synchronization in weighted scale free networks with degree degree correlation abstract we study synchronization phenomena in scale free networks of asymmetrically coupled dynamical systems featuring degree degree correlation in the topology of the connection wiring we show that when the interaction is dominant from the high degree to the low degree or from the low degree to the high degree nodes synchronization is enhanced for assortative or disassortative degree degree correlations

the steiglitz mcbride identification algorithm revisited convergence analysis and accuracy aspects the convergence and accuracy properties of the steiglitz and mcbride identification method are examined the analysis is valid for a sufficiently large number of data it is shown that the method can converge to the true parameter vector only when the additive output noise is white in that case the method is proved to be locally convergent to the true parameters the global convergence properties are also investigated it is pointed out that the method is not always globally convergent some sufficient conditions guaranteeing global convergence are given assuming convergence takes place the estimates are shown to be asymptotically gaussian distributed an explicit expression is given for their asymptotic covariance matrix

brief paper l2 norm performance index of synchronization and lqr control synthesis of complex networks in this paper the synchronizability problem of dynamical networks is addressed where better synchronizability means faster network synchronization with lower vibration the l 2 norm of the error vector e is taken as a performance index to measure this kind of synchronizability for the equilibrium synchronization case it is shown that there is a close relationship between the l 2 norm of the error vector e and the h 2 norm of the transfer function g of the linearized network about the equilibrium point consequently the effect of the network coupling topology on the h 2 norm of the transfer function g is analyzed finally an lqr controller is designed according to the lqr problem in modern control theory which can drive the whole network to its equilibrium point and meanwhile minimize the l 2 norm of the output of the linearized network

on a new adaptive lattice algorithm for recursive filters a new and simplified adaptive algorithm is presented for lattice structured recursive filters implementing the two multiplier form based on itakura and saito a comparison is also presented between the results obtained from this new algorithm and the algorithm introduced recently by parikh ahmed and stearns

texture enhanced histogram equalization using tv rm l 1 image decomposition histogram transformation defines a class of image processing operations that are widely applied in the implementation of data normalization algorithms in this paper we present a new variational approach for image enhancement that is constructed to alleviate the intensity saturation effects that are introduced by standard contrast enhancement ce methods based on histogram equalization in this paper we initially apply total variation tv minimization with a l1 fidelity term to decompose the input image with respect to cartoon and texture components contrary to previous papers that rely solely on the information encompassed in the distribution of the intensity information in this paper the texture information is also employed to emphasize the contribution of the local textural features in the ce process this is achieved by implementing a nonlinear histogram warping ce strategy that is able to maximize the information content in the transformed image our experimental study addresses the ce of a wide variety of image data and comparative evaluations are provided to illustrate that our method produces better results than conventional ce strategies

synchronization in complex dynamical networks with nonsymmetric coupling based on the work of nishikawa and motter who have extended the well known master stability framework to include non diagonalizable cases we develop another extension of the master stability framework to obtain criteria for global synchronization several criteria for global synchronization are provided which generalize some previous results the jordan canonical transformation method is used in stead of the matrix diagonalization method especially we show clearly that the synchronizability of a dynamical network with nonsymmetric coupling is not always characterized by its second largest eigenvalue even though all the eigenvalues of the nonsymmetric coupling matrix are real furthermore the effects of the asymmetry of coupling on synchronizability of networks with different structures are analyzed numerical simulations are also done to illustrate and verify the theoretical results on networks in which each node is a dynamical limit cycle oscillator consisting of a two cell cellular neural network

very robust low complexity lattice filters in this paper a novel lattice filter structure is derived by combining the tapped numerator and injected numerator lattices y c lim on the synthesis of iir digital filters derived from single channel ar lattice network ieee trans acoust speech signal process vol assp 32 no 4 pp 741 749 august 1984 the injector coefficients are optimized for finite wordlength performance while the tapped coefficients synthesize the transfer function of the filters for an n th order digital filter the proposed tapped numerator and injected numerator hybrid lattice structure after optimization has only 2n 1 multipliers it is not only canonic in the number of multipliers but also possesses much improved finite wordlength properties such as very low parameter sensitivity and very uniform signal powers across signal nodes the excellent finite wordlength performance of the proposed structure is demonstrated with a design example and compared with those of traditional structures including several well known lattice structures

image contrast enhancement based on a histogram transformation of local standard deviation the adaptive contrast enhancement ace algorithm which uses contrast gains cgs to adjust the high frequency components of images is a well known technique for medical image processing conventionally the cg is either a constant or inversely proportional to the local standard deviation lsd however it is known that conventional approaches entail noise overenhancement and ringing artifacts in this paper the authors present a new ace algorithm that eliminates these problems first a mathematical model for the lsd distribution is proposed by extending hunt s 1976 image model then the cg is formulated as a function of the lsd the function which is nonlinear is determined by the transformation between the lsd histogram and a desired lsd distribution using the authors formulation it can be shown that conventional aces use linear functions to compute the new cgs it is the proposed nonlinear function that produces an adequate cg resulting in little noise overenhancement and fewer ringing artifacts finally simulations using some x ray images are provided to demonstrate the effectiveness of the the authors new algorithm

enhancing synchronizability of diffusively coupled dynamical networks a survey in this paper we review the literature on enhancing synchronizability of diffusively coupled dynamical networks with identical nodes the last decade has witnessed intensive investigations on the collective behavior over complex networks and synchronization of dynamical systems is the most common form of collective behavior for many applications it is desired that the synchronizability the ability of networks in synchronizing activity of their individual dynamical units is enhanced there are a number of methods for improving the synchronization properties of dynamical networks through structural perturbation in this paper we survey such methods including adding removing nodes and or edges rewiring the links and graph weighting these methods often try to enhance the synchronizability through minimizing the eigenratio of the laplacian matrix of the connection graph a synchronizability measure based on the master stability function formalism we also assess the performance of the methods by numerical simulations on a number of real world networks as well as those generated through models such as preferential attachment watts strogatz and erdos renyi

the number and degree distribution of spanning trees in the tower of hanoi graph the number of spanning trees of a graph is an important invariant related to topological and dynamic properties of the graph such as its reliability communication aspects synchronization and so on however the practical enumeration of spanning trees and the study of their properties remain a challenge particularly for large networks in this paper we study the number and degree distribution of the spanning trees in the hanoi graph we first establish recursion relations between the number of spanning trees and other spanning subgraphs of the hanoi graph from which we find an exact analytical expression for the number of spanning trees of the n disc hanoi graph this result allows the calculation of the spanning tree entropy which is then compared with those for other graphs with the same average degree then we introduce a vertex labeling which allows to find for each vertex of the graph its degree distribution among all possible spanning trees

a new framework for convergence analysis and algorithm development of adaptive iir filters a parameterization of an adaptive infinite impulse response iir filter s poles is developed based on balanced realization theory from this we develop a local approximation of the actual adapted pole parameters in which convergence speed is related to a certain eigenvalue spread this in turn is shown to relate to the hankel singular values of the system to be identified as well as certain coefficient sensitivity functions of the adapted filter the local approximation is not restricted to stationary points at these points however it is equivalent to a hessian approximation with the benefit of decomposing the hessian matrix into terms related to the aforementioned singular values and sensitivity functions the description of the adaptation process by means of the developed approximation leads to a greater understanding of the effects on convergence speed of factors such as the hankel singular values of the system its order the distribution of its poles and the choice of adapted parameters in particular the use of direct form and lattice parameters are compared in detail based on these properties a new adaptive iir algorithm with faster convergence and relatively low computational complexity has recently been proposed which is briefly mentioned results also indicate a potential for variable gain algorithms

predicting the synchronization time in coupled map networks an analytical expression for the synchronization time in coupled map networks is given by means of the expression the synchronization time for any given network can be predicted accurately furthermore for networks in which the distributions of nontrivial eigenvalues of coupling matrices have some unique characteristics analytical results for the minimal synchronization time are given

adaptive iir filtering using parallel form realizations several parallel form adaptive iir infinite impulse response filters are presented including a frequency domain implementation based on the discrete fourier transform and a recursive frequency sampling structure the performance of the frequency domain adaptive iir filter is investigated in a system identification application which includes an analysis of its modeling capabilities and a discussion of the mean square error performance surface computer simulation results are presented to illustrate the robust convergence properties of the adaptive algorithm and to demonstrate the stability of the filter

fast design of multichannel fir least squares filters with optimum lag this paper is mainly concerned with the efficient design of optimum lag fir least squares filters these filters result when the minimization of the total mean square error encompasses a time shift between the input signal and the desired response the solution of this problem leads to a family of normal systems of equations whose associated matrix is the same while the right hand side members are parametrized by the lag ranging within a specified interval the fast algorithm derived here for the determination of the optimum lag filter provides the solutions of the above family of systems by step up step down levinson like order recursions coupled with time updating kalman like relations and offers a recursive error capability as well this is achieved by exploiting the near to toeplitz structure of the matrix and a certain shift invariance property the right hand side members possess finally motivated by the optimum lag problem systems of equations with near to toeplitz parameters are considered and a fast algorithm is developed the proposed schemes find important applications in seismic signal processing system identification economic forecasting etc

analysis of a general recursive prediction error identification algorithm a general class of algorithms for recursive identification of stochastic dynamical systems is studied in this class the discrepancy between the measured output and the output predicted from previous data according to a candidate model the prediction error is minimized over the model set using a stochastic approximation approach it is proved that this class of methods has the same convergence properties as its off line counterparts under mild and general assumptions these assumptions do not for example include stationary conditions or conditions that the true system can be exactly represented within the model set the considered class of methods contains as special cases several well known algorithms other common recursive identification methods like the extended least squares method and the extended kalman filter can be interpreted as approximate prediction error methods with simplified gradient calculations therefore the approach taken here may also serve as a basis for unified description of many recursive identification methods

onset of synchronization in large networks of coupled oscillators we study the transition from incoherence to coherence in large networks of coupled phase oscillators we present various approximations that describe the behavior of an appropriately defined order parameter past the transition and generalize recent results for the critical coupling strength we find that under appropriate conditions the coupling strength at which the transition occurs is determined by the largest eigenvalue of the adjacency matrix we show how with an additional assumption a mean field approximation recently proposed is recovered from our results we test our theory with numerical simulations and find that it describes the transition when our assumptions are satisfied we find that our theory describes the transition well in situations in which the mean field approximation fails we study the finite size effects caused by nodes with small degree and find that they cause the critical coupling strength to increase

brief paper some properties of the output error method the output error identification method is studied in various respects the stationary points of the associated loss function are investigated sufficient conditions for a unique local minimum are given the loss functions can be minimized using a quasilinearization algorithm such an algorithm will give good local convergence it is however shown that global convergence does not always occur the output error method is also compared with some other estimation methods from the accuracy point of view it is proved that a prediction error method will give better accuracy an instrumental variable technique may give better or worse accuracy depending on the actual noise correlation

the number of spanning trees of an infinite family of outerplanar small world and self similar graphs abstract in this paper we give an exact analytical expression for the number of spanning trees of an infinite family of outerplanar small world and self similar graphs this number is an important graph invariant related to different topological and dynamic properties of the graph such as its reliability synchronization capability and diffusion properties the calculation of the number of spanning trees is a demanding and difficult task in particular for large graphs and thus there is much interest in obtaining closed expressions for relevant infinite graph families we have also calculated the spanning tree entropy of the graphs which we have compared with those for graphs with the same average degree

improvement of the fast recursive least squares algorithms via normalization a comparative study this paper deals with the derivation and the properties of fast optimal least squares algorithms and particularly with their normalization it is shown how the well known fast kalman algorithm written in the most general form can be normalized through a purely algebraic point of view leading to the normalized least squares transversal filter derived by cioffi kailath and lev ari from the geometric approach an improved form of the algorithm is presented the different algorithms have been compared from a practical point of view as regards their convergence initialization procedures complexity and numerical properties normalized transversal algorithms are shown to be interesting because of their nice structured form simplicity of conception and improved good numerical behavior

closed loop least mean square time delay estimator an lms closed loop time delay estimator is presented it uses the error between two samples of the incoming signal the difference between the delayed signal and the reference signal passed through a known delay as a performance index for the estimator the lms algorithm adaptively controls the delay so as to minimize the mean square of this error the controlled delay is implemented using surface acoustic wave devices certain design conditions are applied resulting in a unique minimum for the performance surface it is shown that the proposed estimator is unbiased and has a small variance if the input signal occupies most of the system bandwidth in fact the variance depends on the input noise power and the generalized noise to signal power ratio r n 0 r s 0 as well as on the loop gain the analysis performed also gives a bound on the loop gain required for convergence of the estimator and predicts its rate of convergence computer simulation results show good agreement with the theory

enumeration of spanning trees in planar unclustered networks abstract among a variety of subgraphs spanning trees are one of the most important and fundamental categories they are relevant to diverse aspects of networks including reliability transport self organized criticality loop erased random walks and so on in this paper we introduce a family of modular self similar planar networks with zero clustering relevant properties of this family are comparable to those networks associated with technological systems having low clustering like power grids some electronic circuits the internet and some biological systems so it is very significant to research on spanning trees of planar networks however for a large network evaluating the relevant determinant is intractable in this paper we propose a fairly generic linear algorithm for counting the number of spanning trees of a planar network using the algorithm we derive analytically the exact numbers of spanning trees in planar networks our result shows that the computational complexity is o t which is better than that of the matrix tree theorem with o m 2 t 2 where t is the number of steps and m is the girth of the planar network we also obtain the entropy for the spanning trees of a given planar network we find that the entropy of spanning trees in the studied network is small which is in sharp contrast to the previous result for planar networks with the same average degree we also determine an upper bound and a lower bound for the numbers of spanning trees in the family of planar networks by the algorithm as another application of the algorithm we give a formula for the number of spanning trees in an outerplanar network with small world features

synchronization optimal networks obtained using local structure information abstract in this paper the networks with optimal synchronizability are obtained using the local structure information in scale free networks a node will be coupled by its neighbors with maximal degree among the neighbors if and only if the maximal degree is larger than its own degree if the obtained coupled networks are connected they are synchronization optimal networks the connection probability of coupled networks is greatly affected by the average degree which usually increases with the average degree this method could be further generalized by taking into account the degree of next nearest neighbors which will sharply increase the connection probability compared to the other proposed methods that obtain synchronization optimal networks our method uses only local structure information and can hold the structure properties of the original scale free networks to some extent our method may present a useful way to manipulate the synchronizability of real world scale free networks

network synchronization diffusion and the paradox of heterogeneity many complex networks display strong heterogeneity in the degree connectivity distribution heterogeneity in the degree distribution often reduces the average distance between nodes but paradoxically may suppress synchronization in networks of oscillators coupled symmetrically with uniform coupling strength here we offer a solution to this apparent paradox our analysis is partially based on the identification of a diffusive process underlying the communication between oscillators and reveals a striking relation between this process and the condition for the linear stability of the synchronized states we show that for a given degree distribution the maximum synchronizability is achieved when the network of couplings is weighted and directed and the overall cost involved in the couplings is minimum this enhanced synchronizability is solely determined by the mean degree and does not depend on the degree distribution and system size numerical verification of the main results is provided for representative classes of small world and scale free networks

on rayleigh ritz ratios of a generalized laplacian matrix of directed graphs abstract in c w wu algebraic connectivity of directed graphs linear and multilinear algebra in press a generalization of fiedler s notion of algebraic connectivity to directed graphs was presented that inherits many properties of the algebraic connectivity of undirected graphs and has applications to the synchronization of coupled dynamical systems with both constant and time varying coupling however it did not inherit nonnegativity and some of its bounds for combinatorial properties such as maximum directed cut and isoperimetric number are less strict that their undirected counterparts in particular these bounds do not have the corresponding bounds for undirected graphs as limiting cases the purpose of this paper is to present a refinement of this algebraic connectivity which preserve nonnegativity for strongly connected graphs and have bounds which contain the undirected graphs as special cases in particular we study quantities related to a generalized laplacian matrix of directed graphs and obtain bounds on combinatorial properties such as diameter bandwidth and bisection width for general directed graphs finally we give an application to the synchronization of coupled dynamical systems with constant coupling in particular we show that strong enough cooperative coupling will synchronize a network of coupled systems if the underlying directed graph is strongly connected

application of benveniste s convergence results in the study of adaptive iir filtering algorithms it is shown that the weak convergence results of a benveniste et al ieee trans automat contr vol ac 25 p 1042 58 dec 1980 can be used to prove convergence of some adaptive infinite impulse response iir filtering algorithms the association of the algorithms with some ordinary differential equations for constant gains which parallels the theory of l ljung et al 1983 is suitable for constant gain adaptive filtering applications convergence proofs for a prefiltering algorithm for a simple constant gain version of the recursive maximum likelihood algorithm and for the well known simple hyperstable adaptive recursive filter sharf algorithm are given as examples

an iteration method for computing the total number of spanning trees and its applications in graph theory abstract calculating and analyzing the number of spanning trees of graphs network models is an important and interesting research project in wide variety of fields such as mathematics physics theoretical computer science chemistry and so on the number of spanning trees of graphs models displays amounts of information on its structural features and also on some relevant dynamical properties in particular network security random walks and percolation in this paper firstly due to lots of graphs models are built on the basis of various simple and small elements components we provide primarily some helpful network operation such as link operation and merge operation to generate more realistic and complicated graphs models secondly considering reliability of fault tolerance to random faults and of intrusion tolerance to selectively remove attacks synchronization capability and diffusion properties of networks we present an iterative method algorithm for computing the total number of spanning trees as a pellucid example we apply our method to tree space and cycle space notice that it is proved to be indeed a better tool in order to reflect more widely practical meanings we study its applications in graph theory including ladder graph with zero clustering coefficient wheel graph having nonzero clustering coefficient as constituent ingredients of maximal planar graphs in the rest of this paper we make a brief summary that the method described by us can be designed a program algorithm for obtaining easily the exact number of spanning trees of some models

counting spanning trees of a type of generalized farey graphs abstract the farey graph f n is derived from the famous farey sequence and it is a small world network with a connectivity distribution decaying exponentially by using the matrix tree theorem zhang et al 2012 obtained the exact formula of the number of spanning trees of f n in this paper by using the electrical network method we consider a type of generalized farey graphs and give the exact solution for the number of spanning trees of these generalized farey graphs which generalizes some previous results about the farey graphs

synchronization in complex delayed dynamical networks with nonsymmetric coupling abstract a new general complex delayed dynamical network model with nonsymmetric coupling is introduced and then we investigate its synchronization phenomena several synchronization criteria for delay independent and delay dependent synchronization are provided which generalize some previous results the matrix jordan canonical formalization method is used instead of the matrix diagonalization method so in our synchronization criteria the coupling configuration matrix of the network does not required to be diagonalizable and may have complex eigenvalues especially we show clearly that the synchronizability of a delayed dynamical network is not always characterized by the second largest eigenvalue even though all the eigenvalues of the coupling configuration matrix are real furthermore the effects of time delay on synchronizability of networks with unidirectional coupling are studied under some typical network structures the results are illustrated by delayed networks in which each node is a two dimensional limit cycle oscillator system consisting of a two cell cellular neural network numerical simulations show that these networks can realize synchronization with smaller time delay and will lose synchronization when the time delay increase larger than a threshold

tracking properties and steady state performance of rls adaptive filter algorithms adaptive signal processing algorithms derived from ls least squares cost functions are known to converge extremely fast and have excellent capabilities to track an unknown parameter vector this paper treats analytically and experimentally the steady state operation of rls recursive least squares adaptive filters with exponential windows for stationary and nonstationary inputs a new formula for the estimation noise has been derived involving second and fourth order statistics of the filter input as well as the exponential windowing factor and filter length furthermore it is shown that the adaptation process associated with lag effects depends solely on the exponential weighting parameter in addition the calculation of the excess mean square error due to the lag for an assumed markov channel provides the necessary information about tradeoffs between speed of adaptation and steady state error it is also the basis for comparison to the simple lms algorithm in a simple case of channel identification it is shown that the lms and rls adaptive filters have the same tracking behavior finally in the last part we present new rls restart procedures applied to transversal structures for mitigating the disastrous results of the third source of noise namely finite precision arithmetic

a class of vertex edge growth small world network models having scale free self similar and hierarchical characters abstract the problem of uncovering the internal operating function of network models is intriguing demanded and attractive in researches of complex networks notice that in the past two decades a great number of artificial models are built to try to answer the above mentioned task based on the different growth ways these previous models can be divided into two categories one type possessing the preferential attachment follows a power law p k k 2 3 the other has exponential scaling feature p k k however there are no models containing above two kinds of growth ways to be presented even the study of interconnection between these two growth manners in the same model is lacking hence in this paper we construct a class of planar and self similar graphs motivated from a new attachment way vertex edge growth network operation more precisely the couple of both them we report that this model is sparse small world and hierarchical and then not only is scale free feature in our model but also lies the degree parameter 3 242 out the typical range note that we suggest that the coexistence of multiple vertex growth ways will have a prominent effect on the power law parameter and the preferential attachment plays a dominate role on the development of networks over time at the end of this paper we obtain an exact analytical expression for the total number of spanning trees of models and also capture spanning trees entropy which we have compared with those of their corresponding component elements

clustering and the synchronization of oscillator networks by manipulating the clustering coefficient of a network without changing its degree distribution we examine the effect of clustering on the synchronization of phase oscillators on networks with poisson and scale free degree distributions for both types of networks increased clustering hinders global synchronization as the network splits into dynamical clusters that oscillate at different frequencies surprisingly in scale free networks clustering promotes the synchronization of the most connected nodes hubs even though it inhibits global synchronization as a result they show an additional advanced transition instead of a single synchronization threshold this cluster enhanced synchronization of hubs may be relevant to the brain that is scale free and highly clustered

round off error propagation in four generally applicable recursive least squares estimation schemes abstract the numerical robustness of four generally applicable recursive least squares estimation schemes is analysed by means of a theoretical round off propagation study this study highlights a number of practical interesting insights into the widely used recursive least squares schemes these insights have been confirmed in an experimental verification study

maximum likelihood estimation of time varying delay part i this paper presents for the first time the exact theoretical solution to the problem of maximum likelihood ml estimation of time varying delay d t between a random signal s t received at one point in the presence of uncorrelated noise and the time delayed scaled version s t d t of that signal received at another point in the presence of uncorrelated noise the signal is modeled as a sample function of a nonstationary gaussian random process and the observation interval is arbitrary the analysis of this paper represents a generalization of that of knapp and carter 1 who derived the ml estimator for the case that the delay is constant d t d 0 the signal process is stationary and the received processes are observed over the infinite interval we show that the ml estimator of d t can be implemented in any of four canonical forms which in general are time varying systems we also show that our results reduce to a generalized cross correlator for the special case treated in 1

cascade lattice iir adaptive filters the feedback lattice filter forms including the two multiplier form and the normalized form are examined with respect to their relationships to the feedback direct form filter specifically the transformation matrix between the lattice forms and the direct form is derived parameter and state relationships between the lattice forms and the direct form are therefore obtained an iir filter structure the cascade lattice iir structure is constructed based on this structure three iir adaptive filtering algorithms in the two multiplier form can then be developed following the gradient approach the steiglitz mcbride approach and the hyperstability approach convergence of these algorithms is theoretically analyzed using either the ode approach or the hyperstability theorem these algorithms are then simplified into forms computationally as efficient as their corresponding direct form algorithms relationships of the simplified algorithms to the direct form algorithms are also studied which disclose a consistency in algorithm structure regardless of the filter form three normalized lattice algorithms can also be derived from the two multiplier lattice algorithms experimental results show much improved performance of the normalized lattice algorithms over the two multiplier lattice algorithms and the direct form algorithms

spectra of sparse regular graphs with loops we derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary lengths the implications of our results for the structural and dynamical properties of network models are discussed by showing how loops influence the size of the spectral gap and the propensity for synchronization analytical formulas for the spectrum are obtained for specific lengths of the loops

enumeration of spanning trees on contact graphs of disk packings abstract obtaining the number of spanning trees of complex networks is an outstanding challenge since traditional approaches such as calculating the eigenvalues of the matrix and decomposing of spanning subgraphs are awkward or even infeasible for a large scale network the foundation and importance of this quantity relating to some topological and dynamic properties prompt us to explore the role of determinant identities for laplace matrices we introduce the basic electrically equivalent technique to determine an exact analytical expression for the quantity on the contact graph of disk packings which is proposed by zhang et al 2009 our theoretical results shed light on the relationship between the microscopic change of the quantity and topological iteration of the network in particular we compare the entropy of spanning trees on the network with the other two dimensional and three dimensional lattices we show that the new model is a small world scale free network with the maximum entropy so far found in addition our method for employing the electrically equivalent technique to enumerate spanning trees is general and can be easily extended to other complex networks

a structural view of asymptotic convergence speed of adaptive iir filtering algorithms i infinite precision implementation for pt i see ibid vol 41 no 4 p 1493 1517 1993 finite precision fp implementation is the ultimately inevitable reality of all adaptive filters including adaptive infinite impulse response iir filters this paper continues to examine the asymptotic convergence speed of adaptive iir filters of various structures and algorithms including the simple constant gain type and the newton type but under fp implementation a stochastic differential equation sde approach is used in the analysis such an approach not only greatly simplifies the fp analysis which is traditionally very involved algebraically but it also provides valuable information about the first order as well as the second order moments that the latter are not available using the ordinary differential equation ode approach the asymptotic convergence speed as well as the convergent values of the pertinent moments of fp errors are examined in terms of unknown system pole zero locations the adverse effects of lightly damped low frequency ldlf poles resulting from fast sampling on the local transient and convergent behavior of various structures and algorithms are analyzed and compared the new results agree with the existing ones when reduced to the finite impulse response fir case in particular the explosive behavior of pertinent error variances of newton type iir algorithms when the forgetting factor spl lambda 1 is also concluded computer simulation verifies the predicted theoretical results

a variational approach to the radiometric enhancement of digital imagery in this correspondence we present a variational approach to the problem of finding suitable radiometric image transformations that optimize desirable characteristics of the output image histogram this variational approach can be interpreted as the minimization of the cumulative spacing between histogram bars in the least squares sense subject to some weight function most of the common histogram transformation procedures used in remote sensing applications can be deduced from this general variational approach with an appropriate choice of the weight function

a stable and efficient adaptive notch filter for direct frequency estimation we investigate the problem of direct frequency estimation a new adaptive algorithm is developed for constrained pole zero notch filters the basic characteristic of this algorithm is that the notch filter is cascaded and hence purely parametrized by the notching frequencies this makes the algorithm much simpler and hence more efficient and more robust such that the poles and zeros are automatically located on the respective constrained circle no matter if the algorithm is implemented with infinite or finite precision the algorithm is analyzed and compared with some existing algorithms several numerical examples are given as well as the corresponding simulations

a structural view of stability in adaptive iir filters this correspondence deals with the stability issue in adaptive iir filters from a structural view a new condition under which the bounded input bounded output bibo stability of the filters can be ensured is derived based on this result a normal state space realization for second order iir filters is proposed it is shown that the adaptive iir filter realized with such a structure is bibo stable no matter it is implemented with infinite or finite precision this property is very important for real time applications though both the proposed and the normalized lattice based structures are bibo stable the former is simpler and has minimal pole sensitivities two adaptive iir filter structures are developed based on a cascade form of second order filters the first structure is fit for the filters whose poles are all complex and the second one is for the constrained notch filters simulations are given to demonstrate the performance of the proposed structures

tracing the evolution of physics on the backbone of citation networks many innovations are inspired by past ideas in a nontrivial way tracing these origins and identifying scientific branches is crucial for research inspirations in this paper we use citation relations to identify the descendant chart i e the family tree of research papers unlike other spanning trees that focus on cost or distance minimization we make use of the nature of citations and identify the most important parent for each publication leading to a treelike backbone of the citation network measures are introduced to validate the backbone as the descendant chart we show that citation backbones can well characterize the hierarchical and fractal structure of scientific development and lead to an accurate classification of fields and subfields

stabilizing weighted complex networks real networks often consist of local units which interact with each other via asymmetric and heterogeneous connections in this paper the v stability problem is investigated for a class of asymmetric weighted coupled networks with nonidentical node dynamics which includes the unweighted network as a special case pinning control is suggested to stabilize such a coupled network the complicated stabilization problem is reduced to measuring the semi negative property of the characteristic matrix which embodies not only the network topology but also the node self dynamics and the control gains it is found that network stabilizability depends critically on the second largest eigenvalue of the characteristic matrix the smaller the second largest eigenvalue is the more the network is pinning controllable numerical simulations of two representative networks composed of non chaotic systems and chaotic systems respectively are shown for illustration and verification

maximum performance at minimum cost in network synchronization we consider two optimization problems on synchronization of oscillator networks maximization of synchronizability and minimization of synchronization cost we first develop an extension of the well known master stability framework to the case of non diagonalizable laplacian matrices we then show that the solution sets of the two optimization problems coincide and are simultaneously characterized by a simple condition on the laplacian eigenvalues among the optimal networks we identify a subclass of hierarchical networks characterized by the absence of feedback loops and the normalization of inputs we show that most optimal networks are directed and non diagonalizable necessitating the extension of the framework we also show how oriented spanning trees can be used to explicitly and systematically construct optimal networks under network topological constraints our results may provide insights into the evolutionary origin of structures in complex networks for which synchronization plays a significant role

synchronization analysis of delayed complex networks with time varying couplings abstract in this paper a new method is presented to analyze the linear stability of the synchronized state in arbitrarily coupled complex dynamical systems with time delays the coupling configurations are not restricted to the symmetric and irreducible connections or the non negative off diagonal links the stability criteria are obtained by using lyapunov krasovskii functional method and subspace projection method these criteria reveal the relationship between coupling matrices and stability of the dynamical networks

persistence of excitation conditions and the convergence of adaptive schemes in the study of the behavior of adaptive filtering algorithms persistence of excitation of the input process arises as a sufficient condition for convergence and perhaps more importantly for convergence rate of the parameter estimates in this paper the underlying nature of the persistence requirement is presented and discussed relating its normal specification in terms of moment conditions with covariance decays etc to sample path properties deterministic and stochastic persistence conditions and persistence measures are treated as well as persistence conditions for output error equation error and adaptive control schemes

on local synchronisability of nonlinear networked systems with a unit inner coupling matrix and switching topology the local synchronisation of the nonlinear networked systems with switching topology is studied in this article for the special case in which the inner coupling matrix is a unit matrix the critical idea is to convert synchronisation problem to consensus problem such that the switching topology can be dealt with effectively without any extra assumption on the relationship among the involved topologies a novel local synchronous criterion consisting of the maximum lyapunov exponent of nodal self dynamics and the consensus convergent rate of the switching topology is given to illustrate the effectiveness of the analytical results two numerical examples on chaos synchronisation are simulated respectively for the periodic switching case and randomly switching case

b spline signal processing i theory the use of continuous b spline representations for signal processing applications such as interpolation differentiation filtering noise reduction and data compressions is considered the b spline coefficients are obtained through a linear transformation which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering the same property also applies for the indirect b spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines the filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for b splines of any order applications to differentiation filtering smoothing and least squares approximation are examined the extension of such operators for higher dimensional signals such as digital images is considered

synchronization is optimal in nondiagonalizable networks we consider maximization of the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology by extending the master stability formalism to all possible network structures we show that unless some oscillator is linked to all the others maximally synchronizable networks are necessarily nondiagonalizable and can always be obtained by imposing unidirectional information flow with normalized input strengths the results provide insights into hierarchical structures observed in complex networks in which synchronization is important

optimization of synchronization in gradient clustered networks we consider complex clustered networks with a gradient structure where the sizes of the clusters are distributed unevenly such networks describe actual networks in biophysical systems and in technological applications more closely than the previous models theoretical analysis predicts that the network synchronizability can be optimized by the strength of the gradient field but only when the gradient field points from large to small clusters a remarkable finding is that if the gradient field is sufficiently strong synchronizability of the network is mainly determined by the properties of the subnetworks in the two largest clusters these results are verified by numerical eigenvalue analysis and by direct simulation of synchronization dynamics on coupled oscillator networks

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

detecting link failures in complex network processes using remote monitoring abstract we study whether local structural changes in a complex network can be distinguished from passive remote time course measurements of the network s dynamics specifically the detection of link failures in a network synchronization process from noisy measurements at a single network component is considered by phrasing the detection task as a maximum a posteriori probability hypothesis testing problem we are able to obtain conditions under which the detection is 1 improved over the a priori and 2 asymptotically perfect in terms of the network spectrum and graph we find that in the case where the detector has knowledge of the network s state perfect detection is possible under general connectivity conditions regardless of the measurement location when the detector does not have state knowledge a remote signature permits improved but not perfect detection under the same connectivity conditions at its essence detectability is achieved because of the close connection between a network s topology its eigenvalues and local response characteristics

analysis of relative influence of nodes in directed networks many complex networks are described by directed links in such networks a link represents for example the control of one node over the other node or unidirectional information flows some centrality measures are used to determine the relative importance of nodes specifically in directed networks we analyze such a centrality measure called the influence the influence represents the importance of nodes in various dynamics such as synchronization evolutionary dynamics random walk and social dynamics we analytically calculate the influence in various networks including directed multipartite networks and a directed version of the watts strogatz small world network the global properties of networks such as hierarchy and position of shortcuts rather than local properties of the nodes such as the degree are shown to be the chief determinants of the influence of nodes in many cases the developed method is also applicable to the calculation of the pagerank we also numerically show that in a coupled oscillator system the threshold for entrainment by a pacemaker is low when the pacemaker is placed on influential nodes for a type of random network the analytically derived threshold is approximately equal to the inverse of the influence we numerically show that this relationship also holds true in a random scale free network and a neural network

fast recursive least squares transversal filters for adaptive filtering fast transversal filter ftf implementations of recursive least squares rls adaptive filtering algorithms are presented in this paper substantial improvements in transient behavior in comparison to stochastic gradient or lms adaptive algorithms are efficiently achieved by the presented algorithms the true not approximate solution of the rls problem is always obtained by the ftf algorithms even during the critical initialization period first n iterations of the adaptive filter this true solution is recursively calculated at a relatively modest increase in computational requirements in comparison to stochastic gradient algorithms factor of 1 6 to 3 5 depending upon application additionally the fast transversal filter algorithms are shown to offer substantial reductions in computational requirements relative to existing fast rls algorithms such as the fast kalman algorithms of morf ljung and falconer 1976 and the fast ladder lattice algorithms of morf and lee 1977 1981 they are further shown to attain steady state unnormalized or improve upon first n initialization steps the very low computational requirements of the efficient rls solutions of carayannis manolakis and kalouptsidis 1983 finally several efficient procedures are presented by which to ensure the numerical stability of the transversal filter algorithms including the incorporation of soft constraints into the performance criteria internal bounding and rescuing procedures and dynamic range increasing square root normalized variations of the transversal filters

abnormal synchronizing path of delay coupled chaotic oscillators on the edge of stability abstract in this paper the transition of synchronizing path of delay coupled chaotic oscillators in a scale free network is highlighted mainly through the critical transmission delay makes chaotic oscillators be coupled on the edge of stability we find that the transition of synchronizing path is abnormal which is characterized by the following evidences a synchronization process starts with low degree rather than high degree ones b the high degree nodes do not undertake the role of hub c the synchronized subnetworks show a poor small world property as a result of hubs absence d the clustering synchronization behavior emerges even community structure is absent in the scale free network this abnormal synchronizing path suggests that the diverse synchronization behaviors occur in the same topology which implies that the relationship between dynamics and structure of network is much more complicated than the common sense that the structure is the foundation of dynamics moreover it also reveals the potential connection from the transition of synchronization behavior to disorder in real complex networks e g alzheimer disease

a matrix factorization based structure for digital filters in this correspondence a novel digital filter structure is derived using matrix factorization this structure called the lcw structure is an improved version of the so called lgs structure proposed by li gevers and sun ldquoperformance analysis of a new structure for digital filter implementation rdquo ieee transactions on circuits and systems i vol 47 no 4 pp 474 482 april 2000 for a digital filter of order this new structure requires 4n 1 multiplications and 4n 1 additions for computing one filter output sample instead of 7n 3 and 6n 3 respectively which are needed for the lgs structure an expression of the roundoff noise gain is derived for the lcw structure design examples are presented to demonstrate the behavior of this structure and to compare with several well known digital filter structures in terms of minimizing roundoff noise and implementation efficiency

effects of degree correlation on the controllability of networks abstract in this paper we investigate the effects of degree correlation on the controllability of undirected networks with different degree mixing patterns based on simulation analysis considering random pinning max degree pinning and mix degree pinning some relevance factors on controllability such as the control gain and the number of pinned nodes are discussed in detail it is found that disassortative mixing enhances the network controllability contrast to assortative mixing to which the network controllability is sensible furthermore too large or too low value of the feedback gain can reduce the controllability from the viewpoint of practical application mix degree pinning strategy is suggested in assortative network while in disassortative network max degree pinning scheme is better than random pinning

adaptive algorithms for joint time delay estimation and iir filtering a new class of gradient based algorithms for joint adaptive time delay estimation and iir filtering for the recursive identification of systems with long pure delays is introduced the algorithms update an adaptive delay estimate and the coefficients of an iir filter using familiar gradient descent methods in addition interpolation of the input sequence is used to obtain delays that are not constrained to integer numbers of samples three algorithms using a direct form filter parametrization and one using a normalized lattice filter are derived and computer simulations are used to demonstrate their convergence and tracking properties

choosing effective controlled nodes for scale free network synchronization abstract previous studies concerning pinning control of complex network synchronization have very often demonstrated that in an unweighted symmetrical scale free network controlling the high degree nodes is more efficient than controlling randomly chosen ones due to the heterogeneity of the node degree or edge connection distribution of the scale free network small degree nodes have relatively high probabilities of being chosen at random but their control has less influence on the other nodes through the network this raises the question of whether or not controlling the high degree nodes is always better than controlling the small ones in scale free networks our answer to this is yes and no in this study we carry out extensive numerical simulations to show that in an unweighted symmetrical barabasi albert scale free network when the portion of controlled nodes is relatively large controlling the small nodes becomes better than controlling the big nodes and controlling randomly chosen nodes has approximately the same effect as controlling the big ones however we also show that for normalized weighted scale free networks controlling the big nodes is in fact always better than controlling the small ones

joint time delay estimation and adaptive recursive least squares filtering a general estimation model is defined in which two observations are available a noisy and a noise filtered and delayed version of the transmitted signal the delay and the filter must be estimated the joint estimator is composed of an adaptive delay element operating in conjunction with an adaptive transversal filter the delay is updated using a form of derivative with respect to the delay of the sum of squared errors the adaptive delay is limited to integer values and is defined as the lag the lag value is computed and updated so that the optimum least squares solution is attained the joint algorithm is obtained by combining the lag update relations with a version of the fast transversal filter rls algorithm simulations show that both stationary and time varying delays are effectively tracked and that the adaptive filter properly estimates the reference filter impulse response

lattice form adaptive infinite impulse response filtering algorithm for active noise control in some situations of active noise control infinite impulse response iir filters are more suitable than finite impulse response fir filters owing to the poles in the transfer function a number of algorithms have been derived for applying iir filters in active noise control however most of them use the direct form iir filter structure which faces the difficulties of checking stability and relatively slow convergence speed for noise composed of narrow band components with large power disparity to overcome these difficulties along with using the direct form iir filters a new adaptive algorithm is proposed in this paper which uses and updates the lattice form adaptive iir filter in an active noise control system full mathematical derivations of the proposed algorithm are presented and the comparison between the proposed algorithm and the commonly used filtered u lms and filtered v lms algorithms shows the superiority of the proposed algorithm

stable and efficient lattice algorithms for adaptive iir filtering previous attempts at applying lattice structures to adaptive infinite impulse response iir filtering have met with gradient computations of o n sup 2 complexity to overcome this computational burden two new lattice based algorithms are proposed for adaptive iir filtering and system identification with both algorithms of o n complexity the first algorithm is a reinterpretation of the steiglitz mcbride method 1965 while the second is a variation on the output error method state space models are employed to make the derivations transparent and the methods can be extended to other parameterizations if desired the set of possible stationary points of the algorithms is shown to be consistent with the convergent points obtained from the direct form versions of the steiglitz mcbride and output error methods whose properties are well studied the derived algorithms are as computationally efficient as existing direct form based algorithms while overcoming the stability problems associated with time varying direct form filters

rational subspace estimation using adaptive lossless filters rational models have been studied as a tractable attempt to account for frequency dependencies using a finite parameter description in this context the following problem is addressed given time domain measurements estimate rational orthonormal spanning vectors for the signal and noise subspaces it is shown that the problem can be rephrased as adapting a lossless transfer matrix so as to maximize the power split between two sets of output bins an efficient and numerically robust adaptive filtering algorithm is derived for lossless multivariable lattice filters and the system can be programmed in real time using cordic processors the adaptive filter equations are consistent with the proper subspace identification if the subspace filter satisfies a sufficient order condition in under modeled scenarios the stable stationary points are characterized by a minimized rayleigh quotient which leads to good subspace fits the proposed adaptive filter makes real time rational subspace estimation an accessible alternative to computationally expensive offline techniques

exact maximum likelihood time delay estimation for short observation intervals an exact solution is presented to the problem of maximum likelihood time delay estimation for a gaussian source signal observed at two different locations in the presence of additive spatially uncorrelated gaussian white noise the solution is valid for arbitrarily small observation intervals that is the assumption t tau sub c mod d mod made in the derivation of the conventional asymptotic maximum likelihood aml time delay estimator where tau sub c is the correlation time of the various random processes involved and d is the differential time delay is relaxed the resulting exact maximum likelihood eml instrumentation is shown to consist of a finite time delay and sum beamformer followed by a quadratic postprocessor based on the eigenvalues and eigenfunctions of a one dimensional integral equation with nonconstant weight the solution of this integral equation is obtained for the case of stationary signals with rational power spectral densities finally the performance of the eml and aml estimators is compared by means of computer simulations

a mildly weaker sufficient condition in iir adaptive filtering the cross covariance matrix of two stable autoregressive ar sequences is considered a mildly weaker condition is identified that ensures the nonsingularity of this matrix as one consequence of this result a weaker sufficient condition is obtained that would guarantee the unimodality of the mean square output error surface of an iir adaptive filter with white noise excitation

stochastic synchronization in blinking networks of chaotic maps in this paper we analyze stochastic synchronization of coupled chaotic maps over blinking networks composed of a pristine static network and stochastic on off couplings between any pair of nodes we focus on mean square linear stability of the synchronized state by analyzing the time evolution of the second moment of the variation transverse to the synchronization manifold by projecting the variational equations on the eigenvectors of a higher order state matrix describing this variational dynamics we establish a necessary and sufficient condition for stochastic synchronization based on the largest lyapunov exponent of the map and the spectral radius of such matrix this condition is further simplified by computing closed form results for the spectral properties of the moments of the graph laplacian associated to the intermittent coupling and using classical eigenvalue bounds we illustrate the main results through simulations on synchronization of chaotic henon maps