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“Informatics and Applications” scientific journalVolume 16, Issue 2, 2022Content Abstract and Keywords About Authors MULTIDIMENSIONAL BINARY MARKETS AND CC-VaR
Abstract: The work further investigates the problems of using the continuous VaR-criterion (CC VaR) in financial markets. It deals with some technical problems arising in multidimensional markets - markets generated by several stochastically connected underliers. The multidimensional extension of binary markets, a simplified markets variant of traditional options such as calls and puts, is considered. They are also the simplest extension of scenario markets in discrete-on-instruments markets. Based on the supposition that scenario indicators are not fully traded in the market directly, an approach to replicating such indicators by binary instruments is suggested. This approach is based on the parity theorems for one-dimensional markets. It is formed for multidimensional markets and is described in details for two-dimensional markets. The constructions of bases for both single-type versions and the natural mixed version with a fixed market center are given. The theoretical constructions with optimal portfolios representations in these bases are illustrated on the example of a specific two-dimensional market. Keywords: underliers; multidimensional market; investor's risk preferences function; continuous VaR-criterion; cost and forecast densities; scenario indicators; bases; binary options; one-type portfolio; market center; mixed portfolio MODEL SETTING USING STATIONARITY CRITERIA FOR TIME SERIES FORECASTING
Abstract: The article discusses the possibility of using the information on the stationarity of residuals to improve the procedure of forecasting nonstationary time series. In the traditional approach, this procedure is used only to confirm or reject the hypothesis of nonstationarity of residuals. In this article, the stationarity test is used for fine-tuning of hyperparameters of the forecasting models. The technique is based on the Granger cointegration approach property to find a statistically significant relationship between time series. The author used the p-value of stationarity tests as a loss function. Economic and generated time series were used as data for verification. The experiments have shown that this approach is often more effective in comparison with the traditional methods of tuning models. Keywords: time series; stationarity; decision trees; regression analysis LINEAR OUTPUT CONTROL OF MARKOV CHAIN BY SQUARE CRITERION. COMPLETE INFORMATION CASE
Abstract: The problem of optimal control of the linear output of a stochastic differential system, formed by an additive jumping input, was solved. The goal of optimization is set by a quadratic criterion of a special type which allows one to formalize the tasks of tracking an abruptly changing target and stabilizing the system near the directions determined by the input. The problem is solved under the assumption that there is complete information, i. e., the known state of the input Markov chain. This statement complements the previously obtained solution of the problem with incomplete information, in which the control and estimation problems are separated, provided by the optimal in this case Wonham filter. The result obtained in the article, in addition to its independent significance, also provides a reference solution for analyzing the quality of control under conditions of indirect observations. The solution of the problem under consideration, as in the statement with incomplete information, is provided by the direct application of the dynamic programming method. The Bellman's equation is refined for a given input model - a martingale representation of the chain and a range of values limited by unit coordinate vectors are used. A numerical experiment was carried out, the results of which illustrate the efficiency of the obtained control algorithms in both settings, with complete information and indirect observations. Keywords: Markov jump process; linear stochastic differential system; optimal control; quadratic criterion; dynamic programming ON MONOTONICITY OF SOME CLASSES OF MARKOV CHAINS
Abstract: The authors define a relation of partial order for Markov chains and study conditions of monotonicity for some classes of continuous-time Markov processes. The corresponding theorems of monotonicity are formulated.
Keywords: monotonicity of Markov processes; nonstationary queuing system; Markov chains with interval intensities; limit characteristics ON THE APPLICATION OF A TOPOLOGICAL APPROACH TO ANALYSIS OF POORLY FORMALIZED PROBLEMS FOR CONSTRUCTING ALGORITHMS FOR VIRTUAL SCREENING OF QUANTUM-MECHANICAL PROPERTIES OF ORGANIC MOLECULES II: COMPARISON OF FORMALISM WITH CONSTRUCTIONS OF QUANTUM MECHANICS AND EXPERIMENTAL APPROBATION OF THE PROPOSED ALGORITHMS
Abstract: Correspondences between descriptions of molecules in the framework of the theory of chemographs, internal coordinates of molecules, and Keywords: algebraic approach; chemoinformatics; labeled graphs; combinatorial solvability analysis THE USE OF THE FDR METHOD OF MULTIPLE HYPOTHESIS TESTING WHEN INVERTING LINEAR HOMOGENEOUS OPERATORS
Abstract: One of the important tasks when processing large data arrays is their economical representation. To solve this task, it is necessary to identify significant features and remove noise. Such problems are found in a wide variety of fields such as genetics, biology, astronomy, computer graphics, audio and video data processing, etc. Modern research in this area describes various filtering methods based on a sparse representation of the obtained experimental data. To construct statistical estimates based on the observed data, the procedure of multiple testing of hypotheses about the significance of observations is widely used. The present authors consider the FDR (false discovery rate) method based on the control of the expected proportion of false rejections of the null hypothesis and the Benjamin-Hochberg algorithm for multiple hypothesis testing. Often, the information available for observation is some kind of transformation of the data of interest. This additionally raises the problem of inverting this transformation. The present authors consider the case when the original data vector is subjected to some linear homogeneous transformation. Such situations are typical, for example, in astrophysical and tomographic applications. Keywords: wavelets; thresholding; multiple hypothesis testing; linear homogeneous operator; unbiased risk estimate PRINCIPLES OF DESCRIBING MARKERS OF LOGICAL-SEMANTIC RELATIONS AND THEIR HIERARCHY
Abstract: The article deals with annotation strategies in corpora with discourse markup. It is shown that Rhetorical Structure Theory (RST)-based corpora only contain annotations of coherence relations, or rhetorical relations (RR). In contrast, the Penn Discourse Treebank (PDTB) of the University of Pennsylvania annotates relations markers, as does the Supracorpora Database of Connectives. The RST Signaling Corpus (RST-SC), also based on RST, has been shown to annotate RR markers, but cannot combine the markup of RRs and their markers in a single annotation. This problem is solved by the GUM corpus and the Supracorpora Database of Hierarchy of Logical-Semantic Relations. The latter has a few advantages: the ability to search, to obtain statistics, and to form bilingual annotations. This makes it possible to identify both universal phenomena in the discursive organization of the text and language-specific phenomena. Keywords: supracorpora database; corpus of texts' annotation; discourse relations; connective MEDIUM MODELS FOR DISCOVERING NOVEL TERMS AND SENTIMENTS FROM TEXTS
Abstract: The models of informatics (= computer and information science), called medium models, are considered.
Keywords: sentiments; discovering new terms; ITO model; text analysis; ITO-Sent model; information technology design CAUSE-AND-EFFECT CHAIN ANALYSIS
Abstract: The paper is devoted to the analysis of the possibilities of using cause-and-effect relationships in the control of the realization of information technologies in distributed information systems. To carry out this analysis, the simple example of a fragment of some fixed information technology has been built which examines situations where control can rely on cause-and-effect relationships between actions in information technologies and when alleged cause-and-effect relationships simply do not exist. The paper shows the limitations of using cause-and-effect relationships to increase confidence in the results of complex computer calculations. This limitation is based on the fact that in order to get causal relationships in waiting of the certain result, it is often impossible to control the relationships of characteristics that are mandatory for the desired consequence to be obtained from actions that are assumed to be its cause. To use cause-and-effect relationships in information technology, it is necessary to supplement the actions of information technology with actions to control the relationships between characteristics. Without this condition, the properly constructed sequence of information technology actions is a necessary but insufficient condition of the expected consequence. Keywords: information security; cause-and-effect relations; monitoring of information technologies ON THE ANALYTICAL STRUCTURE OF SOME KINDS OF TARGET FUNCTIONALS ASSOCIATED WITH THE CONTROL PROBLEMS OF SEMI-MARKOV STOCHASTIC PROCESSES
Abstract: The present author investigates the analytical structure of three kinds of functionals from a controllable semi-Markov process with a finite set of states. It is proved that all these mathematical objects can be represented in the form of a fractional-linear integral functional defined on a finite set of probability measures that determine the control strategy of the corresponding semi-Markov process. For each of these functionals, explicit representations for the integrand functions of the numerator and denominator through the initial probabilistic characteristics of the controlled semi-Markov process are obtained. This result allows one to reduce the problem of optimal control of a semi-Markov process with a particular target functional to the problem of investigation on the global extremum of a given function of a finite number of variables. Keywords: stochastic control models; optimal control of semi-Markovian processes; partial-linear integral functional; basic function of partial-linear integral functional JOINT FILTRATION AND RECOGNITION OF NORMAL PROCESSES IN STOCHASTIC SYSTEMS WITH UNSOLVED DERIVATIVES
Abstract: Methodological and algorithmic support for analytical modeling, estimation, identification, and calibration for essentially nonstationary (e. g., shock) stochastic systems with unsolved derivatives (StS USD) is worked out. It is supposed that state equations contain observation vector. After survey, classes of regression equations for StS USD are considered. Basic results: (i) for general StS USD, optimal algorithms of joint filtration and recognition are presented; (ii) for linear Gaussian equations, optimal algorithms of joint linear filtration and recognition are given; (iii) for StS USD, linear relatively on Xt and nonlinear relatively on Yt algorithm is described; and (iv) in case of result (iii), using the method of normal approximation, the corresponding algorithm is developed. A scalar example of nonlinear StS USD with Gaussian noise corresponding algorithm is given and discussed. Some potential generalizations are presented. Keywords: stochastic systems with unsolved derivatives; joint filtration and recognition; regression VISUAL REPRESENTATION OF THE DECREASE IN CONFLICT INTENSITY AND ITS RESOLUTION IN HYBRID INTELLIGENT MULTIAGENT SYSTEMS
Abstract: Many practical problems require a collective solution ensuring pluralism of opinions, integration of private points of view, and reduction of errors. The authors propose to model the work of such groups of specialists with hybrid intelligent multiagent systems considering the peculiarities of their group dynamics. Such approach would provide improving the quality and efficiency of the solution as well as comprehensive consideration of the problem and the process of its overcoming including visualization of conflicts and processes of their management. The latter would provide a new information on conflict resolution both in the system and in the real group of specialists.
Keywords: collective of specialists; conflict; visualization of the conflict DENSITY ANALYSIS OF mmWave NR DEPLOYMENTS FOR DELIVERING SCALABLE AR/VR VIDEO SERVICES
Abstract: The 5G New Radio (NR) technology operating in millimeter-wave (mmWave) frequency band is designed to support bandwidth-greedy applications requiring extraordinary rates at the access interface. In NR systems, the use of antenna arrays that form directional radiation patterns allows to avoid high propagation losses and interference but at the same time reduces the coverage area of a single beam and, hence, the number of multicast users that can be served by the beam. As a result, efficient algorithms are required to support such services in both terrestrial systems and drone-assisted systems that utilize unmanned aerial vehicles as access points. The present authors consider the streaming data delivery of virtual reality services using scalable video coding technology which utilizes multicast capabilities for baseline layer and unicast transmissions for delivering an enhanced experience.
Keywords: 5G; New Radio; mmWave; multi-layer VR; multicasting; scalable video coding; clustering CONTROLLING A BOUNDED TWO-DIMENSIONAL MARKOV CHAIN WITH A GIVEN INVARIANT MEASURE
Abstract: Consideration is given to the two-dimensional discrete-time Markov chain (random walk) with the bounded continuous state space (rectangle). Upon each transition, depending on its current position and if not on the boundary, the chain moves in one of four possible directions (north, south, east, or west). Having selected a direction, the length of the jump within the admissible interval is determined by the random variable. Assuming that some (reference) distribution on the state space is given, one seeks to solve the inverse control problem, i. e., to find such a control strategy (probabilities of choosing either direction) which brings the stationary distribution of the chain close (in a certain sense) to the reference distribution. The solution based on the policy gradient method is proposed. Illustrative examples are provided. Keywords: Markov chain control; continuous state space; policy gradient; unmanned air vehicles
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functions are shown. The results obtained are comparable: (i) with the solutions of the one-electron Schrodinger equation on fragments of molecules with allowance for the overlap of fragments; (ii) with additive schemes for calculating electron density in the electron density functional theory; and (iii) with allowance for overlap integrals in the theory of molecular orbitals. Approbation of the algorithms on a sample of 134 thousand organic molecules showed rank correlations of the order of 0.75 (95%, reliable interval
0. 67-0.85) between the results of calculations using the proposed algorithms and the values of the investigated quantum mechanical properties of molecules. The calculation speed of the proposed algorithms is several orders of magnitude higher than the speed of quantum mechanical calculations which is important for screening the molecules.
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