An Efficient Coding Technique for Stochastic Processes.
Ontology highlight
ABSTRACT:
SUBMITTER: Garca JE
PROVIDER: S-EPMC8775014 | biostudies-literature |
REPOSITORIES: biostudies-literature
Similar Datasets
Project description:We present the Stochastic Simulator Compiler (SSC), a tool for exact stochastic simulations of well-mixed and spatially heterogeneous systems. SSC is the first tool to allow a readable high-level description with spatially heterogeneous simulation algorithms and complex geometries; this permits large systems to be expressed concisely. Meanwhile, direct native-code compilation allows SSC to generate very fast simulations.
| S-EPMC2734316 | biostudies-literature
Project description:A shift-periodic map is a one-dimensional map from the real line to itself which is periodic up to a linear translation and allowed to have singularities. It is shown that iterative sequences x n+1 = F(x n ) generated by such maps display rich dynamical behaviour. The integer parts ⌊xn⌋ give a discrete-time random walk for a suitable initial distribution of x 0 and converge in certain limits to Brownian motion or more general Lévy processes. Furthermore, for certain shift-periodic maps with small holes on [0,1], convergence of trajectories to a continuous-time random walk is shown in a limit.
| S-EPMC6894602 | biostudies-literature
Project description:For many stochastic processes, the probability [Formula: see text] of not-having reached a target in unbounded space up to time [Formula: see text] follows a slow algebraic decay at long times, [Formula: see text]. This is typically the case of symmetric compact (i.e. recurrent) random walks. While the persistence exponent [Formula: see text] has been studied at length, the prefactor [Formula: see text], which is quantitatively essential, remains poorly characterized, especially for non-Markovian processes. Here we derive explicit expressions for [Formula: see text] for a compact random walk in unbounded space by establishing an analytic relation with the mean first-passage time of the same random walk in a large confining volume. Our analytical results for [Formula: see text] are in good agreement with numerical simulations, even for strongly correlated processes such as Fractional Brownian Motion, and thus provide a refined understanding of the statistics of longest first-passage events in unbounded space.
| S-EPMC6611868 | biostudies-literature
Project description:For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer (estimate) their dominant modes from observations in real time. The modes can be real or complex. For a real mode (monotone decay), the goal is to infer its damping rate and mode shape. For a complex mode (oscillatory decay), the goal is to infer its frequency, damping rate and (complex) mode shape. Their amplitudes and correlations are encoded in a mode covariance matrix that is also to be inferred. The work is motivated and illustrated by the problem of detection of oscillations in power flow in AC electrical networks. Suggestions of some other applications are given.
| S-EPMC8059618 | biostudies-literature
Project description:Several researchers have described two-part models with patient-specific stochastic processes for analysing longitudinal semicontinuous data. In theory, such models can offer greater flexibility than the standard two-part model with patient-specific random effects. However, in practice, the high dimensional integrations involved in the marginal likelihood (i.e. integrated over the stochastic processes) significantly complicates model fitting. Thus, non-standard computationally intensive procedures based on simulating the marginal likelihood have so far only been proposed. In this paper, we describe an efficient method of implementation by demonstrating how the high dimensional integrations involved in the marginal likelihood can be computed efficiently. Specifically, by using a property of the multivariate normal distribution and the standard marginal cumulative distribution function identity, we transform the marginal likelihood so that the high dimensional integrations are contained in the cumulative distribution function of a multivariate normal distribution, which can then be efficiently evaluated. Hence, maximum likelihood estimation can be used to obtain parameter estimates and asymptotic standard errors (from the observed information matrix) of model parameters. We describe our proposed efficient implementation procedure for the standard two-part model parameterisation and when it is of interest to directly model the overall marginal mean. The methodology is applied on a psoriatic arthritis data set concerning functional disability.
| S-EPMC5723155 | biostudies-literature
Project description:Efficient computation of geophysical turbulence, such as occurs in the atmosphere and ocean, is a formidable challenge for the following reasons: the complex combination of waves, jets, and vortices; significant energetic backscatter from unresolved small scales to resolved large scales; a lack of dynamical scale separation between large and small scales; and small-scale instabilities, conditional on the large scales, which do not saturate. Nevertheless, efficient methods are needed to allow large ensemble simulations of sufficient size to provide meaningful quantifications of uncertainty in future predictions and past reanalyses through data assimilation and filtering. Here, a class of efficient stochastic superparameterization algorithms is introduced. In contrast to conventional superparameterization, the method here (i) does not require the simulation of nonlinear eddy dynamics on periodic embedded domains, (ii) includes a better representation of unresolved small-scale instabilities, and (iii) allows efficient representation of a much wider range of unresolved scales. The simplest algorithm implemented here radically improves efficiency by representing small-scale eddies at and below the limit of computational resolution by a suitable one-dimensional stochastic model of random-direction plane waves. In contrast to heterogeneous multiscale methods, the methods developed here do not require strong scale separation or conditional equilibration of local statistics. The simplest algorithm introduced here shows excellent performance on a difficult test suite of prototype problems for geophysical turbulence with waves, jets, and vortices, with a speedup of several orders of magnitude compared with direct simulation.
| S-EPMC3607027 | biostudies-literature
Project description:DNA mismatch repair (MMR) is a DNA excision-resynthesis process that principally enhances replication fidelity. Highly conserved MutS (MSH) and MutL (MLH/PMS) homologs initiate MMR and in higher eukaryotes act as DNA damage sensors that can trigger apoptosis. MSH proteins recognize mismatched nucleotides, whereas the MLH/PMS proteins mediate multiple interactions associated with downstream MMR events including strand discrimination and strand-specific excision that are initiated at a significant distance from the mismatch. Remarkably, the biophysical functions of the MLH/PMS proteins have been elusive for decades. Here we consider recent observations that have helped to define the mechanics of MLH/PMS proteins and their role in choreographing MMR. We highlight the stochastic nature of DNA interactions that have been visualized by single-molecule analysis and the plasticity of protein complexes that employ thermal diffusion to complete the progressions of MMR.
| S-EPMC6461355 | biostudies-literature
Project description:A major goal of microbial community ecology is to understand the forces that structure community composition. Deterministic selection by specific environmental factors is sometimes important, but in other cases stochastic or ecologically neutral processes dominate. Lacking is a unified conceptual framework aiming to understand why deterministic processes dominate in some contexts but not others. Here we work toward such a framework. By testing predictions derived from general ecological theory we aim to uncover factors that govern the relative influences of deterministic and stochastic processes. We couple spatiotemporal data on subsurface microbial communities and environmental parameters with metrics and null models of within and between community phylogenetic composition. Testing for phylogenetic signal in organismal niches showed that more closely related taxa have more similar habitat associations. Community phylogenetic analyses further showed that ecologically similar taxa coexist to a greater degree than expected by chance. Environmental filtering thus deterministically governs subsurface microbial community composition. More importantly, the influence of deterministic environmental filtering relative to stochastic factors was maximized at both ends of an environmental variation gradient. A stronger role of stochastic factors was, however, supported through analyses of phylogenetic temporal turnover. Although phylogenetic turnover was on average faster than expected, most pairwise comparisons were not themselves significantly non-random. The relative influence of deterministic environmental filtering over community dynamics was elevated, however, in the most temporally and spatially variable environments. Our results point to general rules governing the relative influences of stochastic and deterministic processes across micro- and macro-organisms.
| S-EPMC3498916 | biostudies-literature
Project description:The structure of microbiomes is often classified into discrete or semi-discrete types potentially differing in community-scale functional profiles. Elucidating the mechanisms that generate such "alternative states" of microbiome compositions has been one of the major challenges in ecology and microbiology. In a time-series analysis of experimental microbiomes, we here show that both deterministic and stochastic ecological processes drive divergence of alternative microbiome states. We introduced species-rich soil-derived microbiomes into eight types of culture media with 48 replicates, monitoring shifts in community compositions at six time points (8 media × 48 replicates × 6 time points = 2304 community samples). We then confirmed that microbial community structure diverged into a few state types in each of the eight medium conditions as predicted in the presence of both deterministic and stochastic community processes. In other words, microbiome structure was differentiated into a small number of reproducible compositions under the same environment. This fact indicates not only the presence of selective forces leading to specific equilibria of community-scale resource use but also the influence of demographic drift (fluctuations) on the microbiome assembly. A reference-genome-based analysis further suggested that the observed alternative states differed in ecosystem-level functions. These findings will help us examine how microbiome structure and functions can be controlled by changing the "stability landscapes" of ecological community compositions.
| S-EPMC10897905 | biostudies-literature
Project description:BackgroundBiochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need for numerical methods that are both fast and accurate. The Bulirsch-Stoer method is an established method for solving ordinary differential equations that possesses both of these qualities.ResultsIn this paper, we present the Stochastic Bulirsch-Stoer method, a new numerical method for simulating discrete chemical reaction systems, inspired by its deterministic counterpart. It is able to achieve an excellent efficiency due to the fact that it is based on an approach with high deterministic order, allowing for larger stepsizes and leading to fast simulations. We compare it to the Euler ?-leap, as well as two more recent ?-leap methods, on a number of example problems, and find that as well as being very accurate, our method is the most robust, in terms of efficiency, of all the methods considered in this paper. The problems it is most suited for are those with increased populations that would be too slow to simulate using Gillespie's stochastic simulation algorithm. For such problems, it is likely to achieve higher weak order in the moments.ConclusionsThe Stochastic Bulirsch-Stoer method is a novel stochastic solver that can be used for fast and accurate simulations. Crucially, compared to other similar methods, it better retains its high accuracy when the timesteps are increased. Thus the Stochastic Bulirsch-Stoer method is both computationally efficient and robust. These are key properties for any stochastic numerical method, as they must typically run many thousands of simulations.
| S-EPMC4085235 | biostudies-literature