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Journal articles on the topic 'Probabilities – Mathematical models'
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1
Raup, David M. "Mathematical models of cladogenesis." Paleobiology 11, no. 1 (1985): 42–52. http://dx.doi.org/10.1017/s0094837300011386.
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The evolutionary pattern of speciation and extinction in any biologic group may be described by a variety of mathematical models. These models provide a framework for describing the history of taxonomic diversity (clade shape) and other aspects of larger evolutionary patterns. The simplest model assumes time homogeneity: that is, speciation and extinction probabilities are constant through time and within taxonomic groups. In some cases the homogeneous model provides a good fit to real world paleontological data, but in other cases the model serves only as a null hypothesis that must be rejected before more complex models can be applied. In cases where the homogeneous model does not fit the data, time-inhomogeneous models can be formulated that specify change, regular or episodic, in speciation and extinction probabilities. An appendix provides a list of the most useful equations based on the homogeneous model.
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Bronevich, A. G., and I. N. Rosenberg. "Applying models of imprecise probabilities in the mathematical theory of criteria importance." Automation and Remote Control 78, no. 8 (August 2017): 1460–73. http://dx.doi.org/10.1134/s0005117917080070.
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Lomeli, Luis Martinez, Abdon Iniguez, Prasanthi Tata, Nilamani Jena, Zhong-Ying Liu, Richard Van Etten, Arthur D. Lander, Babak Shahbaba, John S. Lowengrub, and Vladimir N. Minin. "Optimal experimental design for mathematical models of haematopoiesis." Journal of The Royal Society Interface 18, no. 174 (January 2021): 20200729. http://dx.doi.org/10.1098/rsif.2020.0729.
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The haematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. It is known that feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in haematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. We have developed a novel Bayesian hierarchical framework for optimal design of perturbation experiments and proper analysis of the data collected. We use a deterministic model that accounts for feedback and feedforward regulation on cell division rates and self-renewal probabilities. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. We overcome this difficulty by modelling the unobserved cellular levels as latent variables. We then use principles of Bayesian experimental design to optimally distribute time points at which the haematopoietic cells are quantified. We evaluate our approach using synthetic and real experimental data and show that an optimal design can lead to better estimates of model parameters.
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Loucopoulos, Constantine. "Effect of prior probabilities on the classificatory performance of parametric and mathematical programming approaches to the two-group discriminant problem." Journal of Applied Mathematics and Decision Sciences 1, no. 1 (January 1, 1997): 45–51. http://dx.doi.org/10.1155/s1173912697000047.
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A mixed-integer programming model (MIP) incorporating prior probabilities for the two-group discriminant problem is presented. Its classificatory performance is compared against that of Fisher's linear discrimininant function (LDF) and Smith's quadradic discriminant function (QDF) for simulated data from normal and nonnormal populations for different settings of the prior probabilities of group membership. The proposed model is shown to outperform both LDF and QDF for most settings of the prior probabilities when the data are generated from nonnormal populations but underperforms the parametric models for data generated from normal populations.
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Forrester, P. J., and G. E. Andrews. "Height probabilities in solid-on-solid models. II." Journal of Physics A: Mathematical and General 20, no. 13 (September 11, 1987): 4465–81. http://dx.doi.org/10.1088/0305-4470/20/13/046.
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Forrester, P. J., and G. E. Andrews. "Height probabilities in solid-on-solid models. I." Journal of Physics A: Mathematical and General 19, no. 15 (October 21, 1986): L923—L926. http://dx.doi.org/10.1088/0305-4470/19/15/011.
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Zhao, Ming-Jie, and Herbert Jaeger. "Norm-Observable Operator Models." Neural Computation 22, no. 7 (July 2010): 1927–59. http://dx.doi.org/10.1162/neco.2010.03-09-983.
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Hidden Markov models (HMMs) are one of the most popular and successful statistical models for time series. Observable operator models (OOMs) are generalizations of HMMs that exhibit several attractive advantages. In particular, a variety of highly efficient, constructive, and asymptotically correct learning algorithms are available for OOMs. However, the OOM theory suffers from the negative probability problem (NPP): a given, learned OOM may sometimes predict negative probabilities for certain events. It was recently shown that it is undecidable whether a given OOM will eventually produce such negative values. We propose a novel variant of OOMs, called norm-observable operator models (NOOMs), which avoid the NPP by design. Like OOMs, NOOMs use a set of linear operators to update system states. But differing from OOMs, they represent probabilities by the square of the norm of system states, thus precluding negative probability values. While being free of the NPP, NOOMs retain most advantages of OOMs. For example, NOOMs also capture (some) processes that cannot be modeled by HMMs. More importantly, in principle, NOOMs can be learned from data in a constructive way, and the learned models are asymptotically correct. We also prove that NOOMs capture all Markov chain (MC) describable processes. This letter presents the mathematical foundations of NOOMs, discusses the expressiveness of the model class, and explains how a NOOM can be estimated from data constructively.
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PYKACZ, JAROSŁAW, and BART D'HOOGHE. "BELL-TYPE INEQUALITIES IN FUZZY PROBABILITY CALCULUS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 09, no. 02 (April 2001): 263–75. http://dx.doi.org/10.1142/s021848850100079x.
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Bell-type inequalities, used in mathematical physics as a criterion to check whether a physical situation allows description in terms of classical (Kolmogorovian) or quantum probability calculus are applied to various fuzzy probability models. It occurs that the standard set of Bell-type inequalities does not allow to distinguish Kolmogorovian probabilities from fuzzy probabilities based on the most frequently used Zadeh intersection or probabilistic intersection, but it allows to distinguish all these models from fuzzy probability models based on Giles (Łukasiewicz) intersection. It is proved that if we use fuzzy set intersections pointwisely generated by Frank's fundamental triangular norms Ts(x,y), then the borderline between fuzzy probability models that can be distinguished from Kolmogorovian ones and these fuzzy probability models that cannot be distinguished is for [Formula: see text].
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Raza, Ahmed, and Vladimir Ulansky. "Optimization of Condition Monitoring Decision Making by the Criterion of Minimum Entropy." Entropy 21, no. 12 (December 4, 2019): 1193. http://dx.doi.org/10.3390/e21121193.
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Condition-based maintenance (CBM) is a promising technique for a wide variety of deteriorating systems. Condition-based maintenance’s effectiveness largely depends on the quality of condition monitoring. The majority of CBM mathematical models consider perfect inspections, in which the system condition is assumed to be determined error-free. This article presents a mathematical model of CBM with imperfect condition monitoring conducted at discrete times. Mathematical expressions were derived for evaluating the probabilities of correct and incorrect decisions when monitoring the system condition at a scheduled time. Further, these probabilities were incorporated into the equation of the Shannon entropy. The problem of determining the optimal preventive maintenance threshold at each inspection time by the criterion of the minimum of Shannon entropy was formulated. For the first time, the article showed that Shannon’s entropy is a convex function of the preventive maintenance threshold for each moment of condition monitoring. It was also shown that the probabilities of correct and incorrect decisions depend on the time and parameters of the degradation model. Numerical calculations show that the proposed approach to determining the optimal preventive maintenance threshold can significantly reduce uncertainty when deciding on the condition of the monitoring object.
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Neustroev, S. S., V. I. Serdyukov, N. A. Serdyukova, and S. I. Shishkina. "Mathematical Modeling-based Analysis from the Great Patriotic War Events." Mathematics and Mathematical Modeling, no. 3 (August 25, 2019): 25–35. http://dx.doi.org/10.24108/mathm.0319.0000189.
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When fighting against terrorism in modern armed conflicts, combat vehicles, including tanks, are widely used. To minimise own losses of vehicles and personnel for overthrowing enemy is a relevant task. To solve it, the paper considers certain events in the history of the Great Patriotic War, which are associated with battle of tanks that spring an ambush. A mathematical model of the battle is built. The state graph of the system is given. Using this graph, a probability of tank kills and a ratio of mathematical expectations of losses have been calculated. This mathematical model generalizes the models, previously published in this journal, based on the Markov chain apparatus. The paper gives an example of calculations for this model in the particular case in which experimental data are used as a basis. The ratios of mathematical expectations of losses of the warring parties are obtained. Further, we consider the mathematical models, in which it is assumed that probabilities for tank crews to provide operations of targets detection in firing are known. With technology development and its mathematical support it becomes increasingly more real. The formulas to obtain the probability of tank kills are given according to the graph of states using the known probabilities of transition from one state to another. In each of the three mathematical models under consideration there is a graph of the system state, which allows calculation of the tank kills probability. We have analysed the models to prove a significant dependence of the loss ratio of the warring parties on the number of firing positions used by the tank in ambush in case re-siting is unnoticeable for the enemy. The authors-considered models that use the examples of historical events confirm that the tactics of organising and conducting ambushes in tank battles can be successfully used nowadays, when the technology intensiveness of the opposing forces significantly grows. The obtained results can be applied to organise and conduct tank ambushes in modern armed conflicts and fight against terrorist army.
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Kimmel, M., and D. E. Axelrod. "Mathematical models of gene amplification with applications to cellular drug resistance and tumorigenicity." Genetics 125, no. 3 (July 1, 1990): 633–44. http://dx.doi.org/10.1093/genetics/125.3.633.
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Abstract An increased number of copies of specific genes may offer an advantage to cells when they grow in restrictive conditions such as in the presence of toxic drugs, or in a tumor. Three mathematical models of gene amplification and deamplification are proposed to describe the kinetics of unstable phenotypes of cells with amplified genes. The models differ in details but all assume probabilistic mechanisms of increase and decrease in gene copy number per cell (gene amplification/deamplification). Analysis of the models indicates that a stable distribution of numbers of copies of genes per cell, observed experimentally, exists only if the probability of deamplification exceeds the probability of amplification. The models are fitted to published data on the loss of methotrexate resistance in cultured cell lines, due to the loss of amplified dihydrofolate reductase gene. For two mouse cell lines unstably resistant to methotrexate the probabilities of amplification and deamplification of the dihydrofolate reductase gene on double minute chromosomes are estimated to be approximately 2% and 10%, respectively. These probabilities are much higher than widely presumed. The models explain the gradual disappearance of the resistant phenotype when selective pressure is withdrawn, by postulating that the rate of deamplification exceeds the rate of amplification. Thus it is not necessary to invoke a growth advantage of nonresistant cells which has been the standard explanation. For another analogous process, the loss of double minute chromosomes containing the myc oncogene from SEWA tumor cells, the growth advantage model does seem to be superior to the amplification and deamplification model. In a more theoretical section of the paper, it is demonstrated that gene amplification/deamplification can result in reduction to homozygosity, such as is observed in some tumors. Other applications are discussed.
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Joseph, Dominic. "Estimating credit default probabilities using stochastic optimisation." Data Science in Finance and Economics 1, no. 3 (2021): 253–71. http://dx.doi.org/10.3934/dsfe.2021014.
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<abstract> <p>Banks and financial institutions all over the world manage portfolios containing tens of thousands of customers. Not all customers are high credit-worthy, and many possess varying degrees of risk to the Bank or financial institutions that lend money to these customers. Hence assessment of default risk that is calibrated and reflective of actual credit risk is paramount in the field of credit risk management. This paper provides a detailed mathematical framework using the concepts of Binomial distribution and stochastic optimisation, in order to estimate the Probability of Default for credit ratings. The empirical results obtained from the study have been illustrated to have potential application value and perform better compared to other estimation models currently in practise.</p> </abstract>
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Efimov, Stefan, Sergey Bokarev, and Sergey Pribytkov. "Durability of operated reinforced concrete superstructures of railroad bridges." MATEC Web of Conferences 216 (2018): 01005. http://dx.doi.org/10.1051/matecconf/201821601005.
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The paper describes method to evaluate residual service life of reinforced concrete structures of railroad bridges, enabling to consider the presence of defects, operation history, and climatic factor to calculate probabilities of the structural state at any given moment of time. The model based on semi-Markov process was used to predict the state and calculate reliability indicators of structures and their elements. The data sources for reliability models are results of observations of the structural state, mathematical models of occurrence and development of defects. The example of determining residual service life of reinforced concrete superstructure is given based on the mathematical model of working reinforcement corrosion development.
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Teufel, Ashley, Andrew Ritchie, Claus Wilke, and David Liberles. "Using the Mutation-Selection Framework to Characterize Selection on Protein Sequences." Genes 9, no. 8 (August 13, 2018): 409. http://dx.doi.org/10.3390/genes9080409.
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When mutational pressure is weak, the generative process of protein evolution involves explicit probabilities of mutations of different types coupled to their conditional probabilities of fixation dependent on selection. Establishing this mechanistic modeling framework for the detection of selection has been a goal in the field of molecular evolution. Building on a mathematical framework proposed more than a decade ago, numerous methods have been introduced in an attempt to detect and measure selection on protein sequences. In this review, we discuss the structure of the original model, subsequent advances, and the series of assumptions that these models operate under.
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Raza, Ahmed, and Vladimir Ulansky. "Optimal Preventive Maintenance of Wind Turbine Components with Imperfect Continuous Condition Monitoring." Energies 12, no. 19 (October 8, 2019): 3801. http://dx.doi.org/10.3390/en12193801.
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Among the different maintenance techniques applied to wind turbine (WT) components, online condition monitoring is probably the most promising technique. The maintenance models based on online condition monitoring have been examined in many studies. However, no study has considered preventive maintenance models with incorporated probabilities of correct and incorrect decisions made during continuous condition monitoring. This article presents a mathematical model of preventive maintenance, with imperfect continuous condition monitoring of the WT components. For the first time, the article introduces generalized expressions for calculating the interval probabilities of false positive, true positive, false negative, and true negative when continuously monitoring the condition of a WT component. Mathematical equations that allow for calculating the expected cost of maintenance per unit of time and the average lifetime maintenance cost are derived for an arbitrary distribution of time to degradation failure. A numerical example of WT blades maintenance illustrates that preventive maintenance with online condition monitoring reduces the average lifetime maintenance cost by 11.8 times, as compared to corrective maintenance, and by at least 4.2 and 2.6 times, compared with predetermined preventive maintenance for low and high crack initiation rates, respectively.
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Baranov, V. V. "Models and methods for assessing the security of an informatization object." Herald of the Siberian State University of Telecommunications and Informatics, no. 3 (October 1, 2022): 14–28. http://dx.doi.org/10.55648/1998-6920-2022-16-3-14-28.
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The paper substantiates the need of creation an information decision support system in the development of systems for protecting informatization objects. Analyzes of existing systems in various fields of activity, the requirements for the functionality of the system in relation to the field of information protection, methods for developing models of functioning of protected information systems in a destructive environment impact on the basis of Bayesian networks are considered. The paper gives a description of a typical module functioning of this model. The structures of probabilistic models of the relationship of vulnerabilities, information security threats, methods and scenarios for their implementation, the formation of measures to protect informatization objects, the formation and assessment of the risks of incidents and their damage are considered. Clusters of typical information security events, methodological apparatus for calculating the joint distribution of the probabilities of protective and destructive events are determined. Finally, typical chains of interconnections of such events are identified. Mathematical apparatus for calculating their probabilities, a verbal description of the patterns of their mutual influence, and a method for converting quantitative probabilistic values of informatization object security indicators into qualitative ones are presented, and the results of the study are summarized.
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Gamboa, Maria, and Maria Lopez-Herrero. "On the Number of Periodic Inspections During Outbreaks of Discrete-Time Stochastic SIS Epidemic Models." Mathematics 6, no. 8 (July 24, 2018): 128. http://dx.doi.org/10.3390/math6080128.
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This paper deals with an infective process of type SIS, taking place in a closed population of moderate size that is inspected periodically. Our aim is to study the number of inspections that find the epidemic process still in progress. As the underlying mathematical model involves a discrete time Markov chain (DTMC) with a single absorbing state, the number of inspections in an outbreak is a first-passage time into this absorbing state. Cumulative probabilities are numerically determined from a recursive algorithm and expected values came from explicit expressions.
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Donati, Luca, Marcus Weber, and Bettina G. Keller. "A review of Girsanov reweighting and of square root approximation for building molecular Markov state models." Journal of Mathematical Physics 63, no. 12 (December 1, 2022): 123306. http://dx.doi.org/10.1063/5.0127227.
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Dynamical reweighting methods permit to estimate kinetic observables of a stochastic process governed by a target potential [Formula: see text] from trajectories that have been generated at a different potential V( x). In this article, we present Girsanov reweighting and square root approximation: the first method reweights path probabilities exploiting the Girsanov theorem and can be applied to Markov state models to reweight transition probabilities; the second method was originally developed to discretize the Fokker–Planck operator into a transition rate matrix, but here we implement it into a reweighting scheme for transition rates. We begin by reviewing the theoretical background of the methods and then present two applications relevant to molecular dynamics, highlighting their strengths and weaknesses.
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FENG, ZHILAN, and JOHN W. GLASSER. "ESTIMATING AGE-SPECIFIC HAZARD RATES OF INFECTION FROM CROSS-SECTIONAL OBSERVATIONS." Revista de Matemática: Teoría y Aplicaciones 27, no. 1 (December 5, 2019): 123–40. http://dx.doi.org/10.15517/rmta.v27i1.39952.
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Mathematical models of pathogen transmission in age-structured host populations, can be used to design or evaluate vaccination programs. For reliable results, their forces or hazard rates of infection (FOI) must be formulated correctly and the requisite contact rates and probabilities of infection on contact estimated from suitable observations. Elsewhere, we have described methods for calculating the probabilities of infection on contact from the contact rates and FOI. Here, we present methods for estimating the FOI from cross-sectional serological surveys or disease surveillance in populations with or without concurrent vaccination. We consider both continuous and discrete age, and present estimates of the FOI for vaccinepreventable diseases that confer temporary or permanent immunity.
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de Cooman, Gert, Filip Hermans, and Erik Quaeghebeur. "IMPRECISE MARKOV CHAINS AND THEIR LIMIT BEHAVIOR." Probability in the Engineering and Informational Sciences 23, no. 4 (August 4, 2009): 597–635. http://dx.doi.org/10.1017/s0269964809990039.
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When the initial and transition probabilities of a finite Markov chain in discrete time are not well known, we should perform a sensitivity analysis. This can be done by considering as basic uncertainty models the so-calledcredal setsthat these probabilities are known or believed to belong to and by allowing the probabilities to vary over such sets. This leads to the definition of animprecise Markov chain. We show that the time evolution of such a system can be studied very efficiently using so-calledlowerandupper expectations, which are equivalent mathematical representations of credal sets. We also study how the inferred credal set about the state at timenevolves asn→∞: under quite unrestrictive conditions, it converges to a uniquely invariant credal set, regardless of the credal set given for the initial state. This leads to a non-trivial generalization of the classical Perron–Frobenius theorem to imprecise Markov chains.
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Kuniba, A., and T. Yajima. "Local state probabilities for an infinite sequence of solvable lattice models." Journal of Physics A: Mathematical and General 21, no. 2 (January 21, 1988): 519–27. http://dx.doi.org/10.1088/0305-4470/21/2/029.
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Romansky, Radi. "Mathematical Model Investigation of a Technological Structure for Personal Data Protection." Axioms 12, no. 2 (January 18, 2023): 102. http://dx.doi.org/10.3390/axioms12020102.
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The contemporary digital age is characterized by the massive use of different information technologies and services in the cloud. This raises the following question: “Are personal data processed correctly in global environments?” It is known that there are many requirements that the Data Controller must perform. For this reason, this article presents a point of view for transferring some activities for personal data processing from a traditional system to a cloud environment. The main goal is to investigate the differences between the two versions of data processing. To achieve this goal, a preliminary deterministic formalization of the two cases using a Data Flow Diagram is made. The second phase is the organization of a mathematical (stochastic) model investigation on the basis of a Markov chain apparatus. Analytical models are designed, and their solutions are determined. The final probabilities for important states are determined based on an analytical calculation, and the higher values for the traditional version are defined for data processing in registers (“2”: access for write/read −0.353; “3”: personal data updating −0.212). The investigation of the situations based on cloud computing determines the increasing probability to be “2”. Discussion of the obtained assessment based on a graphical presentation of the analytical results is presented, which permits us to show the differences between the final probabilities for the states in the two versions of personal data processing.
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Grana, Dario. "Bayesian petroelastic inversion with multiple prior models." GEOPHYSICS 85, no. 5 (June 26, 2020): M57—M71. http://dx.doi.org/10.1190/geo2019-0625.1.
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Bayesian methods are commonly used for geophysical inverse problems, such as seismic and rock-physics inversion, for the prediction of petroelastic properties. Bayesian inversion is based on Bayes’ theorem and combines the information from a prior distribution and a likelihood function; in geophysical applications, the prior model generally includes the available geologic information about the model variables, whereas the likelihood includes the geophysical models that link the model to the data. The goal of Bayesian inversion is to estimate the posterior distribution of the model variables conditioned by the measured data. The focus is on the prior model and its parameters. Typically, the parameters of the prior distributions are assumed to be fixed, for example, the mean and standard deviation of the prior distribution of petroelastic properties in seismic inversion or the facies proportions and transition probabilities in facies classification. I have studied the posterior distribution of the model given the data in a Bayesian setting using multiple prior models. The posterior distribution is assessed by summing the contributions of all of the likelihood functions of the model given the data, using different sets of parameters, weighted by the probabilities of the parameters. I apply the mathematical formulation in different problems, including log-facies classification, seismic-facies classification, and petrophysical property prediction and using different methods for the prior model generation such as transition matrices, training images, and Gaussian mixture models with multiple modes. The results show that multiple prior models can match the data and that the uncertainty in the prior parameters should be accounted for in the posterior distribution of the reservoir properties.
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Yuan, Linglong. "Kingman’s Model with Random Mutation Probabilities: Convergence and Condensation II." Journal of Statistical Physics 181, no. 3 (July 9, 2020): 870–96. http://dx.doi.org/10.1007/s10955-020-02609-w.
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Abstract A generalisation of Kingman’s model of selection and mutation has been made in a previous paper which assumes all mutation probabilities to be i.i.d.. The weak convergence of fitness distributions to a globally stable equilibrium was proved. The condensation occurs if almost surely a positive proportion of the population travels to and condensates on the largest fitness value due to the dominance of selection over mutation. A criterion of condensation was given which relies on the equilibrium whose explicit expression is however unknown. This paper tackles these problems based on the discovery of a matrix representation of the random model. An explicit expression of the equilibrium is obtained and the key quantity in the condensation criterion can be estimated. Moreover we examine how the design of randomness in Kingman’s model affects the fitness level of the equilibrium by comparisons between different models. The discovered facts are conjectured to hold in other more sophisticated models.
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Goldberg, Kenneth P. "Applications: Using Technology to Understand the Jury Decision-making Process." Mathematics Teacher 87, no. 2 (February 1994): 110–14. http://dx.doi.org/10.5951/mt.87.2.0110.
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Two of the recommendations of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) are to use technology to enhance teaching and learning mathematics and to relate school mathematics to the world in which the students Jive through developing and interpreting mathematical models. This article demonstrates how computer or graphing-calculator technology can be used to help students develop and interpret three increasingly realistic models of jwy behavior and explore the potential effect of such decisions as changing jury size. The only mathematics required is an understanding of simple binomial probabilities and the use of sigma, or summation, notation
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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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Kharin, Alexey Yu. "Statistical sequential hypotheses testing on para meters of probability distributions of random binary data." Journal of the Belarusian State University. Mathematics and Informatics, no. 2 (August 5, 2021): 60–66. http://dx.doi.org/10.33581/2520-6508-2021-2-60-66.
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An important mathematical problem of computer data analysis – the problem of statistical sequential testing of simple hypotheses on parameters of probability distributions of observed binary data – is considered in the paper. This problem is being solved for two models of observation: for independent observations and for homogeneous Markov chains. Explicit expressions of the sequential tests statistics are derived, transparent for interpretation and convenient for computer realisation. An approach is developed to calculate the performance characteristics – error probabilities and mathematical expectations of the random number of observations required to guarantee the requested accuracy for decision rules. Asymptotic expansions for the mentioned performance characteristics are constructed under «contamination» of the probability distributions of observed data.
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Аврашков, Lyev Avrashkov, Графова, Galina Grafova, Графов, Andrey Grafov, Шахватова, and S. Shakhvatova. "Criteria and Figures of Bankruptcy Predictive Modeling by the Implementation of Business Activities." Auditor 3, no. 5 (May 31, 2017): 38–44. http://dx.doi.org/10.12737/article_5922aefea074c5.29816973.
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Th e article considers a number of economic-mathematical models on the basis of which probabilities of bankruptcy of the enterprises of various branches can be predicted. Information base for calculation of the fi nancial and economic indicators refl ecting a state and results of economic activity of the enterprise is presented in detail. It is noted that results of calculation of criterion of bankruptcies is for the management of the enterprise of a signal of the early prevention of bankruptcy.
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Kirakosyan, Zara, David B. Saakian, and Chin-Kun Hu. "Finite Genome Length Corrections for the Mean Fitness and Gene Probabilities in Evolution Models." Journal of Statistical Physics 144, no. 1 (July 2011): 198–212. http://dx.doi.org/10.1007/s10955-011-0254-3.
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Kizilova, N. M., and N. L. Rychak. "Probabilistic models of water resources management on urbanized areas." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 4 (2020): 22–27. http://dx.doi.org/10.17721/1812-5409.2020/4.3.
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Gradual global climate change poses new challenges to the mathematical sciences, which are related to forecasting of meteorological conditions, preparing the infrastructure for possible rains, storms, droughts, and other climatic disasters. One of the most common approaches is synthetic regression-probability models, which use the spatio-temporal probability density functions of precipitation level. This approach is applied to the statistics of precipitation in the Kharkiv region, which shows the tendency to a gradual increase in air temperature, high indices of basic water stress, indices of drought and riverside flood threats. Open data on temperature distributions and precipitation were processed using various probability statistics. It is shown that the lognormal distribution most accurately describes the measurement data and allows making more accurate prognoses. Estimates of drought and flood probabilities in Kharkiv region under different scenarios of climate change dynamics have been carried out. The results of the study can be used for management of water resources on urban territories at global climate warming.
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Qiu, Ruozhen, and Yizhi Wang. "Supply Chain Network Design under Demand Uncertainty and Supply Disruptions: A Distributionally Robust Optimization Approach." Scientific Programming 2016 (2016): 1–15. http://dx.doi.org/10.1155/2016/3848520.
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We develop a robust optimization model for designing a three-echelon supply chain network that consists of manufacturers, distribution centers, and retailers under both demand uncertainty and supply disruptions. The market demands are assumed to be random variables with known distribution and the supply disruptions caused by some of the facilities faults or connection links interruptions are formulated by several scenarios with unknown occurrence probabilities. In particular, we assume the probabilities that the disruption scenarios happen belong to the two predefined uncertainty sets, named box and ellipsoid uncertainty sets, respectively. Through mathematical deductions, the proposed robust SCN design models can be transformed into the tractable linear program for box uncertainty and into second-order cone program for ellipsoid uncertainty. We further offer propositions with proof to show the equivalence of the transformed problems with the original ones. The applications of the proposed models together with solution approaches are investigated in a real case to design a tea supply chain network and validate their effectiveness. Numerical results obtained from model implementation and sensitivity analysis arrive at important practical insights.
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Kern, Patrick, Axel Simroth, and Henryk Zähle. "First-order sensitivity of the optimal value in a Markov decision model with respect to deviations in the transition probability function." Mathematical Methods of Operations Research 92, no. 1 (March 2, 2020): 165–97. http://dx.doi.org/10.1007/s00186-020-00706-w.
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Abstract Markov decision models (MDM) used in practical applications are most often less complex than the underlying ‘true’ MDM. The reduction of model complexity is performed for several reasons. However, it is obviously of interest to know what kind of model reduction is reasonable (in regard to the optimal value) and what kind is not. In this article we propose a way how to address this question. We introduce a sort of derivative of the optimal value as a function of the transition probabilities, which can be used to measure the (first-order) sensitivity of the optimal value w.r.t. changes in the transition probabilities. ‘Differentiability’ is obtained for a fairly broad class of MDMs, and the ‘derivative’ is specified explicitly. Our theoretical findings are illustrated by means of optimization problems in inventory control and mathematical finance.
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CHAYES, L., and H. K. LEI. "CARDY'S FORMULA FOR CERTAIN MODELS OF THE BOND-TRIANGULAR TYPE." Reviews in Mathematical Physics 19, no. 05 (June 2007): 511–65. http://dx.doi.org/10.1142/s0129055x0700305x.
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We introduce and study a family of 2D percolation systems which are based on the bond percolation model of the triangular lattice. The system under study has local correlations, however, bonds separated by a few lattice spacings act independently of one another. By avoiding explicit use of microscopic paths, it is first established that the model possesses the typical attributes which are indicative of critical behavior in 2D percolation problems. Subsequently, the so-called Cardy–Carleson functions are demonstrated to satisfy, in the continuum limit, Cardy's formula for crossing probabilities. This extends the results of S. Smirnov to a non-trivial class of critical 2D percolation systems.
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Rykov, Vladimir V., Mikhail G. Sukharev, and Victor Yu Itkin. "Investigations of the Potential Application of k-out-of-n Systems in Oil and Gas Industry Objects." Journal of Marine Science and Engineering 8, no. 11 (November 16, 2020): 928. http://dx.doi.org/10.3390/jmse8110928.
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The purpose of this paper was to demonstrate the possibilities of assessing the reliability of oil and gas industry structures with the help of mathematical models of k-out-of-n systems. We show how the reliability of various structures in the oil and gas complex can be described and investigated using k-out-of-n models. Because the initial information about the life and repair time of components of systems is only usually known on the scale of one and/or two moments, we focus on the problem of the sensitivity analysis of the system reliability indices to the shape of its components repair time distributions. To address this problem, we used the so-called markovization method, based on the introduction of supplementary variables, to model the system behavior with the help of the two-dimensional Markov process with discrete-continuous states. On the basis of the forward Kolmogorov equations for the time-dependent process’ state probabilities, relevant balance equations for the process’ stationary probabilities are presented. Using these equations, stationary probabilities and some reliability indices for two examples from the oil and gas industry were calculated and their sensitivity to the system component’s repair time distributions was analyzed. Calculations show that under “rare” component failures, most system reliability indices become practically insensitive to the shape of the components repair time distributions.
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Martinec, Tomislav, Stanko Škec, Fanika Lukačević, and Mario Štorga. "MODELLING PROPORTIONS AND SEQUENCES OF OPERATIONS IN TEAM DESIGN ACTIVITIES." Proceedings of the Design Society 1 (July 27, 2021): 2187–96. http://dx.doi.org/10.1017/pds.2021.480.
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AbstractThe presented research aims at modelling and formalising the process of team design activity as an interplay between the evolution of design problems and solutions. The motivation founds primarily on a presumption that there exist regularities in designing which can be captured and formalised using the appropriate models. The study thus investigates whether the identified design operation proportions and sequence probabilities are consistent throughout the different parts of team conceptual design activities. It does so by exploring the utility of mathematical models built based on the correlations and statistically significant sequences underlying the previously identified designing patterns. The developed mathematical model was tested by replicating moving-average analyses of design operation proportions and sequences, which were originally observed in the protocol analysis study. A close fit was found between the simulated and the observed data, particularly in providing insights regarding operation patterns and proportion trends. The presented models and modelling methodology are potentially an appropriate means for the next steps in describing, and consequently predicting and supporting team design activity dynamics.
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Zatserkovnyi, V., L. Plichko, and M. Bohoslavskyi. "ANALYSIS OF THE APPROACHES TO THE DEVELOPMENT OF THE MATHEMATICAL MODEL FOR THE MONITORING OF NATURAL AND ANTHROPOGENIC SYSTEMS ON THE BASIS OF DETERMINATION OF GRADUAL FAILURES PROBABILITY." Visnyk of Taras Shevchenko National University of Kyiv. Geology, no. 2 (85) (2019): 86–91. http://dx.doi.org/10.17721/1728-2713.85.12.
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The approaches for creating a mathematical model for monitoring natural and technogenic systems (PTS) and emergency situations (ES) based on the probability of gradual failures are outlined. The monitoring of the NAS and ES provides for comprehensive monitoring of changes in the natural and anthropogenic environment and its components. The complexity of this process is determined mainly by the complexity of the diagnostics of the monitoring objects and the precise measurement of a large number of indicators that determine the conditions and factors of the state of the NAS, environmental pollution, etc. The practical solution of this problem is possible on the basis of the use of modern mathematical and geo-information methods of modeling that provide a comprehensive reflection of heterogeneous and multi-linked processes of formation and development of emergency situations of different origins, which can not be achieved with the use of traditional technologies. To describe the functioning of monitoring systems, it is worth building a mathematical model of the research object. The most complete state of the object of the study is characterized by its mathematical functional and statistical model. However, a more complete description of the static and dynamic state of the monitoring object is a probabilistic description of the state of objects with the help of distribution laws of the probabilities of the parameters of the input influences elements, output parameters and vector-operators. Since the probabilities of sudden bounces are determined by known formulas of the reliability theory, the main attention is drawn to the determination of the probability of the gradual failures occurrence.It is established that three mathematical models may be applied to determine the probability of gradual failures (a mathematical model based on the integration of differential equations; a mathematical model based on the Monte Carlo method; a mathematical model based on the quasilinear disturbances method). The results show, that the proposed method of research may use to simulate various scenarios of flooding in the territories of the Chernihiv region.
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TSOULARIS, A., and J. WALLACE. "A MARKOV CHAIN MODEL OF PREDATOR-MODEL-MIMIC INTERACTIONS." Journal of Biological Systems 13, no. 03 (September 2005): 273–86. http://dx.doi.org/10.1142/s0218339005001483.
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The population dynamics for predator and prey environments have been studied extensively, and several major mathematical models have been introduced to quantify this. The situation becomes more complex, however, when the prey incorporates preservation strategies for survival. One of the most interesting approaches here is the use of mimicry of prey which are unacceptable to the predator, to avoid being consumed. Here we develop a Markov chain model of interactions between a predator and a prey population comprising unpalatable models, general mimics and specific mimics. This incorporates a simple stochastic procedure for the predator, enabling modifiable behavior to be modeled. We calculate equilibrium consumption probabilities and introduce a fitness measure for each type of prey. Finally, by taking into account the population size of each type of prey, we extend the previously reported notion of a predator benefit function for this more complex situation and provide various mathematical forms of optimal benefit for the predator under selected scenarios of biological importance.
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LEE, SOOMIN, HEEYOUNG LEE, JOO-YEON LEE, PANAGIOTIS SKANDAMIS, BEOM-YOUNG PARK, MI-HWA OH, and YOHAN YOON. "Mathematical Models To Predict Kinetic Behavior and Growth Probabilities of Listeria monocytogenes on Pork Skin at Constant and Dynamic Temperatures." Journal of Food Protection 76, no. 11 (November 1, 2013): 1868–72. http://dx.doi.org/10.4315/0362-028x.jfp-13-197.
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In this study, mathematical models were developed to predict the growth probability and kinetic behavior of Listeria monocytogenes on fresh pork skin during storage at different temperatures. A 10-strain mixture of L. monocytogenes was inoculated on fresh pork skin (3 by 5 cm) at 4 log CFU/cm2. The inoculated samples were stored aerobically at 4, 7, and 10°C for 240 h, at 15 and 20°C for 96 h, and at 25 and 30°C for 12 h. The Baranyi model was fitted to L. monocytogenes growth data on PALCAM agar to calculate the maximum specific growth rate, lag-phase duration, the lower asymptote, and the upper asymptote. The kinetic parameters were then further analyzed as a function of storage temperature. The model simulated growth of L. monocytogenes under constant and changing temperatures, and the performances of the models were evaluated by the root mean square error and bias factor (Bf). Of the 49 combinations (temperature × sampling time), the combinations with significant growth (P < 0.05) of L. monocytogenes were assigned a value of 1, and the combinations with nonsignificant growth (P ≥ 0.05) were given a value of 0. These data were analyzed by logistic regression to develop a model predicting the probabilities of L. monocytogenes growth. At 4 to 10°C, obvious L. monocytogenes growth was observable after 24 h of storage; but, at other temperatures, the pathogen had obvious growth after 12 h of storage. Because the root mean square error value (0.184) and Bf (1.01) were close to 0 and 1, respectively, the performance of the developed model was acceptable, and the probabilistic model also showed good performance. These results indicate that the developed model should be useful in predicting kinetic behavior and calculating growth probabilities of L. monocytogenes as a function of temperature and time.
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Boiko, Evgueny, Igor Polikarpov, Aleksey Bobrov, Sergey Sizintsov, Valeriy Volnev, and Pavel Shishmarev. "A digital solution for risk-oriented management of thermal power plant process equipment condition." Energy Safety and Energy Economy 5 (November 2020): 42–54. http://dx.doi.org/10.18635/2071-2219-2020-5-42-54.
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According to digital engineering, an intelligent digital infrastructure is intended to optimize performance of thermal power plants. This paper presents an intelligent digital approach to power facility management. As an example, Siberian Generating Company thermal power plants were considered. The authors have developed specialized software able to control and predict thermal power plant process equipment conditions comparing monitoring data and failure probabilities with appropriate mathematical models. Based on a life-cycle monitoring model, a management methodology was created to be applied to technical and business processes of a power facility to improve its maintenance strategy.
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Deyme, Laure, Marine Gilabert, Laurent Mineur, Clemence Toullec, Mohamed Gasmi, Joseph Ciccolini, Dominique Barbolosi, and Florence Gattacceca. "A PK/PD mathematical model to forecast severe toxicities in pancreatic cancer patients treated with FOLFIRINOX regimen." Journal of Clinical Oncology 38, no. 15_suppl (May 20, 2020): e16774-e16774. http://dx.doi.org/10.1200/jco.2020.38.15_suppl.e16774.
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e16774 Background: FOLFIRINOX regimen is the most efficient treatment in pancreatic adenocarcinoma. However, this triple-therapy causes significant and dose-limiting toxic effects leading to empirical dose-reduction, postponement of the forthcoming courses and sometimes treatment discontinuation. Dose-limiting toxicities with FOLFIRINOX are mostly oxaliplatin-induced peripheral neuropathy (OIPN) and irinotecan-induced diarrhoea (IID). The first aim of our study was to establish dose-concentration-toxicity relationships for these two main ordinal toxicities. Second, we aimed to perform in silico simulations to define the optimal FOLFIRINOX administration protocol (i.e., dosing, scheduling, sequencing) for a maximal benefit to risk ratio. Methods: We performed a retrospective pharmacometric analysis from clinical data collected in three French institutes. Patients had all confirmed diagnosis of PDAC treated with FOLFIRINOX as first line regimen. Demographic characteristics, toxicity data and dosage modifications were collected. Two mathematical models connecting dose – concentration – toxicity (PKPD Tox model) were developed using Monolix2019 to describe both OIPN and IID. Results: Data from 75 patients (36 females/39 males) treated with FOLFIRINOX regimen between 2015-2018 and representing 566 courses were collected. Median age was 65.4 years (range 29-78). The performance status at the start of treatment was 0-1 for 70% of patients. The most frequent location of the tumor was pancreatic head (50%). 91% of patients were subject to empirical dose reduction during their treatment. Oxaliplatin doses were decreased in 258 courses and stopped in 66 courses. Irinotecan doses were decreased in 257 courses and stopped in 33 courses. Overall, 130 IID and 198 OIPN events were observed. From these data, two different PKPD Tox models were developed. The individual concentrations of SN38 (active metabolite of irinotecan) and oxaliplatin were simulated with population PK models, either home-built or taken from the literature. Concentrations were translated into adequate exposure via an interface model developed by our group. Exposure was finally related to a pharmacodynamic model to predict probabilities assigned to each grade of IID or OIPN. Conclusions: These PKPD Tox models help to predict dose-limiting toxicities upon FOLFIRINOX and are useful to select the administration protocol of FOLFIRINOX minimizing the occurrence probabilities of treatment-related neuropathy and diarrhoea, while maintaining efficacy.
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Andriushchenko, Kateryna, Anastasiia Liezina, Vitalii Lavruk, Liudmyla Sliusareva, and Viktoriia Rudevska. "Intelligent enterprise capital control based on Markov chain." Acta Innovations, no. 45 (July 4, 2022): 18–30. http://dx.doi.org/10.32933/actainnovations.45.2.
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This scientific work is devoted to the processes of creating technologies, as well as the use of their mathematical representation in the form of models in the context of the formation and development of the intellectual capital of an enterprise. To select a goal, a vision was formed to prove or refute any possibility of using Markov's theory in practice, namely the creation of a stochastic model of the intellectual capital of an enterprise in monetary terms, which manifests itself in investments in intangible assets. As an initial model hypothesis, the statement is accepted that investments in the enterprise's intangible assets are a factor in the transformation of intellectual capital into the company's value. Based on the results of applying the stochastic Markov chain model, the potential profit of the company's intangible assets was estimated, the main elements of which were intellectual capital assets during the study. A matrix of transition probabilities has been formed and modeling of the limiting probabilities of the system states has been implemented. The necessary conditions and boundaries of the scope of the mathematical model are also determined. The mathematical method of modeling the company's intellectual capital proposed in the article allows determining the contribution of each of the structural components to the formation of the value of the enterprises intellectual capital, thereby making it possible to establish a current balance between all its elements, which contributes to a comprehensive study of the company's intellectual assets.
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Rămescu, Doriana Andreea, Nicoleta Sîrghi, and Mihaela Neamțu. "DYNAMIC ANALYSIS OF THE COOPERATION AND COMPETITION RELATIONSHIP IN THE OIL AND GAS INDUSTRY IN ROMANIA." Oradea Journal of Business and Economics 4, no. 2 (September 2019): 16–25. http://dx.doi.org/10.47535/1991ojbe074.
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The aim of the paper is to analyse the cooperation and competition relationship in the oil and gas industry in Romania using the game theory. The players are the companies, the payoffs are the profits obtained by the entities and there are two strategies as cooperation and competition. Two cases are considered: duopolistic and triopolistic market. The mathematical models have as variables the probabilities of choosing cooperation and competition by each player. They are described by two and three nonlinear differential equations. The time delay is introduced in order to highlight the time between choosing a strategy and its effect. The case studies use real data for two and three companies, respectively, with two scenarios related to the obtained payoffs if they cooperate or not. The time evolutions of the variables are carried out using Wolfram Mathematica 9. Finally, some conclusions and future research are drawn.
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Lambert, M. F., J. P. Whiting, and A. V. Metcalfe. "A non-parametric hidden Markov model for climate state identification." Hydrology and Earth System Sciences 7, no. 5 (October 31, 2003): 652–67. http://dx.doi.org/10.5194/hess-7-652-2003.
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Abstract. Hidden Markov models (HMMs) can allow for the varying wet and dry cycles in the climate without the need to simulate supplementary climate variables. The fitting of a parametric HMM relies upon assumptions for the state conditional distributions. It is shown that inappropriate assumptions about state conditional distributions can lead to biased estimates of state transition probabilities. An alternative non-parametric model with a hidden state structure that overcomes this problem is described. It is shown that a two-state non-parametric model produces accurate estimates of both transition probabilities and the state conditional distributions. The non-parametric model can be used directly or as a technique for identifying appropriate state conditional distributions to apply when fitting a parametric HMM. The non-parametric model is fitted to data from ten rainfall stations and four streamflow gauging stations at varying distances inland from the Pacific coast of Australia. Evidence for hydrological persistence, though not mathematical persistence, was identified in both rainfall and streamflow records, with the latter showing hidden states with longer sojourn times. Persistence appears to increase with distance from the coast. Keywords: Hidden Markov models, non-parametric, two-state model, climate states, persistence, probability distributions
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Raskin, Lev, Oksana Sira, Larysa Sukhomlyn, and Roman Korsun. "DEVELOPMENT OF A MODEL FOR THE DYNAMICS OF PROBABILITIES OF STATES OF SEMI-MARKOV SYSTEMS." Innovative Technologies and Scientific Solutions for Industries, no. 3 (17) (October 20, 2021): 62–68. http://dx.doi.org/10.30837/itssi.2021.17.062.
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The subject is the study of the dynamics of probability distribution of the states of the semi-Markov system during the transition process before establishing a stationary distribution. The goal is to develop a technology for finding analytical relationships that describe the dynamics of the probabilities of states of a semi-Markov system. The task is to develop a mathematical model that adequately describes the dynamics of the probabilities of the states of the system. The initial data for solving the problem is a matrix of conditional distribution laws of the random duration of the system's stay in each of its possible states before the transition to some other state. Method. The traditional method for analyzing semi-Markov systems is limited to obtaining a stationary distribution of the probabilities of its states, which does not solve the problem. A well-known approach to solving this problem is based on the formation and solution of a system of integral equations. However, in the general case, for arbitrary laws of distribution of the durations of the stay of the system in its possible states, this approach is not realizable. The desired result can only be obtained numerically, which does not satisfy the needs of practice. To obtain the required analytical relationships, the Erlang approximation of the original distribution laws is used. This technique significantly increases the adequacy of the resulting mathematical models of the functioning of the system, since it allows one to move away from overly obligatory exponential descriptions of the original distribution laws. The formal basis of the proposed method for constructing a model of the dynamics of state probabilities is the Kolmogorov system of differential equations for the desired probabilities. The solution of the system of equations is achieved using the Laplace transform, which is easily performed for Erlang distributions of arbitrary order. Results. Analytical relations are obtained that specify the desired distribution of the probabilities of the states of the system at any moment of time. The method is based on the approximation of the distribution laws for the durations of the stay of the system in each of its possible states by Erlang distributions of the proper order. A fundamental motivating factor for choosing distributions of this type for approximation is the ease of their use to obtain adequate models of the functioning of probabilistic systems. Conclusions. A solution is given to the problem of analyzing a semi-Markov system for a specific particular case, when the initial distribution laws for the duration of its sojourn in possible states are approximated by second-order Erlang distributions. Analytical relations are obtained for calculating the probability distribution at any time.
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Khrennikov, Andrei. "Bell Could Become the Copernicus of Probability." Open Systems & Information Dynamics 23, no. 02 (June 2016): 1650008. http://dx.doi.org/10.1142/s1230161216500086.
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Our aim is to emphasize the role of mathematical models in physics, especially models of geometry and probability. We briefly compare developments of geometry and probability by pointing to similarities and differences: from Euclid to Lobachevsky and from Kolmogorov to Bell. In probability, Bell could play the same role as Lobachevsky in geometry. In fact, violation of Bell’s inequality can be treated as implying the impossibility to apply the classical probability model of Kolmogorov (1933) to quantum phenomena. Thus the quantum probabilistic model (based on Born’s rule) can be considered as the concrete example of the non-Kolmogorovian model of probability, similarly to the Lobachevskian model — the first example of the non-Euclidean model of geometry. This is the “probability model” interpretation of the violation of Bell’s inequality. We also criticize the standard interpretation—an attempt to add to rigorous mathematical probability models additional elements such as (non)locality and (un)realism. Finally, we compare embeddings of non-Euclidean geometries into the Euclidean space with embeddings of the non-Kolmogorovian probabilities (in particular, quantum probability) into the Kolmogorov probability space. As an example, we consider the CHSH-test.
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Ramírez-López, Adán, Omar Dávila-Maldonado, Alfonso Nájera-Bastida, Rodolfo Dávila Morales, Carlos Rodrigo Muñiz-Valdés, and Jafeth Rodríguez-Ávila. "Computer Modeling of Grain Structure Formation during Quenching including Algorithms with Pre- and Post-Solidification." Metals 12, no. 4 (April 4, 2022): 623. http://dx.doi.org/10.3390/met12040623.
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Simulation of the grain growth process, as a function of steel heat transfer conditions, is helpful for predicting grain structures of continuous cast steel products. Many authors have developed models based on numerical methods to simulate grain growth during metal solidification. Nevertheless, the anisotropic nature of grain structures makes necessary the employment of new mathematical methods such as chaos theory, fractals, and probabilistic and stochastic theories of simulation. The problem is significant for steelmakers to avoid defects in products and to control the steel microstructure during the continuous casting process. This work discusses the influence of nodal solidification times and computer algorithms on the dynamic formation of the chill, columnar, and equiaxed zones including physical phenomena such as nucleation and grain growth. Moreover, the model incorporates pre-nucleation and pre-growth routines in the original algorithm. There is a description of the influence of the mathematical parameter criteria and probabilities over the grain morphology obtained after solidification. Finally, an analysis of these algorithms elucidates the differences between these structures and those obtained from models considering only the solidification.
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Ullah, Khalil, and Muhammad Aslam. "Bayesian Analysis of the Weibull Paired Comparison Model Using Numerical Approximation." Journal of Mathematics 2020 (December 14, 2020): 1–6. http://dx.doi.org/10.1155/2020/6628379.
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The method of paired comparisons (PC) is widely used to rank items using sensory evaluations. The PC models are developed to provide basis for such comparisons. In this study, the Weibull PC model is analyzed under the Bayesian paradigm using noninformative priors and different loss functions, namely, Squared Error Loss Function (SELF), Quadratic Loss Function (QLF), DeGroot Loss Function (DLF), and Precautionary Loss Function (PLF). Numerical approximation is used to illustrate the entire estimation procedure. A real dataset showing usage preferences for different cellphone brands, Huawei (HW), Samsung (SS), Oppo (OP), QMobile (QM), and Nokia (NK), is used. Quadrature method is used to evaluate the Bayes estimates, their posterior risks, preference probabilities, predictive probabilities, and posterior probabilities to establish and verify ranking order of the competing cellphone brands under study. The results show that the paired comparison model under the study using Bayesian approach involving various loss functions can offer mathematical approach to evaluate cellphone brand preferences. The ranking provided by the model is justifiable according to the usage preference for these cellphone brands. The ranking given by the model indicates that cellphone brand Samsung is preferred the most and QMobile is the least preferred. The plausibility of the model is also assessed using the Chi square test of goodness of fit.
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Solodov, A. A. "Markov model of representation of sensual images for the formation of the model of the outside world." Statistics and Economics 15, no. 5 (November 13, 2018): 81–88. http://dx.doi.org/10.21686/2500-3925-2018-5-81-88.
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The aim of the studyis a probabilistic description of the functioning of the cognitive system, taking into account its internal logic and interaction with the external environment.Such concepts of cognitive theory as sensory imaginative representations, models, systems are the most common, so the attempt to formalize them is by obtaining the most common results. One of the key concepts of cognitive theory is Gestalt, which is understood in this work as a kind of holistic perception of the sensual image, as well as the sensual image. Formalization (mathematical description) of Gestalt, as well as other concepts of cognitive theory meets the natural difficulties associated with the uncertainty of these concepts. On the other hand, there are well-developed mathematical models of behavior of quite specific organizational systems, allowing obtaining meaningful results. In this regard, the mathematical description of a wide class of cognitive systems, not limited to the specific content of their functioning, is an urgent task. In this study, it is assumed that sensory images occur at random times and affect the cognitive system with certain probabilities. In this regard, one of the adequate mathematical tools are, apparently, probability-theoretic methods, in particular, the application of the theory of Markov processes. The methodof research within the framework of the adopted model is the application of the theory of Markov processes developing at fixed points in time, i.e. Markov chains. It is believed that the functioning of the cognitive system is described by abstract probabilities of changes in the system states. This approach allows formalizing the processes of representation of sensory images in the cognitive system, taking into account both the internal logic of the system and the interaction of the system with the outside world. The main attention is paid to the study of the influence on the behavior of the system external to her sensual images.As a resultof the study shows that the inclusion of the interactions of the system is achieved by introducing the stochastic matrix of probabilities of the system response to external influences. Taking into account the well-developed theory of Markov chains, analytical expressions for the probabilities of the system in each of the possible states are obtained. The influence on the behavior of the system of elements of the matrix of probability reactions of the system is investigated, the corresponding graphs are presented. The asymptotic behavior of the system is studied with an unlimited increase in the number of steps that change the state of the system, as well as the average characteristics of the system. It is noted that the presented description is formal, operates only with probabilistic characteristics of the system and does not take into account specific signals that can enter the system from its sensors, and generally sensitive elements. In this regard, the further development of the model may be associated with the assessment of the probability of the system response to external influences, taking into account the characteristics of these specific signals, as well as the development of optimal algorithms for decision-making about the presence or absence of impacts on the system from the outside world.
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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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Gaver, Donald P., and Patricia A. Jacobs. "Performing Counter-High Energy Laser Evasive Tactics." International Journal of Operations Research and Information Systems 4, no. 3 (July 2013): 47–60. http://dx.doi.org/10.4018/joris.2013070104.
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The purpose of this article is to present several physics-based mathematical probabilistic models for Counter Directed Energy Weapon operational planning. The scenario analyzed is that of a surge of friendly Blue aircraft closing on a single High Energy Laser. The surge is a mixture of Blue active platforms, and Blue low-value decoys. Blue is targetable for a finite time. Blue response/measures of effectiveness quantify the survivability of Blue Actives. Red response is the number of Blues killed. Red defense tactics trade off longer engagement times, resulting in higher probabilities of kill, and the number of Blues it can engage in the finite time.