26,580 research outputs found
BioSimulator.jl: Stochastic simulation in Julia
Biological systems with intertwined feedback loops pose a challenge to
mathematical modeling efforts. Moreover, rare events, such as mutation and
extinction, complicate system dynamics. Stochastic simulation algorithms are
useful in generating time-evolution trajectories for these systems because they
can adequately capture the influence of random fluctuations and quantify rare
events. We present a simple and flexible package, BioSimulator.jl, for
implementing the Gillespie algorithm, -leaping, and related stochastic
simulation algorithms. The objective of this work is to provide scientists
across domains with fast, user-friendly simulation tools. We used the
high-performance programming language Julia because of its emphasis on
scientific computing. Our software package implements a suite of stochastic
simulation algorithms based on Markov chain theory. We provide the ability to
(a) diagram Petri Nets describing interactions, (b) plot average trajectories
and attached standard deviations of each participating species over time, and
(c) generate frequency distributions of each species at a specified time.
BioSimulator.jl's interface allows users to build models programmatically
within Julia. A model is then passed to the simulate routine to generate
simulation data. The built-in tools allow one to visualize results and compute
summary statistics. Our examples highlight the broad applicability of our
software to systems of varying complexity from ecology, systems biology,
chemistry, and genetics. The user-friendly nature of BioSimulator.jl encourages
the use of stochastic simulation, minimizes tedious programming efforts, and
reduces errors during model specification.Comment: 27 pages, 5 figures, 3 table
Bootstrapping Macroeconometric Models
This paper outlines a bootstrapping approach to the estimation and analysis of macroeconometric models. It integrates for dynamic, nonlinear, simultaneous equation models the bootstrapping approach to evaluating estimators initiated by Efron (1979) and the stochastic simulation approach to evaluating models' properties initiated by Adelman and Adelman (1959). It also estimates for a particular model the gain in coverage accuracy from using bootstrap confidence intervals over asymptotic confidence intervals.Bootstrapping, stochastic simulation
The transition between stochastic and deterministic behavior in an excitable gene circuit
We explore the connection between a stochastic simulation model and an
ordinary differential equations (ODEs) model of the dynamics of an excitable
gene circuit that exhibits noise-induced oscillations. Near a bifurcation point
in the ODE model, the stochastic simulation model yields behavior dramatically
different from that predicted by the ODE model. We analyze how that behavior
depends on the gene copy number and find very slow convergence to the large
number limit near the bifurcation point. The implications for understanding the
dynamics of gene circuits and other birth-death dynamical systems with small
numbers of constituents are discussed.Comment: PLoS ONE: Research Article, published 11 Apr 201
Fat vs. thin threading approach on GPUs: application to stochastic simulation of chemical reactions
We explore two different threading approaches on a graphics processing unit (GPU) exploiting two different characteristics of the current GPU architecture. The fat thread approach tries to minimise data access time by relying on shared memory and registers potentially sacrificing parallelism. The thin thread approach maximises parallelism and tries to hide access latencies. We apply these two approaches to the parallel stochastic simulation of chemical reaction systems using the stochastic simulation algorithm (SSA) by Gillespie (J. Phys. Chem, Vol. 81, p. 2340-2361, 1977). In these cases, the proposed thin thread approach shows comparable performance while eliminating the limitation of the reaction system’s size
Portfolio Management: An investigation of the implications of measurement errors in stock prices on the creation, management and evaluation of stock portfolios, using stochastic simulations
In this paper, we investigate the implications of measurement errors in the daily published stock prices on the creation and management of efficient portfolios. Using stochastic simulation techniques and the Markowitz Mean Variance approach in the creation of the weights of the various stocks of a portfolio, we conclude that measurement errors have significant implications on the efficiency of the management of a stock portfolio.Markowitz Mean Variance, Measurement Errors in Returns, Stochastic Simulation.
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