Статті в журналах: "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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Wilks, Daniel S. "Effects of stochastic parametrization on conceptual climate models." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1875 (April 29, 2008): 2475–88. http://dx.doi.org/10.1098/rsta.2008.0005.

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Conceptual climate models are very simple mathematical representations of climate processes, which are especially useful because their workings can be readily understood. The usual procedure of representing effects of unresolved processes in such models using functions of the prognostic variables (parametrizations) that include no randomness generally results in these models exhibiting substantially less variability than do the phenomena they are intended to simulate. A viable yet still simple alternative is to replace the conventional deterministic parametrizations with stochastic parametrizations, which can be justified theoretically through the central limit theorem. The result is that the model equations are stochastic differential equations. In addition to greatly increasing the magnitude of variability exhibited by these models, and their qualitative fidelity to the corresponding real climate system, representation of unresolved influences by random processes can allow these models to exhibit surprisingly rich new behaviours of which their deterministic counterparts are incapable.

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12

Averina, Tatyana A., and Konstantin A. Rybakov. "Using maximum cross section method for filtering jump-diffusion random processes." Russian Journal of Numerical Analysis and Mathematical Modelling 35, no. 2 (April 28, 2020): 55–67. http://dx.doi.org/10.1515/rnam-2020-0005.

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Abstract The paper is focused on problem of filtering random processes in dynamical systems whose mathematical models are described by stochastic differential equations with a Poisson component. The solution of a filtering problem supposes simulation of trajectories of solutions to a stochastic differential equation. The trajectory modelling procedure includes simulation of a Poisson flow permitting application of the maximum cross section method and its modification.

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13

Щелкалін, Віталій Миколайович. "Mathematical models and methods for prediction and control of interrelated nonstationary stochastic processes." Technology audit and production reserves 6, no. 4(8) (December 13, 2012): 29–30. http://dx.doi.org/10.15587/2312-8372.2012.5643.

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14

MELNIK, RODERICK V. N., XILIN WEI, and GABRIEL MORENO–HAGELSIEB. "NONLINEAR DYNAMICS OF CELL CYCLES WITH STOCHASTIC MATHEMATICAL MODELS." Journal of Biological Systems 17, no. 03 (September 2009): 425–60. http://dx.doi.org/10.1142/s0218339009002879.

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Cell cycles are fundamental components of all living organisms and their systematic studies extend our knowledge about the interconnection between regulatory, metabolic, and signaling networks, and therefore open new opportunities for our ultimate efficient control of cellular processes for disease treatments, as well as for a wide variety of biomedical and biotechnological applications. In the study of cell cycles, nonlinear phenomena play a paramount role, in particular in those cases where the cellular dynamics is in the focus of attention. Quantification of this dynamics is a challenging task due to a wide range of parameters that require estimations and the presence of many stochastic effects. Based on the originally deterministic model, in this paper we develop a hierarchy of models that allow us to describe the nonlinear dynamics accounting for special events of cell cycles. First, we develop a model that takes into account fluctuations of relative concentrations of proteins during special events of cell cycles. Such fluctuations are induced by varying rates of relative concentrations of proteins and/or by relative concentrations of proteins themselves. As such fluctuations may be responsible for qualitative changes in the cell, we develop a new model that accounts for the effect of cellular dynamics on the cell cycle. Finally, we analyze numerically nonlinear effects in the cell cycle by constructing phase portraits based on the newly developed model and carry out a parametric sensitivity analysis in order to identify parameters for an efficient cell cycle control. The results of computational experiments demonstrate that the metabolic events in gene regulatory networks can qualitatively influence the dynamics of the cell cycle.

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15

Safarova, Aygun, and Javida Damirova. "Research and modeling of oil refining technological processes operating in the condition of stochastic uncertainty." EUREKA: Physics and Engineering, no. 5 (September 30, 2022): 91–98. http://dx.doi.org/10.21303/2461-4262.2022.002523.

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As it is known, one of the initial and important stages in the creation of optimal control systems of oil refining technological units is the development of a mathematical model that can adequately record the processes at any time. The operative and accurate measurement of all input and output variables is one of the important conditions in the development of a mathematical model of technological processes. Studies have shown that the lack of information about the state of complex oil refining processes in many cases reduces their efficiency and effectiveness. On the other hand, the wide range of both quality and quantity of raw materials for processing makes their efficiency even more unsatisfactory. Under these conditions, it is difficult to develop mathematical models that can adequately describes the static modes of technological processes; the development of mathematical models is relevant both in scientific and practical terms. A priori information required on input and output variables during normal operation of the technological complex in order to implement mathematical models identification for the vacuum block of the oil refining process unit is provided in the article. On the basis of this static information, mathematical dependencies were constructed between the variables characterizing the static mode of technological processes and the adequacy of the obtained mathematical models was confirmed through the statistical apparatus In order to solve the problems, the research was determined to be able adequately describe the current technological conditions, which can quickly adapt to current technological situations and ensure the production of oil fractions with relatively stable quality, regardless of the disturbing effects of the system

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16

Victorov, Alexey S., and Olga N. Trapeznikova. "Stochastic Models Of Dynamic Balance State For The Morphological Patterns Of Cryolithozone Landscapes." GEOGRAPHY, ENVIRONMENT, SUSTAINABILITY 12, no. 3 (October 3, 2019): 6–15. http://dx.doi.org/10.24057/2071-9388-2018-68.

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The paper deals with mathematical modeling of a morphological pattern for a broad spectrum of cryolithozone landscapes in a state of a dynamic balance. The state of the dynamic balance means that all the elements of this morphological pattern are in continuous changing while its general parameters as a whole are stable. Two contradirectional processes at the same territory is a precondition for a state of dynamic balance.We developed a morphological pattern model for lacustrine thermokarst plains with fluvial erosion on the base of the mathematical morphology of landscape using the random process theory. The contra-directional processes here include thermokarst lakes appearing and increasing in size from one side and drainage of the lakes by fluvial erosion, from the other. Thus, the regularities of the structure and dynamics of each landscape morphological pattern are theoretically substantiated. The results of the mathematical modeling were empirically verified at some key sites.

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17

Artikis, Constantinos T., and Panagiotis T. Artikis. "Processes of educational informatics incorporating stochastic models." Journal of Interdisciplinary Mathematics 12, no. 4 (August 2009): 553–64. http://dx.doi.org/10.1080/09720502.2009.10700646.

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18

Batchelder, William H., and John P. Boyd. "Models for behavior: Stochastic processes in psychology." Journal of Mathematical Psychology 29, no. 1 (March 1985): 122–27. http://dx.doi.org/10.1016/0022-2496(85)90022-7.

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19

Diosi, L. "Quantum stochastic processes as models for state vector reduction." Journal of Physics A: Mathematical and General 21, no. 13 (July 7, 1988): 2885–98. http://dx.doi.org/10.1088/0305-4470/21/13/013.

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20

Schall, Jeffrey D., Thomas J. Palmeri, and Gordon D. Logan. "Models of inhibitory control." Philosophical Transactions of the Royal Society B: Biological Sciences 372, no. 1718 (February 27, 2017): 20160193. http://dx.doi.org/10.1098/rstb.2016.0193.

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We survey models of response inhibition having different degrees of mathematical, computational and neurobiological specificity and generality. The independent race model accounts for performance of the stop-signal or countermanding task in terms of a race between GO and STOP processes with stochastic finishing times. This model affords insights into neurophysiological mechanisms that are reviewed by other authors in this volume. The formal link between the abstract GO and STOP processes and instantiating neural processes is articulated through interactive race models consisting of stochastic accumulator GO and STOP units. This class of model provides quantitative accounts of countermanding performance and replicates the dynamics of neural activity producing that performance. The interactive race can be instantiated in a network of biophysically plausible spiking excitatory and inhibitory units. Other models seek to account for interactions between units in frontal cortex, basal ganglia and superior colliculus. The strengths, weaknesses and relationships of the different models will be considered. We will conclude with a brief survey of alternative modelling approaches and a summary of problems to be addressed including accounting for differences across effectors, species, individuals, task conditions and clinical deficits. This article is part of the themed issue ‘Movement suppression: brain mechanisms for stopping and stillness’.

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21

Maccone, Claudio. "Evolution and mass extinctions as lognormal stochastic processes." International Journal of Astrobiology 13, no. 4 (July 21, 2014): 290–309. http://dx.doi.org/10.1017/s147355041400010x.

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AbstractIn a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely calledEvo-SETI. The relevant mathematical tools are:(1)Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3.5 billion years. This GBM is well known in the mathematics of finances (Black–Sholes models). Its main features are that its probability density function (pdf) is a lognormal pdf, and its mean value is either an increasing or, more rarely, decreasing exponential function of the time.(2)The probability distributions known asb-lognormals, i.e. lognormals starting at a certain positive instantb>0 rather than at the origin. Theseb-lognormals were then forced by us to have their peak value located on the exponential mean-value curve of the GBM (Peak-Locus theorem). In the framework of Darwinian Evolution, the resulting mathematical construction was shown to be what evolutionary biologists callCladistics.(3)The (Shannon)entropyof suchb-lognormals is then seen to represent the ‘degree of progress’ reached by each living organism or by each big set of living organisms, like historic human civilizations. Having understood this fact, human history may then be cast into the language ofb-lognormals that are more and more organized in time (i.e. having smaller and smaller entropy, or smaller and smaller ‘chaos’), and have their peaks on the increasing GBM exponential. This exponential is thus the ‘trend of progress’ in human history.(4)All these results also match with SETI in that the statistical Drake equation (generalization of the ordinary Drake equation to encompass statistics) leads just to the lognormal distribution as the probability distribution for the number of extra-terrestrial civilizations existing in the Galaxy (as a consequence of the central limit theorem of statistics).(5)But the most striking new result is that the well-known ‘Molecular Clock of Evolution’, namely the ‘constant rate of Evolution at the molecular level’ as shown by Kimura's Neutral Theory of Molecular Evolution,identifieswith growth rate of the entropy of our Evo-SETI model, because they both grewlinearlyin time since the origin of life.(6)Furthermore, we apply our Evo-SETI model to lognormal stochastic processesother than GBMs.For instance, we provide two models for the mass extinctions that occurred in the past: (a) one based on GBMs and (b) the other based on aparabolicmean value capable of covering both the extinction and the subsequent recovery of life forms.(7)Finally, we show that the Markov & Korotayev (2007, 2008) model for Darwinian Evolution identifies with an Evo-SETI model for which the mean value of the underlying lognormal stochastic process is acubicfunction of the time.In conclusion: we have provided a new mathematical model capable of embracing molecular evolution, SETI and entropy into a simple set of statistical equations based uponb-lognormals and lognormal stochastic processes with arbitrary mean, of which the GBMs are theparticular case of exponential growth.

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22

Duso, Lorenzo, and Christoph Zechner. "Stochastic reaction networks in dynamic compartment populations." Proceedings of the National Academy of Sciences 117, no. 37 (August 31, 2020): 22674–83. http://dx.doi.org/10.1073/pnas.2003734117.

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Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and typically very challenging to analyze computationally. Recent studies have made progress toward addressing this problem in the context of specific biological systems, but a general and sufficiently effective approach remains lacking. In this work, we propose a mathematical framework based on counting processes that allows us to study dynamic compartment populations with arbitrary interactions and internal biochemistry. We derive an efficient description of the dynamics in terms of differential equations which capture the statistics of the population. We demonstrate the relevance of our approach by analyzing models inspired by different biological processes, including subcellular compartmentalization and tissue homeostasis.

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23

CARNAFFAN, SEAN. "ANOMALOUS DIFFUSION PROCESSES: STOCHASTIC MODELS AND THEIR PROPERTIES." Bulletin of the Australian Mathematical Society 101, no. 3 (March 27, 2020): 514–17. http://dx.doi.org/10.1017/s0004972720000258.

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24

LOWEN, STEVEN B., and MALVIN C. TEICH. "ESTIMATION AND SIMULATION OF FRACTAL STOCHASTIC POINT PROCESSES." Fractals 03, no. 01 (March 1995): 183–210. http://dx.doi.org/10.1142/s0218348x95000151.

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We investigate the properties of fractal stochastic point processes (FSPPs). First, we define FSPPs and develop several mathematical formulations for these processes, showing that over a broad range of conditions they converge to a particular form of FSPP. We then provide examples of a wide variety of phenomena for which they serve as suitable models. We proceed to examine the analytical properties of two useful fractal dimension estimators for FSPPs, based on the second-order properties of the points. Finally, we simulate several FSPPs, each with three specified values of the fractal dimension. Analysis and simulation reveal that a variety of factors confound the estimate of the fractal dimension, including the finite length of the simulation, structure or type of FSPP employed, and fluctuations inherent in any FSPP. We conclude that for segments of FSPPs with as many as 106 points, the fractal dimension can be estimated only to within ±0.1.

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25

Pfeiffer, F., and A. Kunert. "Rattling models from deterministic to stochastic processes." Nonlinear Dynamics 1, no. 1 (January 1990): 63–74. http://dx.doi.org/10.1007/bf01857585.

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26

WEIDLICH, WOLFGANG. "SOCIODYNAMICS — A SYSTEMATIC APPROACH TO MATHEMATICAL MODELLING IN THE SOCIAL SCIENCES." Fluctuation and Noise Letters 03, no. 02 (June 2003): L223—L232. http://dx.doi.org/10.1142/s0219477503001294.

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A general concept is presented which allows of setting up mathematical models for stochastic and quasi deterministic dynamic processes in social systems. The basis of this concept is the master equation for the probability distribution over appropriately chosen personal and material macrovariables of the society. The probabilistic transition rates depend on motivation potentials governing the decisions and actions of the social agents. The transition from the probability distribution to quasi-meanvalues leads to in general nonlinear coupled differential equations for the macrovariables of the chosen social sector. Up to now several models about population dynamics, collective political opinion formation, dynamics of economic processes and the formation of settlements have been published.

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27

Brockwell, Peter J. "Stochastic models in cell kinetics." Journal of Applied Probability 25, A (1988): 91–111. http://dx.doi.org/10.2307/3214149.

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We discuss the role of stochastic processes in modelling the life-cycle of a biological cell and the growth of cell populations. Results for multiphase age-dependent branching processes have proved invaluable for the interpretation of many of the basic experimental studies of the life-cycle. Moreover problems from cell kinetics, in particular those related to diurnal rhythm in cell-growth, have stimulated research into ‘periodic' renewal theory, and the asymptotic behaviour of populations of cells with periodic death rate.

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28

COSTANTINI, CRISTINA, and THOMAS G. KURTZ. "DIFFUSION APPROXIMATION FOR TRANSPORT PROCESSES WITH GENERAL REFLECTION BOUNDARY CONDITIONS." Mathematical Models and Methods in Applied Sciences 16, no. 05 (May 2006): 717–62. http://dx.doi.org/10.1142/s0218202506001339.

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Diffusion approximations are obtained for space inhomogeneous linear transport models with reflection boundary conditions. The collision kernel is not required to satisfy any balance condition and the scattering kernel on the boundary is general enough to include all examples of boundary conditions known to the authors (with conservation of the number of particles) and, in addition, to model the Debye sheath. The mathematical approach does not rely on Hilbert expansions, but rather on martingale and stochastic averaging techniques.

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29

Cordoni, Francesco, and Luca Di Persio. "Backward Stochastic Differential Equations Approach to Hedging, Option Pricing, and Insurance Problems." International Journal of Stochastic Analysis 2014 (September 11, 2014): 1–11. http://dx.doi.org/10.1155/2014/152389.

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In the present work we give a self-contained introduction to financial mathematical models characterized by noise of Lévy type in the framework of the backward stochastic differential equations theory. Such techniques will be then used to analyse an innovative model related to insurance and death processes setting.

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30

Lazarova, Meglena Delcheva, Krasimira Prodanova, and Leda Minkova. "Research Project DN 12/11/December 2017-January 2022 financed by the National Science Fund at the Ministry of Education and Science: "Stochastic and Simulation Models in medcine, social sciences and dynamic systems"." Biomath Communications 9, no. 1 (February 16, 2022): 1. http://dx.doi.org/10.11145/bmc.2022.02.161.

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The project " Stochastics and Simulation Models in the Medcine, Social Sciences and Dynamical Systems" is focused on the stochastic models and their applications in the field of medicine, insurance, astrophysics and some simulation models applicable in social sciences and thermotydraulic processes. There are six work packages included in the research. The introduced models had been adapted to real data by three phd students, two post doctoral students and four Bulgarian scientists which are leaders in the field of mathematical modeling. The participants' research results are published in eight scientific papers with impact factor and thirthy six papers with impact rang. The obtained results are approbated in more than twenty prestigious international conferences. As a good result of the participation three PhD scientific degrees and two scientific postions had been acquired.

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31

Lobato, Lucas C., Stephan Paul, Júlio A. Cordioli, and Thiago G. Ritto. "Stochastic model of the human middle ear using a nonparametric probabilistic approach." Journal of the Acoustical Society of America 151, no. 3 (March 2022): 2055–65. http://dx.doi.org/10.1121/10.0009763.

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Several mathematical models of the human middle ear dynamics have been studied since the mid-twentieth century. Despite different methods applied, all of these models are based on deterministic approaches. Experimental data have shown that the middle ear behaves as an uncertain system due to the variability among individuals. In this context, stochastic models are useful because they can represent a population of middle ears with its intrinsic uncertainties. In this work, a nonparametric probabilistic approach is used to model the human middle ear dynamics. The lumped-element method is adopted to develop deterministic baseline models, and three different optimization processes are proposed and applied to the adjustment of the stochastic models. Results show that the stochastic models proposed can reproduce the experimental data in terms of mean and coefficient of variation. In addition, this study shows the importance of properly defining the acceptable range of each input parameter in order to obtain a reliable stochastic model.

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32

Hughes-Oliver, Jacqueline M., and Graciela González-Farı́as. "Parametric covariance models for shock-induced stochastic processes." Journal of Statistical Planning and Inference 77, no. 1 (February 1999): 51–72. http://dx.doi.org/10.1016/s0378-3758(98)00186-4.

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33

Hwan Cha, Ji, and Sophie Mercier. "Transformed Lévy processes as state-dependent wear models." Advances in Applied Probability 51, no. 2 (June 2019): 468–86. http://dx.doi.org/10.1017/apr.2019.21.

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AbstractMany wear processes used for modeling accumulative deterioration in a reliability context are nonhomogeneous Lévy processes and, hence, have independent increments, which may not be suitable in an application context. In this work we consider Lévy processes transformed by monotonous functions to overcome this restriction, and provide a new state-dependent wear model. These transformed Lévy processes are first observed to remain tractable Markov processes. Some distributional properties are derived. We investigate the impact of the current state on the future increment level and on the overall accumulated level from a stochastic monotonicity point of view. We also study positive dependence properties and stochastic monotonicity of increments.

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34

Loomis, Samuel P., and James P. Crutchfield. "Strong and Weak Optimizations in Classical and Quantum Models of Stochastic Processes." Journal of Statistical Physics 176, no. 6 (June 26, 2019): 1317–42. http://dx.doi.org/10.1007/s10955-019-02344-x.

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35

Lee, Mei-Ling Ting, and G. Alex Whitmore. "Stochastic processes directed by randomized time." Journal of Applied Probability 30, no. 2 (June 1993): 302–14. http://dx.doi.org/10.2307/3214840.

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The paper investigates stochastic processes directed by a randomized time process. A new family of directing processes called Hougaard processes is introduced. Monotonicity properties preserved under subordination, and dependence among processes directed by a common randomized time are studied. Results for processes subordinated to Poisson and stable processes are presented. Potential applications to shock models and threshold models are also discussed. Only Markov processes are considered.

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36

Velichkin, Vladimir, Vladimir Zavyalov, Elena Solodovnikova, and Elena Filippova. "Mathematical descriptions of heat-mass-exchange processes in construction industry at control automation." E3S Web of Conferences 97 (2019): 06021. http://dx.doi.org/10.1051/e3sconf/20199706021.

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The paper covers matters arising in building mathematical model of processes at thermal treatment of construction materials. On the basis of analysis of heat energy and moisture flows in intermittent steam chamber and continuous tunnel drying chamber, analytic and structure models of heat-mass-exchange processes in processing vessels are drawn. The structural model of heat-mass-exchange processes allowed to evaluate the relationship of heat energy and moisture flows at heat treatment processes for gypsum and reinforced-concrete articles. The resulting system of interrelated differential equations is based on a structural model. Analytical studies showed that the considering heat treatment units are characterized by non-stationary, non-linear, stochastic and distributed technological parameters. An experimental study of technological devices has shown that in a limited time range, the processes of heat-mass-exchange can be characterized by a system of linear differential equations with constant coefficients with sufficient accuracy for practice. Acceptable allowances and simplifying assumptions at analytical description of heat-mass-exchange processes in processing vessels are considered. As a result of performed research, various mathematical forms (differential equation system, matrix and operator forms) of mathematical models of processing vessels are obtained. The built mathematical models may be applied for constructing the processing vessels with preset dynamic properties, as well for control-system designing by those vessels.

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37

Etchegaray, Christèle, and Nicolas Meunier. "A Stochastic Model For Protrusion Activity." ESAIM: Proceedings and Surveys 62 (2018): 56–67. http://dx.doi.org/10.1051/proc/201862056.

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In this work we approach cell migration under a large-scale assumption, so that the system reduces to a particle in motion. Unlike classical particle models, the cell displacement results from its internal activity: the cell velocity is a function of the (discrete) protrusive forces exerted by filopodia on the substrate. Cell polarisation ability is modeled in the feedback that the cell motion exerts on the protrusion rates: faster cells form preferentially protrusions in the direction of motion. By using the mathematical framework of structured population processes previously developed to study population dynamics [4], we introduce rigorously the mathematical model and we derive some of its fundamental properties. We perform numerical simulations on this model showing that different types of trajectories may be obtained: Brownian-like, persistent, or intermittent when the cell switches between both previous regimes. We find back the trajectories usually described in the literature for cell migration.

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38

Otunuga, Olusegun M., and Gangaram Ladde. "Two-Scale Network Dynamic Model for Energy Commodity Processes." Journal of Energy 2020 (April 20, 2020): 1–59. http://dx.doi.org/10.1155/2020/2075258.

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In this work, we examine the relationship between different energy commodity spot prices. To do this, multivariate stochastic models with and without external random interventions describing the price of energy commodities are developed. Random intervention process is described by a continuous jump process. The developed mathematical model is utilized to examine the relationship between energy commodity prices. The time-varying parameters in the stochastic model are estimated using the recently developed parameter identification technique called local lagged adapted generalized method of moment (LLGMM). The LLGMM method provides an iterative scheme for updating statistic coefficients in a system of generalized method of moment/observation equations. The usefulness of the LLGMM approach is illustrated by applying to energy commodity data sets for state and parameter estimation problems. Moreover, the forecasting and confidence interval problems are also investigated (U.S. Patent Pending for the LLGMM method described in this manuscript).

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39

Chigarev, Anatoliy V., Michael A. Zhuravkov, and Vitaliy A. Chigarev. "Deterministic and stochastic models of infection spread and testing in an isolated contingent." Journal of the Belarusian State University. Mathematics and Informatics, no. 3 (November 19, 2021): 57–67. http://dx.doi.org/10.33581/2520-6508-2021-3-57-67.

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The mathematical SIR model generalisation for description of the infectious process dynamics development by adding a testing model is considered. The proposed procedure requires the expansion of states’ space dimension due to variables that cannot be measured directly, but allow you to more adequately describe the processes that occur in real situations. Further generalisation of the SIR model is considered by taking into account randomness in state estimates, forecasting, which is achieved by applying the stochastic differential equations methods associated with the application of the Fokker – Planck – Kolmogorov equations for posterior probabilities. As COVID-19 practice has shown, the widespread use of modern means of identification, diagnosis and monitoring does not guarantee the receipt of adequate information about the individual’s condition in the population. When modelling real epidemic processes in the initial stages, it is advisable to use heuristic modelling methods, and then refine the model using mathematical modelling methods using stochastic, uncertain-fuzzy methods that allow you to take into account the fact that flow, decision-making and control occurs in systems with incomplete information. To develop more realistic models, spatial kinetics must be taken into account, which, in turn, requires the use of systems models with distributed parameters (for example, models of continua mechanics). Obviously, realistic models of epidemics and their control should include models of economic, sociodynamics. The problems of forecasting epidemics and their development will be no less difficult than the problems of climate change forecasting, weather forecast and earthquake prediction.

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40

Aase, Knut K. "Stochastic control of geometric processes." Journal of Applied Probability 24, no. 1 (March 1987): 97–104. http://dx.doi.org/10.2307/3214062.

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Stochastic optimization of semimartingales which permit a dynamic description, like a stochastic differential equation, leads normally to dynamic programming procedures. The resulting Bellman equation is often of a very genera! nature, and analytically hard to solve. The models in the present paper are formulated in terms of the relative change, and the optimality criterion is to maximize the expected rate of growth. We show how this can be done in a simple way, where we avoid using the Bellman equation. An application is indicated.

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41

Aase, Knut K. "Stochastic control of geometric processes." Journal of Applied Probability 24, no. 01 (March 1987): 97–104. http://dx.doi.org/10.1017/s0021900200030643.

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Анотація:

Stochastic optimization of semimartingales which permit a dynamic description, like a stochastic differential equation, leads normally to dynamic programming procedures. The resulting Bellman equation is often of a very genera! nature, and analytically hard to solve. The models in the present paper are formulated in terms of the relative change, and the optimality criterion is to maximize the expected rate of growth. We show how this can be done in a simple way, where we avoid using the Bellman equation. An application is indicated.

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42

Andriyanov, Nikita A., Madina-Bonu R. Atakhodzhaeva, and Evgeny I. Borodin. "Mathematical modeling of recommender system and data processing of a telecommunications company using machine learning models." Bulletin of the South Ural State University. Ser. Computer Technologies, Automatic Control & Radioelectronics 22, no. 2 (April 2022): 17–28. http://dx.doi.org/10.14529/ctcr220202.

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The purpose of the study is to develop data modeling methods for projecting recommender algorithms using doubly stochastic autoregressive models of random processes and checking their adequacy by applying machine learning algorithms to cluster users in a simulated data set and predict probabilities of interest. Research methods. The article discusses the methods used in the construction of recommender systems. At the same time, the problem of modeling user behavior using a doubly stochastic model is considered. This model is proposed for generating artificial data. The doubly stochastic model allows generating non-stationary processes, thus creating users with different probabilistic properties in different groups of objects of interest. After that, artificially created users (and their activity) are clustered based on a modified K-means algorithm. The main modification is the need for automatic pre-estimation of the number of clusters, and not its choice by a person. Next, the behavior of representatives of each user group for new events is modeled. Based on the generated information and training data, the problem of predictiing and ranking the services offered is solved. At the same time, at the first stage, the use of regression models is sufficient to assign users to a group and form offers for this user. Results of the study. On the training data in 2 clusters, high determination indices were achieved, which indicates approximately 90% of the explained variance when using the proposed doubly stochastic model. Particular attention is paid to the work of modern recommender systems on the example of the Disco system developed by Yandex. In addition, pre-processing and preliminary analysis of data from the real sector was performed, namely, the data of a telecommunications company are being studied. For the purpose of issuing relevant proposals for communication services, a test recommender system has been developed. Conclusion. Thus, the main results of the work include a mathematical model that simulates the reaction of users to various services, as well as a logistic regression model used to predict the probability of a user's interest in a new service. Based on predicted probabilities, it is not difficult to rank new proposals. Approbation on the synthesized data showed the high efficiency of the model.

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43

Filatov, V. O., A. L. Yerokhin, O. V. Zolotukhin, and M. S. Kudryavtseva. "Hybrid simulation models for complex decision-making problems with partial uncertainty." Information extraction and processing 2022, no. 50 (December 19, 2022): 78–86. http://dx.doi.org/10.15407/vidbir2022.50.078.

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Specific features of application of hybrid simulation and control models in information systems and system support for decision-making in solving practical problems under conditions of uncertainty, vagueness, inaccuracy, stochasticity of processes of subject areas are considered. To obtain reliable data, it is necessary to use poorly formalized operational and long-term data on the state of the object of control, expert knowledge, application of mathematical programming methods with stochastic or fuzzy constraints, as well as many cause-and-effect relations between processes that may be presented in the form of production rules: “condition–action”. Based on research and analysis of complex decision-making problems using hybrid simulation-control models in conditions of partial uncertainty, an estimate of their complexity in terms of practical implementations, which did not exceed the quadratic dependence on the number of operations is obtained. The peculiarities of their use in real developments are determined, which allowed us to increase the reliability of decisions in information systems, to reduce development time to 12% in the conditions of fuzzy, stochastic character of researched processes of real objects. The results that confirm their effective use in solving practical problems: an example of solving situational analysis using hybrid simulation-control models in the information-analytical decision support system, are presented.

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44

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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45

Dumont, Grégory, Jacques Henry, and Carmen Oana Tarniceriu. "A theoretical connection between the Noisy Leaky integrate-and-fire and the escape rate models: The non-autonomous case." Mathematical Modelling of Natural Phenomena 15 (2020): 59. http://dx.doi.org/10.1051/mmnp/2020017.

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Finding a mathematical model that incorporates various stochastic aspects of neural dynamics has proven to be a continuous challenge. Among the different approaches, the noisy leaky integrate-and-fire and the escape rate models are probably the most popular. These two models are generally thought to express different noise action over the neural cell. In this paper we investigate the link between the two formalisms in the case of a neuron subject to a time dependent input. To this aim, we introduce a new general stochastic framework. As we shall prove, our general framework entails the two already existing ones. Our results have theoretical implications since they offer a general view upon the two stochastic processes mostly used in neuroscience, upon the way they can be linked, and explain their observed statistical similarity.

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46

Cairoli, Andrea, Rainer Klages, and Adrian Baule. "Weak Galilean invariance as a selection principle for coarse-grained diffusive models." Proceedings of the National Academy of Sciences 115, no. 22 (May 14, 2018): 5714–19. http://dx.doi.org/10.1073/pnas.1717292115.

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How does the mathematical description of a system change in different reference frames? Galilei first addressed this fundamental question by formulating the famous principle of Galilean invariance. It prescribes that the equations of motion of closed systems remain the same in different inertial frames related by Galilean transformations, thus imposing strong constraints on the dynamical rules. However, real world systems are often described by coarse-grained models integrating complex internal and external interactions indistinguishably as friction and stochastic forces. Since Galilean invariance is then violated, there is seemingly no alternative principle to assess a priori the physical consistency of a given stochastic model in different inertial frames. Here, starting from the Kac–Zwanzig Hamiltonian model generating Brownian motion, we show how Galilean invariance is broken during the coarse-graining procedure when deriving stochastic equations. Our analysis leads to a set of rules characterizing systems in different inertial frames that have to be satisfied by general stochastic models, which we call “weak Galilean invariance.” Several well-known stochastic processes are invariant in these terms, except the continuous-time random walk for which we derive the correct invariant description. Our results are particularly relevant for the modeling of biological systems, as they provide a theoretical principle to select physically consistent stochastic models before a validation against experimental data.

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47

Linde, W. "STABLE NON-GAUSSIAN RANDOM PROCESSES: STOCHASTIC MODELS WITH INFINITE VARIANCE." Bulletin of the London Mathematical Society 28, no. 5 (September 1996): 554–56. http://dx.doi.org/10.1112/blms/28.5.554.

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48

TSENG, JIE-JUN, MING-JER LEE, and SAI-PING LI. "HEAVY-TAILED DISTRIBUTIONS IN FATAL TRAFFIC ACCIDENTS: ROLE OF HUMAN ACTIVITIES." International Journal of Modern Physics C 20, no. 08 (August 2009): 1281–90. http://dx.doi.org/10.1142/s0129183109014345.

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Human activities can play a crucial role in the statistical properties of observables in many complex systems such as social, technological, and economic systems. We demonstrate this by looking into the heavy-tailed distributions of observables in fatal plane and car accidents. Their origin is examined and can be understood as stochastic processes that are related to human activities. Simple mathematical models are proposed to illustrate such processes and compared with empirical results obtained from existing databanks.

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49

Potapova, Nadin, Lyudmila Volontyr, and Oksana Zelinska. "MATHEMATICAL AND STATISTICAL EVALUATION OF PROCESSES OF USING INFORMATION TECHNOLOGIES." ENGINEERING, ENERGY, TRANSPORT AIC, no. 4(111) (December 18, 2020): 61–71. http://dx.doi.org/10.37128/2520-6168-2020-4-7.

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The article covers the methodological issues of mathematical and statistical evaluation of the information technology use. The necessity of using information technologies to ensure control system flexibility has been substantiated. The impact of the level of integration of implemented information technologies on the increase of production management efficiency through data processing models and use of a single information space has been determined. To achieve the appropriate characteristics of stochastic processes of information technology, it is proposed to use methodological approaches to modeling on the basis of mathematical and statistical evaluation with elements of correlation and regression analysis. We have established the features of regression model development on the basis of which the estimation of the modeled process is carried out in the forecasting period. The paper investigates the issue of modeling methodology based on correlation and regression models and special cases in their evaluation. The main stages of model development and the sequence of their implementation are given. The impact on the number of enterprises that use computer technology in their activities, such factors as: Internet connection, the use of social media and the availability of websites has been assessed. Particular attention is paid to the use of social media as one of the key resources in defining the ideology of using information resources. The model parameters were estimated by the least square method. The analysis of the influence of the studied factors has been carried out based on the obtained regression model parameters taking into account their significance on the influence of the process of information technology use. The necessity of theoretical substantiation of interdependent factor effect with the application of variance analysis and mathematical theory of hypotheses has been proved.

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50

Lawson, Michael J., Linda Petzold, and Andreas Hellander. "Accuracy of the Michaelis–Menten approximation when analysing effects of molecular noise." Journal of The Royal Society Interface 12, no. 106 (May 2015): 20150054. http://dx.doi.org/10.1098/rsif.2015.0054.

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Quantitative biology relies on the construction of accurate mathematical models, yet the effectiveness of these models is often predicated on making simplifying approximations that allow for direct comparisons with available experimental data. The Michaelis–Menten (MM) approximation is widely used in both deterministic and discrete stochastic models of intracellular reaction networks, owing to the ubiquity of enzymatic activity in cellular processes and the clear biochemical interpretation of its parameters. However, it is not well understood how the approximation applies to the discrete stochastic case or how it extends to spatially inhomogeneous systems. We study the behaviour of the discrete stochastic MM approximation as a function of system size and show that significant errors can occur for small volumes, in comparison with a corresponding mass-action system. We then explore some consequences of these results for quantitative modelling. One consequence is that fluctuation-induced sensitivity, or stochastic focusing, can become highly exaggerated in models that make use of MM kinetics even if the approximations are excellent in a deterministic model. Another consequence is that spatial stochastic simulations based on the reaction–diffusion master equation can become highly inaccurate if the model contains MM terms.

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