PartitionSim:一个面向众核结构的并行模拟器

该文提出了一个面向众核处理器的并行模拟器:PartitionSim.PartitionSim采用了一种新颖的方法——时序分割来加速众核结构模拟.时序分割的提出基于这样的观察:在众核结构中,有些模块之间频繁交互而有的模块之间没有交互.有鉴于此,该方法将目标结构分割成两部分:交互部分和非交互部分.当模拟交互部分时,主机线程严格同步,维持时序精确.当模拟非交互部分时,主机线程通过异步运行,提高模拟速度,并且产生较小的时序损失.文中所述工作在一个16核的SMP机器上用PartitionSim模拟了千核规模的Godson-T众核结构.实验结果显示,PartitionSim展示出良好的加速比,达到最高25MIPS的模拟速度,时序损失平均值为0.92%.

An Estimate of the Enumeration Function of Multiplicative Partitions

Let f(n) denote the number of multiplicative partitions of a positive intger. We prove that if n is an odd number,then f(n)≤n/15+7/5.

(k,k-1)-双正则图的平衡Judicious Partitions(英文)

Bollobás和Scott提出猜想:任意一个边数为m且最小度大于1的图存在顶点集的平衡二部划分使得每一部分点集的导出子图包含的边数不超过m/3.Bollobás和Scott证明了绝大部分正则图存在顶点集的平衡二部划分使得每一部分点集的导出子图包含的边数比m/4小.这里讨论(k,k-1)-双正则图的平衡二部划分,证明了每一个(k,k-1)-双正则图存在平衡二部划分使得每一部分点集的导出子图包含的边数是m/4左右.

SYNCHRONIZATION OF CHAOTIC SYSTEMS VIA LINEAR PARTITIONS

In this paper, a new method for synchronization of chaotic systems is proposed. The method is based on the linear partitions of the chaotic system under consideration. A chaotic system is partitioned into a linear part and a nonlinear part. Under some assumptions, another chaotic system which can synchronize with the original one can be contructed. The proposed method is easier to verify and more general than the conventional one in some sense.

Singly Covered Minimal Elements of Linked Partitions and Cycles of Permutations

Linked partitions were introduced by Dykema(Dykema K J. Multilinear function series and transforms in free probability theory. Adv. Math., 2005, 208(1):351–407) in the study of the unsymmetrized T-transform in free probability theory.Permutation is one of the most classical combinatorial structures. According to the linear representation of linked partitions, Chen et al.(Chen W Y C, Wu S Y J, Yan C H. Linked partitions and linked cycles. European J. Combin., 2008, 29(6): 1408–1426) de?ned the concept of singly covered minimal elements. Let L(n, k) denote the set of linked partitions of [n] with k singly covered minimal elements and let P(n, k) denote the set of permutations of [n] with k cycles. In this paper, we mainly establish two bijections between L(n, k) and P(n, k). The two bijections from a different perspective show the one-to-one correspondence between the singly covered minimal elements in L(n, k) and the cycles in P(n, k).

Bijections between Lattice Paths and Plane Partitions

By using lattice paths in the three-dimensional space we obtain bijectively an interpretation for the overpartitions of a positive integer n in terms of a set of plane partitions of n . We also exhibit two bijections between unrestricted partitions of n and different subsets of plane partitions of n .

Root-Patterns to Algebrising Partitions

The study of the confluences of the roots of a given set of polynomials—root-pattern problem— does not appear to have been considered. We examine the situation, which leads us on to Young tableaux and tableaux representations. This in turn is found to be an aspect of multipartite partitions. We discover, and show, that partitions can be expressed algebraically and can be “differentiated” and “integrated”. We show a complete set of bipartite and tripartite partitions, indicating equivalences for the root-pattern problem, for select pairs and triples. Tables enumerating the number of bipartite and tripartite partitions, for small pairs and triples are given in an appendix.

A New Formula for Partitions in a Set of Entities into Empty and Nonempty Subsets, and Its Application to Stochastic and Agent-Based Computational Models

In combinatorics, a Stirling number of the second kind S (n,k)? is the number of ways to partition a set of n objects into k nonempty subsets. The empty subsets are also added in the models presented in the article in order to describe properly the absence of the corresponding type i of state in the system, i.e. when its “share” Pi =0?. Accordingly, a new equation for partitions P (N, m)? in a set of entities into both empty and nonempty subsets was derived. The indistinguishableness of particles (N identical atoms or molecules) makes only sense within a cluster (subset) with the size?0≤ni ≥N. The first-order phase transition is indeed the case of transitions, for example in the simplest interpretation, from completely liquid state?typeL = {n1 =N, n2 = 0} to the completely crystalline state??typeC= {n1 =0, n2 = N }. These partitions are well distinguished from the physical point of view, so they are ‘typed’ differently in the model. Finally, the present developments in the physics of complex systems, in particular the structural relaxation of super-cooled liquids and glasses, are discussed by using such stochastic cluster-based models.

The Fractal and the Recurrence Equations Concerning the Integer Partitions

This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the pentagonal number theorem.

A Study on Associated Rules and Fuzzy Partitions for Classification

The amount of data for decision making has increased tremendously in the age of the digital economy. Decision makers who fail to proficiently manipulate the data produced may make incorrect decisions and therefore harm their business. Thus, the task of extracting and classifying the useful information efficiently and effectively from huge amounts of computational data is of special importance. In this paper, we consider that the attributes of data could be both crisp and fuzzy. By examining the suitable partial data, segments with different classes are formed, then a multithreaded computation is performed to generate crisp rules (if possible), and finally, the fuzzy partition technique is employed to deal with the fuzzy attributes for classification. The rules generated in classifying the overall data can be used to gain more knowledge from the data collected.

Cytotoxic Effect of Methanol Extracts and Partitions of Two Mexican Desert Plants against the Murine Lymphoma L5178Y-R

Pachycereus marginatus (DC.) Britton & Rose and Ibervillea sonorae (S. Watson) Greene have been used in the Mexican traditional medicine for the treatment of various diseases, including cancer. The present study aims to investigate the cytotoxic activity of these plants against a murine lymphoma. Soxhlet extraction of dried and powdered plant material was performed with methanol. Also, a further partitioning of these methanolic extracts with hexane and ethyl acetate was achieved. The in vitro cytotoxic activity against the murine lymphoma L5178Y-R cell line was assessed via the colorimetric MTT assay. The methanol extract from P. marginatus exhibited high cytotoxic activity (up to 94%) at concentrations ranging from 3.9 to 500 μg/mL;however, hexane and ethyl acetate partitions from this methanolic extract showed lower but significant (p < 0.05) concentration-dependent cytotoxicity (hexane partition up to 94% at 500 μg/mL;ethyl acetate partition up to 94% at 65.5 μg/mL). The methanolic extract and partitions derived from I. sonorae also showed significant (p < 0.05) and concentration-dependent cytotoxicity against L5178Y-R cells at concentrations ranging from 7.81 to 500 μg/mL (methanolic extract up to 63% at 500 μg/mL;hexane partition up to 76% at 250 μg/mL;ethyl acetate partition up to 73% at 500 μg/mL). These results demonstrate that the methanol extracts and partitions from P. marginatus and I. sonorae possess significant cytotoxic activity against the murine lymphoma L5178Y-R and validate the ethnobotanical use of these plants for the treatment of diseases consistent with cancer symptomatology. Previous scientific reports describe the isolation of isoquinoline alkaloids of P. marginatus as well as cucurbitacins from I. sonorae, phytochemicals that could be responsible for their observed cytotoxic activity in this research. The direct extraction with methanol of medicinal plants allows extracting of both high and low-polarity compounds, contrary to the simple extraction with water that only allows obtaining compounds of high polarity. The subsequent partition of the methanol extract with a solvent of low polarity (hexane) and another of medium polarity (ethyl acetate) allows making a preliminary fractionation of the bioactive molecules present in the plant that will facilitate the bioguided chromatographic isolation of the pure compounds responsible for the biological activity of the plant.

Quantitative analysis of microstructure evolution,stress partitioning and thermodynamics in the dynamic transformation of Fe-14Ni alloy

Dynamic transformation(DT)of austenite(γ)to ferrite(α)in the hot deformation of various carbon steels was widely investigated.However,the nature of DT remains unclear due to the lack of quantitative analysis of stress partitioning between two phases and the uncertainty of local distribution of substitu-tional elements at the interface in multi-component carbon steels used in the previous studies.Therefore,in the present study,a binary Fe-Ni alloy withα+γduplex microstructure in equilibrium was prepared and isothermally compressed inα+γtwo-phase region to achieve a quantitative analysis of microstruc-ture evolution,stress partitioning,and thermodynamics during DT.γtoαDT during isothermal compres-sion andαtoγreverse transformation on isothermal annealing under unloaded condition after deforma-tion were accompanied by Ni partitioning.The lattice strains during thermomechanical processing were obtained via in-situ neutron diffraction measurement,based on which the stress partitioning behavior betweenγandαwas discussed by using the generalized Hooke’s law.A thermodynamic framework for the isothermal deformation in solids was established based on the basic laws of thermodynamics,and it was shown that the total Helmholtz free energy change in the deformable material during the isothermal process should be smaller than the work done to the deformable material.Under the present thermody-namic framework,the microstructure evolution in the isothermal compression of Fe-14Ni alloy was well explained by considering the changes in chemical free energy,plastic and elastic energies,and the work done to the material.In addition,the stabilization of the softαphase in Fe-14Ni alloy by deformation was rationalized since theγtoαtransformation decreased the total Helmholtz free energy by decreasing the elastic and dislocation energies.

Entropy of Partitions on Quantum Logic

Partition and entropy of partitions in quantum logic are introduced and their properties are investigated.The results are generalized to the general case of T-norm and T-conorm.

A heuristic clustering algorithm based on high density-connected partitions

Clustering data with varying densities and complicated structures is important,while many existing clustering algorithms face difficulties for this problem. The reason is that varying densities and complicated structure make single algorithms perform badly for different parts of data. More intensive parts are assumed to have more information probably,an algorithm clustering from high density part is proposed,which begins from a tiny distance to find the highest density-connected partition and form corresponding super cores,then distance is iteratively increased by a global heuristic method to cluster parts with different densities. Mean of silhouette coefficient indicates the cluster performance. Denoising function is implemented to eliminate influence of noise and outliers. Many challenging experiments indicate that the algorithm has good performance on data with widely varying densities and extremely complex structures. It decides the optimal number of clusters automatically.Background knowledge is not needed and parameters tuning is easy. It is robust against noise and outliers.

A Sharding Scheme Based on Graph Partitioning Algorithm for Public Blockchain

Blockchain technology,with its attributes of decentralization,immutability,and traceability,has emerged as a powerful catalyst for enhancing traditional industries in terms of optimizing business processes.However,transaction performance and scalability has become the main challenges hindering the widespread adoption of blockchain.Due to its inability to meet the demands of high-frequency trading,blockchain cannot be adopted in many scenarios.To improve the transaction capacity,researchers have proposed some on-chain scaling technologies,including lightning networks,directed acyclic graph technology,state channels,and shardingmechanisms,inwhich sharding emerges as a potential scaling technology.Nevertheless,excessive cross-shard transactions and uneven shard workloads prevent the sharding mechanism from achieving the expected aim.This paper proposes a graphbased sharding scheme for public blockchain to efficiently balance the transaction distribution.Bymitigating crossshard transactions and evening-out workloads among shards,the scheme reduces transaction confirmation latency and enhances the transaction capacity of the blockchain.Therefore,the scheme can achieve a high-frequency transaction as well as a better blockchain scalability.Experiments results show that the scheme effectively reduces the cross-shard transaction ratio to a range of 35%-56%and significantly decreases the transaction confirmation latency to 6 s in a blockchain with no more than 25 shards.

Response of partitioning to cooling rate for different solutes in aluminum alloys

It is commonly recognized that the cooling rate has a substantial effect on solute partitioning and its resultant microsegregation during solidification.The classical dendrite tip undercooling theory clarifies the mitigation of microsegregation by increasing the cooling rate.However,most of the studies focused on binary alloys,leaving an open question as to whether the microsegregation of different solutes in a multi-component alloy system exhibits a relieving degree similar to increasing cooling rate.Taking a widely used 6022-type Al alloy(Al-0.76Mg-0.93Si-0.2Fe)as a model alloy,the current study reveals that the microsegregation of Mg gets alleviated to the greatest extent,followed by those of Si and Fe when the cooling rate increases from 5 to 128 K/s.This phenomenon is attributed to the solute-based difference in response to partitioning to cooling rate(denoted as Rk).We propose a theoretical equation to quantify Rk,and the R_(k)values of solute Mg,Si,and Fe successfully explain the rank of solute partitioning in exper-iments.Furthermore,a broad range of R_(k)values of other commonly used alloying elements in Al alloys were calculated and ranked,delivering a handy tool to predict the microsegregation behavior and sol-ubility of different solute elements upon sub-rapid solidification,which is consistent with experimental observation.This framework can also be extended to other multi-component alloy systems.

Hybrid Strategy of Partitioned and Monolithic Methods for Solving Strongly Coupled Analysis of Inverse and Direct Piezoelectric and Circuit Coupling

The inverse and direct piezoelectric and circuit coupling are widely observed in advanced electro-mechanical systems such as piezoelectric energy harvesters.Existing strongly coupled analysis methods based on direct numerical modeling for this phenomenon can be classified into partitioned or monolithic formulations.Each formulation has its advantages and disadvantages,and the choice depends on the characteristics of each coupled problem.This study proposes a new option:a coupled analysis strategy that combines the best features of the existing formulations,namely,the hybrid partitioned-monolithic method.The analysis of inverse piezoelectricity and the monolithic analysis of direct piezoelectric and circuit interaction are strongly coupled using a partitioned iterative hierarchical algorithm.In a typical benchmark problem of a piezoelectric energy harvester,this research compares the results from the proposed method to those from the conventional strongly coupled partitioned iterative method,discussing the accuracy,stability,and computational cost.The proposed hybrid concept is effective for coupled multi-physics problems,including various coupling conditions.

Restraint effect of partition wall on the tunnel floor heave in layered rock mass

The presence of horizontal layered rocks in tunnel engineering significantly impacts the stability and strength of the surrounding rock mass,leading to floor heave in the tunnel.This study focused on preparing layered specimens of rock-like material with varying thickness to investigate the failure behaviors of tunnel floors.The results indicate that thin-layered rock mass exhibits weak interlayer bonding,causing rock layers near the surface to buckle and break upwards when subjected to horizontal squeezing.With an increase in the layer thickness,a transition in failure mode occurs from upward buckling to shear failure along the plane,leading to a noticeable reduction in floor heave deformation.The primary cause of significant deformation in floor heave is upward buckling failure.To address this issue,the study proposes the installation of a partition wall in the middle of the floor to mitigate heave deformation of the rock layers.The results demonstrate that the partition wall has a considerable stabilizing effect on the floor,reducing the zone of buckling failure and minimizing floor heave deformation.It is crucial for the partition wall to be sufficiently high to prevent buckling failure and ensure stability.Through simulation calculations on an engineering example,it is confirmed that implementing a partition wall can effectively reduce floor heave and enhance the stability of tunnel floor.

Algorithm Selection Method Based on Coupling Strength for Partitioned Analysis of Structure-Piezoelectric-Circuit Coupling

In this study, we propose an algorithm selection method based on coupling strength for the partitioned analysis ofstructure-piezoelectric-circuit coupling, which includes two types of coupling or inverse and direct piezoelectriccoupling and direct piezoelectric and circuit coupling. In the proposed method, implicit and explicit formulationsare used for strong and weak coupling, respectively. Three feasible partitioned algorithms are generated, namely(1) a strongly coupled algorithm that uses a fully implicit formulation for both types of coupling, (2) a weaklycoupled algorithm that uses a fully explicit formulation for both types of coupling, and (3) a partially stronglycoupled and partially weakly coupled algorithm that uses an implicit formulation and an explicit formulation forthe two types of coupling, respectively.Numerical examples using a piezoelectric energy harvester,which is a typicalstructure-piezoelectric-circuit coupling problem, demonstrate that the proposed method selects the most costeffectivealgorithm.

Partitioning Calculation Method of Short-Circuit Current for High Proportion DG Access to Distribution Network

Aiming at the problemthat the traditional short-circuit current calculationmethod is not applicable to Distributed Generation(DG)accessing the distribution network,the paper proposes a short-circuit current partitioning calculation method considering the degree of voltage drop at the grid-connected point of DG.Firstly,the output characteristics of DG in the process of low voltage ride through are analyzed,and the equivalent output model of DG in the fault state is obtained.Secondly,by studying the network voltage distribution law after fault in distribution networks under different DG penetration rates,the degree of voltage drop at the grid-connected point of DG is used as a partition index to partition the distribution network.Then,iterative computation is performed within each partition,and data are transferred between partitions through split nodes to realize the fast partition calculation of short-circuit current for high proportion DG access to distribution network,which solves the problems of long iteration time and large calculation error of traditional short-circuit current.Finally,a 62-node real distribution network model containing a high proportion of DG access is constructed onMATLAB/Simulink,and the simulation verifies the effectiveness of the short-circuit current partitioning calculation method proposed in the paper,and its calculation speed is improved by 48.35%compared with the global iteration method.