sparsity cognizant total least squares for perturbed compressive sampling solving linear regression problems based on the total least squares tls criterion has well documented merits in various applications where perturbations appear both in the data vector as well as in the regression matrix however existing tls approaches do not account for sparsity possibly present in the unknown vector of regression coefficients on the other hand sparsity is the key attribute exploited by modern compressive sampling and variable selection approaches to linear regression which include noise in the data but do not account for perturbations in the regression matrix the present paper fills this gap by formulating and solving regularized tls optimization problems under sparsity constraints near optimum and reduced complexity suboptimum sparse s tls algorithms are developed to address the perturbed compressive sampling and the related dictionary learning challenge when there is a mismatch between the true and adopted bases over which the unknown vector is sparse the novel s tls schemes also allow for perturbations in the regression matrix of the least absolute selection and shrinkage selection operator lasso and endow tls approaches with ability to cope with sparse under determined errors in variables models interesting generalizations can further exploit prior knowledge on the perturbations to obtain novel weighted and structured s tls solvers analysis and simulations demonstrate the practical impact of s tls in calibrating the mismatch effects of contemporary grid based approaches to cognitive radio sensing and robust direction of arrival estimation using antenna arrays

integral representation for the dimensionally renormalized feynman amplitude a compact convergent integral representation for dimensionally renormalized feynman amplitudes is explicitly constructed the subtracted integrand is expressed as a distribution in the schwinger parametric space and is obtained by applying upon the bare integrand a new subtraction operatorr which respects zimmermann s forest structure

on a backward parabolic problem with local lipschitz source abstract we consider the regularization of the backward in time problem for a nonlinear parabolic equation in the form u t a u t f u t t u 1 where a is a positive self adjoint unbounded operator and f is a local lipschitz function as known it is ill posed and occurs in applied mathematics e g in neurophysiological modeling of large nerve cell systems with action potential f in mathematical biology a new version of quasi reversibility method is described we show that the regularized problem with a regularization parameter 0 is well posed and that its solution u t converges on 0 1 to the exact solution u t as 0 these results extend some earlier works on the nonlinear backward problem

investigation of the forest fire model on a small world network it is shown that the forest fire model of bak et al run on a square lattice network with additional long range interactions in the spirit of a small world network results in a scale free system reminiscent of self organized criticality without recourse to fine tuning as the number of these long range interactions is increased the cluster size distribution exponent is found to decrease in magnitude as the small world regime is entered indicating a change in its universality class it is suggested that such a model could have applicability in the study of disease spreading in human populations

detecting the number of clusters in n way probabilistic clustering recently there has been a growing interest in multiway probabilistic clustering some efficient algorithms have been developed for this problem however not much attention has been paid on how to detect the number of clusters for the general n way clustering n 2 to fill this gap this problem is investigated based on n way algebraic theory in this paper a simple yet efficient detection method is proposed by eigenvalue decomposition evd which is easy to implement we justify this method in addition its effectiveness is demonstrated by the experiments on both simulated and real world data sets

parallel factor analysis in sensor array processing this paper links multiple invariance sensor array processing mi sap to parallel factor parafac analysis which is a tool rooted in psychometrics and chemometrics parafac is a common name for low rank decomposition of three and higher way arrays this link facilitates the derivation of powerful identifiability results for mi sap shows that the uniqueness of single and multiple invariance esprit stems from uniqueness of low rank decomposition of three way arrays and allows tapping on the available expertise for fitting the parafac model the results are applicable to both data domain and subspace mi sap formulations the paper also includes a constructive uniqueness proof for a special parafac model

forest fire model with immune trees abstract we present a generalization of the forest fire model of p bak et al by including the immunity g which is the probability that a tree is not ignited although one of its neighbors is burning when g reaches a critical value gc p which depends on the tree growth rate p the fire cannot survive any more i e a continuous phase transition takes place from a steady state with fire to a steady state without fire we present results of computer simulations and explain them by analytic calculations the fire spreading at the phase transition represents a new type of percolation which is called fluctuating site percolation

higher order svd based subspace estimation to improve the parameter estimation accuracy in multidimensional harmonic retrieval problems multidimensional harmonic retrieval problems are encountered in a variety of signal processing applications including radar sonar communications medical imaging and the estimation of the parameters of the dominant multipath components from mimo channel measurements r dimensional subspace based methods such as r d unitary esprit r d rare or r d music are frequently used for this task since the measurement data is multidimensional current approaches require stacking the dimensions into one highly structured matrix however in the conventional subspace estimation step e g via an svd of the latter matrix this structure is not exploited in this paper we define a measurement tensor and estimate the signal subspace through a higher order svd this allows us to exploit the structure inherent in the measurement data already in the first step of the algorithm which leads to better estimates of the signal subspace we show how the concepts of forward backward averaging and the mapping of centro hermitian matrices to real valued matrices of the same size can be extended to tensors as examples we develop the r d standard tensor esprit and the r d unitary tensor esprit algorithms however these new concepts can be applied to any multidimensional subspace based parameter estimation scheme significant improvements of the resulting parameter estimation accuracy are achieved if there is at least one of the r dimensions which possesses a number of sensors that is larger than the number of sources this can already be observed in the two dimensional case

self organized criticality in a forest fire model a forest fire model is introduced which contains a lightning probability f this leads to a self organized critical state in the limit f 0 provided that the time scales of free growth and burning down of forest clusters are separated we derive scaling laws and calculate all critical exponents the values of the critical exponents are confirmed by computer simulations for a two dimensional system there is evidence that the forest density in the critical state assumes its minimum possible value i e that energy dissipation is maximum

coarrays music and the cramer rao bound sparse linear arrays such as coprime arrays and nested arrays have the attractive capability of providing enhanced degrees of freedom by exploiting the coarray structure an augmented sample covariance matrix can be constructed and mutiple signal classification music can be applied to identify more sources than the number of sensors while such a music algorithm works quite well its performance has not been theoretically analyzed in this paper we derive a simplified asymptotic mean square error mse expression for the music algorithm applied to the coarray model which is applicable even if the source number exceeds the sensor number we show that the directly augmented sample covariance matrix and the spatial smoothed sample covariance matrix yield the same asymptotic mse for music we also show that when there are more sources than the number of sensors the mse converges to a positive value instead of zero when the signal to noise ratio snr goes to infinity this finding explains the saturation behavior of the coarray based music algorithms in the high snr region observed in previous studies finally we derive the cramer rao bound for sparse linear arrays and conduct a numerical study of the statistical efficiency of the coarray based estimator experimental results verify theoretical derivations and reveal the complex efficiency pattern of coarray based music algorithms

calibrating nested sensor arrays with model errors we consider the problem of direction of arrival doa estimation based on a nonuniform linear nested array which is known to provide o n 2 degrees of freedom dofs using only n sensors both subspace based and sparsity based algorithms require certain modeling assumptions e g exactly known array geometry including sensor gain and phase in practice however the actual sensor gain and phase are often perturbed from their nominal values which disrupts the existing doa estimation algorithms in this paper we investigate the self calibration problem for perturbed nested arrays proposing corresponding robust algorithms to estimate both the model errors and the doas the partial toeplitz structure of the covariance matrix is employed to estimate the gain errors and the sparse total least squares stls is used to deal with the phase error issue in addition we provide the cramer rao bound crb to analyze the robustness of the estimation performance of the proposed approaches furthermore we extend the calibration strategies to general nonuniform linear arrays numerical examples are provided to verify the effectiveness of the proposed strategies

on a self organized critical forest fire model the author studies a forest fire model introduced in a paper by drossel and schwabl 1992 by means of simulations with high statistics and very close to the critical point in this way he can correct some statements made in that paper in particular he finds that the critical exponents are not the classical ones proposed by drossel and schwabl in spite of scaling laws with anomalous exponents the typical states of the system are not critical in the sense of being marginally stable locally

regularization and convergence for ill posed backward evolution equations in banach spaces abstract this work is concerned with a mathematical study of ill posed backward evolution equations associated with densely defined linear differential operators in banach spaces a general approach is presented to investigate the convergence and stability of a class of regularized solutions for ill posed backward evolution equations associated with sectorial or half strip operators generalized concepts of qualification pairs and index functions are introduced to characterize the explicit convergence rates of the concerned regularized solutions applications of our results to general backward evolution equations are also investigated

dynamics of driven interfaces near isotropic percolation transition we consider the dynamics and kinetic roughening of interfaces embedded in uniformly random media near percolation treshold in particular we study simple discrete forest fire lattice models through monte carlo simulations in two and three spatial dimensions an interface generated in the models is found to display complex behavior away from the percolation transition the interface is self affine with asymptotic dynamics consistent with the kardar parisi zhang universality class however in the vicinity of the percolation transition there is a different behavior at earlier times by scaling arguments we show that the global scaling exponents associated with the kinetic roughening of the interface can be obtained from the properties of the underlying percolation cluster our numerical results are in good agreement with theory however we demonstrate that at the depinning transition the interface as defined in the models is no longer self affine finally we compare these results with those obtained from a more realistic reaction diffusion model of slow combustion s1063 651x 98 08708 x

on the behavior of information theoretic criteria for model order selection the akaike 1974 information criterion aic and the minimum description length mdl are two well known criteria for model order selection in the additive white noise case our aim is to study the influence on their behavior of a large gap between the signal and the noise eigenvalues and of the noise eigenvalue dispersion our results are mostly qualitative and serve to explain the behavior of the aic and the mdl in some cases of great practical importance we show that when the noise eigenvalues are not clustered sufficiently closely then the aic and the mdl may lead to overmodeling by ignoring an arbitrarily large gap between the signal and the noise eigenvalues for fixed number of data samples overmodeling becomes more likely for increasing the dispersion of the noise eigenvalues for fixed dispersion overmodeling becomes more likely for increasing the number of data samples undermodeling may happen in the cases where the signal and the noise eigenvalues are not well separated and the noise eigenvalues are clustered sufficiently closely we illustrate our results by using simulations from the effective channel order determination area

improved source number detection and direction estimation with nested arrays and ulas using jackknifing we consider the problem of source number detection and direction of arrival doa estimation based on uniform linear arrays ulas and the newly proposed nested arrays a ula with n sensors can detect at most n 1 sources whereas a nested array provides o n2 degrees of freedom with o n sensors enabling us to detect k sources with sensors in order to make full use of the available limited valuable data we propose a novel strategy which is inspired by the jackknifing resampling method exploiting numerous iterations of subsets of the whole data set this strategy greatly improves the results of the existing source number detection and doa estimation methods with the assumption that the subsets of the data set contain enough information we theoretically prove that the improvement of detection or estimation performance compared with the original performance without jackknifing is guaranteed when the detection or estimation accuracy is greater than or equal to 50 numerical simulations demonstrate the superiority of our strategy when applied to source number detection and doa estimation both for ulas and nested arrays

nested vector sensor array processing via tensor modeling we propose a new class of nested vector sensor arrays which is capable of significantly increasing the degrees of freedom dof this is not a simple extension of the nested scalar sensor array but a novel signal model the structure is obtained by systematically nesting two or more uniform linear arrays with vector sensors by using one component s information of the interspectral tensor which is equivalent to the higher dimensional second order statistics of the received data the proposed nested vector sensor array can provide o n2 dof with only n physical sensors to utilize the increased dof a novel spatial smoothing approach is proposed which needs multilinear algebra in order to preserve the data structure and avoid reorganization thus the data is stored in a higher order tensor both the signal model of the nested vector sensor array and the signal processing strategies which include spatial smoothing source number detection and direction of arrival doa estimation are developed in the multidimensional sense based on the analytical results we consider two main applications electromagnetic em vector sensors and acoustic vector sensors the effectiveness of the proposed methods is verified through numerical examples

tensor decompositions and applications this survey provides an overview of higher order tensor decompositions their applications and available software a tensor is a multidimensional or n way array decompositions of higher order tensors i e n way arrays with n geq 3 have applications in psycho metrics chemometrics signal processing numerical linear algebra computer vision numerical analysis data mining neuroscience graph analysis and elsewhere two particular tensor decompositions can be considered to be higher order extensions of the matrix singular value decomposition candecomp parafac cp decomposes a tensor as a sum of rank one tensors and the tucker decomposition is a higher order form of principal component analysis there are many other tensor decompositions including indscal parafac2 candelinc dedicom and paratuck2 as well as nonnegative variants of all of the above the n way toolbox tensor toolbox and multilinear engine are examples of software packages for working with tensors

spreading of percolation in three and four dimensions the authors present monte carlo simulations of the spreading of bond percolation on three and four dimensional simple hyper cubic lattices the algorithm is the same as that applied previously in two dimensions with the spreading proceeding from a hyperplane they find the spreading dimension to be d 1 82 or 0 02 three dimensional and d 1 88 or 0 03 four dimensional also they obtain values of the percolation probability and of the static exponents with errors at least comparable to the best values from the literature

formation of space time structure in a forest fire model we present a general stochastic forest fire model which shows a variety of different structures depending on the parameter values the model contains three possible states per site tree burning tree empty site and three parameters tree growth probability p lightning probability f and immunity g we review analytic and computer simulation results for a quasideterministic state with spiral shaped fire fronts for a percolation like phase transition and a self organized critical state possible applications to excitable systems are discussed

detection of the number of coherent signals by the mdl principle an approach is presented to the problem of detecting the number of sources impinging on a passive sensor array that is based on j rissanen s 1983 minimum description length mdl principle the approach is applicable to any type of sources including the case of sources which are fully correlated referred to as the coherent signals case two slightly different detection criteria are derived both requiring the estimation of the locations of the sources the first is tailored to the detection problem per se whereas the second is tailored to the combined detection estimation problem consistency of the two criteria is proved and their performance is demonstrated by computer simulations

transmit array interpolation for doa estimation via tensor decomposition in 2 d mimo radar in this paper we propose a two dimensional joint transmit array interpolation and beamspace design for planar array mono static multiple input multiple output radar for direction of arrival doa estimation via tensor modeling our underlying idea is to map the transmit array to a desired array and suppress the transmit power outside the spatial sector of interest in doing so the signal to noise ratio is improved at the receive array then we fold the received data along each dimension into a tensorial structure and apply tensor based methods to obtain doa estimates in addition we derive a closed form expression for doa estimation bias caused by interpolation errors and argue for using a specially designed look up table to compensate for the bias the corresponding cramer rao bound crb is also derived simulation results are provided to show the performance of the proposed method and compare its performance to crb

invasion percolation a new form of percolation theory a new kind of percolation problem is described which differs from ordinary percolation theory in that it automatically finds the critical points of the system the model is motivated by the problem of one fluid displacing another from a porous medium under the action of capillary forces but in principle it may be applied to any kind of invasion process which proceeds along a path at least resistance the name invasion percolation is proposed for this new process similarities to and differences from ordinary percolation theory are discussed

spreading analysis and finite size scaling study of the critical behavior of a forest fire model with immune trees abstract in a forest fire model with immune trees ffmit recently proposed by drossel and schwabl physica a 199 1993 183 the sites of the lattice are either empty a tree or a burning tree and at each time step the system is updated in parallel according to the following rules i a burning tree becomes an empty site ii trees grow with probability p from empty sites and iii a green tree becomes a burning tree with probability 1 g if at least one next neighbor is burning fixing an arbitrary grow probability p and starting with a small immunity g increments of g causes the fire density of the steady state to decrease until the fire becomes irreversibly extinguished at a certain critical point of coordinates pc gc the set of critical points defines a critical curve gc p which in the l limit divides the p g plane in two regions a steady state with fire fronts for g

nested arrays in two dimensions part i geometrical considerations a new class of two dimensional arrays with sensors on lattice s is proposed whose difference co array can give rise to a virtual two dimensional array with much larger number of elements on a dense lattice this structure is obtained by systematically nesting two arrays one with sensors on a sparse lattice and the other on a dense lattice where the lattices bear a certain relation with each other the difference co array of such an array with m and n elements respectively on the two lattices is a two dimensional array with o mn elements present contiguously without holes on the dense lattice the difference co array can be realized on any arbitrary lattice by choosing the dense and sparse lattices appropriately the generator matrices of the sparse and the dense lattices are related by an integer matrix the smith form of this integer matrix is shown to provide a very insightful perspective which is exploited heavily in the construction of nested arrays the design of the two dimensional nested array gives rise to several interesting geometrical orientations of the co array which are addressed in detail and it is shown how the orientations can be manipulated to yield more virtual sensors in a continuum on the dense lattice the increased number of elements in the virtual difference co array can be exploited to perform two dimensional direction of arrival doa estimation of many more sources than what traditional methods can achieve a novel algorithm for application of the nested array in two dimensional direction of arrival estimation is reported in the accompanying part ii of the paper

length scales and power laws in the two dimensional forest fire model abstract we re examine a two dimensional forest fire model via monte carlo simulations and show the existence of two length scales with different critical exponents associated with clusters and with the usual two point correlation function of trees we check resp improve previously obtained values for other critical exponents and perform a first investigation of the critical behaviour of the slowest relaxational mode we also investigate the possibility of describing the critical point in terms of a distribution of the global density we find that some qualitative features such as a temporal oscillation and a power law of the cluster size distribution can nicely be obtained from such a model that discards the spatial structure

modified quasi reversibility method for final value problems in banach spaces this paper is concerned with the final value problem associated with a linear operator a in a banach space where a is the generator of a uniformly bounded analytic semigroup based on the delaubenfels functional calculus we use new quasi reversibility method introduced by boussetila and rebbani recently to form an approximate problem we obtain some results in a banach space similar to those in a hilbert space

on a forest fire model with supposed self organized criticality we study a stochastic forest fire model introduced by p baket al as a model showing self organized criticality this model involves a growth parameterp and the criticality is supposed to show up in the limitp 0 by simulating the model on much larger lattices and with much smaller values ofp we find that the correlations with longest range do not show a nontrivial critical phenomenon in this limit though we cannot rule out percolation like critical behavior on a smaller but still divergent length scale in contrast the model shows nontrivialdeterministic evolution over time scales 1 p in the limitp 0

fourth order cumulant based blind identification of underdetermined mixtures in this paper we study two fourth order cumulant based techniques for the estimation of the mixing matrix in underdetermined independent component analysis the first method is based on a simultaneous matrix diagonalization the second is based on a simultaneous off diagonalization the number of sources that can be allowed is roughly quadratic in the number of observations for both methods explicit expressions for the maximum number of sources are given simulations illustrate the performance of the techniques

critical properties of the one dimensional forest fire model abstract a one dimensional forest fire model including lightnings is studied numerically and analytically for the tree correlation function a new correlation length with critical exponent v 5 6 is found by simulations a hamiltonian formulation is introduced which enables one to study the stationary state close to the critical point using quantum mechanical perturbation theory with this formulation also the structure of the low lying relaxation spectrum and the critical behaviour of the smallest complex gap are investigated numerically finally it is shown that critical correlation functions can be obtained from a simplified model involving only the total number of trees although such simplified models are unable to reproduce the correct off critical behaviour

gaussian source detection and spatial spectral estimation using a coprime sensor array with the min processor a coprime sensor array csa interleaves two undersampled uniform linear arrays with coprime undersampling factors and has recently found broad applications in signal detection and estimation csas commonly use the product processor by multiplying the scanned responses of two colinear subarrays to estimate the spatial power spectral density psd of the received signal this paper proposes a new csa processor the csamin processor which chooses the minimum between the two csa subarray periodograms at each bearing to estimate the spatial psd the proposed csamin processor resolves the csa subarray spatial aliasing equally well as the product processor for an extended aperture csa the csamin reduces the peak sidelobe height and total sidelobe area over the product processor for the same csa geometry moreover unlike the psd estimate from the product processor the psd estimate from the csamin is guaranteed to be positive semidefinite this paper derives the probability density function the complementary cumulative distribution function ccdf or tail distribution and the first two moments of the csamin psd estimator in closed form for gaussian sources in white gaussian noise numerical simulations verify the derived csamin statistics and demonstrate that the csamin improves the performance over the product processor in detecting narrowband gaussian sources in the presence of loud interferers and noise the csamin spatial psd estimate achieves lower variance than the product processor estimate and keeps the psd estimate unbiased for white gaussian processes and asymptotically unbiased for nonwhite gaussian processes

nested arrays in two dimensions part ii application in two dimensional array processing this paper explores the practical application of a new class of two dimensional arrays namely the two dimensional nested arrays in array processing problems like two dimensional direction of arrival estimation nested arrays constitute a class of two dimensional arrays with physical sensors on lattice s whose difference co array gives rise to a virtual two dimensional array with o mn elements although the number of physical sensors used is m n the structure of the two dimensional nested array was proposed in a companion paper and several issues related to the geometrical orientation of the difference co array in the two dimensional space were addressed in this paper the practical aspects of the application of the nested array in two dimensional array processing are considered which can enable us to exploit the increased degrees of freedom offered by the co array under the constraint of a fixed total number of physical sensors the optimal structure of the 2d nested array is solved which maximizes the number of elements in the virtual co array this provides closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors it is shown that one can obtain o n2 virtual elements in the co array using only n physical sensors to exploit the increased degrees of freedom large number of virtual sensors offered by the virtual array for two dimensional doa estimation of more sources than sensors a novel algorithm based on the concept of two dimensional spatial smoothing is proposed and several issues related to identifiability in two dimensional doa estimation problem which is a fundamental issue in two dimensions are addressed the validity of the proposed methods is verified through several numerical examples

renormalization scheme for forest fire models we introduce a renormalization scheme for forest fire models in order to characterize the nature of the critical state and its scale invariant dynamics we study one and two dimensional models defining a characterization of the phase space that allows us to describe the evolution of the dynamics under a scale transformation we show the existence of a relevant critical parameter associated with a repulsive fixed point in the phase space from the renormalization group point of view these models are therefore critical in the usual sense because the fixed point value of the control parameter is crucial in order to get criticality this general scheme allows us to calculate analytically the critical exponent which describes the approach to the critical point along the repulsive direction and the exponent that characterizes the distribution of forest clusters at the critical point we obtain and respectively for the one and two dimensional cases in very good agreement with exact and numerical results

further results on the cramer rao bound for sparse linear arrays sparse linear arrays such as co prime and nested arrays can identify up o m 2 uncorrelated sources with only o m sensors by utilizing their difference coarray model in our previous work we derived closed form asymptotic mean squared error mse expressions for two coarray based music algorithms and analyzed the cramer rao bound crb in high signal to noise ratio snr regions under the assumption of uncorrelated sources in this paper we provide further analysis of the crb presented in our previous work we first establish the connection between two crbs the crb derived with the assumption that the sources are uncorrelated and the classical stochastic crb derived without this assumption we show that they are asymptotically equal in high snr regions for uncorrelated sources next we analyze the behavior of the former crb for co prime and nested arrays with a large number of sensors we investigate the effect of configuration parameters on this crb we show that for co prime and nested arrays this crb can decrease at a rate of o m 5 for large values of m while this rate is only o m 3 for an m sensor ula this finding analytically demonstrates that co prime and nested arrays can achieve better asymptotic estimation performance when the number of sensors is a limiting factor we also show that for a fixed aperture co prime and nested arrays require more snapshots to achieve the same performance as ulas showing the trade off between the number of spatial samples and the number of temporal samples finally we demonstrate our analytical results with numerical experiments

spatio temporal self organization in a model of disease spreading abstract we investigate an extended version of the probabilistic forest fire model conceived as a model of disease spreading we show that the model self organizes spatially and temporally from random initial conditions into a well defined state with a characteristic length and time scale the time scale has a power law dependence on the correlation length i e z with a non trivial exponent of 0 83 in d 2 we show that stochastic input of susceptible individuals is essential for this behaviour a mean field approximation is presented predicting an exponent of z 1 2

vector sensor array processing for electromagnetic source localization the authors present a new approach for localizing electromagnetic sources using sensors where the output of each is a vector consisting of the complete six electric and magnetic field components two types of source transmissions are considered 1 single signal transmission sst and 2 dual signal transmission dst the model is given in terms of several parameters including the wave direction of arrival doa and state of polarization a compact expression is derived for the cramer rao bound crb on the estimation errors of these parameters for the multi source multi vector sensor model quality measures including mean square angular error msae and covariance of vector angular error cvae are introduced and their lower bounds are derived the advantage of using vector sensors is highlighted by explicit evaluation of the msae and cvae bounds for source localization with a single vector sensor a simple algorithm for estimating the source doa with this sensor is presented along with its statistical performance analysis

logarithmic well posed approximation of the backward heat equation in banach space abstract in this paper we apply a logarithmic approximation introduced by boussetila and rebbani in order to study an ill posed cauchy problem in banach space the proposed method induces a well posed problem whose approximation parameter yields continuous dependence on modeling throughout properties of holomorphic semigroups are utilized culminating in the motivating application which is the backward heat equation in l p r 1 p

ill posed problems associated with sectorial operators in banach space abstract ill posed problems of the form u t a u h 0 t t u 0 are studied in banach space under two related scenarios both of which consider a well posed logarithmic approximation in the first scenario a generates a bounded holomorphic semigroup of angle 2 and so a is sectorial of angle 0 in the second where may be relaxed to any value in 0 2 we impose an additional assumption that e a is sectorial regularization results for the original ill posed problem are then established in the linear case where h h t and subsequently extended to nonlinear problems where h is replaced by h t u t we compare the two cases in terms of regularization convergence rates and apply our results to backward heat equations both linear and nonlinear in l p r n 1 p

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

regularization for ill posed cauchy problems associated with generators of analytic semigroups this paper is concerned with the ill posed cauchy problem associated with a densely defined linear operator a in a banach space our main result is that if a is the generator of an analytic semigroup then there exists a family of regularizing operators for such an ill posed cauchy problem by using the quasi reversibility method fractional powers and semigroups of linear operators the applications to ill posed partial differential equations are also given

blind deconvolution of ds cdma signals by means of decomposition in rank 1 l l terms in this paper we present a powerful technique for the blind extraction of direct sequence code division multiple access ds cdma signals from convolutive mixtures received by an antenna array the technique is based on a generalization of the canonical or parallel factor decomposition candecomp parafac in multilinear algebra we present a bound on the number of users under which blind separation and deconvolution is guaranteed the solution is computed by means of an alternating least squares als algorithm the excellent performance is illustrated by means of a number of simulations we include an explicit expression of the cramer rao bound crb of the transmitted symbols

detection of the number of signals a predicted eigen threshold approach a novel method for detecting the number of signals incident upon an array of sensors is described the method is based on finding upper thresholds for the observed eigenvalues of the correlation matrix of the array output the asymptotic normality of the multifold eigenvalue estimate is used to derive a prediction formula for the thresholds due to the fact that the detection error of the method can be controlled by a parameter t the performance of the method is superior to the mdl minimum description length under low snr signal to noise ratio and superior to an aic akaike information criterion under high snr the distribution functions of both missing and false alarm errors are evaluated so that the performance of the method can be analyzed and so that t can be chosen simulation results are presented to confirm the analysis

continuous dependence on modeling for nonlinear ill posed problems abstract the nonlinear ill posed cauchy problem d u d t a u t h t u t u 0 where a is a positive self adjoint operator on a hilbert space h h and h 0 t h h is a uniformly lipschitz function is studied in order to establish continuous dependence results for solutions to approximate well posed problems the authors show here that solutions of the problem if they exist depend continuously on solutions to corresponding approximate well posed problems if certain stabilizing conditions are imposed the approximate problem is given by d v d t f a v t h t v t v 0 for suitable functions f the main result is that u t v t c 1 t t m t t where c and m are computable constants independent of and 0 1 this work extends to the nonlinear case earlier results by the authors and by ames and hughes

structure functions in a model of turbulent energy dissipation a stochastic activity transfer model previously proposed to apply to turbulence is studied and simulated on a 256 256 lattice introduction of random self activation does not allow stable fronts to develop in the limit of small growth probability by assigning discrete density values equal to the threshold values in a related continuous and deterministic model the structure functions for distancesr in the lattice are calculated they have a functional form different from the power behavior which in the case of the deterministic version was interpreted as another sign of self organized criticality future studies of these and other models may be facilitated by the algorithm developed for structure function calculations

computer simulations of the forest fire model abstract we present results of simulations of the forest fire model proposed by p bak et al containing a tree growth rate p and fire spreading to nearest neighbors the space time structure of the fire and the scaling properties of the forest clusters show that the model cannot be critical in the limit p 0 instead we observe regular and quasideterministic spiral shaped fire fronts we present a deterministic forest fire model that helps understand the origin of these spirals

nested arrays a novel approach to array processing with enhanced degrees of freedom a new array geometry which is capable of significantly increasing the degrees of freedom of linear arrays is proposed this structure is obtained by systematically nesting two or more uniform linear arrays and can provide o n2 degrees of freedom using only n physical sensors when the second order statistics of the received data is used the concept of nesting is shown to be easily extensible to multiple stages and the structure of the optimally nested array is found analytically it is possible to provide closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors this cannot be done for existing classes of arrays like minimum redundancy arrays which have been used earlier for detecting more sources than the number of physical sensors in minimum input minimum output mimo radar the degrees of freedom are increased by constructing a longer virtual array through active sensing the method proposed here however does not require active sensing and is capable of providing increased degrees of freedom in a completely passive setting to utilize the degrees of freedom of the nested co array a novel spatial smoothing based approach to doa estimation is also proposed which does not require the inherent assumptions of the traditional techniques based on fourth order cumulants or quasi stationary signals as another potential application of the nested array a new approach to beamforming based on a nonlinear preprocessing is also introduced which can effectively utilize the degrees of freedom offered by the nested arrays the usefulness of all the proposed methods is verified through extensive computer simulations

theory of sparse coprime sensing in multiple dimensions coprime sampling and coprime sensor arrays have been introduced recently for the one dimensional 1 d case and applications in beamforming and direction finding discussed a pair of coprime arrays can be used to sample a wide sense stationary signal sparsely and then reconstruct the autocorrelation at a significantly denser set of points all applications based on autocorrelation e g spectrum and doa estimation benefit from this property it was also shown in the past that coprimality can be exploited in the frequency domain by using a pair of coprime dft filter banks to produce the effect of a much denser tiling in the frequency domain compared to what the two filter banks can individually achieve this paper extends these ideas to multiple dimensions in the 1 d case the samples or sensors lie on a pair of uniform grids whereas in the multidimensional case they lie on a pair of multidimensional lattices not necessarily rectangular this makes the developments mathematically more intricate first several properties of coarrays of lattices are derived it is shown how one can get dense coarrays from sparse arrays on non rectangular lattices this requires that the lattice generating matrices m and n be commuting and coprime to be defined multidimensional dft filter banks for applications such as beamforming with commuting coprime lattice arrays are then described and it is shown that a very dense tiling of the frequency plane can be obtained from the two sparse lattice arrays a particular family of commuting coprime matrices called adjugate pairs are considered in some detail and shown to have attractive properties a brief review of the 1 d case is included at the beginning for convenience

self organized criticality in forest fire models we review properties of the self organized critical soc forest fire model ffm self organized critical systems drive themselves into a critical state without fine tuning of parameters after an introduction the rules of the model and the conditions for spiral shaped and soc large scale structures are given for the soc state critical exponents and scaling relations are introduced the existence of an upper critical dimension and the universal behavior of the model are discussed the relations and differences between ffm and percolation systems are outlined considering an extension of the ffm into the regions beyond the critical point phase transitions and the various structures found in these regions are illustrated