subspace averaging and order determination for source enumeration in this paper we address the problem of subspace averaging with special emphasis placed on the question of estimating the dimension of the average the results suggest that the enumeration of sources in a multi sensor array which is a problem of estimating the dimension of the array manifold and as a consequence the number of radiating sources may be cast as a problem of averaging subspaces this point of view stands in contrast to conventional approaches which cast the problem as one of identifiying covariance models in a factor model we present a robust formulation of the proposed order fitting rule based on majorization minimization algorithms a key element of the proposed method is to construct a bootstrap procedure based on a newly proposed discrete distribution on the manifold of projection matrices for stochastically generating subspaces from a function of experimentally determined eigenvalues in this way the proposed subspace averaging sa technique determines the order based on the eigenvalues of an average projection matrix rather than on the likelihood of a covariance model penalized by functions of the model order by means of simulation examples we show that the proposed sa criterion is especially effective in high dimensional scenarios with low sample support

generalized bayesian information criterion for source enumeration in array processing we investigate the problem of enumerating source signals impinging on an array of sensors in an information theoretic framework the conventional bayesian information criterion bic does not yield satisfactory performance for this problem because it only considers the density of the observations in order to remedy the limitations of the bic we propose a generalized bayesian information criterion gbic rule by incorporating the density of the sample eigenvalues or corresponding statistics such a density contains extra information and complements the density of the observations in constructing the gbic as a result two different expressions for the gbic are suggested simulation results validate the superiority of the proposed gbic over the conventional bic in terms of correctly determining the number of sources while their computational costs are comparable

calderon zygmund estimates in generalized orlicz spaces abstract we establish the w 2 solvability of the linear elliptic equations in non divergence form under a suitable essentially minimal condition of the generalized orlicz function x t by deriving calderon zygmund type estimates the class of generalized orlicz spaces we consider here contains as special cases classical lebesgue and orlicz spaces as well as non standard growth cases like variable exponent and double phase growth

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

interconnection and damping assignment passivity based control of port controlled hamiltonian systems passivity based control pbc is a well established technique that has shown to be very powerful to design robust controllers for physical systems described by euler lagrange el equations of motion for regulation problems of mechanical systems which can be stabilized shaping only the potential energy pbc preserves the el structure and furthermore assigns a closed loop energy function equal to the difference between the energy of the system and the energy supplied by the controller thus we say that stabilization is achieved via energy balancing unfortunately these nice properties of el pbc are lost when used in other applications which require shaping of the total energy for instance in electrical or electromechanical systems or even some underactuated mechanical devices our main objective in this paper is to develop a new pbc theory which extends to a broader class of systems the aforementioned energy balancing stabilization mechanism and the structure invariance towards this end we depart from the el description of the systems and consider instead port controlled hamiltonian models which result from the network modelling of energy conserving lumped parameter physical systems with independent storage elements and strictly contain the class of el models

stabilization of a class of underactuated mechanical systems via interconnection and damping assignment we consider the application of a formulation of passivity based control pbc known as interconnection and damping assignment ida to the problem of stabilization of underactuated mechanical systems which requires the modification of both the potential and the kinetic energies our main contribution is the characterization of a class of systems for which ida pbc yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction the class is given in terms of solvability of certain partial differential equations one important feature of ida pbc stemming from its hamiltonian formulation is that it provides new degrees of freedom for the solution of these equations using this additional freedom we are able to show that the method of controlled lagrangians in its original formulation may be viewed as a special case of our approach as illustrations we design asymptotically stabilizing ida pbcs for the classical ball and beam system and a novel inertia wheel pendulum

optimal simultaneous detection and estimation under a false alarm constraint this paper addresses the problem of finite sample simultaneous detection and estimation which arises when estimation of signal parameters is desired but signal presence is uncertain in general a joint detection and estimation algorithm cannot simultaneously achieve optimal detection and optimal estimation performance we develop a multihypothesis testing framework for studying the tradeoffs between detection and parameter estimation classification for a finite discrete parameter set our multihypothesis testing problem is based on the worst case detection and worst case classification error probabilities of the class of joint detection and classification algorithms which are subject to a false alarm constraint this framework leads to the evaluation of greatest lower bounds on the worst case decision error probabilities and a construction of decision rules which achieve these lower bounds for illustration we apply these methods to signal detection order selection and signal classification for a multicomponent signal in noise model for two or fewer signals an snr of 3 db and signal space dimension of n 10 numerical results are obtained which establish the existence of fundamental tradeoffs between three performance criteria probability of signal detection probability of correct order selection and probability of correct classification furthermore based on numerical performance comparisons between our optimal decision rule and other suboptimal penalty function methods we observe that rissanen s 1978 order selection penalty method is nearly min max optimal in some nonasymptotic regimes

model order selection based on information theoretic criteria design of the penalty information theoretic criteria itc have been widely adopted in engineering and statistics for selecting among an ordered set of candidate models the one that better fits the observed sample data the selected model minimizes a penalized likelihood metric where the penalty is determined by the criterion adopted while rules for choosing a penalty that guarantees a consistent estimate of the model order are known theoretical tools for its design with finite samples have never been provided in a general setting in this paper we study model order selection for finite samples under a design perspective focusing on the generalized information criterion gic which embraces the most common itc the theory is general and as case studies we consider a the problem of estimating the number of signals embedded in additive white gaussian noise awgn by using multiple sensors b model selection for the general linear model glm which includes e g the problem of estimating the number of sinusoids in awgn the analysis reveals a trade off between the probabilities of overestimating and underestimating the order of the model we then propose to design the gic penalty to minimize underestimation while keeping the overestimation probability below a specified level for the considered problems this method leads to analytical derivation of the optimal penalty for a given sample size a performance comparison between the penalty optimized gic and common aic and bic is provided demonstrating the effectiveness of the proposed design strategy

regularity results for a class of functionals with non standard growth we consider the integral functional under non standard growth assumptions that we call p x type namely we assume that a relevant model case being the functional under sharp assumptions on the continuous function p x 1 we prove regularity of minimizers energies exhibiting this growth appear in several models from mathematical physics

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

analysis of the performance and sensitivity of eigendecomposition based detectors a new framework is presented for the analysis of the performance of detection methods such as aic and mdl which are based on the eigenvalues of the sample covariance matrix it is shown that theoretical analysis of the probabilities of overestimation and underestimation can be much more conveniently carried out via a proposed particularly simple sequence of statistics also the breakdown of these detection methods in the presence of model nonidealities is explored by theory simulations and experimentation with real array data for example theoretical arguments are given to demonstrate the high degree of sensitivity of the detectors to unknown deviations of the noise from whiteness

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

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

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

estimation of the directions of arrival of signals in unknown correlated noise i the map approach and its implementation the authors propose a method of direction of arrival doa estimation of signals in the presence of noise whose covariance matrix is unknown and arbitrary other than being positive definite they examine the projection of the data onto the noise subspace the conditional probability density function pdf of the projected data given the signal parameters and the unknown projected noise covariance matrix is first formed the a posteriori pdf of the signal parameters alone is then obtained by assigning a noninformative a priori pdf to the unknown noise covariance matrix and integrating out this quantity a simple criterion for the maximum a posteriori map estimate of the doas of the signals is established some properties of this criterion are discussed and an efficient numerical algorithm for the implementation of this criterion is developed the advantage of this method is that the noise covariance matrix does not have to be known nor must it be estimated

on a relation between maximum likelihood classification and minimum relative entropy classification corresp maximum likelihood ml and minimum relative entropy mre minimum cross entropy classification of samples from an unknown probability density when the hypotheses comprise an exponential family are considered it is shown that ml and mre lead to the same classification nde and the result is illustrated in terms of a method for estimating covariance matrices recently developed by burg luenberger and wenger mre classification applies to the general case in which it cannot be assumed that the samples were generated by one of the hypothesis densities the common use of ml in this case is technically incorrect but the equivalence of mre and ml provides a theoretical justification

discontinuous galerkin finite element approximation of hamilton jacobi bellman equations with cordes coefficients we propose an hp version discontinuous galerkin finite element method for fully nonlinear second order elliptic hamilton jacobi bellman equations with cordes coefficients the method is proved to be consistent and stable with convergence rates that are optimal with respect to mesh size and suboptimal in the polynomial degree by only half an order numerical experiments on problems with nonsmooth solutions and strongly anisotropic diffusion coefficients illustrate the accuracy and computational efficiency of the scheme an existence and uniqueness result for strong solutions of the fully nonlinear problem and a semismoothness result for the nonlinear operator are also provided

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

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

universal coding information prediction and estimation a connection between universal codes and the problems of prediction and statistical estimation is established a known lower bound for the mean length of universal codes is sharpened and generalized and optimum universal codes constructed the bound is defined to give the information in strings relative to the considered class of processes the earlier derived minimum description length criterion for estimation of parameters including their number is given a fundamental information theoretic justification by showing that its estimators achieve the information in the strings it is also shown that one cannot do prediction in gaussian autoregressive moving average arma processes below a bound which is determined by the information in the data

lp λ regularity for fully nonlinear elliptic equations abstract we establish the variable exponent morrey spaces l p estimate to the dirichlet problem for fully nonlinear elliptic equations on a c 1 1 bounded domain for variable exponents p and

weighted estimates for nondivergence parabolic equations in orlicz spaces abstract we obtain the global weighted orlicz regularity of the maximum order derivatives of the solution to the dirichlet problem for nondivergence parabolic equations in a bounded domain we find correct conditions on the associated weight and young function the coefficients are assumed to have small bounded mean oscillation bmo seminorms

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

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

interpolation inequalities for derivatives in variable exponent lebesgue sobolev spaces abstract we show the interpolation inequalities for derivatives in variable exponent lebesgue sobolev spaces by applying the boundedness of the hardy littlewood maximal operator on l p as applications we prove a new landau komogorov type inequality for the second order derivative and an embedding theorem and discuss the equivalent norms in the space w 0 1 p w 2 p

gradient estimates for a class of parabolic systems we establish local calderon zygmund type estimates for a class of parabolic problems whose model is the nonhomogeneous degenerate singular parabolic p laplacian system ut div du p 2du div f p 2f proving that f lqloc du lqloc q p we also treat systems with discontinuous coefficients of vanishing mean oscillation vmo type

global lorentz estimates with variable power to linear parabolic integro differential equations abstract we shall establish a global estimate in the framework of the lorentz spaces for variable power of the fractional derivative of solutions to the cauchy dirichlet problems of linear parabolic integro differential equations with smooth coefficients m t x y 1 2 in a bounded domain here we assume that some higher order derivatives of m t x y in y are merely measurable in the time variable t and satisfy uniformly continuous in the spatial variables x the boundaries of domains are c 1 1 and the variable exponents satisfy log holder continuity

source association doa and fading coefficients estimation for multipath signals this paper addresses the source association sa direction of arrival doa and fading coefficients fcs estimation problem in multipath environment first we establish a rank reduction property for a multipath signal model with the existence of multiple groups of coherent signals subsequently based on this property effective algorithms for sa doa and fcs estimation have been developed the proposed doa and fcs estimation methods exploit the multipath structure information to achieve improved accuracy the new doa estimation methods work well even in the case that the doas of the multipath signals associated with different sources are nearly overlapped meanwhile the new methods are applicable to arbitrary array geometry while without decreasing the effective array aperture then the stochastic cramer rao bound on doa and fcs estimation of multipath model mcrb exploiting the multipath structure information is derived in closed form numerical simulations have been provided to demonstrate the effectiveness of the proposed methods

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

local higher integrability of the gradient of a quasiminimizer under generalized orlicz growth conditions abstract we study local quasiminimizers of the dirichlet energy under generalized growth conditions special cases include standard variable exponent and double phase growths we show that the gradient of a local quasiminimizer has local higher integrability

un music and un cle an application of generalized correlation analysis to the estimation of the direction of arrival of signals in unknown correlated noise a new approach is proposed for the consistent estimation of the directions of arrival doa of signals in an unknown spatially correlated noise environment the signal and noise model used is based on the assumption that the data are received by two arrays well separated so that their noise outputs are uncorrelated the generalized correlation decomposition of the cross correlation matrix between the two arrays is then introduced of particular interest is the canonical correlation decomposition the analysis of the generalized correlation leads to various interesting geometric and asymptotic properties of the eigenspace structure two algorithms un music and un cle are developed to estimate the doa of signals in unknown spatially correlated noise based on the utilization of these properties computer simulations show that these methods are superior in performance compared to conventional methods furthermore it is demonstrated that the new methods are equally effective even when only one sensor array is employed

discontinuous galerkin finite element approximation of nondivergence form elliptic equations with cordes coefficients nondivergence form elliptic equations with discontinuous coefficients do not generally possess a weak formulation thus presenting an obstacle to their numerical solution by classical finite element methods we propose a new hp version discontinuous galerkin finite element method for a class of these problems which satisfy the cordes condition it is shown that the method exhibits a convergence rate that is optimal with respect to the mesh size h and suboptimal with respect to the polynomial degree p by only half an order numerical experiments demonstrate the accuracy of the method and illustrate the potential of exponential convergence under hp refinement for problems with discontinuous coefficients and nonsmooth solutions

remarks on certain criteria for detection of number of signals in this paper we derive the asymptotic distribution of the logarithm of the likelihood ratio statistic for testing the hypothesis that the number of signals is equal to q against the alternative that it is equal to k specified for a special case this distribution is not chi square the above statistic also rises in studying consistency property of the mdl criterion and aic for detection of the number of signals

reduced rank processing for oversampled arrays in this paper we study array processing techniques for oversampled passive arrays oversampling occurs when an array contains sensors that are closely spaced relative to the operational wavelength or when the sources are known a priori to be confined to a limited angular range we examine here the application of the recently introduced reduced rank processing rrp approach to several widely used array processing methods for source detection and bearing estimation such as maximum likelihood and music and show how when an array is oversampled rrp can be used to reduce their computational load furthermore we use asymptotic performance analysis to show that rrp for oversampled arrays can significantly enhance the performance of signal subspace based methods

source enumeration for high resolution array processing using improved gerschgorin radii without eigendecomposition accurate detection of sources with low complexity is of considerable interest in practical applications of high resolution array processing this paper addresses a new computationally efficient method for source enumeration by using enhanced gerschgorin radii without eigendecompositofion the proposed method can calculate the gerschgorin radii in a more efficient manner in which the additive background noise can be efficiently suppressed and the computational complexity can be considerably reduced therefore the method is more accurate and computationally attractive furthermore the method does not rely on the eigenvalues of a covariance matrix or the signal noise power making it robust against deviations from the assumption of spatially white noise model numerical results are presented to demonstrate the performance of the method

strong iiss is preserved under cascade interconnection in a recent paper we have introduced the notion of strong iiss as a compromise between the strength of input to state stability iss and the generality of integral iss iiss in this note we continue the investigations around this property by studying its behavior in an interconnection context in particular we show that the cascade of strongly iiss systems is itself strongly iiss and we recall some useful tools to study strongly iiss systems in feedback interconnection

maximum a posteriori maximum entropy order determination an instance crucial to most problems in signal processing is the selection of the order of a presupposed model examples are the determination of the putative number of signals present in white gaussian noise or the number of noise contaminated sources impinging on a passive sensor array it is shown that maximum a posteriori bayesian arguments coupled with maximum entropy considerations offer an operational and consistent model order selection scheme competitive with the minimum description length criterion

enhanced nonlinear damping for a class of singularly perturbed interconnected nonlinear systems in this paper we propose a method of enhanced nonlinear damping control for a class of singularly perturbed interconnected nonlinear systems spinss instead of simply canceling out the interconnection between slow and fast subsystems the proposed method transforms spins into a feedback connection of two output strictly passive subsystems then enhanced nonlinear damping is implemented to improve the transient behavior of slow subsystem the proposed method provides weighting factors for each tracking error which enable the energy function to be designed to shape the tracking performance for each state we also design an augmented state observer to estimate unknown disturbances and unmeasurable states using a composite lyapunov function we prove that the origin of the tracking error dynamics is globally exponentially stable it is also analyzed that the tracking errors are globally uniformly ultimately bounded for a time varying bounded disturbance experiments were performed to evaluate the tracking performance of the proposed method and our results validate the effectiveness of the proposed method

holder estimates for parabolic p x t laplacian systems in this paper we establish the local holder continuity of the spatial gradient of weak solutions to the parabolic p x t laplacian system begin array lll partial t u rm div left a x t du p x t 2 du right 0 end array more precisely we prove that begin array lll du in c rm loc 0 alpha alpha 2 quad rm for some alpha in 0 1 end array provided p and a are holder continuous

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

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

hessian estimates for fully nonlinear equations via the large m inequality principle abstract the approach using the large m inequality principle introduced by acerbi and mingione 2 has been broadly used in w 1 p regularity theory for nonlinear equations in divergence form we apply this approach to determine an alternative proof of the local w 2 p estimate for viscosity solutions to the fully nonlinear equations f d 2 u x f x using our method we derive weighted hessian estimates in variable exponent spaces for the viscosity solutions when nonlinearity f is assumed to be asymptotically convex

detecting the number of signals in wireless ds cdma networks in this paper a new information theoretic algorithm is proposed for signal enumeration in ds cdma networks the approach is based on the predictive description length pdl of the observation vector the pdl is the length of a predictive code of observations for signal detection the pdl criterion is computed for the candidate models and is minimized to determine the number of signals the proposed technique uses the maximum likelihood ml estimate of the correlation matrix the only information used in the ml estimation of the correlation matrix is the multiplicity of the smallest eigenvalue the pdl algorithm has a signal to noise ratio resolution threshold that is smaller than that of the minimum description length mdl the proposed method can be used on line and can be applied to time varying and non stationary systems

channel matrix recursion for blind effective channel order estimation channel order estimation is a critical task for blind system identification the performance of the blind system identification algorithms depends on the accuracy and robustness of the channel order estimation in this paper a new effective channel order estimation algorithm with high accuracy and robustness is proposed for single input multi output simo systems the proposed algorithm is guaranteed to find the true channel order for the noise free case and it performs significantly better than the alternative algorithms for noisy observations this algorithm shows a consistent performance when the number of observations channels and channel order are changed the proposed algorithm is integrated with the least squares smoothing lss algorithm for blind identification of the channel coefficients comparisons are done with a variety of different algorithms including linear prediction lp based methods it is shown that significant gain can be obtained compared to the alternative approaches in effective channel order estimation

reduced rank mdl method for source enumeration in high resolution array processing this paper proposes a reduced rank minimum description length mdl method to enumerate the incident waves impinging on a uniform linear array ula first a new observation data and a reference signal are formed from sensor data by means of the shift invariance property of the ula a cross correlation between them is calculated which is able to capture signal information and efficiently suppress additive noise second the normalized cross correlation is used as initial information for a recursion procedure to quickly partition the observation data into two orthogonal components in a signal subspace and a reduced rank noise subspace the components in the noise subspace are employed to calculate the total code length that is required to encode the observation data finally the model with the shortest code length namely the minimum description length is chosen as the best model unlike the traditional mdl methods this method partitions the observation data into the cleaner signal and noise subspace components by means of the recursion procedure avoiding the estimation of a covariance matrix and its eigendecomposition thus the method has the advantage of computational simplicity its performance is demonstrated via numerical results

maximum entropy as a special case of the minimum description length criterion corresp the maximum entropy me and maximum likelihood ml criteria are the bases for two approaches to statistical inference problems a new criterion called the minimum description length mdl has been recently introduced this criterion generalizes the ml method so it can be applied to more general situations e g when the number of parameters is unknown it is shown that me is also a special case of the mdl criterion maximizing the entropy subject to some constraints on the underlying probability function is identical to minimizing the code length required to represent all possible i i d realizations of the random variable such that the sample frequencies or histogram satisfy those given constraints

w 2 p cdot regularity for elliptic equations in nondivergence form with bmo coefficients we establish an optimal w 2 p cdot estimate to the dirichlet problem for an elliptic equation in nondivergence form with discontinuous coefficients on a c 1 1 bounded domain for every variable exponent p cdot with log holder continuity the matrix of the coefficients is assumed to have a small bmo semi norm depending on the exponent the boundary of the domain and the matrix itself

source enumeration in array processing using a two step test we investigate the problem of enumerating source signals impinging on an array of sensors given noisy limited observations the assumption of a large sample size is indispensable for most of the existing approaches so that they suffer significant performance degradation when only a small number of samples is available random matrix theory can capture the asymptotic distributions of the eigenvalues accurately and provide good approximations even for a finite sample size in this paper we take into account the relationship and distributions of the noise and signal eigenvalues based on random matrix theory and derive a simple two step test numerical simulations demonstrate that it is capable of correctly determining the number of sources in the case of small sample sizes

2 solvability of the dirichlet problem for nondivergence elliptic equations with vmo coefficients we prove a well posedness result in the class w 2 p w 0 1 p for the dirichlet problem lu f a e in u 0 on we assume the coefficients of the elliptic nondivergence form equation that we study are in vmo l

optimality of high resolution array processing using the eigensystem approach in the classical approach to underwater passive listening the medium is sampled in a convenient number of look directions from which the signals are estimated in order to build an image of the noise field in contrast a modern trend is to consider the noise field as a global entity depending on few parameters to be estimated simultaneously in a gaussian context it is worthwhile to consider the application of likelihood methods in order to derive a detection test for the number of sources and estimators for their locations and spectral levels this paper aims to compute such estimators when the wavefront shapes are not assumed known a priori this justifies results previously found using the asymptotical properties of the eigenvalue eigenvector decomposition of the estimated spectral density matrix of the sensor signals they have led to a variety of high resolution array processing methods more specifically a covariance matrix test for equality of the smallest eigenvalues is presented for source detection for source localization a best fit method and a test of orthogonality between the smallest eigenvectors and the source vectors are discussed

flexible detection criterion for source enumeration in array processing two new procedures are proposed using random matrix theory to evaluate theoretically the performance of the bayesian information criterion bic for source enumeration in array processing the proposed procedures can predict precisely the estimation results of the bic also they shed light on the behavior of the bic in order to remedy the limitation of the bic that is the bic tends to underestimate the number of sources by one in most cases an extra parameter is introduced into the bic formulation which results in a new criterion for source enumeration referred to as the flexible detection criterion fdc by carefully choosing this parameter the fdc is capable of substantially reducing the probability of underestimation which is validated by theoretical analysis and simulations note that the fdc is consistent and has low computational complexity as the bic

w 1 p regularity for elliptic equations with measurable coefficients in nonsmooth domains we establish global w 1 p estimates for second order elliptic equations in divergence form under the natural assumption that p is log holder continuous to this end we assume that the coefficients are measurable in one variable and have small bmo semi norms in the other variables and the boundary of the domain is reifenberg flat our work is an optimal and natural extension of w 1 p regularity for such equations with merely measurable coefficients beyond lipschitz domains

design of partially adaptive array beamformers based on information theoretic criteria in this paper two basic problems in designing partially adaptive array beamformers based on the structure of generalized sidelobe canceller gsc are considered the first problem is to decide the proper dimension of the required adaptive weight vector using the information of the array output power we develop the detection formulas for the information theoretic criteria aic and mdl to decide the proper dimension of the adaptive weight vector if the input noise power is unknown a priori efficient methods are proposed for estimating the input noise power in both cases with and without the desired signal to make the detection formulas still feasible the second problem is to find the most appropriate channel signals for weight adaptation for efficiently canceling interference an efficient method based on the maximum power reduction criterion is presented for selecting the most desired channel signals from the output of the signal blocking matrix theoretical analysis concerning the performance of the proposed methods is made computer simulations showing the effectiveness of the proposed methods are also provided

gradient estimates for the p x laplacean system we prove calderon and zygmund type estimates for a class of elliptic problems whose model is the non homogeneous p x laplacean system div jduj p x 2 du div jf j p x 2 f

source number estimators using transformed gerschgorin radii we introduce effective uses of gerschgorin radii of the unitary transformed covariance matrix for source number estimation there are two approaches likelihood and heuristic used for developing the detection criteria the likelihood approach combines the gerschgorin radii to the well known source number detectors and improves their detection performances for gaussian and white noise processes it is verified that the gerschgorin likelihood estimators gle are consistent the gerschgorin aic yields a consistent estimate and the gerschgorin mdl criterion does not tend to underestimate for small or moderate data samples the heuristic approach applying the gerschgorin disk estimator gde developed from the projection concept overcomes the problem in cases of small data samples an unknown noise model and data dependency furthermore the detection performances of both approaches through the suggested rotations and averaging can be further improved finally the proposed and existing criteria are evaluated in various conditions by using simulated and measured experimental data

svd based information theoretic criteria for detection of the number of damped undamped sinusoids and their performance analysis following the information theoretic approach to model selection the authors develop criteria for detection of the number of damped undamped sinusoids these criteria are matched to the singular value decomposition svd based methods such as modified forward backward and forward backward linear prediction so well that the extra computations needed over and above those required for computing the svd are marginal next an analytical framework for analyzing the performance of these criteria is developed in the development of the analysis some approximations which become better for large signal to noise ratio are made simulations are used to verify the usefulness of the analysis and to compare the performance of the method with that of j j fuchs 1988

detection of signals by information theoretic criteria general asymptotic performance analysis detecting the number of sources is a well known and a well investigated problem in this problem the number of sources impinging on an array of sensors is to be estimated the common approach for solving this problem is to use an information theoretic criterion like the minimum description length mdl or the akaike information criterion aic although it has been gaining much popularity and has been used in a variety of problems the performance of information theoretic criteria based estimators for the unknown number of sources has not been sufficiently studied yet in the context of array processing the performance of such estimators were analyzed only for the special case of gaussian sources where no prior knowledge of the array structure if given is used based on the theory of misspecified models this paper presents a general asymptotic analysis of the performance of any information theoretic criterion based estimator and especially of the mdl estimator in particular the performance of the mdl estimator which assumes gaussian sources and structured array when applied to gaussian sources is analyzed in addition it is shown that the performance of a certain mdl estimator is not very sensitive to the actual distribution of the source signals however appropriate use of prior knowledge about the array geometry can lead to significant improvement in the performance of the mdl estimator simulation results show a good fit between the empirical and the theoretical results