spectra of complex networks we propose a general approach to the description of spectra of complex networks for the spectra of networks with uncorrelated vertices and a local treelike structure exact equations are derived these equations are generalized to the case of networks with correlations between neighboring vertices the tail of the density of eigenvalues ensuremath rho ensuremath lambda at large ensuremath lambda is related to the behavior of the vertex degree distribution p k at large k in particular as p k ensuremath sim k ensuremath ensuremath gamma ensuremath rho ensuremath lambda ensuremath sim ensuremath lambda 1 ensuremath 2 ensuremath gamma we propose a simple approximation which enables us to calculate spectra of various graphs analytically we analyze spectra of various complex networks and discuss the role of vertices of low degree we show that spectra of locally treelike random graphs may serve as a starting point in the analysis of spectral properties of real world networks e g of the internet

models of social networks based on social distance attachment we propose a class of models of social network formation based on a mathematical abstraction of the concept of social distance social distance attachment is represented by the tendency of peers to establish acquaintances via a decreasing function of the relative distance in a representative social space we derive analytical results corroborated by extensive numerical simulations showing that the model reproduces the main statistical characteristics of real social networks large clustering coefficient positive degree correlations and the emergence of a hierarchy of communities the model is confronted with the social network formed by people that shares confidential information using the pretty good privacy pgp encryption algorithm the so called web of trust of pgp

a new kernel based approach for linear system identification this paper describes a new kernel based approach for linear system identification of stable systems we model the impulse response as the realization of a gaussian process whose statistics differently from previously adopted priors include information not only on smoothness but also on bibo stability the associated autocovariance defines what we call a stable spline kernel the corresponding minimum variance estimate belongs to a reproducing kernel hilbert space which is spectrally characterized compared to parametric identification techniques the impulse response of the system is searched for within an infinite dimensional space dense in the space of continuous functions overparametrization is avoided by tuning few hyperparameters via marginal likelihood maximization the proposed approach may prove particularly useful in the context of robust identification in order to obtain reduced order models by exploiting a two step procedure that projects the nonparametric estimate onto the space of nominal models the continuous time derivation immediately extends to the discrete time case on several continuous and discrete time benchmarks taken from the literature the proposed approach compares very favorably with the existing parametric and nonparametric techniques

tabu search directed by direct search methods for nonlinear global optimization abstract in recent years there has been a great deal of interest in metaheuristics in the optimization community tabu search ts represents a popular class of metaheuristics however compared with other metaheuristics like genetic algorithm and simulated annealing contributions of ts that deals with continuous problems are still very limited in this paper we introduce a continuous ts called directed tabu search dts method in the dts method direct search based strategies are used to direct a tabu search these strategies are based on the well known nelder mead method and a new pattern search procedure called adaptive pattern search moreover we introduce a new tabu list conception with anti cycling rules called tabu regions and semi tabu regions in addition diversification and intensification search schemes are employed numerical results show that the proposed method is promising and produces high quality solutions

on the estimation of transfer functions this paper treats the close conceptual relationships between basic approaches to the estimation of transfer functions of linear systems the classical methods of frequency and spectral analysis are shown to be related to the well known time domain methods of prediction error type via a common empirical transfer function estimate asymptotic properties of the estimates obtained by the respective methods are also described and discussed an important feature that is displayed by this treatment is a frequency domain weighting function that determines the distribution of bias in case the true system cannot be exactly described within the chosen model set the choice of this weighting function is made in terms of noise models for time domain methods the noise model thus has a dual character from the system approximation point of view

recent progress in unconstrained nonlinear optimization without derivatives we present an introduction to a new class of derivative free methods for unconstrained optimization we start by discussing the motivation for such methods and why they are in high demand by practitioners we then review the past developments in this field before introducing the features that characterize the newer algorithms in the context of a trust region framework we focus on techniques that ensure a suitable geometric quality of the considered models we then outline the class of algorithms based on these techniques as well as their respective merits we finally conclude the paper with a discussion of open questions and perspectives

approximation of delay systems by fourier laguerre series abstract error estimates are given for the approximation of stable recorded delay systems in the l 2 and h norms using two recently advocated techniques based on laguerre series in addition some theoretical results on l 0 approximation are derived

mesh adaptive direct search algorithms for constrained optimization this paper addresses the problem of minimization of a nonsmooth function under general nonsmooth constraints when no derivatives of the objective or constraint functions are available we introduce the mesh adaptive direct search mads class of algorithms which extends the generalized pattern search gps class by allowing local exploration called polling in an asymptotically dense set of directions in the space of optimization variables this means that under certain hypotheses including a weak constraint qualification due to rockafellar mads can treat constraints by the extreme barrier approach of setting the objective to infinity for infeasible points and treating the problem as unconstrained the main gps convergence result is to identify limit points hat x where the clarke generalized derivatives are nonnegative in a finite set of directions called refining directions although in the unconstrained case nonnegative combinations of these directions span the whole space the fact that there can only be finitely many gps refining directions limits rigorous justification of the barrier approach to finitely many linear constraints for gps the main result of this paper is that the general mads framework is flexible enough to allow the generation of an asymptotically dense set of refining directions along which the clarke derivatives are nonnegative we propose an instance of mads for which the refining directions are dense in the hypertangent cone at hat x with probability 1 whenever the iterates associated with the refining directions converge to a single hat x the instance of mads is compared to versions of gps on some test problems we also illustrate the limitation of our results with examples

dynamic computation of network statistics via updating schema given a large network computing statistics such as clustering coefficient or modularity is costly for large networks when one more edge or vertex is added traditional methods require that the full expensive computation be redone on this slightly modified graph alternatively we introduce here a new approach under modification to the graph we update the statistics instead of computing them from scratch in this paper we provide update schemes for a number of popular statistics to include degree distribution clustering coefficient assortativity and modularity our primary aim is to reduce the computational complexity needed to track the evolving behavior of large networks as an important consequence this approach provides efficient methods which may support modeling the evolution of dynamic networks to identify and understand critical transitions using the updating scheme the network statistics can be computed much faster than re calculating each time that the network evolves we also note that the update formula can be used to determine which edge or node will lead to the extremal change of network statistics providing a way of predicting or designing network evolution rules that would optimize some chosen statistic we present our evolution methods in terms of a network statistics differential notation

on the convergence of the multidirectional search algorithm this paper presents the convergence analysis for the multidirectional search algorithm a direct search method for unconstrained minimization the analysis follows the classic lines of proofs of convergence for gradient related methods the novelty of the argument lies in the fact that explicit calculation of the gradient is unnecessary although it is assumed that the function is continuously differentiable over some subset of the domain the proof can be extended to treat most nonsmooth cases of interest the argument breaks down only at points where the derivative exists but is not continuous finally it is shown how a general convergence theory can be developed for an entire class of direct search methods which includes such methods as the factorial design algorithm and the pattern search algorithm that share a key feature of the multidirectional search algorithm

integral constraints on the accuracy of least squares estimation it is common to need to estimate the frequency response of a system from observed input output data this paper uses integral constraints to characterise the undermodelling induced errors involved in solving this problem via parametric least squares methods this is achieved by exploiting the hilbert space structure inherent in the least squares solution in order to provide a geometric interpretation of the nature of frequency domain errors the result is that an intuitive process can be applied in which for a given data collection method and model structure one identifies the sides of a right triangle and then by noting the hypotenuse to be the longest side integral constraints on the magnitude estimation error are obtained by also noting that the triangle sides both lie in a particular plane integral constraints on phase estimation error are derived this geometric approach is in contrast to earlier work in this area which has relied on algebraic manipulation

generalized binary noise test signal concept for improved identification experiment design abstract when accurate identification of a parametrized linear process model is required an external disturbance test signal will often be introduced to improve the statistical information content of the measured data in industrial practice a specific pseudo random binary sequence or binary noise is frequently used this is a stochastic signal which randomly switches between two fixed signal levels at discrete points in time the paper shows that this test signal has serious shortcomings when used in conjunction with one step ahead prediction error estimators such estimators appear to given an unfair advantage to higher frequency components as a higher intensity of lower frequencies seems desirable a generalized binary noise concept gbn is introduced which involves a generalized stochastic distribution of the switching moments this allows manipulation of the frequency spectrum of the input signal such that most energy is concentrated in the lower frequencies it is argued that the gbn concept indeed gives much better identification results than the conventional concept considering the stochastic features of gbn and an analytical result on optimal gbn design for stable first order processes in addition using stochastic simulation techniques near to optimal gbn designs are specified for four types of stable second order processes for several signal to noise ratios and observation lengths of the experiment it turns out that not only bias but also variance of the model step response is reduced dramatically finally using theoretical and simulation results a practical guideline for gbn design is presented together with a pascal procedure for gbn generation which demonstrates the conceptual simplicity and industrial appeal of the gbn concept

paper unprejudiced optimal open loop input design for identification of transfer functions the problem to estimate transfer functions of linear systems is considered the quality of the resulting estimate depends among other things on the input used during the identification experiment we measure the quality using a quadratic norm in the frequency domain the problem to determine optimal inputs i e inputs that minimize the chosen norm subject to constrained input variance has long been studied we point out that such procedures may involve a prejudice that the system is to be found in a certain model set that may have some surprising effects we discuss how such a prejudice can be reduced by allowing the possibility that the true system cannot be exactly described in the chosen model set we also calculate explicit expressions for the resulting unprejudiced optimal inputs these expressions relate the signal to noise ratio as a function of frequency to the chosen weighting function in the quadratic norm we also point out the role of the employed noise model for the design

hamiltonian dynamics of preferential attachment prediction and control of network dynamics are grand challenge problems in network science the lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades here we study the dynamics of networks evolving according to preferential attachment pa known to approximate well the large scale growth dynamics of a variety of real networks we show that this dynamics is hamiltonian thus casting the study of complex networks dynamics to the powerful canonical formalism in which the time evolution of a dynamical system is described by hamilton s equations we derive the explicit form of the hamiltonian that governs network growth in pa this hamiltonian turns out to be nearly identical to graph energy in the configuration model which shows that the ensemble of random graphs generated by pa is nearly identical to the ensemble of random graphs with scale free degree distributions in other words pa generates nothing but random graphs with power law degree distribution the extension of the developed canonical formalism for network analysis to richer geometric network models with non degenerate groups of symmetries may eventually lead to a system of equations describing network dynamics at small scales

recursive prediction error identification using the nonlinear wiener model the nonlinear wiener model consisting of a linear dynamic block in cascade with a static nonlinearity is considered a recursive prediction error identification algorithm based on the wiener model is derived the linear dynamic block is modelled as a siso transfer function operator and the static nonlinearity is approximated with a piecewise linear function a theoretical analysis of the method is carried out and conditions for local convergence to the true parameter vector are given in particular the analysis shows that the input signal should be such that there is signal energy in the whole range of the piecewise linear approximation a numerical example illustrates the performance of the algorithm further practical guidelines on how to apply the algorithm are also included in the paper

cyber swarm algorithms improving particle swarm optimization using adaptive memory strategies particle swarm optimization pso has emerged as an acclaimed approach for solving complex optimization problems the nature metaphors of flocking birds or schooling fish that originally motivated pso have made the algorithm easy to describe but have also occluded the view of valuable strategies based on other foundations from a complementary perspective scatter search ss and path relinking pr provide an optimization framework based on the assumption that useful information about the global solution is typically contained in solutions that lie on paths from good solutions to other good solutions shared and contrasting principles underlying the pso and the ss pr methods provide a fertile basis for combining them drawing especially on the adaptive memory and responsive strategy elements of ss and pr we create a combination to produce a cyber swarm algorithm that proves more effective than the standard pso 2007 recently established as a leading form of pso applied to the challenge of finding global minima for continuous nonlinear functions the cyber swarm algorithm not only is able to obtain better solutions to a well known set of benchmark functions but also proves more robust under a wide range of experimental conditions

a hybrid method combining continuous tabu search and nelder mead simplex algorithms for the global optimization of multiminima functions abstract tabu search ts is a metaheuristic which proved efficient to solve various combinatorial optimization problems however few works deal with its application to the global minimization of functions depending on continuous variables to perform this task we propose an hybrid method combining tabu search and simplex search ss ts allows to cover widely the solution space to stimulate the search towards solutions far from the current solution and to avoid the risk of trapping into a local minimum ss is used to accelerate the convergence towards a minimum the nelder mead simplex algorithm is a classical very powerful local descent algorithm making no use of the objective function derivatives a simplex is a geometrical figure consisting in n dimensions of n 1 points if any point of a simplex is taken as the origin the n other points define vector directions that span the n dimension vector space through a sequence of elementary geometric transformations reflection contraction and extension the initial simplex moves expands or contracts to select the appropriate transformation the method only uses the values of the function to be optimized at the vertices of the simplex considered after each transformation the current worst vertex is replaced by a better one our algorithm called continuous tabu simplex search ctss implemented in two different forms ctsssingle ctssmultiple is made up of two steps first an adaptation of ts to continuous optimization problems allowing to localize a promising area then intensification within this promising area involving ss the efficiency of ctss is extensively tested by using analytical test functions of which global and local minima are known a comparison is proposed with several variants of tabu search genetic algorithms and simulated annealing ctss is applied to the design of a eddy current sensor aimed at non destructive control

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

direct search methods then and now we discuss direct search methods for unconstrained optimization we give a modern perspective on this classical family of derivative free algorithms focusing on the development of direct search methods during their golden age from 1960 to 1971 we discuss how direct search methods are characterized by the absence of the construction of a model of the objective we then consider a number of the classical direct search methods and discuss what research in the intervening years has uncovered about these algorithms in particular while the original direct search methods were consciously based on straightforward heuristics more recent analysis has shown that in most but not all cases these heuristics actually suffice to ensure global convergence of at least one subsequence of the sequence of iterates to a first order stationary point of the objective function

principles of scatter search scatter search is an evolutionary method that has been successfully applied to hard optimization problems the fundamental concepts and principles of the method were first proposed in the 1970s based on formulations dating back to the 1960s for combining decision rules and problem constraints in contrast to other evolutionary methods like genetic algorithms scatter search is founded on the premise that systematic designs and methods for creating new solutions afford significant benefits beyond those derived from recourse to randomization it uses strategies for search diversification and intensification that have proved effective in a variety of optimization problems this paper provides the main principles and ideas of scatter search and its generalized form path relinking we first describe a basic design to give the reader the tools to create relatively simple implementations more advanced designs derive from the fact that scatter search and path relinking are also intimately related to the tabu search ts metaheuristic and gain additional advantage by making use of ts adaptive memory and associated memory exploiting mechanisms capable of being tailored to particular contexts these and other advanced processes described in the paper facilitate the creation of sophisticated implementations for hard problems that often arise in practical settings due to their flexibility and proven effectiveness scatter search and path relinking can be successfully adapted to tackle optimization problems spanning a wide range of applications and a diverse collection of structures as shown in the papers of this volume

weighted self similar networks under preferential attachment abstract we introduce an abstract evolutionary formalism that generates weighted networks whose growth under stochastic preferential attachment triggers unrestricted weight rearrangements in existing links the class of resulting algorithms for different parameter values includes the barabasi albert and barrat barthelemy vespignani models as special cases we solve the recursions that describe the average growth to derive exact solutions for the expected degree and strength distribution the individual strength and weight development and the joint distribution of neighboring degrees we find that the network exhibits a particular form of self similarity namely every sufficiently interconnected node has on average the same constitution of small degree neighbors as any other node of large degree finally we suggest potential applications in several fields of interest

detection of topological patterns in complex networks correlation profile of the internet abstract a general scheme for detecting and analyzing topological patterns in large complex networks is presented in this scheme the network in question is compared with its properly randomized version that preserves some of its low level topological properties statistically significant deviation of any topological property of a network from this null model likely reflects its design principles and or evolutionary history we illustrate this basic scheme using the example of the correlation profile of the internet quantifying correlations between degrees of its neighboring nodes this profile distinguishes the internet from previously studied molecular networks with a similar scale free degree distribution we finally demonstrate that the clustering in a network is very sensitive to both the degree distribution and its correlation profile and compare the clustering in the internet to the appropriate null model

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

paper on the estimation of transfer functions this paper treats the close conceptual relationships between basic approaches to the estimation of transfer functions of linear systems the classical methods of frequency and spectral analysis are shown to be related to the well known time domain methods of prediction error type via a common empirical transfer function estimate asymptotic properties of the estimates obtained by the respective methods are also described and discussed an important feature that is displayed by this treatment is a frequency domain weighting function that determines the distribution of bias in case the true system cannot be exactly described within the chosen model set the choice of this weighting function is made in terms of noise models for time domain methods the noise model thus has a dual character from the system approximation point of view

grey box modelling and identification using physical knowledge and bayesian techniques abstract advanced control design requires a model that describes process behaviour adequately such a model can be constructed using physical modelling or statistical identification techniques both have their disadvantages physical models are rigorous and thus often expensive to construct while black box model structures are not necessarily compatible with physical reality since both approaches have undeniable merits as well their combination seems to be attractive and rewarding this paper discusses an approach to statistical estimation where a best linearly parametrized dynamic regression model is identified which is also consistent with specified knowledge about process responses such characteristics are forced upon the black box models yielding a grey box model set it will be shown that crucial physical knowledge such as process stability and sign of stationary gains can be translated into linear inequality constraints on the black box model parameters in order to select best estimators in the grey box class a bayesian approach is adopted given a prior distribution associated with the physical knowledge and given the data likelihood a posterior distribution is constructed maximum and average a posteriori estimators are analysed explicit solutions are given for special cases of gaussian likelihood and a prior which is uniformly or piece wise linearly distributed on a linearly constrained grey box model class finally simulation results and an application to a distillation process show the advantage of the contrained estimates under realistic experiment conditions considerable variance reductions at the cost of a somewhat larger bias can be achieved indicating the potential for e g adaptive control applications

finding local optima of high dimensional functions using direct search methods this paper focuses on a subclass of box constrained non linear optimization problems we are particularly concerned with settings where gradient information is unreliable or too costly to calculate and the function evaluations themselves are very costly this encourages the use of derivative free optimization methods and especially a subclass of these referred to as direct search methods the thrust of our investigation is twofold first we implement and evaluate a number of traditional direct search methods according to the premise that they should be suitable as local optimizers when used in a metaheuristic framework second we introduce a new direct search method based on scatter search designed to remedy the lack of a good derivative free method for solving problems of high dimensions our new direct search method has convergence properties comparable to those of existing methods in addition to being able to solve larger problems more effectively

automatic tuning of pid controllers based on transfer function estimation abstract a method for the automatic tuning of pid controllers in a closed loop based on the estimation of a parametric black box transfer function model is proposed the system is excited by generating limit cycle oscillations at two different frequencies which are approximately the crossover frequency and the critical frequency for the feedback loop a discrete parametric transfer function model is estimated from the experimental data important parameters concerning the estimation such as the prefilter cut off frequency and the sampling interval are determined automatically from the experimental data the pid parameters are determined from a constrained optimization in the frequency domain the constraints are classical control system properties such as the maximum amplitudes of the sensitivity and the complementary sensitivity functions given these constraints the pid parameters are determined such that the low frequency amplitude characteristic for the controller is maximized simulation experiments show that the tuning procedure has low sensitivity to disturbances and noise during the tuning experiment

visibility graph approach to exchange rate series abstract by means of a visibility graph we investigate six important exchange rate series it is found that the series convert into scale free and hierarchically structured networks the relationship between the scaling exponents of the degree distributions and the hurst exponents obeys the analytical prediction for fractal brownian motions the visibility graph can be used to obtain reliable values of hurst exponents of the series the characteristics are explained by using the multifractal structures of the series the exchange rate of euro to japanese yen is widely used to evaluate risk and to estimate trends in speculative investments interestingly the hierarchies of the visibility graphs for the exchange rate series of these two currencies are significantly weak compared with that of the other series

percolation on correlated networks we reconsider the problem of percolation on an equilibrium random network with degree degree correlations between nearest neighboring vertices focusing on critical singularities at a percolation threshold we obtain criteria for degree degree correlations to be irrelevant for critical singularities we present examples of networks in which assortative and disassortative mixing leads to unusual percolation properties and new critical exponents

genetic and nelder mead algorithms hybridized for a more accurate global optimization of continuous multiminima functions abstract a hybrid method combining two algorithms is proposed for the global optimization of multiminima functions to localize a promising area likely to contain a global minimum it is necessary to well explore the whole search domain when a promising area is detected the appropriate tools must be used to exploit this area and obtain the optimum as accurately and quickly as possible both tasks are hardly performed through only one method we propose an algorithm using two processes each one devoted to one task global metaheuristics such as simulated annealing tabu search and genetic algorithms gas are efficient to localize the best areas on the other hand local search methods are classically available in particular the hill climbing e g the quasi newton method and the nelder mead simplex search ss therefore we worked out an hybrid method called continuous hybrid algorithm cha performing the exploration with a ga and the exploitation with a nelder mead ss to evaluate the efficiency of cha we implemented a set of benchmark functions and compared our results to the ones supplied by other competitive methods

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

optimization by direct search new perspectives on some classical and modern methods direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because they lacked coherent mathematical analysis nonetheless users remained loyal to these methods most of which were easy to program some of which were reliable in the past fifteen years these methods have seen a revival due in part to the appearance of mathematical analysis as well as to interest in parallel and distributed com puting this review begins by briefly summarizing the history of direct search methods and considering the special properties of problems for which they are well suited our focus then turns to a broad class of methods for which we provide a unifying framework that lends itself to a variety of convergence results the underlying principles allow general ization to handle bound constraints and linear constraints we also discuss extensions to problems with nonlinear constraints

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

degree distribution and scaling in the connecting nearest neighbors model we present a detailed analysis of the connecting nearest neighbors model by vazquez phys rev e 67 056104 2003 we show that the degree distribution follows a power law but the scaling exponent can vary with the parameter setting moreover the correspondence of the growing version of the connecting nearest neighbors model to the particular random walk model and recursive search model is established

enhancing robustness and immunization in geographical networks we find that different geographical structures of networks lead to varied percolation thresholds although these networks may have similar abstract topological structures thus strategies for enhancing robustness and immunization of a geographical network are proposed using the generating function formalism we obtain an explicit form of the percolation threshold q c for networks containing arbitrary order cycles for three cycles the dependence of q c on the clustering coefficients is ascertained the analysis substantiates the validity of the strategies with analytical evidence

adaptive parameter estimation for a constrained low pass system a novel algorithm is presented for adaptive parameter estimation for a constrained low pass butterworth system model the algorithm will estimate the system cutoff frequency and gain online when it is known that the true system has a low pass butterworth structure or some transfer function similar to it and its true order is used the algorithm will lead to a substantial savings in computation and more accurate results than unconstrained algorithms potential applications include filter design and adaptive decision on nyquist rate for systems

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

arma spectral estimation of narrow band processes via model reduction the problem of estimating autoregressive moving average arma models for narrowband processes is considered the following approach is proposed estimate a high order autoregressive ar approximation of the process by model reduction based on a truncated internally balanced realization or optimal hankel norm model reduction reduce the order of this high order ar estimate to find a lower order arma model this algorithm gives arma spectral estimates with excellent resolution properties without using iterative numerical minimization methods as for the maximum likelihood method how to take the narrowband assumption into account in the model reduction step is discussed in detail

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

structural and spectral properties of a family of deterministic recursive trees rigorous solutions as one of the most significant models the uniform recursive tree urt has found many applications in a variety of fields in this paper we study rigorously the structural features and spectral properties of the adjacency matrix for a family of deterministic uniform recursive trees durts that are deterministic versions of urt firstly from the perspective of complex networks we investigate analytically the main structural characteristics of durts and obtain the accurate solutions for these properties which include degree distribution average path length distribution of node betweenness and degree correlations then we determine the complete eigenvalues and their corresponding eigenvectors of the adjacency matrix for durts our research may shed light on a better understanding of the features for urt also the analytical methods used here are capable of being extended to many other deterministic networks making the precise computation of their properties especially the full spectrum characteristics possible

heterogeneous bond percolation on multitype networks with an application to epidemic dynamics considerable attention has been paid in recent years to the use of networks in modeling complex real world systems among the many dynamical processes involving networks propagation processes in which the final state can be obtained by studying the underlying network percolation properties have raised formidable interest in this paper we present a bond percolation model of multitype networks with an arbitrary joint degree distribution that allows heterogeneity in the edge occupation probability as previously demonstrated the multitype approach allows many nontrivial mixing patterns such as assortativity and clustering between nodes we derive a number of useful statistical properties of multitype networks as well as a general phase transition criterion we also demonstrate that a number of previous models based on probability generating functions are special cases of the proposed formalism we further show that the multitype approach by naturally allowing heterogeneity in the bond occupation probability overcomes some of the correlation issues encountered by previous models we illustrate this point in the context of contact network epidemiology

quantifying the error in estimated transfer functions with application to model order selection previous results on estimating errors or error bounds on identified transfer functions have relied on prior assumptions about the noise and the unmodeled dynamics this prior information took the form of parameterized bounding functions or parameterized probability density functions in the time or frequency domain with known parameters it is shown that the parameters that quantify this prior information can themselves be estimated from the data using a maximum likelihood technique this significantly reduces the prior information required to estimate transfer function error bounds the authors illustrate the usefulness of the method with a number of simulation examples how the obtained error bounds can be used for intelligent model order selection that takes into account both measurement noise and under modeling is shown another simulation study compares the method to akaike s well known fpe and aic criteria

some asymptotic properties of multivariable models identified by equation error techniques some interesting properties are derived for simple equation error identification techniques least squares and basic instrumental variable methods applied to a class of linear time invariant time discrete multivariable models the system at hand is not supposed to be contained in the chosen model set assuming that the input is unit variance white noise it is shown that the markov parameters of the system are estimated asymptotically unbiased over a certain interval around t 0

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

the emergence of scale free networks with a seceding mechanism in order to explore further the underlying mechanism of the scale free networks we study stochastic secession as a mechanism for the creation of complex networks in this evolution the network growth incorporates the addition of new links between existing nodes the deleting and rewiring of some existing links and the stochastic secession of nodes to random growing networks with preferential attachment the model yields scale free behavior for the degree distribution furthermore we get the analytical expression of the power law degree distribution with scaling exponent ranges from 1 1 to 9 the analytical expressions are in good agreement with the numerical simulation results

system identification using laguerre models the traditional approach of expanding transfer functions and noise models in the delay operator to obtain linear in the parameters predictor models leads to approximations of very high order in cases of rapid sampling and or dispersion in time constants by using prior information about the time constants of the system more appropriate expansions related to laguerre networks are introduced and analyzed it is shown that the model order can be reduced compared to arx fir ar modeling by using laguerre models furthermore the numerical accuracy of the corresponding linear regression estimation problem is improved by a suitable choice of the laguerre parameter consistency error bounds persistence of excitation conditions and asymptotic statistical properties are investigated this analysis is based on the result that the covariance matrix of the regression vector of a laguerre model has a toeplitz structure

approximating spectral impact of structural perturbations in large networks determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures but also their dynamical behavior such as synchronization and cascading processes on networks here we develop a theory for estimating the change of the largest eigenvalue of the adjacency matrix or the extreme eigenvalues of the graph laplacian when small but arbitrary set of links are added or removed from the network we demonstrate the effectiveness of our approximation schemes using both real and artificial networks showing in particular that we can accurately obtain the spectral ranking of small subgraphs we also propose a local iterative scheme which computes the relative ranking of a subgraph using only the connectivity information of its neighbors within a few links our results may not only contribute to our theoretical understanding of dynamical processes on networks but also lead to practical applications in ranking subgraphs of real complex networks

model sets and parametrizations for identification of multivariable equation error models abstract equation error or linear regression models are known to inherently require the a priori choice for specific signal variables to be considered as regressand and or regressor this implies that a model set should be a priori restricted in some way in order to define an acceptable identification problem in the case of approximate identification i e the system to be modelled is not contained in the model set this restriction acts as a design variable with the identified models being dependent on its specific choice in this paper the necessity of this restriction is quantified by the property of discriminability i e the ability of an identification criterion to distinguish between all the different models in a model set employing a deterministic signal oriented framework several sets of sufficient conditions are derived for model sets to be discriminable by a least squares identification criterion to this end use is made of polynomial model representations in two shift operators although it is of a different nature the problem discussed is shown to be closely related to the problem of constructing identifiable parametrizations for sets of rational transfer functions it is shown that the pseudo canonical or overlapping parametrization of all transfer functions with fixed mcmillan degree constitutes a nonoverlapping set of equation error models that is discriminable by a least squares identification criterion

the susceptible infected recovered model on a euclidean network we consider a susceptible infected recovered sir epidemic model on a euclidean network in one dimension in which nodes at a distance l are connected with probability p l l in addition to nearest neighbors the topology of the network changes as is varied and its effect on the sir model is studied r t the recovered fraction of population up to time t and the total duration of the epidemic are calculated for different values of the infection probabilities q and a threshold behavior is observed for all up to 2 0 above the threshold value q qc the saturation value rsat attains a finite value both rsat and show scaling behavior in a finite system of size n and qc is constant for 0 qc the results are compared to static percolation phenomena and also to mean field results for finite systems discussions on the properties of the euclidean network are made in the light of the present results

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

analysis of generalized pattern searches this paper contains a new convergence analysis for the lewis and torczon generalized pattern search gps class of methods for unconstrained and linearly constrained optimization this analysis is motivated by a desire to understand the successful behavior of the algorithm under hypotheses that are satisfied by many practical problems specifically even if the objective function is discontinuous or extended valued the methods find a limit point with some minimizing properties simple examples show that the strength of the optimality conditions at a limit point depends not only on the algorithm but also on the directions it uses and on the smoothness of the objective at the limit point in question the contribution of this paper is to provide a simple convergence analysis that supplies detail about the relation of optimality conditions to objective smoothness properties and to the defining directions for the algorithm and it gives previous results as corollaries

in and out forests on combinatorial landscapes abstract fitness landscape theory is a mathematical framework for numerical analysis of search algorithms on combinatorial optimization problems we study a representation of fitness landscape as a weighted directed graph we consider out forest and in forest structures in this graph and establish important relationships among the forest structures of a directed graph the spectral properties of the laplacian matrices and the numbers of local optima of the landscape these relationships provide a new approach for computing the numbers of local optima for various problem instances and neighborhood structures

design variables for bias distribution in transfer function estimation estimation of transfer functions of linear systems is one of the most common system identification problems several different design variables chosen by the user for the identification procedure affect the properties of the resulting estimate in this paper it is investigated how the choices of prefilters noise models sampling interval and prediction horizon i e the use of k step ahead prediction methods influence the estimate an important aspect is thai the true system is not assumed to be exactly represented within the chosen model set the estimate will thus be biased it is shown how the distribution of bias in the frequency domain is governed by a weighting function which emphasizes different frequency bands the weighting function in turn is a result of the previously listed design variables it is shown e g thai the common least squares method has a tendency to emphasize high frequencies and that this can be counteracted by prefiltering it is also shown that asymptotically it is only the prediction horizon itself and not how it is split up into sampling interval times number of predicted sampling instants that affects this weighting function

model reductions of high order estimated models the asymptotic ml approach abstract the reduction of order of high order models obtained from an identification experiment is discussed from a statistical point of view the asymptotic maximum likelihood ml approach is defined to reduce the order of an estimated model this approach considers the maximum likelihood criterion given the asymptotic statistics both in the number of data and the order of the estimated model and corresponds to frequency weighted l 2 norm model reduction by using the insight from the asymptotic ml approach an identification algorithm is proposed based on a high order arx estimate and model reduction via a frequency weighted balanced realization the advantage of this algorithm is that iterative minimization methods are not required to find the estimate

the fundamental role of general orthonormal bases in system identification the purpose of this paper is threefold firstly it is to establish that contrary to what might be expected the accuracy of well known and frequently used asymptotic variance results can depend on choices of fixed poles or zeros in the model structure secondly it is to derive new variance expressions that can provide greatly improved accuracy while also making explicit the influence of any fixed poles or zeros this is achieved by employing certain new results on generalized fourier series and the asymptotic properties of toeplitz like matrices in such a way that the new variance expressions presented here encompass pre existing ones as special cases via this latter analysis a new perspective emerges on recent work pertaining to the use of orthonormal basis structures in system identification namely that orthonormal bases are much more than an implementational option offering improved numerical properties in fact they are an intrinsic part of estimation since as shown here orthonormal bases quantify the asymptotic variability of the estimates whether or not they are actually employed in calculating them

modeling of time series arrays by multistep prediction or likelihood methods abstract an estimation theory is provided for the fitting of possibly incorrect invertible short memory models to short or long memory time series or time series arrays by multistep prediction error minimization or gaussian likelihood maximization by array we mean data y t t 1 t t that depend on the number of observations t such as regression or other estimated model residuals or the outputs of time varying filters for example seasonal adjustments our theory only requires the modeled array to have basic properties for a s i p convergence of parameter estimates the array s sample lagged second moments must converge a s i p and its end values y 1 j t and y t j t must be of order less than t 1 2 or an appropriately differenced version of the observed array must have these properties in findley et al ann statist 29 2001 815 broad classes of arrays were shown to have these properties even for the special case of autoregressive moving average models fit to stationary gaussian time series data our result on the convergence of parameter estimates minimizing p step ahead prediction error sums of squares is new

scale free property of directed networks with two intrinsic node weights abstract this paper proposes a network model to understand the scale free property of directed networks the proposed model assigns two intrinsic variables incoming and outgoing weights to every node a directed link is established from node i to node j if the sum of the outgoing weight of node i and the incoming weight of node j exceeds a predetermined threshold the proposed model allows us to know the exact analytical expressions for degree distributions and clustering we analytically find that the in degree and out degree distributions have power law tails and their scaling exponents are controllable within the range 1 the average clustering coefficient of nodes with out degree or in degree n also has a power law tail as a function of n we also find that the scaling exponent of the clustering coefficient depends on the correlation between incoming and outgoing weights

hierarchical coefficient of a multifractal based network abstract the hierarchical property for a general class of networks stands for a power law relation between clustering coefficient c c and connectivity k c c k this relation is empirically verified in several biologic and social networks as well as in random and deterministic network models in special for hierarchical networks in this work we show that the hierarchical property is also present in a lucena network to create a lucena network we use the dual of a multifractal lattice ml the vertices are the sites of the ml and links are established between neighbouring lattices therefore this network is space filling and planar besides a lucena network shows a scale free distribution of connectivity we deduce a relation for the maximal local clustering coefficient c c i max of a vertex i in a planar graph this condition expresses that the number of links among neighbour n of a vertex i is equal to its connectivity k i that means n k i the lucena network fulfils the condition n k i independent of k i and the anisotropy of ml in addition c c max implies the threshold 1 for the hierarchical property for any scale free planar network

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

subspace based methods for the identification of linear time invariant systems subspace based methods for system identification have attracted much attention during the past few years this interest is due to the ability of providing accurate state space models for multivariable linear systems directly from input output data the methods have their origin in classical state space realization theory as developed in the 1960s the main computational tools are the qr and the singular value decompositions here an overview of existing subspace based techniques for system identification is given the methods are grouped into the classes of realization based and direct techniques similarities between different algorithms are pointed out and their applicability is commented upon we also discuss some recent ideas for improving and extending the methods a simulation example is included for comparing different algorithms the subspace based approach is found to perform competitive with respect to prediction error methods provided the system is properly excited

a unifying construction of orthonormal bases for system identification this paper develops a general and very simple construction for complete orthonormal bases for system identification this construction provides a unifying formulation of many previously studied orthonormal bases since the common fir and recently popular laguerre and two parameter kautz model structures are restrictive special cases of the construction presented here however in contrast to these special cases the basis vectors in the unifying construction of this paper can have arbitrary placement of pole position according to the prior information the user wishes to inject results characterizing the completeness of the bases and the accuracy properties of models estimated using the bases are provided

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

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

continuous scatter search an analysis of the integration of some combination methods and improvement strategies scatter search is an evolutionary method that shares with genetic algorithms a well known evolutionary approach the employment of a combination method that combines the features of two parent vectors to form several offspring furthermore it uses improvement strategies to efficiently produce the local tuning of the solutions an important aspect concerning scatter search is the trade off between the exploration abilities of the combination method and the exploitation capacity of the improvement mechanism in this paper we deal with a continuous version of the scatter search which works directly with vectors of real components our objective is to study the balance between the reliability induced by the combination method and the accuracy levels provided by the improvement mechanism in continuous scatter search to do this we analyse two combination methods that may be applied to continuous scatter search 1 the blx a operator which is one of the most effective combination methods for real coded genetic algorithms and 2 the average combination method which is the classical combination method for continuous scatter search we investigate the interrelations that exist between

minimization by random search techniques we give two general convergence proofs for random search algorithms we review the literature and show how our results extend those available for specific variants of the conceptual algorithm studied here we then exploit the convergence results to examine convergence rates and to actually design implementable methods finally we report on some computational experience

multivariate stochastic approximation using a simultaneous perturbation gradient approximation the problem of finding a root of the multivariate gradient equation that arises in function minimization is considered when only noisy measurements of the function are available a stochastic approximation sa algorithm for the general kiefer wolfowitz type is appropriate for estimating the root the paper presents an sa algorithm that is based on a simultaneous perturbation gradient approximation instead of the standard finite difference approximation of keifer wolfowitz type procedures theory and numerical experience indicate that the algorithm can be significantly more efficient than the standard algorithms in large dimensional problems

asymptotic variance expressions for identified black box transfer function models identification of black box transfer function models is considered it is assumed that the transfer function models possess a certain shift property which is satisfied for example by all polynomial type models expressions for the variances of the transfer function estimates are derived that are asymptotic both in the number of observed data and in the model orders the result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance respectively is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additive output noise the factor of proportionality is the ratio of model order to number of data this result is independent of the particular model structure used the result is applied to evaluate the performance degradation due to variance for a number of typical model uses some consequences for input design are also drawn

zero pearson coefficient for strongly correlated growing trees we obtained pearson s coefficient of strongly correlated recursive networks growing by preferential attachment of every new vertex by m edges we found that the pearson coefficient is exactly zero in the infinite network limit for the recursive trees m 1 if the number of connections of new vertices exceeds one mg1 then the pearson coefficient in the infinite networks equals zero only when the degree distribution exponent ensuremath gamma does not exceed 4 we calculated the pearson coefficient for finite networks and observed a slow power law like approach to an infinite network limit our findings indicate that pearson s coefficient strongly depends on size and details of networks which makes this characteristic virtually useless for quantitative comparison of different networks

a control relevant identification strategy for gpc the question of a suitable control relevant identification strategy for a class of long range predictive controllers is addressed it is shown that under certain conditions the best process model for predictive control is that which is estimated using an identification objective function that is a dual of the control objective function the resulting nonlinear least squares calculation is asymptotically equal to a standard recursive least squares with an appropriate model and controller dependent fir data prefilter experimental results demonstrate the validity and practicality of the proposed estimation law

some remarks on the bias distribution analysis of discrete time identification algorithms based on pseudo linear regressions abstract in 1998 a karimi and i d landau published in this journal an article entitled comparison of the closed loop identication methods in terms of bias distribution one of its main purposes was to provide a bias distribution analysis in the frequency domain of closed loop output error identication algorithms that had been recently developed the expressions provided in that paper are only valid for prediction error identification methods pem not for pseudo linear regression plr ones for which we give the correct frequency domain bias analysis both in open and closed loop although plr was initially and is still considered as an approximation of pem we show that it gives better results at high frequencies