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

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

a deconvolution problem related to a singular system we present a recursive deconvolution algorithm for a volterra integral equation which corresponds to a singular differential equation in a hilbert space the algorithm is robust with respect to errors in the sampling of the output and to the sampling times

the deconvolution problem fast algorithms including the preconditioned conjugate gradient to compute a map estimator different aspects of the deconvolution problem are discussed and a solution by the map estimator using the a priori knowledge of smoothness and nonnegativity of the unknown signal is proposed several fast algorithms are examined and the conjugate gradient cg method is show to have several advantages it allows computation of a constrained solution and when used with a preconditioning technique it can be faster than other algorithms for general near to toeplitz systems in particular for toeplitz block toeplitz systems

common structure of techniques for choosing smoothing parameters in regression problems on tente de relier deux methodes de choix du parametre de lissage l une basee sur la mesure du risque et l autre sur le degre d ajustement de la regression aux donnees

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

a recursive deconvolution approach to disturbance reduction active noise control anc uses an estimate of the noise affecting a system in order to remove its effect from the output in some applications it is possible to directly measure the noise and a feedforward compensator can be used other applications require instead that the noise be estimated from its effect on the system this results in an adaptive feedback anc see a previous paper by gan and kuo the identification of the disturbance from the output of the linear system is a deconvolution problem in this paper we study a deconvolution technique for the active reduction of the influence of the disturbance on the output of a linear control system the regulator that we present does not affect the behavior of the system in the absence of disturbances

asymptotic feedback stabilization a sufficient condition for the existence of control lyapunov functions abstract in this paper we study the feedback stabilization problem for a wide class of nonlinear systems that are affine in the control we offer sufficient conditions for the existence of control lyapunov functions that according to 3 23 and 28 30 guarantee stabilization at a specified equilibrium by means of a feedback law which is smooth except possibly at the equilibrium we note that the results of the paper present a local nature

fast inversion of triangular toeplitz matrices an algorithm requiring 0 n log n operations is proposed for the inversion of triangular toeplitz matrices this algorithm is faster than existing techniques even for relatively small values of n and can easily be written in fortran

identifiability of the deconvolution problem abstract a deconvolution problem is stated and its identifiability properties are analysed the information assumed available consists of the spectral density of the output measurements and a dynamical description of the system the input to the system and the measurement noise are modelled as independent arma processes in order to obtain an optimal estimate in a mean square sense of the input signal the parameters of the input model and measurement noise are required either to be known a priori or correctly estimated since the normal situation requires estimation of the parameters a successful estimate of the input signal depends crucially on the identifiability properties hence necessary and sufficient conditions for parameter identifiability are derived in terms of model orders with the aid of spectral factorization an example shows that when these conditions are violated only generic results can be obtained a sufficient condition for generic parameter identifiability is given

a theorem on global stabilization of nonlinear systems by linear feedback abstract in this paper we investigate the global stabilizability problem for a wide class of single input nonlinear systems whose the linearization at the equilirrium is controllable we show that under general assumptions there exists a linear feedback law which globally exponentially stabilizes the system at its equilibrium the proof of our main theorem is based on some ideas from a previous paper we use the theorem to recover a recent result of gauthier et al concerning the observer design problem

a singular perturbation approach to a recursive deconvolution problem following the approach described by a v kryazhimskii and yu s osipov we present a recursive algorithm which can be applied to solve the deconvolution problem of linear finite dimensional input output systems the method gives an on line approximation of the unknown input based on approximate samples of the output key features of this approach are the introduction of an associated singularly perturbed system and the use of a quasi canonical form due to morse

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

brief paper solutions of nonlinear control and estimation problems in reproducing kernel hilbert spaces existence and numerical determination many nonlinear optimal control and estimation problems can be formulated as tikhonov variational problems in an infinite dimensional reproducing kernel hilbert space this paper shows that any closed ball contained in such spaces is compact in the sup norm topology this result is exploited to obtain conditions which guarantee existence of solutions for the aforementioned problems as well as numerical algorithms whose convergence is guaranteed in the space of continuous functions

brief fast spline smoothing via spectral factorization concepts when tuning the smoothness parameter of nonparametric regression splines the evaluation of the so called degrees of freedom is one of the most computer intensive tasks in the paper a closed form expression of the degrees of freedom is obtained for the case of cubic splines and equally spaced data when the number of data tends to infinity state space methods kalman filtering and spectral factorization techniques are used to prove that the asymptotic degrees of freedom are equal to the variance of a suitably defined stationary process the closed form expression opens the way to fast spline smoothing algorithms whose computational complexity is about one half of standard methods or even one fourth under further approximations

on the existence of control lyapunov functions generalizations of vidyasagar s theorem on nonlinear stabilization in this paper the well known vidyasagar s theorem concerning the feedback stabilizability problem for interconnected control systems is generalized in particular sufficient conditions are provided for the existence of control lyapunov functions that according to the results of artstein sontag and tsinias guarantees asymptotic stabilization by means of a feedback law that is smooth except possibly at the equilibrium at which it is wished to stabilize the system

the effect of weight on community structure of networks abstract the effect of weight on community structures is investigated in this paper we use weighted modularity q w to evaluate the partitions and weighted extremal optimization algorithm to detect communities starting from empirical and idealized weighted networks the matching between weights and edges are disturbed then using similarity function s to measure the difference between community structures it is found that the redistribution of weights does strongly affect the community structure especially in dense networks this indicates that the community structure in networks is a suitable property to reflect the role of weight

stationary and nonstationary properties of evolving networks with preferential linkage networks evolving by preferential attachment of both external and internal links are investigated the rate of adding an external link is assumed to depend linearly on the degree of a preexisting node to which a new node is connected the process of creating an internal link between a pair of existing vertices is assumed to be controlled entirely by the vertex that has more links than the other vertex in the pair and the rate of creation of such a link is assumed to be in general nonlinear in the degree of the more strongly connected vertex it is shown that degree distributions of networks evolving only by creating internal links display for large degrees a nonstationary power law decay with a time dependent scaling exponent nonstationary power law behaviors are numerically shown to persist even when the number of nodes is not fixed and both external and internal connections are introduced provided that the rate of preferential attachment of internal connections is nonlinear it is argued that nonstationary effects are not unlikely in real networks although these effects may not be apparent especially in networks with a slowly varying mean degree

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

bayes and empirical bayes semi blind deconvolution using eigenfunctions of a prior covariance we consider the semi blind deconvolution problem i e estimating an unknown input function to a linear dynamical system using a finite set of linearly related measurements where the dynamical system is known up to some system parameters without further assumptions this problem is often ill posed and ill conditioned we overcome this difficulty by modeling the unknown input as a realization of a stochastic process with a covariance that is known up to some finite set of covariance parameters we first present an empirical bayes method where the unknown parameters are estimated by maximizing the marginal likelihood posterior and subsequently the input is reconstructed via a tikhonov estimator with the parameters set to their point estimates next we introduce a bayesian method that recovers the posterior probability distribution and hence the minimum variance estimates for both the unknown parameters and the unknown input function both of these methods use the eigenfunctions of the random process covariance to obtain an efficient representation of the unknown input function and its probability distributions simulated case studies are used to test the two methods and compare their relative performance

nonparametric spline regression with prior information summary by using prior information about the regression curve we propose new nonparametric regression estimates we incorporate two types of information first we suppose that the regression curve is similar in shape to a family of parametric curves characterized as the solution to a linear differential equation the regression curve is estimated by penalized least squares with the differential operator defining the smoothness penalty we discuss in particular growth and decay curves and take a time transformation to obtain a tractable solution the second type of prior information is linear equality constraints we estimate unknown parameters by generalized cross validation or maximum likelihood and obtain efficient 0 n algorithms to compute the estimate of the regression curve and the cross validation and maximum likelihood criterion functions

a smoothness priors time varying ar coefficient modeling of nonstationary covariance time series a smoothness priors time varying ar coefficient model approach for the modeling of nonstationary in the covariance time series is shown smoothness priors in the form of a difference equation constraint excited by an independent white noise are imposed on each ar coefficient the unknown white noise variances are hyperparameters of the ar coefficient distribution the critical computation is of the likelihood of the hyperparameters of the bayesian model this computation is facilitated by a state space representation kalman filter implementation the best difference equation order best ar model order best hyperparameter model locally in time is selected using the minimum aic method also an instantaneous spectral density is defined in terms of the instantaneous ar model coefficients and a smoothed estimate of the instantaneous time series variance an earthquake record is analyzed the changing spectral analysis of the original data and of simulations from a time varying ar coefficient model of that data are shown

on the emergence of scaling in weighted networks abstract general conditions for the appearance of the power law distribution of total weights concentrated in vertices of complex network systems are established by use of the rate equation approach for networks evolving by connectivity governed attachment of every new node to p 1 exiting nodes and by ascription to every new link a weight taken from algebraic distributions independent of network topologies it is shown that the distribution of the total weight w asymptotically follows the power law p w w with the exponent 0 2 the power law dependence of the weight distribution is also proved to hold for asymptotically large w in the case of networks in which a link between nodes i and j carries a load w ij determined by node degrees k i and k j at the final stage of the network growth according to the relation w ij k i k j with 1 0 for this class of networks the scaling exponent describing the weight distribution is found to satisfy the relationship 1 where is the scaling index characterizing the distribution of node degrees n k k

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

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

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

bayesian confidence intervals for the cross validated smoothing spline summary we consider the model y t g ti ei i 17 2 n where g t t 0 1 is a smooth function and the ei are independent n 0 a2 errors with g2 unknown the cross validated smoothing spline can be used to estimate g non parametrically from

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

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

nonparametric input estimation in physiological systems problems methods and case studies input estimation from output data is an important problem in the analysis of physiological systems because many signals of interest are not directly accessible to measurement when the system is time invariant this problem is often referred to as deconvolution three representative physiological problems regarding hormone secretion insulin dynamics and hepatic glucose production are used to illustrate the major challenges ill conditioning confidence intervals assessment infrequent and nonuniform sampling nonnegativity constraints and computational efficiency the paper provides a critical overview of the existing techniques focusing on regularization theory and bayesian estimation in order to overcome some inadequacies of the existing methods some new results are derived in particular the connection between the maximum likelihood estimate of the regularization parameter and the notion of equivalent degree of freedom is studied moreover a fast svd based numerical algorithm is developed that includes the optimization of the regularization parameter and the computation of confidence intervals the proposed techniques are validated on a benchmark problem and are shown to provide effective solutions to the three physiological case studies

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

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

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

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

simultaneous input and state estimation for stochastic nonlinear systems with additive unknown inputs abstract this paper investigates simultaneous input and state estimation for a class of nonlinear stochastic systems we propose a recursive filter to concurrently estimate system states and unknown inputs we show that the estimation errors of the proposed filter are practically exponentially stable in probability and the estimation error covariance matrices are uniformly bounded

input estimation in nonlinear dynamical systems using differential algebra techniques the paper considers the problem of estimating the unknown input of a nonlinear dynamical system described by polynomial or rational differential equations from a finite set of noisy output samples without additional information this problem is ill posed since the unknown function may belong to an arbitrary infinite dimensional space we tackle this difficulty by designing a novel class of fast regularization algorithms that relies upon differential algebra techniques monte carlo studies are used to demonstrate the effectiveness of the new approach

a unified filter for simultaneous input and state estimation of linear discrete time stochastic systems in this paper we present a unified optimal and exponentially stable filter for linear discrete time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum variance sense without making any assumptions on the direct feedthrough matrix we also provide the connection between the stability of the estimator and a system property known as strong detectability and discuss the global optimality of the proposed filter finally an illustrative example is given to demonstrate the performance of the unified unbiased minimum variance filter

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

a generalization of vidyasagar s theorem on stability using state detection in this paper we generalize the vidyasagar s well known theorem on the local stabilizability problem of nonlinear systems using state detection 11 our purpose is to prove that if a system is weakly detectable and stabilizable by means of a continuous state feedback u x for which no differentiability assumption is imposed then the system is also stabilized by the law u z where z is the output of a weak detector for the state x the result above is applicable to several cases not covered by other works

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

brief regularization networks for inverse problems a state space approach linear inverse problems with discrete data are equivalent to the estimation of the continuous time input of a linear dynamical system from samples of its output the solution obtained by means of regularization theory has the structure of a neural network similar to classical rbf networks however the basis functions depend in a nontrivial way on the specific linear operator to be inverted and the adopted regularization strategy by resorting to the bayesian interpretation of regularization we show that such networks can be implemented rigorously and efficiently whenever the linear operator admits a state space representation an analytic expression is provided for the basis functions as well as for the entries of the matrix of the linear system used to compute the weights the results are illustrated through a deconvolution problem where the spontaneous secretory rate of luteinizing hormone lh of the hypophisis is reconstructed from measurements of plasma lh concentrations

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

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

scaling in weighted networks and complex systems abstract network systems evolving by preferential attachment of new vertices and by link loading are considered the probability of node attaching is assumed to depend linearly on degrees of existing nodes to which new ones are connected the rule of the network loading allows both deterministic and random processes of distributing weights among links specifically the rule is determined by assigning to each link a weight dependent on randomly modified intervals between times at which linked vertices are connected to the system this enables the investigation of the influence of local and global loading processes on statistical properties of weighted networks it is demonstrated that for different values of parameters controlling these processes the distribution of weights concentrated at vertices of such networks displays a large variety of scale free and truncated scale free behaviors it is also shown that statistical properties of the studied weighted networks and statistical properties of some complex evolving spatial systems exhibit a close relationship

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

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

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

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

fluctuation driven dynamics of the internet topology we study the dynamics of the internet topology based on empirical data on the level of the autonomous systems it is found that the fluctuations occurring in the stochastic process of connecting and disconnecting edges are important features of the internet dynamics the network s overall growth can be described approximately by a single characteristic degree growth rate g eff approximately 0 016 and the fluctuation strength sigma eff approximately 0 14 together with the vertex growth rate alpha approximately 0 029 a stochastic model which incorporates these values and an adaptation rule newly introduced reproduces several features of the real internet topology such as the correlations between the degrees of different vertices

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

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

on the representer theorem and equivalent degrees of freedom of svr support vector regression svr for discrete data is considered an alternative formulation of the representer theorem is derived this result is based on the newly introduced notion of pseudoresidual and the use of subdifferential calculus the representer theorem is exploited to analyze the sensitivity properties of e insensitive svr and introduce the notion of approximate degrees of freedom the degrees of freedom are shown to play a key role in the evaluation of the optimism that is the difference between the expected in sample error and the expected empirical risk in this way it is possible to define a cp like statistic that can be used for tuning the parameters of svr the proposed tuning procedure is tested on a simulated benchmark problem and on a real world problem boston housing data set

brief paper identifiability of the stochastic semi blind deconvolution problem for a class of time invariant linear systems semi blind deconvolution is the process of estimating the unknown input of a linear system starting from output data when the kernel of the system contains unknown parameters in this paper identifiability issues related to such a problem are investigated in particular we consider time invariant linear models whose impulse response is given by a sum of exponentials and assume that smoothness is the sole available a priori information on the unknown signal we state the semi blind deconvolution problem in a bayesian setting where prior knowledge on the smoothness of the unknown function is mathematically formalized by describing the system input as a brownian motion this leads to a tychonov type estimator containing unknown smoothness and system parameters which we estimate by maximizing their marginal likelihood posterior the mathematical structure of this estimator is studied in the ideal situation of output data noiseless with their number tending to infinity simulated case studies are used to illustrate the practical implications of the theoretical findings in system modeling finally we show how semi blind deconvolution can be improved by proposing a new prior for signals that are initially highly nonstationary but then become as time progresses more regular

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

scale free characteristics of random networks the topology of the world wide web the world wide web forms a large directed graph whose vertices are documents and edges are links pointing from one document to another here we demonstrate that despite its apparent random character the topology of this graph has a number of universal scale free characteristics we introduce a model that leads to a scale free network capturing in a minimal fashion the self organization processes governing the world wide web c 2000 elsevier science b v all rights reserved pacs 84 35 i 64 60 fr 87 23 ge

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

sontag s input to state stability condition and global stabilization using state detection this paper deals with the global stabilization problem for nonlinear system using state detection sufficient algebraic conditions for stabilization and detectability concerning particular classes of systems are included these conditions are based to a version of a lyapunov like condition proposed by sontag which guarantees input to state stability

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved