maximum likelihood estimation of a structured covariance matrix with a condition number constraint in this paper we deal with the problem of estimating the disturbance covariance matrix for radar signal processing applications when a limited number of training data is present we determine the maximum likelihood ml estimator of the covariance matrix starting from a set of secondary data assuming a special covariance structure i e the sum of a positive semi definite matrix plus a term proportional to the identity and a condition number upper bound constraint we show that the formulated constrained optimization problem falls within the class of maxdet problems and develop an efficient procedure for its solution in closed form remarkably the computational complexity of the algorithm is of the same order as the eigenvalue decomposition of the sample covariance matrix at the analysis stage we assess the performance of the proposed algorithm in terms of achievable signal to interference plus noise ratio sinr both for a spatial and a doppler processing the results show that interesting sinr improvements with respect to some existing covariance matrix estimation techniques can be achieved

fast converging adaptive detection of doppler shifted range distributed targets a generalized likelihood ratio test glrt for the adaptive detection of a target or targets that are doppler shifted and distributed in range is derived the unknown parameters associated with the hypothesis test are the complex amplitudes in range of the desired target and the unknown covariance matrix of the additive interference which is assumed to be characterized as complex zero mean correlated gaussian random variables the target s or targets complex amplitudes are assumed to be distributed across the entire input data block sensor spl times range the unknown covariance matrix is constrained to have the reasonable form of the identity matrix the internal noise contribution plus an unknown positive semidefinite psdh matrix the external interference contribution it is shown via simulation for a variety of interference scenarios that the new detector has the characteristic of having a bounded constant false alarm rate cfar i e for our problem the probability of false alarm p sub f for a given detection threshold is bounded by the p sub f that results when no external interference is present it is also shown via simulation that the new detector converges relatively fast with respect to the number of sample vectors k necessary in order to achieve a given probability of detection p sub d

a new parametric glrt for multichannel adaptive signal detection a parametric generalized likelihood ratio test glrt for multichannel signal detection in spatially and temporally colored disturbance was recently introduced by modeling the disturbance as a multichannel autoregressive ar process the detector however involves a highly nonlinear maximum likelihood estimation procedure which was solved via a two dimensional iterative search method initialized by a suboptimal estimator in this paper we present a simplified glrt along with a new estimator for the problem both the estimator and the glrt are derived in closed form at considerably lower complexity with adequate training data the new glrt achieves a similar detection performance as the original one however for the more interesting case of limited training the original glrt may become inferior due to poor initialization because of its simpler form the new glrt also offers additional insight into the parametric multichannel signal detection problem the performance of the proposed detector is assessed using both a simulated dataset which was generated using multichannel ar models and the kassper dataset a widely used dataset with challenging heterogeneous effects found in real world environments

glrt based direction detectors in homogeneous noise and subspace interference in this paper we derive and assess decision schemes to discriminate resorting to an array of sensors between the h0 hypothesis that data under test contain disturbance only i e noise plus interference and the h1 hypothesis that they also contain signal components along a direction which is a priori unknown but constrained to belong to a given subspace of the observables the disturbance is modeled in terms of complex normal random vectors plus deterministic interference assumed to belong to a known subspace we assume that a set of noise only secondary data is available which possess the same statistical characterization of noise in the cells under test at the design stage we resort to either the plain generalized likelihood ratio test glrt or the two step glrt based design procedure the performance analysis conducted resorting to simulated data shows that the one step glrt performs better than the detector relying on the two step design procedure when the number of secondary data is comparable to the number of sensors moreover it outperforms a one step glrt based subspace detector when the dimension of the signal subspace is sufficiently high

regular article a fast adaptive multipole algorithm in three dimensions we present an adaptive fast multipole method for the laplace equation in three dimensions it uses both new compression techniques and diagonal forms for translation operators to achieve high accuracy at a reasonable cost

radar detection of distributed targets in homogeneous interference whose inverse covariance structure is defined via unitary invariant functions in this paper we deal with the problem of detecting an extended target embedded in homogeneous gaussian interference with unknown but structured covariance matrix we model the possible target echo from each range bin under test as a deterministic signal with an unknown scaling factor accounting for the target response at the design stage we exploit some a priori knowledge about the operating environment enforcing the inverse interference plus noise covariance matrix to belong to a set described via unitary invariant continuous functions hence we derive the constrained maximum likelihood ml estimates of the unknown parameters under both the h0 and h1 hypotheses and design the generalized likelihood ratio test glrt for the considered decision problem at the analysis stage we assess the performance of the devised glrt for some covariance matrix uncertainty sets of practical relevance both for spatial and doppler processing the results highlight that correct use of the a priori knowledge can lead to a detection performance quite close to the optimum receiver which supposes the perfect knowledge of the interference plus noise covariance matrix

joint estimation of inverse covariance matrices lying in an unknown subspace we consider the problem of joint estimation of inverse covariance matrices lying in an unknown subspace of the linear space of symmetric matrices we perform the estimation using groups of measurements with different covariances assuming the inverse covariances span a low dimensional subspace our aim is to determine this subspace and to exploit this knowledge in order to improve the estimation we develop a novel optimization algorithm discovering and exploiting the underlying low dimensional subspace we provide a computationally efficient algorithm and derive a tight upper performance bound numerical simulations on synthetic and real world data are presented to illustrate the performance benefits of the algorithm

subspace based adaptive generalized likelihood ratio detection subspace based adaptive detection performance is examined for the generalized likelihood ratio detector based on wilks spl lambda statistic the problem considered here is detecting the presence of one or more signals of known shape embedded in gaussian distributed noise with unknown covariance structure the data is mapped into a subspace prior to detection the probability of false alarm is independent of the subspace transformation and depends only on subspace dimension the probability of detection depends on the subspace transformation through a nonadaptive signal to noise ratio snr parameter subspace processing results in an snr loss that tends to decrease performance and a gain in statistical stability that tends to increase performance it is shown that the statistical stability effect dominates the snr loss for short data records and subspace detectors can require substantially less snr than full space detectors for equivalent performance a method for designing the subspace transformation to minimize the snr loss is proposed and illustrated through simulations

adaptive array detection of uncertain rank one waveforms adaptive array detection of known within a complex scaling rank one space time waveforms in unknown spatial noise has received considerable attention the two published solutions are the adaptive matched filter and the glrt we expand on this work to consider the case of rank one waveforms that are uncertain i e only partially known more precisely we model the space time steering vector as the kronecker product of two vectors each of which is unknown but is known to lie in a known subspace applications for such a model include detection in the presence of multipath and spectral or polarization diversity in both radar processing and wireless communication using the principle of invariance we construct detectors based on the maximal invariant we show that the snr required to achieve a given detection probability for a given false alarm rate is only weakly impacted by waveform uncertainty thus our detector approaches the performance of earlier detectors which entail known waveforms

knowledge aided parametric adaptive matched filter with automatic combining for covariance estimation in this paper a knowledge aided parametric adap tive matched filter ka pamf is proposed that utilizing both observations including the test and training signals and ap riori knowledge of the spatial covariance matrix unlike existing ka pamf methods the proposed ka pamf is able to automat ically adjust the combining weight of ap rioricovariance matrix thus gaining enhanced robustness against uncertainty in the prior knowledge meanwhile the proposed ka pamf is significantly more efficient than its ka nonparametric counterparts when the amount of training signals is limited one distinct feature of the proposed ka pamf is the inclusion of both the test and training signals for automatic determination of the combining weights for the prior spatial covariance matrix and observations numerical results are presented to demonstrate the effectiveness of the proposed ka pamf especially in the limited training scenarios

fast analytical methods for macroscopic electrostatic models in biomolecular simulations we review recent developments of fast analytical methods for macroscopic electrostatic calculations in biological applications including the poisson boltzmann pb and the generalized born models for electrostatic solvation energy the focus is on analytical approaches for hybrid solvation models especially the image charge method for a spherical cavity and also the generalized born theory as an approximation to the pb model this review places much emphasis on the mathematical details behind these methods

adaptive double subspace signal detection in gaussian background part i homogeneous environments in this two part paper we consider the problem of adaptive multidimensional multichannel signal detection in gaussian noise with unknown covariance matrix the test data primary data is assumed as a collection of sample vectors arranged as the columns of a rectangular data array the rows and columns of the signal matrix are both assumed to lie in known subspaces but with unknown coordinates due to this feature of the signal structure we name this kind of signal as the double subspace signal part i of this paper focuses on the adaptive detection in homogeneous environments while part ii deals with the adaptive detection in partially homogeneous environments precisely in this part we derive the generalized likelihood ratio test glrt rao test wald test as well as their two step variations in homogeneous environments three types of spectral norm tests snts are also introduced all these detectors are shown to possess the constant false alarm rate cfar property moreover we discuss the differences between them and show how they work another contribution is that we investigate various special cases of these detectors remarkably some of them are well known existing detectors while some others are still new at the stage of performance evaluation conducted by monte carlo simulations both matched and mismatched signals are dealt with for each case more than one scenario is considered

diffuse multipath exploitation for adaptive radar detection we deal with the problem of detecting point like targets in diffuse multipath environments modeling the target echo as the superposition of a deterministic signal with an unknown scaling factor due to the direct path plus a zero mean complex circular symmetric gaussian random vector with an unknown covariance matrix accounting for the echoes from the glistening surface we devise a constrained generalized likelihood ratio test glrt for the resulting hypothesis testing problem enforcing the primary data covariance matrix due to both interference and multipath echoes to belong to a neighborhood of the secondary data sample covariance matrix remarkably the proposed decision scheme ensures the desirable constant false alarm rate cfar property with respect to the unknown parameters of the interference the performance assessment conducted on simulated data in terms of detection probability also in comparison with existing solutions highlights the effectiveness of the new approach to cope with diffuse multipath phenomena

theta dichotomy for unitary groups some recent work of gross and prasad 14 suggests that the root numbers attached to certain symplectic representations of the weil deligne group of a local field f control certain branching rules for representations of orthogonal groups over f on a global level this local phenomenon should have implications for the structure of the value at the center of symmetry for certain l functions of arithmetic interest 12 this conjectural picture is based to some extent on the now classic work of tunnell 47 and waldspurger 49 as well as on the case of the triple product l function 13 34 17 in all of these examples the local root number detects the existence of a certain type of invariant linear functional it is possible to set up analogous conjectures for the isometry groups of hermitian or quaternion hermitian forms it turns out that root numbers also play a role in the local and global theta correspondence roughly speaking certain local root numbers should control the occurrence of representations in the local theta correspondence between groups of the same size e g for dual pairs of the form sp n o 2n 1 and u n u n as will be seen the theta correspondence for such pairs is connected with a certain induced representation in s at the point s 0 on the unitary axis by contrast the correspondence for the pairs sp n o 2n and sp n o 2n 2 discussed by prasad 35 is connected to the behavior of a similar induced representation at the points 12 in which case no epsilon factor arises in this paper we consider the local theta correspondence for unitary groups in the non archimedean case let f be a non archimedean local field of characteristic not equal to 2 and let e be a quadratic extension of f for further notation see the notation section at the end of this introduction let v and w be e vector spaces of dimensions m and n equipped respectively with a hermitian form v v e and a skew hermitian form w w e then the isometry groups g v and g w of the spaces v and w form a dual reductive pair in the symplectic group sp w where w v e w viewed as an f vector space of dimension 2mn and equipped with the symplectic form

mellin transform and image charge method for dielectric sphere in an electrolyte we revisit the image charge method for the green s function problem of the poisson boltzmann equation for a dielectric sphere immersed in ionic solutions using finite mellin transformation we represent the reaction potential due to a source charge inside the sphere in terms of a one dimensional distribution of image charges the image charges are generically composed of a point image at the kelvin point and a line image extending from the kelvin point to infinity with an oscillatory line charge strength we further develop an efficient and accurate algorithm for discretization of the line image using pade approximation and finite fraction expansion finally we illustrate the power of our method by applying it in a multiscale reaction field monte carlo simulation of monovalent electrolytes

adaptive detection of range distributed targets a modified generalized likelihood ratio test mglrt for the adaptive detection of a target or targets that are distributed in range is derived the unknown parameters associated with the hypothesis test are the complex amplitudes in range of the desired target and the unknown covariance matrix of the additive interference which is assumed to be characterized as complex zero mean correlated gaussian random variables the target s or targets complex amplitudes are assumed to be distributed across the entire input data block sensor spl times range results on probabilities of false alarm and detection are derived and a bounded constant false alarm rate cfar detector is developed simulation results are presented it is shown that the derived mglrt of range distributed targets is much more effective in detecting targets distributed in range than an m out of k detector which is cascaded with a single point target kelly 1986 detector

on tensor product l functions for quaternion unitary groups and gl 2 over totally real number fields mixed weight cases abstract we prove an algebraicity of special values of tensor product l functions for quaternion unitary groups and gl 2 in the mixed weight cases over any totally real number field as a consequence we can prove a period relation for automorphic forms of quaternion unitary groups of degree 2 and gsp 4 when these automorphic forms correspond under the conjectural jacquet langlands correspondence and a period relation for endoscopic liftings of gsp 4 in very general situations

on the nonvanishing of the central value of the rankin selberg l functions first published in journal of the american mathematical society in volume 17 issue 3 published by the american mathematical society

trilinear forms and the central values of triple product l functions we give an explicit formula for certain global trilinear forms that appear in jacquet s conjecture in terms of local trilinear forms and the central values of triple product l functions

generalised form of a conjecture of jacquet and a local consequence following the work of harris and kudla we prove a general form of a conjecture of jacquet relating the non vanishing of a certain period integral to non vanishing of the central critical value of a certain l function as a consequence we deduce a theorem relating the existence of gl 2 k invariant linear forms on irreducible admissible representations of gl 2 k for a commutative semi simple cubic algebra k over a non archimedean local field k in terms of local epsilon factors which was proved only in some cases by the first author in his earlier work in d prasad invariant forms for representations of gl 2 over a local field amer j math 114 1992 no 6 1317 1363 this has been achieved by globalising a locally distinguished supercuspidal representation to a globally distinguished representation a result of independent interest which is proved by an application of the relative trace formula

image charge approximations of reaction fields in solvents with arbitrary ionic strength in this paper we report a new development of image charge approximations of reaction fields for a charge inside a dielectric spherical cavity immersed in an ionic solvent with arbitrary ionic strength this new development removes the requirement of low ionic strength of the solvent in a previous result s deng w cai extending the fast multipole method for charges inside a dielectric sphere in an ionic solvent high order image approximations for reaction fields j comput phys 227 2007 1246 1266 thus extending the applicability of the image charge approximations of reaction fields in the modeling of biomolecular solvation

glrt based adaptive detection algorithms for range spread targets we address adaptive detection of a range spread target or targets embedded in gaussian noise with unknown covariance matrix to this end we assume that cells referred to in the following as secondary data that are free of signal components are available those secondary data are supposed to possess either the same covariance matrix or the same structure of the covariance matrix of the cells under test in this context we design detectors relying on the generalized likelihood ratio test glrt and on a two step glrt based design procedure remarkably both criteria lead to receivers ensuring the constant false alarm rate cfar property with respect to the unknown quantities a thorough performance assessment of the proposed detection strategies together with the evaluation of their processing cost highlights that the two step design procedure is to be preferred with respect to the plain glrt in fact the former leads to detectors that achieve satisfactory performance under several situations of practical interest and are simpler to implement than those designed resorting to the latter