Abstract Causal laws are defined in terms of concepts and the causal relations between them. Following Kemp et al. (2010), we investigate the performance of the hierarchical Bayesian model, in which causal systems are represented by directed acyclic graphs (DAGs) with nodes divided into distinct categories. This paper presents two non-reversible search and score algorithms (Q1 and Q2) and their application to the causal learning system. The algorithms run through the pairs of class-assignment vectors and graph structures and choose the one which maximizes the probability of given observations. The model discovers latent classes in relational data and the number of these classes and predicts relations between objects belonging to them. We evaluate its performance on prediction tasks from the behavioural experiment about human cognition. Within the discussed approach, we solve a simplified prediction problem when object classification is known in advance. Finally, we describe the experimental procedure allowing in-depth analysis of the efficiency and scalability of both search and score algorithms.
{"title":"Learning causal theories with non-reversible MCMC methods","authors":"Antonina Krajewska","doi":"10.2478/candc-2021-0021","DOIUrl":"https://doi.org/10.2478/candc-2021-0021","url":null,"abstract":"Abstract Causal laws are defined in terms of concepts and the causal relations between them. Following Kemp et al. (2010), we investigate the performance of the hierarchical Bayesian model, in which causal systems are represented by directed acyclic graphs (DAGs) with nodes divided into distinct categories. This paper presents two non-reversible search and score algorithms (Q1 and Q2) and their application to the causal learning system. The algorithms run through the pairs of class-assignment vectors and graph structures and choose the one which maximizes the probability of given observations. The model discovers latent classes in relational data and the number of these classes and predicts relations between objects belonging to them. We evaluate its performance on prediction tasks from the behavioural experiment about human cognition. Within the discussed approach, we solve a simplified prediction problem when object classification is known in advance. Finally, we describe the experimental procedure allowing in-depth analysis of the efficiency and scalability of both search and score algorithms.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"323 - 361"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49179257","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}
Zohreh Hayati, M. Shafieirad, I. Zamani, Amir Hossein, A. Mehra, Zohreh Abbasi
Abstract This paper presents an iterative method for the unbiased identification of linear Multiple-Input Multiple-Output (MIMO) discrete two-dimensional (2D) systems. The system discussed here has Auto-Regressive Moving-Average model with exogenous inputs (ARMAX model). The proposed algorithm functions on the basis of the traditional Iterative Generalized Least Squares (IGLS) method. In summary, this paper proposes a two-dimensional Multiple-Input Multiple-Output Iterative Generalized Least Squares (2DMIGLS) algorithm to estimate the unknown parameters of the ARMAX model. Finally, simulation results show the efficiency and accuracy of the presented algorithm in estimating the unknown parameters of the model in the presence of colored noise.
{"title":"Parameter estimation of MIMO two-dimensional ARMAX model based on IGLS method","authors":"Zohreh Hayati, M. Shafieirad, I. Zamani, Amir Hossein, A. Mehra, Zohreh Abbasi","doi":"10.2478/candc-2021-0020","DOIUrl":"https://doi.org/10.2478/candc-2021-0020","url":null,"abstract":"Abstract This paper presents an iterative method for the unbiased identification of linear Multiple-Input Multiple-Output (MIMO) discrete two-dimensional (2D) systems. The system discussed here has Auto-Regressive Moving-Average model with exogenous inputs (ARMAX model). The proposed algorithm functions on the basis of the traditional Iterative Generalized Least Squares (IGLS) method. In summary, this paper proposes a two-dimensional Multiple-Input Multiple-Output Iterative Generalized Least Squares (2DMIGLS) algorithm to estimate the unknown parameters of the ARMAX model. Finally, simulation results show the efficiency and accuracy of the presented algorithm in estimating the unknown parameters of the model in the presence of colored noise.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"303 - 322"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43225920","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}
Mohamed Elkhail Danine, A. Bernoussi, Abdelaziz Bel Fekih
Abstract In this work, we consider the partial observability problem for finite dimensional dynamical linear systems that are not necessarily observable. For that purpose we introduce the so called “observable subspaces” and “partial observability” to find a way to reconstruct the observable part of the system state. Some characterizations of “observable subspaces” have been provided. The reconstruction of the orthogonal projection of the state on the observable subspace is obtained. We give some examples to illustrate our theoretical approach.
{"title":"Partial observability of finite dimensional linear systems","authors":"Mohamed Elkhail Danine, A. Bernoussi, Abdelaziz Bel Fekih","doi":"10.2478/candc-2021-0014","DOIUrl":"https://doi.org/10.2478/candc-2021-0014","url":null,"abstract":"Abstract In this work, we consider the partial observability problem for finite dimensional dynamical linear systems that are not necessarily observable. For that purpose we introduce the so called “observable subspaces” and “partial observability” to find a way to reconstruct the observable part of the system state. Some characterizations of “observable subspaces” have been provided. The reconstruction of the orthogonal projection of the state on the observable subspace is obtained. We give some examples to illustrate our theoretical approach.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"269 - 300"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46967291","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}
Abstract The article studies the nutrient transfer mechanism for cropping systems in polluted soils from a mathematical and optimal control point of view. The problem under consideration is governed by an advection-diffusion PDE in a bounded domain. The existence of a solution is obtained. We also determine the optimal amount of required nutrients at the root surface for plants where the soil is polluted by an unknown source. The characterization of the optimal control by a singular optimality system is obtained.
{"title":"Optimal control of advection-diffusion problems for cropping systems in polluted soils","authors":"L. Louison, A. Omrane","doi":"10.2478/candc-2021-0013","DOIUrl":"https://doi.org/10.2478/candc-2021-0013","url":null,"abstract":"Abstract The article studies the nutrient transfer mechanism for cropping systems in polluted soils from a mathematical and optimal control point of view. The problem under consideration is governed by an advection-diffusion PDE in a bounded domain. The existence of a solution is obtained. We also determine the optimal amount of required nutrients at the root surface for plants where the soil is polluted by an unknown source. The characterization of the optimal control by a singular optimality system is obtained.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"253 - 268"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41322331","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}
Abstract The problem of finding the maximum number of d-vertices cliques (d = 3) in d-partite graph (d = 3) when graph density q is lower than 1 is an important problem in combinatorial optimization and it is one of many NP-complete problems. For this problem a meta-heuristic algorithm has been developed, namely an ant colony optimization algorithm. In this paper a new development of this ant algorithm and experimental results are presented. The problem of finding the maximum number of 3-vertices cliques can be encountered in computer image analysis, computer vision applications, automation and robotic vision systems. The optimal solution of this problem boils down to finding a set of 3-vertices cliques in a 3-partite graph and this set should have cardinality as high as possible. The elaborated ant colony algorithm can be easily modified for d-dimensional problems, that is for finding the maximum number of d-vertices cliques in a d-partite graph.
{"title":"An ant algorithm for the maximum number of 3-cliques in 3-partite graphs","authors":"Krzysztof Schiff","doi":"10.2478/candc-2021-0018","DOIUrl":"https://doi.org/10.2478/candc-2021-0018","url":null,"abstract":"Abstract The problem of finding the maximum number of d-vertices cliques (d = 3) in d-partite graph (d = 3) when graph density q is lower than 1 is an important problem in combinatorial optimization and it is one of many NP-complete problems. For this problem a meta-heuristic algorithm has been developed, namely an ant colony optimization algorithm. In this paper a new development of this ant algorithm and experimental results are presented. The problem of finding the maximum number of 3-vertices cliques can be encountered in computer image analysis, computer vision applications, automation and robotic vision systems. The optimal solution of this problem boils down to finding a set of 3-vertices cliques in a 3-partite graph and this set should have cardinality as high as possible. The elaborated ant colony algorithm can be easily modified for d-dimensional problems, that is for finding the maximum number of d-vertices cliques in a d-partite graph.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"347 - 358"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44578718","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}
Abstract In this paper, we introduce a Q2n(x) Q_2^nleft( x right) matrix, whose elements are balancing polynomials, and develop a new coding and decoding method following from the Q2n(x) Q_2^nleft( x right) matrix. We establish the relations between the code matrix elements, error detection and correction for this coding theory.
{"title":"Coding theory based on balancing polynomials","authors":"B. Prasad","doi":"10.2478/candc-2021-0017","DOIUrl":"https://doi.org/10.2478/candc-2021-0017","url":null,"abstract":"Abstract In this paper, we introduce a Q2n(x) Q_2^nleft( x right) matrix, whose elements are balancing polynomials, and develop a new coding and decoding method following from the Q2n(x) Q_2^nleft( x right) matrix. We establish the relations between the code matrix elements, error detection and correction for this coding theory.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"335 - 346"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42519861","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}
Abstract The paper proposes a method for solving systems of linear inequalities. This method determines in a finite number of iterations whether the given system of linear ineqalities has a solution. If it does, the solution for the given system of linear inequalities is provided. The computational complexity of the proposed method is locally polynomial.
{"title":"A locally polynomial method for solving a system of linear inequalities","authors":"Y. Evtushenko, K. Szkatula, A. Tretyakov","doi":"10.2478/candc-2021-0015","DOIUrl":"https://doi.org/10.2478/candc-2021-0015","url":null,"abstract":"Abstract The paper proposes a method for solving systems of linear inequalities. This method determines in a finite number of iterations whether the given system of linear ineqalities has a solution. If it does, the solution for the given system of linear inequalities is provided. The computational complexity of the proposed method is locally polynomial.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"301 - 314"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44347333","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}
Abstract The article is devoted to the development and study of a model of a minimal risk portfolio under conditions of hybrid uncertainty of possibilistic-probabilistic type. In this model, the interaction of fuzzy parameters is described by both the strongest and the weakest triangular norms. The formula for variance of a portfolio is given that allows for estimating its risk. Models of acceptable portfolios are based on the principle of expected possibility or on the basis of fulfilling the restriction on the possibility/necessity and probability of the level of portfolio return that is acceptable to an investor. Equivalent deterministic analogues of the models are constructed and their solution methods are developed. Theorems describing a set of investment opportunities are proven. The obtained results are demonstrated on a model example.
{"title":"Model of a minimal risk portfolio under hybrid uncertainty","authors":"A. Yazenin, I. Soldatenko","doi":"10.2478/candc-2021-0016","DOIUrl":"https://doi.org/10.2478/candc-2021-0016","url":null,"abstract":"Abstract The article is devoted to the development and study of a model of a minimal risk portfolio under conditions of hybrid uncertainty of possibilistic-probabilistic type. In this model, the interaction of fuzzy parameters is described by both the strongest and the weakest triangular norms. The formula for variance of a portfolio is given that allows for estimating its risk. Models of acceptable portfolios are based on the principle of expected possibility or on the basis of fulfilling the restriction on the possibility/necessity and probability of the level of portfolio return that is acceptable to an investor. Equivalent deterministic analogues of the models are constructed and their solution methods are developed. Theorems describing a set of investment opportunities are proven. The obtained results are demonstrated on a model example.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"315 - 333"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48720354","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}
Abstract We report some additional examples of explicit solutions to an inverse first-passage place problem for one-dimensional diffusions with jumps, introduced in a previous paper. If X(t) is a one-dimensional diffusion with jumps, starting from a random position η ∈ [a, b], let be τa,b the time at which X(t) first exits the interval (a, b), and πa = P (X(τa,b) ≤ a) the probability of exit from the left of (a, b). Given a probability q ∈ (0, 1), the problem consists in finding the density g of η (if it exists) such that πa = q; it can be seen as a problem of optimization.
{"title":"Some examples of solutions to an inverse problem for the first-passage place of a jump-diffusion process","authors":"M. Abundo","doi":"10.2478/candc-2022-0003","DOIUrl":"https://doi.org/10.2478/candc-2022-0003","url":null,"abstract":"Abstract We report some additional examples of explicit solutions to an inverse first-passage place problem for one-dimensional diffusions with jumps, introduced in a previous paper. If X(t) is a one-dimensional diffusion with jumps, starting from a random position η ∈ [a, b], let be τa,b the time at which X(t) first exits the interval (a, b), and πa = P (X(τa,b) ≤ a) the probability of exit from the left of (a, b). Given a probability q ∈ (0, 1), the problem consists in finding the density g of η (if it exists) such that πa = q; it can be seen as a problem of optimization.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"51 1","pages":"31 - 42"},"PeriodicalIF":0.0,"publicationDate":"2021-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47815964","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}
Abstract We consider a heat conduction problem S with mixed boundary conditions in an n-dimensional domain Ω with regular boundary and a family of problems Sα with also mixed boundary conditions in Ω, where α > 0 is the heat transfer coefficient on the portion of the boundary Γ1. In relation to these state systems, we formulate Neumann boundary optimal control problems on the heat flux q which is definite on the complementary portion Γ2 of the boundary of Ω. We obtain existence and uniqueness of the optimal controls, the first order optimality conditions in terms of the adjoint state and the convergence of the optimal controls, the system state and the adjoint state when the heat transfer coefficient α goes to infinity. Furthermore, we formulate particular boundary optimal control problems on a real parameter λ, in relation to the parabolic problems S and Sα and to mixed elliptic problems P and Pα. We find an explicit form for the optimal controls, we prove monotony properties and we obtain convergence results when the parameter time goes to infinity.
{"title":"Neumann boundary optimal control problems governed by parabolic variational equalities","authors":"Carolina M. Bollo, C. Gariboldi, D. Tarzia","doi":"10.2478/candc-2021-0012","DOIUrl":"https://doi.org/10.2478/candc-2021-0012","url":null,"abstract":"Abstract We consider a heat conduction problem S with mixed boundary conditions in an n-dimensional domain Ω with regular boundary and a family of problems Sα with also mixed boundary conditions in Ω, where α > 0 is the heat transfer coefficient on the portion of the boundary Γ1. In relation to these state systems, we formulate Neumann boundary optimal control problems on the heat flux q which is definite on the complementary portion Γ2 of the boundary of Ω. We obtain existence and uniqueness of the optimal controls, the first order optimality conditions in terms of the adjoint state and the convergence of the optimal controls, the system state and the adjoint state when the heat transfer coefficient α goes to infinity. Furthermore, we formulate particular boundary optimal control problems on a real parameter λ, in relation to the parabolic problems S and Sα and to mixed elliptic problems P and Pα. We find an explicit form for the optimal controls, we prove monotony properties and we obtain convergence results when the parameter time goes to infinity.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"227 - 252"},"PeriodicalIF":0.0,"publicationDate":"2021-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48299816","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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