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Uniform distribution theory最新文献

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Sur Les Parties Fractionnaires Des Suites (βn)n≥1 序列(βn)n≥1的分数部分
Uniform distribution theory Pub Date : 2019-12-01 DOI: 10.2478/udt-2019-0014
Anne Bertrand-Mathis
{"title":"Sur Les Parties Fractionnaires Des Suites (βn)n≥1","authors":"Anne Bertrand-Mathis","doi":"10.2478/udt-2019-0014","DOIUrl":"https://doi.org/10.2478/udt-2019-0014","url":null,"abstract":"Abstract We show that for an arbitrary sequence of intervals In with constant length c, there exist real numbers β such that for all n βn belongs to In modulo one.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"8 1","pages":"69 - 72"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87688572","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}
引用次数: 0
Quasi-Random Graphs, Pseudo-Random Graphs and Pseudorandom Binary Sequences, I. (Quasi-Random Graphs) 拟随机图，伪随机图和伪随机二值序列，1(拟随机图)
Uniform distribution theory Pub Date : 2019-12-01 DOI: 10.2478/udt-2019-0017
Jozsef Borbely, A. Sárközy
{"title":"Quasi-Random Graphs, Pseudo-Random Graphs and Pseudorandom Binary Sequences, I. (Quasi-Random Graphs)","authors":"Jozsef Borbely, A. Sárközy","doi":"10.2478/udt-2019-0017","DOIUrl":"https://doi.org/10.2478/udt-2019-0017","url":null,"abstract":"Abstract In the last decades many results have been proved on pseudo-randomness of binary sequences. In this series our goal is to show that using many of these results one can also construct large families of quasi-random, pseudo-random and strongly pseudo-random graphs. Indeed, it will be proved that if the first row of the adjacency matrix of a circulant graph forms a binary sequence which possesses certain pseudorandom properties (and there are many large families of binary sequences known with these properties), then the graph is quasi-random, pseudo-random or strongly pseudo-random, respectively. In particular, here in Part I we will construct large families of quasi-random graphs along these lines. (In Parts II and III we will present and study constructions for pseudo-random and strongly pseudo-random graphs, respectively.)","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"23 1","pages":"103 - 126"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73755472","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}
引用次数: 0
On the Maximum Order Complexity of the Thue-Morse and Rudin-Shapiro Sequence 论Thue-Morse和Rudin-Shapiro序列的最大阶复杂度
Uniform distribution theory Pub Date : 2019-10-30 DOI: 10.2478/udt-2019-0012
Zhimin Sun, Arne Winterhof
{"title":"On the Maximum Order Complexity of the Thue-Morse and Rudin-Shapiro Sequence","authors":"Zhimin Sun, Arne Winterhof","doi":"10.2478/udt-2019-0012","DOIUrl":"https://doi.org/10.2478/udt-2019-0012","url":null,"abstract":"Abstract Expansion complexity and maximum order complexity are both finer measures of pseudorandomness than the linear complexity which is the most prominent quality measure for cryptographic sequences. The expected value of the Nth maximum order complexity is of order of magnitude log N whereas it is easy to find families of sequences with Nth expansion complexity exponential in log N. This might lead to the conjecture that the maximum order complexity is a finer measure than the expansion complexity. However, in this paper we provide two examples, the Thue-Morse sequence and the Rudin-Shapiro sequence with very small expansion complexity but very large maximum order complexity. More precisely, we prove explicit formulas for their N th maximum order complexity which are both of the largest possible order of magnitude N. We present the result on the Rudin-Shapiro sequence in a more general form as a formula for the maximum order complexity of certain pattern sequences.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"69 1","pages":"33 - 42"},"PeriodicalIF":0.0,"publicationDate":"2019-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91528298","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}
引用次数: 8
Quantization for a Mixture of Uniform Distributions Associated with Probability Vectors 与概率向量相关的均匀分布混合的量化
Uniform distribution theory Pub Date : 2019-08-29 DOI: 10.2478/udt-2020-0006
M. Roychowdhury, Wasiela Salinas
{"title":"Quantization for a Mixture of Uniform Distributions Associated with Probability Vectors","authors":"M. Roychowdhury, Wasiela Salinas","doi":"10.2478/udt-2020-0006","DOIUrl":"https://doi.org/10.2478/udt-2020-0006","url":null,"abstract":"Abstract The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability distribution by a discrete distribution. Mixtures of probability distributions, also known as mixed distributions, are an exciting new area for optimal quantization. In this paper, we investigate the optimal quantization for three different mixed distributions generated by uniform distributions associated with probability vectors.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"111 1","pages":"105 - 142"},"PeriodicalIF":0.0,"publicationDate":"2019-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80524564","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}
引用次数: 2
The Sixth International Conference on Uniform Distribution Theory (UDT 2018) 第六届均匀分配理论国际会议(UDT 2018)
Uniform distribution theory Pub Date : 2019-06-01 DOI: 10.2478/udt-2019-0009
O. Karpenkov, R. Nair, J. Verger-Gaugry
{"title":"The Sixth International Conference on Uniform Distribution Theory (UDT 2018)","authors":"O. Karpenkov, R. Nair, J. Verger-Gaugry","doi":"10.2478/udt-2019-0009","DOIUrl":"https://doi.org/10.2478/udt-2019-0009","url":null,"abstract":"Abstract This volume contains papers originally presented or inspired by the Sixth International Conference on Uniform Distribution Theory, which was held at CIRM in Luminy, Marseilles, France, October 1–5, 2016.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"41 1","pages":"i - x"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82379721","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}
引用次数: 0
Partitioning the Set of Primes to Create r-Dimensional Sequences Which are Uniformly Distributed Modulo [0, 1)r 划分素数集以建立一致分布模[0,1)r的r维序列
Uniform distribution theory Pub Date : 2019-06-01 DOI: 10.2478/udt-2019-0002
J. De Koninck, I. Kátai
{"title":"Partitioning the Set of Primes to Create r-Dimensional Sequences Which are Uniformly Distributed Modulo [0, 1)r","authors":"J. De Koninck, I. Kátai","doi":"10.2478/udt-2019-0002","DOIUrl":"https://doi.org/10.2478/udt-2019-0002","url":null,"abstract":"Abstract Expanding on our previous results, we show that by partitioning the set of primes into a finite number of subsets of roughly the same size, we can create r-dimensional sequences of real numbers which are uniformly distributed modulo [0, 1)r.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"7 1","pages":"11 - 18"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82253629","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}
引用次数: 0
A Complete Classification of Digital (0,m, 3)-Nets and Digital (0, 2)-Sequences in Base 2 基数2中数字(0,m, 3)-网和数字(0,2)-序列的完全分类
Uniform distribution theory Pub Date : 2019-06-01 DOI: 10.2478/udt-2019-0004
Roswitha Hofer, Kosuke Suzuki
{"title":"A Complete Classification of Digital (0,m, 3)-Nets and Digital (0, 2)-Sequences in Base 2","authors":"Roswitha Hofer, Kosuke Suzuki","doi":"10.2478/udt-2019-0004","DOIUrl":"https://doi.org/10.2478/udt-2019-0004","url":null,"abstract":"Abstract We give a complete classification of all matrices C1,C2,C3 ∈ C3∈𝔽 2m×m {C_3} in mathbb{F}_2^{m times m} which generate a digital (0,m, 3)-net in base 2 and a complete classification of all matrices C1,C2 ∈ C2∈𝔽 2ℕ×ℕ {C_2} in mathbb{F}_2^{mathbb{N} times mathbb{N}} which generate a digital (0, 2)-sequence in base 2.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"114 1","pages":"43 - 52"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74824981","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}
引用次数: 1
Distribuion of Leading Digits of Numbers II 数前导数的分布2
Uniform distribution theory Pub Date : 2019-06-01 DOI: 10.2478/udt-2019-0003
Y. Ohkubo, O. Strauch
{"title":"Distribuion of Leading Digits of Numbers II","authors":"Y. Ohkubo, O. Strauch","doi":"10.2478/udt-2019-0003","DOIUrl":"https://doi.org/10.2478/udt-2019-0003","url":null,"abstract":"Abstract In this paper, we study the sequence (f (pn))n≥1,where pn is the nth prime number and f is a function of a class of slowly increasing functions including f (x)=logb xr and f (x)=logb(x log x)r,where b ≥ 2 is an integer and r> 0 is a real number. We give upper bounds of the discrepancy DNi*(f(pn),g) D_{{N_i}}^*left( {fleft( {{p_n}} right),g} right) for a distribution function g and a sub-sequence (Ni)i≥1 of the natural numbers. Especially for f (x)= logb xr, we obtain the effective results for an upper bound of D Ni*(f(pn)g) D_{{N_i}}^*left( {fleft( {{p_n}} right),g} right) .","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"1 1","pages":"19 - 42"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78540353","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}
引用次数: 2
Cyclotomic Expressions for Representation Functions 表示函数的环切分表达式
Uniform distribution theory Pub Date : 2019-06-01 DOI: 10.2478/udt-2019-0008
C. Hélou
{"title":"Cyclotomic Expressions for Representation Functions","authors":"C. Hélou","doi":"10.2478/udt-2019-0008","DOIUrl":"https://doi.org/10.2478/udt-2019-0008","url":null,"abstract":"Abstract Given a subset A of the natural numbers 𝕅 = {0, 1, 2, ···} (resp. of the ring 𝕑/ N𝕑 of residue classes modulo a positive integer N), we introduce certain sums of roots of unity associated with A. We study some of their properties, and we use them to obtain new expressions for the classical functions that characterize A, i.e. of the representation function, the counting function and the characteristic function of A. We also give an example of computations of the representation function using such expressions.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"64 1","pages":"123 - 140"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77947494","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}
引用次数: 0
The Distributional Asymptotics Mod 1 of (logb n) (logn)的分布渐近模1
Uniform distribution theory Pub Date : 2019-06-01 DOI: 10.2478/udt-2019-0007
Chuang Xu
{"title":"The Distributional Asymptotics Mod 1 of (logb n)","authors":"Chuang Xu","doi":"10.2478/udt-2019-0007","DOIUrl":"https://doi.org/10.2478/udt-2019-0007","url":null,"abstract":"Abstract This paper studies the distributional asymptotics of the slowly changing sequence of logarithms (logb n) with b ∈ 𝕅 {1}. It is known that (logb n) is not uniformly distributed modulo one, and its omega limit set is composed of a family of translated exponential distributions with constant log b. An improved upper estimate ( logN/N sqrt {log N} /N ) is obtained for the rate of convergence with respect to (w. r. t.)the Kantorovich metric on the circle, compared to the general results on rates of convergence for a class of slowly changing sequences in the author’s companion in-progress work. Moreover, a sharp rate of convergence (log N/N)w. r. t. the Kantorovich metric on the interval [0, 1], is derived. As a byproduct, the rate of convergence w.r.t. the discrepancy metric (or the Kolmogorov metric) turns out to be (log N/N) as well, which verifies that an upper bound for this rate derived in [Ohkubo, Y.—Strauch, O.: Distribution of leading digits of numbers, Unif. Distrib. Theory, 11 (2016), no.1, 23–45.] is sharp.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"9 1","pages":"105 - 122"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84423538","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}
引用次数: 2
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