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

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

spatio temporal spectral analysis by eigenstructure methods this paper presents new algorithms for estimating the spatio temporal spectrum of the signals received by a passive array the algorithms are based on the eigenstructure of the covariance and spectral density matrices of the received signals they allow partial correlation between the sources and thus are applicable to certain kinds of multipath problems simulation results that illustrate the performance of the new algorithms are presented

symplectic topology and hamiltonian dynamics on etudie des applications symplectiques non lineaires capacites symplectiques construction d une capacite symplectique problemes de plongement problemes de rigidite

subspace based channel estimation for code division multiple access communication systems we consider the estimation of channel parameters for code division multiple access cdma communication systems operating over channels with either single or multiple propagation paths the multiuser channel estimation problem is decomposed into a series of single user problems through a subspace based approach by exploiting the eigenstructure of the received signal s sample correlation matrix the observation space can be partitioned into a signal subspace and a noise subspace without prior knowledge of the unknown parameters the channel estimate is formed by projecting a given user s spreading waveform into the estimated noise subspace and then either minimizing the likelihood or minimizing the euclidean norm of this projection both of these approaches yield algorithms which are near far resistant and do not require a preamble

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

a 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

detection of the number of signals in the presence of white noise in decentralized processing the problem of estimating the number of signals under a white noise model is solved when the data are received from many different places that are widely apart by using modified information criterion proposed by the author this criterion involves the eigenvalues of the sample canonical correlation matrix some simulation results are also presented

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

estimation of the number of sources in unbalanced arrays via information theoretic criteria estimating the number of sources impinging on an array of sensors is a well known and well investigated problem a common approach for solving this problem is to use an information theoretic criterion such as minimum description length mdl or the akaike information criterion aic the mdl estimator is known to be a consistent estimator robust against deviations from the gaussian assumption and nonrobust against deviations from the point source and or temporally or spatially white additive noise assumptions over the years several alternative estimation algorithms have been proposed and tested usually these algorithms are shown using computer simulations to have improved performance over the mdl estimator and to be robust against deviations from the assumed spatial model nevertheless these robust algorithms have high computational complexity requiring several multidimensional searches in this paper which is motivated by real life problems a systematic approach toward the problem of robust estimation of the number of sources using information theoretic criteria is taken an mdl type estimator that is robust against deviation from assumption of equal noise level across the array is studied the consistency of this estimator even when deviations from the equal noise level assumption occur is proven a novel low complexity implementation method avoiding the need for multidimensional searches is presented as well making this estimator a favorable choice for practical applications

on a non vanishing conjecture of kawamata and the core of an ideal we show under suitable hypothesis which are sharp in a certain sense that the core of an m primary ideal in a regular local ring of dimension d is equal to the adjoint or multiplier ideal of its d th power this generalizes the fundamental formula for the core of an integrally closed ideal in a two dimensional regular local ring due to huneke and swanson we also find a generalization of this result to singular non regular settings which we show to be intimately related to the problem of finding non zero sections of ample line bundles on projective varieties in particular we show that a graded analog of our formula for core would imply a remarkable conjecture of kawamata predicting that every adjoint ample line bundle on a smooth variety admits a non zero section

order selection of autoregressive models the problem of determining the order of autoregressive models by bayesian predictive densities is addressed a criterion employing noninformative prior densities of the model parameters is derived simulation results which demonstrate the good performance of the criterion are presented comparisons with four popular approaches verify its superiority in many cases

estimating the parameters of exponentially damped sinusoids and pole zero modeling in noise we have presented techniques 1 6 based on linear prediction lp and singular value decomposition svd for accurate estimation of closely spaced frequencies of sinusoidal signals in noise in this note we extend these techniques to estimate the parameters of exponentially damped sinusoidal signals in noise the estimation procedure presented here makes use of backward prediction in addition to svd first the method is applied to data consisting of one and two exponentially damped sinusoids the choice of one and two signal components facilitates the comparison of estimation error in pole damping factors and pole frequencies to the appropriate cramer rao cr bounds and to traditional methods of linear prediction second our method is applied to an example due to steiglitz 8 in which the data consists of noisy values of the impulse response samples composed of many exponentially damped sinusoids of a linear system having both poles and zeros the poles of the system are accurately determined by our method and the zeros are obtained subsequently using shanks method

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

number of source signal estimation by the mean squared eigenvalue error detection of the number of source signals noss in the presence of additive noise is considered we present a new approach denoted by the mean squared eigenvalue error msee the msee is the mean squared error between the desired noise free eigenvalues and the available estimated eigenvalues the approach investigates and analyzes the probabilistic distribution of the available eigenvalue estimates and revisits proper thresholding of these sorted values the optimum noss is provided by minimizing the msee a probabilistic worst case technique is proposed to estimate the value of the msee by using only the available data it is shown that the proposed method is consistent as the data length increases it is also shown that the method is consistent as the signal to noise ratio snr increases simulation results illustrate advantages of the msee over competing approaches and confirm effectiveness and robustness of the msee even in low snr or small sample size scenarios

the mdl criterion for rank determination via effective singular values konstantinides and yao 1988 have considered the problem of rank determination by use of effective singular values in this correspondence we show how to use the minimum description length criterion of rissanen to provide an alternative means of estimating the index of the smallest nonzero singular value of a matrix when given estimates of the singular values

discreteness and rationality of f jumping numbers on singular varieties we prove that the f jumping numbers of the test ideal tau x delta mathfrak a t are discrete and rational under the assumptions that x is a normal and f finite scheme over a field of positive characteristic p kx is mathbb q cartier of index not divisible p and either x is essentially of finite type over a field or the sheaf of ideals mathfrak a is locally principal this is the largest generality for which discreteness and rationality are known for the jumping numbers of multiplier ideals in characteristic zero

detection of the number of signals using the benjamini hochberg procedure this paper presents a novel approach to detect multiple signals embedded in noisy observations from a sensor array we formulate the detection problem as a multiple hypothesis test to control the global level of the multiple test we apply the false discovery rate fdr criterion proposed by benjamini and hochberg compared to the classical familywise error rate fwe criterion the fdr controling procedure leads to a significant gain in power for large size problems in addition we apply the bootstrap technique to estimate the observed significance level required by the fdr controling procedure simulations show that the fdr controling procedure always provides higher probability of correct detection than the fwe controling procedure furthermore the reliability of the proposed test procedure is not affected by the gain in power of the test

an information theoretic approach to source enumeration in array signal processing in this paper a new information theoretic algorithm is proposed for signal enumeration in array processing the approach is based on predictive description length pdl that is defined as the length of a predictive code for the set of observations we assume that several models with each model representing a certain number of sources will compete the pdl criterion is computed for the candidate models and is minimized over all models to select the best model and to determine the number of signals in the proposed method the correlation matrix is decomposed into two orthogonal components in the signal and noise subspaces the maximum likelihood ml estimates of the angles of arrival are used to find the projection of the sample correlation matrix onto the signal and noise subspaces the summation of the ml estimates of these matrices is the ml estimate of the correlation matrix this method can detect both coherent and noncoherent signals the proposed method can be used online and can be applied to time varying systems and target tracking

valuations and multiplier ideals this article is the third of a series of work on a new approach to the study of singularities of various objects in a local two dimensional setting our focus in the present paper is on multiplier ideals and singularity exponents in the discussion below we fix an equicharacteristic zero two dimensional regular local ring r m with algebraically closed residue field an important example is the ring r do o holomorphic germs at the origin in c2 in fj1 we introduced the space v consisting of all r u 00 valued valuations on r centered at m and normalized by m 1 this space is naturally a tree it is a union of uncountably many real segments patched together in such a way that v remains homotopic to a point it is also an r tree in the classical sense for a natural metric we hence call v the valuative tree it encodes in a natural way all possible blowups of r centered at m and therefore gives a way of measuring quite precisely singularities of different kinds of objects the points in v that are not ends form the subtree vqm of quasimonomial valuations these valuations which can alternatively be characterized as abhyankar valuations of rank 1 or as

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

poincare series of multiplier ideals in two dimensional local rings with rational singularities abstract we study the multiplicity of the jumping numbers of an m primary ideal a in a two dimensional local ring with a rational singularity the formula we provide for the multiplicities leads to a very simple and efficient method to detect whether a given rational number is a jumping number we also give an explicit description of the poincare series of multiplier ideals associated to a proving in particular that it is a rational function

new invariants of open symplectic and contact manifolds the first specifically symplectic invariant of open symplectic manifolds the width was defined by m gromov in gr gromov s width was generalized by h hofer i ekeland e zehnder and a floer see eh hz fh they defined numerous new invariants i e symplectic capacities all these invariants are monotonic with respect to the inclusion and serve as obstructions for symplectic embeddings for contact manifolds so far no invariants are known except overtwisting phenomenon in dimension three see bel ell it turns out that much more rich obstructions for symplectic see 2 2 and what is especially interesting for contact embeddings see 3 2 and 3 5 can be defined if we consider embeddings in a prescribed homotopy class this paper is inspired by a recent discovery by benci and sikorav see bc sil ls and 2 4 1 below recently j c sikorav see si2 independently developed some of the ideas discussed in this paper his interests are exclusively in the symplectic field while i am interested mainly in applications to the contact topology the most interesting result of this paper is theorem 3 5 1 which shows in particular the existence of nonisomorphic open solid tori in the standard contact s3

contribution of jumping numbers by exceptional divisors abstract we investigate some necessary and sufficient conditions for an exceptional divisor to contribute jumping numbers of an effective divisor on a variety of arbitrary dimension inspired by the results for curves on surfaces by smith and thompson 17 and tucker 18 in particular we construct an example of an exceptional divisor that is not contracted in the log canonical model and does not contribute any jumping numbers

the poincare series of multiplier ideals of a simple complete ideal in a local ring of a smooth surface abstract for a simple complete ideal of a local ring at a closed point on a smooth complex algebraic surface we introduce an algebraic object named poincare series p that gathers in a unified way the jumping numbers and the dimensions of the vector space quotients given by consecutive multiplier ideals attached to this paper is devoted to prove that p is a rational function giving an explicit expression for it

on posterior distributions for signals in gaussian noise with unknown covariance matrix a bayesian approach to estimate parameters of signals embedded in complex gaussian noise with unknown color is presented the study specifically focuses on a bayesian treatment of the unknown noise covariance matrix making up a nuisance parameter in such problems by integrating out uncertainties regarding the noise color an enhanced ability to estimate both the signal parameters as well as properties of the error is exploited several noninformative priors for the covariance matrix such as the reference prior the jeffreys prior and modifications to this are considered some of the priors result in analytical solutions whereas others demand numerical approximations in the linear signal model connections are made between the standard adaptive maximum likelihood aml estimate and a bayesian solution using the jeffreys prior with adjustments to the jeffreys prior correspondence to the regularized solution is also established this in turn enables a formal treatment of the regularization parameter simulations indicate that significant improvements compared to the aml estimator can be obtained by considering both the derived regularized solutions as well as the one obtained using the reference prior the simulations also indicate the possibility of enhancing the predictions of properties of the error as uncertainties in the noise color are acknowledged

tight contact structures on solid tori in this paper we study properties of tight contact structures on solid tori in particular we discuss ways of distinguishing two solicl tori with tight contact structures we also give examples of unusual tight contact structures on solid tori we prove the existence of a 2 valued and a llt 27re valued invaria nt of a closed solid torus we call them the self linking number and the rotation number respectively we then extend these definitions to the case of an open solid torus we show that these invariants exhibit certain monotonicity properties with respect to inclusion we also prove a number of results which give sufficient conditions for two solid tori to be contactomorphic at the same time we discuss various ways of constructing a tight contact structure on a solid torus we then produce examples of solid tori with tight contact structures and calculate self linking and rotation numbers for these tori these examples show that the invariants we defined do not give a complete classification of tight contact structure on open solid tori at the end we construct a family of tight contact structure on a solid torus such that the induced contact structure on a finite sheeted cover of that solid torus is no longer tight this answers negatively a question asked by eliashberg in 1990 we also give an example of tight contact structure on an open solid torus which cannot be contactly embedded into a sphere with the standard contact structure another example o1 unexpected behavior

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

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

a formula for jumping numbers in a two dimensional regular local ring abstract in this article we give an explicit formula for the jumping numbers of an ideal of finite colength in a two dimensional regular local ring with an algebraically closed residue field for this purpose we associate a certain numerical semigroup to each vertex of the dual graph of a log resolution of the ideal

poles of the topological zeta function associated to an ideal in dimension two to an ideal in mathbb c x y one can associate a topological zeta function this is an extension of the topological zeta function associated to one polynomial but in this case we use a principalization of the ideal instead of an embedded resolution of the curve in this paper we will study two questions about the poles of this zeta function first we will give a criterion to determine whether or not a candidate pole is a pole it turns out that we can know this immediately by looking at the intersection diagram of the principalization together with the numerical data of the exceptional curves afterwards we will completely describe the set of rational numbers that can occur as poles of a topological zeta function associated to an ideal in dimension two the same results are valid for related zeta functions as for instance the motivic zeta function

on the use of order statistics for improved detection of signals by the mdl criterion the minimum description length mdl criterion for model selection has been successfully applied to the problem of estimating the number of sources in noise we show that by employing an order statistics approach in the existing solution a new processor with uniformly improved performance is constructed at the cost of greater complexity we prove that the resulting mdl based processor is consistent results of simulations of practical scenarios of interest demonstrate how significant the performance improvement can be