Abstract This paper solves the phase trajectory approximation problem. Quasiperiodic time series form its trajectory in high dimensional space. The trajectory is represented in the spherical coordinate system. To approximate the trajectory the authors use a directional regression technique. It finds space of minimal dimension with the phase trajectory has no self-intersections. Its self-intersections

Abstract A finite computational process using arithmetic operations only is called a rational algorithm. Presently, no rational algorithm is available that is able to check the congruence of arbitrary complex matrices A and B. In this paper, we propose a rational algorithm of verification that works under less stringent conditions than all the conditions known by now.

Abstract Linear controlled multistep processes are considered with an additive quality functional under a phase constraint and a terminal condition. These processes are of interest for control theory and its applications. An existence theorem for optimum control is proved for the controlled processes under consideration. In analogy with backward constructions in the positional theory of differential

Abstract Procedures for multiple hypothesis testing are widely used in analyzing data arrays. Transformation is done first, producing an economic (sparse) array representation. Data is then processed by testing hypotheses of data significance and using inverse transformation. Noise suppression and/or data compression are the main goals of this approach. Such techniques are used in the theory of communication

Abstract Numerical modeling is performed of movement control processes in higher regions of the human brain during the planning and execution of voluntary tracking movements, based on the internal model hypothesis. Such measures as a Kalman filter, linear–quadratic estimator, and linear–quadratic regulator are used. A way of determining moments of the activation of controls is proposed, based on an

Abstract The motion of a group of people is modeled for an emergency where it is necessary to evacuate people from a building of complicated structure as quickly as possible without stampede. To build the model, it is important to determine which information is available for a current analysis of the situation and which parameters can be used as controls. A macroscopic model of crowd flows is considered

AbstractAbsolute lower bound \(2^{n}\) is established for the length of a full conditional diagnostic test for a Cardot circuit that implements the sum of \(n\) variables.

AbstractAn investigation is performed of individual behavioral characteristics of text input that are based on the keystroke dynamics using a virtual keyboard, and their application in the authentication of mobile device users. Key hold time, time between two consecutive keystrokes, and keystroke pressure are used as features to build a user model. A feature vector of a freely typed text is constructed

AbstractThe problem of testing real-time constraints for modular computational systems (MCSes) is exemplified by systems of integrated modular avionics. The requirements to the software for testing these constraints are formulated. An approach to modeling MCSes based on the mathematical apparatus of timed automata with suspended timers is described, and a tool system that implements this approach is

AbstractResults are presented from developing a parallel code for a joint solution to the nonlinear three-dimensional heat equation and the Poisson equation in creating a multiscale model for phase-change memory based on amorphous carbon nanofilms (a-C). Their numerical convergence is investigated. The parallel effectiveness of the new code is examined on the IBM BlueGene/P supercomputer.

AbstractA model is presented of the financial market with a discrete-time uncertain deterministic evolution of prices in which asset prices evolve under uncertainty described using a priori information on possible price increments; i.e., it is assumed that they lie in given compact sets that depend on the prehistory of prices. Trading constraints depending on the history of prices are assumed to be

AbstractRegister machines with counters are arithmetized in class \(\mathcal{E}^{0}\) of the Grzegorczyk hierarchy. As a sequence, we construct a new simple basis via superpositioning in Grzegorczyk class \(\mathcal{E}^{2}\).

AbstractA study is performed of the asymptotic independence of intermediate order statistics and the ‘‘lower’’ and ‘‘upper’’ extreme order statistics as the sample size grows infinitely large. The result is used to refine Rossberg’s theorem.

AbstractPeculiarities of the Toeplitz and polar decompositions of an involutive matrix are described. For instance, it is shown that the unitary factor in both polar decompositions of such a matrix is itself an involution; consequently, it is not only a unitary matrix but a Hermitian matrix as well.

AbstractThe class \(\textrm{EP}_{\mathbb{N}}\) of all exponential-polynomial functions that can be obtained from the functions \(0,1,x+y,x\cdot y,\) and \(x^{y}\) by arbitrary superpositions is considered. In \(\textrm{EP}_{\mathbb{N}}\), six precomplete (with respect to the superposition operation) classes are efficiently defined so that a completeness criterion and a recognition algorithm for completeness

AbstractAn \(n\)-dimensional economic model is considered that has a Cobb–Douglas production function on the infinite planning horizon such that the utility function is an integral-type functional with a discount and a logarithm-type integrant. It is assumed that all of the model’s amortization factors are equal to one another. The constructed optimum control contains \(n-1\) special segments that

AbstractA study is performed of the main approaches to investigating the stochastic process of population dynamics. Continuous time and space and immovable individuals are used to derive a denumerable system of integrodifferential equations corresponding to the dynamics of the spatial momentum of this process. A way to find an approximate solution using the momentum approach is described.

AbstractA grid analog of the formula of integration by parts is constructed and studied for a two-dimensional case in which one of the grid functions is defined at nodes, and the second function is defined at the midpoints of the sides of cells of a simplicial grid in the Cartesian and cylindrical systems of coordinates. Grid analogs of such first-order differential operators as the gradient, divergence

AbstractCombinations of the cross-products of Bessel functions that arise in oblique derivative boundary-value problems for the Laplace operator in a ring are considered. The behavior of zeros of these functions as the ring thickness tends to zero is studied. It is shown that the zeros are divided into two classes, as in the case of Neumann boundary conditions. Some of them remain finite in the limit

AbstractThe problem of synthesizing an asymptotic observer for a linear system with \(l\) measurable outputs \(y=Cx\) and \(m\) unknown inputs \(f(t)\) acting on the system through the matrix \(D\) is considered. A case of hyperoutput systems is examined; such systems have output dimensions larger than that of an unknown input (\(l>m\)). Ways of constructing observers are well-known for such systems

AbstractThe problem of constructing a simultaneous confidence tube of the mean value of multiple responses in a multivariate linear normal multiregression model is considered. Simultaneous confidence multivariate ellipsoidal limits for the mean of multiple responses are obtained to solve it. Using a simple bivariate regression model, simultaneous confidence tubes are numerically modeled and analyzed

AbstractThe familiar results on ergodicity of priority queueing systems were obtained under the assumption that the input streams of requests of all priorities are Poisson. This assumption is weakened by finding the sufficient conditions of ergodicity of queueing systems with two classes of priorities, where the stream of requests of higher priority is hyperexponential, and the one of lower priority

AbstractAn asymptotical approach to the statistical estimation problem is considered under the assumption that the number of observations is a random variable. This leads to distributions with heavy tails and changes in the efficiency of the normally used statistical procedures. Statistical estimates based on random-size and nonrandom-size samples are asymptotically compared against one another. The

AbstractA case is considered in which when the solution to the boundary value problem for a third-order singularly perturbed ordinary differential equation has a strong boundary layer. A difference scheme on piecewise uniform Shishkin meshes is used to solve the problem numerically. It is proved that the solution to the difference problem is reduced to solving the original problem uniformly in a small

AbstractThe basics of load tests for a computer cluster with a large number of GPUs (graphics processing units) distributed over the cluster’s nodes are presented and implemented as a program code. Information about the time delays in the transfer of data of different sizes among all GPUs in the system is collected as a result. Two modes of tests, ‘‘all to all’’ and ‘‘one to one,’’ are developed. In

A class of schemes of functional elements in the standard basis of conjunction, disjunction, and negation elements is considered. For each scheme Σ from this class, in addition to depth D(Σ), its dimension R(Σ) is determined and found to be equal to the minimum dimension of the unit (Boolean) cube that allows isomorphic embedding Σ. In addition to results obtained earlier, it is proved that within

The problem of the least number of multiplications required to compute the product of a 2 × 2-matrix X and a 2 × m-matrix Y over an arbitrary finite field is considered by assuming that the elements of the matrices are independent variables. No commutativity of elements of matrix X with elements of matrix Y is assumed (i.e., bilinear complexity is considered). Upper bound \(\frac{{7m}}{2}\) for this

The problem of program equivalence, checking whether programs have the same (equivalent) behavior in a given model, is investigated. The considered models of programs with “gateway” procedures were proposed somewhat recently, and almost nothing is known about solving the problem of equivalence for them. An approach is proposed to solving the problem of the consistent halting of programs without procedures

Several families of exact solutions expressed in terms of elementary and special functions are constructed for one nonlinear Sobolev-type equation. The qualitative behavior of these solutions is analyzed.

The problem of stabilizing a mathematical hybrid system with switchings between the operating modes is solved. Each of these modes is associated with nonlinear differential equations that have control parameters. The switching instances (conditions) are control components. A stabilizer must be designed in positional form that allows the trajectory of the entire nonlinear system to reach the target

A single-server queuing system with infinite capacity and a recurrent input flow is considered. Service times of the customer units have an exponential distribution with random parameter. The current value of the parameter is chosen from a finite set with given probabilities at the time the service of a certain customer is completed. Sequential values of the parameters form a special kind of Markov

New upper bound 3n is presented for the cardinality of the definition domain of a universal function for a class of linear Boolean functions in which n is the number of variables.

Outlier detection methods are now used extensively, particularly in systems for detecting internal intrusions, in medicine, and in systems for detecting extremism in public political discussions on forums and social media. The aim of this work is to consider a fuzzy method of detecting outliers, based on elliptic clustering in the higher-dimensional space of attributes and using the Mahalanobis metrics

A finite computational process using only arithmetical operations is called a rational algorithm. Presently, there is no known rational algorithm for checking congruence between arbitrary complex matrices A and B. The situation may be different if A and B belong to a special matrix class. For instance, there exist rational algorithms for the cases where both matrices are Hermitian, unitary, or accretive

A nonclassical queuing-theory problem with calls arising in a space is considered. Stations must be placed to minimize the service time for arising calls. The service time is an increasing function that depends on the distance between a call and a station. The time spent to overcome the same distance frequently depends on the direction of motion. In this case, a metric that considers the nonequivalence

Estimates are obtained for the Shannon function of the length of a diagnostic test with respect to cyclic shifts of scheme inputs, and for the Shannon function of fault detection and length of a diagnostic test with respect to a single stuck-at fault and a cyclic shift of scheme inputs.

The optimum allocation of resources for a Gale problem of supply and demand with uncertain factors is considered. The Dantzig-Wolfe decomposition and the generalized potential method developed earlier by the author for a deterministic version of the problem are used to construct and validate the algorithm for a numerical solution.

The problem of estimating a probability density with a given weight is considered. Probability densities of this type arise in different cases, e.g., analyzing order statistics and studying random-size samples in problems of reliability theory, insurance, and other areas. When constructing an estimator, expansion is used with respect to a wavelet basis based on wavelet functions with bounded spectrum

A way of reconstructing tomographic images based on wavelet-vaguelette decomposition is considered for a model with correlated additive noise. The asymptotic properties of an unbiased estimator are studied for the mean-square risk with stabilized hard thresholding of the coefficients of decomposition. It is shown that under certain conditions, this estimator is strongly consistent and asymptotically

It is proved that in programs of register machines with counters, only the equal-to/not-equal-to relations between registers and counters are essential without loss of computational capabilities.

It is proven that for any k ⩾ 2, operators of equational closure and closure with respect to enumeration (Π-operator) generate one and the same classification on set Pk* of partial k-valued logic functions. Thirteen II-precomplete classes are identified in class P3*.

The problem of calculating an analog of volatility index (VIX) in exponential Levy models is considered. To obtain the relation for the original index, an assumption is made about the market diffusion model. Unlike Levy models, diffusion models are not able to describe sharp changes of asset prices and offer a poorer calibration flexibility. Relations for calculating an analog of VIX for the exponential

The problem of constructing an explicit formula for a majorant of a number sequence specified by recurrence relations is considered. Problems of this kind arise when estimating the error of recursive methods for calculating certain functions of a real variable. A special approach to studying the given recurrence relations is proposed in this work, based on which it is established that a majorant can

The problem of constructing a confidence tube of the mean value of multiple responses in a multivariate linear normal multiregression model is considered. To solve it, confidence multivariate ellipsoidal limits of the mean value of multiple responses are obtained. In the case of a simple bivariate regression model, confidence tubes are numerically modelled and analyzed by comparing them for the mean

For stationary diffusion-type equations, we study the convergence of grid inhomogeneous boundary-value problems of a version of the mimetic finite difference (MFD) technique in which grid scalars are defined inside grid cells and grid vectors are specified by their local normal coordinates on the plane faces of grid cells. Grid equations and boundary conditions are formulated in operator form using

A graph is called pseudocubic if the degrees of all its vertices, with a single exception, do not exceed three, and the degree of an exceptional vertex does not exceed four. In this work, it is proved that the vertices of a pseudocubic graph without induced subgraphs that are isomorphic to K4 or K −4 can be colored in three colors. In addition, it is shown that the problem of 3-coloring of pseudocubic

The problem of computing the width of simplices generated by the convex hull of their integer vertices is considered. An FPT algorithm, in which the parameter is the maximum absolute value of the rank minors of the matrix consisting from the simplex vertices, is presented.

An example of applying a generalized allocation scheme to studying the asymptotic behavior of combinatorial objects is considered. The allocation of tuples of zeros and ones onto a circle generated by a shift register under certain conditions is analyzed.

Quantum walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element. We show that if the search space contains more than one marked element, their placement may drastically affect the performance of the search. More specifically, we study search

The results of the author’s collective research on the theory of associative steganography are systematized in order to bring them to a wide range of developers and users of stegosystems. The concept of associative steganography is associated with the associative protection of a finite set of object types and their coordinates, the decimal code symbols of which are represented by masked binary matrices

In this work, we consider a well-known “Single Source Shortest Path Search” problems for weighted directed acyclic graphs (DAGs). We suggest a quantum algorithm with time complexity \(O(\sqrt {nm} \,\log \;n)\) and O(1/n) error probability, where n is a number of Vertexes, m is the number of edges. We use quantum dynamic programming approach (Khadiev, 2018) and Dürr and Høyer minimum search algorithm

We consider functions of k-valued logic closed with respect to superposition classes containing all functions linear modulo k (these classes are related to divisors d of number k). Canonical relations are determined for the elements in such classes, and complete systems and bases are found. The lattice of the introduced classes with respect to the inclusion relation is described. Earlier results are

Using the Lyapunov–Yablonsky approach based on cybernetics, we construct and study a mathematical model of an adaptive control system for conflicting flows of nonhomogeneous customers. The state of the facility and queue lengths for conflicting input flows are chosen as the state of the control system. The Markov property of the sequence of states of the system is proved and they are classified. A

Three problems closely related to the classical unbiased optimal filtration problem: an unbiased optimal filtration problem without a control in the system,a biased optimal filtration problem where the bias does not exceed a given value, and the joint problem of stabilization and optimal filtration. It is proposed these problems be reduced to ones of nonlinear optimization. For unbiased filtration

Game-theoretic properties of joint decision making are considered. Procedures based on sequential open voting by veto are investigated. The paper is aimed at the question how to make voters’ behavior intuitively rational when they choose their optimal strategies. The review of the existing results is also presented and the connection between them is established. Further research is discussed as well

The classical two-dimensional Fuller problem is considered. The boundary value problem of Pontryagin’s maximum principle is considered. Based on the central symmetry of solutions to the boundary value problem, the Pontryagin maximum principle as a necessary condition of optimality, and the hypothesis of the form of the switching line, a solution to the boundary value problem is constructed and its

The problem of selecting the optimum system of models for forecasting short-term railway traffic volumes is considered. The historical data is the daily volume of railway traffic between pairs of stations for different types of cargo. The given time series are highly volatile, noisy, and nonstationary. A system is proposed that selects the optimum superpositioning of forecasting models with respect

An iterative procedure is proposed for calculating the number of k-valued functions of n variables such that each one has an endomorphism different from any constant and permutation. Based on this procedure, formulas are found for the number of three-valued functions of n variables such that each one has nontrivial endomorphisms. For any arbitrary semigroup of endomorphisms, the power is found of the

An equation containing a finite sum of singular integral operators with non-Carleman shifts is considered. The unique solvability of this equation in the Hölder classes under certain constraints imposed on the coefficients is proved. It is shown that the solution can be written in quadratures.

A class of circuits of functional elements over the standard basis of the conjunction, disjunction, and negation elements is considered. For each circuit Σ in this class, its depth D(Σ) and dimension R(Σ) equal to the minimum dimension of the Boolean cube allowing isomorphic embedding Σ are defined. It is established that for n = 1, 2,… and an arbitrary Boolean function f of n variables there exists