19,819 research outputs found
Numerical Fitting-based Likelihood Calculation to Speed up the Particle Filter
The likelihood calculation of a vast number of particles is the computational
bottleneck for the particle filter in applications where the observation
information is rich. For fast computing the likelihood of particles, a
numerical fitting approach is proposed to construct the Likelihood Probability
Density Function (Li-PDF) by using a comparably small number of so-called
fulcrums. The likelihood of particles is thereby analytically inferred,
explicitly or implicitly, based on the Li-PDF instead of directly computed by
utilizing the observation, which can significantly reduce the computation and
enables real time filtering. The proposed approach guarantees the estimation
quality when an appropriate fitting function and properly distributed fulcrums
are used. The details for construction of the fitting function and fulcrums are
addressed respectively in detail. In particular, to deal with multivariate
fitting, the nonparametric kernel density estimator is presented which is
flexible and convenient for implicit Li-PDF implementation. Simulation
comparison with a variety of existing approaches on a benchmark 1-dimensional
model and multi-dimensional robot localization and visual tracking demonstrate
the validity of our approach.Comment: 42 pages, 17 figures, 4 tables and 1 appendix. This paper is a
draft/preprint of one paper submitted to the IEEE Transaction
Factorizing the Stochastic Galerkin System
Recent work has explored solver strategies for the linear system of equations
arising from a spectral Galerkin approximation of the solution of PDEs with
parameterized (or stochastic) inputs. We consider the related problem of a
matrix equation whose matrix and right hand side depend on a set of parameters
(e.g. a PDE with stochastic inputs semidiscretized in space) and examine the
linear system arising from a similar Galerkin approximation of the solution. We
derive a useful factorization of this system of equations, which yields bounds
on the eigenvalues, clues to preconditioning, and a flexible implementation
method for a wide array of problems. We complement this analysis with (i) a
numerical study of preconditioners on a standard elliptic PDE test problem and
(ii) a fluids application using existing CFD codes; the MATLAB codes used in
the numerical studies are available online.Comment: 13 pages, 4 figures, 2 table
Simulated single molecule microscopy with SMeagol
SMeagol is a software tool to simulate highly realistic microscopy data based
on spatial systems biology models, in order to facilitate development,
validation, and optimization of advanced analysis methods for live cell single
molecule microscopy data. Availability and Implementation: SMeagol runs on
Matlab R2014 and later, and uses compiled binaries in C for reaction-diffusion
simulations. Documentation, source code, and binaries for recent versions of
Mac OS, Windows, and Ubuntu Linux can be downloaded from
http://smeagol.sourceforge.net.Comment: v2: 14 pages including supplementary text. Pre-copyedited,
author-produced version of an application note published in Bioinformatics
following peer review. The version of record, and additional supplementary
material is available online at:
https://academic.oup.com/bioinformatics/article-lookup/doi/10.1093/bioinformatics/btw10
A finite state projection algorithm for the stationary solution of the chemical master equation
The chemical master equation (CME) is frequently used in systems biology to
quantify the effects of stochastic fluctuations that arise due to biomolecular
species with low copy numbers. The CME is a system of ordinary differential
equations that describes the evolution of probability density for each
population vector in the state-space of the stochastic reaction dynamics. For
many examples of interest, this state-space is infinite, making it difficult to
obtain exact solutions of the CME. To deal with this problem, the Finite State
Projection (FSP) algorithm was developed by Munsky and Khammash (Jour. Chem.
Phys. 2006), to provide approximate solutions to the CME by truncating the
state-space. The FSP works well for finite time-periods but it cannot be used
for estimating the stationary solutions of CMEs, which are often of interest in
systems biology. The aim of this paper is to develop a version of FSP which we
refer to as the stationary FSP (sFSP) that allows one to obtain accurate
approximations of the stationary solutions of a CME by solving a finite
linear-algebraic system that yields the stationary distribution of a
continuous-time Markov chain over the truncated state-space. We derive bounds
for the approximation error incurred by sFSP and we establish that under
certain stability conditions, these errors can be made arbitrarily small by
appropriately expanding the truncated state-space. We provide several examples
to illustrate our sFSP method and demonstrate its efficiency in estimating the
stationary distributions. In particular, we show that using a quantised tensor
train (QTT) implementation of our sFSP method, problems admitting more than 100
million states can be efficiently solved.Comment: 8 figure
A finite state projection algorithm for the stationary solution of the chemical master equation
The chemical master equation (CME) is frequently used in systems biology to
quantify the effects of stochastic fluctuations that arise due to biomolecular
species with low copy numbers. The CME is a system of ordinary differential
equations that describes the evolution of probability density for each
population vector in the state-space of the stochastic reaction dynamics. For
many examples of interest, this state-space is infinite, making it difficult to
obtain exact solutions of the CME. To deal with this problem, the Finite State
Projection (FSP) algorithm was developed by Munsky and Khammash (Jour. Chem.
Phys. 2006), to provide approximate solutions to the CME by truncating the
state-space. The FSP works well for finite time-periods but it cannot be used
for estimating the stationary solutions of CMEs, which are often of interest in
systems biology. The aim of this paper is to develop a version of FSP which we
refer to as the stationary FSP (sFSP) that allows one to obtain accurate
approximations of the stationary solutions of a CME by solving a finite
linear-algebraic system that yields the stationary distribution of a
continuous-time Markov chain over the truncated state-space. We derive bounds
for the approximation error incurred by sFSP and we establish that under
certain stability conditions, these errors can be made arbitrarily small by
appropriately expanding the truncated state-space. We provide several examples
to illustrate our sFSP method and demonstrate its efficiency in estimating the
stationary distributions. In particular, we show that using a quantised tensor
train (QTT) implementation of our sFSP method, problems admitting more than 100
million states can be efficiently solved.Comment: 8 figure
- …