Algorithm for complex network diameter based on distance matrix

The network diameter is an important characteristic parameter of a complex network. Calculation for a large-scale complex network’s diameter has been an important subject in the study of complex networks. If the network diameter is calculated directly, the problem mainly exists in efficiency for searching and counting the shortest paths. If the network diameter is calculated indirectly by studying the statistical function about the relationship between the network diameter and parameters affecting the diameter, the problems not only exist in the efficiency of statistic, but also exist in the function which may be not applicable to all kinds of networks. An algorithm for the complex network diameter based on the k order distance matrix is proposed with a matrix multiplication approach, and a mathematical proof for the algorithm correctness is given as well. Furthermore, some relevant propositions and deductions for reducing the complexity of this algorithm are put forward. With a good theoretical basis and a simple calculation process, this algorithm can be used to calculate the diameter of a large-scale complex network with small-world effect more accurately and efficiently. Two cases about the advanced research projects agency(ARPA) network model and the Chinese airline network model are adopted to verify the effect of this algorithm.

Distance Matrix and Markov Chain Based Sensor Localization in WSN

Applications based on Wireless Sensor Networks(WSN)have shown to be quite useful in monitoring a particular geographic area of interest.Relevant geometries of the surrounding environment are essential to establish a successful WSN topology.But it is literally hard because constructing a localization algorithm that tracks the exact location of Sensor Nodes(SN)in a WSN is always a challenging task.In this research paper,Distance Matrix and Markov Chain(DM-MC)model is presented as node localization technique in which Distance Matrix and Estimation Matrix are used to identify the position of the node.The method further employs a Markov Chain Model(MCM)for energy optimization and interference reduction.Experiments are performed against two well-known models,and the results demonstrate that the proposed algorithm improves performance by using less network resources when compared to the existing models.Transition probability is used in the Markova chain to sustain higher energy nodes.Finally,the proposed Distance Matrix and Markov Chain model decrease energy use by 31%and 25%,respectively,compared to the existing DV-Hop and CSA methods.The experimental results were performed against two proven models,Distance VectorHop Algorithm(DV-HopA)and Crow Search Algorithm(CSA),showing that the proposed DM-MC model outperforms both the existing models regarding localization accuracy and Energy Consumption(EC).These results add to the credibility of the proposed DC-MC model as a better model for employing node localization while establishing a WSN framework.

An Algorithm for the Inverse Problem of Matrix Processing: DNA Chains, Their Distance Matrices and Reconstructing

We continue to consider one of the cybernetic methods in biology related to the study of DNA chains. Exactly, we are considering the problem of reconstructing the distance matrix for DNA chains. Such a matrix is formed on the basis of any of the possible algorithms for determining the distances between DNA chains, as well as any specific object of study. At the same time, for example, the practical programming results show that on an average modern computer, it takes about a day to build such a 30 × 30 matrix for mnDNAs using the Needleman-Wunsch algorithm;therefore, for such a 300 × 300 matrix, about 3 months of continuous computer operation is expected. Thus, even for a relatively small number of species, calculating the distance matrix on conventional computers is hardly feasible and the supercomputers are usually not available. Therefore, we started publishing our variants of the algorithms for calculating the distance between two DNA chains, then we publish algorithms for restoring partially filled matrices, i.e., the inverse problem of matrix processing. Previously, we used the method of branches and boundaries, but in this paper we propose to use another new algorithm for restoring the distance matrix for DNA chains. Our recent work has shown that even greater improvement in the quality of the algorithm can often be achieved without improving the auxiliary heuristics of the branches and boundaries method. Thus, we are improving the algorithms that formulate the greedy function of this method only. .

Novel Distance-Related Matrix Index and QSPR Research for Thermodynamics of Methyl Halides

A novel topological index W F is defined by the matrices X,W and L as W F=XWL.The topological index WF based on the distance-related matrix of molecular graphs is used to code the structural environment of each atom-type in a molecular graph.Good QSPR models have been obtained for standard formation enthalpy of methyl halides.The result indicates that the idea of using multiple matrices to define the distance-related matrix topological index is valid.

SMITH NORMAL FORMAL OF DISTANCE MATRIX OF BLOCK GRAPHS

A connected graph, whose blocks are all cliques （of possibly varying sizes）, is called a block graph. Let D（G） be its distance matrix. In this note, we prove that the Smith normal form of D（G） is independent of the interconnection way of blocks and give an explicit expression for the Smith normal form in the case that all cliques have the same size, which generalize the results on determinants.

Distance Integral Complete Multipartite Graphs with s=5, 6

Let D(G) =(d_(ij))_(n×n) denote the distance matrix of a connected graph G with order n, where d_(ij) is equal to the distance between vertices viand vjin G. A graph is called distance integral if all eigenvalues of its distance matrix are integers. In 2014, Yang and Wang gave a sufficient and necessary condition for complete r-partite graphs K_(p1,p2,···,pr)=K_(a1·p1,a2·p2,···,as···ps) to be distance integral and obtained such distance integral graphs with s = 1, 2, 3, 4. However distance integral complete multipartite graphs K_(a1·p1,a2·p2,···,as·ps) with s > 4 have not been found. In this paper, we find and construct some infinite classes of these distance integral graphs K_(a1·p1,a2·p2,···,as·ps) with s = 5, 6. The problem of the existence of such distance integral graphs K_(a1·p1,a2·p2,···,as·ps) with arbitrarily large number s remains open.

Reforming of Wiener Index

Based on distance matrixW, the novel topological indexW F is defined by the matricesX, W, L, asW F=WXL. WhereX is a row matrix, which expresses the bonding characteristics between adjacent atoms;L is a column matrix expressing the characteristic of vertexes in molecules;W is a distance matrix, which expresses the chemical environment of the atoms in the molecule. the properties, the chemical environments and the interaction of the vertexes in a molecule are taken into account in this definition. Hence the application of the indexW F to multiple bonds and heteroatomcontaining organic systems or inorganic systems is possible. Good correlation coefficients are achieved not only in the prediction of the standard formation enthalpy of methyl halides, titanium halides, but also the retention index of gas chromatography of the hydrocarbons. Key words distance matrix - Wiener index - QSPR - organic systems - inorganic systems CLC number O 651 Foundation item: Supported by the National Natural Science Foundation of China (20177018) and the Educational Bureau Foundation of Hubei (2003B001)Biography: Huang Yun-ping (1963-), female, Professor, research direction: biophysical chemistry

Metabasin dynamics of supercooled polymer melt

We employ molecular dynamic simulation to investigate metabasin dynamics for supercooled polymer melt. We find that, in a small system, the α-relaxation process is composed of a few crossing events that the monomers hops from one metabasin to another. Each crossing event is very rapid and involves a democratic movement of many particles,whereas such collective motion is not string-like. Evaluation on the contributions of metabasin exploration and democratic movement shows that the structural relaxation is mostly governed by the latter. Our calculated results show that the metabasin–metabasin transitions are not the main reason of spatially dynamical heterogeneity. It is different from the binary Lennard–Jones mixture model in which the metabasin–metabasin transitions are relevant for the spatially dynamical heterogeneity.

Use of FFT in Protein Sequence Comparison under Their Binary Representations

The paper considers Voss type representation of amino acids and uses FFT on the represented binary sequences to get the spectrum in the frequency domain. Based on the analysis of this spectrum by using the method of inter coefficient difference (ICD), it compares protein sequences of ND5 and ND6 category. Results obtained agree with the standard ones. The purpose of the paper is to extend the ICD method of comparison of DNA sequences to comparison of protein sequences. The topic of discussion is to develop a novel method of comparing protein sequences. The main achievements of the work are that the method applied is completely new of its kind, so far as protein sequence comparison is concerned and moreover the results of comparison agree with the previous results obtained by other methods for the same category of protein sequences.

Study on Phylogenetic Relationships of Five Breeds of Pigs by Random Amplified Polymorphic DNA(RAPD)

RAPD was used to study the genetic divergency and phylogenetic relationships of five breeds of domestic pigs,including Min pig,Duroc,Yorkshired,Landrace and Junmu I pig.We selected fourteen primers from eighty random primers,caculated genetic distance index matrix and constructed phylogenetic tree with UPGMA methods.Genetic distance index matrix indicated that the genetic relationship between Junmu I pig and Landrace was the closest and the farthest between Duroc and min pig.

A Model of Vary in Distance Leslie Matrix of the Giant Panda's Population at Wu-YiPeng,Wolong

A new Vary in Distance Leslie Matrix is adopted to process the observed data of a giant panda population’s development trend dynamics with unequal distance age groups. Results show that this new method adopted is much simpler than the usual lesile Matrix analysis, and no need of deviding the pandas into equal distance age groups and no so many asumptions are needed as in the usual Leslie Methods. We only changed the meaning of some elements in Leslie Matrix and processed the developmental trend of panda population in Wolong Wu Yi Peng successfully we also carried out a sensitivity analysis of many parameters as well as the computer simulation.

On Distance Laplacian Spectra of Certain Finite Groups

For a finite group G,the power graph P(G)is a simple connected graph whose vertex set is the set of elements of G and two distinct vertices x and y are adjacent if and only if x^(i)=y or y^(i)=x,for 2≤i,j≤n.In this paper,we obtain the distance Laplacian spectrum of power graphs of finite groups such as cyclic groups,dihedral groups,dicyclic groups,abelian groups and elementary abelian p groups.Moreover,we find the largest and second smallest distance Laplacian eigenvalue of power graphs of such groups.

Conditional Quadratic Semidefinite Programming:Examples and Methods

The conditional quadratic semidefinite programming(cQSDP)refers to a class of matrix optimization problems whose matrix variables are required to be positive semidefinite on a subspace,and the objectives are quadratic.The chief purpose of this paper is to focus on two primal examples of cQSDP:the problem of matrix completion/approximation on a subspace and the Euclidean distance matrix problem.For the latter problem,we review some classical contributions and establish certain links among them.Moreover,we develop a semismooth Newton method for a special class of cQSDP and establish its quadratic convergence under the condition of constraint nondegeneracy.We also include an application in calibrating the correlation matrix in Libor market models.We hope this work will stimulate new research in cQSDP.