Pub Date : 2023-01-01DOI: 10.21638/11701/spbu35.2023.306
Dmitry Dmitriyevich Averianov, Mikhail Valerievich Zheludev, Vladimir Ilyich Kiyaev
The work is devoted to the development of an algorithm for classifying human behavior in the context of detecting the truthfulness or falsity of statements presented in video file format. The analysis of the video file was carried out within the time window, in which both changes in the micromotility of the facial muscles and speech signs were analyzed. In our case, facial expressions are represented by a mathematical representation in the form of a vector containing the necessary digital information about the state of the face, which is characterized by the positions of special points (key points of the nose, eyebrows, eyes, eyelids, etc.). The mimic vector is formed as a result of training non-linear models. The speech characterizing vector is formed on the basis of the heuristic characteristics of the audio signal. The temporal aggregation of vectors for the final classification of behavior is performed by a separate neural network. The paper presents the results of the accuracy and speed of the algorithm, which show that the new approach is competitive with respect to existing methods.
{"title":"Construction of an Emotional Image of a Person Based on the Analysis of Key Points in Consecutive Frames of a Video Sequence","authors":"Dmitry Dmitriyevich Averianov, Mikhail Valerievich Zheludev, Vladimir Ilyich Kiyaev","doi":"10.21638/11701/spbu35.2023.306","DOIUrl":"https://doi.org/10.21638/11701/spbu35.2023.306","url":null,"abstract":"The work is devoted to the development of an algorithm for classifying human behavior in the context of detecting the truthfulness or falsity of statements presented in video file format. The analysis of the video file was carried out within the time window, in which both changes in the micromotility of the facial muscles and speech signs were analyzed. In our case, facial expressions are represented by a mathematical representation in the form of a vector containing the necessary digital information about the state of the face, which is characterized by the positions of special points (key points of the nose, eyebrows, eyes, eyelids, etc.). The mimic vector is formed as a result of training non-linear models. The speech characterizing vector is formed on the basis of the heuristic characteristics of the audio signal. The temporal aggregation of vectors for the final classification of behavior is performed by a separate neural network. The paper presents the results of the accuracy and speed of the algorithm, which show that the new approach is competitive with respect to existing methods.","PeriodicalId":36965,"journal":{"name":"Differencialnie Uravnenia i Protsesy Upravlenia","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136202281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21638/11701/spbu35.2023.301
Sergei Yu. Pilyugin
This paper is a survey of some recent results giving sufficient conditions of shadowing for dynamical systems in the absence of hyperbolicity. The main topics of the survey are as follows: method of pairs of Lyapunov type functions, shadowing in a neighborhood of a nonisolated fixed point, conditional multiscale shadowing for sequences of mappings of a Banach space, conditional shadowing for dynamical systems on so-called simple time scales. The paper contains a new result on conditional multiscale shadowing in the case of an infinite family of projections of the phase space.
{"title":"Methods of Nonhyperbolic Shadowing","authors":"Sergei Yu. Pilyugin","doi":"10.21638/11701/spbu35.2023.301","DOIUrl":"https://doi.org/10.21638/11701/spbu35.2023.301","url":null,"abstract":"This paper is a survey of some recent results giving sufficient conditions of shadowing for dynamical systems in the absence of hyperbolicity. The main topics of the survey are as follows: method of pairs of Lyapunov type functions, shadowing in a neighborhood of a nonisolated fixed point, conditional multiscale shadowing for sequences of mappings of a Banach space, conditional shadowing for dynamical systems on so-called simple time scales. The paper contains a new result on conditional multiscale shadowing in the case of an infinite family of projections of the phase space.","PeriodicalId":36965,"journal":{"name":"Differencialnie Uravnenia i Protsesy Upravlenia","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136203135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21638/11701/spbu35.2023.302
George Osipenko
A diffeomorphism f is hyperbolic on a chain-recurrent set if the Morse spectrum does not contain zero. The symbolic image is a directed graph approximating a dynamical system. The chain-recurrent set is localized using this graph. The symbolic image of the differential allows us to estimate the Morse spectrum. A diffeomorphism f is structurally stable if the dual differential has only trivial bounded trajectories. The symbolic image of the dual differential makes it possible to check the absence of bounded trajectories of the dual differential.
{"title":"Computer-oriented Tests for Hyperbolicity and Structural Stability of Dynamical System","authors":"George Osipenko","doi":"10.21638/11701/spbu35.2023.302","DOIUrl":"https://doi.org/10.21638/11701/spbu35.2023.302","url":null,"abstract":"A diffeomorphism f is hyperbolic on a chain-recurrent set if the Morse spectrum does not contain zero. The symbolic image is a directed graph approximating a dynamical system. The chain-recurrent set is localized using this graph. The symbolic image of the differential allows us to estimate the Morse spectrum. A diffeomorphism f is structurally stable if the dual differential has only trivial bounded trajectories. The symbolic image of the dual differential makes it possible to check the absence of bounded trajectories of the dual differential.","PeriodicalId":36965,"journal":{"name":"Differencialnie Uravnenia i Protsesy Upravlenia","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136202469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21638/11701/spbu35.2023.304
Adetunji Adedotun Adeyanju, Daniel Oluwasegun Adams
In this paper, we investigate by means of second method of Lyapunov, sufficient conditions that guarantee uniform-asymptotic stability of the trivial solution and ultimate boundedness of all solutions to a certain second order differential equation. We construct a complete Lyapunov function in order to discuss the qualitative properties mentioned earlier. The boundedness result in this paper is new and also complement some boundedness results in literature obtained by using an incomplete Lyapunov function together with a signum function. Finally, we demonstrate the correctness of our results with two numerical examples and graphical representation of the trajectories of solutions to the examples using Maple software.
{"title":"On the Stability and Boundedness of Solutions to Certain Second Order Differential Equation","authors":"Adetunji Adedotun Adeyanju, Daniel Oluwasegun Adams","doi":"10.21638/11701/spbu35.2023.304","DOIUrl":"https://doi.org/10.21638/11701/spbu35.2023.304","url":null,"abstract":"In this paper, we investigate by means of second method of Lyapunov, sufficient conditions that guarantee uniform-asymptotic stability of the trivial solution and ultimate boundedness of all solutions to a certain second order differential equation. We construct a complete Lyapunov function in order to discuss the qualitative properties mentioned earlier. The boundedness result in this paper is new and also complement some boundedness results in literature obtained by using an incomplete Lyapunov function together with a signum function. Finally, we demonstrate the correctness of our results with two numerical examples and graphical representation of the trajectories of solutions to the examples using Maple software.","PeriodicalId":36965,"journal":{"name":"Differencialnie Uravnenia i Protsesy Upravlenia","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136202032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21638/11701/spbu35.2023.303
Khanlar Mehbali oglu Gamzaev
The problem of identifying the multiplier of the right side of a one-dimensional wave equation depending on a spatial variable is considered. As additional information, the condition of the final redefinition is set. A discrete analogue of the inverse problem is constructed using the finite difference method. To solve the resulting difference problem, a special representation is proposed, with the help of which the difference problem splits into two independent difference problems. As a result, an explicit formula is obtained for determining the approximate value of the desired function for each discrete value of a spatial variable. The presented results of numerical experiments conducted for model problems demonstrate the effectiveness of the proposed computational algorithm.
{"title":"Numerical Identification of the Dependence of the Right Side of the Wave Equation on the Spatial Variable","authors":"Khanlar Mehbali oglu Gamzaev","doi":"10.21638/11701/spbu35.2023.303","DOIUrl":"https://doi.org/10.21638/11701/spbu35.2023.303","url":null,"abstract":"The problem of identifying the multiplier of the right side of a one-dimensional wave equation depending on a spatial variable is considered. As additional information, the condition of the final redefinition is set. A discrete analogue of the inverse problem is constructed using the finite difference method. To solve the resulting difference problem, a special representation is proposed, with the help of which the difference problem splits into two independent difference problems. As a result, an explicit formula is obtained for determining the approximate value of the desired function for each discrete value of a spatial variable. The presented results of numerical experiments conducted for model problems demonstrate the effectiveness of the proposed computational algorithm.","PeriodicalId":36965,"journal":{"name":"Differencialnie Uravnenia i Protsesy Upravlenia","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136202482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21638/11701/spbu35.2023.305
Gerasim Vladimirovich Krivovichev, Nikolay Vasil'evich Egorov
The paper is devoted to the construction and analysis of implicit finite-difference schemes for a system of one-dimensional equations of hemodynamics. The schemes are based on the use of finite differences, which approximate spatial derivative with the fourth order. The schemes are based on the splitting on physical processes. According to this approach, at one time step, two mechanical processes are considered: the deformation of the vessel filled with fluid and the fluid flow in the deformed vessel. This approach makes it possible to separately consider finite-difference schemes, which approximate governing equations. In the practical implementation of the proposed schemes, they are reduced to systems of linear algebraic equations with pentadiagonal matrices. The stability analysis of constructed schemes is based on the von Neumann method and the principle of frozen coefficients. In the numerical solution of problems with known analytical solutions, it is demonstrated that the schemes lead to numerical solutions with a fourth-order convergence rate. In the computational experiments on simulation of blood flow in model vascular systems, it is demonstrated that the developed schemes make it possible to perform calculations in much less time than well-known explicit finite-difference and finite-volume schemes.
{"title":"Implicit Finite-difference Schemes for Equations of One-dimensional Hemodynamics","authors":"Gerasim Vladimirovich Krivovichev, Nikolay Vasil'evich Egorov","doi":"10.21638/11701/spbu35.2023.305","DOIUrl":"https://doi.org/10.21638/11701/spbu35.2023.305","url":null,"abstract":"The paper is devoted to the construction and analysis of implicit finite-difference schemes for a system of one-dimensional equations of hemodynamics. The schemes are based on the use of finite differences, which approximate spatial derivative with the fourth order. The schemes are based on the splitting on physical processes. According to this approach, at one time step, two mechanical processes are considered: the deformation of the vessel filled with fluid and the fluid flow in the deformed vessel. This approach makes it possible to separately consider finite-difference schemes, which approximate governing equations. In the practical implementation of the proposed schemes, they are reduced to systems of linear algebraic equations with pentadiagonal matrices. The stability analysis of constructed schemes is based on the von Neumann method and the principle of frozen coefficients. In the numerical solution of problems with known analytical solutions, it is demonstrated that the schemes lead to numerical solutions with a fourth-order convergence rate. In the computational experiments on simulation of blood flow in model vascular systems, it is demonstrated that the developed schemes make it possible to perform calculations in much less time than well-known explicit finite-difference and finite-volume schemes.","PeriodicalId":36965,"journal":{"name":"Differencialnie Uravnenia i Protsesy Upravlenia","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136202477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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