the beta model maximum likelihood cramer rao bounds and hypothesis testing we study the maximum likelihood estimator in a setting where the dependent variable is a random graph and covariates are available on a graph level the model generalizes the well known beta model for random graphs by replacing the constant model parameters with regression functions cramer rao bounds are derived for special cases of the undirected beta model the directed beta model and the covariate based beta model the corresponding maximum likelihood estimators are compared with the bounds by means of simulations moreover examples are given on how to use the presented maximum likelihood estimators to test for directionality and significance finally the applicability of the model is demonstrated using temporal social network data describing communication among healthcare workers

theoretical performance limits of massive mimo with uncorrelated rician fading channels this paper considers a massive mimo network with l cells each comprising a base stations bs with m antennas and k single antenna user equipments within this setting we are interested in deriving approximations of the achievable rates in the uplink and downlink under the assumption that single cell linear processing is used at each bs and that each intracell link forms an uncorrelated mimo rician fading channel matrix that is with a deterministic line of sight los path and a stochastic non los component describing a spatial uncorrelated multipath environment the analysis is conducted assuming that n and k grow large with a given ratio textbf n k under the assumption that the data transmission in each cell is affected by channel estimation errors pilot contamination an arbitrary large scale attenuation and los components numerical results are used to prove that the approximations are asymptotically tight but accurate for systems with finite dimensions the asymptotic results are also used to evaluate the impact of los components in particular we exemplify how the number of antennas for achieving a target rate can be substantially reduced with los links of only a few dbs of strength

joint estimation of porosity and saturation using stochastic rock physics modeling sediment porosity and saturation affect bulk modulus shearmodulus anddensity consequently estimatinghydrocarbon saturation and reservoir porosity from seismic data is a joint estimation problem uncertainty in porosity will lead toerrorsinsaturationprediction andviceversa porosityand saturation can be jointly estimated using stochastic rockphysicsmodelingandformalbayesianestimationmethodology knowledge of shear impedance reduces the uncertainty inporosityandthusalsoreducesuncertaintyinsaturationestimation this study investigates joint estimation of porosity and saturation by using rock physics stochastic modeling and bayesian estimation theory to derive saturation and porosity maps of expected pay sands in the field example the uncertainty in porosity quantified by the standard deviation stdassociatedwiththeposteriorprobabilitydensityfunctionpdf derivedfrominversionofseismicdataismuchless than the uncertainty in the derived saturation for a typical case the std associated with saturation is 24 while porositystdisabout1 34porosityunitsgivenseismic derived inversionattributeswithreasonableaccuracy comparisonof these numbers with prior estimates showed that inversion of seismic data decreased the uncertainty in porosity to 15 of the prior uncertainty while saturation uncertainty was only reduced to 92 of the prior uncertainty although these resultsmayvaryfromonelocationtoanother themethodology isgeneralandcanbeappliedtootherlocations

limits of sensing temporal concentration changes by single cells berg and purcell biophys j 20 193 1977 calculated how the accuracy of concentration sensing by single celled organisms is limited by noise from the small number of counted molecules here we generalize their results to the sensing of concentration ramps which is often the biologically relevant situation e g during bacterial chemotaxis we calculate lower bounds on the uncertainty of ramp sensing by three measurement devices a single receptor an absorbing sphere and a monitoring sphere we contrast two strategies simple linear regression of the input signal versus maximum likelihood estimation and show that the latter can be twice as accurate as the former finally we consider biological implementations of these two strategies and identify possible signatures that maximum likelihood estimation is implemented by real biological systems

adaptive bem with inexact pcg solver yields almost optimal computational costs we consider the preconditioned conjugate gradient method pcg with optimal preconditioner in the frame of the boundary element method for elliptic first kind integral equations our adaptive algorithm steers the termination of pcg as well as the local mesh refinement besides convergence with optimal algebraic rates we also prove almost optimal computational complexity in particular we provide an additive schwarz preconditioner which can be computed in linear complexity and which is optimal in the sense that the condition numbers of the preconditioned systems are uniformly bounded as model problem serves the 2d or 3d laplace operator and the associated weakly singular integral equation with energy space widetilde h 1 2 gamma the main results also hold for the hyper singular integral equation with energy space h 1 2 gamma

robust linear channel estimation methods for per subcarrier transmit antenna selection the linear minimum mean squared error mse channel estimator for systems employing per subcarrier transmit antenna selection is developed frequency domain correlations after the selection process are shown to be approximated well using a simple function which makes near optimal channel estimation practically possible however the resultant estimators are not robust to errors in the assumed model in terms of the antenna to subcarrier assignment used at transmission as we motivate both analytically and via simulations this is an issue when the channels for conveying this information to the receiver are severely constrained we present windowed channel estimations and new robust estimation algorithms either individually or in combination as solutions to counter this sensitivity the robust estimators are developed based on the principles of 1 minimising the worst case mse over the set of possible models and 2 minimising the expected mse over the set of possible models the latter estimator is preferred due to the lower implementation complexity and better mse performance we also prove theoretical asymptotic in signal to noise ratio performances of the two estimators used with the proposed correlation model simulation results illustrate the performance gains and improved robustness offered by the developed estimators

adaptive bem with optimal convergence rates for the helmholtz equation abstract we analyze an adaptive boundary element method for the weakly singular and hypersingular integral equations for the 2d and 3d helmholtz problem the proposed adaptive algorithm is steered by a residual error estimator and does not rely on any a priori information that the underlying meshes are sufficiently fine we prove convergence of the error estimator with optimal algebraic rates independently of the coarse initial mesh as a technical contribution we prove certain local inverse type estimates for the boundary integral operators associated with the helmholtz equation

active learning applied to rcs computations with nonuniform sampling using different objective functions an active learning framework is introduced to reduce the number of frequencies and angles one must consider for wideband monostatic scattering computations or measurements this method is used to optimally select those frequencies and angles that would be most informative resulting in nonuniform sampling and often a reduced number of points vis agrave vis uniform sampling in this paper we focus on jointly two dimensional optimal sampling in frequency and incident angle thetas for monostatic scattering the method consists of two basic steps one step involves estimation of model parameters using a least square ls algorithm the next step is to optimally choose the next point frequency and thetas for analysis by the computational model or experiment this new point is selected with the goal of reducing uncertainty in the parametric model quantified via the fisher information matrix iterating these two steps a sequence of numerical computations or measurements are performed each at the most informative point for learning the parameters of the associated simpler parametric model this idea is demonstrated here in the context of reducing the number of points frequencies and orientations at which a computational model must be employed and in order to avoid repeatedly gathering samplings at the edge of the input space an alternative objective function is applied which makes the actively selected points closer to a region of interest

approximation classes for adaptive higher order finite element approximation we provide an almost characterization of the approximation classes appearing when using adaptive finite elements of lagrange type of any fixed polynomial degree the characterization is stated in terms of besov regularity and requires the approximation within spaces with integrability indices below one this article generalizes to higher order finite elements the results presented for linear finite elements by binev et al bddp 2002

convergence of adaptive finite element methods for general second order linear elliptic pdes we prove convergence of adaptive finite element methods afems for general nonsymmetric second order linear elliptic pdes thereby extending the result of morin nochetto and siebert it siam j numer anal 38 2000 pp 466 488 it siam rev 44 2002 pp 631 658 the proof relies on quasi orthogonality which accounts for the bilinear form not being a scalar product together with novel error and oscillation reduction estimates which now do not decouple we show that afems are a contraction for the sum of energy error plus oscillation numerical experiments including oscillatory coefficients and both coercive and noncoercive convection diffusion pde illustrate the theory and yield optimal meshes

quasi optimal convergence rate of an adaptive discontinuous galerkin method we analyze an adaptive discontinuous finite element method adfem for symmetric second order linear elliptic operators the method is formulated on nonconforming meshes made of simplices or quadrilaterals with any polynomial degree and in any dimension geq2 we prove that the adfem is a contraction for the sum of the energy error and the scaled error estimator between two consecutive adaptive loops we design a refinement procedure that maintains the level of nonconformity uniformly bounded and prove that the approximation classes using continuous and discontinuous finite elements are equivalent the geometric decay and the equivalence of classes are instrumental in deriving the optimal cardinality of the adfem we show that the adfem and the afem on nonconforming meshes yields a decay rate of energy error plus oscillation in terms of the number of degrees of freedom as dictated by the best approximation for this combined nonlinear quantity

optimal adaptivity for the supg finite element method abstract for convection dominated problems the streamline upwind petrov galerkin method supg also named streamline diffusion finite element method sdfem ensures a stable finite element solution even on coarse meshes i e in the preasymptotic range based on some a posteriori error estimators from the literature we formulate an adaptive mesh refining algorithm for supg we prove that the adaptively generated supg solutions converge at asymptotically optimal rates towards the exact solution the main focus thus is on the mathematical proof that the supg stabilization does not spoil the asymptotic convergence behavior of the adaptive scheme

massive mimo with spatially correlated rician fading channels this paper considers multi cell massive multiple input multiple output systems where the channels are spatially correlated rician fading the channel model is composed of a deterministic line of sight path and a stochastic non line of sight component describing a practical spatially correlated multipath environment we derive the statistical properties of the minimum mean squared error mmse element wise mmse and least square channel estimates for this model using these estimates for maximum ratio combining and precoding rigorous closed form uplink ul and downlink dl achievable spectral efficiency se expressions are derived and analyzed the asymptotic se behavior when using the different channel estimators are also analyzed the numerical results show that the se is higher when using the mmse estimator than that of the other estimators and the performance gap increases with the number of antennas

retinal vessel centerline extraction using multiscale matched filters confidence and edge measures motivated by the goals of improving detection of low contrast and narrow vessels and eliminating false detections at nonvascular structures a new technique is presented for extracting vessels in retinal images the core of the technique is a new likelihood ratio test that combines matched filter responses confidence measures and vessel boundary measures matched filter responses are derived in scale space to extract vessels of widely varying widths a vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile vessel boundary measures and associated confidences are computed at potential vessel boundaries combined these responses form a six dimensional measurement vector at each pixel a training technique is used to develop a mapping of this vector to a likelihood ratio that measures the vesselness at each pixel results comparing this vesselness measure to matched filters alone and to measures based on the hessian of intensities show substantial improvements both qualitatively and quantitatively the hessian can be used in place of the matched filter to obtain similar but less substantial improvements or to steer the matched filter by preselecting kernel orientations finally the new vesselness likelihood ratio is embedded into a vessel tracing framework resulting in an efficient and effective vessel centerline extraction algorithm

a goal oriented adaptive finite element method with convergence rates an adaptive finite element method is analyzed for approximating functionals of the solution of symmetric elliptic second order boundary value problems we show that the method converges and derive a favorable upper bound for its convergence rate and computational complexity we illustrate our theoretical findings with numerical results

adaptive fem with optimal convergence rates for a certain class of nonsymmetric and possibly nonlinear problems we analyze adaptive mesh refining algorithms for conforming finite element discretizations of certain nonlinear second order partial differential equations we allow continuous polynomials of arbitrary but fixed polynomial order the adaptivity is driven by the residual error estimator we prove convergence even with optimal algebraic convergence rates in particular our analysis covers general linear second order elliptic operators unlike prior works for linear nonsymmetric operators our analysis avoids the interior node property for the refinement and the differential operator has to satisfy a g rarding inequality only if the differential operator is uniformly elliptic no additional assumption on the initial mesh is posed

iterative cdma multiuser receiver with soft decision directed channel estimation we develop an iterative code division multiple access cdma receiver for multipath block fading channels in the uplink the mean square error mse of the channel estimates is reduced iteratively by using soft data estimates as additional pilots the multiuser detector performs parallel interference cancellation pic with subsequent linear filtering we consider a single user matched filter sumf and develop a low complexity linear minimum mse lmmse filter for intersymbol interference isi channels that allows for 33 more users than the sumf we investigate two choices of training sequences for initial channel estimation the first is a random pilot symbol sequence modulated by a short spreading sequence rand and the second is a perfect root of unity sequence prus used as long sounding chip sequence we observe that the rand scheme approaches the single user bound up to 2 db and in case of prus up to 1 db at a target bit error rate ber of 10 3 further several channel estimators are developed that use various combinations of soft decision symbols and statistical a priori knowledge about the channel these are the approximated least squares als approximated linear mmse almmse and linear mmse lmmse estimators the iterative estimators show an improvement of 2 5 and 5 db with prus and rand pilots respectively over estimators that do not exploit soft feedback symbols at a ber of 10 3 the als is sacrificing less than 0 6 db to obtain a ber of 10 3 in a system at load 1 5 when compared with the almmse and lmmse schemes the load is understood as the ratio of the number of users to the spreading factor this paper shows that significant improvements in system capacity can be achieved in multipath scenarios with low complexity choices of multiuser detectors and channel estimators

adaptive finite element methods with convergence rates adaptive finite element methods for numerically solving elliptic equations are used often in practice only recently 12 17 have these methods been shown to converge however this convergence analysis says nothing about the rates of convergence of these methods and therefore does in principle not guarantee yet any numerical advantages of adaptive strategies versus non adaptive strategies the present paper modifies the adaptive method of morin nochetto and siebert 17 for solving the laplace equation with piecewise linear elements on domains in 2 by adding a coarsening step and proves that this new method has certain optimal convergence rates in the energy norm which is equivalent to the h1 norm namely it is shown that whenever s 0 and the solution u is such that for each n 1 it can be approximated to accuracy o n s in the energy norm by a continuous piecewise linear function on a triangulation with n cells using complete knowledge of u then the adaptive algorithm constructs an approximation of the same type with the same asymptotic accuracy while using only information gained during the computational process moreover the number of arithmetic computations in the proposed method is also of order o n for each n 1 the construction and analysis of this adaptive method relies on the theory of nonlinear approximation

a new accurate residual based a posteriori error indicator for the bem in 2d acoustics in this work we construct a new reliable efficient and local a posteriori error estimate for the single layer and hyper singular boundary integral equations associated to the helmholtz equation in two dimensions it uses a localization technique based on a generic operator which is used to transport the residual into l2 under appropriate conditions on the construction of we show that it is asymptotically exact with respect to the energy norm of the error the single layer equation and the hyper singular equation are treated separately while the current analysis requires the boundary to be smooth numerical experiments show that the new error estimators also perform well for non smooth boundaries

equilibrated residual error estimator for edge elements reliable a posteriori error estimates without generic constants can be obtained by a comparison of the finite element solution with a feasible function for the dual problem a cheap computation of such functions via equilibration is well known for scalar equations of second order we simplify and modify the equilibration such that it can be applied to the curl curl equation and edge elements the construction is more involved for edge elements since the equilibration has to be performed on subsets with different dimensions for this reason raviart thomas elements are extended in the spirit of distributions

on minimum variance unbiased estimation of clock offset in a two way message exchange mechanism for many applications distributed networks require the local clocks of the constituent nodes to run close to an agreed upon notion of time most of the widely used clock synchronization algorithms in such systems employ the sender receiver protocol based on a two way timing message exchange paradigm maximum likelihood estimator mle of the clock offset based on the timing message exchanges between two clocks was derived in d r jeske on maximum likelihood estimation of clock offset ieee trans commun vol 53 pp 53 54 jan 2005 when the fixed delays are symmetric and the variable delays in each direction assume an exponential distribution with an unknown mean herein the best linear unbiased estimate using order statistics blue os of the clock offset between two nodes is derived assuming both symmetric and asymmetric exponential network delays respectively the rao blackwell lehmann scheffe theorem is then exploited to obtain the minimum variance unbiased estimate mvue for the clock offset which it is shown to coincide with the blue os in addition it is found that the mvue of the clock offset in the presence of symmetric network delays also coincides with the mle finally in the presence of asymmetric network delays although the mle is biased it is shown to achieve lesser mean square error mse than the mvue in the region around the point where the bidirectional network link delays are symmetric and hence its merit as the most versatile estimator is fairly justified

representation of mutual information via input estimates a relationship between information theory and estimation theory was recently shown for the gaussian channel relating the derivative of mutual information with the minimum mean square error this paper generalizes the link between information theory and estimation theory to arbitrary channels giving representations of the derivative of mutual information as a function of the conditional marginal input distributions given the outputs we illustrate the use of this representation in the efficient numerical computation of the mutual information achieved by inputs such as specific codes or natural language

optimal additive schwarz methods for the h p bem we propose and analyze an overlapping schwarz preconditioner for the p and h p boundary element method for the hypersingular integral equation in 3d we consider surface triangulations consisting of triangles the condition number is bounded uniformly in the mesh size h and the polynomial order p the preconditioner handles adaptively refined meshes and is based on a local multilevel preconditioner for the lowest order space numerical experiments on different geometries illustrate its robustness

convergence and quasi optimality of adaptive fem with inhomogeneous dirichlet data we consider the solution of a second order elliptic pde with inhomogeneous dirichlet data by means of adaptive lowest order fem as is usually done in practice the given dirichlet data are discretized by nodal interpolation as model example serves the poisson equation with mixed dirichlet neumann boundary conditions for error estimation we use an edge based residual error estimator which replaces the volume residual contributions by edge oscillations for 2d we prove convergence of the adaptive algorithm even with optimal convergence rate for 2d and 3d we show convergence if the nodal interpolation operator is replaced by the l 2 projection or the scott zhang quasi interpolation operator as a byproduct of the proof we show that the scott zhang operator converges pointwise to a limiting operator as the mesh is locally refined this property might be of independent interest besides the current application finally numerical experiments conclude the work

improvement of tdoa position fixing using the likelihood curvature a conventional multilateration is a two step process where in the first step the time difference of arrivals tdoa of a signal at multiple sensors are estimated and in the second step these tdoas are used in some position fixing technique to estimate the location of an emitter several estimators have been proposed over the years for the estimation of the tdoas many techniques have been proposed for position fixing as well much of the research on position fixing has been focused on obtaining a simplified closed form solution for the unknown deterministic signal model stein had derived the maximum likelihood estimator mle for the tdoa between two sensors which is the peak location of the cross correlation function since the asymptotic variance of an mle approaches the cramer rao lower bound crlb which is the inverse of the negative of the expected value of the curvature of the log likelihood function using this as a motivation we propose a weighted least squares type position fixing technique where the weights are computed from the curvature of the log likelihood function

quasi optimal convergence rate for an adaptive finite element method we analyze the simplest and most standard adaptive finite element method afem with any polynomial degree for general second order linear symmetric elliptic operators as is customary in practice the afem marks exclusively according to the error estimator and performs a minimal element refinement without the interior node property we prove that the afem is a contraction for the sum of the energy error and the scaled error estimator between two consecutive adaptive loops this geometric decay is instrumental to derive the optimal cardinality of the afem we show that the afem yields a decay rate of the energy error plus oscillation in terms of the number of degrees of freedom as dictated by the best approximation for this combined nonlinear quantity

auditory motivated level crossing approach to instantaneous frequency estimation we address the problem of estimating the instantaneous frequency if of a phase signal using its level crossing lc information based on front end auditory processing motivation we show that the problem of if estimation using lc information can be cast in the framework of estimation from irregularly sampled data the formulation has the generality of estimating different types of if without the need for a quasistationary assumption we consider two types of if polynomial and bandlimited we use polynomial interpolating functions for the former and for the latter we propose a novel line plus sum of sines model the model parameters are estimated by linear regression considering the noisy case lc data for different levels is analyzed and methods for combining different estimators from lcs are discussed theoretical and extensive simulation results show that the performance of the zero crossing zc based if estimator and the level crossing based if estimator with smaller level values is better than those obtained with higher level values or their combinations the new technique reaches the crame spl acute r rao bound crb roughly above 4 db signal to noise ratio snr and its performance does not deteriorate rapidly with mismatch in the if order compared with the other techniques in the literature

optimal convergence behavior of adaptive fem driven by simple h h 2 type error estimators abstract for some poisson type model problem we prove that adaptive fem driven by the h h 2 type error estimators from ferraz leite et al 2010 leads to convergence with optimal algebraic convergence rates besides the implementational simplicity another striking feature of these estimators is that they can provide guaranteed lower bounds for the energy error with known efficiency constant 1

low complexity lmmse based mimo ofdm channel estimation via angle domain processing in many situations multiple input multiple output with orthogonal frequency division multiplexing mimo ofdm channels tend to be spatially correlated due for example to limited scattering prior knowledge of this channel spatial correlation and the channel frequency correlation can be exploited by using the linear minimum mean square error lmmse technique however the complexity of the 2 d lmmse technique which fully utilizes both the channel spatial and frequency correlation is quite high to solve this problem this paper presents and analyzes several low complexity suboptimal approximated lmmse channel estimation techniques in the angle domain where the channel model lends itself to a physical interpretation the choice of angle domain techniques is largely dependent on the extent of channel stochastic information e g channel correlation or power that is available to the receiver nevertheless all the proposed angle domain techniques have much lower complexity compared to the 2 d lmmse technique further all the angle domain techniques improve over the conventional least square ls technique for all the typical mimo ofdm models under consideration more importantly our simulation results show that the angle domain quasi 1 d ql d lmmse technique can achieve similar performance compared to the 2 d lmmse technique for all typical mimo ofdm models with significantly lower complexity

integral representation of holomorphic mappings on fully nuclear spaces abstract we obtain the following integral representation f z e e z w f d w d w for all z e a fully nuclear space with basis where and belong to e l 1 f is a holomorphic function of exponential type on e is a gaussian measure on e and d is a densely defined diagonal mapping from e into e

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

adaptive fem with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems we prove that for compactly perturbed elliptic problems where the corresponding bilinear form satisfies a garding inequality adaptive mesh refinement is capable of overcoming the preasymptotic behavior and eventually leads to convergence with optimal algebraic rates as an important consequence of our analysis one does not have to deal with the a priori assumption that the underlying meshes are sufficiently fine hence the overall conclusion of our results is that adaptivity has stabilizing effects and can overcome possibly pessimistic restrictions on the meshes in particular our analysis covers adaptive mesh refinement for the finite element discretization of the helmholtz equation from where our interest originated

data oscillation and convergence of adaptive fem data oscillation is intrinsic information missed by the averaging process associated with finite element methods fem regardless of quadrature ensuring a reduction rate of data oscillation together with an error reduction based on a posteriori error estimators we construct a simple and efficient adaptive fem for elliptic partial differential equations pdes with linear rate of convergence without any preliminary mesh adaptation nor explicit knowledge of constants any prescribed error tolerance is thus achieved in a finite number of steps a number of numerical experiments in two and three dimensions yield quasi optimal meshes along with a competitive performance

decay rates of adaptive finite elements with dorfler marking we investigate the decay rate for an adaptive finite element discretization of a second order linear symmetric elliptic pde we allow for any kind of estimator that is locally equivalent to the standard residual estimator this includes in particular hierarchical estimators estimators based on the solution of local problems estimators based on local averaging equilibrated residual estimators the zz estimator etc the adaptive method selects elements for refinement with dorfler marking and performs a minimal refinement in that no interior node property is needed based on the local equivalence to the residual estimator we prove an error reduction property in combination with minimal dorfler marking this yields an optimal decay rate in terms of degrees of freedom

fundamental limits of linear equalizers diversity capacity and complexity linear equalizers les have been widely adopted for practical systems due to their low computational complexity however it is also well known that les provide inferior performance relative to a maximum likelihood equalizer mle or other near mles because les usually cannot collect the diversity order enabled by the transmitter and at the same time they lose mutual information more importantly unlike mle or near mles the performance of les has not been well quantified this hinders more general applications of les in wireless systems in this paper we reveal a fundamental link between a channel parameter orthogonality deficiency od of the channel matrix and the diversity and capacity of les we identify that when the od of channel matrix has an upper bound strictly less than 1 the same diversity order as that of mles is collected by les and the outage capacity loss relative to mles is also a constant over signal to noise ratio snr these results can be applied to designing a framework for hybrid equalizers furthermore by studying the statistical properties of the od and comparing the complexity of different equalizers we show that hybrid equalizers can trade off between performance and complexity by tuning the channel matrix od the theoretical analysis is corroborated by computer simulations

a convergent adaptive algorithm for poisson s equation we construct a converging adaptive algorithm for linear elements applied to poisson s equation in two space dimensions starting from a macro triangulation we describe how to construct an initial triangulation from a priori information then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions it is proved that the error measured in the energy norm decreases at a constant rate in each step until a prescribed error bound is reached extension to higher order elements in two space dimension and numerical results are included

integral representation of holomorphic functions on banach spaces abstract in this paper we discuss the problem of integral representation of analytic functions over a complex banach space e we obtain for a wide class of functions integral representations of the form f x e e x f 1 d w and f x e 1 1 x f 2 d w where w is an abstract wiener measure on e and f 1 f 2 are transformations of f involving the covariance operator of w

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

axioms of adaptivity this paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of discrete lower bounds inexact solvers inhomogeneous boundary data or the use of equivalent error estimators solely four axioms guarantee the optimality in terms of the error estimators compared to the state of the art in the temporary literature the improvements of this article can be summarized as follows first a general framework is presented which covers the existing literature on optimality of adaptive schemes the abstract analysis covers linear as well as nonlinear problems and is independent of the underlying finite element or boundary element method second efficiency of the error estimator is neither needed to prove convergence nor quasi optimal convergence behavior of the error estimator in this paper efficiency exclusively characterizes the approximation classes involved in terms of the best approximation error and data resolution and so the upper bound on the optimal marking parameters does not depend on the efficiency constant third some general quasi galerkin orthogonality is not only sufficient but also necessary for the r linear convergence of the error estimator which is a fundamental ingredient in the current quasi optimality analysis due to stevenson 2007 finally the general analysis allows for equivalent error estimators and inexact solvers as well as different non homogeneous and mixed boundary conditions

lp representable functions on banach spaces in this paper we discuss the problem of integral representation of analytic functions over a complex banach space e we define the class of l p representable and representable functions and prove that they verify some growth conditions the aim of this work is to characterize these classes of functions it is also shown that it is possible to give an alternative representation for integral polynomials over a hilbert space h using a universal wiener measure

estimation of flows in flow networks abstract let g be a directed graph with an unknown flow on each edge such that the following flow conservation constraint is maintained except for sources and sinks the sum of flows into a node equals the sum of flows going out of a node given a noisy measurement of the flow on each edge the problem we address which we call the m ost p robable f low e stimation problem mpfe is to estimate the most probable assignment of flow for every edge such that the flow conservation constraint is maintained we provide an algorithm called y mpfe for solving the mpfe problem when the measurement error is gaussian g aussian mpfe the algorithm works in o e v 2 when the underlying undirected graph of g is a 2 connected planar graph and in o e v when it is a 2 connected serial parallel graph or a tree this result is applicable to any m inimum c ost f low problem for which the cost function is e x e e 2 for edge e where e and e are constants and x e is the flow on edge e we show that for all topologies the g aussian mpfe s precision for each edge is analogous to the equivalent resistance measured in series to this edge in an electrical network built by replacing every edge with a resistor reflecting the measurement s precision on that edge

hybrid fm polynomial phase signal modeling parameter estimation and cramer rao bounds parameter estimation for a class of nonstationary signal models is addressed the class contains combination of a polynomial phase signal pps and a frequency modulated fm component of the sinusoidal or hyperbolic type such signals appear in radar and sonar applications involving moving targets with vibrating or rotating components a novel approach is proposed that allows us to decouple estimation of the fm parameters from those of the pps relying on properties of the multilag high order ambiguity function ml haf the accuracy achievable by any unbiased estimator of the hybrid fm pps parameters is investigated by means of the cramer rao lower bounds crlbs both exact and large sample approximate expressions of the bounds are derived and compared with the performance of the proposed methods based on monte carlo simulations

quasi ml period estimation from incomplete timing data given a noisy sequence of possibly shifted integer multiples of a certain period it is often of interest to accurately estimate the period with known integer regressors the problem is classical linear regression in many applications however the regressors are unknown integers and only loose bounds on the period are available examples include hop period and timing estimation wherein hops may be missed at the output of the frequency discriminator or the emitter may hop out of band pulse repetition interval pri analysis and passive rotating beam radio scanning we study several pertinent period estimators our emphasis is on a quasi maximum likelihood approach developed herein and an earlier method based on the fourier transform of a dirac delta train representation of the data surprisingly both are capable of attaining the clairvoyant crame spl acute r rao bound at moderate signal to noise ratios snrs even for short e g 10 samples we carefully address parameter identifiability issues and corroborate our findings with extensive simulations

new results on deterministic cramer rao bounds for real and complex parameters the cramer rao bounds crb is a lower bound of great interest for system analysis and design in the asymptotic region high signal to noise ratio snr and or large number of snapshots as it is simple to calculate and it is usually possible to obtain closed form expressions the first part of the paper is a generalization to complex parameters of the barankin rationale for deriving mse lower bounds that is the minimization of a norm under a set of linear constraints with the norm minimization approach the study of fisher information matrix fim singularity constrained crb and regularity conditions become straightforward corollaries of the derivation the second part provides new results useful for system analysis and design a general reparameterization inequality the equivalence between reparameterization and equality constraints and an explicit relationship between parameters unidentifiability and fim singularity

the completion of locally refined simplicial partitions created by bisection recently in found comput math 7 2 2007 245 269 we proved that an adaptive finite element method based on newest vertex bisection in two space dimensions for solving elliptic equations which is essentially the method from sinum 38 2000 466 488 by morin nochetto and siebert converges with the optimal rate the number of triangles n in the output partition of such a method is generally larger than the number m of triangles that in all intermediate partitions have been marked for bisection because additional bisections are needed to retain conforming meshes a key ingredient to our proof was a result from numer math 97 2004 219 268 by binev dahmen and devore saying that n n 0 cm for some absolute constant c where n 0 is the number of triangles from the initial partition that have never been bisected in this paper we extend this result to bisection algorithms of n simplices with that generalizing the result concerning optimality of the adaptive finite element method to general space dimensions

robust rls in the presence of correlated noise using outlier sparsity relative to batch alternatives the recursive least squares rls algorithm has well appreciated merits of reduced complexity and storage requirements for online processing of stationary signals and also for tracking slowly varying nonstationary signals however rls is challenged when in addition to noise outliers are also present in the data due to e g impulsive disturbances existing robust rls approaches are resilient to outliers but require the nominal noise to be white an assumption that may not hold in e g sensor networks where neighboring sensors are affected by correlated ambient noise prewhitening with the known noise covariance is not a viable option because it spreads the outliers to noncontaminated measurements which leads to inefficient utilization of the available data and unsatisfactory performance in this correspondence a robust rls algorithm is developed capable of handling outliers and correlated noise simultaneously in the proposed method outliers are treated as nuisance variables and estimated jointly with the wanted parameters identifiability is ensured by exploiting the sparsity of outliers which is effected via regularizing the least squares ls criterion with the l1 norm of the outlier vectors this leads to an optimization problem whose solution yields the robust rls estimates for low complexity real time operation a suboptimal online algorithm is proposed which entails closed form updates per time step in the spirit of rls simulations demonstrate the effectiveness and improved performance of the proposed method in comparison with the nonrobust rls and its state of the art robust renditions

inhomogeneous dirichlet conditions in a priori and a posteriori finite element error analysis the numerical solution of elliptic boundary value problems with finite element methods requires the approximation of given dirichlet data ud by functions ud h in the trace space of a finite element space on d in this paper quantitative a priori and a posteriori estimates are presented for two choices of ud h namely the nodal interpolation and the orthogonal projection in l2 d onto the trace space two corresponding extension operators allow for an estimate of the boundary data approximation in global h1 and l2 a priori and a posteriori error estimates the results imply that the orthogonal projection leads to better estimates in the sense that the influence of the approximation error on the estimates is of higher order than for the nodal interpolation