detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

the existence of almost periodic solutions of certain perturbation systems abstract certain almost periodic perturbation systems are considered in this paper by using the roughness theory of exponential dichotomies and the contraction mapping principle some sufficient conditions are obtained for the existence and uniqueness of almost periodic solution of the above systems our results generalize those in j k hale ordinary differential equations krieger huntington 1980 c he existence of almost periodic solutions of perturbation systems ann differential equations 9 1992 173 181 m lin the existence of almost periodic solution and bounded solution of perturbation systems acta math sinica 22a 2002 61 70 in chinese w a coppel almost periodic properties of ordinary differential equations ann math pura appl 76 1967 27 50 a m fink almost periodic differential equations lecture notes in math vol 377 springer verlag new york 1974 y xia f chen a chen j cao existence and global attractivity of an almost periodic ecological model appl math comput 157 2004 449 475

a robust adaptive generalized sidelobe canceller with decision feedback conventional generalized sidelobe canceller gsc is sensitive to a mismatch between the estimated and actual direction of arrival doa of the desired signal such a mismatch induces signal cancellation in the gsc and it severely degrades the beamforming performance in this paper we propose a new decision feedback df technique to increase the robustness against the doa mismatch our new scheme introduces a blind equalizer and a feedback filter in the gsc structure we first derive wiener solutions for the df gsc with perfectly matched and mismatched doa and show that the problem of signal cancellation can be avoided then we consider the adaptive gsc implementation in which the least mean square lms algorithm is used for weight adaptation in addition to the improved robustness the proposed scheme also remedies the slow convergence problem inherent in the conventional adaptive gsc structure the convergence behavior of the lms based df gsc is fully analyzed and the analytic signal to interference plus noise ratio sinr is also derived finally simulation results demonstrate that while the proposed structure can considerably enhance the overall performance it has greatly improved robustness as compared to other existing robust adaptive beamformers

a parametric method for determining the number of signals in narrow band direction finding a novel and more accurate method to determine the number of signals in the multisource direction finding problem is developed the information theoretic criteria of y yin and p krishnaiah 1988 are applied to a set of quantities which are evaluated from the log likelihood function based on proven asymptotic properties of the maximum likelihood estimation these quantities have the properties required by the criteria since the information theoretic criteria use these quantities instead of the eigenvalues of the estimated correlation matrix this approach possesses the advantage of not requiring a subjective threshold and also provides higher performance than when eigenvalues are used simulation results are presented and compared to those obtained from the nonparametric method given by h wax and t kailath 1985

robust adaptive beamforming based on the eigenstructure method in a linearly constrained beamformer with imperfect arrays the authors investigate the cause of cancelling the desired signal from a viewpoint based on the eigenstructure properties of the array covariance matrix based on this cause they propose a robust beamforming algorithm as an adaptive algorithm of the proposed beamformer the present a data domain signal subspace updating algorithm

stability properties of linear volterra equations where a t and b t t s are almost periodic in t when eq e is of convolution type that is a t a a constant and b t s b t s miller 121 and grossman and miller 7 have shown that the null solution of e with b e l 0 co is uniformly asymptotically stable if and only if the resolvent r t s r t s for e is of class l 0 cc in section 3 we show theorem 3 1 that the null solution of e is uniformly asymptotically stable if and only if sup a r a o 1 z t a j iz t s l ds co where z t s is the principal matrix solution of e introduced by becker 11 as will be noted later z t s is identical with the resolvent r t s therefore our theorem 3 1 is an extension of 12

a fast randomized algorithm for overdetermined linear least squares regression we introduce a randomized algorithm for overdetermined linear least squares regression given an arbitrary full rank m n matrix a with m n any m 1 vector b and any positive real number e the procedure computes an n 1 vector x such that x minimizes the euclidean norm ax b to relative precision e the algorithm typically requires log n log 1 e mn n 3 floating point operations this cost is less than the mn 2 required by the classical schemes based on qr decompositions or bidiagonalization we present several numerical examples illustrating the performance of the algorithm

determination of the dimension of a signal subspace from short data records a nested sequence of constant false alarm rate cfar hypothesis tests is presented for rank determination over short data records the procedure is based on the interpretation of sum of squares of singular values as energy in a particular subspace the cfar thresholds are set up based on distributions derived from matrix perturbation ideas expressions for probability of overestimation and underestimation are presented

optimal subsampling for large sample logistic regression for massive data the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden existing studies focus on approximating the ordinary least square esti

the determination of optimum structures for the state space representation of multivariate stochastic processes when identifying a model for a multivariate stationary stochastic process an important problem is that of determining the structure of the state variable model several overlapping parameterizations can usually be fitted to a given process and the question arises as to which structure leads to the most accurate parameter estimates the accuracy of parameter estimates is often measured by the determinant of the fisher information matrix we show that all admissible structures will give asymptotically the same value to this criterion for finite data some structures may still be better than others and two heuristic structure estimation methods are analyzed some simulation results are also presented

detection of coherent signals using weighted subspace smoothing a new approach to detecting the number of coherent signals incident upon a uniformly spaced linear array is presented the approach combines a modified spatial smoothing scheme and a modified mdl criterion the modified spatial smoothing scheme referred to as weighted subspace smoothing is actually a generalization of the post smoothing approach proposed by krim and proakis in 1994 it is shown that the noise eigenvalues obtained with weighted subspace smoothing are more accurate than those obtained with the original spatial smoothing we thus attempt to improve the detection performance using these more accurate eigenvalues a novel modification of the minimum description length mdl criterion is proposed to accomplish this computer simulations are presented to study the performance improvement of this new approach

on almost automorphic type solutions of abstract integral equations a bohr neugebauer type property and some applications abstract in the present work we give some sufficient conditions to obtain a unique almost automorphic solution to abstract nonlinear integral equations which are simultaneously of advanced and delayed type and also a unique asymptotically almost automorphic mild solution to abstract integro differential equations with nonlocal initial conditions both situations are posed on banach spaces also we develop a bohr neugebauer type result for the abstract integral equations before that we introduce the notion of bounded functions develop the appropriate abstract theory and discuss the almost periodic situation as applications we study the existence of an asymptotically almost automorphic solution to integro differential equations modeling heat conduction in materials with memory and also the existence of the almost automorphic solution to semilinear parabolic evolution equations with finite delay

nonparametric detection of signals by information theoretic criteria performance analysis and an improved estimator determining the number of sources from observed data is a fundamental problem in many scientific fields in this paper we consider the nonparametric setting and focus on the detection performance of two popular estimators based on information theoretic criteria the akaike information criterion aic and minimum description length mdl we present three contributions on this subject first we derive a new expression for the detection performance of the mdl estimator which exhibits a much closer fit to simulations in comparison to previous formulas second we present a random matrix theory viewpoint of the performance of the aic estimator including approximate analytical formulas for its overestimation probability finally we show that a small increase in the penalty term of aic leads to an estimator with a very good detection performance and a negligible overestimation probability

on information theoretic criteria for determining the number of signals in high resolution array processing an important problem in high resolution array processing is the determination of the number of signals arriving at the array information theoretic criteria provide a means to achieve this two commonly used criteria are the akaike information criterion aic and minimum descriptive length mdl criterion while the aic tends to overestimate even at a high signal to noise ratio snr the mdl criterion tends to underestimate at low or moderate snr by excluding irrelevant parameters a new log likelihood function has been chosen utilizing this new log likelihood function gives a set of more accurate estimates of the eigenvalues and in the establishment of modified information theoretic criteria which moderate the performance of the aic and the mdl criterion computer simulations confirm that the modified criteria have superior performance

almost periodic solutions of n species competitive system with feedback controls abstract in this paper the following almost periodic n species competitive system with feedback controls x i t x i t b i t j 1 n a ij t x j t j 1 j i n c ij t x i t x j t d i t u i t u i t r i t e i t u i t f i t x i t i 1 2 n are studied by using the comparison theorem and constructing suitable lyapunov function where some important factors such as the effect of toxic and the age structure are also considered simultaneously some sufficient conditions are obtained for the existence of a unique almost periodic solution of above model examples show that the obtained criteria are new general and easily verifiable

paper selecting the best linear transfer function model statistics currently used to determine the best model order based on the covariance of the parameter estimates or the instrumental product moment matrix are critically examined particularly for their applicability to situations where input and output units differ or where there is a large or small steady state gain a normalization process is advocated which extends the usefulness and reliability of the statistics in these situations a procedure for comparing determinant statistics for models of different orders is described which simplifies current methods the improved procedures and statistics are compared using simulated data and an instrumental variable estimation method confirming their worth

non parametric detection of the number of signals hypothesis testing and random matrix theory detection of the number of signals embedded in noise is a fundamental problem in signal and array processing this paper focuses on the non parametric setting where no knowledge of the array manifold is assumed first we present a detailed statistical analysis of this problem including an analysis of the signal strength required for detection with high probability and the form of the optimal detection test under certain conditions where such a test exists second combining this analysis with recent results from random matrix theory we present a new algorithm for detection of the number of sources via a sequence of hypothesis tests we theoretically analyze the consistency and detection performance of the proposed algorithm showing its superiority compared to the standard minimum description length mdl based estimator a series of simulations confirm our theoretical analysis

an analysis of the projection method for robust adaptive beamforming two causes of performance degradation in adaptive beamforming are perturbation error and sample covariance error these causes were discussed by feldman and griffihs see ieee trans signal processing vol 42 p 867 april 1994 which proposed an approach termed the projection method to reduce the sensitivity of the beamformer performance to both types of error this paper contains an analysis of the expected performance of the beamformer when it is implemented either with or without using the projection method based on a second order taylor series expansion of an approximate expression for the signal to interference plus noise ratio sinr at the beamformer output the analysis provides accurate results when either perturbation error or sample covariance error occurs a less accurate analysis based on a zeroth order taylor series expansion includes results presented by jablon 1986 and chang and yeh see ibid vol 40 no 11 p 1336 1992 as special cases

simple and efficient nonparametric method for estimating the number of signals without eigendecomposition inspired by the computational simplicity and numerical stability of qr decomposition a nonparametric method for estimating the number of signals without eigendecomposition mense is proposed for the coherent narrowband signals impinging on a uniform linear array ula by exploiting the array geometry and its shift invariance property to decorrelate the coherency of signals through subarray averaging the number of signals is revealed in the rank of the qr upper trapezoidal factor of the autoproduct of a combined hankel matrix formed from the cross correlations between some sensor data since the infection of additive noise is defused signal detection capability is improved a new detection criterion is then formulated in terms of the row elements of the qr upper triangular factor when finite array data are available and the number of signals is determined as a value of the running index for which this ratio criterion is maximized where the qr decomposition with column pivoting is also used to improve detection performance the statistical analysis clarifies that the mense detection criterion is asymptotically consistent furthermore the proposed mense algorithm is robust against the array uncertainties including sensor gain and phase errors and mutual coupling and against the deviations from the spatial homogeneity of noise model the effectiveness of the mense is verified through numerical examples and the simulation results show that the mense is superior in detecting closely spaced signals with a small number of snapshots and or at relatively low signal to noise ratio snr

h k trichotomies and asymptotics of nonautonomous difference systems abstract discrete nonautonomous nonlinear systems possessing h k trichotomies are considered we specialize to the case of solutions moving inside and in a neighborhood of an invariant manifold of a special kind which we call h k hyperbolic the aulbach coppel knobloch transformation is then developed and used to state conditions for granting asymptotic equivalence of solutions our results generalize some of aulbach s results in which the manifold considered was made of stationary points and the system taken was autonomous

existence and global attractivity of an almost periodic ecological model the almost periodic lotka volterra model with m predators and n preys is considered in this paper by constructing suitable lyapunov function some sufficient conditions are obtained for the existence and global attractivity of a unique positive almost periodic solution of this model examples show that our criteria are new general and easily verifiable

fast approximation of matrix coherence and statistical leverage the statistical leverage scores of a matrix a are the squared row norms of the matrix containing its top left singular vectors and the coherence is the largest leverage score these quantities are of interest in recently popular problems such as matrix completion and nystrom based low rank matrix approximation as well as in large scale statistical data analysis applications more generally moreover they are of interest since they define the key structural nonuniformity that must be dealt with in developing fast randomized matrix algorithms our main result is a randomized algorithm that takes as input an arbitrary n d matrix a with n d and that returns as output relative error approximations to all n of the statistical leverage scores the proposed algorithm runs under assumptions on the precise values of n and d in o nd logn time as opposed to the o nd2 time required by the naive algorithm that involves computing an orthogonal basis for the range of a our analysis may be viewed in terms of computing a relative error approximation to an underconstrained least squares approximation problem or relatedly it may be viewed as an application of johnson lindenstrauss type ideas several practically important extensions of our basic result are also described including the approximation of so called cross leverage scores the extension of these ideas to matrices with n d and the extension to streaming environments

automatic determination of the number of targets present when using the time reversal operator acoustical time reversal mirrors have been shown to provide a highly accurate means of studying and focusing on acoustical sources the dort method is a derivation of the time reversal process which allows for focusing on multiple targets an important step in this process is the determination of the number of targets or sources present this is achieved by examining the eigenvalues of the time reversal operator tro the number of significant eigenvalues is then chosen as the number of sources present however as mentioned in n mordant c prada and m fink j acoust soc am 105 2634 2642 1999 and c prada m tanter and m fink in proceedings of the ieee symposium 1997 pp 679 683 factors such as low signal to noise ratio snr small data sample array configuration and the target location may result in the eigenvalues corresponding to the targets no longer being distinguishable from the background noise eigenvalues this paper proposes a robust method of automatically determining the

widely linear versus linear blind multiuser detection with subspace based channel estimation finite sample size effects in a recent paper a s cacciapuoti et al ldquofinite sample performance analysis of widely linear multiuser receivers in ds cdma systems ieee transactions on signal processing vol 56 no 4 pp 1572 1588 apr 2008 we presented the finite sample theoretical performance comparison between linear l and widely linear wl minimum output energy moe receivers for direct sequence code division multiple access ds cdma systems worked out under the assumption that the channel impulse response of the desired user is exactly known the main scope of this paper is to extend such an analysis taking into account not only autocorrelation matrix acm estimation effects but also the accuracy of subspace based blind channel estimation ce we aim to answer the two following questions which of the two estimation processes acm or ce is the main source of degradation when implementing the receivers on the basis of a finite sample size compared with the l moe one is the finite sample wl moe receiver with blind ce capable of achieving the performance gains predicted by the theory to this goal simple and easily interpretable formulas are developed for the signal to interference plus noise ratio sinr at the output of the l and wl moe receivers with blind ce when they are implemented using either the sample acm or its eigendecomposition in addition the derived formulas which are validated by simulations allow one to recognize and discuss interesting tradeoffs between the main parameters of the ds cdma system

performance of dmi and eigenspace based beamformers the performance of the direct matrix inversion dmi method for antenna arrays of arbitrary geometry is analyzed by asymptotic statistical techniques the effects of eigenspace disturbance caused by finite samples on the output interference and noise powers are examined under the unit gain constraint in the direction of the desired signal the results show that the performance of the dmi method is degraded mostly by the disturbed noise subspace that suggests the use of an eigenspace based beamformer in which the weight vector is computed by using the signal plus interference subspace component of the sample correlation matrix convergence properties of the eigenspace based beamformer are evaluated for the cases in which the source number is known and in which it is overestimated theoretical analyses validated by computer simulations indicate that the eigenspace based beamformer has faster convergence rate than the dmi method

fitting logistic models under case control or choice based sampling on compare deux approches dans le cas important de l ajustement des modeles de regression logistique

robust adaptive beamforming with a novel interference plus noise covariance matrix reconstruction method recently a new robust adaptive beamforming rab technique was proposed to remove the signal of interest soi component from the sample covariance matrix based on interference plus noise covariance matrix reconstruction which utilizes the capon spectrum estimator integrated over a region separated from the direction of the soi however the extreme condition of the reconstruction based technique that the precise information about the array structure is known in advance is almost impossible in practice in this paper a novel method to reconstruct the interference plus noise covariance matrix is proposed considering the imprecise prior information about the array structure which means that the array may be uncalibrated we use an annulus uncertainty set to constrain the steering vectors of the interferences then we integrate the capon spectrum over the surface of the annulus by which we can obtain the reconstructed interference matrix without containing the soi since the integral interval is a high dimensional domain which is very difficult to solve we use a discrete sum method to calculate the integral approximately with the reconstructed interference plus noise matrix the nominal steering vector can be corrected via maximizing the beamformer output power by solving a quadratically constrained quadratic programming qcqp problem the previous reconstruction method can be seen as a special case of the proposed one the main advantage is that the proposed algorithm is robust against unknown arbitrary type mismatches theoretical analysis and simulation results demonstrate the effectiveness and robustness of the proposed algorithm

on some nonparametric methods for detection of the number of signals a simpler more elegant and more flexible method for estimating the number of signals is proposed strong consistency is proved bounds for error probabilities are given this method depends on choosing a function with a parameter r the previous methods correspond to the case r 1 it seems the larger the r the faster the convergence we can choose r as any positive integer even applications are discussed including the coherent cases

on the existence of maximum likelihood estimators for the binomial response models summary necessary and sufficient conditions are given for the existence of maximum likelihood estimators of the linear regression parameter in binomial response this includes logit and probit models the question of existence of maximum likelihood estimators mle for logit models arose in an analysis of the relationship of psychiatric caseness to scores on a psychiatric screening questionnaire tennant 1977 administered the ghq general health questionnaire goldberg 1972 to 120 patients attending a general practitioner s surgery and also gave each one a standardized psychiatric interview from the interview patients were classified as psychiatric case non case in a secondary analysis of tennant s data duncan jones and henderson 1978 fitted a logit regression of caseness on ghq score and obtained a good fit with the model

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

low complexity and high resolution line spectral estimation using cyclic minimization the line spectral estimation problem has applications in radar wireless communications spectroscopy and power electronics among others the signal is modeled as a sparse linear combination of complex sinusoids and the problem target is to estimate the number of sinusoids in the mixture and respective parameters of each individual sinusoid such as magnitude phase and frequency in this work we first introduce a novel formulation of the rank function which involves the solution of a multi convex optimization problem using the multi convex reformulation of the rank function an over parameterization of the line estimation problem is proposed together with a cyclic minimization procedure to obtain a solution the cyclic method iterates between the optimization of the signal subspace and null space and stops when the two are orthogonal every limit point of the sequence of iterates is shown to be a stationary point of the original problem numerical experiments show that only a small number of iterations is required for convergence the signal subspace optimization is a semidefinite program sdp and the null space optimization has a closed form solution the cost per iteration of a general purpose interior point method ipm to solve the sdp is a quartic function of the problem dimension it is shown that by exploiting the problem structure the cost per iteration of the ipm may be reduced to a cubic function of the problem dimension comparable to the cost of the alternating direction method of multipliers admm however contrarily to the latter the former achieves the precision necessary for fine frequency localization a large set of numerical experiments show the effectiveness of the proposed approach

on the performance of signal subspace processing part i narrow band systems this paper presents an analytical evaluation of detection determination of the number of sources and estimation performances of narrow band signal subspace processing for multiple source direction finding the probabilities of underestimating and overestimating the number of sources are derived under asymptotic conditions and around the threshold regions in terms of the choice of a penalty function and signal noise and array parameters for the cases of at most two closely spaced sources in the spatially white noise a scalar measure is introduced for the evaluation of the quality of the estimated signal subspace based on the statistics of this measure performance thresholds are demonstrated for the signal to noise ratio angle separation and correlation between two equipowered sources

roughness of h k dichotomies abstract in this paper we prove a roughness theorem for a class of dichotomies of linear systems of differential equations the so called h k dichotomies these include a great variety of dichotomies among them the ordinary and exponential dichotomies exponential ordinary dichotomies levinson dichotomies for diagonal systems etc we prove that under general uniform conditions upon the functions h and k these dichotomies are not destroyed by integrable perturbations this result generalizes the property of roughness of ordinary dichotomies under integrable perturbations

on the linearization theorem of fenner and pinto this paper reports an improvement of the linearization theorem of fenner and pinto 1999 22 fenner and pinto presented a version of hartman s result they showed that there exists a one to one correspondence between solutions of the linear system and the nonlinear system moreover if h t x denotes the transformation then h t x x is uniformly bounded however no proof of the holder regularity of the transformation h t x appears in fenner and pinto 1999 22 the main objective in this paper is precisely to give a proof of the holder regularity of the transformation h t x namely we show that the conjugating function h t x in the hartman grobman theorem is always holder continuous and has holder continuous inverse moreover we weakened an important assumption in fenner and pinto 1999 22 fenner and pinto obtained the linearization theorem by setting that the whole linear system should satisfy is condition in this paper this assumption is reduced in fact it is enough to assume that the linear system partially satisfies is condition therefore we improve the linearization theorem of fenner and pinto

dichotomies and asymptotic formulas for the solutions of differential equations abstract the new concept of h k dichotomy is studied extensively and is used in asymptotic equivalence problems

statistical analysis of the performance of information theoretic criteria in the detection of the number of signals in array processing the performances of the akaike 1974 information criterion and the minimum descriptive length criterion methods are examined the events which lead to erroneous decisions are considered and on the basis of these events the probabilities of error for the two criteria are derived the probabilities of the first two events are derived based on the asymptotic distribution of the sample eigenvalues of an estimated hermitian matrix it is further shown that the probabilities of missing and false alarm for these two criteria can be evaluated to a close approximation although the derivation of the probabilities of error is based on an asymptotic analysis the results are confirmed to be in very close agreement with computer simulation results

local case control sampling efficient subsampling in imbalanced data sets for classification problems with significant class imbalance subsampling can reduce computational costs at the price of inflated variance in estimating model parameters we propose a method for subsampling efficiently for logistic regression by adjusting the class balance locally in feature space via an accept reject scheme our method generalizes standard case control sampling using a pilot estimate to preferentially select examples whose responses are conditionally rare given their features the biased subsampling is corrected by a post hoc analytic adjustment to the parameters the method is simple and requires one parallelizable scan over the full data set standard case control sampling is inconsistent under model misspecification for the population risk minimizing coefficients by contrast our estimator is consistent for provided that the pilot estimate is moreover under correct specification and with a consistent independent pilot estimate our estimator has exactly twice the asymptotic variance of the full sample mle even if the selected subsample comprises a miniscule fraction of the full data set as happens when the original data are severely imbalanced the factor of two improves to formula see text if we multiply the baseline acceptance probabilities by c 1 and weight points with acceptance probability greater than 1 taking roughly formula see text times as many data points into the subsample experiments on simulated and real data show that our method can substantially outperform standard case control subsampling

infinitely imbalanced logistic regression in binary classification problems it is common for the two classes to be imbalanced one case is very rare compared to the other in this paper we consider the infinitely imbalanced case where one class has a finite sample size and the other class s sample size grows without bound for logistic regression the infinitely imbalanced case often has a useful solution under mild conditions the intercept diverges as expected but the rest of the coefficient vector approaches a non trivial and useful limit that limit can be expressed in terms of exponential tilting and is the minimum of a convex objective function the limiting form of logistic regression suggests a computational shortcut for fraud detection problems

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

faster least squares approximation least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution in a typical setting one lets n be the number of constraints and d be the number of variables with n gg d then existing exact methods find a solution vector in o nd 2 time we present two randomized algorithms that provide accurate relative error approximations to the optimal value and the solution vector of a least squares approximation problem more rapidly than existing exact algorithms both of our algorithms preprocess the data with the randomized hadamard transform one then uniformly randomly samples constraints and solves the smaller problem on those constraints and the other performs a sparse random projection and solves the smaller problem on those projected coordinates in both cases solving the smaller problem provides relative error approximations and if n is sufficiently larger than d the approximate solution can be computed in o nd ln d time

a projection approach for robust adaptive beamforming it is well known that calibration errors can seriously degrade performance in adaptive arrays particularly when the input signal to noise ratio is large the effect is caused by the perturbation of the presumed steering vector from its optimal value although it is not as widely known similar degradation occurs in sampled matrix inversion processing when the covariance matrix is estimated while the desired signal is present in the snapshot data under these conditions performance loss is due to errors in the estimated covariance matrix and occurs even when the steering vector is known exactly in the paper a new method based of modification of the steering vector is proposed to overcome both the problems of perturbation and of sample covariance errors the method involves projection of the presumed steering vector onto the observed signal plus interference subspace an analysis is also presented illustrating that the sample covariance errors can be viewed as a particular type of perturbation error and a simple approximation is derived for the expected beamformer performance as a function of the number of data snapshots both analytical and experimental results are presented that illustrate the advantages of the proposed method

dichotomy and existence of periodic solutions of quasilinear functional differential equations abstract using krasnoselskii s fixed point theorem functional analysis methods and dichotomy theory we study the existence and uniqueness of the periodic solutions of integro differential equations with bounded and unbounded delays

almost periodic solutions for delay differential equations with infinite delays one of the most widely methods for establishing the existence of almost periodic a p for short solutions of systems or ordinary differential equations is based on a general result due to amerio 1 j a generalization of an earlier result for linear a p systems due to favard in essence this basic method consists of showing that if a solution is in a compact set in the statespace for all t and has a certain separation property with respect to other such solutions then if this same property holds for all systems in the socalled hull of the given system this solution will be a p this result in fact relates to a necessary as well as sufficient stability condition for a fairly general dynamical system to have an a p solution cf 2 chap 51 in fact miller 3 used the idea of embedding the a p system in a more general dynamical system and was thus able to obtain a local stability condition for the existence of a p solutions without using the separation conditions due to favard and amerio most stability conditions for the existence of a p solutions known prior to miller s result were in terms of global stability conditions for a fairly complete and comprehensive discussion of a p solutions for a p systems the books by fink 4 and yoshizawa 5 are recommended for a more general discussion of the idea of embedding a p systems in dynamical systems cf sell 6 for ordinary differential equations with fixed finite time delays much of the method based on amerio s separation result can and has been adapted to obtain similar stability conditions for the existence of a p solutions cf 7 for example miller in 3 shows that local stability conditions can also be used for such delay differential equations results for delay equations with infinite time delays based on amerio s separation condition have also been obtained cf for example hino b however for such systems which do not involve substantially fading memory not much seems to have been done one of the main difficulties in such infinite delay systems arises from the fact that bounded solutions may no longer remain in compact subsets of the state

on h k manifolds with asymptotic phase abstract we introduce the notion of h k manifolds and give conditions under which the property of being a manifold with asymptotic phase holds these conditions allow the construction of a transformation of the variational equation of a nonlinear nonautonomous systems with h k dichotomies into an almost decoupled quasilinear system the class of admissiblehandkfunctions is also briefly analyzed