An effective multi-level algorithm based on ant colony optimization for graph bipartitioning

Partitioning is a fundamental problem with applications to many areas including data mining, parellel processing and Very-large-scale integration （VLSI） design. An effective multi-level algorithm for bisecting graph is proposed. During its coarsening phase, an improved matching approach based on the global information of the graph core is developed with its guidance function. During the refinement phase, the vertex gain is exploited as ant＇s heuristic information and a positive feedback method based on pheromone trails is used to find the global approximate bipartitioning. It is implemented with American National Standards Institute （ANSI） C and compared to MeTiS. The experimental evaluation shows that it performs well and produces encouraging solutions on 18 different graphs benchmarks.

Hybrid Duodenal Transit Bipartition: An Endoscopic and Laparoscopic Metabolic Procedure

Obesity has been increasing significantly in Brazil and worldwide, becoming a major public health issue. Traditional prevention and treatment strategies, including behavioral interventions, nutritional modifications, physical activity, pharmacotherapy, and metabolic/bariatric procedures, have proven insufficient to reverse this trend. Bariatric surgery is recognized as the most effective treatment for obesity and its comorbidities, but it carries potential long-term risks. Hybrid Duodenal Transit Bipartition is proposed as a minimally invasive “endobariatric” procedure combining endoscopic sleeve gastroplasty (ESG) with laparoscopic duodenoileal or distal duodenojejunal anastomosis. The main objective of this study is to demonstrate the importance of the intestinal metabolic component of hybrid duodenal transit bipartition. This intestinal component is responsible for optimizing and attempting to maintain weight loss and control comorbidities from an ESG through the incretin stimulus generated by the early arrival of food in the ileum or distal jejunum (duodenoileal or distal duodenojejunal anastomosis). Additionally, it is a minimally invasive procedure that preserves the entire digestive system and does not involve gastrointestinal exclusion, allowing for endoscopic and nutritional access. To date, only one patient has undergone the hybrid duodenal bipartition procedure, with satisfactory early postoperative results at 60 days and weight loss exceeding the scientific literature on patients who underwent isolated endoscopic sleeve gastroplasty. Further studies are needed to validate these results and assess the long-term metabolic benefits of this new approach.

Bipartite consensus problems of Lurie multi-agent systems over signed graphs: A contraction approach

This paper examines the bipartite consensus problems for the nonlinear multi-agent systems in Lurie dynamics form with cooperative and competitive communication between different agents. Based on the contraction theory, some new conditions for the nonlinear Lurie multi-agent systems reaching bipartite leaderless consensus and bipartite tracking consensus are presented. Compared with the traditional methods, this approach degrades the dimensions of the conditions, eliminates some restrictions of the system matrix, and extends the range of the nonlinear function. Finally, two numerical examples are provided to illustrate the efficiency of our results.

Event-Triggered Bipartite Consensus Tracking and Vibration Control of Flexible Timoshenko Manipulators Under Time-Varying Actuator Faults

For bipartite angle consensus tracking and vibration suppression of multiple Timoshenko manipulator systems with time-varying actuator faults,parameter and modeling uncertainties,and unknown disturbances,a novel distributed boundary event-triggered control strategy is proposed in this work.In contrast to the earlier findings,time-varying consensus tracking and actuator defects are taken into account simultaneously.In addition,the constructed event-triggered control mechanism can achieve a more flexible design because it is not required to satisfy the input-to-state condition.To achieve the control objectives,some new integral control variables are given by using back-stepping technique and boundary control.Moreover,adaptive neural networks are applied to estimate system uncertainties.With the proposed event-triggered scheme,control inputs can reduce unnecessary updates.Besides,tracking errors and vibration states of the closed-looped network can be exponentially convergent into some small fields,and Zeno behaviors can be excluded.At last,some simulation examples are given to state the effectiveness of the control algorithms.

Weak External Bisection of Some Graphs

Let G be a graph. A bipartition of G is a bipartition of V (G) with V (G) = V1 ∪ V2 and V1 ∩ V2 = ∅. If a bipartition satisfies ∥V1∣ - ∣V2∥ ≤ 1, we call it a bisection. The research in this paper is mainly based on a conjecture proposed by Bollobás and Scott. The conjecture is that every graph G has a bisection (V1, V2) such that ∀v ∈ V1, at least half minuses one of the neighbors of v are in the V2;∀v ∈ V2, at least half minuses one of the neighbors of v are in the V1. In this paper, we confirm this conjecture for some bipartite graphs, crown graphs and windmill graphs.

A New Proof on the Bipartite Turán Number of Bipartite Graphs

The bipartite Turán number of a graph H, denoted by ex(m,n;H), is the maximum number of edges in any bipartite graph G=(A,B;E(G))with | A |=mand | B |=nwhich does not contain H as a subgraph. Whenmin{ m,n }>2t, the problem of determining the value of ex(m,n;Km−t,n−t)has been solved by Balbuena et al. in 2007, whose proof focuses on the structural analysis of bipartite graphs. In this paper, we provide a new proof on the value of ex(m,n;Km−t,n−t)by virtue of algebra method with the tool of adjacency matrices of bipartite graphs, which is inspired by the method using { 0,1 }-matrices due to Zarankiewicz [Problem P 101. Colloquium Mathematicum, 2(1951), 301].

A Study on the Reflection of ~3He, ~4He Ions With Low Energy From the Solid Surface by Bipartition Model

1 Introduction The investigation on the reflection of low energy light ions from the solid surface is very important for the fusion research, surface analysis and ion beam implantation technology. The Monte-Carlo simulation is the main method for calculating the reflection coefficient of light ions with low energy, but it costs too much computer time.

Practical bipartite consensus for multi-agent systems:A barrier function-based adaptive sliding-mode control approach

This paper is concerned with bipartite consensus tracking for multi-agent systems with unknown disturbances.A barrier function-based adaptive sliding-mode control(SMC)approach is proposed such that the bipartite steady-state error is converged to a predefined region of zero in finite time.Specifically,based on an error auxiliary taking neighboring antagonistic interactions into account,an SMC law is designed with an adaptive gain.The gain can switch to a positive semi-definite barrier function to ensure that the error auxiliary is constrained to a predefined neighborhood of zero,which in turn guarantees practical bipartite consensus tracking.A distinguished feature of the proposed controller is its independence on the bound of disturbances,while the input chattering phenomenon is alleviated.Finally,a numerical example is provided to verify the effectiveness of the proposed controller.

Event-Triggered Asymmetric Bipartite Consensus Tracking for Nonlinear Multi-Agent Systems Based on Model-Free Adaptive Control

In this paper,an asymmetric bipartite consensus problem for the nonlinear multi-agent systems with cooperative and antagonistic interactions is studied under the event-triggered mechanism.For the agents described by a structurally balanced signed digraph,the asymmetric bipartite consensus objective is firstly defined,assigning the agents'output to different signs and module values.Considering with the completely unknown dynamics of the agents,a novel event-triggered model-free adaptive bipartite control protocol is designed based on the agents'triggered outputs and an equivalent compact form data model.By utilizing the Lyapunov analysis method,the threshold of the triggering condition is obtained.Subsequently,the asymptotic convergence of the tracking error is deduced and a sufficient condition is obtained based on the contraction mapping principle.Finally,the simulation example further demonstrates the effectiveness of the protocol.

Cycle Multiplicity of Total Graph of Complete Bipartite Graph

Cycle multiplicity of a graph G is the maximum number of edge disjoint cycles in G. In this paper, we determine the cycle multiplicity of and then obtain the formula of cycle multiplicity of total graph of complete bipartite graph, this generalizes the result for, which is given by M.M. Akbar Ali in [1].

The Evolving Bipartite Network and Semi-Bipartite Network Models with Adjustable Scale and Hybrid Attachment Mechanisms

The bipartite graph structure exists in the connections of many objects in the real world, and the evolving modeling is a good method to describe and understand the generation and evolution within various real complex networks. Previous bipartite models were proposed to mostly explain the principle of attachments, and ignored the diverse growth speed of nodes of sets in different bipartite networks. In this paper, we propose an evolving bipartite network model with adjustable node scale and hybrid attachment mechanisms, which uses different probability parameters to control the scale of two disjoint sets of nodes and the preference strength of hybrid attachment respectively. The results show that the degree distribution of single set in the proposed model follows a shifted power-law distribution when parameter r and s are not equal to 0, or exponential distribution when r or s is equal to 0. Furthermore, we extend the previous model to a semi-bipartite network model, which embeds more user association information into the internal network, so that the model is capable of carrying and revealing more deep information of each user in the network. The simulation results of two models are in good agreement with the empirical data, which verifies that the models have a good performance on real networks from the perspective of degree distribution. We believe these two models are valuable for an explanation of the origin and growth of bipartite systems that truly exist.

New Vertex-Degree Condition for Pancyclic Graphs

Let G be a 2 connected graph with n vertices. In this paper, we prove that if there exist two vertices of any there independent vertices in G such that the sum of whose degree is at least n , then G is pancyclic, or G is K n/2,n/2 , or G is K n/2,n/2 -e , or G is a cycle of length 5.

Damaging impacts of energetic charge particles on materials in plasma energy explosive events

To provide some reference data for estimation of the erosion rates and lifetimes of some candidate plasma facing component （PFC） materials in the plasma stored energy explosive events （PSEEE）, this paper calculates the sputtering yields of Mo, W and deuterium saturated Li surface bombarded by energetic charged particles by a new sputtering physics description method based on bipartition model of charge particle transport theory. The comparisons with Monte Carlo data of TRIM code and experimental results axe made. The dependences of maximum energy deposition, particle and energy reflection coefficients on the incident energy of energetic runaway electrons impinging on the different material surfaces are also calculated. Results may be useful for estimating the lifetime of PFC and analysing the impurity contamination extent, especially in the PSEEE for high power density and with high plasma current fusion reactor.

L-Shell X-Ray Production Cross Sections of Ta and Tm by Electron Impact near the Threshold Region

We present experimental measurements of L-shell production cross sections Lα, Lβ and Lγ for tantalum and thulium by electron impact at incident electron energies from about one to three times the threshold energy. From the experimental data, the total production cross section and mean ionization cross section are deduced. The influence of electrons reflected from the substrate is corrected by the electron transport bipartition model. Tile measured cross sections are compared with the theoretical predictions.

L-Shell Ionization Cross Section Measurements of Dysprosium and Samarium by Low-Energy Electron Impact

The Lα, Lβ and Lγ x-ray production cross sections of Dy and Sm by electron impact are measured at energies from near threshold to tens of keV. In the experiments, thin targets with thick substrates are used. Meanwhile, the electron transport bipartition model is used to eliminate the influence of electrons reflected from the thick substrates on measurements. The measured x-ray production cross sections are also compared with the theoretical predictions by Gryzinski and McGuire.

Fast Identification of Recycling Properties of Wall-Released Hydrogenic Neutrals in Divertor Plasma

A new bipartition neutral transport model was developed for quick identification of the recycling properties of the wall-released hydrogenic neutral particles in the vicinity of the divertor target plate. Based on this model, the numerical calculation results are fairly consistent with the results obtained with the ＇multi-generation method＇. This model can not only be utilized to provide a source term from neutral transport calculations for the B2 edge plasma transport code, which has been used to simulate edge plasma transport of an HL-2A divertor configuration, but can also be specifically applied for fast classification of the divertor plasma as high recycling or low recycling. Our results also show that the transmissivity is lower in the high-recycling regime.

CORRECTION OF INFLUENCE OF SUBSTRATE ON MEASUREMENT OF INNER SHELL IONIZATION CROSS SECTIONS

The energy spectra of reflected electrons from the substrates of targets have been calculated by the bipartition model of electron transport, the contributions of the inner shen ionization events produced by the reflected electrons from the substrates in the targets to the x-ray counting in a St(Li) detector have been estimated. It has been confirmed that, by such correction to the measured data, the experimental results of inner shell ionization cross sections by electron impact with fine precision may be obtained under the condition of thick substrate.

基于Web使用挖掘技术的聚类算法改进

Web使用挖掘中的聚类算法可以聚集相似特性的用户和页面,以便从中提取有用的感兴趣的信息。通过深入分析基于Hamming距离的聚类算法,指出其中存在的不合理性和低效性,然后根据这些不足引入了加权的bipartite图来表示整个数据集,修改了Hamming距离计算公式以便更准确地描述两对象间的相似度,并对算法进行了改进。实验结果表明,改进的算法是准确且高效的。

Vertex-distinguishing E-total Coloring of Complete Bipartite Graph K 7,n when7≤n≤95

Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints. For an E-total coloring f of a graph G and any vertex x of G, let C（x） denote the set of colors of vertex x and of the edges incident with x, we call C（x） the color set of x. If C（u） ≠ C（v） for any two different vertices u and v of V （G）, then we say that f is a vertex-distinguishing E-total coloring of G or a VDET coloring of G for short. The minimum number of colors required for a VDET coloring of G is denoted by Хvt^e（G） and is called the VDE T chromatic number of G. The VDET coloring of complete bipartite graph K7,n （7 ≤ n ≤ 95） is discussed in this paper and the VDET chromatic number of K7,n （7 ≤ n ≤ 95） has been obtained.

Pilot Domain NOMA for Grant-Free Massive Random Access in Massive MIMO Marine Communication System

We propose a pilot domain non-orthogonal multiple access(NOMA)for uplink massive devices grant-free random access scenarios in massive multiple-input multiple-output(MIMO)maritime communication systems.These scenarios are characterized by numerous devices with sporadic access behavior,and therefore only a subset of them are active.Due to massive potential devices in the network,it is infeasible to assign a unique orthogonal pilot to each device in advance.In such scenarios,pilot decontamination is a crucial problem.In this paper,the devices are randomly assigned non-orthogonal pilots which are constructed by a linear combination of some orthogonal pilots.We show that a bipartite graph can conveniently describe the interference cancellation(IC)processes of pilot decontamination.High spectrum efficiency(SE)and low outage probability can be obtained by selecting the numbers of orthogonal pilots according to the given probability distribution.Numerical evaluatioDs show that the proposed pilot domain NOMA decreases the outage probability from 20%to 2 e-12 at the SE of 4 bits/s/Hz for a single device,compared to the conventional method of slotted ALOHA with 1024 antennas at the BS,or increases the spectrum efficiency from 1.2 bits/s/Hz to 4 bit/s/Hz at the outage probability of2 e-12 in contrast with the Welch bound equality(WBE)non-orthogonal pilots.