28,864 research outputs found
The pseudo-compartment method for coupling PDE and compartment-based models of diffusion
Spatial reaction-diffusion models have been employed to describe many
emergent phenomena in biological systems. The modelling technique most commonly
adopted in the literature implements systems of partial differential equations
(PDEs), which assumes there are sufficient densities of particles that a
continuum approximation is valid. However, due to recent advances in
computational power, the simulation, and therefore postulation, of
computationally intensive individual-based models has become a popular way to
investigate the effects of noise in reaction-diffusion systems in which regions
of low copy numbers exist.
The stochastic models with which we shall be concerned in this manuscript are
referred to as `compartment-based'. These models are characterised by a
discretisation of the computational domain into a grid/lattice of
`compartments'. Within each compartment particles are assumed to be well-mixed
and are permitted to react with other particles within their compartment or to
transfer between neighbouring compartments.
We develop two hybrid algorithms in which a PDE is coupled to a
compartment-based model. Rather than attempting to balance average fluxes, our
algorithms answer a more fundamental question: `how are individual particles
transported between the vastly different model descriptions?' First, we present
an algorithm derived by carefully re-defining the continuous PDE concentration
as a probability distribution. Whilst this first algorithm shows strong
convergence to analytic solutions of test problems, it can be cumbersome to
simulate. Our second algorithm is a simplified and more efficient
implementation of the first, it is derived in the continuum limit over the PDE
region alone. We test our hybrid methods for functionality and accuracy in a
variety of different scenarios by comparing the averaged simulations to
analytic solutions of PDEs for mean concentrations.Comment: MAIN - 24 pages, 10 figures, 1 supplementary file - 3 pages, 2
figure
Nested Sequential Monte Carlo Methods
We propose nested sequential Monte Carlo (NSMC), a methodology to sample from
sequences of probability distributions, even where the random variables are
high-dimensional. NSMC generalises the SMC framework by requiring only
approximate, properly weighted, samples from the SMC proposal distribution,
while still resulting in a correct SMC algorithm. Furthermore, NSMC can in
itself be used to produce such properly weighted samples. Consequently, one
NSMC sampler can be used to construct an efficient high-dimensional proposal
distribution for another NSMC sampler, and this nesting of the algorithm can be
done to an arbitrary degree. This allows us to consider complex and
high-dimensional models using SMC. We show results that motivate the efficacy
of our approach on several filtering problems with dimensions in the order of
100 to 1 000.Comment: Extended version of paper published in Proceedings of the 32nd
International Conference on Machine Learning (ICML), Lille, France, 201
Sequential Monte Carlo for Graphical Models
We propose a new framework for how to use sequential Monte Carlo (SMC)
algorithms for inference in probabilistic graphical models (PGM). Via a
sequential decomposition of the PGM we find a sequence of auxiliary
distributions defined on a monotonically increasing sequence of probability
spaces. By targeting these auxiliary distributions using SMC we are able to
approximate the full joint distribution defined by the PGM. One of the key
merits of the SMC sampler is that it provides an unbiased estimate of the
partition function of the model. We also show how it can be used within a
particle Markov chain Monte Carlo framework in order to construct
high-dimensional block-sampling algorithms for general PGMs
Capacity estimation of two-dimensional channels using Sequential Monte Carlo
We derive a new Sequential-Monte-Carlo-based algorithm to estimate the
capacity of two-dimensional channel models. The focus is on computing the
noiseless capacity of the 2-D one-infinity run-length limited constrained
channel, but the underlying idea is generally applicable. The proposed
algorithm is profiled against a state-of-the-art method, yielding more than an
order of magnitude improvement in estimation accuracy for a given computation
time
Dynamic wetting with two competing adsorbates
We study the dynamic properties of a model for wetting with two competing
adsorbates on a planar substrate. The two species of particles have identical
properties and repel each other. Starting with a flat interface one observes
the formation of homogeneous droplets of the respective type separated by
nonwet regions where the interface remains pinned. The wet phase is
characterized by slow coarsening of competing droplets. Moreover, in 2+1
dimensions an additional line of continuous phase transition emerges in the
bound phase, which separates an unordered phase from an ordered one. The
symmetry under interchange of the particle types is spontaneously broken in
this region and finite systems exhibit two metastable states, each dominated by
one of the species. The critical properties of this transition are analyzed by
numeric simulations.Comment: 11 pages, 12 figures, final version published in PR
Exploring Human Vision Driven Features for Pedestrian Detection
Motivated by the center-surround mechanism in the human visual attention
system, we propose to use average contrast maps for the challenge of pedestrian
detection in street scenes due to the observation that pedestrians indeed
exhibit discriminative contrast texture. Our main contributions are first to
design a local, statistical multi-channel descriptorin order to incorporate
both color and gradient information. Second, we introduce a multi-direction and
multi-scale contrast scheme based on grid-cells in order to integrate
expressive local variations. Contributing to the issue of selecting most
discriminative features for assessing and classification, we perform extensive
comparisons w.r.t. statistical descriptors, contrast measurements, and scale
structures. This way, we obtain reasonable results under various
configurations. Empirical findings from applying our optimized detector on the
INRIA and Caltech pedestrian datasets show that our features yield
state-of-the-art performance in pedestrian detection.Comment: Accepted for publication in IEEE Transactions on Circuits and Systems
for Video Technology (TCSVT
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