Disjoint bases in a polymatroid

Let f : 2^N → ⁺ be a polymatroid (an integer‐valued non‐decreasing submodular set function with f(??) = 0). We call S ? N a base if f(S) = f(N). We consider the problem of finding a maximum number of disjoint bases; we denote by m* be this base packing number. A simple upper bound on m* is given by k* = max{k : Σ_iεNf_A(i) ≥ kf_A(N),?A ? N} where f_A(S) = f(A ∪ S) ‐ f(A). This upper bound is a natural generalization of the bound for matroids where it is known that m* = k*. For polymatroids, we prove that m* ≥ (1 ? o(1))k*/lnf(N) and give a randomized polynomial time algorithm to find (1 ? o(1))k*/lnf(N) disjoint bases, assuming an oracle for f. We also derandomize the algorithm using minwise independent permutations and give a deterministic algorithm that finds (1 ? ε)k*/lnf(N) disjoint bases. The bound we obtain is almost tight because it is known there are polymatroids for which m* < (1 + o(1))k*/lnf(N). Moreover it is known that unless NP ? DTIME(n^{log log n}), for any ε > 0, there is no polynomial time algorithm to obtain a (1 + ε)/lnf(N)‐approximation to m*. Our result generalizes and unifies two results in the literature. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

Numerical characterization of DNA sequences based on the k-step Markov chain transition probability

A DNA sequence can be regarded as a discrete-time Markov chain. Based on k-step transition probabilities, we construct a series of 4 x 4 k-step transition matrices to characterize the DNA primary sequences. According to the properties of Markov chains, we obtain distributions of A, T, C and G, and analyze the changes among them from yesterday to tomorrow. We can calculate the probabilities of nucleotide triples of DNA primary sequences. Finally, we introduce a correlation of this kind of transition matrices and consider it as an invariant to analyze the similarities/dissimilarities of DNA sequences.     

基于关键词的对等网络节点群相似性度量模型研究

为了进一步提高基于P2P的内容分发网CDN（content delivery network）的搜索效率,对用户就近组成的节点群（peer group）进行了研究,提出了节点群相似的概念和基于关键词的节点群相似性度量模型.当一个需求在本节点群不能满足时,优先到相似性高的节点群中查找,以较快地满足跨节点群的需求.度量模型对任意两个节点群首先根据节点中各文档关键词的一致程度判断对应两个节点的相似度,然后根据相似节点对的数量和相似度来判断两个节点群相似度.实验表明,使用所提出的度量模型得出的计算结果比传统的基于VSM的算法更接近于实际情况.     

New Similarity Reduction Solutions for the(2+1)-Dimensional Nizhnik-Novikov-Veselov Equation

In this paper,some new formal similarity reduction solutions for the(2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system of the admitted one-dimensional subalgebras.Secondly,by analyzing the reduced equation,three types of similarity solutions are derived,such as multi-soliton like solutions,variable separations solutions,and KdV type solutions.     

A weight’s agglomerative method for detecting communities in weighted networks based on weight’s similarity

This paper proposes the new definition of the community structure of the weighted networks that groups of nodes in which the edge's weights distribute uniformly but at random between them. It can describe the steady connections between nodes or some similarity between nodes' functions effectively. In order to detect the community structure efficiently, a threshold coefficient κ to evaluate the equivalence of edges' weights and a new weighted modularity based on the weight's similarity are proposed. Then, constructing the weighted matrix and using the agglomerative mechanism, it presents a weight's agglomerative method based on optimizing the modularity to detect communities. For a network with n nodes, the algorithm can detect the community structure in time O(n²log₂ⁿ). Simulations on networks show that the algorithm has higher accuracy and precision than the existing techniques. Furthermore, with the change of κ the algorithm discovers a special hierarchical organization which can describe the various steady connections between nodes in groups.     

Similarity solutions to viscous flow and heat transfer of nanofluid over nonlinearly stretching sheet

The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the distance from the origin. The governing partial differential equation and auxiliary conditions are reduced to coupled nonlinear ordinary differential equations with the appropriate corresponding auxiliary conditions. The resulting nonlinear ordinary differential equations (ODEs) are solved numerically. The effects of various relevant parameters, namely, the Eckert number Ec, the solid volume fraction of the nanoparticles φ, and the nonlinear stretching parameter n are discussed. The comparison with published results is also presented. Different types of nanoparticles are studied. It is shown that the behavior of the fluid flow changes with the change of the nanoparticles type.     

基于层间相似性的时序网络节点重要性研究

时序网络可以更加准确地描述节点之间的交互顺序和交互关系.结合多层耦合网络分析法,本文提出了基于节点层间相似性的超邻接矩阵时序网络节点重要性识别方法,与经典的认为所有层间关系为常数不同,层间关系用节点的邻居拓扑重叠系数进行度量.Workspace和Enrons数据集上的结果显示:相比经典的方法,使用该方法得到的Kendall’sτ值在各时间层上的平均提高,最高为17.72%和12.44%,结果表明层间相似性的度量对于时序网络的节点重要性度量具有十分重要的意义.     

Community detection in signed networks based on discrete-time model

Community detection in signed networks has been studied widely in recent years. In this paper, a discrete difference equation is proposed to imitate the consistently changing phases of the nodes. During the interaction, each node will update its phase based on the difference equation. Each node has many different nodes connected with it, and these neighbors have different influences on it. The similarity between two nodes is applied to describe the influences between them. Nodes with high positive similarities will get together and nodes with negative similarities will be far away from each other.Communities are detected ultimately when the phases of the nodes are stable. Experiments on real world and synthetic signed networks show the efficiency of detection performance. Moreover, the presented method gains better detection performance than two existing good algorithms.     

Encryption of color images using MSVD in DCST domain

In this paper, a new image encryption and decryption algorithm based on Multiresolution Singular Value Decomposition (MSVD) and Discrete Cosine Stockwell Transform (DCST) is proposed. An original image is first transformed in DCST domain and then decomposed into four subbands using MSVD, all the four subbands are further decomposed into four subimages according to their indexing and masked by the parameters generated by MSVD. We have used number of bands of DCST, arrangement of MSVD subbands, arrangement of various subimages obtained from MSVD subbands, values and arrangement of a 4×4 matrix generated by MSVD and the arrangement of masked subimages as encryption and decryption keys. To ensure the correct decryption of encrypted image, it is indeed necessary to have correct knowledge of all keys in correct order along with their exact values. If all the keys are correct but a single key is wrong even though it would be almost impossible to guess the original image. The efficiency of proposed algorithm is evaluated by comparing it with some recent published works and it is evident from the experimental results and analysis that the proposed algorithm can transmit the images more securely and efficiently over the network.