Sufficient Conditions for Maximally Edge-Connected Hypergraphs

The edge-connectivity of a graph or a hypergraph is defined as the minimum number of edges whose removal renders the graph or hypergraph disconnected.A graph or hypergraph is called maximally edge-connected if the edge-connectivity equals its minimum degree.In this paper,we show that some classical sufficient conditions for graphs to be maximally edge-connected can be generalized to hypergraphs.

Sufficient Conditions for Maximally Edge-connected and Super-edge-connected Digraphs Depending on the Size

Let D be a finite and simple digraph with vertex set V(D).The minimum degreeδof a digraph D is defined as the minimum value of its out-degrees and its in-degrees.If D is a digraph with minimum degreeδand edge-connectivity λ,then λ≤δ.A digraph is maximally edge-connected ifλ=δ.A digraph is called super-edge-connected if every minimum edge-cut consists of edges incident to or from a vertex of minimum degree.In this note we show that a digraph is maximally edge-connected or super-edge-connected if the number of arcs is large enough.

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。

Continuity of truncated Hardy-Littlewood maximal function

This paper focuses on the continuity of the truncated Hardy-Littlewood maximal function.We first show that the truncated Hardy-Littlewood maximal function is lower semi-continuous.Then by investigating the behavior of the truncated Hardy-Littlewood maximal function when the truncated parameterγchanges,we obtain an equivalent condition of the continuity of the truncated Hardy-Littlewood maximal function.

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.

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%.

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.

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.

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.

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.

Hybrid Block Diagonalization Precoding for Multi-User Weighted Sum-Rate Maximization

This paper studies large-scale multi-input multi-output(MIMO)orthogonal frequency division multiplexing(OFDM)communications in a broadband frequency-selective channel,where a massive MIMO base station(BS)communicates with multiple users equipped with multi-antenna.We develop a hybrid precoding design to maximize the weighted sum-rate(WSR)of the users by optimizing the digital and the analog precoders alternately.For the digital part,we employ block-diagonalization to eliminate inter-user interference and apply water-filling power allocation to maximize the WSR.For the analog part,the optimization of the PSN is formulated as an unconstrained problem,which can be efficiently solved by a gradient descent method.Numerical results show that the proposed block-diagonal hybrid precoding algorithm can outperform the existing works.

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.

Screening for Anti-tumor Activity of Fractions from Buddleja officinalis Maxim

[Objectives]The anti-tumor activity of fractions from Buddleja officinalis Maxim.by petroleum ether,ethyl acetate,n-butanol and water solvent was studied.[Methods]The ethanol extract from B.officinalis Maxim.was extracted and then concentrated with petroleum ether,ethyl acetate,n-butanol and water,respectively,and the extracts were obtained.The inhibitory effects of the four different fractions on the growth of three tumor cell lines in vitro were detected by CCK-8 method,and the median inhibitory concentration(IC 50 value)was calculated.[Results]The four fractions inhibited the growth of the three tumor cell lines in vitro,among which the n-butanol fraction had the best anti-tumor activity.The IC 50 values of the n-butanol fraction on human gastric cancer(SGC-7901),human breast cancer(MCF-7)and human liver cancer(BEL-7404)cell lines were 0.08,1.58 and 0.12 mg/mL,respectively.[Conclusions]Petroleum ether,ethyl acetate,n-butanol and water fractions from the ethanol extract of B.officinalis Maxim.had certain anti-tumor effects,and the n-butanol fraction had the best anti-tumor activity.

Exploring the molecular mechanism of Epimedium brevicornu Maxim.in treating breast cancer via network pharmacology and in vitro experiments

Objective:To evaluate the therapeutic effects of Epimedium brevicornu Maxim.(EBM,Yin Yang Huo)on breast cancer using network pharmacology and in vitro validation.It also aimed to explore the novel targets and mechanisms of EBM in the treatment of breast cancer to facilitate the discovery of new drugs and their clinical application.Methods: Network pharmacology was used to identify and screen the components and targets of EBM for breast cancer treatment.Molecular docking was further screened the effective components and targets of EBM.Wound-healing assays and flow cytometry analysis were used to detect the ability of two compounds to intervene in the migration and apoptosis of MDA-MB-231 cells,and their mechanism of action was further explored using western blotting experiments.Results: EBM contained 19 active components.Among them wereβ-anhydroicaritin(Anhy)and isoliquiritigenin(Iso),which were selected for in vitro experiments.Treatment resulted in a dose-dependent suppression of MDA-MB-231 cell viability,with an IC_(50) of 23.73μmol/L for Iso and 21.28μmol/L for Anhy.In the wound healing assay,cells in Anhy and Iso groups exhibited considerable inhibition of migration at 48 h.In flow cytometry analysis,treatment with Iso(20μmol/L)for 96 h resulted in significantly higher levels of both early and late apoptosis in the Iso group than that in the control group(P=.004 and P=.014,respectively).Additionally,both Iso(20μmol/L)and Anhy(10 and 20μmol/L)induced cell necrosis at 96 h.Western blotting revealed that Anhy and Iso increased the expression of Bax and TBK1/NAK.Conclusion: These findings suggested that Anhy and Iso,the two components of EBM,inhibit MDA-MB-231 cell proliferation and migration of and induce their apoptosis,providing substantial support for future studies on breast cancer.

Determination of Total Flavonoids in Acanthopanax senticosus(Rupr. et Maxim.) Harms by Enzymolysis and Its Technological Optimization

In order to optimize the ultrasonic extraction technique for the total flavonoid of leaf yellows plus, the contents of 21 leaf yellows plus total flavonoid from four regions in Heilongjiang Province were comparatively analyzed. The ultrasonic extraction technology was optimized by Box-Behnken response surface method, and the total flavonoid content of 21 kinds of Acanthopanax senticosus(Rupr. et Maxim.) Harms from different producing areas were analyzed by cluster analysis. The optimal process conditions were determined as ultrasonic time 30 min, solid-liquid ratio 1 : 12 and ultrasonic power 250 W, and the average yield of the total flavonoid was 1.453 mg·g^ (-1). By optimizing the ultrasonic-assisted extraction method, the total flavonoid content from different producing areas was compared in the experiment, which provided certain data support for the optimization of the extraction process in the future and laid a certain theoretical foundation for the quality analysis of Chinese medicinal materials.

The Janus of mIS in hepatobiliary surgery:Importance of maximally invasive surgery in an era of minimally invasive surgery

As surgeons formidably continue to forge into the twentytwenties,after a considerably coronavirus-induced rocky start,one can predict that the era of minimally invasive surgery(mIS),an era of robotics,telehealth,and enhanced recovery after surgery(ERAS■),is not only here to stay but will continue to thrive,develop,and transform our practices.Critics of robotics platforms would be hard pressed not to indulge in this prediction.Will the satisfyingly large midline“stem to stern”,the impressing exposuregenerating Makuuchi or transverse abdominal,the Kocher,paramedian,McBurney,Chevron,and Pfannenstiel incisions begin to disappear and fade away into a scar minimizing future precluding trauma laparotomies?Most likely not.Understanding and developing the skill and technique for a minimally invasive“mIS”approach does not negate or abrogate the maximally invasive“MIS”ones.It is not one or the other;not a“to be or not to be”Shakespearean scenario.Hepatobiliary surgery is a qualified landscape upon which to illuminate and exemplify this declaration:the necessity and companionship of“mIS”and“MIS”–minimally and maximally invasive surgery.

Quantum Secure Direct Communication Using Six-Particle Maximally Entangled States and Teleportation

The sender shares six-particle maximally entangled states as quantum channel with the receiver. If the quantum channel is secure, the sender performs projective measurements and tells the measurement outcome to the receiver. The receiver performs the unitary transformations and makes projective measurements on his particles to obtain the secret information. Using teleportation, the transmission of three-qubit secret information can be completed in each quantum channel