The notion of stable configuration in a Sn' cell space which is invariant under any application of local majority transformation (LMT) was introduced in Kitagawa and Yamaguchi [1] and the notion of determinative subspace in a 4(71) cell space which determines a structure of a stable configuration was introduced in our paper [2]. Some structual properties of determinative subspace in ZI(n) cell space were suggested throughout various examples of determinative subspace in Kitagawa and Yamaguchi [3]. According to the definitions of generative and non-generative determinative subspace in 4(n) cell space given by Kitagawa [4] in view of propagation of determined cells, these examples are mostly concerned with those of generative determinative subspace in 4(n) cell space. The purpose of this paper is to give a deeper investigation for the constructions of determinative subspaces in 4(n) cell space. In SECTION 2 we shall introduce several notions which are indispensable for a construction procedure of generative determinative subspace in 4(m) cell space such as a convex set, a spiny convex set and a two-cell extension of a set and so on. In SECTION 3 we shall give a certain type of construction procedure of any generative determinative subspace in zl(n) cell space. In APPENDIX we shall give an example of our construction process of a generative determinative subspace obtained by using this proceduce. In SECTION 4 we shall introduce several notions of elementary subsets and superposition of elementary subsets and decomposition of the whole cell space into a family of superposed elementary subsets. These nations are fundamental tools for proving THEOREM 3 and 4, which give us a construction procedure and hence a structural characteristic feature of any non-generative determinative subspace in 4(n) cell space. The last SECTION 5 is devoted to the another proof of THEOREM 2 in our previours paper [2] which appeals to LEMMA 4 in the present paper prepared for giving our construction procedure of non-generative determinative determinative
{"title":"STRUCTURE OF DETERMINATIVE SUBSPACE IN TRIANGULAR CELL SPACE : INFORMATION SCIENCE APPROACH TO BIOMATHEMATICS, VIII","authors":"M. Yamaguchi","doi":"10.5109/13056","DOIUrl":"https://doi.org/10.5109/13056","url":null,"abstract":"The notion of stable configuration in a Sn' cell space which is invariant under any application of local majority transformation (LMT) was introduced in Kitagawa and Yamaguchi [1] and the notion of determinative subspace in a 4(71) cell space which determines a structure of a stable configuration was introduced in our paper [2]. Some structual properties of determinative subspace in ZI(n) cell space were suggested throughout various examples of determinative subspace in Kitagawa and Yamaguchi [3]. According to the definitions of generative and non-generative determinative subspace in 4(n) cell space given by Kitagawa [4] in view of propagation of determined cells, these examples are mostly concerned with those of generative determinative subspace in 4(n) cell space. The purpose of this paper is to give a deeper investigation for the constructions of determinative subspaces in 4(n) cell space. In SECTION 2 we shall introduce several notions which are indispensable for a construction procedure of generative determinative subspace in 4(m) cell space such as a convex set, a spiny convex set and a two-cell extension of a set and so on. In SECTION 3 we shall give a certain type of construction procedure of any generative determinative subspace in zl(n) cell space. In APPENDIX we shall give an example of our construction process of a generative determinative subspace obtained by using this proceduce. In SECTION 4 we shall introduce several notions of elementary subsets and superposition of elementary subsets and decomposition of the whole cell space into a family of superposed elementary subsets. These nations are fundamental tools for proving THEOREM 3 and 4, which give us a construction procedure and hence a structural characteristic feature of any non-generative determinative subspace in 4(n) cell space. The last SECTION 5 is devoted to the another proof of THEOREM 2 in our previours paper [2] which appeals to LEMMA 4 in the present paper prepared for giving our construction procedure of non-generative determinative determinative","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1971-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122266896","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":"STABLE CONFIGURATION UNDER LOCAL MAJORITY TRANSFORMATIONS ON CELL SPACE : INFORMATION SCIENCE APPROACH TO BIOMATHEMATICS, V","authors":"M. Yamaguchi","doi":"10.5109/13055","DOIUrl":"https://doi.org/10.5109/13055","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1971-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122026278","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 purpose of this paper is to discuss statistical properties of an estimate of a probability density function based on the first n observations under the assumption of continuity or uniform continuity of the probability density function in case where we observe a sequence of random vectors which come from a population with the probability density function. Let X1, X2,X3,••• be a sequence of independent identically distributed m-dimensional random vectors having a probability density function f(x). Suppose the first n observations be denoted by X1, X2, ••• Xn. Then a natural estimate of the probability density function f(x) may be denoted as follows for a suitable positive constant h
{"title":"SEQUENTIAL ESTIMATION OF A CONTINUOUS PROBABILITY DENSITY FUNCTION AND MODE","authors":"Hajime Yamato","doi":"10.5109/13049","DOIUrl":"https://doi.org/10.5109/13049","url":null,"abstract":"The purpose of this paper is to discuss statistical properties of an estimate of a probability density function based on the first n observations under the assumption of continuity or uniform continuity of the probability density function in case where we observe a sequence of random vectors which come from a population with the probability density function. Let X1, X2,X3,••• be a sequence of independent identically distributed m-dimensional random vectors having a probability density function f(x). Suppose the first n observations be denoted by X1, X2, ••• Xn. Then a natural estimate of the probability density function f(x) may be denoted as follows for a suitable positive constant h","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1971-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115069282","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":"APPLICATION OF KITAGAWA'S FUNCTIONAL INTEGRAL TO SOLUTIONS OF NON-LINEAR INTEGRAL EQUATIONS OF TWO VARIABLES","authors":"P. Strait","doi":"10.5109/13052","DOIUrl":"https://doi.org/10.5109/13052","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1971-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121368889","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 THE PATTERN CLASSIFICATION PROBLEMS BY LEARNING I","authors":"Kensuke Tanaka","doi":"10.5109/13043","DOIUrl":"https://doi.org/10.5109/13043","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"330 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1970-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132194541","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":"FUNDAMENTAL THEOREMS IN A BAYES CONTROLLED PROCESS","authors":"N. Furukawa","doi":"10.5109/13048","DOIUrl":"https://doi.org/10.5109/13048","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1970-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133688046","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 NOTE ON THE EFFICIENCY OF TAMURA'S $ Q $","authors":"T. Yanagawa","doi":"10.5109/13042","DOIUrl":"https://doi.org/10.5109/13042","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"218 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1970-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131492387","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":"STOPPED DECISION PROCESS ON COMPACT METRIC SPACES","authors":"Seiichi Iwamoto, 岩本 誠一","doi":"10.5109/13044","DOIUrl":"https://doi.org/10.5109/13044","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1970-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131259285","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}
various attempts have been made to construct nonparametric tests by authors such as Mood [9], Sukhatme [11], Freund and Ansari [7], Barton and David [4], Tamura [12], Siegel and Tukey [10], Capon [5], Klotz [8] and others. But as Klotz [8] has pointed out, there is (at least asymptotically) an equivalence in the sense of test statistics among the test of Freund-Ansari, Barton-David and Siegel-Turkey, and hence we shall restrict our consideration to the tests of Sukhatme, Tamura, Mood and Freund-Ansari, whose test statistics are given as follows. Let denote min (x, y) and max (x, y) by x Ay and x V y, respedtively. Sukhatme's T: 1 ni T1" = E E 46(xi, YJ)
Mood[9]、Sukhatme[11]、Freund and Ansari[7]、Barton and David[4]、Tamura[12]、Siegel and Tukey[10]、Capon[5]、Klotz[8]等人尝试构建非参数检验。但正如Klotz[8]所指出的那样，Freund-Ansari、Barton-David和Siegel-Turkey的检验在检验统计量意义上存在(至少是渐近的)等价，因此我们将把我们的考虑限制在Sukhatme、Tamura、Mood和Freund-Ansari的检验上，他们的检验统计量给出如下。令最小(x, y)和最大(x, y)分别用x Ay和x vy表示。Sukhatme's T: 1 ni T1 ' = E E 46(xi, YJ)
{"title":"A FURTHER COMPARISON OF TWO-SAMPLE NONPARAMETRIC TESTS FOR DISPERISON I","authors":"T. Yanagawa","doi":"10.5109/13041","DOIUrl":"https://doi.org/10.5109/13041","url":null,"abstract":"various attempts have been made to construct nonparametric tests by authors such as Mood [9], Sukhatme [11], Freund and Ansari [7], Barton and David [4], Tamura [12], Siegel and Tukey [10], Capon [5], Klotz [8] and others. But as Klotz [8] has pointed out, there is (at least asymptotically) an equivalence in the sense of test statistics among the test of Freund-Ansari, Barton-David and Siegel-Turkey, and hence we shall restrict our consideration to the tests of Sukhatme, Tamura, Mood and Freund-Ansari, whose test statistics are given as follows. Let denote min (x, y) and max (x, y) by x Ay and x V y, respedtively. Sukhatme's T: 1 ni T1\" = E E 46(xi, YJ)","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1970-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129682547","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}
Stochastic approximation method first introduced by Robbins-Monro [10] has been proved to be very useful for a learning system in the sense that its algorithm is very simple and that, at any given time in the learning process, the past samples are not required to retain in memory as shown by Albert and Gardner [1] , Blum [3] etc. In this paper we are concerned with its applications . After giving some preliminaries and notations in Section 2, we shall treat in Section 3 the problem of finding threshold elements, which is fundamental in pattern classification . In Section 4 we shall consider the problem of parameter identification in linear system with an additive noise.
{"title":"SOME APPLICATIONS OF STOCHASTIC APPROXIMAION METHOD","authors":"H. Fukamichi","doi":"10.5109/13046","DOIUrl":"https://doi.org/10.5109/13046","url":null,"abstract":"Stochastic approximation method first introduced by Robbins-Monro [10] has been proved to be very useful for a learning system in the sense that its algorithm is very simple and that, at any given time in the learning process, the past samples are not required to retain in memory as shown by Albert and Gardner [1] , Blum [3] etc. In this paper we are concerned with its applications . After giving some preliminaries and notations in Section 2, we shall treat in Section 3 the problem of finding threshold elements, which is fundamental in pattern classification . In Section 4 we shall consider the problem of parameter identification in linear system with an additive noise.","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1970-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134487533","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：