共查询到20条相似文献,搜索用时 31 毫秒
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Guillaume Lecué Matthieu Lerasle 《Stochastic Processes and their Applications》2019,129(11):4385-4410
New robust estimators are introduced, derived from median-of-means principle and Le Cam’s aggregation of tests. Minimax sparse rates of convergence are obtained with exponential probability, under weak moment’s assumptions and possible contamination of the dataset. These derive from general risk bounds of the following informal structure In this result, the number of outliers may be as large as (number of data)(minimax rate) without affecting the rates. As an example, minimax rates of recovery of -sparse vectors in holding with exponentially large probability, are deduced for median-of-means versions of the LASSO when the noise has moments for some , the entries of the design matrix have moments and the dataset is corrupted by up to outliers. 相似文献
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《Indagationes Mathematicae》2022,33(6):1172-1188
Let be linear recursive sequences of integers with characteristic polynomials respectively. Assume that has a dominating and simple real root , while has a pair of conjugate complex dominating and simple roots . Assume further that and are not roots of unity and . Then there are effectively computable constants such that the inequality holds for all with . We present explicitly. 相似文献
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In this paper, we consider the question of when a strongly regular graph with parameters can exist. A strongly regular graph with such parameters is called a pseudo-generalized quadrangle. A pseudo-generalized quadrangle can be derived from a generalized quadrangle, but there are other examples which do not arise in this manner. If the graph is derived from a generalized quadrangle then and , while for pseudo-generalized quadrangles we still have the former bound but not the latter. Previously, Neumaier has proved a bound for which is cubic in , but we improve this to one which is quadratic. The proof involves a careful analysis of cliques and cocliques in the graph. This improved bound eliminates many potential parameter sets which were otherwise feasible. 相似文献
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Le Chen Yaozhong Hu David Nualart 《Stochastic Processes and their Applications》2019,129(12):5073-5112
This paper studies the nonlinear stochastic partial differential equation of fractional orders both in space and time variables: where is the space–time white noise, , , and . Fundamental solutions and their properties, in particular the nonnegativity, are derived. The existence and uniqueness of solution together with the moment bounds of the solution are obtained under Dalang’s condition: . In some cases, the initial data can be measures. When , we prove the sample path regularity of the solution. 相似文献
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The Erd?s–Gallai Theorem states that every graph of average degree more than contains a path of order for . In this paper, we obtain a stability version of the Erd?s–Gallai Theorem in terms of minimum degree. Let be a connected graph of order and be disjoint paths of order respectively, where , , and . If the minimum degree , then except several classes of graphs for sufficiently large , which extends and strengths the results of Ali and Staton for an even path and Yuan and Nikiforov for an odd path. 相似文献
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《Discrete Mathematics》2020,343(6):111866
This note introduces some bijections relating core partitions and tuples of integers. We apply these bijections to count the number of cores with various types of restriction, including fixed number of parts, limited size of parts, parts divisible by some integer, and distinct parts. For example, we prove that the number of -core partitions into even parts equals the number of -core partitions into parts. We also generalize one expression for simultaneous cores, which was given by Baek, Nam and Yu, recently. Subsequently, we use this expression to obtain recurrence satisfied by numbers of core partitions for . 相似文献
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Yongsheng Song 《Stochastic Processes and their Applications》2019,129(6):2066-2085
As is known, if is a -Brownian motion, a process of form , , is a non-increasing -martingale. In this paper, we shall show that a non-increasing -martingale cannot be form of or , , which implies that the decomposition for generalized -Itô processes is unique: For arbitrary , and non-increasing -martingales , if then we have , and. As an application, we give a characterization to the -Sobolev spaces introduced in Peng and Song (2015). 相似文献
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We consider online metric minimum bipartite matching problems with random arrival order and show that the greedy algorithm assigning each request to the nearest unmatched server is -competitive, where is the number of requests. This result is complemented by a lower bound exhibiting that the greedy algorithm has a competitive ratio of at least , even when the underlying metric space is the real line. 相似文献
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Cory Palmer Michael Tait Craig Timmons Adam Zsolt Wagner 《Discrete Mathematics》2019,342(6):1553-1563
Let be a graph. We say that a hypergraph is a Berge- if there is a bijection such that for every . Note that Berge- actually denotes a class of hypergraphs. The maximum number of edges in an -vertex -graph with no subhypergraph isomorphic to any Berge- is denoted . In this paper, we investigate the case when and establish an upper-bound when , and a lower-bound when and is large enough compared to . Additionally, we prove a counting result for -graphs of girth five that complements the asymptotic formula of Lazebnik and Verstraëte (2003). 相似文献
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