empirical extraction of mechanisms underlying real world network generation abstract the generation mechanisms of real world networks have been described using multiple models the mathematical features of these models are usually extrapolated from statistical properties of a snapshot of these networks we here propose an alternative method based on direct measurement of a sequence of consecutive snapshots to uncover the dynamics underlying real world generation we assume that the probability of adding a node or an edge depends only on local features surrounding the newly added node edge and directly measure the contribution of these features to the node edge addition probability these measurements are performed using newly defined n node local structures each n node local structure represents the configuration of edges surrounding a newly added edge the n node local structure measurements reproduce for some networks the now classical addition of edges between high degree node mechanisms it also provides quantitative estimates of more complex mechanisms driving other networks evolution such as the effect of common first and second neighbors this new methodology reveals the relative importance of different generation mechanisms we show for example that the main mechanism driving hyperlink addition between two websites is the existence of a third website linking to both the source and the target of the new hyperlink

topological fractal networks introduced by mixed degree distribution abstract several fundamental properties of real complex networks such as the small world effect the scale free degree distribution and recently discovered topological fractal structure have presented the possibility of a unique growth mechanism and allow for uncovering universal origins of collective behaviors however highly clustered scale free network with power law degree distribution or small world network models with exponential degree distribution are not self similarity we investigate networks growth mechanism of the branching deactivated geographical attachment preference that learned from certain empirical evidence of social behaviors it yields high clustering and spectrums of degree distribution ranging from algebraic to exponential average shortest path length ranging from linear to logarithmic we observe that the present networks fit well with small world graphs and scale free networks in both limit cases exponential and algebraic degree distribution respectively obviously lacking self similar property under a length scale transformation interestingly we find perfect topological fractal structure emerges by a mixture of both algebraic and exponential degree distributions in a wide range of parameter values the results present a reliable connection among small world graphs scale free networks and topological fractal networks and promise a natural way to investigate universal origins of collective behaviors

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

preferential growth exact solution of the time dependent distributions we consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles a new particle can either form a new cluster with probability q or join an already existing cluster with a probability proportional to the size thereof we calculate exactly the probability pi k t that the size of the ith cluster at time t is k we analyze the asymptotics the scaling properties of the size distribution and of the mean size as well as the relation of our system to recent network models

spectra and eigenvectors of scale free networks we study the spectra and eigenvectors of the adjacency matrices of scale free networks when bidirectional interaction is allowed so that the adjacency matrix is real and symmetric the spectral density shows an exponential decay around the center followed by power law long tails at both spectrum edges the largest eigenvalue ensuremath lambda 1 depends on system size n as ensuremath lambda 1 ensuremath sim n 1 4 for large n and the corresponding eigenfunction is strongly localized at the hub the vertex with largest degree the component of the normalized eigenfunction at the hub is of order unity we also find that the mass gap scales as n ensuremath 0 68

link prediction based on path entropy abstract information theory has been taken as a prospective tool for quantifying the complexity of complex networks in this paper first we study the information entropy or uncertainty of a path using the information theory after that we apply the path entropy to the link prediction problem in real world networks specifically we propose a new similarity index namely path entropy pe index which considers the information entropies of shortest paths between node pairs with penalization to long paths empirical experiments demonstrate that pe index outperforms the mainstream of link predictors

blind equalization of digital communication channels using high order moments the authors describe algorithms for blind equalization of digital communication channels of the quadrature amplitude modulation qam type these algorithms are based on the fourth order statistical moments of the received data sequence the first of the two is a linear least squares type algorithm the second algorithm is of the nonlinear least squares type the algorithms use the fourth order statistical moments of the symbol sequence to explicitly estimate the channel impulse response the estimated impulse response is used in turn to construct a linear mean square error equalizer the performance of this equalizer is not optimal in any sense but it is adequate for channels with mild intersymbol interference or when the number of data points available for estimating the channel response is very large

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

gaussian mixture density modeling of non gaussian source for autoregressive process a new approach is taken to model non gaussian sources of ar processes using gaussian mixture densities that are known to be effective for approximating wide varieties of probability distributions a maximum likelihood estimation algorithm is derived for estimating the ar parameters by solving a generalized normal equation and a clustering algorithm is used for estimating the parameters of gaussian mixture density of the source signals the correlation matrix of the generalized normal equation is not toeplitz but is symmetric and in general positive definite higher order statistics of skewness and kurtosis are used for identifying the source distribution as being gaussian or non gaussian and consequently determining the parameter estimation technique between the conventional method and the proposed method experiments on non gaussian source ar processes demonstrate that under high snr conditions snr spl ges 20 db the proposed algorithm outperforms the conventional ar estimation algorithm and the cumulant based algorithm by an order of magnitude reduction of average estimation errors the proposed algorithm also has very low estimation errors with short data records finally a maximum likelihood prediction method is formulated for non gaussian source ar processes that has shown potential in achieving higher efficiency signal coding than linear predictive coding

a directed network of greek and roman mythology abstract we construct a directed network using a dictionary of greek and roman mythology in which the nodes represent the entries listed in the dictionary and we make directional links from an entry to other entries that appear in its explanatory part we find that this network is clearly not a random network but a directed scale free network in which the distributions of out degree and in degree follow a power law with exponents out 3 0 and in 2 5 respectively also we measure several quantities which describe the topological properties of the network and compare it to that of other real networks

generating structured networks based on a weight dependent deactivation mechanism motivated by the degree dependent deactivation model generating networks with high clustering coefficient k klemm et al phys rev e 65 036123 2002 a weight dependent version is studied to model evolving networks the growth dynamics of the network is based on a naive weight driven deactivation mechanism which couples the establishment of new active vertices and the weights dynamical evolution both analytical solutions and numerical simulations show that the generated networks possess a high clustering coefficient larger than that for regular lattices of the same average connectivity weighted structured scale free networks are obtained as the deactivated vertex is target selected at each time step and weighted structured exponential networks are realized for the random selected case

local world evolving networks with tunable clustering abstract we propose an extended local world evolving network model including a triad formation tf step in the process of network evolution random fluctuation in the number of new edges is involved we derive analytical expressions for degree distribution clustering coefficient and average path length our model can unify the generic properties of real life networks scale free degree distribution high clustering and small inter node separation moreover in our model the clustering coefficient is tunable simply by changing the expected number of tf steps after a single local preferential attachment step

spectra of random graphs with given expected degrees in the study of the spectra of power law graphs there are basically two competing approaches one is to prove analogues of wigner s semicircle law whereas the other predicts that the eigenvalues follow a power law distribution although the semicircle law and the power law have nothing in common we will show that both approaches are essentially correct if one considers the appropriate matrices we will prove that under certain mild conditions the eigenvalues of the normalized laplacian of a random power law graph follow the semicircle law whereas the spectrum of the adjacency matrix of a power law graph obeys the power law our results are based on the analysis of random graphs with given expected degrees and their relations to several key invariants of interest are a number of new values for the exponent where phase transitions for eigenvalue distributions occur the spectrum distributions have direct implications to numerous graph algorithms such as for example randomized algorithms that involve rapidly mixing markov chains

maximal planar networks with large clustering coefficient and power law degree distribution in this article we propose a simple rule that generates scale free networks with very large clustering coefficient and very small average distance these networks are called random apollonian networks rans as they can be considered as a variation of apollonian networks we obtain the analytic results of power law exponent ensuremath gamma 3 and clustering coefficient c frac 46 3 ensuremath 36 phantom rule 0 2em 0ex mathrm ln phantom rule 0 2em 0ex frac 3 2 ensuremath approx 0 74 which agree with the simulation results very well we prove that the increasing tendency of average distance of rans is a little slower than the logarithm of the number of nodes in rans since most real life networks are both scale free and small world networks rans may perform well in mimicking the reality the rans possess hierarchical structure as c k ensuremath sim k ensuremath 1 that are in accord with the observations of many real life networks in addition we prove that rans are maximal planar networks which are of particular practicability for layout of printed circuits and so on the percolation and epidemic spreading process are also studied and the comparisons between rans and barab asi albert ba as well as newman watts nw networks are shown we find that when the network order n the total number of nodes is relatively small as n ensuremath sim 10 4 the performance of rans under intentional attack is not sensitive to n while that of ba networks is much affected by n and the diseases spread slower in rans than ba networks in the early stage of the suseptible infected process indicating that the large clustering coefficient may slow the spreading velocity especially in the outbreaks

scale free networks generated by random walkers we present a simple mechanism for generating undirected scale free networks using random walkers where the network growth is determined by choosing parent vertices by sequential random walks we show that this mechanism produces scale free networks with degree exponent 3 and clustering coefficients depending on random walk length the mechanism can be interpreted in terms of preferential attachment without explicit knowledge of node degrees

structure properties of collaboration network with tunable clustering abstract a collaboration network model with improved triad formation itf step is proposed and denominated as one mode collaboration network with tunable clustering we systematically study its structural features and find this network model can much more accurately reflect cooperative relationship in real society we acquire expression of nodes degree distribution p k that possesses a power law form with exponent whose range is 1 3 expression of clustering coefficient c k for nodes with degree k is also obtained and composes of a power law section and a constant section we verify clustering coefficient of individual nodes increases monotonically with the increase of parameter p that is the probability of itf step occurring when specific forms of p k and c k are given the model s average clustering coefficient c can be derived approximately finally we analytically testify average path length l n increases with network size n in accordance with logarithmic form when n is fixed average path length of entire network decreases with the increase of p all theoretically predicted results are consistent with simulative experimental results

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

growing network with local rules preferential attachment clustering hierarchy and degree correlations the linear preferential attachment hypothesis has been shown to be quite successful in explaining the existence of networks with power law degree distributions it is then quite important to determine if this mechanism is the consequence of a general principle based on local rules in this work it is claimed that an effective linear preferential attachment is the natural outcome of growing network models based on local rules it is also shown that the local models offer an explanation for other properties like the clustering hierarchy and degree correlations recently observed in complex networks these conclusions are based on both analytical and numerical results for different local rules including some models already proposed in the literature

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

estimation of denominator degrees of freedom of f distributions for assessing wald statistics for fixed effect factors in unbalanced mixed models summary tests for fixed effect factors in unbalanced mixed models have previously used t tests on a contrastby contrast basis or wald statistics without a universally accepted method of calculating the denominator degrees of freedom this situation has arisen because the variances of different contrasts are differently weighted sums of the variance components with associated degrees of freedom that are not necessarily equal a simultaneous f test for differences between all levels of a fixed effect factor can be derived by forming new contrasts by rotation of the original contrasts with variances that are close to being the same weighted sum of variance components the associated degrees of freedom for these new contrasts are nearly equal a small simulation study shows the appropriateness of a x2 approximation to the distribution of the weighted sums of variance components three simple examples are used to demonstrate the effects of rotation the last of these examples is also used to compare the proposed simultaneous f test with the distribution of the wald statistic obtained by numerical simulation the method of rotations is then applied to data on the range size of mountain hares lepus timidus to assess the evidence for a two way interaction between season and habitat analysis of data from balanced experiments is traditionally performed by an analysis of variance in which the total sum of squared deviations of observations about their mean is partitioned into sums of squares attributable to either the different treatment effects or the different random effects under standard distributional assumptions each random effect sum of squares follows a multiple of a x2 distribution this multiple being the product of the degrees of freedom the number of independent error contrasts whose square has the required expectation and a linear combination of the different variance components the coefficients in this linear combination being fixed by the design under any null hypothesis concerning the absence of treatment effects the corresponding treatment sum of squares also follows such a multiple of a x2 distribution furthermore the linear combination of variance components in the multiple for the treatment sum of squares is identical to the linear combination for one of the random effect sum of squares hence hypotheses about the treatment effects can be tested by dividing treatment mean squares by the appropriate error mean square to form a variance ratio with an f distribution the benefits of experimental design accrue first through the variance of all contrasts for any given treatment factor or interaction having the same expectation under the null hypothesis second through this variance being as small as possible and third through there being as many error contrasts as possible whose variance is the same as that for the treatment factor or interaction analysis of data that lacks these properties of balance is much less straightforward yet there are many areas in which due to the nature of experimental material the treatment effects cannot be applied in a balanced fashion and so such unbalanced data are the norm rather than the

efficiency of scale free networks error and attack tolerance the concept of network efficiency recently proposed to characterize the properties of small world networks is here used to study the effects of errors and attacks on scale free networks two different kinds of scale free networks i e networks with power law p k are considered 1 scale free networks with no local clustering produced by the barabasi albert model and 2 scale free networks with high clustering properties as in the model by klemm and eguiluz and their properties are compared to the properties of random graphs exponential graphs by using as mathematical measures the global and the local efficiency we investigate the effects of errors and attacks both on the global and the local properties of the network we show that the global efficiency is a better measure than the characteristic path length to describe the response of complex networks to external factors we find that at variance with random graphs scale free networks display both on a global and on a local scale a high degree of error tolerance and an extreme vulnerability to attacks in fact the global and the local efficiency are unaffected by the failure of some randomly chosen nodes though they are extremely sensitive to the removal of the few nodes which play a crucial role in maintaining the network s connectivity

highly clustered scale free networks we propose a model for growing networks based on a finite memory of the nodes the model shows stylized features of real world networks power law distribution of degree linear preferential attachment of new links and a negative correlation between the age of a node and its link attachment rate notably the degree distribution is conserved even though only the most recently grown part of the network is considered as the network grows the clustering reaches an asymptotic value larger than that for regular lattices of the same average connectivity and similar to the one observed in the networks of movie actors coauthorship in science and word synonyms these highly clustered scale free networks indicate that memory effects are crucial for a correct description of the dynamics of growing networks

the effect of generalized deactivation mechanism in weighted networks abstract in this paper we propose a generalized deactivation model to characterize weighted networks by introducing the special aging mechanism the model can produce power law distributions of degree strength and weight as confirmed in many real networks we also characterize the clustering and correlation properties of this class of networks a scaling behavior of clustering coefficient c 1 m is observed where m refers to the number of active nodes the generated network simultaneously exhibits hierarchical organization and disassortative degree correlation all of these structural properties are confirmed by present empirical evidence

mean field theory for clustering coefficients in barabasi albert networks we applied a mean field approach to study clustering coefficients in barabasi albert ba networks we found that the local clustering in ba networks depends on the node degree analytic results have been compared to extensive numerical simulations finding a very good agreement for nodes with low degrees clustering coefficient of a whole network calculated from our approach perfectly fits numerical data

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

effect of node deleting on network structure abstract the ever increasing knowledge of the structure of various real world networks has uncovered their complex multi mechanism governed evolution processes therefore a better understanding of the structure and evolution of these networked complex systems requires us to describe such processes in a more detailed and realistic manner in this paper we introduce a new type of network growth rule which comprises addition and deletion of nodes and propose an evolving network model to investigate the effect of node deleting on network structure it is found that with the introduction of node deleting network structure is significantly transformed in particular degree distribution of the network undergoes a transition from scale free to exponential forms as the intensity of node deleting increases at the same time nontrivial disassortative degree correlation develops spontaneously as a natural result of network evolution in the model we also demonstrate that node deleting introduced in the model does not destroy the connectedness of a growing network so long as the increasing rate of edges is not excessively small in addition it is found that node deleting will weaken but not eliminate the small world effect of a growing network and generally it will decrease the clustering coefficient in a network

exact tests for the random and fixed effects in an unbalanced mixed two way cross classification model the testing of both variance components and fixed effects in an unbalanced mixed model has relied on approximate techniques particularly satterthwaite s approximation of the test statistics the derived tests have unknown distributions both under the null and alternative hypotheses due to the lack of independence and chi squaredness of the mean squares involved hence the appeal for exact testing techniques is understandable this article presents exact tests concerning the variance components of the random effects and estimable linear functions of the fixed effects in an unbalanced mixed two way cross classification with interaction model the derivations are based on techniques similar to those applied by khuri and littell 1987 biometrics 43 545 560 to the same model but with all random effects the proposed methodology requires that the data under consideration contain no empty cells

analysis of scale free networks based on a threshold graph with intrinsic vertex weights many real networks are complex and have power law vertex degree distribution short diameter and high clustering we analyze the network model based on thresholding of the summed vertex weights which belongs to the class of networks proposed by caldarelli et al phys rev lett 89 258702 2002 power law degree distributions particularly with the dynamically stable scaling exponent 2 realistic clustering and short path lengths are produced for many types of weight distributions thresholding mechanisms can underlie a family of real complex networks that is characterized by cooperativeness and the baseline scaling exponent 2 it contrasts with the class of growth models with preferential attachment which is marked by competitiveness and baseline scaling exponent 3

parameter estimation for autoregressive gaussian mixture processes the emax algorithm the problem of estimating parameters of discrete time non gaussian autoregressive ar processes is addressed the subclass of such processes considered is restricted to those whose driving noise samples are statistically independent and identically distributed according to a gaussian mixture probability density function pdf because the likelihood function for this problem is typically unbounded in the vicinity of undesirable degenerate parameter estimates the maximum likelihood approach is not fruitful hence an alternative approach is taken whereby a finite local maximum of the likelihood surface is sought this approach which is termed the quasimaximum likelihood qml approach is used to obtain estimates of the ar parameters as well as the means variances and weighting coefficients that define the gaussian mixture pdf a technique for generating solutions to the qml problem is derived using a generalized version of the expectation maximization principle this technique which is referred to as the emax algorithm is applied in four illustrative examples its performance is compared directly with that of previously proposed algorithms based on the same data model and that of conventional least squares techniques

relationship between the in degree and out degree of www abstract in this paper the relationship between the in degree and out degree of world wide web is studies at each time step a new node with out degree k out is added where k out obeys the power law distribution and its mean value is m the analytical and simulation results suggest that the exponent of in degree distribution would be i 2 1 m depending on the average out degree this finding is supported by the empirical data which has not been emphasized by the previous studies on directed networks

efficient blind system identification of non gaussian autoregressive models with hmm modeling of the excitation we have previously proposed a blind system identification method that exploits the underlying dynamics of non gaussian signals in li and andersen blind identification of non gaussian autoregressive models for efficient analysis of speech signals proceedings of the international conference on acoustics speech and signal processing icassp may 2006 vol 1 pp i 1205 i 1208 the signal model being identified is an autoregressive ar model driven by a discrete state hidden markov process an exact expectation maximization em algorithm was derived for the joint estimation of the ar parameters and the hidden markov model hmm parameters in this paper we extend the system model by introducing an additive measurement noise the identification of the extended system model becomes much more complicated since the system output is now hidden we propose an exact em algorithm that incorporates a novel switching kalman smoother which obtains nonlinear minimum mean square error mmse estimates of the system output based on the state information given by the hmm filter the exact em algorithms for both models are obtainable only by appropriate constraints in the model design and have better convergence properties than algorithms employing generalized em algorithm or empirical iterative schemes the proposed methods also enjoy good data efficiency since only second order statistics are involved in the computation the signal models are general and suitable to numerous signals such as speech and baseband communication signals this paper describes the two system identification algorithms in an integrated form and provides supplementary results to the noise free model and new results to the extended model with applications in speech analysis and channel equalization

epidemic outbreaks in growing scale free networks with local structure abstract the class of generative models has already attracted considerable interest from researchers in recent years and much expanded the original ideas described in ba model most of these models assume that only one node per time step joins the network in this paper we grow the network by adding n interconnected nodes as a local structure into the network at each time step with each new node emanating m new edges linking the node to the preexisting network by preferential attachment this successfully generates key features observed in social networks these include power law degree distribution p k k 3 where n 1 m is a tuning parameter defined as the modularity strength of the network nontrivial clustering assortative mixing and modular structure moreover all these features are dependent in a similar way on the parameter we then study the susceptible infected epidemics on this network with identical infectivity and find that the initial epidemic behavior is governed by both of the infection scheme and the network structure especially the modularity strength the modularity of the network makes the spreading velocity much lower than that of the ba model on the other hand increasing the modularity strength will accelerate the propagation velocity

complex earthquake networks hierarchical organization and assortative mixing to characterize the dynamical features of seismicity as a complex phenomenon the seismic data are mapped to a growing random graph which is a small world scale free network here hierarchical and mixing properties of such a network are studied the clustering coefficient is found to exhibit asymptotic power law decay with respect to connectivity showing hierarchical organization this structure is supported by not only main shocks but also small shocks and may have its origin in the combined effect of vertex fitness and deactivation by stress release at faults the nearest neighbor average connectivity and the pearson correlation coefficient are also calculated it is found that the earthquake network has assortative mixing this is a main difference of the earthquake network from the internet with disassortative mixing physical implications of these results are discussed

exploring complex networks by walking on them we carry out a comparative study of the problem of a walker searching several typical complex networks the search efficiency is evaluated for various strategies having no knowledge of the global properties of the underlying networks and the optimal path between any two given nodes it is found that the best search strategy is the self avoiding random walk the preferentially self avoiding random walk does not help in improving the search efficiency further in return topological information of the underlying networks may be drawn by comparing the results of the different search strategies

generation of scale free networks using a simple preferential rewiring dynamics abstract we propose a simple dynamical process for non growing networks where steady states in the long time limit exhibit power law degree distributions with the exponent 2 at each time step two nodes i and j are randomly selected and one incoming link to i is redirected to j with the rewiring probability r determined only by degrees of two nodes k i and k j while higher degree nodes are preferred to get another link this is an application of the general model introduced earlier s ree phys rev e 73 2006 026115 to take the structure of networks into account we also consider three possible distinctions for the model i how we choose a rewiring link out of all incoming links to i three cases ii whether links are directed or not two cases iii types of networks considering the existence of self loops and multiple links two cases as a result we specify the total of 12 different cases of the model we then observe numerically that networks will evolve to steady states with power law degree distributions when parameters of the model satisfy certain conditions this work is from an effort to find a simple model of the network dynamics generating scale free networks and has a potential to become an underlying mechanism for wide range of scale free non growing networks

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

mimo ar system identification and blind source separation for gmm distributed sources the problem of blind source separation bss and system identification for multiple input multiple output mimo auto regressive ar mixtures is addressed in this paper two new time domain algorithms for system identification and bss are proposed based on the gaussian mixture model gmm for sources distribution both algorithms are based on the generalized expectation maximization gem method for joint estimation of the mimo ar model parameters and the gmm parameters of the sources the first algorithm is derived under the assumption of unstructured input signal statistics while the second algorithm incorporates the prior knowledge about the structure of the input signal statistics due to the statistically independent source assumption these methods are tested via simulations using synthetic and audio signals the system identification performances are tested by comparison between the state transition matrix estimation using the proposed algorithms and the well known multidimensional yule walker solution followed by an instantaneous bss method the results show that the proposed algorithms outperform the yule walker based approach the bss performances were compared to other convolutive bss methods the results show that the proposed algorithms achieve higher signal to interference ratio sir compared to the other tested methods

recursive maximum likelihood algorithm for dependent observations a recursive maximum likelihood algorithm rml is proposed that can be used when both the observations and the hidden data have continuous values and are statistically dependent between different time samples the algorithm recursively approximates the probability density functions of the observed and hidden data by analytically computing the integrals with respect to the state variables where the parameters are updated using gradient steps a full convergence proof is given based on the ordinary differential equation approach which shows that the algorithm converges to a local minimum of the kullback leibler divergence between the true and the estimated parametric probability density functions a result that is useful even for a miss specified parametric model compared to other rml algorithms proposed in the literature this contribution extends the state space model and provides a theoretical analysis in a nontrivial statistical model that was not analyzed so far we further extend the rml analysis to constrained parameter estimation problems two examples including nonlinear state space models are given to highlight this contribution

a tree like complex network model abstract we propose a new tree like network model our results indicate that the tree like model has a small world effect with a small average path length and large clustering coefficient strikingly our tree like model is scale free we also add weight to the links following the network structure with this adding weight method the weight of the nodes shows exponential growth which is ubiquitous in social networks

voter model dynamics in complex networks role of dimensionality disorder and degree distribution we analyze the ordering dynamics of the voter model in different classes of complex networks we observe that whether the voter dynamics orders the system depends on the effective dimensionality of the interaction networks we also find that when there is no ordering in the system the average survival time of metastable states in finite networks decreases with network disorder and degree heterogeneity the existence of hubs i e highly connected nodes in the network modifies the linear system size scaling law of the survival time the size of an ordered domain is sensitive to the network disorder and the average degree decreasing with both however it seems not to depend on network size and on the heterogeneity of the degree distribution

effect of aging on network structure in network evolution the effect of aging is universal in scientific collaboration network scientists have a finite time span of being active in movie actors network once popular stars are retiring from stage devices on the internet may become outmoded with techniques developing so rapidly here we find in citation networks that this effect can be represented by an exponential decay factor e ensuremath ensuremath beta ensuremath tau where ensuremath tau is the node age while other evolving networks the internet for instance may have different types of aging for example a power law decay factor which is also studied and compared it has been found that as soon as such a factor is introduced to the barabasi albert scale free model the network will be significantly transformed the network will be clustered even with infinitely large size and the clustering coefficient varies greatly with the intensity of the aging effect i e it increases linearly with ensuremath beta for small values of ensuremath beta and decays exponentially for large values of ensuremath beta at the same time the aging effect may also result in a hierarchical structure and a disassortative degree degree correlation generally the aging effect will increase the average distance between nodes but the result depends on the type of the decay factor the network appears like a one dimensional chain when exponential decay is chosen but with power law decay a transformation process is observed i e from a small world network to a hypercubic lattice and to a one dimensional chain finally the disparities observed for different choices of the decay factor in clustering average node distance and probably other aspects not yet identified are believed to bear significant meaning on empirical data acquisition

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

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

a highly clustered scale free network evolved by random walking abstract in present paper we propose a highly clustered weighted network model that incorporates the addition of a new node with some links new links between existing nodes and the edge s weight dynamical evolution based on weight dependent walks at each time step the analytical approach and numerical simulation show that the system grows into a weighted network with the power law distributions of strength weight and degree the weight dependent walk length l will not influence the strength distribution but the clustering coefficient of the network is sensitive to l particularly the clustering coefficient is especially high and almost independent of the network size when l 2

from regular to growing small world networks abstract we propose a growing model which interpolates between one dimensional regular lattice and small world networks the model undergoes an interesting phase transition from large to small worlds we investigate the structural properties by both theoretical predictions and numerical simulations our growing model is a complementarity for the important static watts strogatz network model

scale free networks with a large to hypersmall world transition abstract recently there has been a tremendous interest in models of networks with a power law distribution of degree so called scale free networks it has been observed that such networks normally have extremely short path lengths scaling logarithmically or slower with system size as an exotic and counterintuitive example we propose a simple stochastic model capable of generating scale free networks with linearly scaling distances furthermore by tuning a parameter the model undergoes a phase transition to a regime with extremely short average distances apparently slower than log log n which we call a hypersmall world regime we characterize the degree degree correlation and clustering properties of this class of networks

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

blind mimo ar system identification and source separation with finite alphabet in this paper a new method for system identification and blind source separation in a multiple input multiple output mimo system is proposed the mimo channel is modeled by a multi dimensional autoregressive ar system the transmitted signals are assumed to take values from a finite alphabet modeled by the gaussian mixture model gmm with infinitesimal variances the expectation maximization em algorithm for estimation of the mimo ar model parameters is derived the performance of the proposed algorithm in terms of probability of error in signal detection and root mean squared error rmse of the system parameters and system transfer function estimates is evaluated via simulations it is shown that the obtained probability of error is very close to the probability of error of the optimal algorithm which assumes known channel state information

a new measure of network efficiency a b s t r a c t we address the issue of the dynamical origin of scale free link distributions we study a two dimensional lattice of cooperatively interacting units although the units interact only with the four nearest neighbors a sufficiently large cooperation strength generates dynamically a scale free network with the power law index approaching 1 we explain this result by using a new definition of network efficiency determined by the euclidean distance between correlated units according to this definition the link distribution favoring long range connections makes efficiency increase we embed an ad hoc scale free network with power index 1 into a euclidean two dimensional space and show that the network efficiency becomes maximal as approaches 1 we therefore conclude that 1 emerging from the cooperative interaction of units may be a consequence of the principle of network maximal efficiency

scaling of weighted spectral distribution in deterministic scale free networks abstract scale free networks are abundant in the real world in this paper we investigate the scaling properties of the weighted spectral distribution in several deterministic and stochastic models of evolving scale free networks first we construct a new deterministic scale free model whose node degrees have a unified format using graph structure features we derive a precise formula for the spectral metric in this model this formula verifies that the spectral metric grows sublinearly as network size i e the number of nodes grows additionally the mathematical reasoning of the precise formula theoretically provides detailed explanations for this scaling property finally we validate the scaling properties of the spectral metric using some stochastic models the experimental results show that this scaling property can be retained regardless of local world node deleting and assortativity adjustment

robustness of interdependent and interconnected clustered networks abstract in real world most systems show significant clustering and it is more practical to investigate the behaviors of clustered network previous studies are mostly focused on single clustered network and coupled clustered networks with dependency links here we study two clustered networks coupled with both interdependent and interconnected links by introducing generating function of the joint degree distribution when the networks are fully dependent we obtain the analytical solution of giant component p we show rich phase transition phenomena and analyze their behaviors we find that as dependency coupling strength increases the system changes from second order phase transition through hybrid transition to first order phase transition for weak dependency coupling strength q a corresponding to second order phase transition we find that clustering has almost no effect on the robustness of network but for strong dependency coupling strength q a corresponding to first order transition the more clustered system is more vulnerable at the same time we notice that when the system is more clustered the hybrid order region is almost unchangeable the first order region becomes smaller and the second order region is larger additionally we can see that the bigger the clustering coefficient c is the bigger the second order region becomes for the same c the density of connectivity links between networks is higher the second order region becomes smaller and the density of connectivity links within each network is higher the second order region becomes bigger

pseudofractal scale free web we find that scale free random networks are excellently modeled by simple deterministic graphs our graph has a discrete degree distribution degree is the number of connections of a vertex which is characterized by a power law with exponent gamma 1 ln 3 ln 2 properties of this compact structure are surprisingly close to those of growing random scale free networks with gamma in the most interesting region between 2 and 3 we succeed to find exactly and numerically with high precision all main characteristics of the graph in particular we obtain the exact shortest path length distribution for a large network ln n 1 the distribution tends to a gaussian of width approximately sqrt ln n centered at l approximately ln n we show that the eigenvalue spectrum of the adjacency matrix of the graph has a power law tail with exponent 2 gamma

statistical ensemble of scale free random graphs a thorough discussion of the statistical ensemble of scale free connected random tree graphs is presented methods borrowed from field theory are used to define the ensemble and to study analytically its properties the ensemble is characterized by two global parameters the fractal and the spectral dimensions which are explicitly calculated it is discussed in detail how the geometry of the graphs varies when the weights of the nodes are modified the stability of the scale free regime is also considered when it breaks down either a scale is spontaneously generated or else a singular node appears and the graphs become crumpled a new computer algorithm to generate these random graphs is proposed possible generalizations are also discussed in particular more general ensembles are defined along the same lines and the computer algorithm is extended to arbitrary degenerate scale free random graphs

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

impact of initial lattice structures on networks generated by traces of random walks abstract we show that the platform stage of network evolution plays a principal role in the topology of resulting networks generated by short cuts stimulated by the movements of a random walker the mechanism of which tends to produce power law degree distributions to examine the numerical results we have developed a statistical method which relates the power law exponent to random properties of the subgraph developed in the platform stage as a result we find that an important exponent in the network evolution is which characterizes the size of the subgraph in the form v t where v and t denote the number of vertices in the subgraph and the time variable respectively 2d lattices can impose specific limitations on the walker s diffusion which keeps the value of within a moderate range and provides typical properties of complex networks 1d and 3d cases correspond to different ends of the spectrum for with 2d cases in between especially for 2d square lattices a discontinuous change of the network structure is observed which varies according to whether is greater or less than 2 for 1d cases we show that emergence of nearly complete subgraphs is guaranteed by 1 2 although the transient power law is permitted at low increase rates of edges additionally the model exhibits a spontaneous emergence of highly clustered structures regardless of its initial structure

class of correlated random networks with hidden variables we study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices we find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices the expressions obtained are checked by means of numerical simulations in a particular example the general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure we also present an extension of the class to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system

cyclic topology in complex networks we introduce a cyclic coefficient r which characterizes the degree of circulation in complex networks if a network has a perfect treelike structure then r becomes zero the larger value of r represents that the network has more cyclic structure we measure both the cyclic coefficients and the distributions of local cyclic coefficients for various networks and discuss the cyclic structures of them

topology and correlations in structured scale free networks we study a recently introduced class of scale free networks showing a high clustering coefficient and nontrivial connectivity correlations we find that the connectivity probability distribution strongly depends on the fine details of the model we solve exactly the case of low average connectivity providing also exact expressions for the clustering and degree correlation functions the model also exhibits a lack of small world properties in the whole parameter range we discuss the physical properties of these networks in the light of the present detailed analysis

classification of digital amplitude phase modulated signals in time correlated non gaussian channels in this paper a new algorithm is proposed for the classification of digital amplitude phase modulated signals in flat fading channels with time correlated non gaussian noise the first order statistics of the additive noise is modeled by a gaussian mixture distribution and an autoregressive ar process is used to model the time correlation the proposed classifier involves the use of a whitening filter necessary to reduce the complexity of the classification process and maximum likelihood classification for the estimation of the whitening filter coefficients a new blind technique that is based on the use of a robust h filter is developed after whitening the received signal following a composite hypothesis testing approach the unknown fading and noise distribution parameters are estimated results are presented which show that when the noise process is time correlated non gaussian the proposed classifier outperforms maximum likelihood classifiers developed under the assumption that the noise process is either white non gaussian or white gaussian it is also shown that when the noise process is white gaussian the proposed classifier s performance closely approaches that of the maximum likelihood classifier developed for white gaussian noise channels

tree networks with causal structure a geometry of networks endowed with a causal structure is discussed using the conventional framework of the equilibrium statistical mechanics the popular growing network models appear as particular causal models we focus on a class of tree graphs an analytically solvable case general formulas are derived describing the degree distribution the ancestor descendant correlation and the probability that a randomly chosen node lives at a given geodesic distance from the root it is shown that the hausdorff dimension d h of the causal networks is generically infinite in contrast to the maximally random trees where it is generically finite

why social networks are different from other types of networks we argue that social networks differ from most other types of networks including technological and biological networks in two important ways first they have nontrivial clustering or network transitivity and second they show positive correlations also called assortative mixing between the degrees of adjacent vertices social networks are often divided into groups or communities and it has recently been suggested that this division could account for the observed clustering we demonstrate that group structure in networks can also account for degree correlations we show using a simple model that we should expect assortative mixing in such networks whenever there is variation in the sizes of the groups and that the predicted level of assortative mixing compares well with that observed in real world networks

exact tests for the main effects variance components in an unbalanced random two way model abstract exact tests are derived for testing hypotheses concerning the variance components of the main effects in an unbalanced random two way crossed classification with interaction model the tests are based on four sums of squares which are distributed independently as scalar multiples of chi squared variates these sums of squares can also be used to find an exact test concerning the interaction variance component and to obtain simultaneous confidence intervals on all continuous functions of the model s variance components a study is made concerning the power of the proposed tests including a comparison with other approximate tests author

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

a new deterministic complex network model with hierarchical structure abstract we introduce a new simple pseudo tree like network model deterministic complex network dcn the proposed dcn model may simulate the hierarchical structure nature of real networks appropriately and have the unique property of skipping the levels which is ubiquitous in social networks our results indicate that the dcn model has a rather small average path length and large clustering coefficient leading to the small world effect strikingly our dcn model obeys a discrete power law degree distribution p k k with exponent approaching 1 0 we also discover that the relationship between the clustering coefficient and degree follows the scaling law c k k 1 which quantitatively determines the dcn s hierarchical structure

erratum small world networks evidence for a crossover picture phys rev lett 82 3180 1999 we have performed new calculations using the breadth first search algorithm 1 2 we are now able to study systems with sizes up to n 5500 as shown in fig 1 we now find t o 1 in agreement with the simple argument given in our letter but different from the originally reported numerical result st 0 67 6 0 10d the reason for the incorrect numerical result reported initially is the small system sizes we studied which did not allow us to reach the asymptotic regime we thank a barrat 3 and m e j newman and d j watts 4 for alerting us to the possibility of an error on our estimate of t we also thank m argollo de menezes for directing us to the breadth first search algorithm