average path length in random networks analytic solution for the average path length in a large class of uncorrelated random networks with hidden variables is found we apply the approach to classical random graphs of erdos and renyi er evolving networks introduced by barabasi and albert as well as random networks with asymptotic scale free connectivity distributions characterized by an arbitrary scaling exponent alpha 2 our result for 2 infinity there is a saturation effect for the average path length

evolving apollonian networks with small world scale free topologies we propose two types of evolving networks evolutionary apollonian networks eans and general deterministic apollonian networks gdans established by simple iteration algorithms we investigate the two networks by both simulation and theoretical prediction analytical results show that both networks follow power law degree distributions with distribution exponents continuously tuned from 2 to 3 the accurate expression of clustering coefficient is also given for both networks moreover the investigation of the average path length of ean and the diameter of gdan reveals that these two types of networks possess small world feature in addition we study the collective synchronization behavior on some limitations of the ean

a deterministic small world network created by edge iterations abstract small world networks are ubiquitous in real life systems most previous models of small world networks are stochastic the randomness makes it more difficult to gain a visual understanding on how do different nodes of networks interact with each other and is not appropriate for communication networks that have fixed interconnections here we present a model that generates a small world network in a simple deterministic way our model has a discrete exponential degree distribution we solve the main characteristics of the model

a method for the estimation and identification of transfer function models summary this paper proposes an approach to the simultaneous identification and estimation of transfer function models an estimation procedure is advanced consisting of a sequence of four ordinary least squares calculations and the asymptotic properties of each step are presented consistency and asymptotic efficiency being shown a strategy for the identification of the model structure based on a selection criterion that arises naturally from the last step of the estimation algorithm is also investigated consideration is given to the numerical implementation of the techniques discussed and finally a practical example is employed to illustrate the methods

mutual attraction model for both assortative and disassortative weighted networks for most complex networks the connection between a pair of nodes is the result of their mutual affinity and attachment in this letter we will propose a mutual attraction model to characterize weighted evolving networks by introducing the initial attractiveness a and the general mechanism of mutual attraction controlled by parameter m our model can naturally reproduce scale free distributions of degree weight and strength as found in many real systems also simulation results are consistent with theoretical predictions interestingly we obtain nontrivial clustering coefficient c and tunable degree assortativity r depending on the values of m and a our model appears as a more general one that unifies the characterization of both assortative and disassortative weighted networks

numerical study of a stochastic particle algorithm solving a multidimensional population balance model for high shear granulation this paper is concerned with computational aspects of a multidimensional population balance model of a wet granulation process wet granulation is a manufacturing method to form composite particles granules from small particles and binders a detailed numerical study of a stochastic particle algorithm for the solution of a five dimensional population balance model for wet granulation is presented each particle consists of two types of solids containing pores and of external and internal liquid located in the pores several transformations of particles are considered including coalescence compaction and breakage a convergence study is performed with respect to the parameter that determines the number of numerical particles averaged properties of the system are computed in addition the ensemble is subdivided into practically relevant size classes and analysed with respect to the amount of mass and the particle porosity in each class these results illustrate the importance of the multidimensional approach finally the kinetic equation corresponding to the stochastic model is discussed

testing for causality in real time a framework for testing in real time on line the statistical significance of the causality between nonstationary random processes is developed the process representation is that of transfer function tf arma models the causality parameters are prediction error variances and dynamic multipliers the estimation algorithm is that of recursive nonlinear least squares rnls the basic step is made by analyzing the asymptotic distribution of this estimator under an assumption of stationary but in operative conditions given by discounting past observations with exponential weights ew an empirical example based on real economic time series illustrates and checks the method of on line inference

a differentially weighted monte carlo method for two component coagulation the direct simulation monte carlo dsmc method for population balance modeling is capable of retaining the history of each simulation particle and is thus able to deal with multivariate properties in a simple and straightforward manner as opposed to conventional dsmc approaches that track equally weighted simulation particles a differentially weighted monte carlo method is extended to simulate two component coagulation processes and is thereby able to simulate the micromixing of the components a new feature of the method for this bivariate population balance modeling is that it is possible to specify how the simulation particles are distributed over the compositional axis this allows us to obtain information about particles in those regions of the size and composition distribution functions where the non weighted mc methods place insufficient simulation particles to obtain an inaccurate solution the new feature results in lower statistical noise for simulating two component coagulation which is validated by using two component coagulation cases for which analytical solutions exist a discrete process with sum kernel for initial monodisperse populations and a process with constant kernel for initial polydisperse populations

self similar disk packings as model spatial scale free networks the network of contacts in space filling disk packings such as the apollonian packing is examined these networks provide an interesting example of spatial scale free networks where the topology reflects the broad distribution of disk areas a wide variety of topological and spatial properties of these systems is characterized their potential as models for networks of connected minima on energy landscapes is discussed

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

decoupling process for better synchronizability on scale free networks we propose a decoupling process performed in scale free networks to enhance the synchronizability of the network together with preserving the scale free structure simulation results show that the decoupling process can effectively promote the network synchronizability which is measured in terms of eigenratio of the coupling matrix moreover we investigate the correlation between some important structural properties and the collective synchronization and find that the maximum vertex betweenness seems to be the most strongly correlated with the synchronizability among the major structural features considered we explain the effect of the decoupling process from a viewpoint of coupling information transmission our work provides some evidence that the dynamics of synchronization is related to that of information or vehicle traffic because of the low cost in modifying the coupling network the decoupling process may have potential applications

recursive graphs with small world scale free properties we discuss a category of graphs recursive clique trees which have small world and scale free properties and allow a fine tuning of the clustering and the power law exponent of their discrete degree distribution we determine relevant characteristics of those graphs the diameter degree distribution and clustering parameter the graphs have also an interesting recursive property and generalize recent constructions with fixed degree distributions

on tracking characteristics of weighted least squares estimators applied to nonstationary system identification the parameter tracking abilities of weighted least squares wls estimators are characterized in terms of a suitably defined variability matrix and associated frequency characteristics using these concepts the conflict arising between the estimation variance and estimation bandwidth is easily explained and quantified

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

exactly solvable scale free network model we study a deterministic scale free network recently proposed by barabasi ravasz and vicsek we find that there are two types of nodes the hub and rim nodes which form a bipartite structure of the network we first derive the exact numbers p k of nodes with degree k for the hub and rim nodes in each generation of the network respectively using this we obtain the exact exponents of the distribution function p k of nodes with k degree in the asymptotic limit of k infinity we show that the degree distribution for the hub nodes exhibits the scale free nature p k proportional to k gamma with gamma ln 3 ln 2 1 584 962 while the degree distribution for the rim nodes is given by p k proportional to e gamma k with gamma ln 3 2 0 405 465 second we analytically calculate the second order average degree of nodes d third we numerically as well as analytically calculate the spectra of the adjacency matrix a for representing topology of the network we also analytically obtain the exact number of degeneracies at each eigenvalue in the network the density of states i e the distribution function of eigenvalues exhibits the fractal nature with respect to the degeneracy fourth we study the mathematical structure of the determinant of the eigenequation for the adjacency matrix fifth we study hidden symmetry zero modes and its index theorem in the deterministic scale free network finally we study the nature of the maximum eigenvalue in the spectrum of the deterministic scale free network we will prove several theorems for it using some mathematical theorems thus we show that most of all important quantities in the network theory can be analytically obtained in the deterministic scale free network model of barabasi ravasz and vicsek therefore we may call this network model the exactly solvable scale free network

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

self organization of collaboration networks we study collaboration networks in terms of evolving self organizing bipartite graph models we propose a model of a growing network which combines preferential edge attachment with the bipartite structure generic for collaboration networks the model depends exclusively on basic properties of the network such as the total number of collaborators and acts of collaboration the mean size of collaborations etc the simplest model defined within this framework already allows us to describe many of the main topological characteristics degree distribution clustering coefficient etc of one mode projections of several real collaboration networks without parameter fitting we explain the observed dependence of the local clustering on degree and the degree degree correlations in terms of the aging of collaborators and their physical impossibility to participate in an unlimited number of collaborations

a comparative study of different discretizations for solving bivariate aggregation population balance equation in this work a comparative study on how the solution of a pure bivariate aggregation population balance equation depends on different structured grids is presented numerical results obtained using the most commonly used cell average and fixed pivot techniques on four different types of structured grids are compared with the exact solutions as expected the cell average technique predicts more accurate solution than the fixed pivot technique for all different grids moreover the results predicted using the cell average technique using x type grid with logarithmic scale in the radial direction provide solutions of high quality among all other grids

geometric fractal growth model for scale free networks we introduce a deterministic model for scale free networks whose degree distribution follows a power law with the exponent ensuremath gamma at each time step each vertex generates its offspring whose number is proportional to the degree of that vertex with proportionality constant m ensuremath 1 mg1 we consider the two cases first each offspring is connected to its parent vertex only forming a tree structure second it is connected to both its parent and grandparent vertices forming a loop structure we find that both models exhibit power law behaviors in their degree distributions with the exponent ensuremath gamma 1 mathrm ln 2m ensuremath 1 mathrm ln m thus by tuning m the degree exponent can be adjusted in the range 2l ensuremath gamma l3 we also solve analytically a mean shortest path distance d between two vertices for the tree structure showing the small world behavior that is d ensuremath sim mathrm ln n mathrm ln overline k where n is system size and overline k is the mean degree finally we consider the case that the number of offspring is the same for all vertices and find that the degree distribution exhibits an exponential decay behavior

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

generalized local and nonlocal master equations for some stochastic processes in this paper we present a study on generalized local and nonlocal equations for some stochastic processes by considering the net flux change in a region determined by the transition probability we derive the master equation to describe the evolution of the probability density function some examples such as classical fokker planck equations models for levy process and stochastic coagulation equations are provided as illustrations a particular application is a consistent derivation of coupled dynamical systems for spatially inhomogeneous stochastic coagulation processes

on the asymptotic distribution of exponentially weighted prediction error estimators the authors establish the distribution of the exponentially weighted prediction error estimators for a class of general possibly nonlinear discrete time systems an explicit formula for the covariance matrix of the estimation errors is provided the distributional results presented hold for a large number n of data points and a weighting or forgetting factor lambda close to one

a general algorithm for exact simulation of multicomponent aggregation processes a monte carlo mc algorithm is presented for the simulation of the time evolution of aggregation processes featuring multiple components properties or conservation laws instead of using deterministic differential population balance equations the mc algorithm utilizes a stochastic approach to aggregation kinetics as a result exact simulation of spatially independent aggregation processes is possible without the need for numerical approximations furthermore simulations exactly predict all moments of the size and composition distributions of aggregating particles for both nongelling and gelling kernels and extend these results to the postgelation period the algorithm is shown to require at most o 1 2 1 1 rate limiting operations per time step for a component aggregation process featuring i monomers of each component i a substantial performance improvement over the potential of previous methods simulation results are presented for bivariate sum product and constant kernels and for the perikinetic brownian kernel

forecasting turning points in international output growth rates using bayesian exponentially weighted autoregression time varying parameter and pooling techniques abstract in this paper two variants of an autoregressive leading indicator arli model are employed to forecast turning points in the growth rates of 18 countries annual real output for the years 1974 1986 bayesian predictive densities have been employed to compute probabilities of downturns and upturns and they have been employed in a bayesian decision theoretic framework to obtain optimal turning point forecasts various versions of the arli model with and without pooling of data across countries produced about 70 to 80 percent correct forecasts for 158 turning points time varying parameter models performed slightly better than others the performance of the arli models in forecasting turning points is shown to be considerably better than that of four naive methods of forecasting turning points

a new event driven constant volume method for solution of the time evolution of particle size distribution direct simulation monte carlo dsmc method is an important approach for numerical solution of the population balance equation which characterizes the dynamic evolution of particle size distribution in dispersed systems one sample of the whole system i e subsystem is taken into account in most dsmc methods it means that a spatially isotropic whole system is considered and simulation particles having same number weight are tracked a new event driven constant volume edcv method for population balance modeling is proposed to describe the dynamic evolution in dispersed systems under influence of coagulation breakage nucleation surface growth dissolution condensation evaporation and deposition settling the method adopts the concept of differentially weighting simulation particles and several schemes of sample restoration are developed to maintain simulation particle number within prescribed bounds at the same time the constant volume computational domain is tracked by comparing of several popular monte carlo methods it is concluded that the proposed edcv method exhibits comparatively high precision and efficiency

frequency domain tracking characteristics of adaptive algorithms the problem of tracking time varying linear systems is discussed the focus is on the model quality in terms of the mean square error mse between the true momentary transfer function and the estimated one this mse is thus a function of frequency the exact expression for the mse is complicated but simple expressions that are asymptotic in the model order are developed for model structures of finite impulse response fir character simulations verify that these simple expressions are quite reliable and insightful even for moderate model orders expressions are developed for three basic adaptation algorithms recursive identification algorithms viz the least mean squares algorithm the recursive least squares algorithm with exponential forgetting and a tracking algorithm based on the kalman filter the results apply both to slowly time varying systems and to the model recovery after an abrupt change in the system dynamics

complex networks created by aggregation we study aggregation as a mechanism for the creation of complex networks in this evolution process vertices merge together which increases a number of highly connected hubs we study a range of complex network architectures produced by the aggregation fat tailed in particular scale free distributions of connections are obtained for both networks with a finite number of vertices and growing networks we observe a strong variation of a network structure with growing density of connections and find the phase transition of the condensation of edges finally we demonstrate the importance of structural correlations in these networks

enhanced synchronizability by structural perturbations in this brief report we investigate the collective synchronization of a system of coupled oscillators on a barab asi albert scale free network we propose an approach of structural perturbations aiming at those nodes with maximal betweenness this method can markedly enhance the network synchronizability and is easy to realize the simulation results show that the eigenratio will sharply decrease by one half when only 0 6 of those hub nodes occur under three division processes when the network size n 2000 in addition the present study also provides numerical evidence that the maximal betweenness plays a major role in network synchronization

aggregation with multiple conservation laws aggregation processes with an arbitrary number of conserved quantities are investigated on the mean field level an exact solution for the size distribution is obtained the asymptotic form of this solution exhibits nontrivial double scaling while processes with one conserved quantity are governed by a single scale processes with multiple conservation laws exhibit an additional diffusion like scale the theory is applied to ballistic aggregation with mass and momentum conserving collisions and to diffusive aggregation with multiple species