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Relevant bibliographies by topics / Stochastic processes Mathematical models

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Academic literature on the topic 'Stochastic processes Mathematical models'

Author: Grafiati

Published: 4 June 2021

Last updated: 29 January 2023

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Journal articles on the topic "Stochastic processes Mathematical models"

1

Veretennikov, Alexander. "Stochastic Processes and Models." Bulletin of the London Mathematical Society 39, no. 1 (January 16, 2007): 167–69. http://dx.doi.org/10.1112/blms/bdl020.

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Jaeger, Herbert. "Observable Operator Models for Discrete Stochastic Time Series." Neural Computation 12, no. 6 (June 1, 2000): 1371–98. http://dx.doi.org/10.1162/089976600300015411.

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A widely used class of models for stochastic systems is hidden Markov models. Systems that can be modeled by hidden Markov models are a proper subclass of linearly dependent processes, a class of stochastic systems known from mathematical investigations carried out over the past four decades. This article provides a novel, simple characterization of linearly dependent processes, called observable operator models. The mathematical properties of observable operator models lead to a constructive learning algorithm for the identification of linearly dependent processes. The core of the algorithm has a time complexity of O (N + nm3), where N is the size of training data, n is the number of distinguishable outcomes of observations, and m is model state-space dimension.

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Nikolova, Iveta. "On stochastic models in biology and medicine." Asian-European Journal of Mathematics 13, no. 08 (May 21, 2020): 2050168. http://dx.doi.org/10.1142/s1793557120501685.

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Stochastic models along with deterministic models are successfully used for mathematical description of biological processes. They apply knowledge from probability theory and mathematical statistics to analyze specific characteristics of living systems. The paper is devoted to some stochastic models of various phenomena in biology and medicine. Basic concepts and definitions used in classical probability models are considered and illustrated by several examples with solutions. The stochastic kinetic modeling approach is described. A new kinetic model of autoimmune disease is presented. It is a system of nonlinear partial integro-differential equations supplemented by corresponding initial conditions. The modeling problem is solved computationally.

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Butov, Alexander A., Maxim A. Volkov, Viktor N. Golovanov, Anatoly A. Kovalenko, Boris M. Kostishko, and Leonid M. Samoilov. "Mathematical Modeling of Main Classes of Stochastic Productive Systems." Engineering Technologies and Systems 29, no. 4 (December 31, 2019): 496–509. http://dx.doi.org/10.15507/2658-4123.029.201904.496-509.

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Introduction. The article deals with mathematical models of two main classes of processes in stochastic productive systems. For a multistage system, conditions of belonging to a “just-in-time” class or a class with infinite support of the time distribution function for productive operations are determined. Materials and Methods. Descriptions and investigations of models are carried out by trajectory (martingale) methods. For “just-in-time” systems and multistage stochastic productive systems, terms and methods of random walks in a random environment and birth and death processes are used. The results are formulated as descriptions of intensity characteristics of equalizers of point counting processes. Results. Two theorems are given and proved; they justify the proposed classification of the mathematical models of productive systems. The criteria of the belonging of the stochastic productive system to the class “just-in-time” are given. A theorem on the incompatibility of groups of “just-in-time” systems and systems infinite support of the time distribution for operations is proved. Discussion and Conclusion. The results show the feasibility of analyzing stochastic productive systems by martingale methods. The descriptions of terms of intensities of the equalizers time of productive processes admit generalization.

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Larina, Ludmila, Dmitryi Ruslyakov, Olga Tikhonova, and Boris Kalmykov. "Research of processes of the heatmass transfer in the porous environments having stochastic characteristics on the basis of methods of applied synergetic." E3S Web of Conferences 273 (2021): 01023. http://dx.doi.org/10.1051/e3sconf/202127301023.

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On the basis of a synergetic approach, mathematical models of the stochastic similarity of the functioning of heat and mass transfer processes in porous media (grain materials) have been developed. In these models, the indicators of the stochastic characteristics of these media are combined with the parameters of the processes of hygrothermal treatment under vacuum conditions: residual pressure - P, temperature - T, time-τ, with a density of couple - ρ. The resulting models can be used to control hygrothermal processes in the processing of natural tanning and grain materials that have a stochastic character of the building. A method for the formation of mathematical models of stochastic similarity has been developed, including functional dependences of indicators of stochastic characteristics of materials subjected to hygrothermal treatment on parameters characterizing its state: input, setting, disturbing influences and internal (structural) system.

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Rota, Gian-Carlo. "Stochastic models for social processes." Advances in Mathematics 57, no. 1 (July 1985): 91. http://dx.doi.org/10.1016/0001-8708(85)90110-0.

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Belopolskaya, Ya I. "Stochastic Models of Chemotaxis Processes." Journal of Mathematical Sciences 251, no. 1 (October 12, 2020): 1–14. http://dx.doi.org/10.1007/s10958-020-05059-7.

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Holubec, Viktor, Artem Ryabov, Sarah A. M. Loos, and Klaus Kroy. "Equilibrium stochastic delay processes." New Journal of Physics 24, no. 2 (February 1, 2022): 023021. http://dx.doi.org/10.1088/1367-2630/ac4b91.

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Abstract Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is available for linear models only. We introduce a class of stochastic delay processes with nonlinear time-local forces and linear time-delayed forces that obey fluctuation theorems and converge to a Boltzmann equilibrium at long times. From the point of view of control theory, such ‘equilibrium stochastic delay processes’ are stable and energetically passive, by construction. Computationally, they provide diverse exact constraints on general nonlinear stochastic delay problems and can, in various situations, serve as a starting point for their perturbative analysis. Physically, they admit an interpretation in terms of an underdamped Brownian particle that is either subjected to a time-local force in a non-Markovian thermal bath or to a delayed feedback force in a Markovian thermal bath. We illustrate these properties numerically for a setup familiar from feedback cooling and point out experimental implications.

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Anh, V. V., C. C. Heyde, and Q. Tieng. "Stochastic models for fractal processes." Journal of Statistical Planning and Inference 80, no. 1-2 (August 1999): 123–35. http://dx.doi.org/10.1016/s0378-3758(98)00246-8.

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Butusov, O. B., O. P. Nikiforova, and N. I. Redikultseva. "Mathematical methods for the analysis of migration processes on the basis of demographic data." Izvestiya MGTU MAMI 9, no. 1-4 (July 10, 2015): 21–25. http://dx.doi.org/10.17816/2074-0530-67102.

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The problem of mathematical analysis of demographic data was investigated for data, where information on migration flows is taken into account implicitly. Regression techniques, neural networks and stochastic analysis were used for the mathematical analysis of demographic processes. Two age groups were considered: young (0 - 39 years) and elderly (40 - 70 years). While development of stochastic models the theory of Markov chains and transition matrix were used. The parameterization and model identification were conducted according to Rosstat data.

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Dissertations / Theses on the topic "Stochastic processes Mathematical models"

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Cole, D. J. "Stochastic branching processes in biology." Thesis, University of Kent, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270684.

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Le, Truc. "Stochastic volatility models." Monash University, School of Mathematical Sciences, 2005. http://arrow.monash.edu.au/hdl/1959.1/5181.

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Shepherd, Tricia D. "Models for chemical processes : activated dynamics across stochastic potentials." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/27062.

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Gagliardini, Lucia. "Chargaff symmetric stochastic processes." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/8699/.

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Scopo della modellizzazione delle stringhe di DNA è la formulazione di modelli matematici che generano sequenze di basi azotate compatibili con il genoma esistente. In questa tesi si prendono in esame quei modelli matematici che conservano un'importante proprietà, scoperta nel 1952 dal biochimico Erwin Chargaff, chiamata oggi "seconda regola di Chargaff". I modelli matematici che tengono conto delle simmetrie di Chargaff si dividono principalmente in due filoni: uno la ritiene un risultato dell'evoluzione sul genoma, mentre l'altro la ipotizza peculiare di un genoma primitivo e non intaccata dalle modifiche apportate dall'evoluzione. Questa tesi si propone di analizzare un modello del secondo tipo. In particolare ci siamo ispirati al modello definito da da Sobottka e Hart. Dopo un'analisi critica e lo studio del lavoro degli autori, abbiamo esteso il modello ad un più ampio insieme di casi. Abbiamo utilizzato processi stocastici come Bernoulli-scheme e catene di Markov per costruire una possibile generalizzazione della struttura proposta nell'articolo, analizzando le condizioni che implicano la validità della regola di Chargaff. I modelli esaminati sono costituiti da semplici processi stazionari o concatenazioni di processi stazionari. Nel primo capitolo vengono introdotte alcune nozioni di biologia. Nel secondo si fa una descrizione critica e prospettica del modello proposto da Sobottka e Hart, introducendo le definizioni formali per il caso generale presentato nel terzo capitolo, dove si sviluppa l'apparato teorico del modello generale.

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Leung, Ho-yin, and 梁浩賢. "Stochastic models for optimal control problems with applications." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B42841781.

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Zhang, Dongxiao. "Conditional stochastic analysis of solute transport in heterogeneous geologic media." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186553.

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This dissertation develops an analytical-numerical approach to deterministically predict the space-time evolution of concentrations in heterogeneous geologic media conditioned on measurements of hydraulic conductivities (transmissivities) and/or hydraulic heads. Based on the new conditional Eulerian-Lagrangian transport theory by Neuman, we solve the conditional transport problem analytically at early time, and express it in pseudo-Fickian form at late time. The stochastically derived deterministic pseudo-Fickian mean concentration equation involves a conditional, space-time dependent dispersion tensor. The latter not only depends on properties of the medium and the velocity but also on the available information, and can be evaluated numerically along mean "particle" trajectories. The transport equation lends itself to accurate solution by standard Galerkin finite elements on a relatively coarse grid. This approach allows computing without using Monte Carlo simulation and explicitly the following: Concentration variance/covariance (uncertainty), origin of detected contaminant and associated uncertainty, mass flow rate across a "compliance surface", cumulative mass release and travel time probability distribution across this surface, uncertainty associated with the latter, second spatial moment of conditional mean plume about its center of mass, conditional mean second spatial moment of actual plume about its center of mass, conditional co-variance of plume center of mass, and effect of non-Gaussian velocity distribution. This approach can also account for uncertainty in initial mass and/or concentration when predicting the future evolution of a plume, whereas almost all existing stochastic models of solute transport assume the initial state to be known with certainty. We illustrate this approach by considering deterministic and uncertain instantaneous point and nonpoint sources in a two-dimensional domain with a mildly fluctuating, statistically homogeneous, lognormal transmissivity field. We take the unconditional mean velocity to be uniform, but allow conditioning on log transmissivity and hydraulic head data. Conditioning renders the velocity field statistically nonhomogeneous with reduced variances and correlation scales, renders the predicted plume irregular and non-Gaussian, and generally reduces both predictive dispersion and uncertainty.

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Thompson, Mery H. "Optimum experimental designs for models with a skewed error distribution with an application to stochastic frontier models /." Connect to e-thesis, 2008. http://theses.gla.ac.uk/236/.

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Thesis (Ph.D.) - University of Glasgow, 2008.
Ph.D. thesis submitted to the Faculty of Information and Mathematical Sciences, Department of Statistics, 2008. Includes bibliographical references. Print version also available.

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Uyar, Emrah. "Routing in stochastic environments." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26554.

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Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009.
Committee Co-Chair: Erera, Alan L.; Committee Co-Chair: Savelsbergh, Martin W. P.; Committee Member: Ergun, Ozlem; Committee Member: Ferguson, Mark; Committee Member: Kleywegt, Anton J.. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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Gong, Bo. "Numerical methods for backward stochastic differential equations with applications to stochastic optimal control." HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/462.

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The concept of backward stochastic differential equation (BSDE) was initially brought up by Bismut when studying the stochastic optimal control problem. And it has been applied to describe various problems particularly to those in finance. After the fundamental work by Pardoux and Peng who proved the well-posedness of the nonlinear BSDE, the BSDE has been investigated intensively for both theoretical and practical purposes. In this thesis, we are concerned with a class of numerical methods for solving BSDEs, especially the one proposed by Zhao et al.. For this method, the convergence theory of the semi-discrete scheme (the scheme that discretizes the equation only in time) was already established, we shall further provide the analysis for the fully discrete scheme (the scheme that discretizes in both time and space). Moreover, using the BSDE as the adjoint equation, we shall construct the numerical method for solving the stochastic optimal control problem. We will discuss the situation when the control is deterministic as well as when the control is feedback.

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Hashad, Atalla I. "Analysis of non-Gaussian processes using the Wiener model of discrete nonlinear systems." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1994. http://handle.dtic.mil/100.2/ADA297343.

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Dissertation (Ph. D. in Electrical Engineering) Naval Postgraduate School, December 1994.
"December 1994." Dissertation supervisor(s): Charles W. Therrien. Includes bibliographical references. Also available online.

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Books on the topic "Stochastic processes Mathematical models"

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Koroliuk, Vladimir S. Stochastic models of systems. Dordrecht: Kluwer Academic Publishers, 1999.

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Introduction to stochastic models. 2nd ed. Mineola, NY: Dover Publications, 2006.

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Introduction to stochastic models. Menlo Park, Calif: Benjamin/Cummings Pub. Co., 1988.

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Janssen, Jacques. Mathematical fianance: Deterministic and stochastic models. Hoboken, N.J: ISTE/John Wiley, 2008.

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1931-, Jensen Uwe, ed. Stochastic models in reliability. New York: Springer, 1999.

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Koroli͡uk, V. S. Stochastic models of systems. Dordrecht: Kluwer Academic Publishers, 1999.

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Tomasz, Rolski, ed. Stochastic processes for insurance and finance. Chicester: J. Wiley, 1999.

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Janssen, Jacques. Mathematical fianance: Deterministic and stochastic models. Hoboken, N.J: ISTE/John Wiley, 2008.

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N, Limnios, and Oprișan Gheorghe, eds. Introduction to stochastic models. London: ISTE, 2010.

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A, Molchanov S., and Woyczyński W. A. 1943-, eds. Stochastic models in geosystems. New York: Springer, 1997.

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Book chapters on the topic "Stochastic processes Mathematical models"

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Bender, Christian, Tommi Sottinen, and Esko Valkeila. "Fractional Processes as Models in Stochastic Finance." In Advanced Mathematical Methods for Finance, 75–103. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-18412-3_3.

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Silvestrov, Dmitrii S. "Nonlinearly Perturbed Stochastic Processes and Systems." In Mathematical and Statistical Models and Methods in Reliability, 19–37. Boston, MA: Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4971-5_2.

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Chen, Taolue, Klaus Dräger, and Stefan Kiefer. "Model Checking Stochastic Branching Processes." In Mathematical Foundations of Computer Science 2012, 271–82. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-32589-2_26.

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Xue, Chuan, and Gregory Jameson. "Recent Mathematical Models of Axonal Transport." In Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology, 265–85. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-62627-7_12.

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Grindel, Ria, Wieger Hinderks, and Andreas Wagner. "Application of Continuous Stochastic Processes in Energy Market Models." In Mathematical Modeling, Simulation and Optimization for Power Engineering and Management, 25–50. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-62732-4_2.

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Ogorodnikov, Vasily, Nina Kargapolova, and Olga Sereseva. "Numerical Stochastic Models of Meteorological Processes and Fields." In Springer Proceedings in Mathematics & Statistics, 409–17. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-2104-1_40.

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Swishchuk, Anatoly. "Stochastic Stability and Optimal Control of Semi-Markov Risk Processes in Insurance Mathematics." In Semi-Markov Models and Applications, 313–23. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4613-3288-6_19.

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Balakrishnan, V. "Stochastic Processes." In Mathematical Physics, 461–93. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-39680-0_21.

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Palacios, Antonio. "Stochastic Models." In Mathematical Engineering, 431–85. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-04729-9_9.

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Serovajsky, Simon. "Stochastic models." In Mathematical Modelling, 339–60. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003035602-18.

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Conference papers on the topic "Stochastic processes Mathematical models"

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Granita and Arifah Bahar. "Stochastic differential equation model to Prendiville processes." In THE 22ND NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM22): Strengthening Research and Collaboration of Mathematical Sciences in Malaysia. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4932498.

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Maslovskaya, A. G., S. K. Sarukhanian, and Ch Kuttler. "A Stochastic Algorithm for Reaction-Diffusion Model of Communication Processes in Evolving Bacteria." In Mathematical Biology and Bioinformatics. Pushchino: IMPB RAS - Branch of KIAM RAS, 2022. http://dx.doi.org/10.17537/icmbb22.49.

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Musabekova, Leila. "Mathematical model of diffusion-limited aggregation based on a three-dimensional stochastic lattice." In INTERNATIONAL SCIENTIFIC-TECHNICAL SYMPOSIUM (ISTS) «IMPROVING ENERGY AND RESOURCE-EFFICIENT AND ENVIRONMENTAL SAFETY OF PROCESSES AND DEVICES IN CHEMICAL AND RELATED INDUSTRIES». The Kosygin State University of Russia, 2021. http://dx.doi.org/10.37816/eeste-2021-1-145-148.

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This paper is devoted to the problem of developing the newly efficient method for modeling the aggregation processes in polydisperse systems, without limitation of considering only binary collisions. The submitted method is an extension of the method previously developed by the authors for the case of a three-dimensional stochastic lattice. Such an extension increases the practical significance and reliability of the simulation results.

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Ghiocel, Dan M. "Advanced Stochastic Techniques for Jet Engine Component Life Prediction." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-2650.

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Abstract The paper addresses significant aspects of stochastic modeling for jet engine component life prediction. Probabilistic life prediction for gas turbine engine components represents a very difficult engineering problem involving stochastic modeling of multiple, complex random phenomena. A key aspect for developing a probabilistic life prediction tool is to incorporate, and to be open to modeling advances related to dynamic complex random phenomena, including space-time random variabilities of mission environment and material parameters, aero-elastic interactions, friction at contact interfaces, multi-site fatigue, progressive damage mechanism, including loading interactions, etc.. The paper addresses the main aspects involved in stochastic modeling of component fatigue life prediction for jet engine rotating components, specifically fan blades. The paper highlights the need of the use of stochastic process and field models for including space-time varying random aspects. Mission speed profiles produced by pilot’s random maneuvers are modeled by pulse non-Gaussian stochastic processes. These pulse processes are approximated using linear recursive models when the cluster effects are not significant. A more general approach, useful when cluster effects are significant, based on a combination of two pulse processes is used. Aero-pressure distribution on blade as well as blade surface geometry deviations due to manufacturing are idealized by using factorable stochastic field models. Also, stochastic field models are used for modeling strain-life and damage accumulation curves. Stochastic damage accumulation models are based on randomized stress-dependent models (nonlinear damage rule models). The paper also addresses mathematical modeling of stochastic nonlinear responses in multidimensional parameter spaces. Stochastic response surface techniques based on factorable stochastic fields or optimum stochastic models are suggested. An illustrative example of a jet engine blade is used for discussion and to show the consequences of different modeling assumptions.

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Nakamura, Masato, Hanwei Zhang, Karsten Millrath, and Nickolas J. Themelis. "Modeling of Waste-to-Energy Combustion With Continuous Variation of the Solid Waste Fuel." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-55342.

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A mathematical model of a mass-burn, waste-to-energy combustion chamber has been developed that includes stochastic representation of the variability of the fuel (municipal solid waste, MSW). The drying, pyrolysis, gasification and combustion processes on the moving grate are governed by several factors such as proximate and ultimate analysis, particle size, moisture, heating value, and bulk density, all of which change continuously. This extreme variability has not been considered in past mathematical models of WTE combustion that used mean values of the MSW properties. The Monte Carlo stochastic method has been applied to provide a time series description of the continuous variation of solid wastes at the feed end of the traveling grate. The combustion of the solid particles on the grate is simulated using percolation theory. The feed variation and the percolation theory models are combined with the FLIC two-dimensional bed model developed by Sheffield University to project the transient phenomena in the bed, such as the break-up of waste particles and the channeling of combustion air throughout the bed, and their effects on the combustion process.

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Baghdasaryan, Lusine, Wei Chen, Thaweepat Buranathiti, and Jian Cao. "Model Validation via Uncertainty Propagation Using Response Surface Models." In ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/detc2002/dac-34140.

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Model validation has become a primary means to evaluate accuracy and reliability of computational simulations in engineering design. Mathematical models enable engineers to establish what the most likely response of a system is. However, despite the enormous power of computational models, uncertainty is inevitable in all model-based engineering design problems, due to the variation in the physical system itself, or lack of knowledge, and the use of assumptions by model builders. Therefore, realistic mathematical models should contemplate uncertainties. Due to the uncertainties, the assessment of the validity of a modeling approach must be conducted based on stochastic measurements to provide designers with the confidence of using a model. In this paper, a generic model validation methodology via uncertainty propagation is presented. The approach reduces the number of physical testing at each design setting to one by shifting the evaluation effort to uncertainty propagation of the computational model. Response surface methodology is used to create metamodels as less costly approximations of simulation models for uncertainty propagation. The methodology is illustrated with the examination of the validity of a finite-element analysis model for predicting springback angles in a sample flanging process.

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Hu, Zhen, Sankaran Mahadevan, and Xiaoping Du. "Uncertainty Quantification in Time-Dependent Reliability Analysis." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47925.

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One of the essential steps in time-dependent reliability analysis is the characterization of stochastic load processes and system random variables based on experimental or historical data. Limited data results in uncertainty in the modeling of random variables and stochastic loadings. The uncertainty in random variable and stochastic load models later causes uncertainty in the results of reliability analysis. An uncertainty quantification framework is developed in this paper for time-dependent reliability analysis. The effects of two kinds of uncertainty sources, namely data uncertainty and model uncertainty on the results of time-dependent reliability analysis are investigated. The Bayesian approach is employed to model the epistemic uncertainty sources in random variables and stochastic processes. A straightforward formulation of uncertainty quantification in time-dependent reliability analysis results in a double-loop implementation, which is computationally expensive. Therefore, this paper builds a surrogate model for the conditional reliability index in terms of variables with imprecise parameters. Since the conditional reliability index is independent of the epistemic uncertainty, the surrogate model is applicable for any realizations of the epistemic uncertainty. Based on the surrogate model, the uncertainty in time-dependent reliability analysis is quantified without evaluating the original limit-state function, which increases the efficiency of uncertainty quantification. The effectiveness of the proposed method is demonstrated using a mathematical example and an engineering application example.

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Sambaturu, Prathyush, Marco Minutoli, Mahantesh Halappanavar, Ananth Kalyanaraman, and Anil Vullikanti. "Scalable and Memory-Efficient Algorithms for Controlling Networked Epidemic Processes Using Multiplicative Weights Update Method." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/717.

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We study the problem of designing scalable algorithms to find effective intervention strategies for controlling stochastic epidemic processes on networks. This is a common problem arising in agent based models for epidemic spread. Previous approaches to this problem focus on either heuristics with no guarantees or approximation algorithms that scale only to networks corresponding to county-sized populations, typically, with less than a million nodes. In particular, the mathematical-programming based approaches need to solve the Linear Program (LP) relaxation of the problem using an LP solver, which restricts the scalability of this approach. In this work, we overcome this restriction by designing an algorithm that adapts the multiplicative weights update (MWU) framework, along with the sample average approximation (SAA) technique, to approximately solve the linear program (LP) relaxation for the problem. To scale this approach further, we provide a memory-efficient algorithm that enables scaling to large networks, corresponding to country-size populations, with over 300 million nodes and 30 billion edges. Furthermore, we show that this approach provides near-optimal solutions to the LP in practice.

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Dion, Jean-Luc, Fatma Abid, Gaël Chevallier, Hugo Festjens, Nicolas Peyret, Franck Renaud, Moustafa Seifeddine, and Cyrille Stephan. "Compact Model Synthesis for Partially Observed Operational Systems." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12111.

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This work proposes a Compact Model Synthesis (CMS) for Partially Observed Operational Systems (POOS) without using the complete knowledge of models. Series of “grey boxes” fed with partial observations are built in order to synthesize target variables with compact models. The recursive process for real time computation is based on Kalman Filters (KF). This stochastic approach allows to converge in line toward deterministic models with estimated uncertainties and without intrusion on the complete model process. Mathematical context is described first and illustrated secondly with two examples.

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Wang, Zequn, Yan Fu, Ren-Jye Yang, Saeed Barbat, and Wei Chen. "Model Validation of Dynamic Engineering Models Under Uncertainty." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59437.

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Validating dynamic engineering models is critically important in practical applications by assessing the agreement between simulation results and experimental observations. Though significant progresses have been made, the existing metrics lack the capability of managing uncertainty in both simulations and experiments, which may stem from computer model instability, imperfection in material fabrication and manufacturing process, and variations in experimental conditions. In addition, it is challenging to validate a dynamic model aggregately over both the time domain and a model input space with data at multiple validation sites. To overcome these difficulties, this paper presents an area-based metric to systemically handle uncertainty and validate computational models for dynamic systems over an input space by simultaneously integrating the information from multiple validation sites. To manage the complexity associated with a high-dimensional data space, Eigen analysis is performed for the time series data from simulations at each validation site to extract the important features. A truncated Karhunen-Loève (KL) expansion is then constructed to represent the responses of dynamic systems, resulting in a set of uncorrelated random coefficients with unit variance. With the development of a hierarchical data fusion strategy, probability integral transform is then employed to pool all the resulting random coefficients from multiple validation sites across the input space into a single aggregated metric. The dynamic model is thus validated by calculating the cumulative area difference of the cumulative density functions. The proposed model validation metric for dynamic systems is illustrated with a mathematical example, a supported beam problem with stochastic loads, and real data from the vehicle occupant restraint system.

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Reports on the topic "Stochastic processes Mathematical models"

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Perdigão, Rui A. P. Earth System Dynamic Intelligence - ESDI. Meteoceanics, April 2021. http://dx.doi.org/10.46337/esdi.210414.

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Earth System Dynamic Intelligence (ESDI) entails developing and making innovative use of emerging concepts and pathways in mathematical geophysics, Earth System Dynamics, and information technologies to sense, monitor, harness, analyze, model and fundamentally unveil dynamic understanding across the natural, social and technical geosciences, including the associated manifold multiscale multidomain processes, interactions and complexity, along with the associated predictability and uncertainty dynamics. The ESDI Flagship initiative ignites the development, discussion and cross-fertilization of novel theoretical insights, methodological developments and geophysical applications across interdisciplinary mathematical, geophysical and information technological approaches towards a cross-cutting, mathematically sound, physically consistent, socially conscious and operationally effective Earth System Dynamic Intelligence. Going beyond the well established stochastic-dynamic, information-theoretic, artificial intelligence, mechanistic and hybrid techniques, ESDI paves the way to exploratory and disruptive developments along emerging information physical intelligence pathways, and bridges fundamental and operational complex problem solving across frontier natural, social and technical geosciences. Overall, the ESDI Flagship breeds a nascent field and community where methodological ingenuity and natural process understanding come together to shed light onto fundamental theoretical aspects to build innovative methodologies, products and services to tackle real-world challenges facing our planet.

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Siebke, Christian, Maximilian Bäumler, Madlen Ringhand, Marcus Mai, Felix Elrod, and Günther Prokop. Report on integration of the stochastic traffic simulation. Technische Universität Dresden, 2021. http://dx.doi.org/10.26128/2021.246.

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As part of the AutoDrive project, the OpenPASS framework is used to develop a cognitive-stochastic traffic flow simulation for urban intersection scenarios described in deliverable D1.14. This framework was adapted and further developed. The deliverable D5.13 deals with the construction of the stochastic traffic simulation. At this point of the process, the theoretical design aspects of D4.20 are implemented. D5.13 explains the operating principles of the different modules. This includes the foundations, boundary conditions, and mathematical theory of the traffic simulation.

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Chen, Xiaojun, Hailin Sun, and Roger J. Wets. Regularized Mathematical Programs with Stochastic Equilibrium Constraints: Estimating Structural Demand Models. Fort Belvoir, VA: Defense Technical Information Center, July 2013. http://dx.doi.org/10.21236/ada609521.

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Ng, B. Survey of Bayesian Models for Modelling of Stochastic Temporal Processes. Office of Scientific and Technical Information (OSTI), October 2006. http://dx.doi.org/10.2172/900168.

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Yanev, Nikolay M., Vessela Stoimenova, and Dimitar V. Atanasov. Branching Stochastic Processes with Immigration as Models of Covid-19 Pandemic Development. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, November 2020. http://dx.doi.org/10.7546/crabs.2020.11.02.

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Myrskylä, Mikko, and Joshua R. Goldstein. Probabilistic forecasting using stochastic diffusion models, with applications to cohort processes of marriage and fertility. Rostock: Max Planck Institute for Demographic Research, February 2010. http://dx.doi.org/10.4054/mpidr-wp-2010-013.

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Lovianova, Iryna V., Dmytro Ye Bobyliev, and Aleksandr D. Uchitel. Cloud calculations within the optional course Optimization Problems for 10th-11th graders. [б. в.], September 2019. http://dx.doi.org/10.31812/123456789/3267.

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The article deals with the problem of introducing cloud calculations into 10th-11th graders’ training to solve optimization problems in the context of the STEM-education concept. After analyzing existing programmes of optional courses on optimization problems, the programme of the optional course Optimization Problems has been developed and substantiated implying solution of problems by the cloud environment CoCalc. It is a routine calculating operation and not a mathematical model that is accentuated in the programme. It allows considering more problems which are close to reality without adapting the material while training 10th-11th graders. Besides, the mathematical apparatus of the course which is partially known to students as the knowledge acquired from such mathematics sections as the theory of probability, mathematical statistics, mathematical analysis and linear algebra is enough to master the suggested course. The developed course deals with a whole class of problems of conventional optimization which vary greatly. They can be associated with designing devices and technological processes, distributing limited resources and planning business functioning as well as with everyday problems of people. Devices, processes and situations to which a model of optimization problem is applied are called optimization problems. Optimization methods enable optimal solutions for mathematical models. The developed course is noted for building mathematical models and defining a method to be applied to finding an efficient solution.

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Соловйов, Володимир Миколайович, and D. N. Chabanenko. Financial crisis phenomena: analysis, simulation and prediction. Econophysic’s approach. Гумбольдт-Клуб Україна, November 2009. http://dx.doi.org/10.31812/0564/1138.

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With the beginning of the global financial crisis, which attracts the attention of the international community, the inability of existing methods to predict the events became obvious. Creation, testing, adaptation of the models to the concrete financial market segments for the purpose of monitoring, early prediction, prevention and notification of financial crises is gaining currency nowadays. Econophysics is an interdisciplinary research field, applying theories and methods originally developed by physicists in order to solve problems in economics, usually those including uncertainty or stochastic processes and nonlinear dynamics. Its application to the study of financial markets has also been termed statistical finance referring to its roots in statistical physics. The new paradigm of relativistic quantum econophysics is proposed.

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Lieth, J. Heiner, Michael Raviv, and David W. Burger. Effects of root zone temperature, oxygen concentration, and moisture content on actual vs. potential growth of greenhouse crops. United States Department of Agriculture, January 2006. http://dx.doi.org/10.32747/2006.7586547.bard.

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Soilless crop production in protected cultivation requires optimization of many environmental and plant variables. Variables of the root zone (rhizosphere) have always been difficult to characterize but have been studied extensively. In soilless production the opportunity exists to optimize these variables in relation to crop production. The project objectives were to model the relationship between biomass production and the rhizosphere variables: temperature, dissolved oxygen concentration and water availability by characterizing potential growth and how this translates to actual growth. As part of this we sought to improve of our understanding of root growth and rhizosphere processes by generating data on the effect of rhizosphere water status, temperature and dissolved oxygen on root growth, modeling potential and actual growth and by developing and calibrating models for various physical and chemical properties in soilless production systems. In particular we sought to use calorimetry to identify potential growth of the plants in relation to these rhizosphere variables. While we did experimental work on various crops, our main model system for the mathematical modeling work was greenhouse cut-flower rose production in soil-less cultivation. In support of this, our objective was the development of a Rose crop model. Specific to this project we sought to create submodels for the rhizosphere processes, integrate these into the rose crop simulation model which we had begun developing prior to the start of this project. We also sought to verify and validate any such models and where feasible create tools that growers could be used for production management. We made significant progress with regard to the use of microcalorimetry. At both locations (Israel and US) we demonstrated that specific growth rate for root and flower stem biomass production were sensitive to dissolved oxygen. Our work also identified that it is possible to identify optimal potential growth scenarios and that for greenhouse-grown rose the optimal root zone temperature for potential growth is around 17 C (substantially lower than is common in commercial greenhouses) while flower production growth potential was indifferent to a range as wide as 17-26C in the root zone. We had several set-backs that highlighted to us the fact that work needs to be done to identify when microcalorimetric research relates to instantaneous plant responses to the environment and when it relates to plant acclimation. One outcome of this research has been our determination that irrigation technology in soilless production systems needs to explicitly include optimization of oxygen in the root zone. Simply structuring the root zone to be “well aerated” is not the most optimal approach, but rather a minimum level. Our future work will focus on implementing direct control over dissolved oxygen in the root zone of soilless production systems.

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Jury, William A., and David Russo. Characterization of Field-Scale Solute Transport in Spatially Variable Unsaturated Field Soils. United States Department of Agriculture, January 1994. http://dx.doi.org/10.32747/1994.7568772.bard.

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This report describes activity conducted in several lines of research associated with field-scale water and solute processes. A major effort was put forth developing a stochastic continuum analysis for an important class of problems involving flow of reactive and non reactive chemicals under steady unsaturated flow. The field-scale velocity covariance tensor has been derived from local soil properties and their variability, producing a large-scale description of the medium that embodies all of the local variability in a statistical sense. Special cases of anisotropic medium properties not aligned along the flow direction of spatially variable solute sorption were analysed in detail, revealing a dependence of solute spreading on subtle features of the variability of the medium, such as cross-correlations between sorption and conductivity. A novel method was developed and tested for measuring hydraulic conductivity at the scale of observation through the interpretation of a solute transport outflow curve as a stochastic-convective process. This undertaking provided a host of new K(q) relationships for existing solute experiments and also laid the foundation for future work developing a self-consistent description of flow and transport under these conditions. Numerical codes were developed for calculating K(q) functions for a variety of solute pulse outflow shapes, including lognormal, Fickian, Mobile-Immobile water, and bimodal. Testing of this new approach against conventional methodology was mixed, and agreed most closely when the assumptions of the new method were met. We conclude that this procedure offers a valuable alternative to conventional methods of measuring K(q), particularly when the application of the method is at a scale (e.g. and agricultural field) that is large compared to the common scale at which conventional K(q) devices operate. The same problem was approached from a numerical perspective, by studying the feasibility of inverting a solute outflow signal to yield the hydraulic parameters of the medium that housed the experiment. We found that the inverse problem was solvable under certain conditions, depending on the amount of noise in the signal and the degree of heterogeneity in the medium. A realistic three dimensional model of transient water and solute movement in a heterogeneous medium that contains plant roots was developed and tested. The approach taken was to generate a single realization of this complex flow event, and examine the results to see whether features were present that might be overlooked in less sophisticated model efforts. One such feature revealed is transverse dispersion, which is a critically important component in the development of macrodispersion in the longitudinal direction. The lateral mixing that was observed greatly exceeded that predicted from simpler approaches, suggesting that at least part of the important physics of the mixing process is embedded in the complexity of three dimensional flow. Another important finding was the observation that variability can produce a pseudo-kinetic behavior for solute adsorption, even when the local models used are equilibrium.

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