statistical analysis of airport network of china through the study of airport network of china anc composed of 128 airports nodes and 1165 flights edges we show the topological structure of anc conveys two characteristics of small worlds a short average path length 2 067 and a high degree of clustering 0 733 the cumulative degree distributions of both directed and undirected anc obey two regime power laws with different exponents i e the so called double pareto law in degrees and out degrees of each airport have positive correlations whereas the undirected degrees of adjacent airports have significant linear anticorrelations it is demonstrated both weekly and daily cumulative distributions of flight weights frequencies of anc have power law tails besides the weight of any given flight is proportional to the degrees of both airports at the two ends of that flight it is also shown the diameter of each subcluster consisting of an airport and all those airports to which it is linked is inversely proportional to its density of connectivity efficiency of anc and of its subclusters is measured through a simple definition in terms of that the efficiency of anc s subclusters increases as the density of connectivity does anc is found to have an efficiency of 0 484

a novel multigrid based preconditioner for heterogeneous helmholtz problems an iterative solution method in the form of a preconditioner for a krylov subspace method is presented for the helmholtz equation the preconditioner is based on a helmholtz type differential operator with a complex term a multigrid iteration is used for approximately inverting the preconditioner the choice of multigrid components for the corresponding preconditioning matrix with a complex diagonal is validated with fourier analysis multigrid analysis results are verified by numerical experiments high wavenumber helmholtz problems in heterogeneous media are solved indicating the performance of the preconditioner

weighted scale free networks with variable power law exponents abstract we present a weighted scale free network model in which the power law exponents can be controlled by the model parameters the network is generated through the weight driven preferential attachment of new nodes to existing nodes and the growth of the weights of existing links the simplicity of the model enables us to derive analytically the various statistical properties such as the distributions of degree strength and weight the degree strength and degree weight relationship and the dependencies of these power law exponents on the model parameters finally we demonstrate that networks of words coauthorship of researchers and collaboration of actor actresses are quantitatively well described by this model

unwinding the hairball graph pruning algorithms for weighted complex networks empirical networks of weighted dyadic relations often contain noisy edges that alter the global characteristics of the network and obfuscate the most important structures therein graph pruning is the process of identifying the most significant edges according to a generative null model and extracting the subgraph consisting of those edges here we focus on integer weighted graphs commonly arising when weights count the occurrences of an event relating the nodes we introduce a simple and intuitive null model related to the configuration model of network generation and derive two significance filters from it the marginal likelihood filter mlf and the global likelihood filter glf the former is a fast algorithm assigning a significance score to each edge based on the marginal distribution of edge weights whereas the latter is an ensemble approach which takes into account the correlations among edges we apply these filters to the network of air traffic volume between us airports and recover a geographically faithful representation of the graph furthermore compared with thresholding based on edge weight we show that our filters extract a larger and significantly sparser giant component

confidence intervals for a binomial proportion and asymptotic expansions p z 2n 1 2 p 1 p 1 2 is currently in near universal use we first show that the coverage properties of the wald interval are persistently poor and defy virtually all conventional wisdom we then proceed to a theoretical comparison of the standard interval and four additional alternative intervals by asymptotic expansions of their coverage probabilities and expected lengths the four additional interval methods we study in detail are the score test interval wilson the likelihood ratio test interval a jeffreys prior bayesian interval and an interval suggested by agresti and coull the asymptotic expansions for coverage show that the first three of these alternative methods have coverages that fluctuate about the nominal value while the agresti coull interval has a somewhat larger and more nearly conservative coverage function for the five interval methods we also investigate asymptotically their average coverage relative to distributions for p supported within 0 1 in terms of expected length asymptotic expansions show that the agresti coull interval is always the longest of these the remaining three are rather comparable and are shorter than the wald interval except for p near 0 or 1 these analytical calculations support and complement the findings and the recommendations in brown cai and dasgupta statist sci 2001 16 101 133

analysis of weighted networks the connections in many networks are not merely binary entities either present or not but have associated weights that record their strengths relative to one another recent studies of networks have by and large steered clear of such weighted networks which are often perceived as being harder to analyze than their unweighted counterparts here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph allowing us to apply standard techniques for unweighted graphs to weighted ones as well we give a number of examples of the method including an algorithm for detecting community structure in weighted networks and a simple proof of the maximum flow minimum cut theorem

multifractal analysis and topological properties of a new family of weighted koch networks abstract weighted complex networks especially scale free networks which characterize real life systems better than non weighted networks have attracted considerable interest in recent years studies on the multifractality of weighted complex networks are still to be undertaken in this paper inspired by the concepts of koch networks and koch island we propose a new family of weighted koch networks and investigate their multifractal behavior and topological properties we find some key topological properties of the new networks their vertex cumulative strength has a power law distribution there is a power law relationship between their topological degree and weight strength the networks have a high weighted clustering coefficient of 0 41004 which is independent of the scaling factor c in the limit of large generation t the second smallest eigenvalue 2 and the maximum eigenvalue n are approximated by quartic polynomials of the scaling factor c for the general laplacian operator while 2 is approximately a quartic polynomial of c and n 1 5 for the normalized laplacian operator then we find that weighted koch networks are both fractal and multifractal their fractal dimension is influenced by the scaling factor c we also apply these analyses to six real world networks and find that the multifractality in three of them are strong

an iterative method for the helmholtz equation an iterative algorithm for the solution of the helmholtz equation is developed the algorithm is based on a preconditioned conjugate gradient iteration for the normal equations the preconditioning is based on an ssor sweep for the discrete laplacian numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm

synchronization in weighted uncorrelated complex networks in a noisy environment optimization and connections with transport efficiency motivated by synchronization problems in noisy environments we study the edwards wilkinson process on weighted uncorrelated scale free networks we consider a specific form of the weights where the strength and the associated cost of a link is proportional to kikj beta with ki and kj being the degrees of the nodes connected by the link subject to the constraint that the total edge cost is fixed we find that in the mean field approximation on uncorrelated scale free graphs synchronization is optimal at beta 1 numerical results based on exact numerical diagonalization of the corresponding network laplacian confirm the mean field results with small corrections to the optimal value of beta employing our recent connections between the edwards wilkinson process and resistor networks and some well known connections between random walks and resistor networks we also pursue a naturally related problem of optimizing performance in queue limited communication networks utilizing local weighted routing schemes

statistical mechanics of multiedge networks statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones there are however subtle yet important considerations to be made regarding the nature of the weights used in this generalization weights can be either continuous or discrete magnitudes and in the latter case they can additionally have undistinguishable or distinguishable nature this fact has not been addressed in the literature insofar and has deep implications on the network statistics in this work we face this problem introducing multiedge networks as graphs where multiple distinguishable connections between nodes are considered we develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection the latter case is particularly interesting as we show that binary projections can be understood from multiedge processes the implications of these results are important as many real agent based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior

binomial confidence intervals abstract for x with binomial n p distribution section 1 gives a one page table of 95 and 99 confidence intervals for p for n 1 2 30 this interval is equivariant under x n x and p 1 p has approximately equal probability tails is approximately unbiased has crow s property of minimizing the sum of the n 1 possible lengths and each of its ends is increasing in x and decreasing in n with about as regular steps as possible sections 2 and 3 consider the usual approximate confidence intervals calculations and asymptotic results show the need for the continuity correction in these even when n is large because of the nonuniformity of the binomial normal convergence as p 0 these intervals fail to have their stated asymptotic confidence coefficients simple corrections are given for this in the approximate interval x n c n x n 1 x n 1 2n it is shown that the factor c n should be replaced by c n c 2 2c n 1 n

extracting the multiscale backbone of complex weighted networks a large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength in recent years the study of an increasing number of large scale networks has highlighted the statistical heterogeneity of their interaction pattern with degree and weight distributions that vary over many orders of magnitude these features along with the large number of elements and links make the extraction of the truly relevant connections forming the network s backbone a very challenging problem more specifically coarse graining approaches and filtering techniques come into conflict with the multiscale nature of large scale systems here we define a filtering method that offers a practical procedure to extract the relevant connection backbone in complex multiscale networks preserving the edges that represent statistically significant deviations with respect to a null model for the local assignment of weights to edges an important aspect of the method is that it does not belittle small scale interactions and operates at all scales defined by the weight distribution we apply our method to real world network instances and compare the obtained results with alternative backbone extraction techniques

world trade web topological properties dynamics and evolution this paper studies the statistical properties of the web of import export relationships among world countries using a weighted network approach we analyze how the distributions of the most important network statistics measuring connectivity assortativity clustering and centrality have coevolved over time we show that all node statistic distributions and their correlation structure have remained surprisingly stable in the last 20 years and are likely to do so in the future conversely the distribution of positive link weights is slowly moving from a log normal density towards a power law we also characterize the autoregressive properties of network statistics dynamics we find that network statistics growth rates are well proxied by fat tailed densities like the laplace or the asymmetric exponential power finally we find that all our results are reasonably robust to a few alternative economically meaningful weighting schemes

flexible construction of hierarchical scale free networks with general exponent extensive studies have been done to understand the principles behind architectures of real networks recently evidence for hierarchical organization in many real networks has also been reported here we present a hierarchical model that reproduces the main experimental properties observed in real networks scale free of degree distribution p k frequency of the nodes that are connected to k other nodes decays as a power law p k ensuremath sim k ensuremath ensuremath gamma and power law scaling of the clustering coefficient c k ensuremath sim k ensuremath 1 the major points of our model can be summarized as follows a the model generates networks with scale free distribution for the degree of nodes with general exponent ensuremath gamma g2 and arbitrarily close to any specified value being able to reproduce most of the observed hierarchical scale free topologies in contrast previous models cannot obtain values of ensuremath gamma g2 58 b our model has structural flexibility because i it can incorporate various types of basic building blocks e g triangles tetrahedrons and in general fully connected clusters of n nodes and ii it allows a large variety of configurations i e the model can use more than n ensuremath 1 copies of basic blocks of n nodes the structural features of our proposed model might lead to a better understanding of architectures of biological and nonbiological networks

dynamic vaccination in partially overlapped multiplex network in this work we propose and investigate a strategy of vaccination which we call dynamic vaccination in our model susceptible people become aware that one or more of their contacts are infected and thereby get vaccinated with probability ensuremath omega before having physical contact with any infected patient then the nonvaccinated individuals will be infected with probability ensuremath beta we apply the strategy to the susceptible infected recovered epidemic model in a multiplex network composed by two networks where a fraction q of the nodes acts in both networks we map this model of dynamic vaccination into bond percolation model and use the generating functions framework to predict theoretically the behavior of the relevant magnitudes of the system at the steady state we find a perfect agreement between the solutions of the theoretical equations and the results of stochastic simulations in addition we find an interesting phase diagram in the plane ensuremath beta text ensuremath ensuremath omega which is composed of an epidemic and a nonepidemic phase separated by a critical threshold line ensuremath beta c which depends on q as q decreases ensuremath beta c increases i e as the overlap decreases the system is more disconnected and therefore more virulent diseases are needed to spread epidemics surprisingly we find that for all values of q a region in the diagram where the vaccination is so efficient that regardless of the virulence of the disease it never becomes an epidemic we compare our strategy with random immunization and find that using the same amount of vaccines for both scenarios we obtain that the spread of disease is much lower in the case of dynamic vaccination when compared to random immunization furthermore we also compare our strategy with targeted immunization and we find that depending on ensuremath omega dynamic vaccination will perform significantly better and in some cases will stop the disease before it becomes an epidemic

weighted scale free networks in euclidean space using local selection rule received 23 july 2005 revised manuscript received 21 july 2006 published 22 september 2006a spatial scale free network is introduced and studied whose motivation originated in the growing internetas well as airport networks we argue that in these real world networks a new node necessarily selects one ofits neighboring local nodes for connection and is not controlled by preferential attachment as in the barabasi albert ba model this observation is mimicked in our model where the nodes pop up at randomly locatedpositions in the euclidean space and are connected to one end of the nearest link in spite of this crucialdifference it is observed that the leading behavior of our network is like that of the ba model de ning the linkweight as an algebraic power of its euclidean length the weight distribution and the nonlinear dependence ofthe nodal strength on the degree are analytically calculated it is claimed that a power law decay of the linkweights with time ensures such nonlinear behavior switching off the euclidean space from the same modelyields a much simpler de nition of the ba model where numerical effort grows linearly with

preconditioned newton methods using incremental unknowns methods for the resolution of a steady state navier stokes like problem in a previous work one of the authors has studied a numerical treatment by fully implicit discretizations of a two dimensional navier stokes like problem and has proved existence and convergence results for the resulting discretized systems with homogeneous dirichlet boundary conditions in this work we propose some new preconditioned multilevel versions of inexact newton algorithms to solve these equations we also develop another multilevel preconditioner for a nonlinear gmres algorithm all of the preconditioners are based on incremental unknowns formulations

second order absorbing boundary conditions for the wave equation a solution for the corner problem the treatment of domains with corners in the problem of absorbing boundary conditions for the wave equation is very important from a practical point of view a technical difficulty appears as soon as conditions of order greater than or equal to 2 are considered a solution is proposed for the two dimensional case when second order conditions are used this solution consists of prescribing an adequate corner condition the problem thus obtained is analyzed theoretically and the condition is proved to be optimal the results obtained here are illustrated by numerical simulations some extensions to higher space dimensions and higher order conditions are proposed

confidence intervals for a binomial proportion thirteen methods for computing binomial confidence intervals are compared based on their coverage properties widths and errors relative to exact limits the use of the standard textbook method x n 1 96 square root of x n 1 x n n or its continuity corrected version is strongly discouraged a commonly cited rule of thumb stating that alternatives to exact methods may be used when the estimated proportion p is such that np and n 1 p both exceed 5 does not ensure adequate accuracy score limits are easily calculated from closed form solutions to quadratic equations and can be used at all times based on coverage functions the continuity corrected score method is recommended over exact methods its conservative nature should be kept in mind as should the wider fluctuation of actual coverage that accompanies omission of the continuity correction

an empirical study of an agglomeration network recently researchers have reported many models mimicking real network evolution growth among which some are based on network aggregation growth however until now relatively few experiments have been reported accordingly in this paper photomicrographs of real materials the agglomeration in the filtrate of slurry formed by a gap nanoparticle conglomerate dispersed in water are analyzed within the framework of complex network theory by data mapping from photomicrographs we generate undirected networks and as a definition of degree we adopt the number of pixel s nearest neighbors while adjacent pixels define a connection or an edge we study the topological structure of these networks including degree distribution clustering coefficient and average path length in addition we discuss the self similarity and synchronizability of the networks we find that the synchronizability of high concentration agglomeration is better than that of low concentration agglomeration we also find that agglomeration networks possess good self similar features

complex networks embedded in space dimension and scaling relations between mass topological distance and euclidean distance 2 andr exp a 2 suchthat m r d for d e m increases exponentially with as known for 0 while r is constant and independent of f or 2de we find the e

information filtering in complex weighted networks many systems in nature society and technology can be described as networks where the vertices are the system s elements and edges between vertices indicate the interactions between the corresponding elements edges may be weighted if the interaction strength is measurable however the full network information is often redundant because tools and techniques from network analysis do not work or become very inefficient if the network is too dense and some weights may just reflect measurement errors and need to be be discarded moreover since weight distributions in many complex weighted networks are broad most of the weight is concentrated among a small fraction of all edges it is then crucial to properly detect relevant edges simple thresholding would leave only the largest weights disrupting the multiscale structure of the system which is at the basis of the structure of complex networks and ought to be kept in this paper we propose a weight filtering technique based on a global null model global statistical significance gloss filter keeping both the weight distribution and the full topological structure of the network the method correctly quantifies the statistical significance of weights assigned independently to the edges from a given distribution applications to real networks reveal that the gloss filter is indeed able to identify relevant connections between vertices

a parallel fictitious domain method for the three dimensional helmholtz equation the application of a fictitious domain domain embedding method to the three dimensional helmholtz equation with absorbing boundary conditions is considered the finite element discretization is performed by using locally fitted meshes and an algebraic fictitious domain method with a separable preconditioner is used in the iterative solution of the resultant linear systems such a method is based on embedding the original domain into a larger one with a simple geometry with this approach it is possible to realize the gmres iterations in a low dimensional subspace and use the partial solution method to solve the linear systems with the preconditioner an efficient parallel implementation of the iterative algorithm is introduced results of numerical experiments demonstrate good scalability properties on distributed memory parallel computers and the ability to solve high frequency acoustic scattering problems

equation based interpolation and incremental unknowns for solving the three dimensional helmholtz equation abstract in an earlier paper poullet and boag 2007 1 we developed an efficient incremental unknowns iu preconditioner for solving the two dimensional 2d helmholtz problem in both high and low frequency wavenumber regimes the multilevel preconditioning scheme involves separation of each grid into a coarser grid of the following level and a complementary grid on which the ius are defined by interpolation this approach is efficient as long as the mesh size of the coarsest grid is sufficiently small compared to the wavelength in order to overcome this restriction the authors introduced recently in poullet and boag 2010 2 a modified iu method combining the conventional interpolation with the helmholtz equation based interpolation ebi the ebi coefficients are derived numerically using a sufficiently large set of analytic solutions of the helmholtz equation on a special hierarchy of stencils the modified ius using helmholtz ebi are shown to provide improved preconditioning on the coarse scales where the conventional interpolation can not be employed this study deals with the extension of this idea for solving the three dimensional 3d helmholtz equation

hyperbolicity measures democracy in real world networks in this work we analyze the hyperbolicity of real world networks a geometric quantity that measures if a space is negatively curved we provide two improvements in our understanding of this quantity first of all in our interpretation a hyperbolic network is aristocratic since few elements connect the system while a non hyperbolic network has a more democratic structure with a larger number of crucial elements the second contribution is the introduction of the average hyperbolicity of the neighbors of a given node through this definition we outline an influence area for the vertices in the graph we show that in real networks the influence area of the highest degree vertex is small in what we define local networks i e social or peer to peer networks and large in global networks i e power grid metabolic networks or autonomous system networks

a parallel sweeping preconditioner for heterogeneous 3d helmholtz equations a parallelization of a sweeping preconditioner for three dimensional helmholtz equations without large cavities is introduced and benchmarked for several challenging velocity models the setup and application costs of the sequential preconditioner are shown to be o gamma 2 n 4 3 and o gamma n log n where gamma omega denotes the modestly frequency dependent number of grid points per perfectly matched layer several computational and memory improvements are introduced relative to using black box sparse direct solvers for the auxiliary problems and competitive runtimes and iteration counts are reported for high frequency problems distributed over thousands of cores two open source packages are released along with this paper parallel sweeping preconditioner psp and the underlying distributed multifrontal solver clique

a spatial weighted network model based on optimal expected traffic abstract we propose a spatial weighted network model based on the optimal expected traffic the expected traffic represents the prediction of the flow created by two vertices and is calculated by the improved gravity equation the model maximizes the total expected traffic of the network by changing two parameters which control the fitness and the geographical constraints the model can vary its topology and give rise to a variety of statistical properties observed in the real world network notably our study shows that a linear and a nonlinear strength degree correlation can emerge when considering and neglecting the transport effect respectively

scale free properties of weighted networks with connectivity driven topology abstract the rate equations are used to study the scale free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices an analysis of these equations shows that the degree distribution and thereby the weight distribution remain unchanged when the probability rate of attaching new nodes is replaced with an unnormalized rate determined by the ratio of the degree of a randomly selected old node to the maximal node degree at the current stage of the network evolution such a modification of the attachment rule is argued to accelerate considerable numerical simulations of both unweighted and weighted networks belonging to the class of investigated evolving systems it is also proved that the studied rate equations have a solution corresponding to the total weight concentrated at individual vertices distribution displaying the power law behavior for asymptotically large weights

estimation of aquifer scale proportion using equal area grids assessment of regional scale groundwater quality 1 the proportion of an aquifer with constituent concentrations above a specified threshold high concentrations is taken as a nondimensional measure of regional scale water quality if computed on the basis of area it can be referred to as the aquifer scale proportion a spatially unbiased estimate of aquifer scale proportion and a confidence interval for that estimate are obtained through the use of equal area grids and the binomial distribution traditionally the confidence interval for a binomial proportion is computed using either the standard interval or the exact interval research from the statistics literature has shown that the standard interval should not be used and that the exact interval is overly conservative on the basis of coverage probability and interval width the jeffreys interval is preferred if more than one sample per cell is available cell declustering is used to estimate the aquifer scale proportion and kish s design effect may be useful for estimating an effective number of samples the binomial distribution is also used to quantify the adequacy of a grid with a given number of cells for identifying a small target defined as a constituent that is present at high concentrations in a small proportion of the aquifer case studies illustrate a consistency between approaches that use one well per grid cell and many wells per cell the methods presented in this paper provide a quantitative basis for designing a sampling program and for utilizing existing data

dynamic weight evolution network with preferential attachment abstract a dynamic weight evolution network with preferential attachment is introduced the network includes two significant characteristics i topological growth triggered by newly added node with m links at each time step each new edge carries an initial weight growing nonlinearly with time ii weight dynamics the weight between two existing nodes experiences increasing or decreasing in a nonlinear way by using continuum theory and mean field method we study the strength the degree the weight and their distributions we find that the distributions exhibit a power law feature in particular the relationship between the degree and the strength is nonlinear and the power law exponents of the three are the same all the theoretical predictions are successfully contrasted with numerical simulations

laplacian centrality a new centrality measure for weighted networks the centrality of vertices has been a key issue in network analysis for unweighted networks where edges are just present or absent and have no weight attached many centrality measures have been presented such as degree betweenness closeness eigenvector and subgraph centrality there has been a growing need to design centrality measures for weighted networks because weighted networks where edges are attached weights would contain rich information some network measures have been proposed for weighted networks including three common measures of vertex centrality degree closeness and betweenness in this paper we propose a new centrality measure called the laplacian centrality measure for weighted networks the laplacian energy is defined as e l g email protected email protected i 2 where l i s are eigenvalues of the laplacian matrix of weighted network g the importance centrality of a vertex v is reflected by the drop of the laplacian energy of the network to respond to the deactivation deletion of the vertex from the network we also prove an algebraic graph theory result that provides a structural description of the laplacian centrality measure which is in terms of the number of all kinds of 2 walks laplacian centrality unveils more structural information about connectivity and density around v further than its immediate neighborhood that is comparing with other standard centrality measures proposed for weighted networks e g degree closeness or betweenness centrality laplacian centrality is an intermediate measuring between global and local characterization of the importance centrality of a vertex we further investigate the validness and robustness of this new centrality measure by illustrating this method to some classical weighted social network data sets and obtain reliable results which provide strong evidences of the new measure s utility

large scale topological and dynamical properties of the internet we study the large scale topological and dynamical properties of real internet maps at the autonomous system level collected in a 3 yr time interval we find that the connectivity structure of the internet presents statistical distributions settled in a well defined stationary state the large scale properties are characterized by a scale free topology consistent with previous observations correlation functions and clustering coefficients exhibit a remarkable structure due to the underlying hierarchical organization of the internet the study of the internet time evolution shows a growth dynamics with aging features typical of recently proposed growing network models we compare the properties of growing network models with the present real internet data analysis

effects of triad formations stimulated by intermediaries on network topology abstract triad formation of vertices is considered a significant mechanism in the emergence of highly clustered structures in real networks however the net effect of triad formations on network topology has yet to be understood completely since triad formations are usually studied with additional effects including the attachment of new vertices to prevent a saturation of the number of edges where almost all vertices are directly linked to each other in this paper we focus on the net effects of triad formations stimulated by randomly chosen intermediaries on network topologies such as local clustering and evolution of degrees we show that the local clustering of vertices with degree k is divided into an essential term 1 k which can be widely seen in real networks and additional terms depending on the initial network topology also we derive an equation which measures the influence of local structures of networks on the time evolution of vertex degrees according to which triad formations lead to the so called rich get richer phenomenon in the evolution of degrees local events like a triad formation stimulated by pre existing vertices leads not only to highly clustered structures but to a typical power law form in the degree distribution with a power law exponent of about 2

the numerical solution of the helmholtz equation for wave propagation problems in underwater acoustics abstract the helmholtz equation k2n2 u 0 with a variable index of refraction n and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems a numerical algorithm has been developed and a computer code implemented that can effectively solve this equation in the intermediate frequency range the equation is discretized by using the finite element method thus allowing for the modeling of complicated geometries including interfaces and complicated boundary conditions a global radiation boundary condition is imposed at the far field boundary that is exact for an arbitrary number of propagating modes the resulting large nonselfadjoint system of linear equations with indefinite symmetric part is solved by using the preconditioned conjugate gradient method applied to the normal equations a new preconditioner based on the multigrid method is developed this preconditioner is vectorizable and is extremely effective over a wide range of frequencies provided the number of grid levels is reduced for large frequencies a heuristic argument is given that indicates the superior convergence properties of this preconditioner the relevant limit to analyze convergence is for k increasing and a fixed prescribed accuracy level the efficiency and robustness of the numerical algorithm are confirmed for large acoustic models including interfaces with strong velocity contrasts

geographical networks evolving with an optimal policy in this article we propose a growing network model based on an optimal policy involving both topological and geographical measures in this model at each time step a new node having randomly assigned coordinates in a 1 1 square is added and connected to a previously existing node i which minimizes the quantity r 2 k where ri is the geographical distance ki the degree and a free parameter the degree distribution obeys a power law form when 1 and an exponential

from unweighted to weighted networks with local information abstract in this paper we analyze an evolving model with local information which can generate a class of networks by choosing different values of the parameter p the model introduced exhibits the transition from unweighted networks to weighted networks because the distribution of the edge weight can be widely tuned with the increase in the local information the degree correlation of the network transforms from assortative to disassortative we also study the distribution of the degree strength and edge weight which all show crossover between exponential and scale free finally an application of the proposed model to the study of the synchronization is considered it is concluded that the synchronizability is enhanced when the heterogeneity of the edge weight is reduced

a mechanism to synchronize fluctuations in scale free networks using growth models abstract in this paper we study the steady state of the fluctuations of the surface for a model of surface growth with relaxation to any of its lower nearest neighbors sram f family j phys a 19 1986 l441 in scale free networks it is known that for euclidean lattices this model belongs to the same universality class as the model of surface relaxation to the minimum srm for the srm model it was found that for scale free networks with broadness the steady state of the fluctuations scales with the system size n as a constant for 3 and has a logarithmic divergence for 3 a l pastore y piontti p a macri l a braunstein phys rev e 76 2007 046117 it was also shown c e la rocca l a braunstein p a macri phys rev e 77 2008 046120 that this logarithmic divergence is due to non linear terms that arises from the topology of the network in this paper we show that the fluctuations for the sram model scale as in the srm model we also derive analytically the evolution equation for this model for any kind of complex graphs and find that as in the srm model non linear terms appear due to the heterogeneity and the lack of symmetry of the network in spite of that the two models have the same scaling but the srm model is more efficient to synchronize systems

finding modules and hierarchy in weighted financial network using transfer entropy we study the modular structure of financial network based on the transfer entropy te from the comparison with the obtained modular structure using the cross correlation cc we find that te and cc both provide well organized modular structure and the hierarchical relationship between each industrial group when the time scale of the measurement is less than one month however when the time scale of the measurement becomes larger than one month we find that the modular structure from cc cannot correctly reflect the known industrial classification and their hierarchy in addition the measured maximum modularity qmax for te is always larger than that for cc which indicates that te is a better weight measure than cc for the system with asymmetric relationship

transport and percolation theory in weighted networks we study the distribution p of the equivalent conductance for erdos renyi er and scale free sf weighted resistor networks with n nodes each link has conductance geax where x is a random number taken from a uniform distribution between 0 and 1 and the parameter a represents the strength of the disorder we provide an iterative fast algorithm to obtain p and compare it with the traditional algorithm of solving kirchhoff equations we find both analytically and numerically that p for er networks exhibits two regimes i a low conductance regime for eapc where pc 1 k is the critical percolation threshold of the network and k is the average degree of the network in this regime p is independent of n and follows the power law p where 1 k a ii a high conductance regime for eapc in which we find that p has strong n dependence and scales as pf apc n 1 3 for sf networks with degree distribution pkk kminkkmax we find numerically also two regimes similar to those found for er networks

modeling the evolution of weighted networks we present a general model for the growth of weighted networks in which the structural growth is coupled with the edges weight dynamical evolution the model is based on a simple weight driven dynamics and a weights reinforcement mechanism coupled to the local network growth that coupling can be generalized in order to include the effect of additional randomness and nonlinearities which can be present in real world networks the model generates weighted graphs exhibiting the statistical properties observed in several real world systems in particular the model yields a nontrivial time evolution of vertices properties and scale free behavior with exponents depending on the microscopic parameters characterizing the coupling rules very interestingly the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices degree

accuracy properties of the wave ray multigrid algorithm for helmholtz equations helmholtz equations with their highly oscillatory solutions play an important role in physics and engineering these equations present the main computational difficulties typical to acoustic electromagnetic and other wave problems they are often accompanied by radiation boundary conditions and are considered on infinite domains solving them numerically using standard procedures including multigrid is too expensive the wave ray multigrid algorithm efficiently solves the helmholtz equations and naturally incorporates the radiation boundary conditions important accuracy properties of the wave ray solver are discussed in this paper using various mode analyses we show that with the right choice of parameters this algorithm can obtain an approximation to the differential solution with accuracy that equals the accuracy of the target grid discretization moreover the boundary conditions can be introduced with any desired accuracy our theoretical conclusions are confirmed by numerical experiments

scaling of average receiving time and average weighted shortest path on weighted koch networks abstract in this paper we present weighted koch networks based on classic koch networks a new method is used to determine the average receiving time art whose key step is to write the sum of mean first passage times mfpts for all nodes to absorption at the trap located at a hub node as a recursive relation we show that the art exhibits a sublinear or linear dependence on network order thus the weighted koch networks are more efficient than classic koch networks in receiving information moreover average weighted shortest path awsp is calculated in the infinite network order limit the awsp depends on the scaling factor the weighted koch network grows unbounded but with the logarithm of the network size while the weighted shortest paths stay bounded

parallel solution of high frequency helmholtz equations using high order finite difference schemes abstract high frequency helmholtz equations pose a challenging computational task especially at high frequencies this work examines the parallel solution of such problems using 2nd 4th and 6th order finite difference schemes the examples include problems with known analytic solutions enabling error evaluation of the different schemes on various grids including problems on l shaped domains the resulting linear systems are solved with the block parallel carp cg algorithm which succeeded in lowering the relative residual indicating that it is a robust and reliable parallel solver of the resulting linear systems however lowering the error of the solution to reasonable levels with practical mesh sizes is obtained only with the higher order schemes these results corroborate the known limitations of the 2nd order scheme at modeling the helmholtz equation at high frequencies and they indicate that carp cg can also be used effectively with high order finite difference schemes furthermore the parallel scalability of carp cg improves when the wave number is increased on a fixed grid or when for a fixed wave number the grid size is decreased

incremental unknowns for solving partial differential equations incremental unknowns have been proposed in t as a method to approximate fractal attractors by using finite difference approximations of evolution equations in the case of linear elliptic problems the utilization of incremental unknown methods provides a new way for solving such problems using several levels of discretization the method is similar but different from the classical multigrid method in this article we describe the application of incremental unknowns for solving laplace equations in dimensions one and two we provide theoretical results concerning two level approximations and we report on numerical tests done with multi level approximations

influence of weight heterogeneity on random walks in scale free networks many systems are best described by weighted networks in which the weights of the edges are heterogeneous in this paper we focus on random walks in weighted network investigating the impacts of weight heterogeneity on the behavior of random walks we study random walks in a family of weighted scale free tree like networks with power law weight distribution we concentrate on three cases of random walk problems with a trap located at a hub node a leaf adjacent to a hub node and a farthest leaf node from a hub for all these cases we calculate analytically the global mean first passage time gmfpt measuring the efficiency of random walk as well as the leading scaling of gmfpt we find a significant decrease in the dominating scaling of gmfpt compared with the corresponding binary networks in all three random walk problems which implies that weight heterogeneity has a significant influence on random walks in scale free networks

random walks on activity driven networks with attractiveness virtually all real world networks are dynamical entities in social networks the propensity of nodes to engage in social interactions activity and their chances to be selected by active nodes attractiveness are heterogeneously distributed here we present a time varying network model where each node and the dynamical formation of ties are characterized by these two features we study how these properties affect random walk processes unfolding on the network when the time scales describing the process and the network evolution are comparable we derive analytical solutions for the stationary state and the mean first passage time of the process and we study cases informed by empirical observations of social networks our work shows that previously disregarded properties of real social systems such as heterogeneous distributions of activity and attractiveness as well as the correlations between them substantially affect the dynamical process unfolding on the network

rate equation approach for correlations in growing network models we propose a rate equation approach to compute two vertex correlations in scale free growing network models based on the preferential attachment mechanism the formalism based on previous work of szabo et al fphys rev e 67 056102 s2002dg for the clustering spectrum measuring three vertex correlations is based on a rate equation in the continuous degree and time approximation for the average degree of the nearest neighbors of vertices of degree k with an appropriate boundary condition we study the properties of both two and three vertex correlations for linear preferential attachment models and also for a model yielding a large clustering coefficient the expressions obtained are checked by means of extensive numerical simulations the rate equation proposed can be generalized to more sophisticated growing network models and also extended to deal with related correlation measures as an example we consider the case of a recently proposed model of weighted networks for which we are able to compute a weighted two vertex correlation function taking into account the strength of the interactions between connected vertices

estimating trade flow based on network topology abstract betweenness is often considered as a direct or slightly modified approximation of real life flow in the study of transport networks we test this assumption by comparing the estimated traffic pattern with the real life traffic pattern of 53 international trade networks the results reveal that there are fundamental differences between these two traffic patterns and that betweenness is not a good flow estimator to calculate the modified betweenness we propose a new algorithm that assumes the following 1 the transport requirement sent and received by any pair of nodes is in proportion to the product of their node transport requirements and in inverse proportion to their network distance and 2 each node transport requirement is in proportion to the corresponding node modified betweenness the resulting modified betweenness networks have reproduced most real life traffic patterns with a similar probability density distribution of flow local heterogeneity of flow distribution and weighted average nearest neighbours flow

dynamical robustness analysis of weighted complex networks robustness of weighted complex networks is analyzed from nonlinear dynamical point of view and with focus on different roles of high degree and low degree nodes we find that the phenomenon for the low degree nodes being the key nodes in the heterogeneous networks only appears in weakly weighted networks and for weak coupling for all other parameters the heterogeneous networks are always highly vulnerable to the failure of high degree nodes this point is the same as in the structural robustness analysis we also find that with random inactivation heterogeneous networks are always more robust than the corresponding homogeneous networks with the same average degree except for one special parameter thus our findings give an integrated picture for the dynamical robustness analysis on complex networks c 2013 elsevier b v all rights reserved

the origin of preferential attachment and the generalized preferential attachment for weighted networks abstract in this paper we first discuss the origin of preferential attachment then we establish the generalized preferential attachment gpa which has two new properties first it encapsulates both the topological and weight aspects of a network which makes it is neither entirely degree preferential nor entirely weight preferential second it can tell us not only the chance that each already existing vertex being connected but also how much weight each new edge has the gpa can generate four power law distributions besides the three for vertex degrees vertex strengths and edge weights it yields a new power law distribution for the subgraph degrees

entropy of network ensembles in this paper we generalize the concept of random networks to describe network ensembles with nontrivial features by a statistical mechanics approach this framework is able to describe undirected and directed network ensembles as well as weighted network ensembles these networks might have nontrivial community structure or in the case of networks embedded in a given space they might have a link probability with a nontrivial dependence on the distance between the nodes these ensembles are characterized by their entropy which evaluates the cardinality of networks in the ensemble in particular in this paper we define and evaluate the structural entropy i e the entropy of the ensembles of undirected uncorrelated simple networks with given degree sequence we stress the apparent paradox that scale free degree distributions are characterized by having small structural entropy while they are so widely encountered in natural social and technological complex systems we propose a solution to the paradox by proving that scale free degree distributions are the most likely degree distribution with the corresponding value of the structural entropy finally the general framework we present in this paper is able to describe microcanonical ensembles of networks as well as canonical or hidden variable network ensembles with significant implications for the formulation of network constructing algorithms

the architecture of complex weighted networks networked structures arise in a wide array of different contexts such as technological and transportation infrastructures social phenomena and biological systems these highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity along with a complex topological structure real networks display a large heterogeneity in the capacity and intensity of the connections these features however have mainly not been considered in past studies where links are usually represented as binary states i e either present or absent here we study the scientific collaboration network and the world wide air transportation network which are representative examples of social and large infrastructure systems respectively in both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network we define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices this information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network these results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks

a multigrid method enhanced by krylov subspace iteration for discrete helmholtz equations standard multigrid algorithms have proven ineffective for the solution of discretizations of helmholtz equations in this work we modify the standard algorithm by adding gmres iterations at coarse levels and as an outer iteration we demonstrate the algorithm s effectiveness through theoretical analysis of a model problem and experimental results in particular we show that the combined use of gmres as a smoother and outer iteration produces an algorithm whose performance depends relatively mildly on wave number and is robust for normalized wave numbers as large as 200 for fixed wave numbers it displays grid independent convergence rates and has costs proportional to the number of unknowns

self organization versus hierarchy in open source social networks complex networks emerge under different conditions including design i e top down decisions through simple rules of growth and evolution such rules are typically local when dealing with biological systems and most social webs an important deviation from such a scenario is provided by groups collectives of agents engaged in technology development such as open source communities here we analyze their network structure showing that it defines a complex weighted network with scaling laws at different levels as measured by looking at e mail exchanges we also present a simple model of network growth involving nonlocal rules based on betweenness centrality our weighted network analysis suggests that a well defined interplay between the overall goals of the community and the underlying hierarchical organization play a key role in shaping its dynamics

statistical analysis of 22 public transport networks in poland public transport systems in 22 polish cities have been analyzed the sizes of these networks range from n 152 to 2881 depending on the assumed definition of network topology the degree distribution can follow a power law or can be described by an exponential function distributions of path lengths in all considered networks are given by asymmetric unimodal functions clustering assortativity and betweenness are studied all considered networks exhibit small world behavior and are hierarchically organized a transition between dissortative small networks n approximately or 500 is observed

comparison of different generalizations of clustering coefficient and local efficiency for weighted undirected graphs binary undirected graphs are well established but when these graphs are constructed often a threshold is applied to a parameter describing the connection between two nodes therefore the use of weighted graphs is more appropriate in this work we focus on weighted undirected graphs this implies that we have to incorporate edge weights in the graph measures which require generalizations of common graph metrics after reviewing existing generalizations of the clustering coefficient and the local efficiency we proposed new generalizations for these graph measures to be able to compare different generalizations a number of essential and useful properties were defined that ideally should be satisfied we applied the generalizations to two real world networks of different sizes as a result we found that not all existing generalizations satisfy all essential properties furthermore we determined the best generalization for the clustering coefficient and local efficiency based on their properties and the performance when applied to two networks we found that the best generalization of the clustering coefficient is defined in miyajima and sakuragawa 2014 while the best generalization of the local efficiency is proposed in this letter depending on the application and the relative importance of sensitivity and robustness to noise other generalizations may be selected on the basis of the properties investigated in this letter

degree based attacks and defense strategies in complex networks we study the stability of random scale free networks to degree dependent attacks we present analytical and numerical results to compute the critical fraction p c of nodes that need to be removed for destroying the network under this attack for different attack parameters we study the effect of different defense strategies based on the addition of a constant number of links on network robustness we test defense strategies based on adding links to either low degree middegree or high degree nodes we find using analytical results and simulations that the middegree nodes defense strategy leads to the largest improvement to the network robustness against degree based attacks we also test these defense strategies on an internet autonomous systems map and obtain similar results

a study on some urban bus transport networks abstract in this paper we present the empirical investigation results on the urban bus transport networks btns of four major cities in china in btn nodes are bus stops two nodes are connected by an edge when the stops are serviced by a common bus route the empirical results show that the degree distributions of btns take exponential function forms other two statistical properties of btns are also considered and they are suggested as the distributions of so called the number of stops in a bus route represented by s and the number of bus routes a stop joins by r the distributions of r also show exponential function forms while the distributions of s follow asymmetric unimodal functions to explain these empirical results and attempt to simulate a possible evolution process of btn we introduce a model by which the analytic and numerical result obtained agrees well with the empirical facts finally we also discuss some other possible evolution cases where the degree distribution shows a power law or an interpolation between the power law and the exponential decay

mean field diffusive dynamics on weighted networks diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks here we introduce a general formalism that allows to easily write down mean field equations for any diffusive dynamics on weighted networks we also propose the concept of annealed weighted networks in which such equations become exact we show the validity of our approach addressing the problem of the random walk process pointing out a strong departure of the behavior observed in quenched real scale free networks from the mean field predictions additionally we show how to employ our formalism for more complex dynamics our work sheds light on mean field theory on weighted networks and on its range of validity and warns about the reliability of mean field results for complex dynamics