All issues

In this article the experience of reading “CUDA and OpenCL programming” course during high perfomance computing summer school MIPT-2010 is analyzed. Content of lectures and practical tasks, as well as manner of presenting of the material are regarded. Performance issues of different algorithms implemented by students at practical training session are dicussed.

A computer model describing the spatial-temporal dynamics of populations of interacting with renewable resource is proposed. The life cycle of the individual is described. The algorithm for spatial mobility of individuals within an area is proposed, which takes into account nutritional and social activity. The paper presents the computational experiments with the model that mimic the movement of herds of animals in the area, and describes the model experiment when the group type of animal behavior due to changes in the characteristics of the environment and animal behavior the herd animals is formed, which later goes again in the group type of animal behavior.

The paper investigates the features of group dynamics of individuals-agents in the computer model of the animal population interacting with each other and with a renewable resource. This type of dynamics was previously found in [Belotelov, Konovalenko, 2016]. The model population consists of a set of individuals. Each individual is characterized by its mass, which is identified with energy. It describes in detail the dynamics of the energy balance of the individual. The habitat of the simulated population is a rectangular area where the resource grows evenly (grass).

Various computer experiments carried out with the model under different parameter values and initial conditions are described. The main purpose of these computational experiments was to study the group (herd) dynamics of individuals. It was found that in a fairly wide range of parameter values and with the introduction of spatial inhomogeneities of the area, the group type of behavior is preserved. The values of the model population parameters under which the regime of spatial oscillations of the population occurs were found numerically. Namely, in the model population periodically group (herd) behavior of animals is replaced by a uniform distribution over space, which after a certain number of bars again becomes a group. Numerical experiments on the preliminary analysis of the factors influencing the period of these solutions are carried out. It turned out that the leading parameters affecting the frequency and amplitude, as well as the number of groups are the mobility of individuals and the rate of recovery of the resource. Numerical experiments are carried out to study the influence of parameters determining the nonlocal interaction between individuals of the population on the group behavior. It was found that the modes of group behavior persist for a long time with the exclusion of fertility factors of individuals. It is confirmed that the nonlocality of interaction between individuals is leading in the formation of group behavior.

The number of papers addressing the forecasting of the infectious disease morbidity is rapidly growing due to accumulation of available statistical data. This article surveys the major approaches for the shortterm and the long-term morbidity forecasting. Their limitations and the practical application possibilities are pointed out. The paper presents the conventional time series analysis methods — regression and autoregressive models; machine learning-based approaches — Bayesian networks and artificial neural networks; case-based reasoning; filtration-based techniques. The most known mathematical models of infectious diseases are mentioned: classical equation-based models (deterministic and stochastic), modern simulation models (network and agent-based).

Investigation of logical deterministic cellular automata models of population dynamics allows to reveal detailed individual-based mechanisms. The search for such mechanisms is important in connection with ecological problems caused by overexploitation of natural resources, environmental pollution and climate change. Classical models of population dynamics have the phenomenological nature, as they are “black boxes”. Phenomenological models fundamentally complicate research of detailed mechanisms of ecosystem functioning. We have investigated the role of fecundity and duration of resources regeneration in mechanisms of population growth using four models of ecosystem with one species. These models are logical deterministic cellular automata and are based on physical axiomatics of excitable medium with regeneration. We have modeled catastrophic death of population arising from increasing of resources regeneration duration. It has been shown that greater fecundity accelerates population extinction. The investigated mechanisms are important for understanding mechanisms of sustainability of ecosystems and biodiversity conservation. Prospects of the presented modeling approach as a method of transparent multilevel modeling of complex systems are discussed.

Migration has a significant impact on the shaping of the demographic structure of the territories population, the state of regional and local labour markets. As a rule, rapid change in the working-age population of any territory due to migration processes results in an imbalance in supply and demand on labour markets and a change in the demographic structure of the population. Migration is also to a large extent a reflection of socio-economic processes taking place in the society. Hence, the issues related to the study of migration factors, the direction, intensity and structure of migration flows, and the prediction of their magnitude are becoming topical issues these days.

Mathematical tools are often used to analyze, predict migration processes and assess their consequences, allowing for essentially accurate modelling of migration processes for different territories on the basis of the available statistical data. In recent years, quite a number of scientific papers on modelling internal and external migration flows using mathematical methods have appeared both in Russia and in foreign countries in recent years. Consequently, there has been a need to systematize the currently most commonly used methods and tools applied in migration modelling to form a coherent picture of the main trends and research directions in this field.

The presented review considers the main approaches to migration modelling and the main components of migration modelling methodology, i. e. stages, methods, models and model classification. Their comparative analysis was also conducted and general recommendations on the choice of mathematical tools for modelling were developed. The review contains two sections: migration modelling methods and migration models. The first section describes the main methods used in the model development process — econometric, cellular automata, system-dynamic, probabilistic, balance, optimization and cluster analysis. Based on the analysis of modern domestic and foreign publications on migration, the most common classes of models — regression, agent-based, simulation, optimization, probabilistic, balance, dynamic and combined — were identified and described. The features, advantages and disadvantages of different types of migration process models were considered.

This paper discusses the modeling of the deformation of polymer nanocomposites containing "hard" and "soft" inclusions, using cellular automata and parallel computing. The paper describes an algorithm based on the model, a comparison with experimental data is shown, software for the numerical experiment is described.

The paper considers an earlier proposed by the author discrete modification of the A. P. Mikhailov “power – society” model. The modification is based on a stochastic cellular automaton, it’s microdynamics being completely different from the c continuous model based on differential equations. However, the macrodynamics of the discrete modification is shown in previous works to be equivalent to one of the continuous model. This is important, but at the same time raises the question why use the discrete model. The answer lies in its flexibility, which allows adding a variety of factors, the consideration of which in a continuous model either leads to a significant increase in computational complexity or is simply impossible.

This paper considers several examples of such applicability expansion of the model, with the help of which a number of applied problems are solved.

One of the modifications of the model takes into account economic ties between regions and municipalities, which could not be studied in the basic model. Computational experiments confirmed the improvement of the socio-economic indicators of the system under the influence of the ties.

The second modification allows internal migration in the system. Using it we studied the socio-economic development of a more prosperous region that attracts migrants.

Next we studied the dynamics of the system while the number of regions and municipalities changes. The negative impact of this process on the socio-economic indicators of the system was shown and possible control was found to overcome this negative impact.

The results of this study, therefore, include both the solution of some applied problems and the demonstration of the broader applicability of the discrete model compared with the continuous one.

In this paper we consider a new modification of the discrete version of Mikhailov’s ‘power–society’ model, previously proposed by the author. This modification includes social-economical dynamics and corruption of the system similarly to continuous ‘power–society–economics–corruption’ model but is based on a stochastic cellular automaton describing the dynamics of power distribution in a hierarchy. This new version is founded on previously proposed ‘power–society’ system modeling cellular automaton, its cell state space enriched with variables corresponding to population, economic production, production assets volume and corruption level. The social-economical structure of the model is inherited from Solow and deterministic continuous ‘power–society–economics–corruption’ models. At the same time the new model is flexible, allowing to consider regional differentiation in all social and economical dynamics parameters, to use various production and demography models and to account for goods transit between the regions. A simulation system was built, including three power hierarchy levels, five regions and 100 municipalities. and a number of numerical experiments were carried out. This research yielded results showing specific changes of the dynamics in power distribution in hierarchy when corruption level increases. While corruption is zero (similar to the previous version of the model) the power distribution in hierarchy asymptotically tends to one of stationary states. If the corruption level increases substantially, volume of power in the system is subjected to irregular oscillations, and only much later tends to a stationary value. The meaning of these results can be interpreted as the fact that the stability of power hierarchy decreases when corruption level goes up.

The article dwells upon investigating the issue of the most adequate tools developing and justifying to forecast the interregional migration flows value and structure. Migration processes have a significant impact on the size and demographic structure of the population of territories, the state and balance of regional and local labor markets.

To analyze the migration processes and to assess their impact an economic-mathematical tool is required which would be instrumental in modelling the migration processes and flows for different areas with the desired precision. The current methods and approaches to the migration processes modelling, including the analysis of their advantages and disadvantages, were considered. It is noted that to implement many of these methods mass aggregated statistical data is required which is not always available and doesn’t characterize the migrants behavior at the local level where the decision to move to a new dwelling place is made. This has a significant impact on the ability to apply appropriate migration processes modelling techniques and on the projection accuracy of the migration flows magnitude and structure.

The cellular automata model for interregional migration flows modelling, implementing the integration of the households migration behavior model under the conditions of the Bounded Rationality into the general model of the area migration flow was developed and tested based on the Primorye Territory data. To implement the households migration behavior model under the conditions of the Bounded Rationality the integral attractiveness index of the regions with economic, social and ecological components was proposed in the work.

To evaluate the prognostic capacity of the developed model, it was compared with the available cellular automata models used to predict interregional migration flows. The out of sample prediction method which showed statistically significant superiority of the proposed model was applied for this purpose. The model allows obtaining the forecasts and quantitative characteristics of the areas migration flows based on the households real migration behaviour at the local level taking into consideration their living conditions and behavioural motives.