Browse
Submit Data
Databases
API
Help

Dataset Information

0 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Simplification of reversible Markov chains by removal of states with low equilibrium occupancy.

ABSTRACT: We present a practical method for simplifying Markov chains on a potentially large state space when detailed balance holds. A simple and transparent technique is introduced to remove states with low equilibrium occupancy. The resulting system has fewer parameters. The resulting effective rates between the remaining nodes give dynamics identical to the original system's except on very fast timescales. This procedure amounts to using separation of timescales to neglect small capacitance nodes in a network of resistors and capacitors. We illustrate the technique by simplifying various reaction networks, including transforming an acyclic four-node network to a three-node cyclic network. For a reaction step in which a ligand binds, the law of mass action implies a forward rate proportional to ligand concentration. The effective rates in the simplified network are found to be rational functions of ligand concentration.

SUBMITTER: Ullah G

PROVIDER: S-EPMC3930476 | biostudies-literature | 2012 Oct

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Simplification of reversible Markov chains by removal of states with low equilibrium occupancy.

Ullah Ghanim G Bruno William J WJ Pearson John E JE

Journal of theoretical biology 20120720

We present a practical method for simplifying Markov chains on a potentially large state space when detailed balance holds. A simple and transparent technique is introduced to remove states with low equilibrium occupancy. The resulting system has fewer parameters. The resulting effective rates between the remaining nodes give dynamics identical to the original system's except on very fast timescales. This procedure amounts to using separation of timescales to neglect small capacitance nodes in a ...[more]

PMID: 22820127

Similar Datasets

Acceleration of Convergence to Equilibrium in Markov Chains by Breaking Detailed Balance.

Project description:We analyse and interpret the effects of breaking detailed balance on the convergence to equilibrium of conservative interacting particle systems and their hydrodynamic scaling limits. For finite systems of interacting particles, we review existing results showing that irreversible processes converge faster to their steady state than reversible ones. We show how this behaviour appears in the hydrodynamic limit of such processes, as described by macroscopic fluctuation theory, and we provide a quantitative expression for the acceleration of convergence in this setting. We give a geometrical interpretation of this acceleration, in terms of currents that are antisymmetric under time-reversal and orthogonal to the free energy gradient, which act to drive the system away from states where (reversible) gradient-descent dynamics result in slow convergence to equilibrium.

| S-EPMC6979539 | biostudies-literature

Light-fueled dynamic covalent crosslinking of single polymer chains in non-equilibrium states.

Project description:While polymer synthesis proceeds predominantly towards the thermodynamic minimum, living systems operate on the reverse principle - consuming fuel to maintain a non-equilibrium state. Herein, we report the controlled formation of 3D macromolecular architectures based on light-fueled covalent non-equilibrium chemistry. In the presence of green light (525 nm) and a bivalent triazolinedione (TAD) crosslinker, naphthalene-containing polymers can be folded into single chain nanoparticles (SCNPs). At ambient temperature, the cycloaddition product of TAD with naphthalene reverts and the SCNP unfolds into its linear parent polymer. The reported SCNP is the first example of a reversible light triggered folding of single polymer chains and can readily be repeated for several cycles. The folded state of the SCNP can either be preserved through a constant supply of light fuel, kinetic trapping or through a chemical modification that makes the folded state thermodynamically favored. Whereas small molecule bivalent TAD/naphthalene cycloaddition products largely degraded after 3 days in solution, even in the presence of fuel, the SCNP entities were found to remain intact, thereby indicating the light-fueled stabilization of the SCNP to be an inherent feature of the confined macromolecular environment.

| S-EPMC8179028 | biostudies-literature

A methodology for stochastic analysis of share prices as Markov chains with finite states.

Project description:Price volatilities make stock investments risky, leaving investors in critical position when uncertain decision is made. To improve investor evaluation confidence on exchange markets, while not using time series methodology, we specify equity price change as a stochastic process assumed to possess Markov dependency with respective state transition probabilities matrices following the identified state pace (i.e. decrease, stable or increase). We established that identified states communicate, and that the chains are aperiodic and ergodic thus possessing limiting distributions. We developed a methodology for determining expected mean return time for stock price increases and also establish criteria for improving investment decision based on highest transition probabilities, lowest mean return time and highest limiting distributions. We further developed an R algorithm for running the methodology introduced. The established methodology is applied to selected equities from Ghana Stock Exchange weekly trading data.

| S-EPMC4247363 | biostudies-literature

Universal recovery map for approximate Markov chains.

Project description:A central question in quantum information theory is to determine how well lost information can be reconstructed. Crucially, the corresponding recovery operation should perform well without knowing the information to be reconstructed. In this work, we show that the quantum conditional mutual information measures the performance of such recovery operations. More precisely, we prove that the conditional mutual information I(A:C|B) of a tripartite quantum state ?ABC can be bounded from below by its distance to the closest recovered state [Formula: see text], where the C-part is reconstructed from the B-part only and the recovery map [Formula: see text] merely depends on ?BC . One particular application of this result implies the equivalence between two different approaches to define topological order in quantum systems.

| S-EPMC4841654 | biostudies-literature

Multilocus association mapping using variable-length Markov chains.

Project description:I propose a new method for association-based gene mapping that makes powerful use of multilocus data, is computationally efficient, and is straightforward to apply over large genomic regions. The approach is based on the fitting of variable-length Markov chain models, which automatically adapt to the degree of linkage disequilibrium (LD) between markers to create a parsimonious model for the LD structure. Edges of the fitted graph are tested for association with trait status. This approach can be thought of as haplotype testing with sophisticated windowing that accounts for extent of LD to reduce degrees of freedom and number of tests while maximizing information. I present analyses of two published data sets that show that this approach can have better power than single-marker tests or sliding-window haplotypic tests.

| S-EPMC1474089 | biostudies-literature

Fast parallel construction of variable-length Markov chains.

Project description:BackgroundAlignment-free methods are a popular approach for comparing biological sequences, including complete genomes. The methods range from probability distributions of sequence composition to first and higher-order Markov chains, where a k-th order Markov chain over DNA has [Formula: see text] formal parameters. To circumvent this exponential growth in parameters, variable-length Markov chains (VLMCs) have gained popularity for applications in molecular biology and other areas. VLMCs adapt the depth depending on sequence context and thus curtail excesses in the number of parameters. The scarcity of available fast, or even parallel software tools, prompted the development of a parallel implementation using lazy suffix trees and a hash-based alternative.ResultsAn extensive evaluation was performed on genomes ranging from 12Mbp to 22Gbp. Relevant learning parameters were chosen guided by the Bayesian Information Criterion (BIC) to avoid over-fitting. Our implementation greatly improves upon the state-of-the-art even in serial execution. It exhibits very good parallel scaling with speed-ups for long sequences close to the optimum indicated by Amdahl's law of 3 for 4 threads and about 6 for 16 threads, respectively.ConclusionsOur parallel implementation released as open-source under the GPLv3 license provides a practically useful alternative to the state-of-the-art which allows the construction of VLMCs even for very large genomes significantly faster than previously possible. Additionally, our parameter selection based on BIC gives guidance to end-users comparing genomes.

| S-EPMC8501649 | biostudies-literature

Xtrapol8 enables automatic elucidation of low-occupancy intermediate-states in crystallographic studies.

Project description:Unstable states studied in kinetic, time-resolved and ligand-based crystallography are often characterized by a low occupancy, which hinders structure determination by conventional methods. To automatically extract structural information pertaining to these states, we developed Xtrapol8, a program which (i) applies various flavors of Bayesian-statistics weighting to generate the most informative Fourier difference maps; (ii) determines the occupancy of the intermediate states by use of methods hitherto not available; (iii) calculates extrapolated structure factors using the various proposed formalisms while handling the issue of negative structure factor amplitudes, and (iv) refines the corresponding structures in real and reciprocal-space. The use of Xtrapol8 could accelerate data processing in kinetic and time-resolved crystallographic studies, and as well foster the identification of drug-targetable states in ligand-based crystallography.

| S-EPMC9243118 | biostudies-literature

Reversible Removal of Intermixed Shallow States by Light Soaking in Multication Mixed Halide Perovskite Films.

Project description:The highest reported efficiencies of metal halide perovskite (MHP) solar cells are all based on mixed perovskites, such as (FA,MA,Cs)Pb(I1-x Br x )3. Despite demonstrated structural changes induced by light soaking, it is unclear how the charge carrier dynamics are affected across this entire material family. Here, various (FA,MA,Cs)Pb(I1-x Br x )3 perovskite films are light-soaked in nitrogen, and changes in optoelectronic properties are investigated through time-resolved microwave conductivity (TRMC) and optical and structural techniques. To fit the TRMC decay kinetics obtained for pristine (FA,MA,Cs)Pb(I1-x Br x )3 for various excitation densities, additional shallow states have to be included, which are not required for describing TRMC traces of single-cation MHPs. These shallow states can, independently of x, be removed by light soaking, which leads to a reduction in the imbalance between the diffusional motion of electrons and holes. We interpret the shallow states as a result of initially well-intermixed halide distributions, which upon light soaking segregate into domains with distinct band gaps.

| S-EPMC6792222 | biostudies-literature

Geometric fluid approximation for general continuous-time Markov chains.

Project description:Fluid approximations have seen great success in approximating the macro-scale behaviour of Markov systems with a large number of discrete states. However, these methods rely on the continuous-time Markov chain (CTMC) having a particular population structure which suggests a natural continuous state-space endowed with a dynamics for the approximating process. We construct here a general method based on spectral analysis of the transition matrix of the CTMC, without the need for a population structure. Specifically, we use the popular manifold learning method of diffusion maps to analyse the transition matrix as the operator of a hidden continuous process. An embedding of states in a continuous space is recovered, and the space is endowed with a drift vector field inferred via Gaussian process regression. In this manner, we construct an ordinary differential equation whose solution approximates the evolution of the CTMC mean, mapped onto the continuous space (known as the fluid limit).

| S-EPMC6784392 | biostudies-literature

Inferring animal densities from tracking data using Markov chains.

Project description:The distributions and relative densities of species are keys to ecology. Large amounts of tracking data are being collected on a wide variety of animal species using several methods, especially electronic tags that record location. These tracking data are effectively used for many purposes, but generally provide biased measures of distribution, because the starts of the tracks are not randomly distributed among the locations used by the animals. We introduce a simple Markov-chain method that produces unbiased measures of relative density from tracking data. The density estimates can be over a geographical grid, and/or relative to environmental measures. The method assumes that the tracked animals are a random subset of the population in respect to how they move through the habitat cells, and that the movements of the animals among the habitat cells form a time-homogenous Markov chain. We illustrate the method using simulated data as well as real data on the movements of sperm whales. The simulations illustrate the bias introduced when the initial tracking locations are not randomly distributed, as well as the lack of bias when the Markov method is used. We believe that this method will be important in giving unbiased estimates of density from the growing corpus of animal tracking data.

| S-EPMC3632542 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data