To understand the ability and limitations of convolutional neural networks to generate time series that mimic complex temporal signals, we trained a generative adversarial network consisting of convolutional networks to generate chaotic time series and used nonlinear time series analysis to evaluate the generated time series. A numerical measure of determinism and the Lyapunov exponent showed that the generated time series well reproduce the chaotic properties of the original time series. However, error distribution analyses showed that large errors appeared at a low but non-negligible rate. Such errors would not be expected if the distribution were assumed to be exponential.
{"title":"Evaluating generation of chaotic time series by convolutional generative adversarial networks","authors":"Yuki Tanaka, Yutaka Yamaguti","doi":"10.14495/jsiaml.15.117","DOIUrl":"https://doi.org/10.14495/jsiaml.15.117","url":null,"abstract":"To understand the ability and limitations of convolutional neural networks to generate time series that mimic complex temporal signals, we trained a generative adversarial network consisting of convolutional networks to generate chaotic time series and used nonlinear time series analysis to evaluate the generated time series. A numerical measure of determinism and the Lyapunov exponent showed that the generated time series well reproduce the chaotic properties of the original time series. However, error distribution analyses showed that large errors appeared at a low but non-negligible rate. Such errors would not be expected if the distribution were assumed to be exponential.","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":"59 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":"135710797","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}
Fuzzy cellular automaton (CA) is a dynamical system with a continuous state value embedding a CA with a discrete state value. We investigate a fuzzy CA obtained from an elementary CA of rule number 38. Its asymptotic solutions are classified into two types. One is a solution where stable propagating waves exist, and the other is a static uniform solution of constant value.
{"title":"Asymptotic solutions to a fuzzy elementary cellular automaton of rule number 38","authors":"Ko Yamamoto, Daisuke Takahashi","doi":"10.14495/jsiaml.15.93","DOIUrl":"https://doi.org/10.14495/jsiaml.15.93","url":null,"abstract":"Fuzzy cellular automaton (CA) is a dynamical system with a continuous state value embedding a CA with a discrete state value. We investigate a fuzzy CA obtained from an elementary CA of rule number 38. Its asymptotic solutions are classified into two types. One is a solution where stable propagating waves exist, and the other is a static uniform solution of constant value.","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":"86 1","pages":"93-96"},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82203680","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}
The problem of solving a system of multivariate quadratic equations over a finite field is known to be hard in general. However, there have been several algorithms of solving the system of quadratic equations efficiently when the number of variables is sufficiently larger than the number of equations (e.g., Kipnis et al., Eurocrypt 1999, Thomae-Wolf, PKC 2012, Cheng et al., PQCrypto 2014 and Furue et al., PQCrypto 2021). In the present paper, we propose a new algorithm which is available if the number of variables is smaller than that required in the previously given algorithms. We also analyze the security of MAYO, a variant of UOV, proposed in SAC 2021 and submitted to NIST’s standardization project of additional digital signature schemes for Post-Quantum Cryptography.
{"title":"An improvement of algorithms to solve under-defined systems of multivariate quadratic equations","authors":"Yasufumi Hashimoto","doi":"10.14495/jsiaml.15.53","DOIUrl":"https://doi.org/10.14495/jsiaml.15.53","url":null,"abstract":"The problem of solving a system of multivariate quadratic equations over a finite field is known to be hard in general. However, there have been several algorithms of solving the system of quadratic equations efficiently when the number of variables is sufficiently larger than the number of equations (e.g., Kipnis et al., Eurocrypt 1999, Thomae-Wolf, PKC 2012, Cheng et al., PQCrypto 2014 and Furue et al., PQCrypto 2021). In the present paper, we propose a new algorithm which is available if the number of variables is smaller than that required in the previously given algorithms. We also analyze the security of MAYO, a variant of UOV, proposed in SAC 2021 and submitted to NIST’s standardization project of additional digital signature schemes for Post-Quantum Cryptography.","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":"189 1","pages":"53-56"},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75794916","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":"Stability of surfaces with constant mean curvature bounded by two coaxial circles","authors":"Miyuki Koiso, Kento Okuda","doi":"10.14495/jsiaml.15.25","DOIUrl":"https://doi.org/10.14495/jsiaml.15.25","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":"86 1","pages":"25-28"},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75841663","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":"Optimal selection formulas of mesh size and truncation numbers for the double-exponential formula","authors":"Tomoaki Okayama, Yuta Kawai","doi":"10.14495/jsiaml.15.81","DOIUrl":"https://doi.org/10.14495/jsiaml.15.81","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":"83 1","pages":"81-84"},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84546663","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":"Numerical computation for magnetic Hele-Shaw problem using the method of fundamental solutions","authors":"Yusaku Shimoji, S. Yazaki","doi":"10.14495/jsiaml.15.29","DOIUrl":"https://doi.org/10.14495/jsiaml.15.29","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":"40 5","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72573667","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":"Quasi-static frictional contact analysis free from solutions of linear equations: an approach based on primal-dual algorithm","authors":"Y. Kanno","doi":"10.14495/jsiaml.15.49","DOIUrl":"https://doi.org/10.14495/jsiaml.15.49","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":"24 1","pages":"49-52"},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84615582","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}
An application of the Bayesian optimization to an ordinary differential equation-based neural network is proposed. The loss function was considered as a black box function of the coefficients, and Bayesian optimization was applied to obtain desirable parameter values. The proposed method drastically simplifies the implementation because the adjoint method-based updating of coefficients is not required. Numerical experiments demonstrate that the performance of the proposed method is comparable to that of existing methods.
{"title":"An ODE-based neural network with Bayesian optimization","authors":"Hirotada Honda, Takashi Sano, Shugo Nakamura, Mitsuaki Ueno, Hiroki Hanazawa, Nguyen Manh Duc Tuan","doi":"10.14495/jsiaml.15.101","DOIUrl":"https://doi.org/10.14495/jsiaml.15.101","url":null,"abstract":"An application of the Bayesian optimization to an ordinary differential equation-based neural network is proposed. The loss function was considered as a black box function of the coefficients, and Bayesian optimization was applied to obtain desirable parameter values. The proposed method drastically simplifies the implementation because the adjoint method-based updating of coefficients is not required. Numerical experiments demonstrate that the performance of the proposed method is comparable to that of existing methods.","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":"79 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":"136047601","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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