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Journal articles on the topic 'Computational stochastic dynamics'

Author: Grafiati

Published: 6 September 2023

Last updated: 7 September 2023

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1

Capiez-Lernout, E., and C. Soize. "Inverse problems in stochastic computational dynamics." Journal of Physics: Conference Series 135 (November 1, 2008): 012028. http://dx.doi.org/10.1088/1742-6596/135/1/012028.

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2

Johnson, E. A., C. Proppe, B. F. Spencer, L. A. Bergman, G. S. Székely, and G. I. Schuëller. "Parallel processing in computational stochastic dynamics." Probabilistic Engineering Mechanics 18, no. 1 (January 2003): 37–60. http://dx.doi.org/10.1016/s0266-8920(02)00041-3.

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3

Petromichelakis, Ioannis, and Ioannis A. Kougioumtzoglou. "Addressing the curse of dimensionality in stochastic dynamics: a Wiener path integral variational formulation with free boundaries." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2243 (November 2020): 20200385. http://dx.doi.org/10.1098/rspa.2020.0385.

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A Wiener path integral variational formulation with free boundaries is developed for determining the stochastic response of high-dimensional nonlinear dynamical systems in a computationally efficient manner. Specifically, a Wiener path integral representation of a marginal or lower-dimensional joint response probability density function is derived. Due to this a priori marginalization, the associated computational cost of the technique becomes independent of the degrees of freedom (d.f.) or stochastic dimensions of the system, and thus, the ‘curse of dimensionality’ in stochastic dynamics is circumvented. Two indicative numerical examples are considered for highlighting the capabilities of the technique. The first relates to marine engineering and pertains to a structure exposed to nonlinear flow-induced forces and subjected to non-white stochastic excitation. The second relates to nano-engineering and pertains to a 100-d.f. stochastically excited nonlinear dynamical system modelling the behaviour of large arrays of coupled nano-mechanical oscillators. Comparisons with pertinent Monte Carlo simulation data demonstrate the computational efficiency and accuracy of the developed technique.

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Breuer, H. P., and F. Petruccione. "A stochastic approach to computational fluid dynamics." Continuum Mechanics and Thermodynamics 4, no. 4 (1992): 247–67. http://dx.doi.org/10.1007/bf01129331.

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5

To, C. W. S. "On computational stochastic structural dynamics applying finite elements." Archives of Computational Methods in Engineering 8, no. 1 (March 2001): 3–40. http://dx.doi.org/10.1007/bf02736683.

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6

Holm, D. D., and V. Putkaradze. "Dynamics of non-holonomic systems with stochastic transport." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2209 (January 2018): 20170479. http://dx.doi.org/10.1098/rspa.2017.0479.

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This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under non-holonomic constraints. For this purpose, we derive, analyse and numerically study the example of an unbalanced spherical ball rolling under gravity along a stochastic path. Our approach uses the Hamilton–Pontryagin variational principle, constrained by a stochastic rolling condition, which we show is equivalent to the corresponding stochastic Lagrange–d’Alembert principle. In the example of the rolling ball, the stochasticity represents uncertainty in the observation and/or error in the computational simulation of the angular velocity of rolling. The influence of the stochasticity on the deterministically conserved quantities is investigated both analytically and numerically. Our approach applies to a wide variety of stochastic, non-holonomically constrained systems, because it preserves the mathematical properties inherited from the variational principle.

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Bortolussi, Luca, and Alberto Policriti. "Hybrid Dynamics of Stochastic π-Calculus." Mathematics in Computer Science 2, no. 3 (March 2009): 465–91. http://dx.doi.org/10.1007/s11786-008-0065-3.

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8

Erban, Radek. "Coupling all-atom molecular dynamics simulations of ions in water with Brownian dynamics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2186 (February 2016): 20150556. http://dx.doi.org/10.1098/rspa.2015.0556.

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Molecular dynamics (MD) simulations of ions (K + , Na + , Ca 2+ and Cl − ) in aqueous solutions are investigated. Water is described using the SPC/E model. A stochastic coarse-grained description for ion behaviour is presented and parametrized using MD simulations. It is given as a system of coupled stochastic and ordinary differential equations, describing the ion position, velocity and acceleration. The stochastic coarse-grained model provides an intermediate description between all-atom MD simulations and Brownian dynamics (BD) models. It is used to develop a multiscale method which uses all-atom MD simulations in parts of the computational domain and (less detailed) BD simulations in the remainder of the domain.

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9

Zhang, Libin, Zijun Yao, and Bin Wu. "Calculating biodiversity under stochastic evolutionary dynamics." Applied Mathematics and Computation 411 (December 2021): 126543. http://dx.doi.org/10.1016/j.amc.2021.126543.

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Tankhilevich, Evgeny, Jonathan Ish-Horowicz, Tara Hameed, Elisabeth Roesch, Istvan Kleijn, Michael P. H. Stumpf, and Fei He. "GpABC: a Julia package for approximate Bayesian computation with Gaussian process emulation." Bioinformatics 36, no. 10 (February 5, 2020): 3286–87. http://dx.doi.org/10.1093/bioinformatics/btaa078.

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Abstract Motivation Approximate Bayesian computation (ABC) is an important framework within which to infer the structure and parameters of a systems biology model. It is especially suitable for biological systems with stochastic and nonlinear dynamics, for which the likelihood functions are intractable. However, the associated computational cost often limits ABC to models that are relatively quick to simulate in practice. Results We here present a Julia package, GpABC, that implements parameter inference and model selection for deterministic or stochastic models using (i) standard rejection ABC or sequential Monte Carlo ABC or (ii) ABC with Gaussian process emulation. The latter significantly reduces the computational cost. Availability and implementation https://github.com/tanhevg/GpABC.jl.

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11

Hoang-Trong, Tuan Minh, Aman Ullah, William Jonathan Lederer, and Mohsin Saleet Jafri. "A Stochastic Spatiotemporal Model of Rat Ventricular Myocyte Calcium Dynamics Demonstrated Necessary Features for Calcium Wave Propagation." Membranes 11, no. 12 (December 18, 2021): 989. http://dx.doi.org/10.3390/membranes11120989.

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Calcium (Ca2+) plays a central role in the excitation and contraction of cardiac myocytes. Experiments have indicated that calcium release is stochastic and regulated locally suggesting the possibility of spatially heterogeneous calcium levels in the cells. This spatial heterogeneity might be important in mediating different signaling pathways. During more than 50 years of computational cell biology, the computational models have been advanced to incorporate more ionic currents, going from deterministic models to stochastic models. While periodic increases in cytoplasmic Ca2+ concentration drive cardiac contraction, aberrant Ca2+ release can underly cardiac arrhythmia. However, the study of the spatial role of calcium ions has been limited due to the computational expense of using a three-dimensional stochastic computational model. In this paper, we introduce a three-dimensional stochastic computational model for rat ventricular myocytes at the whole-cell level that incorporate detailed calcium dynamics, with (1) non-uniform release site placement, (2) non-uniform membrane ionic currents and membrane buffers, (3) stochastic calcium-leak dynamics and (4) non-junctional or rogue ryanodine receptors. The model simulates spark-induced spark activation and spark-induced Ca2+ wave initiation and propagation that occur under conditions of calcium overload at the closed-cell condition, but not when Ca2+ levels are normal. This is considered important since the presence of Ca2+ waves contribute to the activation of arrhythmogenic currents.

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12

Bernardin, Frédéric, Mireille Bossy, Claire Chauvin, Jean-François Jabir, and Antoine Rousseau. "Stochastic Lagrangian method for downscaling problems in computational fluid dynamics." ESAIM: Mathematical Modelling and Numerical Analysis 44, no. 5 (August 26, 2010): 885–920. http://dx.doi.org/10.1051/m2an/2010046.

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13

Batou, A., C. Soize, and S. Audebert. "Model identification in computational stochastic dynamics using experimental modal data." Mechanical Systems and Signal Processing 50-51 (January 2015): 307–22. http://dx.doi.org/10.1016/j.ymssp.2014.05.010.

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14

Jamali, Y., A. Lohrasebi, and H. Rafii-Tabar. "Computational modelling of the stochastic dynamics of kinesin biomolecular motors." Physica A: Statistical Mechanics and its Applications 381 (July 2007): 239–54. http://dx.doi.org/10.1016/j.physa.2007.03.022.

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15

Cunha, Americo, Christian Soize, and Rubens Sampaio. "Computational modeling of the nonlinear stochastic dynamics of horizontal drillstrings." Computational Mechanics 56, no. 5 (September 4, 2015): 849–78. http://dx.doi.org/10.1007/s00466-015-1206-6.

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16

Augusti, G., and P. M. Mariano. "Introduction to computational models of damage dynamics under stochastic actionst." Probabilistic Engineering Mechanics 11, no. 2 (April 1996): 107–12. http://dx.doi.org/10.1016/0266-8920(95)00031-3.

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17

Grebennikov, Dmitry S. "Computational methods for multiscale modelling of virus infection dynamics." Russian Journal of Numerical Analysis and Mathematical Modelling 38, no. 2 (March 1, 2023): 75–87. http://dx.doi.org/10.1515/rnam-2023-0007.

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Abstract Virus infection dynamics is governed by the processes on multiple scales: on the whole organism level, tissue level, and intracellular level. In this paper, we develop a multi-scale multi-compartment model of HIV infection in a simplified setting and the computational methods for numerical realization of the model. The multiscale model describes the processes from various scales and of different nature (cell motility, virus diffusion, intracellular virus replication). Intracellular replication model is based on a Markov chain with time-inhomogeneous propensities that depend on the extracellular level of virions. Reaction diffusion equations used to model free virion diffusion in the lymphoid tissue have moving sources, which are determined by the positions of the infected cells (immune cell motility model) and the rate of virion secretion from them (intracellular model). Immune cell motility model parameterizes the intercellular interaction forces, friction and the stochastic force of active cell motility. Together, this allows for a proper description of the intracellular stochasticity that propagates across multiple scales. A hybrid discrete-continuous stochastic-deterministic algorithm for simulation of the multiscale model based on the uniformization Monte Carlo method is implemented.

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18

Raza, Ali, Jan Awrejcewicz, Muhammad Rafiq, Nauman Ahmed, and Muhammad Mohsin. "Stochastic Analysis of Nonlinear Cancer Disease Model through Virotherapy and Computational Methods." Mathematics 10, no. 3 (January 25, 2022): 368. http://dx.doi.org/10.3390/math10030368.

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Cancer is a common term for many diseases that can affect anybody. A worldwide leading cause of death is cancer, according to the World Health Organization (WHO) report. In 2020, ten million people died from cancer. This model identifies the interaction of cancer cells, viral therapy, and immune response. In this model, the cell population has four parts, namely uninfected cells (x), infected cells (y), virus-free cells (v), and immune cells (z). This study presents the analysis of the stochastic cancer virotherapy model in the cell population dynamics. The model results have restored the properties of the biological problem, such as dynamical consistency, positivity, and boundedness, which are the considerable requirements of the models in these fields. The existing computational methods, such as the Euler Maruyama, Stochastic Euler, and Stochastic Runge Kutta, fail to restore the abovementioned properties. The proposed stochastic nonstandard finite difference method is efficient, cost-effective, and accommodates all the desired feasible properties. The existing standard stochastic methods converge conditionally or diverge in the long run. The solution by the nonstandard finite difference method is stable and convergent over all time steps.

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19

Manohar, C. S., and R. A. Ibrahim. "Progress in Structural Dynamics With Stochastic Parameter Variations: 1987-1998." Applied Mechanics Reviews 52, no. 5 (May 1, 1999): 177–97. http://dx.doi.org/10.1115/1.3098933.

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This article is an update of an earlier paper by Ibrahim (1987) and is aimed at reviewing the work published during the last decade in the area of vibration of structures with parameter uncertainties. Different types of uncertainty modeling are described in terms of material and geometric properties. These models are considered in terms of Gaussian or non-Gaussian distributions. Computational stochastic algorithms including stochastic finite element methods and Monte Carlo simulation are dominating a major part of current activities. Recent analytical developments of the random eigenvalue problem are reviewed with reference to typical structural elements. These developments include the implementation of statistical energy analysis, stochastic boundary element methods, and interval algebra. Other topics include forced vibration of single- and multi-degree-of-freedom systems including nonlinear systems, localization in disordered periodic structures, and experimental results. Computational stochastic mechanics has found several industrial applications including aerospace, automotive and composite structural elements. The review also covers developments in the areas of statistical modeling of high frequency vibrations. There are 183 references.

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20

Chang, Qingquan, Dandan Li, and Chunyou Sun. "Dynamics for a stochastic degenerate parabolic equation." Computers & Mathematics with Applications 77, no. 9 (May 2019): 2407–31. http://dx.doi.org/10.1016/j.camwa.2018.12.023.

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21

Avrachenkov, Konstantin, and Vivek S. Borkar. "Metastability in Stochastic Replicator Dynamics." Dynamic Games and Applications 9, no. 2 (May 12, 2018): 366–90. http://dx.doi.org/10.1007/s13235-018-0265-7.

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22

Liu, Shitao, Liang Zhang, and Yifan Xing. "Dynamics of a stochastic heroin epidemic model." Journal of Computational and Applied Mathematics 351 (May 2019): 260–69. http://dx.doi.org/10.1016/j.cam.2018.11.005.

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23

HINZ, J., and N. YAP. "SOLUTIONS AND DIAGNOSTICS OF SWITCHING PROBLEMS WITH LINEAR STATE DYNAMICS." ANZIAM Journal 57, no. 3 (January 2016): 339–51. http://dx.doi.org/10.1017/s1446181115000279.

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Optimal control problems of stochastic switching type appear frequently when making decisions under uncertainty and are notoriously challenging from a computational viewpoint. Although numerous approaches have been suggested in the literature to tackle them, typical real-world applications are inherently high dimensional and usually drive common algorithms to their computational limits. Furthermore, even when numerical approximations of the optimal strategy are obtained, practitioners must apply time-consuming and unreliable Monte Carlo simulations to assess their quality. In this paper, we show how one can overcome both difficulties for a specific class of discrete-time stochastic control problems. A simple and efficient algorithm which yields approximate numerical solutions is presented and methods to perform diagnostics are provided.

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24

Arif, Muhammad Shoaib, Kamaleldin Abodayeh, and Yasir Nawaz. "A Computational Scheme for Stochastic Non-Newtonian Mixed Convection Nanofluid Flow over Oscillatory Sheet." Energies 16, no. 5 (February 27, 2023): 2298. http://dx.doi.org/10.3390/en16052298.

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Stochastic simulations enable researchers to incorporate uncertainties beyond numerical discretization errors in computational fluid dynamics (CFD). Here, the authors provide examples of stochastic simulations of incompressible flows and numerical solutions for validating these newly emerging stochastic modeling methods. A numerical scheme is constructed for finding solutions to stochastic parabolic equations. The scheme is second-order accurate in time for the constant coefficient of the Wiener process term. The stability analysis of the scheme is also provided. The scheme is applied to the dimensionless heat and mass transfer model of mixed convective non-Newtonian nanofluid flow over oscillatory sheets. Both the deterministic and stochastic energy equations use temperature-dependent thermal conductivity. The stochastic model is more general than the deterministic model. The results are calculated for both flat and oscillatory plates. Casson parameter, mixed convective parameter, thermophoresis, Brownian motion parameter, Prandtl number, Schmidt number, and reaction rate parameter all impact the velocities, temperatures, and concentrations shown in the graphs. Under the influence of the oscillating plate, the results reveal that the concentration profile decreases with increasing Brownian motion parameters and increases with increasing thermophoresis parameters. The behavior of the velocity profile for the deterministic and stochastic models is provided, and contour plots for the stochastic model are also displayed. This article aims to provide a state-of-the-art overview of recent achievements in the field of stochastic computational fluid dynamics (SCFD) while also pointing out potential future avenues and unresolved challenges for the computational mathematics community to investigate.

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25

Lolla, Tapovan, and Pierre F. J. Lermusiaux. "A Gaussian Mixture Model Smoother for Continuous Nonlinear Stochastic Dynamical Systems: Theory and Scheme." Monthly Weather Review 145, no. 7 (July 2017): 2743–61. http://dx.doi.org/10.1175/mwr-d-16-0064.1.

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Retrospective inference through Bayesian smoothing is indispensable in geophysics, with crucial applications in ocean and numerical weather estimation, climate dynamics, and Earth system modeling. However, dealing with the high-dimensionality and nonlinearity of geophysical processes remains a major challenge in the development of Bayesian smoothers. Addressing this issue, a novel subspace smoothing methodology for high-dimensional stochastic fields governed by general nonlinear dynamics is obtained. Building on recent Bayesian filters and classic Kalman smoothers, the fundamental equations and forward–backward algorithms of new Gaussian Mixture Model (GMM) smoothers are derived, for both the full state space and dynamic subspace. For the latter, the stochastic Dynamically Orthogonal (DO) field equations and their time-evolving stochastic subspace are employed to predict the prior subspace probabilities. Bayesian inference, both forward and backward in time, is then analytically carried out in the dominant stochastic subspace, after fitting semiparametric GMMs to joint subspace realizations. The theoretical properties, varied forms, and computational costs of the new GMM smoother equations are presented and discussed.

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Hanif, Ayub, and Robert Elliott Smith. "State Space Modeling & Bayesian Inference with Computational Intelligence." New Mathematics and Natural Computation 11, no. 01 (March 2015): 71–101. http://dx.doi.org/10.1142/s1793005715500040.

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Recursive Bayesian estimation using sequential Monte Carlos methods is a powerful numerical technique to understand latent dynamics of nonlinear non-Gaussian dynamical systems. It enables us to reason under uncertainty and addresses shortcomings underlying deterministic systems and control theories which do not provide sufficient means of performing analysis and design. In addition, parametric techniques such as the Kalman filter and its extensions, though they are computationally efficient, do not reliably compute states and cannot be used to learn stochastic problems. We review recursive Bayesian estimation using sequential Monte Carlo methods highlighting open problems. Primary of these is the weight degeneracy and sample impoverishment problem. We proceed to detail synergistic computational intelligence sequential Monte Carlo methods which address this. We find that imbuing sequential Monte Carlos with computational intelligence has many advantages when applied to many application and problem domains.

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Silberschmidt, Vadim V. "Dynamics of Stochastic Damage Evolution." International Journal of Damage Mechanics 7, no. 1 (January 1998): 84–98. http://dx.doi.org/10.1177/105678959800700104.

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28

AHLIP, REHEZ, and MAREK RUTKOWSKI. "FORWARD START OPTIONS UNDER STOCHASTIC VOLATILITY AND STOCHASTIC INTEREST RATES." International Journal of Theoretical and Applied Finance 12, no. 02 (March 2009): 209–25. http://dx.doi.org/10.1142/s0219024909005166.

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Forward start options are examined in Heston's (Review of Financial Studies6 (1993) 327–343) stochastic volatility model with the CIR (Econometrica53 (1985) 385–408) stochastic interest rates. The instantaneous volatility and the instantaneous short rate are assumed to be correlated with the dynamics of stock return. The main result is an analytic formula for the price of a forward start European call option. It is derived using the probabilistic approach combined with the Fourier inversion technique, as developed in Carr and Madan (Journal of Computational Finance2 (1999) 61–73).

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29

Botmart, Thongchai, Zulqurnain Sabir, Afaf S. Alwabli, Salem Ben Said, Qasem Al-Mdallal, Maria Emilia Camargo, and Wajaree Weera. "Computational Stochastic Investigations for the Socio-Ecological Dynamics with Reef Ecosystems." Computers, Materials & Continua 73, no. 3 (2022): 5589–607. http://dx.doi.org/10.32604/cmc.2022.032087.

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Hosder, Serhat, Robert W. Walters, and Michael Balch. "Point-Collocation Nonintrusive Polynomial Chaos Method for Stochastic Computational Fluid Dynamics." AIAA Journal 48, no. 12 (December 2010): 2721–30. http://dx.doi.org/10.2514/1.39389.

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31

Soize, C. "Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances." Journal of Sound and Vibration 332, no. 10 (May 2013): 2379–95. http://dx.doi.org/10.1016/j.jsv.2011.10.010.

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32

Steijaert, M. N., J. H. K. Van Den Brink, A. M. L. Liekens, P. A. J. Hilbers, and H. M. M. Ten Eikelder. "Computing the Stochastic Dynamics of Phosphorylation Networks." Journal of Computational Biology 17, no. 2 (February 2010): 189–99. http://dx.doi.org/10.1089/cmb.2009.0059.

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33

Tagade, Piyush M., and Han-Lim Choi. "A Dynamic BI–Orthogonal Field Equation Approach to Efficient Bayesian Inversion." International Journal of Applied Mathematics and Computer Science 27, no. 2 (June 27, 2017): 229–43. http://dx.doi.org/10.1515/amcs-2017-0016.

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AbstractThis paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen-Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE) that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs) define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.

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Ejima, Toshiaki. "Dynamics of Stochastic Relaxation Processes." Systems and Computers in Japan 20, no. 3 (September 5, 2007): 68–77. http://dx.doi.org/10.1002/scj.4690200307.

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35

Chen, Weidong, Yaqin Shi, Jingxin Ma, Chunlong Xu, Shengzhuo Lu, and Xing Xu. "Stochastic Material Point Method for Analysis in Non-Linear Dynamics of Metals." Metals 9, no. 1 (January 21, 2019): 107. http://dx.doi.org/10.3390/met9010107.

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A stochastic material point method is proposed for stochastic analysis in non-linear dynamics of metals with varying random material properties. The basic random variables are parameters of equation of state and those of constitutive equation. In conjunction with the material point method, the Taylor series expansion is employed to predict first- and second-moment characteristics of structural response. Unlike the traditional grid methods, the stochastic material point method does not require structured mesh; instead, only a scattered cluster of nodes is required in the computational domain. In addition, there is no need for fixed connectivity between nodes. Hence, the stochastic material point method is more suitable than the stochastic method based on grids, when solving dynamics problems of metals involving large deformations and strong nonlinearity. Numerical examples show good agreement between the results of the stochastic material point method and Monte Carlo simulation. This study examines the accuracy and convergence of the stochastic material point method. The stochastic material point method offers a new option when solving stochastic dynamics problems of metals involving large deformation and strong nonlinearity, since the method is convenient and efficient.

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36

Weiqiu, Zhu, and Cai Guoqiang. "Nonlinear stochastic dynamics: A survey of recent developments." Acta Mechanica Sinica 18, no. 6 (December 2002): 551–66. http://dx.doi.org/10.1007/bf02487958.

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Xu, Ying, Yeye Guo, Guodong Ren, and Jun Ma. "Dynamics and stochastic resonance in a thermosensitive neuron." Applied Mathematics and Computation 385 (November 2020): 125427. http://dx.doi.org/10.1016/j.amc.2020.125427.

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Barley, Kamal, and Alhaji Cherif. "Stochastic nonlinear dynamics of interpersonal and romantic relationships." Applied Mathematics and Computation 217, no. 13 (March 2011): 6273–81. http://dx.doi.org/10.1016/j.amc.2010.12.117.

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39

Infante, Saba, Luis Sanchez, and Aracelis Hernandez. "Stochastic models to estimate population dynamics." Statistics, Optimization & Information Computing 8, no. 1 (February 17, 2020): 136–52. http://dx.doi.org/10.19139/soic-2310-5070-488.

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The growth dynamics that a population follows is mainly due to births, deaths or migrations, each of thesephenomena is affected by other factors such as public health, birth control, work sources, economy, safety and conditions of quality of life in neighboring countries, among many others. In this paper is proposed two statistical models based on a system of stochastic differential equations (SDE) that model the dynamics of population growth, and three computational algorithms that allow the generation of probability distribution samples in high dimensions, in models that have non-linear structures and that are useful for making inferences. The algorithms allow to estimate simultaneously states solutions and parameters in SDE models. The interpretation of the parameters is important because they are related to the variables of growth, mortality, migration, physical-chemical conditions of the environment, among other factors. The algorithms are illustrated using real data from a sector of the population of the Republic of Ecuador, and are compared with the results obtained with the models used by theWorld Bank for the same data, which shows that stochastic models Proposals based on an SDE more adequately and reliably adjust the dynamics of demographic randomness, sampling errors and environmental randomness in comparison with the deterministic models used by the World Bank. It is observed that the population grows year by year and seems to have a definite tendency; that is, a clearly growing behavior is seen. To measure the relative success of the algorithms, the relative error was estimated, obtaining small percentage errors.

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Fralix, Brian, James Livsey, and Robert Lund. "RENEWAL SEQUENCES WITH PERIODIC DYNAMICS." Probability in the Engineering and Informational Sciences 26, no. 1 (November 25, 2011): 1–15. http://dx.doi.org/10.1017/s0269964811000209.

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Discrete-time renewal sequences play a fundamental role in the theory of stochastic processes. This article considers periodic versions of such processes; specifically, the length of an interrenewal is allowed to probabilistically depend on the season at which it began. Using only elementary renewal and Markov chain techniques, computational and limiting aspects of periodic renewal sequences are investigated. We use these results to construct a time series model for a periodically stationary sequence of integer counts.

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41

Renshaw, Eric. "Metropolis–Hastings from a stochastic population dynamics perspective." Computational Statistics & Data Analysis 45, no. 4 (May 2004): 765–86. http://dx.doi.org/10.1016/s0167-9473(03)00118-x.

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Smolen, Paul, Douglas A. Baxter, and John H. Byrne. "Effects of macromolecular transport and stochastic fluctuations on dynamics of genetic regulatory systems." American Journal of Physiology-Cell Physiology 277, no. 4 (October 1, 1999): C777—C790. http://dx.doi.org/10.1152/ajpcell.1999.277.4.c777.

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To predict the dynamics of genetic regulation, it may be necessary to consider macromolecular transport and stochastic fluctuations in macromolecule numbers. Transport can be diffusive or active, and in some cases a time delay might suffice to model active transport. We characterize major differences in the dynamics of model genetic systems when diffusive transport of mRNA and protein was compared with transport modeled as a time delay. Delays allow for history-dependent, non-Markovian responses to stimuli (i.e., “molecular memory”). Diffusion suppresses oscillations, whereas delays tend to create oscillations. When simulating essential elements of circadian oscillators, we found the delay between transcription and translation necessary for oscillations. Stochastic fluctuations tend to destabilize and thereby mask steady states with few molecules. This computational approach, combined with experiments, should provide a fruitful conceptual framework for investigating the function and dynamic properties of genetic regulatory systems.

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Li, Ming. "Simulation of Quantum Dynamics Based on the Quantum Stochastic Differential Equation." Scientific World Journal 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/424137.

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The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm.

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Warne, David J., Ruth E. Baker, and Matthew J. Simpson. "Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art." Journal of The Royal Society Interface 16, no. 151 (February 2019): 20180943. http://dx.doi.org/10.1098/rsif.2018.0943.

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Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterizing stochastic effects in biochemical systems is essential to understand the complex dynamics of living things. Mathematical idealizations of biochemically reacting systems must be able to capture stochastic phenomena. While robust theory exists to describe such stochastic models, the computational challenges in exploring these models can be a significant burden in practice since realistic models are analytically intractable. Determining the expected behaviour and variability of a stochastic biochemical reaction network requires many probabilistic simulations of its evolution. Using a biochemical reaction network model to assist in the interpretation of time-course data from a biological experiment is an even greater challenge due to the intractability of the likelihood function for determining observation probabilities. These computational challenges have been subjects of active research for over four decades. In this review, we present an accessible discussion of the major historical developments and state-of-the-art computational techniques relevant to simulation and inference problems for stochastic biochemical reaction network models. Detailed algorithms for particularly important methods are described and complemented with Matlab ® implementations. As a result, this review provides a practical and accessible introduction to computational methods for stochastic models within the life sciences community.

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Comboul, Maud, and Roger Ghanem. "MULTISCALE MODELING FOR STOCHASTIC FOREST DYNAMICS." International Journal for Multiscale Computational Engineering 12, no. 4 (2014): 319–29. http://dx.doi.org/10.1615/intjmultcompeng.2014010276.

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Grimm, Felix, Jürgen Dierke, Roland Ewert, Berthold Noll, and Manfred Aigner. "Modelling of combustion acoustics sources and their dynamics in the PRECCINSTA burner test case." International Journal of Spray and Combustion Dynamics 9, no. 4 (July 7, 2017): 330–48. http://dx.doi.org/10.1177/1756827717717390.

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A stochastic, hybrid computational fluid dynamics/computational combustion acoustics approach for combustion noise prediction is applied to the PRECCINSTA laboratory scale combustor (prediction and control of combustion instabilities in industrial gas turbines). The numerical method is validated for its ability to accurately reproduce broadband combustion noise levels from measurements. The approach is based on averaged flow field and turbulence statistics from computational fluid dynamics simulations. The three-dimensional fast random particle method for combustion noise prediction is employed for the modelling of time-resolved dynamics of sound sources and sound propagation via linearised Euler equations. A comprehensive analysis of simulated sound source dynamics is carried out in order to contribute to the understanding of combustion noise formation mechanisms. Therefrom gained knowledge can further on be incorporated for the investigation of onset of thermoacoustic phenomena. The method-inherent stochastic Langevin ansatz for the realisation of turbulence related source decay is analysed in terms of reproduction ability of local one- and two-point statistical input and therefore its applicability to complex test cases. Furthermore, input turbulence statistics are varied, in order to investigate the impact of turbulence on the resulting sound pressure spectra for a swirl stabilised, technically premixed combustor.

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Norman, G. E., and V. V. Stegailov. "Stochastic theory of the classical molecular dynamics method." Mathematical Models and Computer Simulations 5, no. 4 (July 2013): 305–33. http://dx.doi.org/10.1134/s2070048213040108.

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Pienaar, Elsje. "Multifidelity Analysis for Predicting Rare Events in Stochastic Computational Models of Complex Biological Systems." Biomedical Engineering and Computational Biology 9 (January 2018): 117959721879025. http://dx.doi.org/10.1177/1179597218790253.

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Rare events such as genetic mutations or cell-cell interactions are important contributors to dynamics in complex biological systems, eg, in drug-resistant infections. Computational approaches can help analyze rare events that are difficult to study experimentally. However, analyzing the frequency and dynamics of rare events in computational models can also be challenging due to high computational resource demands, especially for high-fidelity stochastic computational models. To facilitate analysis of rare events in complex biological systems, we present a multifidelity analysis approach that uses medium-fidelity analysis (Monte Carlo simulations) and/or low-fidelity analysis (Markov chain models) to analyze high-fidelity stochastic model results. Medium-fidelity analysis can produce large numbers of possible rare event trajectories for a single high-fidelity model simulation. This allows prediction of both rare event dynamics and probability distributions at much lower frequencies than high-fidelity models. Low-fidelity analysis can calculate probability distributions for rare events over time for any frequency by updating the probabilities of the rare event state space after each discrete event of the high-fidelity model. To validate the approach, we apply multifidelity analysis to a high-fidelity model of tuberculosis disease. We validate the method against high-fidelity model results and illustrate the application of multifidelity analysis in predicting rare event trajectories, performing sensitivity analyses and extrapolating predictions to very low frequencies in complex systems. We believe that our approach will complement ongoing efforts to enable accurate prediction of rare event dynamics in high-fidelity computational models.

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Pélissier, Aurélien, Youcef Akrout, Katharina Jahn , Jack Kuipers , Ulf Klein , Niko Beerenwinkel, and María Rodríguez Martínez. "Computational Model Reveals a Stochastic Mechanism behind Germinal Center Clonal Bursts." Cells 9, no. 6 (June 10, 2020): 1448. http://dx.doi.org/10.3390/cells9061448.

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Germinal centers (GCs) are specialized compartments within the secondary lymphoid organs where B cells proliferate, differentiate, and mutate their antibody genes in response to the presence of foreign antigens. Through the GC lifespan, interclonal competition between B cells leads to increased affinity of the B cell receptors for antigens accompanied by a loss of clonal diversity, although the mechanisms underlying clonal dynamics are not completely understood. We present here a multi-scale quantitative model of the GC reaction that integrates an intracellular component, accounting for the genetic events that shape B cell differentiation, and an extracellular stochastic component, which accounts for the random cellular interactions within the GC. In addition, B cell receptors are represented as sequences of nucleotides that mature and diversify through somatic hypermutations. We exploit extensive experimental characterizations of the GC dynamics to parameterize our model, and visualize affinity maturation by means of evolutionary phylogenetic trees. Our explicit modeling of B cell maturation enables us to characterise the evolutionary processes and competition at the heart of the GC dynamics, and explains the emergence of clonal dominance as a result of initially small stochastic advantages in the affinity to antigen. Interestingly, a subset of the GC undergoes massive expansion of higher-affinity B cell variants (clonal bursts), leading to a loss of clonal diversity at a significantly faster rate than in GCs that do not exhibit clonal dominance. Our work contributes towards an in silico vaccine design, and has implications for the better understanding of the mechanisms underlying autoimmune disease and GC-derived lymphomas.

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Richmond, M., A. Kolios, V. S. Pillai, T. Nishino, and L. Wang. "Development of a stochastic computational fluid dynamics approach for offshore wind farms." Journal of Physics: Conference Series 1037 (June 2018): 072034. http://dx.doi.org/10.1088/1742-6596/1037/7/072034.

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