Institute of Applied Mathematical Research of the Karelian Research Centre of the Russian Academy of Sciences

Desktop grids utilize idle computational resources within a research organization. Task scheduling is a very important issue for a desktop grid due to its significant impact on computational performance. In the paper we propose a game-theoretical model of task scheduling in a desktop grid. The model allows to consider the trade-off between the server load and the total time of computations. The numerical results based on a virtual drug screening project are presented, and the Nash equilibrium is found.

Рассматриваются случайные леса Гальтона-Ватсона с $N$ корневыми деревьями и $n$ некорневыми вершинами. Распределение числа прямых потомков генерирующего лес критического однородного ветвящегося процесса имеет бесконечную дисперсию. Такие ветвящиеся процессы используются для исследования структуры случайных конфигурационных графов, предназначенных для моделирования сложных сетей коммуникаций. В работе доказаны теоремы о предельных распределениях числа деревьев заданного объема при различном характере стремления $N$ и $n$ к бесконечности.

“Work-stealing” is one of the most common methods of parallel task balancing. In this method, each core (processor) has a buffer of its tasks—a double-ended queue called “deque”. A core (processor) use one end of the deque to add new tasks or to take already available to execute them. The second end of the deque is accessible by other cores (processors), which have become empty and can intercept tasks—this is the mechanism of “work-stealing”. Algorithms and techniques for the high-performance big data processing are becoming increasingly sought after not only for storing databases but also for the proper handling of big data from a variety of domains such as science and engineering. Models and algorithms of optimal control of large deques belong to this area of research. The goal of this work is to develop, analyze and compare the models and methods of control of work-stealing deques in limited shared memory. For the case of three deques, the following control methods will be discussed: 1. Each of the three deques is located in its separate memory area; 2. Three deques move one after another in a circle; 3. Combined method—two deques are located one after another, one separately. To solve the posed problems, controlled random walks and simulation modeling were used.

We consider Galton–Watson random forests with $$N$$ rooted trees and $$n$$ nonroot vertices. The distribution of the number of offspring of the critical homogeneous branching process generating a forest has infinite variance. Such branching processes are used in the study of the structure of random configuration graphs designed for simulating complex communication networks. We prove theorems on the limit distributions of the number of trees of a given size for various relations between $$N$$ and $$n$$ as they tend to infinity.

According to the portal Math-Net.Ru a graph of journal citation is constructed. To increase the reliability of the model, the citation time interval was chosen from 2010 to 2021, when the distribution of citation articles stabilized at the level of 3500-4500 citations per year. The structure of link aging is studied and it is shown that their half-life is equal to 8 years. Therefore, the publication date of the cited articles was limited to 2002. For the constructed citation graph, the main properties, such as a small diameter and a high density, are obtained, indicating a high level of scientific communication in the Math-Net.Ru. Adequacy of the journal citation graph Math-Net.Ru as a model of scientific communication confirmed by comparing the ranking of journals in the citation graph with their SCIENCE INDEX rating in eLIBRARY.RU. A direct moderate relationship between the two rankings is shown. A number of meaningful conclusions are drawn from the analysis of the citation graph.

In this paper, we present the investigations developing the schumpeterian theory of endogenous evolution of economic systems. The proposed approach allows to simulate the emergence and propagation of new technologies. We develop a mathematical model of dynamics of sector capital distribution over efficiency levels on the base of the system of nonlinear differential equations. In order to take into account the boundedness of the economic growth conditioned by the boundedness of the markets, the resource base and other factors, we introduce the notion of economical niche volume. The scenario of the emergence of the new highest efficiency level is proposed. In order to simulate the process of the emergence of the new highest efficiency level, the notion of intellectual capital is proposed. According to the proposed scenario, the new level emerges when the intellectual capital achieves the threshold value. Herewith, the dimension of the dynamic system is varied. The necessary condition for the functioning of the new level is formulated. The invariant set of the dynamic system is defined. The local stability of the equilibria is investigated. The global stability of the dynamic system is established on the base of a geometrical method. The proposed models allow to evaluate and predict the dynamics of the technological levels of the economic sector firms development.

One of the technological challenges for hydrogen materials science is the currently active search for structural materials with important applications (including the ITER project and gas-separation plants). One had to estimate the parameters of diffusion and sorption to numerically model the different scenarios and experimental conditions of the material usage (including extreme ones). The article presents boundary value problems of hydrogen permeability and thermal desorption with dynamical boundary conditions. A numerical method is developed for TDS spectrum simulation, where only integration of a nonlinear system of low order ordinary differential equations is required. The main final output of the article is a noise-resistant algorithm for solving the inverse problem of parametric identification for the aggregated experiment where desorption and diffusion are dynamically interrelated (without the artificial division of studies into the diffusion limited regime (DLR) and the surface limited regime (SLR)).

The web graph is the most common mathematical model of a website. Constructing a web graph of a real site requires data about the structure of that site: html-pages and/or documents in the site (in particular, data about URLs of web resources) and hyperlinks linking them. Web servers often use pseudonyms and redirections. They also generate the same pages dynamically via different URL requests. This raises a problem in which there are various URLs but with the same content. Thus, we can get a web graph in which some of its vertices correspond to pages of a site with the same content. The paper describes a crawler called RCCrawler that collects information about websites to build the web graphs of these sites. This crawler largely addresses the above problem as confirmed by a series of experiments conducted.

This paper analyzes the problem of optimal control of two work-stealing deques in two-level memory (for example, registers—random access memory), where probabilities of parallel operations with deques are known. The classic sequential cyclic method for representing a deque in memory is considered. In the case of the deque overflowing in fast memory or emptying the FIFO-part or LIFO-part the necessary exchanges between fast and slow memory and shifts of elements in fast memory occur for relocation to the optimal state, which to be found. The task is to find the optimal partition of the total fast memory for deques and to determine the optimal state of each deque in each partition after the memory reallocation, i.e., to find the optimal number of elements, taken from both sides of the deque, to leave in the fast memory if the deque is filled or emptied. Optimality criteria for memory sharing is to maximize the sum of the mean operating times of each deque before the memory is redistributed and to maximize the lowest mean operating time of each deque before the memory is redistributed. The mathematical model in the form of an absorbing Markov chain are constructed. Simulation modeling, based on the proposed mathematical model, was carried out. The results of numerical experiments are presented.

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В данной работе рассматривается задача миграции населения РФ между тремя группами федеральных округов. В первую группу вошли Центральный и Северо-Западный, во вторую — Дальневосточный, Уральский и Сибирский, в третью — Южный, Приволжский и Северо-Кавказский федеральные округа. Предложена модель динамики численностей населения с учетом распределения Больцмана, которое описывает распределение мигрирующего населения по трем заданным территориям. Предложена функция полезности, входящая в распределение Больцмана и, так же предложена, входящая в функцию полезности, мера информированности (притягательности) населения по отношению к рассматриваемым территориям. При этом, мера информированности учитывает экономический фактор — долю населения, живущего выше прожиточного минимума и общую численность населения на рассматриваемых группах федеральных округов. Предполагается, что чем больше общая численность населения на данной территории, тем больше информации об этой территории имеется. Проводится идентификация параметров, характеризующих коэффициенты естественного прироста и доли мигрирующего населения рассматриваемых территорий при различных значениях параметра, характеризующего оптимальность распределения населения по трем заданным территориям. Идентификация параметров модели реализована с помощью метода градиентного спуска с дроблением шага на языке программирования Python3.5. Так же для реализации идентификации параметров использовались данные из официальных статистических источников. На основе проведенной идентификации получены значения распределения Больцмана и миграционных потоков между тремя группами федеральных округов, проведено сравнение модельных данных с реальными, построен прогноз численностей населения для каждой территории. Показано, что значение параметра оптимальности влияет на прогноз численности населения всех трех групп федеральных округов.

The paper analyses the problem of optimal control of several parallel FIFO-queues located in two-level memory (for example, registers—random access memory). The probabilities of parallel operations with each queue are assumed to be known. Our task was to optimally partition the total fast memory between FIFO-queues and to determine for each queue in each partition the number of fast memory elements after redistributions, so that the mean time between queue redistributions is maximized. As optimality criteria for memory sharing, we consider the maximum sum of the average operating times of each queue before the memory is redistributed and the maximum shortest average operating time of each queue before the memory is redistributed. The mean time was calculated on the basis of a simulation model and on the basis of a model of an absorbing Markov chain.

One of the most important requirements for the reactor's active zone materials (made of zirconium alloys) is low hydrogen absorptivity since hydrogen embrittlement may cause zirconium cladding damage. Depending on the hydrogen content and operation temperature, hydrogen may be present in zirconium alloys as a solid solution or as hydrides. Hydrides have the greatest embrittlement effect on alloys as they can form and enlarge cracks. The problem is to model the dynamics of the moving boundary of phase transition and to estimate the concentration distribution in hydride and in solution. This paper presents a mathematical model of zirconium alloy hydrogenation taking into account phase transition (hydride formation), the iterative computational algorithm for solving the nonlinear boundary-value problem with free phase boundary based on implicit difference schemes, and the results of computational experiments.

The quantitative evaluation of quotations in the Russian Wiktionary was performed using the developed Wiktionary parser.It was found that the number of quotations in the dictionary is growing fast (51.5 thousands in 2011, 62 thousands in 2012).These quotations were extracted and saved in the relational database of a machinereadable dictionary.For this database, tables related to the quotations were designed.A histogram of distribution of quotations of literary works written in different years was built.It was made an attempt to explain the characteristics of the histogram by associating it with the years of the most popular and cited (in the Russian Wiktionary) writers of the nineteenth century.It was found that more than one-third of all the quotations (the example sentences) contained in the Russian Wiktionary are taken by the editors of a Wiktionary entry from the Russian National Corpus.

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The quantization dimension of a probability measure defined on a metric compact space $X$ is known not to exceed the box dimension of its support. It is proved that on any metric compact space of box dimension $\dim_BX=a\leq\infty$, for arbitrary two numbers $b\in[0,a]$ and $c\in[b,a]$ there is a probability measure such that its lower quantization dimension is $b$ and its upper quantization dimension is $c$. Bibliography: 6 titles.

Методика термодесорбционного изучения состояний водорода в углеродных материалах и наноматериалах, Нечаев Ю.С., Денисов Е.А., Черетаева А.О., Шурыгина Н.А., Костикова Е.К., Давыдов С.Ю.

The spectra of thermal desorption of hydrogen isotopes from structural materials was studied using mathematical models. Of interest is the identification of the causes and "driving forces" of a physicochemical nature corresponding to each peak and subsequent parametric identification in accordance with the accepted physically based model. The analysis of various mathematical models for two-peak spectra of metallic materials and the results of numerical modeling in Scilab software are presented.

The paper presents a nonlinear mathematical model of alloys hydrogen permeability for membrane technologies of high-purity hydrogen production. Diffusion processes in the material bulk are taken into account as well as physical and chemical phenomena at the surface: adsorption, desorption and relatively fast dissolution. The iterative computational algorithm and software in Scilab have been developed to model the hydrogen permeability with dynamic boundary conditions and concentration-dependent diffusion coefficient.

The methodology of extracting context labels from internet dictionaries was developed. In accordance with this methodology experts constructed a mapping table that establishes a correspondence between Russian Wiktionary context labels (385 labels) and English Wiktionary context labels (1001 labels). As a result the composite system of context labels (1096 labels), which includes both dictionary labels, was constructed. The parser extracting context labels from the Russian Wiktionary was developed. The parser can recognize and extract new context labels, abbreviations and comments placed before the definition in Wiktionary articles. One outstanding feature of this parser is a large number of context labels which are known in advance (385 context labels for Russian Wiktionary). The parser can recognize and extract new context labels, abbreviations and comments placed before the definition in Wiktionary articles. The database of machine-readable Russian Wiktionary including context labels was generated by the parser. An evaluation of numerical parameters of context labels in the Russian Wiktionary was performed. With the help of the developed computer program it was found in the Russian Wiktionary that (1) there are 133 000 definitions with context labels and comments, (2) one and a half thousand definitions were supplied with regional labels, (3) it was calculated a number of definitions with labels for each domain knowledge. This paper is an original contribution to computational lexicography, setting out for the first time an analysis of numerical parameters of context labels in the large dictionary (500 000 entries).