Mesoscale and clusters of synchrony in networks of bursting neurons

We study the role of network architecture in the formation of synchronous clusters in synaptically coupled networks of bursting neurons. We give a simple combinatorial algorithm that finds the largest synchronous clusters from the network topology. We demonstrate that networks with a certain degree of internal symmetries are likely to have cluster decompositions with relatively large clusters, leading potentially to cluster synchronization at the mesoscale network level. We also address the asymptotic stability of cluster synchronization in excitatory networks of Hindmarsh-Rose bursting neurons and derive explicit thresholds for the coupling strength that guarantees stable cluster synchronization.     

Cluster algorithms for anisotropic quantum spin models

We present cluster Monte Carlo algorithms for theXYZ quantum spin models. In the special case ofS=1/2, the new algorithm can be viewed as a cluster algorithm for the 8-vertex model. As an example, we study theS=1/2XY model in two dimensions with a representation in which the quantization axis lies in the easy plane. We find that the numerical autocorrelation time for the cluster algorithm remains of the order of unity and does not show any significant dependence on the temperature, the system size, or the Trotter number. On the other hand, the autocorrelation time for the conventional algorithm strongly depends on these parameters and can be very large. The use of improved estimators for thermodynamic averages further enhances the efficiency of the new algorithms.     

Probability-changing cluster algorithm for Potts models

We propose a new effective cluster algorithm of tuning the critical point automatically, which is an extended version of the Swendsen-Wang algorithm. We change the probability of connecting spins of the same type, p = 1-e(-J/k(B)T), in the process of the Monte Carlo spin update. Since we approach the canonical ensemble asymptotically, we can use the finite-size scaling analysis for physical quantities near the critical point. Simulating the two-dimensional Potts models to demonstrate the validity of the algorithm, we have obtained the critical temperatures and critical exponents which are consistent with the exact values; the comparison has been made with the invaded cluster algorithm.     

无线传感器网络的分布式竞争路由算法

在WSNs体系结构中,路由算法是网络层的关键,分簇技术在路由算法中可提高WSNs的扩展性。提出一种竞争簇头,非均匀分簇和多跳路由相结合的WSNs 分布式竞争路由算法(DSA)．它的核心是构建一个高效的非均匀分簇算法,通过竞争的方式候选簇头,靠近基站的簇头为簇间的数据转发预留能量,根据节点的剩余能量、簇内和簇间通信代价,每个簇头在邻居簇头集中用贪心法确定中继节点,仿真表明,DSA算法能有效平衡了簇头的能耗、均衡了网络能耗、显著延长网络生存周期。     

A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering Problems

Two well-known drawbacks in fuzzy clustering are the requirement of assigning in advance the number of clusters and random initialization of cluster centers. The quality of the final fuzzy clusters depends heavily on the initial choice of the number of clusters and the initialization of the clusters, then, it is necessary to apply a validity index to measure the compactness and the separability of the final clusters and run the clustering algorithm several times. We propose a new fuzzy C-means algorithm in which a validity index based on the concepts of maximum fuzzy energy and minimum fuzzy entropy is applied to initialize the cluster centers and to find the optimal number of clusters and initial cluster centers in order to obtain a good clustering quality, without increasing time consumption. We test our algorithm on UCI (University of California at Irvine) machine learning classification datasets comparing the results with the ones obtained by using well-known validity indices and variations of fuzzy C-means by using optimization algorithms in the initialization phase. The comparison results show that our algorithm represents an optimal trade-off between the quality of clustering and the time consumption.     

Scheme for Implementing Quantum Search Algorithm in a Cluster State Quantum Computer

Using cluster state and single qubit measurement one can perform the one-way quantum computation. Here we give a detailed scheme for realizing a modified Grover search algorithm using measurements on cluster state. We give the measurement pattern for the cluster-state realization of the algorithm and estimated the number of measurement needed for its implementation. It is found that O（2^3n/^2n^2） number of single qubit measurements is required for its realization in a cluster-state quantum computer.     

Witness Trees in the Moser–Tardos Algorithmic Lovász Local Lemma and Penrose Trees in the Hard-Core Lattice Gas

We point out a close connection between the Moser–Tardos algorithmic version of the Lovász local lemma, a central tool in probabilistic combinatorics, and the cluster expansion of the hard-core lattice gas in statistical mechanics. We show that the notion of witness trees given by Moser and Tardos is essentially coincident with that of Penrose trees in the Cluster expansion scheme of the hard-core gas. Such an identification implies that the Moser–Tardos algorithm is successful in a polynomial time if the cluster expansion converges.     

Experimental realization of one-way quantum computing with two-photon four-qubit cluster states

We report an experimental realization of one-way quantum computing on a two-photon four-qubit cluster state. This is accomplished by developing a two-photon cluster state source entangled both in polarization and spatial modes. With this special source, we implemented a highly efficient Grover's search algorithm and high-fidelity two-qubit quantum gates. Our experiment demonstrates that such cluster states could serve as an ideal source and a building block for rapid and precise optical quantum computation.     

Efficient Scheme for One-Way Quantum Computing in Thermal Cavities

We propose a practical scheme for one-way quantum computing based on efficient generation of 2D cluster state in thermal cavities. We achieve a controlled-phase gate that is neither sensitive to cavity decay nor to thermal field by adding a strong classical field to the two-level atoms. We show that a 2D cluster state can be generated directly by making every two atoms collide in an array of cavities, with numerically calculated parameters and appropriate operation sequence that can be easily achieved in practical Cavity QED experiments. Based on a generated cluster state in Box⁽⁴⁾ configuration, we then implement Grover’s search algorithm for four database elements in a very simple way as an example of one-way quantum computing.     

利用空间点过程提取丛集点算法的适用性研究

以二维泊松过程理论为基础,结合空间点过程理论,引入k阶最近邻距离的概念,介绍了基于k阶最近距离的丛集点的提取算法,对该算法的适用范围进行了讨论和分析,发现丛集区域和背景区域疏密程度差异以及所研究的数据点数目对该方法有影响,疏密程度差异较小时,该算法的有效性不强,疏密程度差异较大时,该算法较为适用,同时,数据点的总数不同时,算法的适用范围有所差异,但差异不大.此外,引入权重的思想,对算法中理想数据点的设置进行了一定程度的拓展,将所研究区域内的数据点赋予不同的权重,进行丛集数据点的提取,从而扩展了该算法的使用范围. 关键词： 丛集点 最近邻距离 EM算法 分布参数比值     

基于形态学变换和FFCM聚类的灰度图像颜色迁移算法

针对传统颜色迁移算法计算量大、对图像无法准确进行颜色迁移的问题,提出一种基于形态学变换和快速模糊C均值聚类（FFCM）的灰度图像颜色迁移算法。首先对目标图像进行腐蚀膨胀运算,消除亮度不均匀的区域,通过FFCM聚类算法对目标图像进行准确聚类,然后在目标图像与源图像中选取对应样本块,完成样本块的颜色迁移,并以已上色的样本块为参考,完成图像的全局颜色迁移。实验结果表明:与Welsh和FCM算法相比较,本文算法处理时间分别缩短64.29 %和54.25 %,结果图像在类间交界处的颜色过渡更加自然,证明了算法的有效性。     

Experimental realization of Deutsch's algorithm in a one-way quantum computer

We report the first experimental demonstration of an all-optical one-way implementation of Deutsch's quantum algorithm on a four-qubit cluster state. All the possible configurations of a balanced or constant function acting on a two-qubit register are realized within the measurement-based model for quantum computation. The experimental results are in excellent agreement with the theoretical model, therefore demonstrating the successful performance of the algorithm.     

Simulating nanoscale dielectric response

We introduce a constrained energy functional to describe dielectric response. We demonstrate that the local functional is a generalization of the long-ranged Marcus energy. Our reformulation is used to implement a cluster Monte Carlo algorithm for the simulation of dielectric media. The algorithm avoids solving the Poisson equation and remains efficient in the presence of spatial heterogeneity, nonlinearity, and scale dependent dielectric properties.     

Parallel cluster labeling for large-scale Monte Carlo simulations

We present an optimized version of a cluster labeling algorithm previously introduced by the authors. This algorithm is well suited for large-scale Monte Carlo simulations of spin models using cluster dynamics on parallel computers with large numbers of processors. The algorithm divides physical space into rectangular cells which are assigned to processors and combines a serial local labeling procedure with a relaxation process across nearest-neighbor processors. By controlling overhead and reducing inter-processor communication this method attains good computational speed-up and efficiency. Large systems of up to 65536² spins have been simulated at updating speeds of 11 nanosecs/site (90.7 × 10⁶ spin updates/sec) using state-of-the-art supercomputers. In the second part of the article we use the cluster algorithm to study the relaxation of magnetization and energy on large Ising models using Swendsen-Wang dynamics. We found evidence that exponential and power law factors are present in the relaxation process as has been proposed by Hackl et al. The variation of the power-law exponent λ_M taken at face value indicates that the value of Z_M falls in the interval 0.31–0.49 for the time interval analysed and appears to vanish asymptotically.     

Minimal classical communication and measurement complexity for quantum information splitting of a two-qubit state

We investigate the usefulness of the highly entangled five-partite cluster and Brown states for the quantum information splitting (QIS) of a special kind of two-qubit state using remote state preparation. In our schemes, the information that is to be shared is known to the sender. We show that, QIS can be accomplished with just two classical bits, as opposed to four classical bits, when the information that is to be shared is unknown to the sender. The present algorithm, demonstrated through the cluster and Brown states is deterministic as compared to the previous works in which it was probabilistic.     

One-way quantum computing in the optical frequency comb

One-way quantum computing allows any quantum algorithm to be implemented easily using just measurements. The difficult part is creating the universal resource, a cluster state, on which the measurements are made. We propose a scalable method that uses a single, multimode optical parametric oscillator (OPO). The method is very efficient and generates a continuous-variable cluster state, universal for quantum computation, with quantum information encoded in the quadratures of the optical frequency comb of the OPO.     

Computing Freidlin’s Cycles for the Overdamped Langevin Dynamics. Application to the Lennard-Jones-38 Cluster

The large time behavior of a stochastic system with infinitesimally small noise can be described in terms of Freidlin’s cycles. We show that if the system is gradient and the potential satisfies certain non-restrictive conditions, the hierarchy of cycles has a structure of a full binary tree, and each cycle is exited via the lowest saddle adjacent to it. Exploiting this property, we propose an algorithm for computing the asymptotic zero-temperature path and building a hierarchy of Freidlin’s cycles associated with the transition process between two given local equilibria. This algorithm is suitable for systems with a complex potential energy landscape with numerous minima. We apply it to find the asymptotic zero-temperature path and Freidlin’s cycles involved into the transition process between the two lowest minima of the Lennard-Jones cluster of 38 atoms. D. Wales’s stochastic network of minima and transition states of this cluster is used as an input.     

GPU-based single-cluster algorithm for the simulation of the Ising model

We present the GPU calculation with the common unified device architecture (CUDA) for the Wolff single-cluster algorithm of the Ising model. Proposing an algorithm for a quasi-block synchronization, we realize the Wolff single-cluster Monte Carlo simulation with CUDA. We perform parallel computations for the newly added spins in the growing cluster. As a result, the GPU calculation speed for the two-dimensional Ising model at the critical temperature with the linear size L = 4096 is 5.60 times as fast as the calculation speed on a current CPU core. For the three-dimensional Ising model with the linear size L = 256, the GPU calculation speed is 7.90 times as fast as the CPU calculation speed. The idea of quasi-block synchronization can be used not only in the cluster algorithm but also in many fields where the synchronization of all threads is required.     

半导体激光器光谱的聚类分析

本文提出了分析半导体激光器光谱分布差异的聚类算法.首先,介绍了聚类分析的有关概念和原理,接着给出了分析光谱差异的算法.该算法具有较强的有效性和通用性.最后,给出了一个具体应用.