
is uniformly bounded by where is the
average drift of the process. The method can be used as a guide for planning
simulations of complex queueing systems with non-stationary arrival rates
and/or service time
Brownian motion: a paradigm of soft matter and biological physics
This is a pedagogical introduction to Brownian motion on the occasion of the
100th anniversary of Einstein's 1905 paper on the subject. After briefly
reviewing Einstein's work in its contemporary context, we pursue some lines of
further developments and applications in soft condensed matter and biology.
Over the last century Brownian motion became promoted from an odd curiosity of
marginal scientific interest to a guiding theme pervading all of the modern
(live) sciences.Comment: 30 pages, revie
Network Plasticity as Bayesian Inference
General results from statistical learning theory suggest to understand not
only brain computations, but also brain plasticity as probabilistic inference.
But a model for that has been missing. We propose that inherently stochastic
features of synaptic plasticity and spine motility enable cortical networks of
neurons to carry out probabilistic inference by sampling from a posterior
distribution of network configurations. This model provides a viable
alternative to existing models that propose convergence of parameters to
maximum likelihood values. It explains how priors on weight distributions and
connection probabilities can be merged optimally with learned experience, how
cortical networks can generalize learned information so well to novel
experiences, and how they can compensate continuously for unforeseen
disturbances of the network. The resulting new theory of network plasticity
explains from a functional perspective a number of experimental data on
stochastic aspects of synaptic plasticity that previously appeared to be quite
puzzling.Comment: 33 pages, 5 figures, the supplement is available on the author's web
page http://www.igi.tugraz.at/kappe
Universality and Critical Phenomena in String Defect Statistics
The idea of biased symmetries to avoid or alleviate cosmological problems
caused by the appearance of some topological defects is familiar in the context
of domain walls, where the defect statistics lend themselves naturally to a
percolation theory description, and for cosmic strings, where the proportion of
infinite strings can be varied or disappear entirely depending on the bias in
the symmetry. In this paper we measure the initial configurational statistics
of a network of string defects after a symmetry-breaking phase transition with
initial bias in the symmetry of the ground state. Using an improved algorithm,
which is useful for a more general class of self-interacting walks on an
infinite lattice, we extend the work in \cite{MHKS} to better statistics and a
different ground state manifold, namely , and explore various different
discretisations. Within the statistical errors, the critical exponents of the
Hagedorn transition are found to be quite possibly universal and identical to
the critical exponents of three-dimensional bond or site percolation. This
improves our understanding of the percolation theory description of defect
statistics after a biased phase transition, as proposed in \cite{MHKS}. We also
find strong evidence that the existence of infinite strings in the Vachaspati
Vilenkin algorithm is generic to all (string-bearing) vacuum manifolds, all
discretisations thereof, and all regular three-dimensional lattices.Comment: 62 pages, plain LaTeX, macro mathsymb.sty included, figures included.
also available on
http://starsky.pcss.maps.susx.ac.uk/groups/pt/preprints/96/96011.ps.g
Anomalous diffusion: A basic mechanism for the evolution of inhomogeneous systems
In this article we review classical and recent results in anomalous diffusion
and provide mechanisms useful for the study of the fundamentals of certain
processes, mainly in condensed matter physics, chemistry and biology. Emphasis
will be given to some methods applied in the analysis and characterization of
diffusive regimes through the memory function, the mixing condition (or
irreversibility), and ergodicity. Those methods can be used in the study of
small-scale systems, ranging in size from single-molecule to particle clusters
and including among others polymers, proteins, ion channels and biological
cells, whose diffusive properties have received much attention lately.Comment: Review article, 20 pages, 7 figures. arXiv admin note: text overlap
with arXiv:cond-mat/0201446 by other author
A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?
Predicting historic temperatures based on tree rings, ice cores, and other
natural proxies is a difficult endeavor. The relationship between proxies and
temperature is weak and the number of proxies is far larger than the number of
target data points. Furthermore, the data contain complex spatial and temporal
dependence structures which are not easily captured with simple models. In this
paper, we assess the reliability of such reconstructions and their statistical
significance against various null models. We find that the proxies do not
predict temperature significantly better than random series generated
independently of temperature. Furthermore, various model specifications that
perform similarly at predicting temperature produce extremely different
historical backcasts. Finally, the proxies seem unable to forecast the high
levels of and sharp run-up in temperature in the 1990s either in-sample or from
contiguous holdout blocks, thus casting doubt on their ability to predict such
phenomena if in fact they occurred several hundred years ago. We propose our
own reconstruction of Northern Hemisphere average annual land temperature over
the last millennium, assess its reliability, and compare it to those from the
climate science literature. Our model provides a similar reconstruction but has
much wider standard errors, reflecting the weak signal and large uncertainty
encountered in this setting.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS398 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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