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At present, an actual trend in the development of fuel and energy complexes in a number of countries is the diversification of generation via the involvement of local types of solid fuel. In this case, thermochemical processing of fuel is often carried out in a fluidized state. A significant proportion of dispersed fuels cannot be transferred to a state of stable fluidization. The solution in such cases is to create a fluidized bed of inert carrier, into which particles of the target fuel component are then introduced. In this work, a computational and experimental study of the fluidization of inert bulk material (haydite granules) was carried out. The key purpose of the work was to develop a mathematical model for the formation of a fluidized bed, which makes it possible to calculate the process based on its local characteristics, as well as to identify the model parameters and test it using experiment data. During the study the problems of developing a numerical method for calculating the distribution of velocities and concentrations along the height of the apparatus were solved, parametric identification of the proposed mathematical model was carried out, and empirical verification of the modeling results was carried out. The mathematical apparatus of the theory of Markov chains was used as the mathematical basis for constructing the model. The data from our own laboratory full-scale experiment were used to identify the parameters of the model and verify it. A comparison of calculated and experimental data showed the high predictive efficiency of the model for the given granulometric composition of the fluidizing product. The results of the laboratory full-scale experiments also showed a significant evolution of the granulometric composition of haydite granules during their long-term stay in a fluidized bed, which requires a separate study, as well as the introduction of appropriate amendments to the mathematical model for its further improvement.

Background. The object of the study is digital algorithms and a device for estimating the delay time of quantized radar pulses used in measuring the target range. The purpose of the study is to synthesize and analyse of digital algorithms and estimation devices with increased accuracy of the time of holding quantized pulses. Materials and methods. The optimal algorithm for estimating the delay time of a sequence of binary-quantized signal pulses, which does not impose restrictions on the choice of the time sampling period with respect to the duration of signal pulses, is synthesized using the Markov finite circuit algorithm by the maximum likelihood method. Results. The proposed practical algorithms and a device for estimating the delay time in combination with traditional weightless algorithms for detecting a bundle of binary-quantized signals take into account the temporary overlap of quantized pulses in accordance with the selected engagement zones and do not allow false counts by noise. Conclusions. The computer simulation has shown that the proposed algorithms for joint detection and evaluation can significantly improve the accuracy of estimating the delay time compared to the known algorithms.

The article presents the results of computational and experimental studies of the distribution of a model material (plastic spherical particles with a size of 6 mm) along the height of a laboratory two-dimensional apparatus of the fluidized bed of the periodic principle of action. To experimentally determine the distribution of the solid phase over the height of the apparatus, digital photographs of the fluidized bed were taken, which were then analyzed using an algorithm that had been specially developed for this purpose. The algorithm involved splitting the image by height into separate rectangular areas, identifying the particles and counting their number in each of these areas. Numerical experiments were performed using the previously proposed one-dimensional cell model of the fluidization process, constructed on the basis of the mathematical apparatus of the theory of Markov chains with discrete space and time. The design scheme of the model assumes the spatial decomposition of the layer in height into individual elements of small finite sizes. Thus, the numerically obtained results qualitatively corresponded to the full-scale field experiment that had been set up. To ensure the quantitative reliability of the calculated forecasts, a parametric identification of the model was performed using known empirical dependencies to calculate the particle resistance coefficient and estimate the coefficient of their macrodiffusion. A comparison of the results of numerical and field experiments made us possible to identify the most productive empirical dependencies that correspond to the cellular scheme of modeling the process. The resulting physical and mathematical model has a high predictive efficiency and can be used for engineering calculations of devices with a fluidized bed, as well as for setting and solving problems of optimal control of technological processes in these devices for various target functions.

The paper proposes an approach based on the use of mathematical methods for modeling the behavior of the designed web application and user behavior. This approach allows an evaluation of the usability of this application. The paper discusses the models of user interfaces (UI), which are used to assess the convenience of site navigation. The possibility of using two classes of UI models is shown – structural-logical (ontological) and probabilistic. Models of the first class are used to assess the degree of comprehensibility of the proposed UI navigation on the search web resource in the accepted terms. For this, mathematically defined measures of similarity between the elements of the UI and their relationships and the elements of a hypothetical (but plausible) model of the user’s perception of the search area in a given subject area are used. In particular, the paper substantiates the possibility of using Jaccard and Levenshtein lexicographic distance metrics as such measures of similarity. Probabilistic models are based on Markov chains. With the help of these models, in the presence of reliable statistical data collected during the trial operation of a web application or its prototype, it is proposed to estimate the average number of user steps required to solve a specific problem of finding information about a subject area object. The paper provides some recommendations on the use of similarity measures to improve the usability of the UI of web applications. In addition, data on the technique for estimating the probabilities of transitions of Markov chains and semantic connections are presented. To clarify the features of the UI analysis models proposed in the article, the website of the RTU MIREA Admission Committee (https://priem.mirea.ru) is provided with a fairly simple organization that provides a search for information about admission and training at the University. The application of the approach described in the paper, along with traditional methods of testing the usability of UI, will increase the overall level of usability of applications, and thereby reduce the cost of identifying and correcting related errors.

Subject of Research. The paper considers the inferring of gene regulatory networks in the form of Bayesian networks from gene expression data. We present this problem as the problem of the marginal probability estimation for each edge appearance in the true Bayesian network under the known gene expression levels. Monte Carlo approach based on the Markov chains is proposed. Method. The proposed method involved the sampling of Bayesian network pairs and a discretization policy, providing a way for the network to be applied to continuous gene expression data according to a posteriori distribution. The Markov chain Monte Carlo approach was used for sampling with implementation via the Metropolis-Hastings algorithm. Then, the desired probabilities were estimated based on the obtained sample. Main Results. The proposed method is tested on simulated data from the DREAM4 Challenges. Comparison with the leaders shows that the developed method quality surpasses the leader among the existing methods, the regularized gradient boosting machines method (RGBM), on some tests and is comparable on the others in view of the results. At the same time, the proposed method is flexible enough and can be adapted to the other types of experimental data. Practical Relevance. The method is applicable in computational biology for research of the gene regulation mechanisms in various processes, including the tumor growth or the immune system operation.

We consider a closed queuing network with batch service and movements of customers in continuous time. Each node in the queueing network is an infinite capacity single server queueing system under a RANDOM discipline. Customers move among the nodes following a routing matrix. Customers are served in batches of a fixed size. If a number of customers in a node is less than the size, the server of the system is idle until the required number of customers arrive at the node. An arriving at a node customer is placed in the queue if the server is busy. The batсh service time is exponentially distributed. After a batсh finishes its execution at a node, each customer of the batch, regardless of other customers of the batch, immediately moves to another node in accordance with the routing probability. This article presents an analysis of the queueing network using a Markov chain with continuous time. The qenerator matrix is constructed for the underlying Markov chain. We obtain expressions for the performance measures. Some numerical examples are provided. The results can be used for the performance analysis manufacturing systems, passenger and freight transport systems, as well as information and computing systems with parallel processing and transmission of information.

An unreliable open queueing network with Poisson arrivals is considered. For each queueing system the service and failures times are exponentially distributed random variables. The failures of systems lead to changes in the structure of the network and corresponding changes in the performance measures of the queueing network. It is assumed that the times between changes in the network structure are sufficient for the steady-state regime. The main measure of the quality for the network at each structure constancy interval is the average response time. Repairs of all queueing systems occur immediately when the average response time becomes greater than the threshold value. This article presents a method of the network analysis using continuous time Markov chains. It is shown that the steady-state probability distribution of the unreliable queueing network has a product form solution. Expressions for the stationary performance measures of queueing systems and the network including the average of system repair time intervals are obtained. A numerical example to investigate the dependence of the performance measures on some network parameters is demonstrated.

The process of aircraft operation involves constant effects of various factors on its components leading to accidental or systematic changes in their technical condition. Markov processes are a particular case of stochastic processes, which take place during aeronautical equipment operation. The relationship of the reliability characteristics with the cost recovery of the objects allows us to apply the analytic apparatus of Markov processes for the analysis and optimization of maintainability factors. The article describes two methods of the analysis and control of object maintainability based on stationary and non-stationary Markov chains. The model of a stationary Markov chain is used for the equipment with constant in time intensity of the events. For the objects with time-varying events intensity, a non-stationary Markov chain is used. In order to reduce the number of the mathematical operations for the analysis of aeronautical engineering maintainability by using non-stationary Markov processes an algorithm for their optimization is presented. The suggested methods of the analysis by means of Markov chains allow to execute comparative assessments of expected maintenance and repair costs for one or several one-type objects taking into account their original conditions and operation time. The process of maintainability control using Markov chains includes search of the optimal strategy of maintenance and repair considering each state of an object under which maintenance costs will be minimal. The given approbation of the analysis methods and maintainability control using Markov processes for an object under control allowed to build a predictive-controlled model in which the expected costs for its maintenance and repair are calculated as well as the required number of spare parts for each specified operating time interval. The possibility of using the mathematical apparatus of Markov processes for a large number of objects with different reliability factors distribution is shown. The software implementation of the described methods as well as the usage of tabular adapted software will contribute to reducing the complexity of the calculations and improving data visualization.

The paper is devoted to solving the problem of identifying discrete stochastic processes generated on the basis of automata Markov models. This problem is relevant because of the need to increase the efficiency of automata Markov models recognition. The effectiveness of identifying automata Markov models with a certain confidence probability is determined by the decrease in the length of Markov chains, as well as by the decrease in the computational complexity of algorithms for recognizing and minimizing the error in calculating traits relative to the ergodic stochastic matrices that define automata Markov models. The modified model allows to determine the probability values that a sequence is generated on the basis of the automata Markov model of the given class, which, in turn, is determined by the structure of the stochastic matrix. A feature of this model is the ability of the algorithm to recognize the class of the automata Markov model in the case when some states are not observable in the generated sequence. A modification of the “forward-backward” algorithm and its adaptation to the problem of identification of automata Markov models defined using ergodic stochastic matrices on the basis of the realizations of Markov chains generated by them has been proposed. In the paper, the task of modifying the “forward-backward” algorithm for automata Markov models determined on the basis of cyclic ergodic stochastic matrices has been solved. The estimates of the computational complexity of the proposed identification algorithms have been calculated. The most important of the results obtained are the following. A feature of this model is the ability of the algorithm to recognize the class of the automata Markov model in the case when some states are not observable in the generated sequence. The results obtained make it possible to better identify the automata Markov models by the output sequence. This problem can be applied to solve a wide range of problems of identification of Markov chains, including partially hidden ones.

The abolition of the administrative regulation of economic activity in Russia has triggered the processes of its territorial concentration, leading to the polarization of regions in terms of economic activity. From the theoretical point of view, the territorial concentration of production contributes to an increase in labor productivity. At the same time, the concentration of economic activity leads not only to the growth of productivity in regions of concentration of production, but also influences neighboring territories. The main purpose of this article is to study the dynamics of labor productivity in the regions of the Russian Federation in connection with the ongoing processes of concentration of economic activity, as well as the role of spatial external effects in the dynamics of regional indicators of productivity. The paper uses statistical methods of analysis and an approach to the study of inequality and dynamics of regional distribution based on the use of Markov chains. Conclusions are drawn about the faster growth of labor productivity in regions of concentration of economic activity, about the polarization of regions by the level of labor productivity, and about spatial external effects generated by regional economies with high productivity. The character of these external effects depends on the degree of regional differences. Spatial effects are negative when regional differences are significant, while positive effects manifest when differentiation of regional economies in terms of labor productivity is low.

In this article a statistical analysis of supply volumes of spare parts, components and accessories was carried out, with some persistent patterns and laws of distribution of failures of major components revealed. There are suggested evaluation models of components and assemblies reliability for the formation of order management procedures of spare parts, components and accessories for the maintenance and repair of transport and technological machines. For the purpose of identification of components operational condition there is proposed a model of hidden Markov chain which allows to classify the condition by indirect evidence, based on the collected statistics.

Technical operation of the aircraft and its avionics is investigated as a process with the succession of states of operation. The models of the processes and systems of technical operation of avionics in the form of stationary and non-stationary Markov chains of the first and higher order are proposed. There are examples of the processes for two states of operation - able to work and disabled states.

Using Markov chains the author studies peculiarities of the process of spatial concentration of economic activity in Russia during the period of 2001-2014 as well as the role of spatial external effects in the mentioned process. The researcher concludes following: a) the predominance of economic activity concentration over its dissemination; b) the existence of ‘trap of backwardness’, and as a result significant concentration of economic activity in a small number of regions with simultaneous formation of a large pole of relative backwardness in prospect. The growing inequality of Russian regions in terms of economic activity leads to their polarization, although the speed of this process is very mild. Analysis of spatial effects showed that their peculiarities depend on relative differences in the development of regions and their nearest neighbors, and that high differentiation of regions in terms of economic activity prevents the development of backward regions and contributes to further polarization. In such circumstances, the regional policy aimed at stimulating the developed regions can only reinforce the ongoing process of polarization, and the policy aimed at the emergence of competitive cooperation of regions and limiting the growth of regional inequalities seems to be more appropriate

In this article a polynomial algorithm is described of verification of dynamic properties of Markov chains described by formulas of a subset of temporal logic PLTL (propositional temporal logic of linear time). The algorithm allows to find probability of the validity of the formula on the Markov chain, and also set of trajectories on which the verified formula is true.

The article considers a probabilistic approach to the model of the commodity-money time distribution of the budget of an investment project between enterprises on the basis of Markov chains (discrete model) and on the basis of the system of linear differential equations (continuous model). In order to solve the discrete model, the z-transform method is used, and for solution of the continuous model – the Laplace transform is used. The stochastic matrix of Markov chains completely identifies the discrete model of distribution of the budget of an investment project between enterprises, and the differential matrix – the continuous model of this distribution. The use of z-transform and Laplace transform allows finding a solution of tasks in the analytical form. The obtained expressions simplify analysis and calculation of states of the system compared to other methods. The article establishes interconnection between the discrete and continuous models, in other words, solutions of these tasks are similar if t = n.

The article considers a probabilistic approach to the deficit model of distribution of financial resources between executors of investment projects in the closed system on the basis of Markov chains, which takes into account processes of sales (receipt of money) and purchases (expenditures). This process takes into account influence of local administration, which could result in levelling financial states of project executors. The stochastic matrix of Markov chains provides with a possibility to study every step of the studied process. The use of the z-transformation method allows avoiding difficulties, which arise due to multiplicity of own values of stochastic matrices and gives a possibility to obtain an analytical form of turnover of financial resources in the period under consideration. The obtained expression simplifies analysis and calculation of states of the system compared to other models. The article identifies conditions of interaction of project executors with external systems and volumes of financial resources, which could be planned for exchange at each step of the process.Рассмотрен вероятностный подход к дефицитной модели распределения финансовых ресурсов между исполнителями инвестиционных проектов в закрытой системе на базе цепей Маркова, которая учитывает процессы продаж (получение денег) и покупок (трата денег). В этом процессе учтено влияние местной администрации, которое может приводить к выравниванию финансовых состояний исполнителей проектов. Стохастическая матрица цепей Маркова представляет возможность изучить каждый шаг исследуемого процесса. Использование метода z–преобразования позволяет обойти трудности, которые возникают вследствие кратности собственных значений стохастических матриц и дает возможность получить аналитическую форму оборота финансовых ресурсов в рассматриваемый период. Полученное выражение упрощает анализ и расчет состояний системы по сравнению с другими моделями. Определены условия взаимодействия исполнителей проектов с внешними системами и величины финансовых ресурсов, которые можно планировать для обмена на каждом шаге процесса.

The article presents a simulation cobweb model of price formation with delayed supply. It considers cases with absence and availability of random factors. Randomness is presented in the model as a concept of games with nature with the use of Markov chains. The article studies activity of the retail link in the described environment. [ABSTRACT FROM AUTHOR]

Using long-term direct observations in a Polytrichum-Myrtillus pine forest, we have constructed and verified a homogeneous Markov chain model for two dominant species (Vaccinium myrtillus and V. vitis-idaed) at the late stages of succession. The sampling design features a large sample size (2000 quadrats) on permanent transects, several re-examinations with the interval of 5 years, and the use of species rooted frequency. As a model of the process under concern, the discrete Markov chain accounts for the following four states: both species being absent on the quadrat, one of them being present alone, and the joint presence of the both; the model time step coincides with the time interval between observations. The model is calibrated on the data of two successive examinations and verified on that of one more examination. All possible transitions between the states are revealed to realize in quadrats for one time interval, as well as the absence of transitions at each state, which results in the complete digraph (directed graph) of transitions. Major model results are obtained by the formulae of finite Markov chain theory: the steady-state square distribution, cyclicity characteristics, and the mean durations of stages in the fine-scale dynamics. As a steady-state (stable) outcome of succession, the distribution among quadrats is expected where 30% of quadrats are occupied by V. myrtillus alone, 11% by V. vitis-idaea alone, both species are present on 18% of quadrats, and 41% of quadrats are 'empty'. This demonstrates a possibility for V. myrtillus and V. vitis-idaea to coexist stably at the latest stages of succession, with the clear predominance of V. myrtillus, yet without competitive exclusion. The quantitative characteristics of cyclicity and the durations of stages in the fine-scale dynamics enable us to estimate the total duration of secondary post-fire succession as about 45 years (to reach a distribution of states that differs less than 5% from the steady-state one). Out of the four states specified, the quadrats with V. vitis-idaea alone persist for the least time (8 years) on the average, while 'empty' ones persist for the greatest time (18 years). Forecasting the dynamics for one model time step forward and comparing the forecast with the real square distribution have revealed the measure of difference to be 5.4%. This illustrates the efficiency of the (time-)homogeneous Markov chain as a short-term forecast tool, yet leaves open the question whether the homogeneity hypothesis be true in the longer term.

A microRNA (miRNA) is a small noncoding RNA molecule about 22 nucleotides in length. The paper describes a web server for predicting miRNAs and their precursors and binding sites. The predictions are based on either sequence similarity to known miRNAs of 223 organisms or context-structural hidden Markov models. It has been shown that the proposed methods of prediction of human miRNAs and pre-miRNAs outperform the existing ones in accuracy. The average deviation of predicted 5'-ends of human miRNAs from actual positions is 3.13 nt in the case of predicting one pair of complementary miRNAs (miRNA-miRNA* duplex). A useful option for our application is the prediction of an additional miRNA pair. In this mode, the pairs closest to actual miRNA deviate by 1.61 nt on average. The proposed method also shows good performance in predicting mouse miRNAs. Binding sites for miRNAs are predicted by two known approaches based on complementarity and thermodynamic stability of the miRNA-mRNA duplex and on a new approach, which takes into account miRNAs competition for the site. The role of the secondary structure in miRNA processing is considered. The web server is available at http://wwwmgs.bionet.nsc.ru/mgs/programs/rnaanalys/.

The refined Markov model of cyclic zoogenic successions caused by beaver (Castor fiber L.) life activity represents a discrete chain of the following six states: flooded forest, swamped forest, pond, grassy swamp, shrubby swamp, and wet forest, which correspond to certain stages of succession. Those stages are defined, and a conceptual scheme of probable transitions between them for one time step is constructed from the knowledge of beaver behaviour in small river floodplains of "Bryanskii Les" Reserve. We calibrated the corresponding matrix of transition probabilities according to the optimization principle: minimizing differences between the model outcome and reality; the model generates a distribution of relative areas corresponding to the stages of succession, that has to be compared to those gained from case studies in the Reserve during 2002-2006. The time step is chosen to equal 2 years, and the first-step data in the sum of differences are given various weights, w (between 0 and 1). The value of w = 0.2 is selected due to its optimality and for some additional reasons. By the formulae of finite homogeneous Markov chain theory, we obtained the main results of the calibrated model, namely, a steady-state distribution of stage areas, indexes of cyclicity, and the mean durations (M(j)) of succession stages. The results of calibration give an objective quantitative nature to the expert knowledge of the course of succession and get a proper interpretation. The 2010 data, which are not involved in the calibration procedure, enabled assessing the quality of prediction by the homogeneous model in short-term (from the 2006 situation): the error of model area distribution relative to the distribution observed in 2010 falls into the range of 9-17%, the best prognosis being given by the least optimal matrices (rejected values of w). This indicates a formally heterogeneous nature of succession processes in time. Thus, the refined version of the homogeneous Markov chain has not eliminated all the contradictions between the model results and expert knowledge, which suggests a further model development towards a "logically inhomogeneous" version or/and refusal to postulate the Markov property in the conceptual scheme of succession.

A homogeneous Markov chain of three aggregated states "pond--swamp--wood" is proposed as a model of cyclic zoogenic successions caused by beaver (Castor fiber L.) life activity in a forest biogeocoenosis. To calibrate the chain transition matrix, the data have appeared sufficient that were gained from field studies undertaken in "Bryanskii Les" Reserve in the years of 2002-2008. Major outcomes of the calibrated model ensue from the formulae of finite homogeneous Markov chain theory: the stationary probability distribution of states, thematrix (T) of mean first passage times, and the mean durations (M(j)) of succession stages. The former illustrates the distribution of relative areas under succession stages if the current trends and transition rates of succession are conserved in the long-term--it has appeared close to the observed distribution. Matrix T provides for quantitative characteristics of the cyclic process, specifying the ranges the experts proposed for the duration of stages in the conceptual scheme of succession. The calculated values of M(j) detect potential discrepancies between empirical data, the expert knowledge that summarizes the data, and the postulates accepted in the mathematical model. The calculated M2 value falls outside the expert range, which gives a reason to doubt the validity of expert estimation proposed, the aggregation mode chosen for chain states, or/and the accuracy-of data available, i.e., to draw certain "lessons" from partially successful calibration. Refusal to postulate the time homogeneity or the Markov property of the chain is also discussed among possible ways to improve the model.

Aim of this study was to evaluate the cost-effectiveness of renal denervation (RD) in resistant arterial hypertension (AH) in Russia. Modeling of Markov conducted economic impact of RD on the Russian population of patients with resistant hypertension in combination with optimal medical therapy (OMT) compared with OMT using a model developed by American researchers based on the results of international research. The model contains data on Russian mortality, and costs of major complications of hypertension. The simulation results showed a significant reduction in relative risk reduction of adverse outcomes in patients with resistant hypertension for 10 years (risk of stroke is reduced by 30%, myocardial infarction - 32%). RD saves 0.9 years of quality-adjusted life (QALY) by an average of 1 patient with resistant hypertension. Costs for 1 year stored in the application of quality of life amounted to RD 203 791.6 rubles. Which is below the 1 gross domestic product and therefore indicates the feasibility of this method in Russia.

The paper considers the properties of individual life history corresponding to the Leslie model of age-structured population. The life history is simulated as a finite Markov chain with absorption at a death state of individual. In this model, individual longevity, average number of offspring R(L) (produced by an individual over the entire life), and some other known parameters of the life history have been derived using simple probability methods that do not involve matrix calculus and their individual components have been interpreted. In the Leslie linear population model (derived by simple modification of a Markov chain), R(L) determines the growth or decline of a population. Individuals with higher R(L) values have evolutionary advantages in the population due to accelerated growth in their number The selection of fertility as a factor of the increase in R(L) is considered. In the Leslie model, fertility is a set of correlated quantitative traits, where the age-specific fertility components determined both by multipl loci and the environment. According to the genetic theory of quantitative trait selection, they evolve towards an increase in R(L). Taking into account the limited resources for reproduction, selection optimizes the fertility distribution according to age. Optimal distribution corresponds to the attainment of the maximum R(L). This complies with the maximization of the rate of population growth (r-selection), which is characteristic of linear population models. The search for the RL maximum and optimal distribution of fertility belongs to the field of linear programming.

The goal of this work was to describe an automated system for classification of human sleep stages. Classification of sleep stages is an important problem of diagnosis and treatment of human sleep disorders. The developed classification method is based on calculation of characteristics of the main sleep rhythms. It uses hidden Markov models. The method is highly accurate and provides reliable identification of the main stages of sleep. The results of automatic classification are in good agreement with the results of sleep stage identification performed by an expert somnologist using Rechtschaffen and Kales rules. This substantiates the applicability of the developed classification system to clinical diagnosis.

The genetic differentiation in population with migration according island and two-dimensional stepping stone models was studied with simulation methods. It is shown that migration of one or few individuals per generation is insufficient for leveling differences between subpopulations in allele frequencies. Even if migration is estimated as m = 0.5 (exchange of 50 and 500 individuals per generation) statistically significant differences remain at least in the half of populations with insular structure. Spatial heterogeneity disappears completely only if m = 0.7-0.8. In case of two-dimensional step model the level of genetic differentiation is higher and statistically significant heterogeneity remains at all levels of genetic exchange including that which was estimated as m = 1.

The paper represents an attempt to apply the general principles of modelling vegetation dynamics under climate changes to a study of the long-term vegetation dynamics in the forest-steppe zone of the European territory of Russia, with a purpose to forecast under special climatic scenarios. An original technique is used to construct a Markov chain as a model of vegetation succession. The technique emanated from gebotanic knowledge generalized as a scheme of successional transitions with estimates of the average duration for certain stages of succession. Whenever the knowledge related the stage duration to certain (climate-sensitive) factors of the environment, the fundamental potentiality arises to model the temporal course of succession as a function of a given scenario for how the key factors change. In the formal terms, the model represents a random chain of the Markov kind with a finite number of states and discrete time of transitions by the given scheme. Relative square distributions of succession stages under concern at any time moment (within an adopted scenario) appear as the model outcome (forecasts), as well as estimates of the attainment time for certain states of the vegetation in the territory under study. A method is proposed to describe dynamics of the phytomass production and stores (and the corresponding model trajectories are obtained) for a given scenario.

The chemical structure of DNA is characterized by sequences of four basic nitrogens occurring in one of two nucleic acid chains and in a complementary fashion in the other. Markov chain is the aspect of probability theory that analyzes discrete states in which transition is a fixed probability not affected by the history of the system. It is shown that DNA is represented in the form of regular Markov chain. Ergodicity property and law of large numbers follow from the statistical analysis of stationary transition probabilities.

Aim: To design Markov's model of decision making to study the role of order in the use of most usable basic antirheumatic drugs (methotrexate-MT, parenteral gold--PG and sulfasalasine--SS) in terms of the course duration and cost., Material and Methods: The model was based on metaanalysis made in 2000. The program TreeAge 3.0 was used. The prices for the drugs were taken as mean about Moscow for 2002 and prices presented by ACR for 2002., Results: The sequence MT-PG-SS had the advantage over the other sequences in that less number of patients stopped treatment after 5 and 10 years of therapy. Mean cost of the drugs per patient is the lowest (for five years) if MT is prescribed first. In longer treatment SS-MT-PG is more cost-effective., Conclusion: It is feasible to design Markov's models for making decision on optimal therapy of rheumatoid arthritis both in terms of cost and clinical response.

A stochastic model of localized adsorption of particles on the membrane was constructed. In the model, the transitional processes were neglected, and adsorption was represented as a stationary Markov process. In the framework of this approach, stationary values of average numbers of particles, there dispersion, correlation function, and spectral density were estimated. It was shown that the comparison of theoretical and experimental correlation functions (or spectral density) enables one to obtain new information about the adsorption parameters, namely: formation and decomposition rate constants for a complex of an adsorbed particle with the absorption center.

A new type of selective models extending the possibilities of the existing methods of radiation hybrid mapping has been developed. These models are intended for mapping a "combined" group of genes. The genes are detected in a given clone by either direct molecular genetic methods or methods of isozyme analysis, which allow the gene to be detected indirectly, i.e., by the presence of its protein product. This type of selective models allows for both strict and nonstrict retention of the selective gene in the hybrid clone (the strictly and nonstrictly selective media, respectively). Asymptotic properties of the new type of models have been studied. It has been demonstrated that all of them are pseudo-Markovian and additive and may be used for mapping an unrestricted number of genes. The minimum numbers of genes being localized for which different variants of the models hold true have been estimated.

The paper proposes a mathematical model of development of a cell population with a changing proliferative activity. The model is based on the Markov branching process with cells of several types. A procedure for identifying the constructed model by experimental evidence is being developed. An example of model construction and assessment for cultured diploid fibroblasts is given.

The article deals with the epidemiological model and the corresponding mathematical model of the spread of hospital infection. The mathematical apparatus of Markov's heterogeneous chain is used. The model may be used for the analysis and planning of antiepidemic measures, as well as for the evaluation of their effectiveness. The conditions for the possibility of the application of the newly developed mathematical model have been formulated. The method for calculating the parameters of the model on the basis of data on morbidity in different forms of hospital infection is presented. An example of using the above model for the analysis of the data of observation is considered in detail.