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Machine translation is a natural language text processing task that aims to automatically translate input text from one language into another language. The currently known machine translation models show a fairly high quality of translation between large languages, but for smaller language areas, represented by less data, the problem is still not solved. Different methods are used to deal with various errors in automatic translation systems. This paper discusses approaches that use translation models of reverse language directions and improve consistency between translations of the same text using direct and reverse translation models. The paper presents a general theoretical justification for such methods in terms of solving the likelihood maximization problem and also proposes a method for stable training of modern models using cyclic translations. [ABSTRACT FROM AUTHOR]

The paper is devoted to the problem of deriving synchronizing and homing experiments for nondeterministic Input/Output automata; corresponding input sequences are widely used in testing (non-initialized) discrete event systems. In active testing, there is an opportunity to set a system under test into a known initial state; in passive testing, a known current state allows to reduce the number of properties to be checked. In the paper, we note that such experiments for Input/Output automata are different from so-called "gedanken" experiments with classical Finite State Machines; the existence check conditions of such experiments are established for a predefined discipline of applying inputs and a method for its derivation is proposed when such an experiment exists. The obtained results allow to reduce the problem of deriving synchronizing and homing experiments for Input/Output automata to the well developed problem of deriving such experiments for appropriate classes of Finite State Machines. [ABSTRACT FROM AUTHOR]

This paper considers subsonic turbojet aircraft fuel consumption minimization problem during cruise phase, assuming fixed time of arrival. The problem takes into account real atmosphere data. We utilize tailwind/headwind component values at various flight levels, as well as air temperatures and atmospheric pressures at various altitudes. The solution to the altitude and speed flight profile optimization problem is through constrained coordinate descent method. The paper considers optimizing the fuel consumption of a medium-haul aircraft during the cruise phase using sample data set on temperature, pressure, and wind speed. The proposed approach achieves a decrease in fuel consumption of 1.2% when optimizing with regard to real atmosphere. [ABSTRACT FROM AUTHOR]

This special issue features selected papers from the 14th International Conference "Management of the Development of Large-Scale Systems (MLSD 2021)" held on September 27–29, 2021. [ABSTRACT FROM AUTHOR]

We propose a new approach to the problem of tuning and optimizing the parameters of a PID controller based on reducing the problem to an optimization problem. In this case, the performance of the controller is evaluated by a quadratic criterion of the system output: the PID controller is tuned against the uncertainty in the initial conditions so that the system output is uniformly small; in this case, a given degree of stability of the closed-loop system is additionally guaranteed. A gradient method for finding the PID controller parameters is given. Numerous examples show that the recurrent procedure proposed is very efficient and leads to PID controllers that are quite satisfactory in terms of engineering performance indices. The article continues a series of papers by the present authors devoted to synthesizing feedback in control problems from the standpoint of optimization. [ABSTRACT FROM AUTHOR]

The present paper is a continuation of the series of articles [1-2] and is devoted to solving the problem of estimating the parameters of hidden Markov models. The hidden state is a homogeneous Markov jump process with a finite set of states. The available observations are indirect and contain Wiener processes whose intensities are different and depend on the hidden state. Both the intensity matrix of Markov state transitions and the drift and diffusion parameters of the observations are subject to estimation. For identification, an iterative algorithm based on smoothing the state of the system based on observations over a fixed time interval is proposed. Then, according to these estimates, the parameters are reconstructed. The paper describes in detail all the numerical schemes for estimating the state and for identifying the parameters. A set of illustrative numerical examples is presented, demonstrating the high quality of the proposed identification estimates. [ABSTRACT FROM AUTHOR]

To improve the quality of generated speech signals, this paper proposes a method for taking into account time-varying information about the speaker. Using this technique, the system synthesizes more natural speech with a voice similar to the given target voice in both the voice cloning and voice conversion problems. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of video-based face recognition. Nowadays, facial recognition methods have made a big step forward, but video-based recognition with its poor quality, difficult lighting conditions, and real-time requirements is still a difficult and unfinished task. The paper uses the apparatus of convolutional networks for various stages of processing: for capturing and detecting a face, for constructing a feature vector, and finally for recognition. All algorithms are implemented and studied in the Matlab environment to simplify their further export to embedded applications. [ABSTRACT FROM AUTHOR]

The paper investigates the distillation problem for deep learning models. Knowledge distillation is a metaparameter optimization problem in which information from a model of a more complex structure, called a teacher model, is transferred to a model of a simpler structure, called a student model. The paper proposes a generalization of the distillation problem for the case of optimization of metaparameters by gradient methods. Metaparameters are the parameters of the distillation optimization problem. The loss function for such a problem is the sum of the classification term and the cross-entropy between the responses of the student model and the teacher model. Assigning optimal metaparameters to the distillation loss function is a computationally difficult task. The properties of the optimization problem are investigated so as to predict the metaparameter update trajectory. An analysis of the trajectory of the gradient optimization of metaparameters is carried out, and their value is predicted using linear functions. The proposed approach is illustrated using a computational experiment on CIFAR-10 and Fashion-MNIST samples as well as on synthetic data. [ABSTRACT FROM AUTHOR]

This thematic issue presents selected articles of the 20th All-Russian Conference with international participation "Mathematical Pattern Recognition Methods" (MPRM) held on December 7–10, 2021 in Moscow. [ABSTRACT FROM AUTHOR]

The use of convolutional neural networks trained with the margin-based softmax function allows achieving the highest accuracy in the face recognition problem. The development of embedded systems such as smart intercoms has increased interest in lightweight neural networks. Thus, lightweight neural network models, trained using the margin-based softmax function, were proposed for the face identification problem. In the present paper, we propose a distillation method that allows obtaining greater accuracy than other methods for the face recognition problem on LFW, AgeDB-30, and Megaface datasets. The main idea of our approach is to use the class centers of the teacher network to initialize the student network. Then the student network is trained to produce biometric vectors the angles from which to the class centers are equal to the angles in the teacher network. [ABSTRACT FROM AUTHOR]

In this paper, we solve the problem of detecting anomalies in X-ray images obtained by full-body scanners (FBSs). The paper describes the sequence and description of image preprocessing methods used to convert the original images obtained with an FBS to images with visually distinguishable anomalies. Examples of processed images are given. The first (preliminary) results of using a neural network for anomaly detection are shown. [ABSTRACT FROM AUTHOR]

We study the implementation of the optimal control strategy obtained in [1] and supplemented in [2]. The algorithm for optimal stabilization of a linear stochastic differential system in a position determined by a piecewise constant Markov drift has been tested in a substantial number of model experiments. The drift value is observed indirectly; i.e., the control problem is solved in the statement with incomplete information. Practical implementation is complicated by the instability of Euler–Maruyama numerical schemes that implement the Wonham filter, which is a key element of the optimal control strategy. To perform calculations, the Wonham filter is approximated by stable schemes based on the optimal filtering of Markov chains by discretized observations [3]. These schemes have different implementation complexity and orders of accuracy. The paper presents a comparative analysis of the control performance for various stable approximations to the Wonham filter and its typical implementation using the Euler–Maruyama scheme. In addition, three versions of discretized filters are compared and final recommendations are given for their application in the problem of stabilizing a system with hopping drift. [ABSTRACT FROM AUTHOR]

This paper develops a novel unified approach to designing suboptimal robust control laws for uncertain objects with different criteria based on a priori information and experimental data. The guaranteed estimates of the γ0, generalized H2, and H∞ norms of a closed loop system and the corresponding suboptimal robust control laws are expressed in terms of solutions of linear matrix inequalities considering a priori knowledge and object modeling data. A numerical example demonstrates the improved quality of control systems when a priori and experimental data are used together. [ABSTRACT FROM AUTHOR]

A novel approach is proposed to suppress bounded exogenous disturbances in linear control systems using a PI controller. The approach is based on reducing the original problem to a nonconvex matrix optimization problem. A gradient method for finding the controller's parameters is derived and its justification is provided. The corresponding recurrence procedure is rather effective and yields quite satisfactory controllers in terms of engineering performance criteria. This paper continues a series of the author's research works devoted to the design of feedback control laws from an optimization point of view. [ABSTRACT FROM AUTHOR]

This paper considers the use of machine learning for diagnosis of diseases that is based on the analysis of a complete gene expression profile. This distinguishes our study from other approaches that require a preliminary step of finding a limited number of relevant genes (tens or hundreds of genes). We conducted experiments with complete genetic expression profiles (20 531 genes) that we obtained after processing transcriptomes of 801 patients with known oncologic diagnoses (oncology of the lung, kidneys, breast, prostate, and colon). Using the indextron (instant learning index system) for a new purpose, i.e., for complete expression profile processing, provided diagnostic accuracy that is 99.75% in agreement with the results of histological verification. [ABSTRACT FROM AUTHOR]

This paper is devoted to the guaranteeing estimation method with application to the calibration problem of a gyro unit. Mathematical models are constructed to describe the kinematics of the gyro unit on a test bench. The applicability limits and errors of the models are investigated. A numerical solution procedure is developed for guaranteeing estimation problems based on their reduction to l1-approximation problems. [ABSTRACT FROM AUTHOR]

The paper deals with the problem of triclustering in multivalued triadic contexts in terms of one multidimensional extension of formal concept analysis; triclustering can be viewed as a search for dense subtensors in three-dimensional tensors over the field of real numbers. Two methods are proposed for solving this problem, namely, NOAC—a version of the OAC triclustering method for numerical data based on delta operators—and a triadic version of the -means method with an improved metric based on Manhattan distance and proximity predicates in each of the three dimensions. Numerical experiments are carried out both on real and synthetic data and confirm the superiority of the NOAC method in terms of the performance criteria for the resulting triclusters. [ABSTRACT FROM AUTHOR]

The paper presents a constructive description of the set of all efficient (Pareto-optimal) investment portfolios in a new setting, where the risk measure named "shortfall probability" (SP) is understood as the probability of a shortfall of investor's capital below a prescribed level. Under a normality assumption, it is shown that SP has a generalized convexity property, the set efficient portfolios is constructed. Relations between the set of mean-SP and the set of mean-variance efficient portfolios as well as between mean-SP and mean-Value-at-Risk (VaR) sets of efficient portfolios are studied. It turns out that mean-SP efficient set is a proper subset of the mean-variance efficient set; interrelation with the mean-VaR efficient set is more complicated, however, mean-SP efficient set is proved to be a proper subset of mean-VaR efficient set under a sufficiently high confidence level. Besides a normal distribution, elliptic distributions are considered as an alternative for modeling the investor's total return distribution. The obtained results provides the investor with a risk measure, that is more vivid than the variance and Value-at-Risk, and with determination of the corresponding set of effective portfolios. [ABSTRACT FROM AUTHOR]

This paper is devoted to the mean-square optimal stochastic recovery of a square integrable function with respect to the Lebesgue measure defined on a finite-dimensional compact set. We justify an optimal recovery procedure for such a function observed at each point of its compact domain with Gaussian errors. The existence of the optimal stochastic recovery procedure as well as its unbiasedness and consistency are established. In addition, we propose and justify a near-optimal stochastic recovery procedure in order to: (i) estimate the dependence of the standard deviation on the number of orthogonal functions and the number of observations and (ii) find the number of orthogonal functions that minimizes the standard deviation. [ABSTRACT FROM AUTHOR]

This paper extends the method originally proposed in [1] to systems with an arbitrary number of inputs and outputs. The method ensures that these signals will be in given domains. Two sequential changes of coordinates are introduced to solve the problem. The first change reduces the plant's output to a new variable of a dimension not exceeding that of the control vector (input). The second change allows passing from the control problem with constraints to the one without them. The effectiveness of this method is illustrated for two problems. The first problem is designing a state-feedback controller for linear systems with constraints imposed on the input and state variables. The second problem is designing an output-feedback controller for linear systems with constraints imposed on the output and input. In both problems, the stability of the closed loop system is verified in terms of linear matrix inequalities. The results are accompanied by simulation examples to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper considers aircraft landing on a carrier. We propose two schemes for calculating, first, the probability of a go-around due to disengaging the arresting gear and, second, the maximum descent of the aircraft's trajectory with respect to the deck level immediately after leaving the deck. The instant to increase the aircraft's thrust before touching the deck is a control parameter affecting these characteristics. The requirements imposed on the probability of a go-around and the maximum descent of the aircraft's trajectory allow determining an admissible range for the thrust increase instant. Numerical results are presented for a real aircraft landing on a real carrier. [ABSTRACT FROM AUTHOR]

This paper considers the idea of reducing the debris of near-Earth space by releasing the spent parts of a spacecraft on orbits touching the conditional boundary of the Earth's atmosphere. We optimize the spacecraft transfer trajectory from a circular reference orbit of an artificial Earth satellite to a target elliptical orbit in a modified pulse problem statement. The convergence of Newton's method is improved by introducing a series of auxiliary coordinate systems at each point of applying an impulse action. The derivatives in the transversality conditions are calculated using a special numerical-analytical differentiation technique. [ABSTRACT FROM AUTHOR]

This thematic issue presents selected articles of the 20th All-Russian Conference with international participation "Mathematical Pattern Recognition Methods" (MPRM) held on December 7–10, 2021 in Moscow. [ABSTRACT FROM AUTHOR]

The paper substantiates the concept of autoencoders focused on automatic generation of compressed images. We propose a solution to the problem of synthesizing such autoencoders in the context of machine learning methods, understood here as learning based on the input images themselves (in the bootstrap spirit). For these purposes, a special representation of images has been developed using samples of counts of a controlled size (sampling representations). Based on the specifics of this representation, a generative model of autoencoders is formalized, which is then specified to a probabilistic parametric sampling model in the form of a mixture of components. Based on the concept of receptive fields, a reduction of the general model of a mixture of components to a grid model of finite components of an exponential family is discussed. This allows the synthesis of computationally realistic coding algorithms. [ABSTRACT FROM AUTHOR]

Modern natural language processing models such as transformers operate multimodal data. In the present paper, multimodal data is explored using multimodal topic modeling on transactional data of bank corporate clients. A definition of the importance of modality for the model is proposed on the basis of which improvements are considered for two modeling scenarios: preserving the maximum amount of information by balancing modalities and automatic selection of modality weights to optimize auxiliary criteria based on topic representations of documents. A model is proposed for adding numerical data to topic models in the form of modalities: each topic is assigned a normal distribution with learning parameters. Significant improvements are demonstrated in comparison with standard topic models on the problem of modeling bank corporate clients. Based on the topic representations of the bank's customers, a 90-day delay on the loan is predicted. [ABSTRACT FROM AUTHOR]

Robust stability conditions are established for a family of linear discrete-time systems subjected to uncertainties. The traditional approach, which involves the construction of a common quadratic Lyapunov function for the entire family of systems with uncertainty, often leads to the problem of conservatism. In this connection, constructing parametric quadratic Lyapunov functions seems promising. The main tools of the proposed approach are the apparatus of linear matrix inequalities and a modification, presented here, of the well-known Petersen's lemma. A simple approach to finding the robust quadratic stability radius of the family in question is proposed in the paper as well. The corresponding optimization problems have the form of semidefinite programming and one-dimensional minimization, which can be easily solved numerically. The efficiency of our approach is demonstrated via a numerical example. The results obtained can be generalized to design problems for linear discrete-time systems subjected to uncertainties, to other robust statements, and to the case of exogenous disturbances. [ABSTRACT FROM AUTHOR]

This paper describes a differential game of persons in which the utility functions of the players have a hybrid form; namely, they are changed at a random moment in time. The form of the payoff functional is simplified using integration by parts. For the cooperative scenario, the problem of time-consistency of the optimality principle chosen by the players is studied and a solution is proposed in the form of an adapted imputation procedure. A differential investment game is considered as an example. [ABSTRACT FROM AUTHOR]

The paper presents an image matching method based on heat kernels. The method permits one to single out the most stable features of images at the initial stage using heat kernels on graphs for subsequent comparison. Popular descriptors can be used for this. When using the method, the number of false matches is considerably reduced compared with traditional approaches. [ABSTRACT FROM AUTHOR]

The paper deals with the construction of interpretable machine learning models. The approximation problem is solved for a set of shapes on a contour image. Assumptions that the shapes are second-order curves are introduced. When approximating the shapes, information about the type, location, and shape of curves as well as about the set of their possible transformations is used. Such information is called expert information, and the machine learning method based on expert information is called expert-augmented learning. It is assumed that the set of shapes is approximated by the set of local models. Each local model based on expert information approximates one shape on the contour image. To construct the models, it is proposed to map second-order curves into a feature space in which each local model is linear. Thus, second-order curves are approximated by a set of linear models. In a computational experiment, the problem of approximating an iris on a contour image is considered. [ABSTRACT FROM AUTHOR]

This paper considers a linear discrete-time system operating in a repetitive mode to track a reference trajectory with a given accuracy. The system parameters are incompletely known and are described by the affine uncertainty model. In addition, the system is subjected to random disturbances, and measurements are carried out with noise. During system operation, the reference trajectory changes after a given number of repetitions. The resulting transient error may cause a temporary loss of accuracy. We propose a new iterative learning control design method to compensate the transient error. An example illustrates the effectiveness of this method. [ABSTRACT FROM AUTHOR]

The paper deals with a theoretical study of the coordination of actions of members of a self-managed team using the Stackelberg strategy aimed at increasing their individual gains. It is assumed that the team creates a total income that increases with the growth of efforts made by each agent and obeys the diminishing return law. The unique Nash equilibrium that exists under the conditions of complete autonomy of all agents is Pareto inefficient. It is shown that for the transition to a Pareto-preferential outcome it suffices to form a small group (coalition) in the team whose members trust each other and are not prone to opportunistic behavior. Following a coalition strategy aimed at achieving the maximum coalition gain, the coalition members increase their efforts; this leads to an increase in the total income. Conditions are found under which the coalition can use the Stackelberg leadership strategy. It is shown that the Stackelberg equilibrium outcome dominates in the sense of Pareto over Nash equilibrium outcomes both in noncooperative and coalitional games. [ABSTRACT FROM AUTHOR]

The paper considers the modification and application of the ant colony method for the problem of directed enumeration of the values of system parameters when performing calculated multiple calculations. Interaction with the user makes it possible to stop the process of exhaustive enumeration of sets of parameter values, and the application of a modification of the ant colony method will allow us to consider rational sets at early iterations. If the user does not terminate the algorithm, then the proposed modifications allow one to enumerate all solutions using the ant colony method. To modify the ant colony method, a new probabilistic formula and various algorithms of the ant colony method are proposed, allowing for each agent to find a new set of parameter values. The optimal algorithm, according to the research results, is the use of repeated endless cyclic search for a new solution. This modification allows you to consider all solutions, and at the same time, find all the optimal solutions among the first 5% of the considered solutions. [ABSTRACT FROM AUTHOR]

We consider the intractable problem of finding several edge-disjoint spanning trees of the minimum total weight with a given diameter in complete undirected graph in current paper. The weights of edges of a graph are random variables from several continuous distributions: uniform, biased truncated exponential, biased truncated normal. The approximation algorithm with time complexity (n2), where n is number of vertices in graph, is proposed for solving this problem. The asymptotic optimality conditions for constructed algorithm is presented for each considered probabilistic distribution. [ABSTRACT FROM AUTHOR]

This paper considers a single-server queueing system with an incoming Markovian Arrival Process (MAP) request flow with two states. Explicit expressions are derived for the stationary probability distribution of the states and several numerical characteristics of the system (the probability of idle time of the server, the expected number of requests in the system, and the mean queue length). The resulting numerical characteristics are presented in tables and plotted in graphical form as well. The recurrent MAP flow with two states as a special case of correlated MAP request flows is studied. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) sensors usually require a calibration procedure. In some cases, scale factor errors depend on the signs of the projections of the vector input signal onto the sensitivity axes of the sensor. To eliminate the ambiguity of scale factor errors, the angular positions of the sensor can be restricted so that the corresponding projections have a definite sign. This paper presents an analytical solution of the optimal calibration problem for a 3D sensor under a constraint on its angular positions. [ABSTRACT FROM AUTHOR]

In modern smart manufacturing, robots are often connected via a network, and their task can change according to a predetermined program. Iterative learning control (ILC) is widely used for robots executing high-precision operations. Under network conditions, the efficiency of ILC algorithms may decrease if the program is restructured. In particular, the learning error may temporarily increase to an unacceptable value when changing the reference trajectory. This paper considers a networked system with the following features: the reference trajectory and parameters change between passes according to a known program, agents are subjected to random disturbances, and measurements are carried out with noise. In addition, the network topology changes due to the disconnection of some agents from the network and the connection of new agents to the network according to a given program. A distributed ILC design method is proposed based on vector Lyapunov functions for repetitive processes in combination with Kalman filtering. This method ensures the convergence of the learning error and reduces its increase caused by changes in the reference trajectory and network topology. The effectiveness of the proposed method is confirmed by an example. [ABSTRACT FROM AUTHOR]

In this paper, a heating process control law with steam supply is designed for a fluid in a heat exchanger. The process is described by a linear hyperbolic equation of the first order with a nonlocal boundary condition with a time-delayed argument. The temperature of the supplied steam is found as a linear dependence on fluid temperature values at measurement points in the heat exchanger. Explicit formulas are obtained for the gradient of the objective functional of the control problem in the space of the feedback coefficients (parameters) of this dependence. A numerical scheme is developed for determining the feedback parameters based on these formulas. Finally, an algorithm is proposed for determining the rational (optimal) number of measurement points. [ABSTRACT FROM AUTHOR]

In this paper, the problem of suboptimal stabilization of an object with discrete time, output and control uncertainties, and bounded external perturbation is considered. The autoregressive nominal model coefficients, uncertainty amplification coefficients, norm and external disturbance offset are assumed to be unknown. The quality indicator is the worst-case asymptotic upper bound of the output modulus of the object. The solution of the problem in conditions of non-identifiability of all unknown parameters is based on the method of recurrent target inequalities and optimal online estimation, in which the quality index of the control problem serves as an identification criterion. A non-linear replacement of the unknown parameter perturbations that reduces the optimal online estimation problem to a fractional linear programming problem is proposed. The performance of adaptive suboptimal control is illustrated by numerical simulation results. [ABSTRACT FROM AUTHOR]

The paper proposes three non-additive integration schemes based on various extensions of integrable functions and nonadditive set functions to the corresponding symmetric powers of the original measurable spaces. Within the framework of the developed schemes, integral representations of some classical objects of the theory of cooperative games are given. A unified approach to the consideration of finite and infinite games is proposed. Particular attention is paid to the Shapley vector, the generalized Owen extension, and the support function of the core of a convex game. [ABSTRACT FROM AUTHOR]

We consider the problem of stabilizing a cart moving along a straight line with an inverted pendulum installed on it. The control objective is to stabilize the cart at a given target point so that the pendulum is in the upper vertical position. The main difficulty associated with solving this problem is that the two subsystems (the cart and the pendulum) must be stabilized simultaneously using one control. A new control law is proposed based on the introduction of a second-order reference system, the trajectory of which is taken as the target one for the cart with the pendulum. By extending the reference system to the fourth order and introducing an algebraic condition coupling the two systems, the target trajectory is found in the four-dimensional phase space of the original system and a control law is constructed that ensures the trajectory of the closed-loop system asymptotically approaching the target one. The control law obtained in this paper is applicable to systems with an arbitrary ratio of pendulum and cart masses, since the closed-loop system does not depend on the mass characteristics of the system. The range of the system parameters is found for which the linearized system is stable. The presentation is illustrated with numerical examples that demonstrate the efficiency of the proposed control. [ABSTRACT FROM AUTHOR]

This paper considers an optimal movement routing problem with constraints. One such constraint is due to decomposing the original problem into a preliminary subproblem and a final subproblem; the tasks related to the preliminary problem must be executed before the tasks of the final subproblem begin. In particular, this condition may arise in the tool control problem for thermal cutting machines with computer numerical control (CNC): if there are long parts among workpieces, the cutting process near a narrow material boundary should start with these workpieces since such parts are subject to thermal deformations, which may potentially cause rejects. The problem statement under consideration involves two zones for part processing. The aggregate routing process in the original problem includes a starting point, a route (a permutation of indices), and a particular track consistent with the route and the starting point. Each of the subproblems has specific precedence conditions, and the travel cost functions forming the additive criterion may depend on the list of pending tasks. A special two-stage procedure is introduced to apply dynamic programming as a solution method. The structure of the optimal solution is established and an algorithm based on this structure is developed. The algorithm is implemented on a personal computer and a computational experiment is carried out. [ABSTRACT FROM AUTHOR]

This paper considers a Cournot oligopoly model with an arbitrary number of rational agents under incomplete information in the classical case (linear cost and demand functions). Within the dynamic reflexive collective behavior model, at each time instant each agent adjusts his output, taking a step towards the maximum profit under the expected choice of the competitors. Convergence conditions to a Cournot–Nash equilibrium are analyzed using the errors transition matrices of the dynamics. Restrictions on the ranges of agents' steps are imposed and their effect on the convergence properties of the dynamics is demonstrated. Finally, a method is proposed to determine the maximum step ranges ensuring the convergent dynamics of collective behavior for an arbitrary number of agents. [ABSTRACT FROM AUTHOR]

This paper is devoted to a multifaceted analysis of person re-identification (ReID) in video surveillance systems and modern solution methods using deep learning. The general principles and application of convolutional neural networks for this problem are considered. A classification of person ReID systems is proposed. The existing datasets for training deep neural architectures are studied and approaches to increasing the number of images in databases are described. Approaches to forming human image features are considered. The backbone models of convolutional neural network architectures used for person ReID are analyzed and their modifications as well as training methods are presented. The effectiveness of person ReID is examined on different datasets. Finally, the effectiveness of the existing approaches is estimated in different metrics and the corresponding results are given. [ABSTRACT FROM AUTHOR]

We propose a new approach to filtering under arbitrary bounded exogenous disturbances based on reducing this problem to an optimization problem. The approach has a low computational complexity since only Lyapunov equations are solved at each iteration. At the same time, it possesses advantages essential from an engineering-practical point of view, namely, the possibilities to limit the filter matrix and to construct optimal filter matrices separately for each coordinate of the system's state vector. A gradient method for finding the filter matrix is presented. According to the examples, the proposed recurrence procedure is rather effective and yields quite satisfactory results. This paper continues the series of research works devoted to feedback control design from an optimization perspective. [ABSTRACT FROM AUTHOR]

The paper proposes a predictive approach to assessing special classes of dangerous states in the development of technological processes in order to make proactive decisions. The developed approach is based on a hybrid model based on the combination of an evidence-based classifier, fuzzy logic, and a Dempster–Shafer probabilistic scheme for evidence combination. The article presents a formal description of the predictor of critical states of the technological process. The resulting approach is universal and applicable in the automation of any complex technical systems. As an example, this article considers the application of the developed approach to solve the problem for assessing the safety of the technological process of shunting trains on a hump yard. The presented example shows the high efficiency and practical usefulness of the developed approach. [ABSTRACT FROM AUTHOR]

This paper describes one method for estimating the Hölder exponent based on the -complexity of continuous functions, a concept formulated lately. Computational experiments are carried out to estimate the Hölder exponent for smooth and fractal functions and study the trajectories of discrete deterministic and stochastic systems. The results of these experiments are presented and discussed. [ABSTRACT FROM AUTHOR]

This paper considers the multi-depot vehicle routing problem with object alternation. We propose a formal statement of the problem with two types of objects and a mathematical model with two blocks of Boolean variables. First, the model is studied without gathering vehicles (mobile objects). Then, a special object (a single collection point) is introduced in the model. We show additional constraints of the mathematical model with this object. Special attention is paid to the condition of no subcycles. This condition is considered based on the adjacency matrix. Five greedy algorithms are proposed for solving the problem, two of which are iterative. One of the greedy algorithms is given a probabilistic modification based on the randomization of variables (an adaptive algorithm). Finally, the proposed algorithms are compared in terms of the average value of the objective function and the running time in a computational experiment. Also, the results of another experiment—the parametric tuning of the adaptive algorithm—are presented. [ABSTRACT FROM AUTHOR]

This paper considers an optimal control problem for an object described by a system of nonlinear fractional difference equations. Such problems are a discrete analog of optimal control problems described by fractional ordinary differential equations. The first and second variations of a performance criterion are calculated using a modification of the increment method under the assumption that the control set is open. We establish a first-order necessary optimality condition (an analog of the Euler equation) and a general second-order necessary optimality condition. Adopting the representations of the solution of the linearized fractional difference equations from the general second-order optimality condition, we derive necessary optimality conditions in terms of the original problem parameters. Finally, with a special choice of an admissible variation of control, we formulate a pointwise necessary optimality condition for classical extremals. [ABSTRACT FROM AUTHOR]

The paper deals with obtaining sufficient conditions for existence of an -equilibrium in the sense of piecewise program strategies in zero-sum games associated with a time-varying nonlinear controlled differential equation in a Banach space and a cost functional of a sufficiently general form. The concept of piecewise program strategies in such a game is defined on the base of a concept of Volterra chain for the operator on the right-hand side in the corresponding integral equation controlled by the opponent players and according to a given partition of the time interval. As an example we consider the game associated with a nonlinear pseudoparabolic partial differential equation governing the evolution of electric field in a semiconductor. [ABSTRACT FROM AUTHOR]