二分图中高效计算top-n maximalα-biclique的方法研究

针对当二分图中一类节点的数量固定时,如何搜索另一类型节点数量排序为前n的maximalα-biclique的问题,提出了一种基础搜索算法和一种基于共同邻居概念的改进搜索算法。在使用(1,α)-core剪枝方法加快搜索的算法基础上,基于共同邻居搜索算法使用共同邻居的概念对算法进行了改进,该算法只遍历节点的二跳邻居,并利用节点顺序和最小阈值提高搜索效率。实验结果表明,两种算法都可以有效且高效地搜索节点数量排名为前n的maximalα-biclique。与基础搜索算法相比,基于共同邻居搜索算法的搜索效率提升了80%,在实际应用场景中更具优势。

VARIATIONAL ANALYSIS FOR THE MAXIMAL TIME FUNCTION IN NORMED SPACES

For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smallest enclosing ball problem.Some properties of the maximal time function are proven,including the convexity,the lower semicontinuity,and the exact characterizations of its subdifferential formulas.

PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.

MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

Maximal operators of pseudo-differential operators with rough symbols

Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and a∈L^(∞)S_(ρ)^(m),then for any f∈S(R^(n))and x∈R^(n),we prove that M(T_(a)f)(x)≤C(M(|f|^(p))(x))^(1/p) where M is the Hardy-Littlewood maximal operator.Our theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant.

Maximal Resonance of{(3,4),4}-Fullerene Graphs

A{(3,4),4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating.Let k be a positive integer,S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern.Moreover,if graph S is k-resonant for any integer k,then S is called maximally resonant.In this paper,we show that the maximally resonant{(3,4),4}-fullerene graphs are S_6,S_8,S_(10)^(2),S_(12)^(2),S_(12)^(4),S_(12)^(5),S_(14)^(3),S_(14)^(5),S_(16)^(3),S_(18)^(5),S_(24)as shown in Fig.1.As a corollary,it is shown that if a{(3,4),4}-fullerene graph is 4-resonant,then it is also maximally resonant.

Model-Free Feature Screening via Maximal Information Coefficient (MIC) for Ultrahigh-Dimensional Multiclass Classification

It is common for datasets to contain both categorical and continuous variables. However, many feature screening methods designed for high-dimensional classification assume that the variables are continuous. This limits the applicability of existing methods in handling this complex scenario. To address this issue, we propose a model-free feature screening approach for ultra-high-dimensional multi-classification that can handle both categorical and continuous variables. Our proposed feature screening method utilizes the Maximal Information Coefficient to assess the predictive power of the variables. By satisfying certain regularity conditions, we have proven that our screening procedure possesses the sure screening property and ranking consistency properties. To validate the effectiveness of our approach, we conduct simulation studies and provide real data analysis examples to demonstrate its performance in finite samples. In summary, our proposed method offers a solution for effectively screening features in ultra-high-dimensional datasets with a mixture of categorical and continuous covariates.

The Intersection of a Maximal Intransitive Subgroup with a Maximal Imprimitive Subgroup

In this paper, we investegate the intersection of a maximal intransitive subgroup with a maximal imprimitive subgroup. And, the structure of the second maximal intransitive subgroup of an alternating group is determined.

Lower bound on BER performance for maximal ratio combining with weighting errors

The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower bounds for different channel Doppler spectra are derived. Based on the obtained lower bounds on mean squared channel estimation errors, the limits on bit error rate （BER） for maximal ratio combining （MRC） with Gaussian distributed weighting errors on independent and identically distributed （i. i. d） fading channels are presented. Numerical results show that the BER performances of ideal MRC are the lower bounds on the BER performances of non-ideal MRC and deteriorate as the maximum Doppler frequency increases or the SNR of channel estimate decreases.

MODEL SELECTION METHOD BASED ON MAXIMAL INFORMATION COEFFICIENT OF RESIDUALS

The traditional model selection criterions try to make a balance between fitted error and model complexity. Assumptions on the distribution of the response or the noise, which may be misspecified, should be made before using the traditional ones. In this ar- ticle, we give a new model selection criterion, based on the assumption that noise term in the model is independent with explanatory variables, of minimizing the association strength between regression residuals and the response, with fewer assumptions. Maximal Information Coe^cient （MIC）, a recently proposed dependence measure, captures a wide range of associ- ations, and gives almost the same score to different type of relationships with equal noise, so MIC is used to measure the association strength. Furthermore, partial maximal information coefficient （PMIC） is introduced to capture the association between two variables removing a third controlling random variable. In addition, the definition of general partial relationship is given.

Decompesition of Kernel and Maximal Generalized Bochner-Riesz Means

设l∈N,δ=k/p-k+1/2,以及<p<1.本文的主要结果是建立广义BochnerRiesz平均的核的某种分解: ((1-|ξ|~l)~σ+)^(x)=sum from f=1 to J(k,l,p) b_f((1-|ξ|~2)ь+ζ)^(x)+T(|x|),其中T满足 T^(n+1)(s)≤cmin{(1+s)_(k-n-2),(1+s)^(-k,p)},0<s<∞以及n=[K(1/p-1)]·作为上述分解的一个直接结果,我们得到:临界阶广义Bochner-Riesz平均在H^p(R^k)上的a.e.收敛性。

Mining maximal pattern-based subspace clusters in high dimensional space

The problem of pattern-based subspace clustering, a special type of subspace clustering that uses pattern similarity as a measure of similarity, is studied. Unlike most traditional clustering algorithms that group the close values of objects in all the dimensions or a set of dimensions, clustering by pattern similarity shows an interesting pattern, where objects exhibit a coherent pattern of rise and fall in subspaces. A novel approach, named EMaPle to mine the maximal pattern-based subspace clusters, is designed. The EMaPle searches clusters only in the attribute enumeration spaces which are relatively few compared to the large number of row combinations in the typical datasets, and it exploits novel pruning techniques. EMaPle can find the clusters satisfying coherent constraints, size constraints and sign constraints neglected in MaPle. Both synthetic data sets and real data sets are used to evaluate EMaPle and demonstrate that it is more effective and scalable than MaPle.

Aggregating metasearch engine results based on maximal entropy OWA operator

The maximal entropy ordered weighted averaging （ME-OWA） operator is used to aggregate metasearch engine results, and its newly analytical solution is also applied. Within the current context of the OWA operator, the methods for aggregating metasearch engine results are divided into two kinds. One has a unique solution, and the other has multiple solutions. The proposed method not only has crisp weights, but also provides multiple aggregation results for decision makers to choose from. In order to prove the application of the ME-OWA operator method, under the context of aggregating metasearch engine results, an example is given, which shows the results obtained by the ME-OWA operator method and the minimax linear programming （ minimax-LP ） method. Comparison between these two methods are also made. The results show that the ME-OWA operator has nearly the same aggregation results as those of the minimax-LP method.

Maximal Flow在京津冀公路交通网络管理中的应用

Maximal Flow是运筹学中应用极为广泛的解决网络流量最大问题的理论。文章应用其研究思想,采用Ford-Fulkerson标号法,研究京津冀经济区公路交通网络的最大流通能力问题,并找出影响交通网络流量的最为关键的路段,为更好管理京津冀交通网络提供合理的理论指导。

On S-acts containing no maximal S-subacts

Let S be a semigroup and let A be an S-act. Some necessary and sufficient conditions that S-subacts of A are maximal S-subacts are given. A relation B which is similar to the Green relation in semigroups is defined. By the relation B, it is proved that a non-empty set L of A is a maximal S-subact if and only if A／L is a （maximal） B-class. Finally, the concept of a C-subact is defined, some properties of C-subacts are discussed, and it is proved that A contains no maximal S-subacts if and only if every cyclic S-subact of A is a C-subact. Consequently, the results obtained by Imrich Fabrici that semigroups contain no maximal （left） ideals are the corollary of this paper.

Upper Bounds for the L_p-norms of the Maximal Functions of Martingales

Let 2≤p【∞ and let (f n) be a martingale. Using exponential bounds of the probabilities of the type P(|f n|】λ‖T(f n)‖ ∞) for some quasi-linear operators acting on martingales, we estimate upper bounds for the L p-norms of the maximal functions of martinglaes. Our result is the extension and improvements of the results obtained previously by HITCZENKO and ZENG .

TWO GENERALIZATIONS OF HARDY-LITTLEWOOD MAXIMAL OPERATOR

Two generalizations of Hardy-Littlewood maximal operator are considered. Some estimates for them are obtained.

W ^(1,p)(R^n)-BOUNDEDNESS FOR MAXIMAL FUNCTIONS

In this paper, we get W 1,p(Rn)-boundedness for tangential maximal func- tion and nontangential maximal function , which improves J.Kinnunen, P.Lindqvist and Tananka’s results.

On Maximal, Discrete, and Area Operators

In this paper, we study the boundednesses of maximal operator g., the discrete operator gd, and the area operator A on Bergman spaces.

Efficacy of maximal androgen blockade versus castration alone in the treatment of advanced prostate cancer： a retrospective clinical experience from a Chinese medical centre

In this retrospective study, we evaluated and compared the efficacy and toxicities of maximal androgen blockade （MAB） versus castration alone in Chinese patients with advanced prostate cancer. From 1996 to 2004, 608 patients with advanced prostate cancer were included in the study. Patients were retrospectively divided into two groups according to different therapeutic regimens. Of the 608 patients, 300 patients were treated with MAB （castration plus nonsteroidal antiandrogens） and the remaining 308 were treated with castration alone. The 2- and 5-year overall survival rates of these patients were 73.7% and 56%, respectively. Multivariate analysis showed that, in patients with metastatic prostate cancer, MAB was associated with not only the improvement of progression-free survival （PFS） （increased by 10 months） but also a 20.6% reduction in mortality risk compared with castration alone. In contrast, the efficacy of MAB was not superior to castration alone for patients with nonmetastatic prostate cancer. Interestingly, among patients with MAB, those using bicalutamide had a longer PFS than those using flutamide; this was especially so in patients with metastatic prostate cancer. Almost all of the toxicities due to the hormone therapy were mild to moderate and manageable. To conclude, in China, hormone therapies, including MAB and castration alone, have been standard treatments for advanced prostate cancer. For patients with nonmetastatic prostate cancer, castration alone might be adequately practical and efficient. In patients with metastatic prostate cancer, however, MAB has superior efficacy over castration alone. It is clear that MAB should be considered the first-line standard treatment for patients with metastatic prostate cancer.