Mathematical foundations of computing最新文献

{"title":"Generalized interval AOR method for solving interval linear equations","authors":"Jahnabi Chakravarty, M. Saha","doi":"10.3934/mfc.2023035","DOIUrl":"https://doi.org/10.3934/mfc.2023035","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221069","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}

{"title":"A review of definitions of fractional differences and sums","authors":"Qiushuang Wang, R. Xu","doi":"10.3934/mfc.2022013","DOIUrl":"https://doi.org/10.3934/mfc.2022013","url":null,"abstract":"Given the increasing importance of discrete fractional calculus in mathematics, science engineering and so on, many different concepts of fractional difference and sum operators have been defined. In this paper, we mainly reviews some definitions of fractional differences and sum operators that emerged in the fields of discrete calculus. Moreover, some properties of those operators are also analyzed and compared with each other, including commutation rules, linearity, Leibniz rules, etc.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89854411","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}

{"title":"Shape preserving properties of $ (mathfrak{p}, mathfrak{q}) $ Bernstein Bèzier curves and corresponding results over $ [a, b] $","authors":"V. Sharma, Asif Khan, M. Mursaleen","doi":"10.3934/mfc.2022041","DOIUrl":"https://doi.org/10.3934/mfc.2022041","url":null,"abstract":"<p style='text-indent:20px;'>This article deals with shape preserving and local approximation properties of post-quantum Bernstein bases and operators over arbitrary interval <inline-formula><tex-math id=\"M3\">begin{document}$ [a, b] $end{document}</tex-math></inline-formula> defined by Khan and Sharma (Iran J Sci Technol Trans Sci (2021)). The properties for <inline-formula><tex-math id=\"M4\">begin{document}$ (mathfrak{p}, mathfrak{q}) $end{document}</tex-math></inline-formula>-Bernstein bases and Bézier curves over <inline-formula><tex-math id=\"M5\">begin{document}$ [a, b] $end{document}</tex-math></inline-formula> have been given. A de Casteljau algorithm has been discussed. Further we obtain the rate of convergence for <inline-formula><tex-math id=\"M6\">begin{document}$ (mathfrak{p}, mathfrak{q}) $end{document}</tex-math></inline-formula>-Bernstein operators over <inline-formula><tex-math id=\"M7\">begin{document}$ [a, b] $end{document}</tex-math></inline-formula> in terms of Lipschitz type space having two parameters and Lipschitz maximal functions.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91053183","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}

{"title":"Learning and approximating piecewise smooth functions by deep sigmoid neural networks","authors":"Xia Liu","doi":"10.3934/mfc.2023039","DOIUrl":"https://doi.org/10.3934/mfc.2023039","url":null,"abstract":"Constructing neural networks for function approximation is a classical and longstanding topic in approximation theory, so is it in learning theory. In this paper, we are going to construct a deep neural network with three hidden layers using sigmoid function to approximate and learn the piecewise smooth functions, respectively. In particular, we prove that the constructed deep sigmoid nets can reach the optimal approximation rate in approximating the piecewise smooth functions with controllable parameters but without saturation. Similar results can also be obtained in learning theory, that is, the constructed deep sigmoid nets can also realize the optimal learning rates in learning the piecewise smooth functions. The above two obtained results underlie the advantages of deep sigmoid nets and provide theoretical assessment for deep learning.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135699848","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}

{"title":"Autism spectrum disorder (ASD) classification with three types of correlations based on ABIDE Ⅰ data","authors":"Donglin Wang, Xin Yang, Wandi Ding","doi":"10.3934/mfc.2023042","DOIUrl":"https://doi.org/10.3934/mfc.2023042","url":null,"abstract":"Autism spectrum disorder (ASD) is a type of mental health disorder, and its prevalence worldwide is estimated at about one in 100 children. Accurate diagnosis of ASD as early as possible is very important for the treatment of patients in clinical applications. ABIDE Ⅰ dataset as a repository of ASD is used much for developing classifiers for ASD from typical controls. In this paper, we mainly consider three types of correlations including Pearson correlation, partial correlation, and tangent correlation together based on different numbers of regions of interest (ROIs) from only one atlas, and then twelve deep neural network models are used to train 884 subjects with 5, 10, 15, 20-fold cross-validation on two types of split methods including stratified and non-stratified methods. We first consider six metrics to compare the model performance among the split methods. The six metrics are F1-Score, precision, recall, accuracy, and specificity, area under the precision-recall curve (PRAUC), and area under the Receiver Characteristic Operator curve (ROCAUC). The study achieved the highest accuracy rate of 71.94% for 5-fold cross-validation, 72.64% for 10-fold cross-validation, 72.96% for 15-fold cross-validation, and 73.43% for 20-fold cross-validation.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136367263","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}

{"title":"Output feedback control of interval type-2 T-S fuzzy fractional order systems subject to actuator saturation","authors":"Taoqi Deng, Xuefeng Zhang, Zhe Wang","doi":"10.3934/mfc.2023025","DOIUrl":"https://doi.org/10.3934/mfc.2023025","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220953","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}

{"title":"On Szász-Durrmeyer type modification using Gould Hopper polynomials","authors":"Karunesh Singh, P. Agrawal","doi":"10.3934/mfc.2022011","DOIUrl":"https://doi.org/10.3934/mfc.2022011","url":null,"abstract":"In the present article, we study a generalization of Szász operators by Gould-Hopper polynomials. First, we obtain an estimate of error of the rate of convergence by these operators in terms of first order and second order moduli of continuity. Then, we derive a Voronovkaya-type theorem for these operators. Lastly, we derive Grüss-Voronovskaya type approximation theorem and Grüss-Voronovskaya type asymptotic result in quantitative form.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84420470","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}

{"title":"Some structures of submatrices in solution to the paire of matrix equations $ AX = C $, $ XB = D $","authors":"Radja Belkhiri, Sihem Guerarra","doi":"10.3934/mfc.2022023","DOIUrl":"https://doi.org/10.3934/mfc.2022023","url":null,"abstract":"<p style='text-indent:20px;'>The optimization problems involving local unitary and local contraction matrices and some Hermitian structures have been concedered in this paper. We establish a set of explicit formulas for calculating the maximal and minimal values of the ranks and inertias of the matrices <inline-formula><tex-math id=\"M3\">begin{document}$ X_{1}X_{1}^{ast}-P_{1} $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M4\">begin{document}$ X_{2}X_{2}^{ast}-P_{1} $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M5\">begin{document}$ X_{3}X_{3}^{ast}-P_{2} $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M6\">begin{document}$ X_{4}X_{4}^{ast }-P_{2} $end{document}</tex-math></inline-formula>, with respect to <inline-formula><tex-math id=\"M7\">begin{document}$ X_{1} $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M8\">begin{document}$ X_{2} $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M9\">begin{document}$ X_{3} $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M10\">begin{document}$ X_{4} $end{document}</tex-math></inline-formula> respectively, where <inline-formula><tex-math id=\"M11\">begin{document}$ P_{1}in mathbb{C} ^{n_{1}times n_{1}} $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M12\">begin{document}$ P_{2}in mathbb{C} ^{n_{2}times n_{2}} $end{document}</tex-math></inline-formula> are given, <inline-formula><tex-math id=\"M13\">begin{document}$ X_{1} $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M14\">begin{document}$ X_{2} $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M15\">begin{document}$ X_{3} $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M16\">begin{document}$ X_{4} $end{document}</tex-math></inline-formula> are submatrices in a general common solution <inline-formula><tex-math id=\"M17\">begin{document}$ X $end{document}</tex-math></inline-formula> to the paire of matrix equations <inline-formula><tex-math id=\"M18\">begin{document}$ AX = C $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M19\">begin{document}$ XB = D. $end{document}</tex-math></inline-formula></p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88200490","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}

{"title":"Expression recognition method combining convolutional features and Transformer","authors":"Xiaoning Zhu, Zhongyi Li, Jian Sun","doi":"10.3934/mfc.2022018","DOIUrl":"https://doi.org/10.3934/mfc.2022018","url":null,"abstract":"Expression recognition has been an important research direction in the field of psychology, which can be used in traffic, medical, security, and criminal investigation by expressing human feelings through the muscles in the corners of the mouth, eyes, and face. Most of the existing research work uses convolutional neural networks (CNN) to recognize face images and thus classify expressions, which does achieve good results, but CNN do not have enough ability to extract global features. The Transformer has advantages for global feature extraction, but the Transformer is more computationally intensive and requires a large amount of training data. So, in this paper, we use the hierarchical Transformer, namely Swin Transformer, for the expression recognition task, and its computational power will be greatly reduced. At the same time, it is fused with a CNN model to propose a network architecture that combines the Transformer and CNN, and to the best of our knowledge, we are the first to combine the Swin Transformer with CNN and use it in an expression recognition task. We then evaluate the proposed method on some publicly available expression datasets and can obtain competitive results.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86744988","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}

{"title":"Adaptive attitude determination of bionic polarization integrated navigation system based on reinforcement learning strategy","authors":"HuiYi Bao, Tao Du, Luyue Sun","doi":"10.3934/mfc.2022014","DOIUrl":"https://doi.org/10.3934/mfc.2022014","url":null,"abstract":"The bionic polarization integrated navigation system includes three-axis gyroscopes, three-axis accelerometers, three-axis magnetometers, and polarization sensors, which provide pitch, roll, and yaw. When the magnetometers are interfered or the polarization sensors are obscured, the accuracy of attitude will be decreased due to abnormal measurement. To improve the accuracy of attitude of the integrated navigation system under these complex environments, an adaptive complementary filter based on DQN (Deep Q-learning Network) is proposed. The complementary filter is first designed to fuse the measurements from the gyroscopes, accelerometers, magnetometers, and polarization sensors. Then, a reward function of the bionic polarization integrated navigation system is defined as the function of the absolute value of the attitude angle error. The action-value function is introduced by a fully-connected network obtained by historical sensor data training. The strategy can be calculated by the deep Q-learning network and the action that optimal action-value function is obtained. Based on the optimized action, three types of integration are switched automatically to adapt to the different environments. Three cases of simulations are conducted to validate the effectiveness of the proposed algorithm. The results show that the adaptive attitude determination of bionic polarization integrated navigation system based on DQN can improve the accuracy of the attitude estimation.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82211802","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}