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“Informatics and Applications” scientific journalVolume 17, Issue 2, 2023Content Abstract and Keywords About Authors ON OPTIMIZATION PROBLEMS ARISING FROM THE APPLICATION OF TOPOLOGICAL DATA ANALYSIS TO THE SEARCH FOR FORECASTING ALGORITHMS WITH FIXED CORRECTORS
Abstract: Corrective operations (correctors) in multialgorithmic constructions of the algebraic approach can be based on known physical models and/or multilevel descriptions of physical objects. At the same time, within the framework of the topological approach to the analysis of poorly formalized problems, the search for algorithms included in the corrector can be considered as a combinatorial optimization problem or as a problem ofminimizing a certain loss function. The study of the neighborhoods of chains in the lattice of subsets of objects made it possible to obtain a number of rank optimization criteria that are promising for solving the problems of predicting numerical target variables. The formalism was tested on the problem of ligand-receptor interaction within the framework of the chemokine analysis of drug molecules (data from ProteomicsDB). The best results of predicting constants were observed when using the obtained rank criteria (correlation coefficient on a sliding control 0.86 ± 0.20 averaging over 300 biological activities). Keywords: topological data analysis; lattice theory; optimization problems; regression; chemoinformatics THE MONAD OF DIAGRAMS AS A MATHEMATICAL METAMODEL OF SYSTEMS ENGINEERING
Abstract: The paper addresses issues associated with the development of advanced mathematical methods for systems engineering suitable as the basis of computer tools for automatic synthesis and analysis of systems and processes. Following recent trends, category theory is employed as the framework for the methods. Its application is based on representing the structure of systems, processes, requirements, and other system design results as diagrams in categories whose objects are the algebraic models of parts and morphisms describe relationships between parts. Applying the fundamental Grothendieck flattening construction, the following constructions are described explicitly: categories of diagrams, the monad of diagrams, and the monad and the comonad of pointed diagrams. Application areas of these constructions in systems engineering procedures are identified. An approach is proposed to implement highly automated technologies of the generative design kind for complex multilevel systems. Keywords: category theory; monad of diagrams; Grothendieck construction; colimit; systems engineering; system of systems; generative design MULTIPLAYERS' GAMES COMPOSITIONAL STRUCTURE IN THE MONOIDAL CATEGORY OF BINARY RELATIONS
Abstract: The system approach is suggested for multiplayers' games solution that meets up-to-date network technologies. It allows to optimize the functionality of multiagent systems. The monoidal category of binery relations is applied to make games rules description and players' behavior study and modification. The game problem is to maximize, if possible, the preference relations of all participants in the game. Their composition in the monoidal binary relations category in correspondence with games rules defines resulting game relation (RGR). Players' rational behavior search is reduced to RGR maximum elements choice. The author formalizes the use of various classes of permissible strategies, information exchange processes, and coalitions formation. The RGR existence is proved and maximum RGR elements structure is studied. Moves priority and absolutely optimal preference relations significance are clarified for the coalitions formation process. Keywords: player's preference relations: absolutely optimal relation, guarantied relation, moves priority relation; game graph; permissible strategy; rational solution; coalition characteristic relation; resulting game relation; monoidal category; compositionality MARKET WITH MARKOV JUMP VOLATILITY I: PRICE OF RISK MONITORING AS AN OPTIMAL FILTERING PROBLEM
Abstract: The first part of series is devoted to investigating the market price of risk in a financial system. It contains riskless bank deposits, risky base assets, and their derivatives. The model ofthe underlying price evolution represents a stochastic differential system with stochastic volatility which is a hidden Markov jump process. The investigated market is incomplete and has no arbitrage possibilities. The market price ofrisk, which corresponds to a prevailing martingale measure, can be characterized via the hidden Markov jump process but can not be restored precisely. However, it can be estimated optimally using the observations of both the derivative and underlying prices. Using the concept of the prevailing martingale measure existence, one can derive a system of the partial differential equations which describes an evolution of the derivative prices and represents some analog of the classic Black-Sholes equation. Then, one can convert the calculation problem for the market price of risk to the optimal state filtering in a differential stochastic observation system. The paper also discusses various aspects ofthe numerical realization for the stated estimation problem. Keywords: Markov jump process; optimal filtering; diffusion and counting observations; multiplicative observation noise; numerical approximation accuracy MEAN-SQUARE RISK OF THE FDR PROCEDURE UNDER WEAK DEPENDENCE
Abstract: In many application areas, the problem of processing large amounts of data arises. In this case, before processing, the data array is often subjected to some transformation leading to a "sparse" or "economical" representation in which the absolute value of most elements of the array is equal to zero (or sufficiently small).
Keywords: thresholding; multiple hypothesis testing; mean-square risk ROBUSTNESS INVESTIGATION OF THE NUMERICAL APPROXIMATION OF THE WONHAM FILTER
Abstract: The properties of the optimal continuous Markov chain state filtering problem decision given be the linear observations noisy Wiener process, assuming incomplete information about its intensity, are investigated. The uncertainty of the observation system is set by the upper bound of the noise intensity. Numerical implementation of the optimal solution in the statement with complete information provided by the Wonham filter does not guarantee stability. It is shown that the Wonham filter in the statement with uncertainty is robust with respect to the noise intensity if the model parameters do not lead to its divergence. In the general case, the instability of the Euler-Maruyama numerical scheme of the Wonham filter is preserved. Simple heuristic techniques that provide stable approximations of the Wonham filter show the workability for a wider set of parameters. However, in the statement with uncertainty, it is possible to give examples when such heuristic filters show unacceptably low quality.
Keywords: Markov jump process; stochastic filtering; robust estimation; Wonham filter; Euler-Maruyama numerical scheme; discretized filters CRITERIA FOR CHOOSING THE FACTORIZATION MODEL DIMENSIONALITY
Abstract: The paper is devoted to the choice ofmodel dimension ofmatrix factorization in the presence ofmissing elements. The problem of estimating the parameters of the adopted data model is solved by multidimensional optimization. Estimating the value of reduced dimensionality is a typical example of the problem of choosing a model when an alternative arises during data analysis and the choice means either finding out the preferences of individual options or highlighting the "best" representative. Typically, applied selection criteria are based on likelihood function which requires probabilistic assumptions about the data. But when evaluating the parameters of the factor model under consideration, they are not set and it is impractical to introduce them, so as not to violate the commonality of the formulated task of reducing dimensionality. Therefore, an attempt was made to turn to the idea of reusing the available data for the statistical output. None of the existing approaches (bootstrap, folding knife, rechecks, as well as permutation tests) is suitable; so, an original method for generating new data by additional omissions ofelements ofthe original matrix was proposed. To process the formed samples, it is suggested to use a combination of the model of a mixture of normal distributions in conjunction with nuclear smoothing.
Keywords: lower rank matrix approximation; missing data; criteria for model selection; resampling methods; kernel smoothing ANALYSIS OF THE QUEUEING SYSTEMS WITH MIXED PRIORITIES
Abstract: A one-line queuing system with an infinite number of waiting places, an arbitrary distribution of service time, and Poisson incoming flows of customers is studied. Two models of mixed priorities are considered. In the first model, there is either preemptive repeat priority discipline between the customers of different flows or a head of the line priority discipline. In the second model - preemptive priority discipline either with loss or with repeat of a newly interrupted customer. By the method of additional components, a multidimensional random process is investigated, the components of which are the number of customers of each priority in the system and the time elapsed since the start of servicing the customer located on the device at time t. The distribution of the specified process in the nonstationary mode of the system is found. Keywords: head of the line; preemptive repeat; preemptive loss; one-line; queue length A QUEUEING SYSTEM FOR PERFORMANCE EVALUATION OF A MARKOVIAN SUPERCOMPUTER MODEL
Abstract: Consideration is given to the well-known supercomputer model in the form of a Markovian nonwork- conserving two-server queueing system with unlimited queue capacity, in which customers are served by a random number of servers simultaneously. For the first time, it is shown that its basic probabilistic characteristics can be calculated from an unrelated single-server queueing system with infinite capacity, work conserving scheduling, and forced customers' losses. Based on the known matrix-analytic techniques for quasi-birth-and-death processes, it is shown that in certain special cases, the transient queue-size distribution can be found (in terms of Laplace transform) using the Level Crossing Information method and has a matrix-geometric form. Numerical examples which illustrate some properties of the established connection between the two queueing systems are provided. Keywords: supercomputer model; queueing system; nonwork-conserving scheduling; transient regime ON MODELING THE EFFECTS OF MULTICAST TRAFFIC SERVICING IN 5G NR NETWORKS
Abstract: Multicasting in wireless access networks allows efficient provision of a service to a group of subscribers and is useful for reducing the resource required to serve user equipments requesting the same data. The support of this feature in current 5G New Radio (NR) technology and future subterahertz (sub-THz) 6G systems faces challenges associated with the use of the directional beamforming phased array antennas. The presented multicast and unicast traffic service model allows one to explore the range of 5G/6G network parameters to reduce the density of base stations while maintaining the quality of services provided to subscribers. Keywords: 5G; 6G; multicasting; millimeter wave; terahertz; multibeam antennas; multi-RAT; numerical simulation SELF-LEARNING OF AUTONOMOUS INTELLIGENT ROBOTS IN THE PROCESS OF SEARCH AND EXPLORE ACTIVITIES
Abstract: One of the effective approaches to organizing the goal-seeking behavior of autonomous integral robots in the process of search and explore activities in an a priori undescribed conditions of a problematic environment is considered. It is proposed to use the procedures of visual-effective thinking based on the formalization of the reflex behavior of highly organized living systems as the basis for the goal-seeking behavior of robots. A self-learning algorithm has been developed for the conditions with a high level of uncertainty which allows automatically generating conditional programs of expedient behavior that provide autonomous integral robots with the ability to achieve a given behavioral goal in the process of search and explore activities. The boundary estimates of the functional complexity of the proposed self-learning algorithm under uncertainty are found showing the possibility of its implementation on the onboard computer of autonomous integral robots which have, as a rule, limited computing resources. A modeling of self-learning process for an autonomous integral robot in an a priori undescribed and problematic environment was carried out which confirmed the effectiveness of the proposed approach for organizing the planning of goal-seeking behavior in an a priori undescribed and problematic environments. Keywords: autonomous integral robot; self-learning algorithm; uncertainty conditions; problematic environment; conditional signals COMPLEX CAUSE-AND-EFFECT RELATIONSHIPS
Abstract: The paper discusses the task of constructing a logical inference of the specific property from data selected from a plurality of sets of source data. When solving the problem, it should be taken into account both the possibility of violating the cause-and-effect scheme due to noise and the possibility of not achieving the necessary conclusion.
Keywords: cause-and-effect relationships; approximate logical inference; probability of correct inference under noise conditions METHODOLOGY OF THE CORPUS-BASED STUDIES IN THE FIELD OF CONTRASTIVE PUNCTUATION
Abstract: The paper refines the methodological approach to the contrastive studies of punctuation. Given the recent achievements of information science, computer linguistics, and translation theory, such studies are most likely to be corpus-based. The paper presents a methodological model of research into interlingual punctuation asymmetry the aim of which is to shed light on the functional scope of the same punctuation marks in different languages.
Keywords: contrastive punctuation; translation; corpus-based translation studies; corpus-based studies; parallel corpus; supracorpora database; asymmetry between languages; methodology SELECTION OF SPECIALISTS IN THE ORGANIZATION OF COLLECTIVE SOLVING PROBLEMS
Abstract: The study of small groups (collectives, teams), their characteristics, problems, dynamics, and features of selection of specialists stands at the intersection of psychology of personnel management and social psychology A special place in a wide range of areas of modern science is occupied by modeling the interaction of people in small collectives of specialists, in particular, within the framework of a multiagent approach. At the same time, when developing intelligent systems (artificial heterogeneous collectives) to solve practical problems, it is now required to combine in the system the models of specialists (agents) with incompatible goals and domain models. These agents are created by different development teams. The selection of specialists in natural and models of specialists in artificial heterogeneous teams is an important task, the results of which influence the further decision-making process. The paper presents an analysis of methods and approaches to the selection of specialists and the acquisition of small groups (collectives, teams) whose measuring tools should be exposed to quality assessment. Keywords: group; small collective of specialists; team; methods of selecting specialists and forming small groups; teambuilding
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