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“Informatics and Applications” scientific journalVolume 18, Issue 1, 2024Content Abstract and Keywords About Authors SUBOPTIMAL FILTERING IN STOCHASTIC SYSTEMS WITH RANDOM PARAMETERS AND UNSOLVED DERIVATIVES
Abstract: For observable Gaussian differential stochastic systems (StS) with random parameters in the form of integral canonical expansions (ICE) and StS with unsolved derivatives (USD), methodological support for synthesis of suboptimal filters is presented. Survey in fields of analytical modeling and suboptimal filtering (SOF), extrapolation, and identification is presented. Necessary information concerning multicomponent (MC) ICE is given. Special attention is paid to mean square regressive linearization including MC ICE. Basic results in normal SOF (NSOF) are presented for StS USD reducible to differential StS. Stationary and nonstationary NSOF are considered. An illustrative example for scalar StS USD reducible to differential is given. For future, SOF generalization methods of moments, quasi-moments, and one- and multidimensional densities of orthogonal expansions are recommended. Keywords: normal approximation method (NAM); regression linearization; stochastic process; stochastic systems with unsolved derivatives (StS USD); suboptimal filtering (SOF) ALGEBRAIC SPECIFICATION OF GRAPH COMPUTATIONAL STRUCTURES
Abstract: The previously proposed generalized approach to algebraic specification of distributed systems is developed based on the novel category-theoretic construction called graphalgebra. The graphalgebraic specification is based upon a directed multigraph, the edges of which represent computational operations performed in the nodes of the system and the vertices denote the data exchange ports between the components. Changing the system architecture during the life cycle leads to changes in the graph shape, computation algorithms, and data exchange contents. For a formal description of such changes, a graph transformation technique for graphalgebras is proposed. A novel category-theoretic construction called flexible graphalgebra is introduced which appeared to be closely related to the well-known monad of diagrams. A functor is presented that produces all categories of flexible graphalgebras from their signatures. The theoretical results are illustrated by examples from the field of automatic synthesis of neural network architecture by step-by-step transformations. Keywords: algebraic specification; distributed system; architecture evolution; category theory; graphalgebra; monad of diagrams AUTONOMOUS DIFFERENTIAL SYSTEM LINEAR OUTPUT CONTROL BY SQUARE CRITERION ON AN INFINITE HORIZON
Abstract: The problem of optimal control of the stochastic differential system linear output on an infinite horizon is solved. The solution is considered as the limit form of optimal control in the corresponding problem with a finite horizon. Sufficient conditions for the existence of control are given. They consist of the requirements of the stationarity of nonlinear dynamics, the finiteness of the quadratic target functional, the stabilizability of the linear output, and the existence of a limit in the Feynman-Katz formula describing the nonlinear part of control. The conditions for the linear part of the control are related to the classical results of the existence of a solution to the autonomous Riccati equation. The existence of a limit in the Feynman-Katz formula is associated with the solution of a parabolic equation that sets the coefficients for the nonlinear part of the control. A special case of linear drift is considered in which the nonlinea34qar nature of the problem is preserved but optimal control turns out to be linear both in output and in the state variable. The results of a numerical experiment are presented which makes it possible to analyze the transient process in a problem with a finite horizon and an ergodic process in dynamics. For the control coefficients, the limiting transition to the optimal values of the corresponding optimal autonomous control is illustrated. Keywords: stochastic differential Ito system; output control; optimal control; quadratic criterion; parabolic equation; Feynman-Katz formula MARKET WITH MARKOV JUMP VOLATILITY IV: PRICE OF RISK MONITORING ALGORITHM GIVEN HIGH FREQUENCY OBSERVATION FLOWS OF ASSETS PRICES
Abstract: The fourth part of the series presents a suboptimal algorithm of the market price of risk monitoring given the observations of the underlying and derivative asset prices. As in the previous papers, the market model contains the stochastic volatility described by a hidden Markov jump process. This market has no arbitrage; so, the market price of risk is a function of the Markov process state. The key feature of the investigated market lies in the structure of the available observations. They represent the underlying and derivative prices registered at random instants. The underlying prices are observed accurately, while the derivative prices are corrupted by a random noise. The distribution of the interarrival times between the observable prices and the observation noises depends on the estimated process. The essential feature of the obtained observations is their high arrival intensity compared with the hidden process transition rate. This property allows one to use the central limit theorem for generalized regenerative processes for the filter design. The influence of the estimation performance depending on the observation complexes is illustrated with a numerical example. Keywords: market price of risk; Markov jump process; high frequency observations; multivariate point process; numerical algorithm UNIFORM CONVERGENCE RATE ESTIMATES FOR THE INTEGRAL BALANCE INDEX
Abstract: The paper considers the Bayesian balance model in which the rate of weak convergence of the normalized integral balance index to the digamma distribution is studied in terms of a uniform metric. The integral factors negatively and positively influencing the functioning of the system and their ratio, the integral balance index of the system, are considered. It is assumed that the number of factors is not known a priori and is described by a mixed Poisson distribution with a structural generalized gamma distribution. The rate of weak convergence to the digamma distribution in the described scheme is studied. As an auxiliary statement, the rate of weak convergence of a normalized random sum with an index having a generalized negative binomial distribution to a limiting generalized gamma distribution is estimated. The results of the work may be in demand in the study of models used to describe processes with distributions having an unlimited nonnegative support. Keywords: digamma distribution; mixed distributions; balance index; random summation; weak convergence; estimates of convergence rate ANALYSIS OF NODE MULTIFLOWS IN A MULTIUSER NETWORK SYSTEM
Abstract: Within the framework of computational experiments, exclusive and limit modes of transmission of outgoing node multiflows in a multiuser network system are studied. Internodal flows of different types that are transmitted from all nodes along all shortest routes are analyzed. Within the framework of the algorithmic scheme, the transmission of all internodal flows is calculated. The found values act as components of the multiflow vector originating from each source node to all destination nodes and are interpreted as guaranteed multicriteria estimates of the functioning of a multiuser system. To estimate the minimum unit cost for each node, the monopole mode of transmitting the outgoing multiflow is used without taking into account all the others. To search for the maximum achievable internodal flow, the limiting transmission mode is considered in which all edges of the network are completely loaded. The networks with different structural features and the same total capacity are studied. Keywords: multicommodity flow model; distribution of node multiflows; unit cost of flow transmission LOCAL TREELIKE STRUCTURE IN THE POWER-LAW CONFIGURATION GRAPHS
Abstract: The local treelike structure of configuration graphs intended for modeling complex communication networks is stidued. In such graphs, the vertex degrees are independent and identically distributed according to the power law. In the case of a limited number of graph vertices, the dependences of the maximum volume of a treelike subgraph on the number of graph vertices and the vertex degree distribution parameter are found. The same problem was solved for the number of trees of a given size. Estimates are also given for the average size of a tree in the graph. It is shown that with a limited number of vertices of the configuration graph, the found dependences statistically significantly improve the description of the network structure in comparison with the previously known asymptotic models. Keywords: configuration graph; power-law distribution; local treelike structure; tree size; simulations STATISTICAL CRITERION FOR QUEUING SYSTEM STABILITY BASED ON INPUT AND OUTPUT FLOWS
Abstract: One of the basic properties of a queuing system is stability - the ability of the system to function, maintaining its structure and characteristics unchanged over time. The problem of statistical verification of the stability of the queuing system based on the characteristics of the input A(t) and output D(t) order flows is considered. The confirmation of stability is based on establishing the equality of the rates of these flows. Thus, in the language of statistical data analysis, one obtains the classic problem of comparing rates of occurrence. To solve it, the observation period is divided into fragments that give separate estimates. Together, they make up the sample that participates in the comparison. When analyzing stability, it is necessary to take into account possible dependence of A(t) and D(t); so, it is necessary to turn to methods for processing the so-called matched pairs of observations. Stability control makes it necessary to solve a number of auxiliary tasks: selection of volumetric parameters for rate estimation, checking the normality of the distribution, and analysis of correlations. In the course of experiments with the real system, a number of features were revealed: the effect of substituting the prelimit distribution with the real one during fragmentation as well as the presence of dependence of the rate estimates of analyzed flows which comes to naught for unstable systems. Keywords: queueing system; sample-path stability; matched pairs tests; tests of multinormality SYNTHESIS MODELS OF LAYOUT SCHEME IN THE TASK OF FORMING AN AIRCRAFT IMAGE
Abstract: The article discusses the problems of synthesizing mathematical models of an aircraft at the initial design stage. The central task of the initial design stage is to develop a structural-parametric model of the product and construct its layout diagram. The structural-parametric model of the product describes the space of the main design parameters of the aircraft and the layout diagram represents its structure, the set of main units and systems of the aircraft, their relative arrangement, and structural connections between the units. The layout diagram of the aircraft serves as the basis for further detailing of the project. At the initial design stage, the permissible ranges of values of the design parameters of the units of the layout diagram are determined in which the search for optimal design solutions is carried out. The paper presents a description of structural-parametric models and layout diagrams of a wide class of aircraft which can be implemented using an automated weight design system. Keywords: mathematical modeling; design automation; aircraft; weight design; project generator ON THE GENERATION OF SYNTHETIC FEATURES BASED ON SUPPORT CHAINS AND ARBITRARY METRICS WITHIN A TOPOLOGICAL APPROACH TO DATA ANALYSIS. PART 1. INCLUSION OF EMPIRICAL DISTANCE FUNCTIONS INTO THE FORMALISM
Abstract: The analysis of the formalism of topological recognition theory based on the fundamental concepts of functional analysis made it possible to propose previously unexplored approaches to determining lattice estimates. In particular, the use of support chains for the analysis of Boolean lattices formed over Zhuravlev-regular sets of precedents has pointed to a new direction of research which consists in replacing estimates of lattice elements with certain types of functions and/or vectors. This extension of the formalism also allows for a systematic study of semiempirical distance functionals known in the literature to solve applied problems. Promising directions for further development of the formalism are substantiated including the functionals reducing descriptions of sets of a Boolean lattice to scalars and the development of a mathematical apparatus for the analysis of lattices where operations on the corresponding functions are involved. The latter direction is interesting as it allows defining lattice metrics without using lattice estimates. Keywords: topological data analysis; lattice theory; algebraic approach by Yu. I. Zhuravlev; functional analysis LOGIC OF DECEPTION IN MACHINE LEARNING
Abstract: The issues of potential change in the work of artificial neural networks under various influences on training data is the urgent task. Violation of the correct operation of the artificial neural network with hostile effects on the training sample was called poisoning. The paper provides the simplest model of neural network formation in which the features used in training are based only on the predominance of the number of homogeneous elements. Changes in the samples of the training sample allow one to build Back Doors which, in turn, allow one to implement incorrect classification as well as embed errors into the software system, up to malicious code. The correct model of training sample poisoning which allows one to implement Back Door and triggers for classification errors is constructed in the paper. The simplest nature of the constructed model of functioning and formation of deception allows one to believe that the causal logic of the realization of a possible real attack on a complex artificial intelligence system has been restored correctly. This conclusion allows one in the future to correctly build the subsystems of monitoring, anomaly analysis, and control of the functionality of the entire artificial intelligence system. Keywords: finite classification task; cause-and-effect relationships; machine learning; poisoning LIFE CYCLE OF METHODOLOGY FOR CONSTRUCTING REFLEXIVE-ACTIVE SYSTEMS OF ARTIFICIAL HETEROGENEOUS INTELLIGENT AGENTS
Abstract: The paper presents the temporal structure (life cycle) of the methodology for constructing reflexive-active systems of artificial heterogeneous intelligent agents. These systems are designed for computer modeling of processes and effects that arise when solving practical problems by teams of specialists under the guidance of a decision maker. Artificial heterogeneous intelligent agents of reflexive-active systems are active subjects capable of reasoning, communication, and reflection as the ability to model the reasoning of other agents of the system and themselves. Modeling of reflexive processes ensures the development by agents of a consistent understanding of the control object, the purpose of collective work, and the norms of interaction allowing the system to self-organize and re-develop a relevant hybrid intelligent method for solving the next problem. Keywords: reflection; methodology; reflexive-active system of artificial heterogeneous intelligent agents; hybrid intelligent multiagent system; team of specialists ANALYSIS OF APPROACHES TO DEFINING FUZZY RESOLVENT
Abstract: The article presents the results of a study concerning various definitions of the resolvent in fuzzy logic. Conditions are defined under which the Lee resolvent is a significant logical consequence in the case of the classical definition of fuzzy logical connectives. It is shown that when using triangular norms and conorms for their formalization, it is impossible to obtain a logically significant Lee resolvent. However, if the triangular conorm is defined as max, then the Lee resolvent exists for any triangular norm. Conditions are defined under which the Mukaidano resolvent is a significant logical consequence for classical min and max operations. When using triangular norms and conorms other than classical ones, further research is required. An illustrative example is provided demonstrating the process of constructing the Mukaidano resolvent. Keywords: resolvent; resolution method; triangular norms and conorms
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