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.

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.

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 NILPOTENT IDEALS AND ISOMORPHISMS OF LARGE SUBALGEBRAS OF NEST ALGEBRAS

Let N be a nest of projections on a Hilbert space H and T(N) be the corresponding nest algebra. Let A be a large subalgebra of T(N). It is proved that any maximal n-nilpotent ideal of A is in the form of A∩R F,where F is a finite subnest of N and R F is the Jacobson radical of T(F).Using this result can prove that two large subalgebras are isomorphic if and only if the corresponding nests are similar.

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.

磁共振IDEAL-IQ序列定量分析腹腔内脏脂肪含量与2型糖尿病的关系

目的探讨腹腔内脏脂肪含量与糖尿病发生的关系,进而探讨其预测T2DM发病的可行性。方法收集行腹部3.0T MRI检查并有T2DM患者45例(T2DM组),对照组80例,应用IDEAL软件进行图像自动重组,获得脂肪分数(FF图)、弛豫率(R2*)、脂相、水相、同反相位图像。将FF图传至AW 4.6工作站,由两名观察者采用双盲法对FF图进行测量。应用ITK-SNAP软件采用阈值分割法半自动勾画腹腔内脏脂肪(VAT)及皮下脂肪组织(SAT),并计算体积。采用SPSS 26.0软件对数据进行统计学分析。结果(1)T2DM组的腹腔内脏脂肪组织体积(VATV)、肝脏脂肪分数(HFF)、胰腺脂肪分数(PFF)、甘油三酯(TG)及空腹血糖(FBG)均高于对照组,高密度脂蛋白(HDL)低于对照组,差异有统计学意义(P<0.05);(2)ROC曲线分析示:PFF判断是否患T2DM的曲线下面积(AUC)为0.656(P<0.01,95%CI:0.534~0.777),截断值为8.44%,敏感度为50%,特异度为82.5%;HFF判断是否患T2DM的AUC为0.744(P<0.05,95%CI:0.637~0.851),截断值、敏感度、特异度分别为2.99%、97.5%、42.5%。男性患者VATV判断T2DM的最佳阈值为3466 cm^(3),敏感度为63.2%,特异度为89.5%,AUC为0.78(P<0.01),联合SATV、PFF及HFF时,敏感度为78.9%,特异度为84.2%,AUC为0.839(P<0.01);女性患者利用VATV诊断T2DM的最佳阈值为2103 cm^(3),利用该阈值判断T2DM的敏感度为66.7%,特异度为66.7%,AUC为0.68(P<0.05),联合SATV、PFF及HFF时,敏感度为90.5%,特异度为76.2%,AUC为0.909(P<0.01)。(3)TG和FBG每增加1个单位,患T2DM的风险就分别提升了3986.3%及417.1%,即TG和FBG是T2DM发病的独立预测因子。结论PFF、HFF及VATV单独在预测T2DM发病方面,检验效能较低。VATV联合SATV、PFF、HFF预测T2DM发生的检验效能显著提高,其敏感度及特异度亦均明显提高。IDEAL-IQ技术是评估T2DM患者腹腔内异位脂肪组织沉积定量的便捷的方法,具有简单、稳定性好及重复性高的优势。

Equivalence between Linear Tangle and Maximal Single Ideal

The concept of linear tangle was introduced as an obstruction to mixed searching number. The concept of (maximal) single ideal has been introduced as an obstruction to linear-width. Moreover, it was already known that mixed search number is equivalent to linear-width. Hence, by combining those results, we obtain a proof of the equivalence between linear tangle and maximal single ideal. This short report gives an alternative proof of the equivalence.

On the Optimal Initial Inner-Core Size for Tropical Cyclone Intensification: An Idealized Numerical Study

Recent observational and numerical studies have revealed the dependence of the intensification rate on the inner-core size of tropical cyclones(TCs). In this study, with the initial inner-core size(i.e., the radius of maximum wind—RMW)varied from 20–180 km in idealized simulations using two different numerical models, we found a nonmonotonic dependence of the lifetime maximum intensification rate(LMIR) on the inner-core size. Namely, there is an optimal innercore size for the LMIR of a TC. Tangential wind budget analysis shows that, compared to large TCs, small TCs have large inward flux of absolute vorticity due to large absolute vorticity inside the RMW. However, small TCs also suffer from strong lateral diffusion across the eyewall, which partly offsets the positive contribution from large inward flux of absolute vorticity. These two competing processes ultimately lead to the TC with an intermediate initial inner-core size having the largest LMIR. Results from sensitivity experiments show that the optimal size varies in the range of 40–120 km and increases with higher sea surface temperature, lower latitude, larger horizontal mixing length, and weaker initial TC intensity. The 40–120 km RMW corresponds to the inner-core size most commonly found for intensifying TCs in observations, suggesting the natural selection of initial TC size for intensification. This study highlights the importance of accurate representation of TC inner-core size to TC intensity forecasts by numerical weather prediction models.

INCOMPRESSIBLE LIMIT OF IDEAL MAGNETOHYDRODYNAMICS IN A DOMAIN WITH BOUNDARIES

We study the incompressible limit of classical solutions to compressible ideal magneto-hydrodynamics in a domain with a flat boundary.The boundary condition is characteristic and the initial data is general.We first establish the uniform existence of classical solutions with respect to the Mach number.Then,we prove that the solutions converge to the solution of the incompressible MHD system.In particular,we obtain a stronger convergence result by using the dispersion of acoustic waves in the half space.

A Bitcoin Address Multi-Classification Mechanism Based on Bipartite Graph-Based Maximization Consensus

Bitcoin is widely used as the most classic electronic currency for various electronic services such as exchanges,gambling,marketplaces,and also scams such as high-yield investment projects.Identifying the services operated by a Bitcoin address can help determine the risk level of that address and build an alert model accordingly.Feature engineering can also be used to flesh out labeled addresses and to analyze the current state of Bitcoin in a small way.In this paper,we address the problem of identifying multiple classes of Bitcoin services,and for the poor classification of individual addresses that do not have significant features,we propose a Bitcoin address identification scheme based on joint multi-model prediction using the mapping relationship between addresses and entities.The innovation of the method is to(1)Extract as many valuable features as possible when an address is given to facilitate the multi-class service identification task.(2)Unlike the general supervised model approach,this paper proposes a joint prediction scheme for multiple learners based on address-entity mapping relationships.Specifically,after obtaining the overall features,the address classification and entity clustering tasks are performed separately,and the results are subjected to graph-basedmaximization consensus.The final result ismade to baseline the individual address classification results while satisfying the constraint of having similarly behaving entities as far as possible.By testing and evaluating over 26,000 Bitcoin addresses,our feature extraction method captures more useful features.In addition,the combined multi-learner model obtained results that exceeded the baseline classifier reaching an accuracy of 77.4%.

基于“IDEAL”模式的物理问题解决能力培养研究

学生“物理问题解决能力弱”是长期困扰物理教学的问题,认知心理学关于问题解决的“IDEAL”模式为该问题的研究提供了新的视角。以2022年全国乙卷理综第25题为例,借助“IDEAL”模式可以清晰地梳理问题解决的过程,明确各阶段学生遇到的困难及成因。研究发现,借助“读思达”教学法,通过粗读、精读等过程,可以有效帮助学生建构物理模型、理清物理过程,从而提高物理问题解决能力。

Quantized Decoders that Maximize Mutual Information for Polar Codes

In this paper,we innovatively associate the mutual information with the frame error rate(FER)performance and propose novel quantized decoders for polar codes.Based on the optimal quantizer of binary-input discrete memoryless channels(BDMCs),the proposed decoders quantize the virtual subchannels of polar codes to maximize mutual information(MMI)between source bits and quantized symbols.The nested structure of polar codes ensures that the MMI quantization can be implemented stage by stage.Simulation results show that the proposed MMI decoders with 4 quantization bits outperform the existing nonuniform quantized decoders that minimize mean-squared error(MMSE)with 4 quantization bits,and yield even better performance than uniform MMI quantized decoders with 5 quantization bits.Furthermore,the proposed 5-bit quantized MMI decoders approach the floating-point decoders with negligible performance loss.

CRB:A new rumor blocking algorithm in online social networks based on competitive spreading model and influence maximization

The virtuality and openness of online social platforms make networks a hotbed for the rapid propagation of various rumors.In order to block the outbreak of rumor,one of the most effective containment measures is spreading positive information to counterbalance the diffusion of rumor.The spreading mechanism of rumors and effective suppression strategies are significant and challenging research issues.Firstly,in order to simulate the dissemination of multiple types of information,we propose a competitive linear threshold model with state transition(CLTST)to describe the spreading process of rumor and anti-rumor in the same network.Subsequently,we put forward a community-based rumor blocking(CRB)algorithm based on influence maximization theory in social networks.Its crucial step is to identify a set of influential seeds that propagate anti-rumor information to other nodes,which includes community detection,selection of candidate anti-rumor seeds and generation of anti-rumor seed set.Under the CLTST model,the CRB algorithm has been compared with six state-of-the-art algorithms on nine online social networks to verify the performance.Experimental results show that the proposed model can better reflect the process of rumor propagation,and review the propagation mechanism of rumor and anti-rumor in online social networks.Moreover,the proposed CRB algorithm has better performance in weakening the rumor dissemination ability,which can select anti-rumor seeds in networks more accurately and achieve better performance in influence spread,sensitivity analysis,seeds distribution and running time.

Sum-Rate Maximization in Active RIS-Assisted Multi-Antenna WPCN

In this paper,we propose an active reconfigurable intelligent surface(RIS)enabled hybrid relaying scheme for a multi-antenna wireless powered communication network(WPCN),where the active RIS is employed to assist both wireless energy transfer(WET)from the power station(PS)to energyconstrained users and wireless information transmission(WIT)from users to the receiving station(RS).For further performance enhancement,we propose to employ both transmit beamforming at the PS and receive beamforming at the RS.We formulate a sumrate maximization problem by jointly optimizing the RIS phase shifts and amplitude reflection coefficients for both the WET and the WIT,transmit and receive beamforming vectors,and network resource allocation.To solve this non-convex problem,we propose an efficient alternating optimization algorithm with the linear minimum mean squared error criterion,semidefinite relaxation(SDR)and successive convex approximation techniques.Specifically,the tightness of applying the SDR is proved.Simulation results demonstrate that our proposed scheme with 10 reflecting elements(REs)and 4 antennas can achieve 17.78%and 415.48%performance gains compared to the single-antenna scheme with 10 REs and passive RIS scheme with 100 REs,respectively.

Kinematic calibration under the expectation maximization framework for exoskeletal inertial motion capture system

This study presents a kinematic calibration method for exoskeletal inertial motion capture (EI-MoCap) system with considering the random colored noise such as gyroscopic drift.In this method, the geometric parameters are calibrated by the traditional calibration method at first. Then, in order to calibrate the parameters affected by the random colored noise, the expectation maximization (EM) algorithm is introduced. Through the use of geometric parameters calibrated by the traditional calibration method, the iterations under the EM framework are decreased and the efficiency of the proposed method on embedded system is improved. The performance of the proposed kinematic calibration method is compared to the traditional calibration method. Furthermore, the feasibility of the proposed method is verified on the EI-MoCap system. The simulation and experiment demonstrate that the motion capture precision is significantly improved by 16.79%and 7.16%respectively in comparison to the traditional calibration method.

For the Ideal Homeland

A town planner combines British experience with Chinese concept of harmony to build green,low-carbon,and sustainable cities.YANG Wei is a woman who wears many hats.An internationally renowned town planner and urban designer,she is held in high esteem in the academic and planning communities in the U.K.and is a fellow of the U.K.Academy of Social Sciences and former president of the Royal Town Planning Institute(RTPI)based in London.She is also chief executive and co-founder of the Digital Task Force for Planning(DTFP),a non-profit social enterprise,and founding director of London-based planning and urban design firm Wei Yang&Partners.

Yeats’s Ideals:Women Old and Young

William Butler Yeats ranks among the most widely admired and intensively studied poets of the 20th century.This paper intends to explore the women who have exerted the most critical influences upon Yeats,namely Gonne,Lady Gregory,and Georgie Hyde-Lees.Even in Yeats’s poetry involved with symbolism,it is worth noting that his employment of symbols has used these women as the archetypes,and that the historical context rendered Yeats’s representations of them in his poetry all the more interesting.