how community structure influences epidemic spread in social networks abstract two key features of social networks are the community structure and the high clustering coefficient for understanding their influences on dynamical processes we present a model with both an adjustable clustering coefficient and an adjustable degree of community this model has an invariant degree distribution when its clustering coefficient is being adjusted we find that the efficiency of epidemic spreading in this model depends mainly on the degree of community and decreases with increase of the degree of community for a fixed degree of community the efficiency will decrease with increase of the clustering coefficient numerical simulations have confirmed the theoretic analysis

performance of certain krylov subspace methods for solving convection diffusion equations this paper presents a comparison of the performance of some iterative methods for solving two dimensional convection diffusion equations arising from computational fluid dynamics a number of numerical experiments are performed to compare preconditioned grmes iterative method cgs iterative method with preconditioning and preconditioned bi cgstab iterative method the main subject of the current work is mainly focused on the convergence behaviors of the three iterative methods

spread of information and infection on finite random networks the modeling of epidemic like processes on random networks has received considerable attention in recent years while these processes are inherently stochastic most previous work has been focused on deterministic models that ignore important fluctuations that may persist even in the infinite network size limit in a previous paper for a class of epidemic and rumor processes we derived approximate models for the full probability distribution of the final size of the epidemic as opposed to only mean values in this paper we examine via direct simulations the adequacy of the approximate model to describe stochastic epidemics and rumors on several random network topologies homogeneous networks erd os r enyi er random graphs barabasi albert scale free networks and random geometric graphs we find that the approximate model is reasonably accurate in predicting the probability of spread however the position of the threshold and the conditional mean of the final size for processes near the threshold are not well described by the approximate model even in the case of homogeneous networks we attribute this failure to the presence of other structural properties beyond degree degree correlations and in particular clustering which are present in any finite network but are not incorporated in the approximate model in order to test this hypothesis we perform additional simulations on a set of er random graphs where degree degree correlations and clustering are separately and independently introduced using recently proposed algorithms from the literature our results show that even strong degree degree correlations have only weak effects on the position of the threshold and the conditional mean of the final size on the other hand the introduction of clustering greatly affects both the position of the threshold and the conditional mean similar analysis for the barabasi albert scale free network confirms the significance of clustering on the dynamics of rumor spread for this network though with its highly skewed degree distribution the addition of positive correlation had a much stronger effect on the final size distribution than was found for the simple random graph

magnetohydrodynamics of solar coronal plasmas in cylindrical geometry we describe a three dimensional algorithm for the advancement of the resistive mhd equations in cylindrical geometry with line tied boundary conditions this code has been developed to simulate the behavior of solar coronal plasmas a finite difference discretization is used for the radial and axial coordinates a pseudospectral method is used for the azimuthal coordinate the dependent variables are defined on finite difference meshes that are staggered with respect to each other to facilitate the application of boundary conditions the time advance algorithm features a semi implicit leapfrog scheme for the wave terms a predictor corrector treatment of advection and an implicit advance of the resistive and viscous diffusion terms the semi implicit and implicit operators are inverted using a preconditioned conjugate gradient method special care is taken in maintaining the self adjointness of the discretized operators so that a fast inversion algorithm applicable to symmetric matrices can be used by way of illustration we describe the application of the code to the linear and nonlinear evolution of a kink instability in a twisted flux tube

unified index to quantifying heterogeneity of complex networks abstract although recent studies have revealed that degree heterogeneity of a complex network has significant impact on the network performance and function a unified definition of the heterogeneity of a network with any degree distribution is absent in this paper we define a heterogeneity index 0 h 1 to quantify the degree heterogeneity of any given network we analytically show the existence of an upper bound of h 0 5 for exponential networks thus explain why exponential networks are homogeneous on the other hand we also analytically show that the heterogeneity index of an infinite power law network is between 1 and 0 5 if and only if its degree exponent is between 2 and 2 5 we further show that for any power law network with a degree exponent greater than 2 5 there always exists an exponential network such that both networks have the same heterogeneity index this may help to explain why 2 5 is a critical degree exponent for some dynamic behaviors on power law networks

growing scale free networks with tunable clustering we extend the standard scale free network model to include a triad formation step we analyze the geometric properties of networks generated by this algorithm both analytically and by numerical c

on the spreading and localization of risky information in social networks abstract we propose a model for the localization of risky information in social scale free networks where we assume that risky information can propagate only between mutually trusted nodes mtn we propose an algorithm to construct the mtn network and show that there is a critical value m c 2 of trusted nodes below which information localizes this critical value increases drastically if a fraction p of nodes does not transfer information at all we study the fraction of initial messengers needed to inform a desired fraction of the network as a function of the average number of trusted nodes m and discuss possible applications of the model also to marketing and to the spreading of a disease with very short incubation time

relaxation dynamics of maximally clustered networks we study the relaxation dynamics of fully clustered networks maximal number of triangles to an unclustered state under two different edge dynamics the double edge swap corresponding to degree preserving randomization of the configuration model and single edge replacement corresponding to full randomization of the erd ifmmode mbox h o else h o fi s r enyi random graph we derive expressions for the time evolution of the degree distribution edge multiplicity distribution and clustering coefficient we show that under both dynamics networks undergo a continuous phase transition in which a giant connected component is formed we calculate the position of the phase transition analytically using the erd ifmmode mbox h o else h o fi s r enyi phenomenology

a lattice orthogonalization technique for integrated square error minimization a recursive integrated square error minimization technique is developed to solve integral equations occurring in electromagnetic scattering problems the underlying idea is a generalization of the concept of the second minimization step recently proposed by van den berg this is implemented by a structured lattice algorithm similar to the lattice algorithms which emerged in the last decade in signal processing theory

the application of the preconditioned biconjugate gradient algorithm to nlte rate matrix equations abstract this paper reports the success of the preconditioned biconjugate gradient pbcg and the conjugate gradient square cgs algorithms in solving the matrix equations resulting from the discretization of systems of population rate equations which arise in nonequilibrium kinetics modeling the success of the pbcg and cgs can be attributed to two main ideas first the singularity of the rate matrix resulting from population conservation requirement was removed through a reduction of matrix order so as to improve the condition number of the matrix second an efficient preconditioner was found to reduce the reduce the eigenvalue spread of the rate matrix the preconditioning matrix was selected on the basis of retaining the largest few rates in each column of the well conditioned rate matrix this preconditioner along with the reduced rate matrix enabled the algorithms to converge very rapidly so as to make them an attractive alternative to standard direct methods

dynamical analysis of a iwsr rumor spreading model with considering the self growth mechanism and indiscernible degree abstract propagation of rumor as one of the most important aspects of spreading dynamics on networks which is often accompanied by the self growth of individuals and indiscernible degree of events and the analysis of this phenomenon can help us to better understand the information dissemination in the social network here with the wiseman supplemented to the classical ignorant spreader stifler i s r rumor spreading model a modified ignorant wiseman spreader stifler i w s r model is established with self growth mechanism by considering indiscernible degree of events by mean field equations of i w s r model the spreading threshold c is calculated to describe the theory of steady state dynamics of the rumor spreading numerical simulation is performed to assess the influence of self growth of individual and indiscernible degree of events on dynamic spreading process the results show that when the spreading rate is smaller than the threshold c the rumor will not spread in the population the stronger the self growth ability of the individual is the smaller the range of rumor will be the higher the indiscernible degree of events is the greater influence of the rumor these obtained findings in the present study could not only elaborate our understandings of spreading dynamics in network but also provide us with an insight to develop effective strategies of inhibiting rumor propagation

the use of a preconditioned bi conjugate gradient method for hybrid plasma stability analysis abstract the numerical stability analysis of compact toroidal plasmas using implicit time differencing requires the solution of a set of coupled 2 dimensional elliptic partial differential equations for the field quantities at every timestep when the equations are spatially finite differenced and written in matrix form the resulting matrix is large sparse complex non hermitian and indefinite the use of the preconditioned bi conjugate gradient method for solving these equations is discussed the effect of block diagonal preconditioning and of incomplete block lu preconditioning on the convergence of the method is investigated for typical matrices arising in our studies the eigenvalue spectra of the original and preconditioned matrices are calculated as an illustration of the effectiveness of the preconditioning we show that the preconditioned bi conjugate gradient method converges more rapidly than the conjugate gradient method applied to the normal equations and that it is an effective iterative method for the class of non hermitian indefinite problems of interest

maximizing influence in a social network improved results using a genetic algorithm abstract the influence maximization problem focuses on finding a small subset of nodes in a social network that maximizes the spread of influence while the greedy algorithm and some improvements to it have been applied to solve this problem the long solution time remains a problem stochastic optimization algorithms such as simulated annealing are other choices for solving this problem but they often become trapped in local optima we propose a genetic algorithm to solve the influence maximization problem through multi population competition using this algorithm we achieve an optimal result while maintaining diversity of the solution we tested our method with actual networks and our genetic algorithm performed slightly worse than the greedy algorithm but better than other algorithms

a connection between a system of random walks and rumor transmission abstract we establish a relationship between the phenomenon of rumor transmission on a population and a probabilistic model of interacting particles on the complete graph more precisely we consider variations of the maki thompson epidemic model and the frog model of random walks which were introduced in the scientific literature independently and in different contexts we analyze the markov chains which describe these models and show a coupling between them our connection shows how the propagation of a rumor in a closed homogeneously mixing population can be described by a system of random walks on the complete graph additionally we discuss further applications of the random walk model which are relevant to the modeling of different biological dynamics

improved theoretical and experimental models for the coaxial colinear antenna an improved theoretical model of the coaxial colinear coco antenna is presented that takes into account different element lengths and power transfers between the antenna and the transmission lines the antenna equation now contains an exact kernel instead of an approximate kernel and a piecewise constant basis function is used instead of a piecewise linear function yielding faster results more points are used for better accuracy and yet faster computations the linear systems of equations of the theoretical model are solved using a preconditioned conjugate gradient method uniform and tapered current distributions are obtained experimentally and theoretically on end fed coaxial colinear antennas there is reasonable agreement between theory and measurements the gains of a few coco antennas relative to equivalent lengths of half wave dipoles are given

propagation on networks an exact alternative perspective by generating the specifics of a network structure only when needed on the fly we derive a simple stochastic process that exactly models the time evolution of susceptible infectious dynamics on finite size networks the small number of dynamical variables of this birth death markov process greatly simplifies analytical calculations we show how a dual analytical description treating large scale epidemics with a gaussian approximation and small outbreaks with a branching process provides an accurate approximation of the distribution even for rather small networks the approach also offers important computational advantages and generalizes to a vast class of systems

dynamic behaviour of beams and rectangular plates under moving loads abstract a theory concerning the dynamic response of finite elastic structures rayleigh beams and plates having arbitrary end supports and under an arbitrary number of moving masses is developed the versatile solution technique presented is based on modified generalized finite integral transforms and the modified struble s method various analytical results are presented numerical examples are given and the results compare favourably with existing ones the efficiency of the solution technique is demonstrated and discussed

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

emergence and size of the giant component in clustered random graphs with a given degree distribution standard techniques for analyzing network models usually break down in the presence of clustering here we introduce a new analytic tool the free excess degree distribution which extends the generating function framework making it applicable for clustered networks c 0 the methodology is general and provides a new expression for the threshold point at which the giant component emerges and shows that it scales as 1 c 1 in addition the size of the giant component may be predicted even for more complicated scenarios such as the removal of a fixed fraction of nodes at random

recent developments in the algebraic multiblock method for euler equations abstract in this paper the algebraic multiblock method is presented and applied to the solution of the euler equations used to model inviscid compressible flow problems the method employs two extreme grids aimed at combining multigrid and domain decomposition ideas the fine grid is used by the discretization method the coarse grid results from the fine grid and defines the domain partitioning of the solution procedure the multigrid concept is practically simulated by applying the idea of the substructuring technique in which the inner finite volumes of a block are expressed by their boundary volumes through a matrix inversion process the conjugate gradient squared method is used for the approximate solution of numerous large block pentadiagonal systems emerging at each time step additionally efficient preconditioning and smoothing are employed to accelerate the iterative solution the proposed method is applied for the solution of the time marching euler equations using an implicit upwind finite volume method euflex numerical results and comparisons show the efficiency of the proposed method even for sequential processing

on the choice of expansion and weighting functions in the numerical solution of operator equations one of the objectives of this paper is to discuss the mathematical requirements that the expansion functions must satisfy in the method of moments mm solution of an operator equation a simple differential equation is solved to demonstrate these requirements the second objective is to study the numerical stability of point matching method galerkin s method and the method of least squares pocklington s integral equation is considered and numerical results are presented to illustrate the effect of various choices of weighting functions on the rate of convergence finally it is shown that certain choices of expansion and weighting functions yield numerically acceptable results even though they are not admissible from a strictly mathematical point of view the reason for this paradox is outlined

complex dynamic behavior of a rumor propagation model with spatial temporal diffusion terms a spatial temporal rumor propagation model with discrete and non local delays is regarded stability and hopf bifurcation are proved in a strict mathematical way sensitivity analysis is applied to search active parameters hopf bifurcation causes an oscillation phenomenon in this model numerical simulations provide a new insight into rumor spreading in online social networks rumor propagation as a typical form of social communication in online social networks has had a significant negative impact on a harmonious and stable society with the rapid development of mobile communication equipments traditional rumor propagation models which depend on ordinary differential equations ode may not be suitable for describing rumor propagation in an online social network in this paper based on reaction diffusion equations we propose a novel epidemic like model with both discrete and nonlocal delays for investigating the spatial temporal dynamics of rumor propagation by analyzing the corresponding characteristic equations of this model the local stability conditions of a boundary equilibrium point and a positive equilibrium point are established by applying the linear approximation method of nonlinear systems sufficient conditions are derived for the existence of hopf bifurcation at the above two kinds of equilibrium points moreover a sensitivity analysis method based on the density of spreading users is proposed and then in theoretical and experimental aspect we identify some sensitive parameters in the process of rumor propagation finally numerical simulations are performed to illustrate the theoretical results

iterative solution methods for certain sparse linear systems with a non symmetric matrix arising from pde problems abstract in this paper methods are described for the solution of certain sparse linear systems with a non symmetric matrix the power of these methods is demonstrated by extensive numerical experiments application of the methods is limited to problems where the matrix has only eigenvalues with positive real part an important class of this type of matrix arises from discretisation of second order partial differential equations with first order derivative terms

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

dynamics of rumor propagation on small world networks we study the dynamics of an epidemiclike model for the spread of a rumor on a small world network it has been shown that this model exhibits a transition between regimes of localization and propagation at a finite value of the network randomness here by numerical means we perform a quantitative characterization of the evolution in the two regimes the variant of dynamic small worlds where the quenched disorder of small world networks is replaced by randomly changing connections between individuals is also analyzed in detail and compared with a mean field approximation

dynamics of three agent games we study the dynamics and resulting score distribution of three agent games where after each competition a single agent wins and scores a point a single competition is described by a triplet of numbers p t and q denoting the probabilities that the team with the highest middle or lowest accumulated score wins the three agent game can be regarded as a social model where a player can be favored or disfavored for advancement based on his her accumulated score we study the full family of solutions in the regime where the number of agents and competitions is large which can be regarded as a hydrodynamic limit depending on the parameter values p q t we find six qualitatively different asymptotic score distributions and we provide a qualitative explanation of these results we also compare our analytical results against numerical simulations of the microscopic model and find these to be in excellent agreement it is possible to decide the outcome of a three agent game through a mini tournament of two agent competitions among the participating players and it turns out that the resulting possible score distributions are a subset of those obtained for the general three agent games we discuss how one can add a steady and democratic decline rate to the model and present a simple geometric construction that allows one to obtain the score evolution equations for n agent games

a note on the choice weighting functions in the method of moments the objective is to show from a mathematical standpoint that there are certain rules that must be followed in the choice of weighting functions used in the method of moments mm it is shown that for a particular problem it is the operator that dictates the method galerkin s method or another method such as the method of least squares to be applied and it is not computational considerations only for example it is shown that in solving hallen s and pocklington s equation by the method of moments it is unnatural to choose the weighting functions which are zero at the ends of the domain of the solution the deficiency of certain weighting functions is presented based on mathematical reasoning and a numerical example is given to illustrate the effect of the choice of the weighting functions on the rate of the convergence of the solution

a theorem on the moment methods the inner product involved in the moment methods is usually an integral which is evaluated numerically by summing the integrand at certain discrete points in connection with this inner product a theorem is proved which states that the overall number of points involved in the integration must not be smaller than the number of unknowns involved in the moment method if these two numbers are equal a point matching solution is obtained irrespective of whether one has started with galerkin s method or the least squares method if the number of points involved in the integration is larger than the number of the unknowns a weighted point matching solution is obtained

nonlocal elasticity theory for vibration of nanoplates classical plate theory clpt and first order shear deformation theory fsdt of plates are reformulated using the nonlocal differential constitutive relations of eringen the equations of motion of the nonlocal theories are derived navier s approach has been used to solve the governing equations for simply supported boundary conditions analytical solutions for vibration of the nanoplates such as graphene sheets are presented nonlocal theories are employed to bring out the effect of the nonlocal parameter on natural frequencies of the nanoplates the developed theory has been extended to the analysis of double layered nanoplates effect of i nonlocal parameter ii length iii height iv elastic modulus and v stiffness of winkler foundation of the plate on nondimensional vibration frequencies are investigated the theoretical development as well as numerical solutions presented herein should serve as reference for nonlocal theories of nanoplates and nanoshells

application of conjugate gradient method for static problems involving conductors of arbitrary shape in this paper two implementations of the conjugate gradient method cgm for the solution of problems in electrostatics involving conductors of arbitrary shapes have been discussed the first method uses a least squares approximation for the computation of the pertinent integral operator and is referred to as lsd a second implementation referred to as point matching discretisation pmd effects considerable saving in the computer time since it uses the midpoint rule for the integral arising in lsd both these techniques require o n storage where n is the number of patches used to model the conductor further a matrix interpretation of the present formulation has been derived this has facilitated the comparison of the techniques described in this paper with the well known method of moments mom formulation and has led to better understanding of the convergence of the results using illustrative examples of canonical square and circular discs and arbitrary shape a pyramid mounted on a cube the convergence of and the computer time for both the implementations have been investigated it has been shown that both the techniques yielded monotonically convergent results for all the examples considered and that the lsd offers better estimate of the capacitance than pmd with lower number of patches

a rumor spreading model with variable forgetting rate abstract a rumor spreading model with the consideration of forgetting rate changing over time is examined in small world networks the mean field equations are derived to describe the dynamics of rumor spreading in small world networks further numerical solutions are conducted on livejournal an online social blogging platform to better understand the performance of the model results show that the forgetting rate has a significant impact on the final size of rumor spreading the larger the initial forgetting rate or the faster the forgetting speed the smaller the final size of the rumor spreading numerical solutions also show that the final size of rumor spreading is much larger under a variable forgetting rate compared to that under a constant forgetting rate

phase transition for the maki thompson rumour model on a small world network we consider the maki thompson model for the stochastic propagation of a rumour within a population in this model the population is made up of spreaders ignorants and stiflers any spreader attempts to pass the rumour to the other individuals via pair wise interactions and in case the other individual is an ignorant it becomes a spreader while in the other two cases the initiating spreader turns into a stifler in a finite population the process will eventually reach an equilibrium situation where individuals are either stiflers or ignorants we extend the original hypothesis of homogenously mixed population by allowing for a small world network embedding the model in such a way that interactions occur only between nearest neighbours this structure is realized starting from a k regular ring and by inserting in the average c additional links in such a way that k and c are tuneable parameters for the population architecture we prove that this system exhibits a transition between regimes of localization where the final number of stiflers is at most logarithmic in the population size and propagation where the final number of stiflers grows algebraically with the population size at a finite value of the network parameter c a quantitative estimate for the critical value of c is obtained via extensive numerical simulations

basis function considerations for the method of moments using the fictitious current model in the method of moments mom using the fictitious current model fcm an impulsive basis function is principally employed to expand the fictitious currents for various electromagnetic scattering problems in this paper we introduce the subdomain basis functions and consider the dependence of the solution accuracy and computation time of the mom fcm on the basis functions by means of a canonical two dimensional 2 d scattering problem

blackmail propagation on small world networks abstract the dynamics of the blackmail propagation model based on small world networks is investigated it is found that for a given transmitting probability the dynamical behavior of blackmail propagation transits from linear growth type to logistical growth one with the network randomness p increases the transition takes place at the critical network randomness p c 1 n where n is the total number of nodes in the network for a given network randomness p the dynamical behavior of blackmail propagation transits from exponential decrease type to logistical growth one with the transmitting probability increases the transition occurs at the critical transmitting probability c 1 k where k is the average number of the nearest neighbors the present work will be useful for understanding computer virus epidemics and other spreading phenomena on communication and social networks

on the use of correlation as a measure of network connectivity numerous studies have demonstrated that brain networks derived from neuroimaging data have nontrivial topological features such as small world organization modular structure and highly connected hubs in these studies the extent of connectivity between pairs of brain regions has often been measured using some form of statistical correlation this article demonstrates that correlation as a measure of connectivity in and of itself gives rise to networks with non random topological features in particular networks in which connectivity is measured using correlation are inherently more clustered than random networks and as such are more likely to be small world networks partial correlation as a measure of connectivity also gives rise to networks with non random topological features partial correlation networks are inherently less clustered than random networks network measures in correlation networks should be benchmarked against null networks that respect the topological structure induced by correlation measurements prevalently used random rewiring algorithms do not yield appropriate null networks for some network measures null networks are proposed to explicitly normalize for the inherent topological structure found in correlation networks resulting in more conservative estimates of small world organization a number of steps may be needed to normalize each network measure individually and control for distinct features e g degree distribution the main conclusion of this article is that correlation can and should be used to measure connectivity however appropriate null networks should be used to benchmark network measures in correlation networks

comparison of lanczos and cgs solvers for solving numerical heat transfer problems abstract in this paper we have presented a comparative study of the lanczos solver with out preconditioning and conjugate gradient squared cgs solver with preconditioning for solving numerical heat transfer problem our comparison is mainly focussed on the convergence and the cpu time

vector opinion dynamics in a model for social influence we present numerical simulations of a model of social influence where the opinion of each agent is represented by a binary vector agents adjust their opinions as a result of random encounters whenever the difference between opinions is below a given threshold evolution leads to a steady state which highly depends on the threshold and a convergence parameter of the model we analyze the transition between clustered and homogeneous steady states results of the cases of complete mixing and small world networks are compared

communities clustering phase transitions and hysteresis pitfalls in constructing network ensembles ensembles of networks are used as null models in many applications however simple null models often show much less clustering than their real world counterparts in this paper we study a biased rewiring model where clustering is enhanced by means of a fugacity as in the strauss or triangle model but where the number of links attached to each node is strictly preserved similar models have been proposed previously in milo et al science 298 824 2002 our model exhibits phase transitions as the fugacity is changed for regular graphs identical degrees for all nodes with degree kg2 we find a single first order transition for all nonregular networks that we studied including erd os r enyi scale free and several real world networks multiple jumps resembling first order transitions appear the jumps coincide with the sudden emergence of cluster cores groups of highly interconnected nodes with higher than average degrees where each edge participates in many triangles hence clustering is not smoothly distributed throughout the network once formed the cluster cores are difficult to remove leading to strong hysteresis to study the cluster cores visually we introduce q clique adjacency plots cluster cores constitute robust communities that emerge spontaneously from the triangle generating process rather than being put explicitly into the definition of the model all the quantities we measured including the modularity assortativity clustering and number of four and five cliques exhibit simultaneous jumps and are equivalent order parameters finally we point out that cluster cores produce pitfalls when using the present and similar models as null models for strongly clustered networks due to strong hysteresis which leads to broken ergodicity on realistic sampling time scales

organization of growing random networks the organizational development of growing random networks is investigated these growing networks are built by adding nodes successively and linking each to an earlier node of degree k with an attachment probability a k when a k grows more slowly than linearly with k the number of nodes with k links n k t decays faster than a power law in k while for a k growing faster than linearly in k a single node emerges which connects to nearly all other nodes when a k is asymptotically linear n k t ensuremath sim mathrm tk ensuremath ensuremath nu with ensuremath nu dependent on details of the attachment probability but in the range 2l ensuremath nu l ensuremath infty the combined age and degree distribution of nodes shows that old nodes typically have a large degree there is also a significant correlation in the degrees of neighboring nodes so that nodes of similar degree are more likely to be connected the size distributions of the in and out components of the network with respect to a given node namely its descendants and ancestors are also determined the in component exhibits a robust s ensuremath 2 power law tail where s is the component size the out component has a typical size of order mathrm ln t and it provides basic insights into the genealogy of the network

spr based markov chain method for degree distributions of evolving networks abstract in this paper we develop a stochastic process rules spr based markov chain method to calculate the degree distributions of evolving networks this new approach overcomes two shortcomings of shi chen and liu s use of the markov chain method shi et al 2005 21 in addition we show how an spr based markov chain method can be effectively used to calculate degree distributions of random birth and death networks which we believe to be novel first spr are introduced to replace traditional evolving rules tr making it possible to compute degree distributions in one sample space then the spr based markov chain method is introduced and tested by using it to calculate two kinds of evolving network finally and most importantly the spr based method is applied to the problem of calculating the degree distributions of random birth and death networks

boundary orthogonal biharmonic grids via preconditioned gradient methods a finite difference approximation of the biharmonic equation is solved using three preconditioned gradient methods for the generation of curvilinear boundary orthogonal grids in two dimensions the developed algorithms based on the conjugated gradient the steepest descent and the minimal residual method are applied in a number of domains of engineering interest for the purpose of comparison in terms of cpu time and number of iterations to convergence

an analysis of rumor propagation based on propagation force abstract a propagation force is introduced into the analysis of rumor propagation to address uncertainty in the process the propagation force is portrayed as a fuzzy variable and a category of new parameters with fuzzy variables is defined the classic susceptible infected recovered sir model is modified using these parameters a fuzzy reproductive number is introduced into the modified model and the rationality of the fuzzy reproductive number is illuminated through calculation and comparison rumor control strategies are also discussed

random networks with tunable degree distribution and clustering we present an algorithm for generating random networks with arbitrary degree distribution and clustering frequency of triadic closure we use this algorithm to generate networks with exponential power law and poisson degree distributions with variable levels of clustering such networks may be used as models of social networks and as a testable null hypothesis about network structure finally we explore the effects of clustering on the point of the phase transition where a giant component forms in a random network and on the size of the giant component some analysis of these effects is presented

efficiency of informational transfer in regular and complex networks we analyze the process of informational exchange through complex networks by measuring network efficiencies aiming to study nonclustered systems we propose a modification of this measure on the local level we apply this method to an extension of the class of small worlds that includes declustered networks and show that they are locally quite efficient although their clustering coefficient is practically zero unweighted systems with small world and scale free topologies are shown to be both globally and locally efficient our method is also applied to characterize weighted networks in particular we examine the properties of underground transportation systems of madrid and barcelona and reinterpret the results obtained for the boston subway network

moving load analysis of arbitrarily shaped plates using the b3 spline finite strip method the b3 spline finite strip method is reviewed and its application is extended to the moving load analysis of arbitrarily shaped plates rectangular skew and circular sector plates are traversed by constant force moving loads it is shown that this method gives results comparing favorably with results from the literature

properties of highly clustered networks we propose and solve exactly a model of a network that has both a tunable degree distribution and a tunable clustering coefficient among other things our results indicate that increased clustering leads to a decrease in the size of the giant component of the network we also study susceptible infective recovered type epidemic processes within the model and find that clustering decreases the size of epidemics but also decreases the epidemic threshold making it easier for diseases to spread in addition clustering causes epidemics to saturate sooner meaning that they infect a near maximal fraction of the network for quite low transmission rates

some mathematical considerations in dealing with the inverse problem many problems of mathematical physics can be formulated in terms of the operator equation ax y where a is an integro differential operator given a and x the solution for y is usually straightforward however the inverse problem which consists of the solution for x when given a and y is much more difficult the following questions relative to the inverse problem are explored 1 does specification of the operator a determine the set y for which a solution x is possible 2 does the inverse problem always have a unique solution 3 do small perturbations of the forcing function y always result in small perturbations of the solution 4 what are some of the considerations that enter into the choice of a solution technique for a specific problem the concept of an ill posed problem versus that of a well posed problem is discussed specifically the manner by which an ill posed problem may be regularized to a well posed problem is presented the concepts are illustrated by several examples

on the dual basis for solving electromagnetic surface integral equations a powerful technique for solving electromagnetic em surface integral equations sies for inhomogenous objects by the method of moments mom involves the well known rao wilton glisson rwg basis function to represent the electric current and for field orthogonality and numerical stability reasons a variation of the rwg basis known as the ntilde x rwg basis where ntilde is a unit normal vector at the object surface to represent the magnetic current though this combination provides a numerically efficient and effective solution that has been demonstrated on a variety of structures one cannot feel entirely comfortable because of the presence of fictitious magnetic current associated with the modified basis chen and wilton proposed a different smoother basis in 1990 that avoids the fictitious line charges but because of computational cost issues it has not been used beyond chen s dissertation recently this basis was rediscovered and has received considerable attention our work reexamines the dual basis exploring issues not addressed by chen and wilton and showing accurate solutions for a variety of em scattering structures

sir model on a dynamical network and the endemic state of an infectious disease abstract in this work we performed a numerical study of an epidemic model that mimics the endemic state of whooping cough in the pre vaccine era we considered a stochastic sir model on dynamical networks that involve local and global contacts among individuals and analysed the influence of the network properties on the characterization of the quasi stationary state we computed probability density functions pdf for infected fraction of individuals and found that they are well fitted by gamma functions excepted the tails of the distributions that are q exponentials we also computed the fluctuation power spectra of infective time series for different networks we found that network effects can be partially absorbed by rescaling the rate of infective contacts of the model an explicit relation between the effective transmission rate of the disease and the correlation of susceptible individuals with their infective nearest neighbours was obtained this relation quantifies the known screening of infective individuals observed in these networks we finally discuss the goodness and limitations of the sir model with homogeneous mixing and parameters taken from epidemiological data to describe the dynamic behaviour observed in the networks studied

scale free networks from varying vertex intrinsic fitness a new mechanism leading to scale free networks is proposed in this letter it is shown that in many cases of interest the connectivity power law behavior is neither related to dynamical properties nor to preferential attachment assigning a quenched fitness value x i to every vertex and drawing links among vertices with a probability depending on the fitnesses of the two involved sites gives rise to what we call a good get richer mechanism in which sites with larger fitness are more likely to become hubs i e to be highly connected

network model of human language abstract the phenomenon of human language is widely studied from various points of view it is interesting not only for social scientists antropologists or philosophers but also for those interested in the network dynamics in several recent papers word web or language as a graph has been investigated r f cancho r sole the small world of human language proc r soc london b 268 2001 2261 2265 a e motter p s de moura lai ying cheng p dasgupta topology of the conceptual network of language phys rev e 65 2002 r 065102 m steyvers j b tenenbaum the large scale structure of semantic networks statistical analysis and a model of semantic growth cogn sci 29 2005 41 78 in this paper i revise recent studies of syntactical word web r f cancho r sole the small world of human language proc r soc london b 268 2001 2261 2265 s n dorogovtsev j f f mendes language as an evolving word web proc r soc london b 268 2001 2603 2606 i present a model of growing network in which such processes as node addition edge rewiring and new link creation are taken into account i argue that this model is a satisfactory minimal model explaining measured data r f cancho r sole the small world of human language proc r soc london b 268 2001 2261 2265 m markosova p nather language as a graph in v kvasnicka p trebatick j pospichal eds mind intelligence and life kelemen stu bratislava 2007 pp 298 307 in slovak

tuning degree distributions departing from scale free networks abstract scale free networks are characterized by a degree distribution with power law behavior although scale free networks have been shown to arise in many areas ranging from the world wide web to transportation or social networks degree distributions of other observed networks often differ from the power law type data based investigations require modifications of the typical scale free network we present an algorithm that generates networks in which the shape of the degree distribution is tunable by modifying the preferential attachment step of the barabasi albert construction algorithm the shape of the distribution is represented by dispersion measures such as the variance and the skewness both of which are highly correlated with the maximal degree of the network and therefore adequately represents the influence of superspreaders or hubs by combining our algorithm with work of holme and kim we show how to generate networks with a variety of degree distributions and clustering coefficients

a model for social networks social networks are organized into communities with dense internal connections giving rise to high values of the clustering coefficient in addition these networks have been observed to be assortative i e highly connected vertices tend to connect to other highly connected vertices and have broad degree distributions we present a model for an undirected growing network which reproduces these characteristics with the aim of producing efficiently very large networks to be used as platforms for studying sociodynamic phenomena the communities arise from a mixture of random attachment and implicit preferential attachment the structural properties of the model are studied analytically and numerically using the k clique method for quantifying the communities r 2006 elsevier b v all rights reserved

majority vote model on a dynamic small world network abstract dynamic small world networks combine short range interactions within a fixed neighborhood with stochastic long range interactions the probability of a long range link occurring instead of a short range one is a measure of the mobility of a population here the critical properties of the majority vote model with noise on a two dimensional dynamic small world lattice are investigated via monte carlo simulation and finite size scaling analyses we construct the order disorder phase diagram and find the critical exponents associated with the continuous phase transition findings are consistent with previous results indicating that a model s transitions on static and dynamic small world networks are in the same universality class

tuning clustering in random networks with arbitrary degree distributions we present a generator of random networks where both the degree dependent clustering coefficient and the degree distribution are tunable following the same philosophy as in the configuration model the degree distribution and the clustering coefficient for each class of nodes of degree k are fixed ad hoc and a priori the algorithm generates corresponding topologies by applying first a closure of triangles and second the classical closure of remaining free stubs the procedure unveils an universal relation among clustering and degree degree correlations for all networks where the level of assortativity establishes an upper limit to the level of clustering maximum assortativity ensures no restriction on the decay of the clustering coefficient whereas disassortativity sets a stronger constraint on its behavior correlation measures in real networks are seen to observe this structural bound

assessment of nanotube structures under a moving nanoparticle using nonlocal beam theories abstract dynamic analysis of nanotube structures under excitation of a moving nanoparticle is carried out using nonlocal continuum theory of eringen to this end the nanotube structure is modeled by an equivalent continuum structure ecs according to the nonlocal euler bernoulli timoshenko and higher order beam theories the nondimensional equations of motion of the nonlocal beams acted upon by a moving nanoparticle are then established analytical solutions of the problem are presented for simply supported boundary conditions the explicit expressions of the critical velocities of the nonlocal beams are derived furthermore the capabilities of various nonlocal beam models in predicting the dynamic deflection of the ecs are examined through various numerical simulations the role of the scale effect parameter the slenderness ratio of the ecs and velocity of the moving nanoparticle on the time history of deflection as well as the dynamic amplitude factor of the nonlocal beams are scrutinized in some detail the results show the importance of using nonlocal shear deformable beam theories particularly for very stocky nanotube structures acted upon by a moving nanoparticle with low velocity

guidelines for the usage of incomplete decompositions in solving sets of linear equations as they occur in practical problems abstract this paper presents incomplete decompositions for various types of matrices as they occur in the implicit discretisation of practical problems a review is given of methods for the usual five point discretisation of a self adjoint elliptic second order partial differential equation in two dimensions on a square the matrices which occur in this type of problem are symmetric m matrices of very regular structure the convergence behaviour of the different decompositions for this case is demonstrated by numerical experiments the paper also gives decompositions for the following type of matrices i symmetric m matrices of a different structure ii symmetric positive definite matrices iii non symmetric matrices

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

solution of simultaneous partial differential equations using dynamic adi solution of the streamlined darwin field equations abstract we apply a particular version of adi called dynamic adi dadi to the strongly coupled 2nd order partial differential equations that arise from the streamlined darwin field sdf equations the dadi method is applied in a form that we show is guaranteed to converge to the desired solution of the finite difference equation we give overviews of our test case the sdf problem and the dadi method with some justification for our choice of operator splitting finally we apply dadi to the strongly coupled sdf equations and present the results from our test case our implementation requires a factor of 7 less storage and has proven to be a factor of 4 in the worst case to several orders of magnitude faster than competing methods

theory of rumour spreading in complex social networks we introduce a general stochastic model for the spread of rumours and derive mean field equations that describe the dynamics of the model on complex social networks in particular those mediated by the internet we use analytical and numerical solutions of these equations to examine the threshold behaviour and dynamics of the model on several models of such networks random graphs uncorrelated scale free networks and scale free networks with assortative degree correlations we show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumour spreading rate below which a rumour cannot propagate in the system in the case of scale free networks on the other hand this threshold becomes vanishingly small in the limit of infinite system size we find that the initial rate at which a rumour spreads is much higher in scale free networks than in random graphs and that the rate at which the spreading proceeds on scale free networks is further increased when assortative degree correlations are introduced the impact of degree correlations on the final fraction of nodes that ever hears a rumour however depends on the interplay between network topology and the rumour spreading rate our results show that scale free social networks are prone to the spreading of rumours just as they are to the spreading of infections they are relevant to the spreading dynamics of chain emails viral advertising and large scale information dissemination algorithms on the internet

small scale effect on the vibration of thin nanoplates subjected to a moving nanoparticle via nonlocal continuum theory the vibration of elastic thin nanoplates traversed by a moving nanoparticle involving coulomb friction is investigated using the nonlocal continuum theory of eringen the eigen function technique and the laplace transform method are employed to solve the governing equations of the nanoplate the explicit expressions of the in plane and transverse displacements are obtained when the moving nanoparticle traverses the nanoplate on an arbitrary straight line in a special case the obtained results are also compared with those of other researchers and a reasonably good agreement is achieved the effects of small scale parameters and velocity of the moving nanoparticle on the dynamic response as well as the dynamic amplitude factors dafs of the in plane and transverse displacements are then explored in some detail the results indicate that the magnitude of daf of the transverse displacement of the nanoplate i e daf w increases with the first small scale effect parameter irrespective of the values of the second small scale effect parameter and the velocity of the moving nanoparticle as the first small scale effect parameter grows the maximum values of dafw as a function of the moving nanoparticle velocity increase and generally occur in the lower levels of the moving nanoparticle velocity

bond percolation on a class of clustered random networks analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with nonzero clustering the network s degree distribution and clustering spectrum may be prescribed and theoretical results match well with numerical simulations on both synthetic and real world networks

prediction capabilities of classical and shear deformable beam models excited by a moving mass abstract in this paper a comprehensive assessment of design parameters for various beam theories subjected to a moving mass is investigated under different boundary conditions the design parameters are adopted as the maximum dynamic deflection and bending moment of the beam to this end discrete equations of motion for classical euler bernoulli timoshenko and higher order beams under a moving mass are derived based on hamilton s principle the reproducing kernel particle method rkpm and extended newmark method are utilized for spatial and time discretization of the problem correspondingly the design parameter spectra in terms of the beam slenderness mass weight and velocity of the moving mass are introduced for the mentioned beam theories as well as various boundary conditions the results indicate the existence of a critical beam slenderness mostly as a function of beam boundary condition in which for slenderness lower than this so called critical one the application of euler bernoulli or even timoshenko beam theories would underestimate the real dynamic response of the system moreover there would be a roughly linear relation between the weight of the moving mass and the design parameters for a certain value of the moving mass velocity in most cases of boundary conditions

a study on the interaction between two rumors in homogeneous complex networks under symmetric conditions the propagating dynamics of more than one rumor has received a substantial amount of attention in recent years to investigate the effects of interactions between two rumors under symmetric conditions we built a model based on an ordinary differential equation system while assuming that each individual s spreading rate after receiving one rumor depends on whether he she knows the other rumor in certain cases two rumors accelerate the spread of each other while in a portion of the other cases they impede or decelerate the spread of each other we discuss these effects by dividing the total population into nine groups that correspond to nine states and we subsequently build the mean field equations for the two rumor interaction based on the sir model in a homogeneous complex network and we find their numerical solution with varying interaction factors for the rates of spreading and becoming disinterested the results show that when we change these interaction factors the density curves of the nine states and their maximum values will change accordingly by a series of rules which demonstrates the corresponding effects when there is a positive or negative interaction between the two rumors our work could establish a foundation for further study of this issue

blinking model and synchronization in small world networks with a time varying coupling the paper proposes a new type of small world networks of cells with chaotic behavior this network consists of a regular lattice of cells with constant 2k nearest neighbor couplings and time dependent on off couplings between any other pair of cells in each time interval of duration such a coupling is switched on with probability p and the corresponding switching random variables are independent for different links and for different times at each moment the coupling structure corresponds to a small world graph but the shortcuts change from time interval to time interval which is a good model for many real world dynamical networks it is to be distinguished from networks that have randomly chosen shortcuts fixed in time here we apply the connection graph stability method developed in the companion paper connection graph stability method for synchronized coupled chaotic systems see this issue to the study of global synchronization in this network with the time varying coupling structure in the case where the on off switching is fast with respect to the characteristic synchronization time of the network the synchronization thresholds are explicitly linked with the average path length of the coupling graph and with the probability p of shortcut switchings in this blinking model we prove that for the blinking model a few random shortcut additions significantly lower the synchronization threshold together with the effective characteristic path length short interactions between cells as in the blinking model are important in practice to cite prominent examples computers networked over the internet interact by sending packets of information and neurons in our brain interact by sending short pulses called spikes the rare interaction between arbitrary nodes in the network greatly facilitates synchronization without loading the network much in this respect we believe that it is more efficient than a structure of fixed random connections

survivor statistics and damage spreading on social network with power law degree distributions abstract damage spreading ds of the random graph networks with power law degree distributions is investigated using glauber dynamics various subgraphs defined by the probability of acquaintance show distinct features in ds as measured by hamming distance a heuristic understanding of the long time value of damage is achieved through an analysis of the survivor statistics all survivors are dynamical flipping in unison for the controlled sample and the damaged sample verification of these dynamic survivors is achieved through the introduction of a new measure of self damage