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

delocalization transition for the google matrix we study the localization properties of eigenvectors of the google matrix generated both from the world wide web and from the albert barabasi model of networks we establish the emergence of a delocalization phase for the pagerank vector when network parameters are changed for networks with localized pagerank eigenvalues of the matrix in the complex plane with a modulus above a certain threshold correspond to localized eigenfunctions while eigenvalues below this threshold are associated with delocalized relaxation modes we argue that for networks with delocalized pagerank the efficiency of information retrieval by google type search is strongly affected since the pagerank values have no clear hierarchical structure in this case

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

modified subspace algorithms for doa estimation with large arrays this paper proposes the use of a new generalized asymptotic paradigm in order to analyze the performance of subspace based direction of arrival doa estimation in array signal processing applications instead of assuming that the number of samples is high whereas the number of sensors antennas remains fixed the asymptotic situation analyzed herein assumes that both quantities tend to infinity at the same rate this asymptotic situation provides a more accurate description of a potential situation where these two quantities are finite and hence comparable in magnitude it is first shown that both music and ssmusic are inconsistent when the number of antennas sensors increases without bound at the same rate as the sample size this is done by analyzing and deriving closed form expressions for the two corresponding asymptotic cost functions by examining these asymptotic cost functions one can establish the minimum number of samples per antenna needed to resolve closely spaced sources in this asymptotic regime next two alternative estimators are constructed that are strongly consistent in the new asymptotic situation i e they provide consistent doa estimates not only when the number of snapshots goes to infinity but also when the number of sensors antennas increases without bound at the same rate these estimators are inspired by the theory of g estimation and are therefore referred to as g music and g ssmusic respectively simulations show that the proposed algorithms outperform their traditional counterparts in finite sample size situations although they still present certain limitations

indirect dominant mode rejection a solution to low sample support beamforming under conditions of low sample support a low rank solution of the minimum variance distortionless response mvdr equations can yield a higher output signal to interference plus noise ratio sinr than the full rank mvdr beamformer in this paper we investigate several low rank beam forming techniques and we also propose a new beamformer that we refer to as the indirect dominant mode rejection idmr we analyze the degradation in the output sinr caused by residual cross correlations embedded in the sampled covariance matrix due to low sample support the idmr beamformer is based on a parametric estimate of the covariance matrix in which any cross correlation is canceled out simulations reveal that the idmr beamformer yields a dramatic improvement in output sinr relative to the conjugate gradient cg principal component inverse pci and dominant mode rejection dmr beamformers in our investigation of the low rank cg beamformer we address the issue of whether the unity gain constraint in the look direction should be enforced a priori via the use of a blocking matrix or effected a posteriori through simple scaling of the beamforming vector remarkably it is proven that the two methods yield exactly the same low rank beamformer at each and every rank

localizations on complex networks we study the structural characteristics of complex networks using the representative eigenvectors of the adjacent matrix the probability distribution function of the components of the representative eigenvectors are proposed to describe the localization on networks where the euclidean distance is invalid several quantities are used to describe the localization properties of the representative states such as the participation ratio the structural entropy and the probability distribution function of the nearest neighbor level spacings for spectra of complex networks whole cell networks in the real world and the watts strogatz small world and barabasi albert scale free networks are considered the networks have nontrivial localization properties due to the nontrivial topological structures it is found that the ascending order ranked series of the occurrence probabilities at the nodes behave generally multifractally this characteristic can be used as a structural measure of complex networks

on the virtual array concept for higher order array processing for about two decades many fourth order fo array processing methods have been developed for both direction finding and blind identification of non gaussian signals one of the main interests in using fo cumulants only instead of second order so ones in array processing applications relies on the increase of both the effective aperture and the number of sensors of the considered array which eventually introduces the fo virtual array concept presented elsewhere and allows in particular a better resolution and the processing of more sources than sensors to still increase the resolution and the number of sources to be processed from a given array of sensors new families of blind identification source separation and direction finding methods at an order m 2q q spl ges 2 only have been developed recently in this context the purpose of this paper is to provide some important insights into the mechanisms and more particularly to both the resolution and the maximal processing capacity of numerous 2qth order array processing methods whose previous methods are part of by extending the virtual array concept to an arbitrary even order for several arrangements of the data statistics and for arrays with space angular and or polarization diversity

random matrix analysis of complex networks we study complex networks under random matrix theory rmt framework using nearest neighbor and next nearest neighbor spacing distributions we analyze the eigenvalues of the adjacency matrix of various model networks namely random scale free and small world networks these distributions follow the gaussian orthogonal ensemble statistic of rmt to probe long range correlations in the eigenvalues we study spectral rigidity via the ensuremath delta 3 statistic of rmt as well it follows rmt prediction of linear behavior in semilogarithmic scale with the slope being ensuremath sim 1 ensuremath pi 2 random and scale free networks follow rmt prediction for very large scale a small world network follows it for sufficiently large scale but much less than the random and scale free networks

complex elliptically symmetric distributions survey new results and applications complex elliptically symmetric ces distributions have been widely used in various engineering applications for which non gaussian models are needed in this overview circular ces distributions are surveyed some new results are derived and their applications e g in radar and array signal processing are discussed and illustrated with theoretical examples simulations and analysis of real radar data the maximum likelihood ml estimator of the scatter matrix parameter is derived and general conditions for its existence and uniqueness and for convergence of the iterative fixed point algorithm are established specific ml estimators for several ces distributions that are widely used in the signal processing literature are discussed in depth including the complex t distribution k distribution the generalized gaussian distribution and the closely related angular central gaussian distribution a generalization of ml estimators the m estimators of the scatter matrix are also discussed and asymptotic analysis is provided applications of ces distributions and the adaptive signal processors based on ml and m estimators of the scatter matrix are illustrated in radar detection problems and in array signal processing applications for direction of arrival doa estimation and beamforming furthermore experimental validation of the usefulness of ces distributions for modelling real radar data is given

direction finding with partly calibrated uniform linear arrays a new method for direction finding with partly calibrated uniform linear arrays ulas is presented it is based on the conventional estimation of signal parameters via rotational invariance techniques esprit by modeling the imperfections of the ulas as gain and phase uncertainties for a fully calibrated array it reduces to the conventional esprit algorithm moreover the direction of arrivals doas unknown gains and phases of the uncalibrated sensors can be estimated in closed form without performing a spectral search hence it is computationally very attractive the cramer rao bounds crbs of the partly calibrated ulas are also given simulation results show that the root mean squared error rmse performance of the proposed algorithm is better than the conventional methods when the number of uncalibrated sensors is large it also achieves satisfactory performance even at low signal to noise ratios snrs

an adaptive algorithm for separating and tracking multiple directional sources in linear arrays an algorithm for spatially filtering out enhancing and tracking individual directional sources in an adaptive array is proposed and investigated in this algorithm the sources are separated by using an adaptive beamformer whose outputs are processed by using the lms algorithm to track distinct sources individually from the lms weights used the source locations can be estimated whenever significant changes in these are detected the beamformer is updated so that its outputs will be due to different sources in the steady state with this algorithm the problems of look direction errors in look direction constrained arrays and of large signal power in power inversion arrays are eliminated and the enhancement of multiple moving sources becomes a natural process furthermore because the sources are individually tracked and the beamformer is only updated occasionally the algorithm possesses fast tracking behavior and its implementation complexity is comparable to that of beamformer based adaptive arrays using the lms algorithm

spectral properties of the google matrix of the world wide web and other directed networks we study numerically the spectrum and eigenstate properties of the google matrix of various examples of directed networks such as vocabulary networks of dictionaries and university world wide web networks the spectra have gapless structure in the vicinity of the maximal eigenvalue for google damping parameter equal to unity the vocabulary networks have relatively homogeneous spectral density while university networks have pronounced spectral structures which change from one university to another reflecting specific properties of the networks we also determine specific properties of eigenstates of the google matrix including the pagerank the fidelity of the pagerank is proposed as a characterization of its stability

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

a fast squares power inversion array for tracking nonstationary environments this correspondence presents and investigates a fast algorithm tracking of nonstationary environments in power inversion the algorithm is based on the use of iterative least squares techniques and the introduction of an additional gradient vector in the objective function so that both the optimal weight vector and its rate of change are estimated recursively although the algorithm is computationally more complex than conventional least squares methods it has better performance in moving sources as the velocities of the latter are also being estimated

deformed gaussian orthogonal ensemble description of small world networks the study of spectral behavior of networks has gained enthusiasm over the last few years in particular random matrix theory rmt concepts have proven to be useful in discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the brody type can be used in the present paper we analyze the regular to chaotic behavior of small world sw networks using an extension of the gaussian orthogonal ensemble this rmt ensemble coined the deformed gaussian orthogonal ensemble dgoe supplies a natural foundation of the brody formula sw networks follow goe statistics until a certain range of eigenvalue correlations depending upon the strength of random connections we show that for these regimes of sw networks where spectral correlations do not follow goe beyond a certain range dgoe statistics models the correlations very well the analysis performed in this paper proves the utility of the dgoe in network physics as much as it has been useful in other physical systems

steady state analysis of the multistage constant modulus array the multistage constant modulus cm array is a cascade adaptive beamforming system that can recover several narrowband cochannel signals without training we examine its steady state properties at convergence using a stochastic analysis and computer simulations based on a wiener model of convergence for the gradient adaptive algorithms closed form expressions are derived for the cm array and canceller weight vectors as well as the effective source direction vectors at all stages along the cascade system the signal capture and direction finding capabilities of the system are also discussed computer simulations for stationary and fading sources are presented to confirm the theoretical results and to illustrate the rapid convergence behavior of the adaptive algorithms

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

misleading signatures of quantum chaos the main signature of chaos in a quantum system is provided by spectral statistical analysis of the nearest neighbor spacing distribution p s and the spectral rigidity given by the delta 3 l statistic it is shown that some standard unfolding procedures such as local unfolding and gaussian broadening lead to a spurious saturation of delta 3 l that spoils the relationship of this statistic with the regular or chaotic motion of the system this effect can also be misinterpreted as berry s saturation

doa estimation by exploiting the symmetric configuration of uniform linear array a new direction of arrival doa estimation method is proposed for uniform linear array in this paper when both uncorrelated and coherent sources are present the uncorrelated and coherent sources are estimated at two different stages the uncorrelated sources are first estimated using conventional subspace methods and then they are eliminated by exploiting the symmetric configuration of the array finally the remaining coherent sources are estimated by reconstructing a non toeplitz matrix the number of sources resolved by our method can exceed the number of array elements simulation results demonstrate the effectiveness and efficiency of our proposed method

normal mode analysis of spectra of random networks abstract several spectral fluctuation measures of random matrix theory rmt have been applied in the study of spectral properties of networks however the calculation of those statistics requires performing an unfolding procedure which may not be an easy task in this work network spectra are interpreted as time series and we show how their short and long range correlations can be characterized without implementing any previous unfolding in particular we consider three different representations of erd s renyi er random networks standard er networks er networks with random weighted self edges and fully random weighted er networks in each case we apply singular value decomposition svd such that the spectra are decomposed in trend and fluctuation normal modes we obtain that the fluctuation modes exhibit a clear crossover between the poisson and the gaussian orthogonal ensemble statistics when the average degree of er networks changes moreover by using the trend modes we perform a data adaptive unfolding to calculate for comparison purposes traditional fluctuation measures such as the nearest neighbor spacing distribution number variance 2 as well as 3 and n statistics the thorough comparison of rmt short and long range correlation measures make us identify the svd method as a robust tool for characterizing random network spectra

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

random matrix analysis of localization properties of gene coexpression network we analyze gene coexpression network under the random matrix theory framework the nearest neighbor spacing distribution of the adjacency matrix of this network follows gaussian orthogonal statistics of random matrix theory rmt spectral rigidity test follows random matrix prediction for a certain range and deviates afterwards eigenvector analysis of the network using inverse participation ratio suggests that the statistics of bulk of the eigenvalues of network is consistent with those of the real symmetric random matrix whereas few eigenvalues are localized based on these ipr calculations we can divide eigenvalues in three sets a the nondegenerate part that follows rmt b the nondegenerate part at both ends and at intermediate eigenvalues which deviates from rmt and expected to contain information about important nodes in the network c the degenerate part with zero eigenvalue which fluctuates around rmt predicted value we identify nodes corresponding to the dominant modes of the corresponding eigenvectors and analyze their structural properties

spacing ratio characterization of the spectra of directed random networks previous literature on random matrix and network science has traditionally employed measures derived from nearest neighbor level spacing distributions to characterize the eigenvalue statistics of random matrices this approach however depends crucially on eigenvalue unfolding procedures which in many situations represent a major hindrance due to constraints in the calculation especially in the case of complex spectra here we study the spectra of directed networks using the recently introduced ratios between nearest and next to nearest eigenvalue spacing thus circumventing the shortcomings imposed by spectral unfolding specifically we characterize the eigenvalue statistics of directed erd ifmmode mbox h o else h o fi s r enyi er random networks by means of two adjacency matrix representations namely 1 weighted non hermitian random matrices and 2 a transformation on non hermitian adjacency matrices which produces weighted hermitian matrices for both representations we find that the distribution of spacing ratios becomes universal for a fixed average degree in accordance with undirected random networks furthermore by calculating the average spacing ratio as a function of the average degree we show that the spectral statistics of directed er random networks undergoes a transition from poisson to ginibre statistics for model 1 and from poisson to gaussian unitary ensemble statistics for model 2 eigenvector delocalization effects of directed networks are also discussed

coprime sensing via chinese remaindering over quadratic fields part i array designs a coprime antenna array consists of two or more sparse subarrays featuring enhanced degrees of freedom dof and reduced mutual coupling this paper introduces a new class of planar coprime arrays based on the theory of ideal lattices in quadratic number fields a splitting prime p can be decomposed into the product of two distinct prime ideals which give rise to the two sparse subarrays their virtual difference coarray enjoys a quadratic gain in dof thanks to the generalized chinese remainder theorem crt to enlarge the contiguous aperture of the coarray we present hole free symmetric crt arrays with simple closed form expressions the ring of gaussian integers and the ring of eisenstein integers are considered as examples to demonstrate the procedure of designing coprime arrays with eisenstein integers our design yields a difference coarray that is a subset of the hexagonal lattice offering a significant gain in dof over the rectangular lattice given the same physical areas maximization of crt arrays in the aspect of essentialness and the superior performance in the context of angle estimation will be presented in the companion paper part ii

esprit a subspace rotation approach to estimation of parameters of cisoids in noise the application of a subspace invariance approach esprit to the estimation of parameters frequencies and powers of cisoids in noise is described esprit exploits an underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets the new approach has several advantages including improved resolution over pisarenko s technique for harmonic retrieval

distribution of the ratio of consecutive level spacings in random matrix ensembles we derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices this ratio distribution was recently introduced to study spectral properties of many body problems as contrary to the standard level spacing distributions it does not depend on the local density of states our wigner like surmises are shown to be very accurate when compared to numerics and exact calculations in the large matrix size limit quantitative improvements are found through a polynomial expansion examples from a quantum many body lattice model and from zeros of the riemann zeta function are presented

a simple fast adaptive algorithm for broad band null steering arrays a simple algorithm for adaptively steering the broadband null in a two element power inversion array which uses a tapped delay line filter as the processing element is presented and investigated by performing a simple signal transformation the algorithm constrains some of the filter weights so that a variable length delay line is approximated in the maximally flat sense by using the least mean square lms algorithm to adjust the weights controlling the length and gain of the delay line a broadband null is then adaptively formed to track and reject the broadband jammer as studied analytically and by using simulation results the convergence behavior of the algorithm is fast and depends only on the tolerable level of misadjustment noise its implementation complexity is comparable to that of using the lms algorithm directly

universality in the spectral and eigenfunction properties of random networks by the use of extensive numerical simulations we show that the nearest neighbor energy level spacing distribution p s and the entropic eigenfunction localization length of the adjacency matrices of erd s renyi er fully random networks are universal for fixed average degree n and n being the average network connectivity and the network size respectively we also demonstrate that the brody distribution characterizes well p s in the transition from 0 when the vertices in the network are isolated to 1 when the network is fully connected moreover we explore the validity of our findings when relaxing the randomness of our network model and show that in contrast to standard er networks er networks with diagonal disorder also show universality finally we also discuss the spectral and eigenfunction properties of small world networks

spectra of real world graphs beyond the semicircle law results on the spectra of adjacency matrices corresponding to models of real world graphs we find that when the number of links grows as the number of nodes the spectral density of uncorrelated random matrices does not converge to the semicircle law furthermore the spectra of real world graphs have specific features depending on the details of the corresponding models in particular scale free graphs develop a trianglelike spectral density with a power law tail while small world graphs have a complex spectral density consisting of several sharp peaks these and further results indicate that the spectra of correlated graphs represent a practical tool for graph classification and can provide useful insight into the relevant structural properties of real networks

determination of scale invariance in random matrix spectral fluctuations without unfolding we apply the singular value decomposition svd method based on normal mode analysis to decompose the spectra of finite random matrices of standard gaussian ensembles in trend and fluctuation modes we use the fact that the fluctuation modes are scale invariant and follow a power law to characterize the transition between the extreme regular and chaotic cases thereby we quantify the quantum chaos in systems described by random matrix theory in a direct way without performing any previous unfolding procedure and therefore avoiding possible artifacts

consistency and mse performance of music based doa of a single source in white noise with randomly missing data music is a popular algorithm for estimating the direction of arrival doa in array signal processing applications in this paper we analyze the performance of the music algorithm for a single source system in the presence of noisy and missing data when only a random subset of the entries in the data matrix are observed we prove consistency of the doa estimate when signal from a single source is impinging on low coherence arrays and derive an analytic expression for the mean squared error mse performance of music for the case of uniform linear arrays in the large array and relatively large sample setting our analysis is mathematically justified in both the sample rich and deficient regimes the expression for the mse is a simple function of array geometry signal to noise ratio snr the fraction of entries observed and the ratio of the number of sensors to number of snapshots we derive a phase transition threshold which separates a regime where music is consistent from a regime where music is inconsistent this threshold depends upon the snr the probability of observing entries in the data matrix and number of sensors and snapshots in a simple manner which we make explicit

localization transition on complex networks via spectral statistics the spectral statistics of complex networks are numerically studied the features of the anderson metal insulator transition are found to be similar for a wide range of different networks a metal insulator transition as a function of the disorder can be observed for different classes of complex networks for which the average connectivity is small the critical index of the transition corresponds to the mean field expectation when the connectivity is higher the amount of disorder needed to reach a certain degree of localization is proportional to the average connectivity though a precise transition cannot be identified the absence of a clear transition at high connectivity is probably due to the very compact structure of the highly connected networks resulting in a small diameter even for a large number of sites

adaptive zero tracking complemented by lms weight update for guaranteed convergence a low complexity zero tracking algorithm with fast and guaranteed convergence behavior is proposed and investigated the algorithm implements a zero tracking algorithm and a least mean square lms weight update algorithm in parallel with the former adjusting the zeros of the array in a time multiplexed manner to achieve fast asymptotic and tracking behavior while the latter improves the initial transient behavior of the algorithm and guarantees its convergence to the global optimum by comparing their output powers the relative performances of the two component algorithms are monitored and re initialization of one algorithm by the other may occur periodically this gives the algorithm both fast and guaranteed convergence behavior even though the zeros are directly available and the implementation complexity is only two times that for the conventional lms algorithm

adaptive beam forming using a cascade configuration a new technique for adaptive beam forming based on the davies cascade array configuration 11 is presented first of all it is shown that an n element linear array can be reconfigured as a number of subarrays of two elements each this two element array is capable of steering one null in an arbitrary direction while maintaining a desired gain in some other prespecified look direction to adaptively perform this function at any cascade stage the inverse of a 2 2 correlation matrix of the signal vector at a subarray is computed and substituted in the expression for the constrained optimum weight vector similar processing is performed at subsequent stages of the cascade configuration at each stage of adaptation a noise source contributing maximum power at that stage is nulled out simulation studies carried out verify the validity of this approach and demonstrate the fast convergence property of the proposed technique

on necessary conditions for the existence of finite dimensional filters in discrete time abstract under some regularity assumptions we show that if a finite dimensional filter in discrete time exists then the observation prediction and filtering distributions are all of exponential class our results motivated by analogous results in the field of statistics hold for arbitrary finite dimensions of the state and observation spaces as well as of the filter itself

computational and analytical studies of the randic index in erdos renyi models abstract in this work we perform computational and analytical studies of the randic index r g in erdos renyi models g n p characterized by n vertices connected independently with probability p 0 1 first from a detailed scaling analysis we show that r g r g n 2 scales with the product np so we can define three regimes a regime of mostly isolated vertices when 10 r g n 2 then motivated by the scaling of r g we analytically i obtain new relations connecting r g with other topological indices and characterize graphs which are extremal with respect to the relations obtained and ii apply these results in order to obtain inequalities on r g for graphs in erdos renyi models

a two stage method for inverse medium scattering we present a novel numerical method to the time harmonic inverse medium scattering problem of recovering the refractive index from noisy near field scattered data the approach consists of two stages one pruning step of detecting the scatterer support and one resolution enhancing step with nonsmooth mixed regularization the first step is strictly direct and of sampling type and it faithfully detects the scatterer support the second step is an innovative application of nonsmooth mixed regularization and it accurately resolves the scatterer size as well as intensities the nonsmooth model can be efficiently solved by a semi smooth newton type method numerical results for two and three dimensional examples indicate that the new approach is accurate computationally efficient and robust with respect to data noise

when is a sequence of sufficient algebras a filter system abstract a very general formulation was given by van schuppen in 1979 for stochastic dynamic systems sds in terms of algebra families but not in the same generality for the corresponding filter system as usual filters were defined indirectly as sds solving the filtering problem i e the recursive computation of the conditional state distribution adopting a bayesian point of view we are able to establish a connection between statistical notions and discrete time filtering on a measure theoretic level we show that sufficiency alone is not enough to make a sequence of statistics a filter and that the additional condition required is transitivity we conclude that a transitive sequence of sufficient statistics is a sds namely a filter system

random matrix analysis of network laplacians abstract we analyse the eigenvalue fluctuations of the laplacian of various networks under the random matrix theory framework analyses of random networks scale free networks and small world networks show that the nearest neighbor spacing distribution of the laplacian of these networks follow gaussian orthogonal ensemble statistics of the random matrix theory furthermore we study the nearest neighbor spacing distribution as a function of the random connections and find that the transition to the gaussian orthogonal ensemble statistics occurs at the small world transition

performance analysis of spatial smoothing with interpolated arrays the interpolated spatial smoothing algorithm is a computationally efficient method for estimating the directions of arrival doas of signals some of which may be perfectly correlated it extends the spatial smoothing method to arbitrary array geometries a statistical performance analysis of the algorithm is presented closed form expressions for the covariance matrix of the doa estimation errors are derived using a perturbation analysis evaluating these expressions for specific cases and comparing them to the cramer rao lower bound for the doa estimates provides insight into the statistical efficiency of this algorithm the formulas for the error covariance are quite general and can be specialized to provide results for other doa estimation algorithms as well

exponential family state space models based on a conjugate latent process summary this paper introduces non linear and non gaussian state space models with analytic updating recurnions for filtering and prediction this new class of models involves some well known results in the theory of exponential models and of exponential dispersion models and the latent process is defined in such a way that both the filtering and the prediction distributions turn out to be conjugate to the observation distribution at each step the corresponding analytic and inferential properties are investigated and some simple examples are presented

universality in complex networks random matrix analysis we apply random matrix theory to complex networks we show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks namely scale free small world and random networks follow universal gaussian orthogonal ensemble statistics of random matrix theory second we show an analogy between the onset of small world behavior quantified by the structural properties of networks and the transition from poisson to gaussian orthogonal ensemble statistics quantified by brody parameter characterizing a spectral property we also present our analysis for a protein protein interaction network in budding yeast

sensitivity of complex response zeros of linear power inversion arrays in the presence of random amplitude and phase errors this paper investigates the variation of the complex response zeros commonly used for source location purposes of a linear power inversion array with random amplitude and phase errors in particular after deriving the zero variances in terms of the optimal weights and the variances of the amplitude and phase errors a simple guideline relating the zero variances to the number of elements and the amplitude and phase variances is obtained for situations when the sources are well separated and resolvable by the array some simulation results are then presented to verify the theoretical derivations

spectral analysis of deformed random networks we study spectral behavior of sparsely connected random networks under the random matrix framework subnetworks without any connection among them form a network having perfect community structure as connections among the subnetworks are introduced the spacing distribution shows a transition from the poisson statistics to the gaussian orthogonal ensemble statistics of random matrix theory the eigenvalue density distribution shows a transition to the wigner s semicircular behavior for a completely deformed network the range for which spectral rigidity measured by the dyson mehta ensuremath delta 3 statistics follows the gaussian orthogonal ensemble statistics depends upon the deformation of the network from the perfect community structure the spacing distribution is particularly useful to track very slight deformations of the network from a perfect community structure whereas the density distribution and the ensuremath delta 3 statistics remain identical to the undeformed network on the other hand the ensuremath delta 3 statistics is useful for the larger deformation strengths finally we analyze the spectrum of a protein protein interaction network for helicobacter and compare the spectral behavior with those of the model networks

topological versus spectral properties of random geometric graphs in this work we perform a detailed statistical analysis of topological and spectral properties of random geometric graphs rggs a graph model used to study the structure and dynamics of complex systems embedded in a two dimensional space rggs g n l consist of n vertices uniformly and independently distributed on the unit square where two vertices are connected by an edge if their euclidian distance is less than or equal to the connection radius l 0 sqrt 2 to evaluate the topological properties of rggs we chose two well known topological indices the randic index r g and the harmonic index h g we characterize the spectral and eigenvector properties of the corresponding randomly weighted adjacency matrices by the use of random matrix theory measures the ratio between consecutive eigenvalue spacings the inverse participation ratios and the information or shannon entropies s g first we review the scaling properties of the averaged measures topological and spectral on rggs then we show that i the averaged scaled indices r g and h g are highly correlated with the average number of nonisolated vertices v g and ii surprisingly the averaged scaled shannon entropy s g is also highly correlated with v g therefore we suggest that very reliable predictions of eigenvector properties of rggs could be made by computing topological indices

on the spectral unfolding of chaotic and mixed systems abstract random matrix theory rmt provides a framework to study the spectral fluctuations in physical systems rmt is capable of making predictions for the fluctuations only after the removal of the secular properties of the spectrum spectral unfolding procedure is used to separate the local level fluctuations from overall energy dependence of the level separation the unfolding procedure is not unique several studies showed that statistics of long term correlation in the spectrum are very sensitive to the choice of the unfolding function in polynomial unfolding this can give misleading results regarding the chaoticity of quantum systems in this letter we consider the spectra of ordered eigenvalues of large random matrices we show that the main cause behind the reported sensitivity to the unfolding polynomial degree is the inclusion of specific extreme eigenvalue s in the unfolding process

matrix based higher order spectral analysis for three wave coupling processes composite linear and quadratic systems produce three wave coupling when stimulated by random phase input sinusoids due to the nonlinearity of the system the output frequencies are arithmetically related to the input using third order cumulant statistics and their associated bispectrum techniques are devised based on phase insensitive matrix structures for detection and frequency estimation of coupling frequencies the separation of the third order cumulant series into symmetric and skew symmetric portions allows one to exploit their characteristic eigendecompositions for frequency estimation after symmetrization biphases can be easily extracted as coefficients of the cumulant sequence using a generalized eigenvector representation one can relate symmetric and skew symmetric bases by a subspace rotation algorithm biphases can be estimated directly from generalized eigenvalues of the matrix pencil formed by symmetric and skew symmetric matrices the dimensionality of the matrices can be reduced through the use of cumulant projections that yield a slice of the bispectrum the radon transform procedure is related to bispectral processing through an isotropic radial slice volterra filter the compact third order kronecker product matrix formulation and algorithms for coupling frequency estimation can also be converted for use in biphase estimation simulations showing the performance of the above procedures are also presented for both synthetic and biomedical time series

performance analysis of the enhanced minimum variance spatial spectrum estimator the performance of the enhanced minimum variance emv spatial spectrum estimator is studied expressions are presented fur the variance and bias of direction of arrival estimators based on general functions of the covariance matrix and these expressions are then used to study the emv estimator finite data effects and random perturbations on the ideal modeling assumptions are studied separately

crossover in nonstandard random matrix spectral fluctuations without unfolding recently singular value decomposition svd was applied to standard gaussian ensembles of random matrix theory to determine the scale invariance in spectral fluctuations without performing any unfolding procedure here svd is applied directly to the hermite ensemble and to a sparse matrix ensemble decomposing the corresponding spectra in trend and fluctuation modes in correspondence with known results we obtain that fluctuation modes exhibit a crossover between soft and rigid behavior in this way possible artifacts introduced applying unfolding techniques are avoided by using the trend modes we perform data adaptive unfolding and we calculate traditional spectral fluctuation measures additionally ensemble averaged and individual spectrum averaged statistics are calculated consistently within the same basis of normal modes

spectral properties of directed random networks with modular structure we study spectra of directed networks with inhibitory and excitatory couplings we investigate in particular eigenvector localization properties of various model networks for different values of correlation among their entries spectra of random networks with completely uncorrelated entries show a circular distribution with delocalized eigenvectors whereas networks with correlated entries have localized eigenvectors in order to understand the origin of localization we track the spectra as a function of connection probability and directionality as connections are made directed eigenstates start occurring in complex conjugate pairs and the eigenvalue distribution combined with the localization measure shows a rich pattern moreover for a very well distinguished community structure the whole spectrum is localized except few eigenstates at the boundary of the circular distribution as the network deviates from the community structure there is a sudden change in the localization property for a very small value of deformation from the perfect community structure we search for this effect for the whole range of correlation strengths and for different community configurations furthermore we investigate spectral properties of a metabolic network of zebrafish and compare them with those of the model networks

scaling properties of multilayer random networks multilayer networks are widespread in natural and manmade systems key properties of these networks are their spectral and eigenfunction characteristics as they determine the critical properties of many dynamics occurring on top of them here we numerically demonstrate that the normalized localization length ensuremath beta of the eigenfunctions of multilayer random networks follows a simple scaling law given by ensuremath beta x 1 x with x ensuremath gamma b mathrm eff 2 l ensuremath delta ensuremath delta ensuremath sim 1 and b mathrm eff being the effective bandwidth of the adjacency matrix of the network whose size is l the scaling law for ensuremath beta that we validate on real world networks might help to better understand criticality in multilayer networks and to predict the eigenfunction localization properties of them

kalman based estimator for doa estimations we introduce a new kalman based noise subspace estimator combined with the root music for direction of arrival doa estimation of uncorrelated narrow band plane waves impinging on an array of sensors without both a priori knowledge of the number of sources and the inflation method presented by yang and kaveh 1988 we show that the kalman based estimator can approximately estimate the complete noise subspace with small bias for high input signal to noise ratio snr scenario the proposed algorithm needs slightly more computation operations per adaptive cycle than yang and kaveh s lms based algorithm but with much more rapid convergence simulations demonstrate the effectiveness of the proposed algorithm

first order perturbation analysis of singular vectors in singular value decomposition singular value decomposition svd is an important technique in signal processing in the literature the perturbation analysis of svd has been well documented in the context of subspace decomposition the contribution of the signal subspace to the perturbation of the singular vectors that span the signal subspace is often ignored as it is treated as second and higher order terms and thus the first order perturbation is typically given as the column span of the noise subspace in this correspondence we show that not only the noise subspace but also the signal subspace contribute to the first order perturbation of the singular vectors we further show that the contribution of the signal subspace does not impact on the performance analysis of algorithms that rely on the signal subspace for parameter estimation but it affects the analysis of algorithms that depends on the individual basis vectors for the latter we also give a condition under which the contribution of the signal subspace to the perturbation of singular vectors may be ignored in the statistical sense numerical examples are provided to validate our theoretic claims

source localization in a waveguide using polynomial rooting source localization in acoustic waveguides involves a multidimensional search procedure we propose a new algorithm in which the search in the depth direction is replaced by polynomial rooting using the proposed algorithm range and depth estimation by a vertical array requires a 1 d search procedure for a 3 d localization problem i e range depth and direction of arrival doa estimation the algorithm involves a 2 d search procedure consequently the proposed algorithm requires significantly less computation than other methods that are based on a brute force search procedure over the source location parameters in order to evaluate the performance of the algorithm an error analysis is carried out and monte carlo simulations are performed the results are compared with the cramer rao bound crb and to the maximum likelihood ml simulation performance the algorithm is shown to be efficient while being computationally simpler than the ml or the bartlett processors the disadvantage of the algorithm is that its snr threshold occurs in lower snr than in the ml algorithm

unfolding of the spectrum for chaotic and mixed systems abstract random matrix theory rmt is capable of making predictions for the spectral fluctuations of a physical system only after removing the influence of the level density by unfolding the spectra when the level density is known unfolding is done by using the integrated level density to transform the eigenvalues into dimensionless variables with unit mean spacing when it is not known as in most practical cases one usually approximates the level staircase function by a polynomial we here study the effect of unfolding procedure on the spectral fluctuation of two systems for which the level density is known asymptotically the first is a time reversal invariant chaotic system which is modeled in rmt by a gaussian orthogonal ensemble goe the second is the case of chaotic systems in which m quantum numbers remain almost undistorted in the early stage of the stochastic transition the hamiltonian of a system may be represented by a block diagonal matrix with m blocks of the same size in which each block is a goe unfolding is done once by using the asymptotic level densities for the eigenvalues of the m blocks and once by representing the integrated level density in terms of polynomials of different orders we find that the spacing distribution of the eigenvalues shows a little sensitivity to the unfolding method on the other hand the variance of level number 2 l is sensitive to the choice of the unfolding function unfolding that utilizes low order polynomials enhances 2 l relative to the theoretical value while the use of high order polynomial reduces it the optimal value of the order of the unfolding polynomial depends on the dimension of the corresponding ensemble

von neumann entropy and localization delocalization transition of electron states in quantum small world networks the von neumann entropy for an electron in periodic disorder and quasiperiodic quantum small world networks qswn s is studied numerically for the disorder qswn s the derivative of the spectrum averaged von neumann entropy is maximal at a certain density of shortcut links p which can be as a signature of the localization delocalization transition of electron states the transition point p is agreement with that obtained by the level statistics method for the quasiperiodic qswn s it is found that there are two regions of the potential parameter the behaviors of electron states in different regions are similar to that of periodic and disorder qswn s respectively

reduction of variances of source tracking response zeros of power inversion arrays in the presence of random amplitude and phase errors a new technique to reduce the variances of the source tracking response zeros of power inversion arrays in the presence of random amplitude and phase errors is investigated essentially the zero variances are reduced by dividing the original system into several spatially shifted power inversion arrays averaging the weight vectors of these arrays and determining the zeros of the spatially averaged weight vector equations for the optimal averaging weights and the ensuing variance performance are derived and verified by simulation results it is found that the new technique may reduce the zero variance substantially when compared with taking the entire system as a single array

analytical performance assessment of multi dimensional matrix and tensor based esprit type algorithms in this paper we present a generic framework for the asymptotic performance analysis of subspace based parameter estimation schemes it is based on earlier results on an explicit first order expansion of the estimation error in the signal subspace obtained via an svd of the noisy observation matrix we extend these results in a number of aspects firstly we demonstrate that an explicit first order expansion of the higher order svd hosvd based subspace estimate can be derived secondly we show how to obtain explicit first order expansions of the estimation error of arbitrary esprit type algorithms and provide the expressions for r d standard esprit r d unitary esprit r d standard tensor esprit as well as r d unitary tensor esprit thirdly we derive closed form expressions for the mean square error mse and show that they only depend on the second order moments of the noise hence to apply this framework we only need the noise to be zero mean and possess finite second order moments additional assumptions such as gaussianity or circular symmetry are not needed

subspace leakage analysis and improved doa estimation with small sample size classical methods of doa estimation such as the music algorithm are based on estimating the signal and noise subspaces from the sample covariance matrix for a small number of samples such methods are exposed to performance breakdown as the sample covariance matrix can largely deviate from the true covariance matrix in this paper the problem of doa estimation performance breakdown is investigated we consider the structure of the sample covariance matrix and the dynamics of the root music algorithm the performance breakdown in the threshold region is associated with the subspace leakage where some portion of the true signal subspace resides in the estimated noise subspace in this paper the subspace leakage is theoretically derived we also propose a two step method that improves the performance by modifying the sample covariance matrix such that the amount of the subspace leakage is reduced furthermore we introduce a phenomenon named as root swap which occurs in the root music algorithm in the low sample size region and degrades the performance of the doa estimation a new method is then proposed to alleviate this problem numerical examples and simulation results are given for uncorrelated and correlated sources to illustrate the improvement achieved by the proposed methods moreover the proposed algorithms are combined with the pseudo noise resampling method to further improve the performance