splines in statistics abstract this is a survey article that attempts to synthesize a broad variety of work on splines in statistics splines are presented as a nonparametric function estimating technique after a general introduction to the theory of interpolating and smoothing splines splines are treated in the nonparametric regression setting the method of cross validation for choosing the smoothing parameter is discussed and the general multivariate regression surface estimation problem is addressed an extensive discussion of splines as nonparametric density estimators is followed by a discussion of their role in time series analysis a comparison of the spline and isotonic regression methodologies leads to a formulation of a hybrid estimator the closing section provides a brief overall summary and formulates a number of open unsolved problems relating to splines in statistics

trapezoidal monte carlo integration abstract the approximation of weighted integrals of random processes by the trapezoidal rule based on an ordered random sample is considered for processes that are once mean square continuously differentiable and for weight functions that are twice continuously differentiable it is shown that the rate of convergence of the mean square integral approximation error is precisely n to the minus 4th power and the asymptotic constant is also determined keywords reprints

active antenna selection in multiuser mimo communications the paper develops a dynamic antenna scheduling strategy for downlink mimo communications where a subset of the receive antennas at certain users is selectively disabled the proposed method improves the signal to leakage plus noise slnr ratio performance of the system and it relaxes the condition on the number of transmit receive antennas in comparison to traditional zero forcing and time scheduling strategies the largest value that the slnr can achieve is shown to be equal to the maximum eigenvalue of a certain random matrix combination and the probability distribution of this eigenvalue is characterized in terms of a whittaker function the result shows that increasing the number of antennas at some users can degrade the slnr performance at other users this fact is used to propose an antenna scheduling scheme that leads to improvement in terms of sinr outage probabilities

optimal grouping spacing stratification and piecewise constant approximation a variety of statistical problems of optimal grouping spacing and stratification are seen to be problems of optimal breakpoint selection for piecewise constant text l 2 0 1 approximation of certain functions this allows for the development of conditions that insure the existence and uniqueness of solutions a computational algorithm and simple approximate solutions in addition this approach is shown to provide insight into the relationships between the various problems considered

nonuniform sampling and reconstruction in shift invariant spaces this article discusses modern techniques for nonuniform sampling and reconstruction of functions in shift invariant spaces it is a survey as well as a research paper and provides a unified framework for uniform and nonuniform sampling and reconstruction in shift invariant subspaces by bringing together wavelet theory frame theory reproducing kernel hilbert spaces approximation theory amalgam spaces and sampling inspired by applications taken from communication astronomy and medicine the following aspects will be emphasized a the sampling problem is well defined within the setting of shift invariant spaces b the general theory works in arbitrary dimension and for a broad class of generators c the reconstruction of a function from any sufficiently dense nonuniform sampling set is obtained by efficient iterative algorithms these algorithms converge geometrically and are robust in the presence of noise d to model the natural decay conditions of real signals and images the sampling theory is developed in weighted l p spaces

optimal sensor array configuration in remote image formation determination of optimal sensor configuration is an important issue in many remote imaging modalities such as tomographic and interferometric imaging in this paper a statistical optimality criterion is defined and a search is performed over the space of candidate sensor locations to determine the configuration that optimizes the criterion over all candidates to make the search process computationally feasible a modified version of a previously proposed suboptimal backward greedy algorithm is used a statistical framework is developed which allows for inclusion of several widely used image constraints computational complexity of the proposed algorithm is discussed and a fast implementation is described furthermore upper bounds on the sum of the squared error of the proposed algorithm are derived connections of the method to the deterministic backward greedy algorithm for the subset selection problem are presented and two application examples are described five compelling optimality criteria are considered and their performance is investigated through numerical experiments for a tomographic imaging scenario in all cases it is verified that the configuration designed by the proposed algorithm performs better than wisely chosen alternatives

sampling design for gaussian detection problems we propose an approach for the design of sampling schemes for gaussian hypothesis testing problems our approach for this design is based on the class of ali silvey see j royal stat soc series b vol 28 p 131 43 1996 distance measures closed forms for the bhattacharyya distance the i divergence the j divergence and the chernoff distance between the class conditional densities are obtained for the sampling design problem in the strong signal case a new member of the class of ali silvey distance measures that is suitable for the detection problem in the weak signal case is also derived sampling schemes are determined to maximize those four distance measures as well as the new distance measure for the strong signal case and the weak signal case respectively the detection performance of our sampling schemes is compared with those of various other sampling schemes by means of numerical examples comparisons show that the sampling design based on ali silvey distance measures result in superior performance

distributed field reconstruction in wireless sensor networks based on hybrid shift invariant spaces we use the theory and algorithms developed for so called shift invariant spaces to develop a novel distributed architecture for sampling and reconstructing time varying non bandlimited physical fields in wireless sensor networks we introduce hybrid shift invariant spaces that generalize conventional shift invariant spaces and can adapt to local smoothness properties of the field using shift invariant spaces with compactly supported generator functions allows us to split the global reconstruction into several smaller local problems that can be solved independently capitalizing on the sparsity of the matrices involved in the reconstruction we propose direct and iterative reconstruction algorithms whose complexity per time slot scales only linearly with the number of sensor nodes we furthermore analyze the impact of sensor localization errors on the mean square error of the reconstructed field numerical simulations illustrate that the proposed field reconstruction scheme performs close to bandlimited reconstruction and is less sensitive to sensor location errors while providing a significant reduction in computational complexity

random designs for estimating integrals of stochastic processes the integral of a second order stochastic process z over a d dimensional domain is estimated by a weighted linear combination of observations of z in a random design the design sample points are possibly dependent random variables and are independent of the process z which may be nonstationary necessary and sufficient conditions are obtained for the mean squared error of a random design estimator to converge to zero as the sample size increases towards infinity simple random stratified and systematic sampling designs are considered an optimal simple random design is obtained for fixed sample size and the mean squared errors of the estimators from these designs are compared it is shown for example that for any simple random design there is always a better stratified design 1 introduction we consider the problem of estimating the weighted average of a second order stochastic process z t t e a a c r d the process is assumed to be continuous in quadratic mean with covariance ro s t mean m t and second moment function r s t ro s t m s m t such that 0 fa r t t dt oo we wish to estimate

performance of linear field reconstruction techniques with noise and uncertain sensor locations we consider a wireless sensor network sampling a bandlimited field described by a limited number of harmonics sensor nodes are irregularly deployed over the area of interest or subject to random displacement in addition sensors measurements are affected by noise our goal is to obtain a high quality reconstruction of the field with the mean square error mse of the estimate as performance metric in particular we analytically derive the performance of several reconstruction estimation techniques based on linear filtering for each technique we obtain the mse as well as its asymptotic expression in the case where the number of field harmonics and the number of sensors grow to infinity while their ratio is kept constant through numerical simulations we show the validity of the asymptotic analysis even for a small number of sensors we provide some novel guidelines for the design of sensor networks when many parameters such as field bandwidth number of sensors reconstruction quality and sensor displacement characteristics to be traded off

a density quantile function approach to optimal spacing selection in this paper design techniques for continuous parameter time series regression analysis are employed to develop a general approach to optimal spacing selection for the linear estimation of location and scale parameters by sample quantiles from uncensored or censored samples the spacings derived from this approach are asymptotically optimal in the sense that they result in near optimal asymptotic relative efficiencies for large values of k the number of spacing elements a comparison with the optimum efficiencies for several distribution types indicates that the asymptotically optimum spacings perform well for k 7 the regression framework is also utilized to develop sufficient conditions for optimal spacing unicity and to obtain asymptotically optimal spacings for quantile estimation

a whittaker function of matrix argument abstract whittaker functions arise naturally in many topics in physical biological and social sciences such as input output situations in econometric problems storage consumption situations growth decay situations when dealing with bilinear forms in random variables and so on an account of some of these is available in mathai 1993 the matrix variate analogue is considered in this article a whittaker function of matrix argument is defined and several new results on this function are established in this paper complementing the results given earlier by mathai and pederzoli 1996 some of these generalize the corresponding results in the scalar variable case

notes on fast moving strings we review the recent work on the mechanics of fast moving strings in anti de sitter space times a sphere and discuss the role of conserved charges an interesting relation between the local conserved charges of rigid solutions was found in the earlier work we propose a generalization of this relation for arbitrary solutions not necessarily rigid we conjecture that an infinite combination of local conserved charges is an action variable generating periodic trajectories in the classical string phase space it corresponds to the length of the operator on the field theory side

random sampling of deterministic signals statistical analysis of fourier transform estimates this paper considers the estimation of the fourier transform of continuous time deterministic signals from a finite number n of discrete time nonuniform observations we first extend the recent results mean and variance of tarczynski and allay by providing both distributional properties as well as rates of almost sure convergence for the simple random sampling scheme of tarczynski and allay the primary focus is to consider and investigate the properties of a class of stratified random sampling estimates we establish the statistical properties of the estimates including precise expressions and rate of convergence of the mean square errors we also establish the asymptotic normality of the estimates useful for confidence interval calculations further we optimize over the class of the estimates in order to obtain the best performance in particular we show that for functions with a first order continuous derivative the mean square estimation error decays precisely at the fast rate of 1 n sup 3 this rate is significantly higher than the rate of 1 n for simple random sampling estimates the analytical results are illustrated by numerical examples the effect of observation errors on the performance is also investigated

channel estimation in wireless ofdm systems with irregular pilot distribution this paper addresses pilot assisted channel estimation for wireless orthogonal frequency division multiplexing ofdm systems with irregular pilot arrangements using nonuniform sampling techniques we propose a novel channel estimator that is based on conjugate gradient iterations and features very low computational complexity we investigate the impact of the pilot arrangement on the channel estimation mean square error and we provide a heuristic stopping criterion for early termination of the conjugate gradient iterations one dimensional and two dimensional channel estimator implementations and applications of our method to multiple antenna and multiuser ofdm systems are discussed extensive numerical simulations corroborate that the proposed method performs similarly to computationally much more expensive minimum mean square error estimators

quadrature of smooth stochastic processes the integral of a stochastic process is estimated by means of classical quadrature formulae in contrast to certain conventional methods knowledge of covariances is not required and no regularity conditions are assumed explicit error representations and error bounds with respect to thel p norm are established

sampling schemes for sequential detection with dependent observations several sampling schemes and their corresponding sequential detection procedures in autoregressive noise are presented in this paper two of them use uniform sampling procedures with high and low sampling rates respectively the other two employ groups of samples which are separated by long intergroup delays such that the intergroup correlations are negligible one of the group sampling schemes also employs optimal signaling waveforms to further improve its energy efficiency in all the schemes data sampling and transformation are designed in such a way that wald s sequential probability ratio test sprt can still be implemented the performances of different schemes in terms of average termination time att are derived analytically when all the schemes employ the same sampling interval and under a constant signal amplitude constraint their performances are compared through analytical and numerical methods in addition under a constant power constraint their atts and energy efficiency are compared it is theoretically proved that the scheme using groups of samples with the optimal signaling waveform is the most energy efficient

asymptotics of multifold vandermonde matrices with random entries we study the performance of systems for signal parameters estimation which are based on the linear minimum mean square error lmmse filtering such an estimation technique is widely used in practical scenarios specifically wireless sensor networks and mimo communications we model the estimation system through sums and products of random matrices involving a d fold vandermonde matrix d 1 with entries uniformly distributed on the complex unit circle then we derive the mean square error mse of the estimated signal by resorting to asymptotic analysis and by applying the transform operator we describe how our results can be exploited for the study of practical systems and we show the agreement existing between the asymptotic results derived through our analysis and the simulation results obtained for small values of d

optimal sampling schemes for the gaussian hypothesis testing problem a class of sampling designs for a continuous time gaussian hypothesis testing problem is discussed this problem arises frequently in systems where it is necessary to sample the continuous time signal to produce discrete time data for computer processing a class of periodic nonuniform sampling designs which optimizes performance under an asymptotic probability of error criterion is investigated a design algorithm for the optimal sampler is presented

the algebraic curve of classical superstrings on ads5 s5 we investigate the monodromy of the lax connection for classical iib superstrings on ads5 s5 for any solution of the equations of motion we derive a spectral curve of degree 4 4 the curve consists purely of conserved quantities all gauge degrees of freedom have been eliminated in this form the most relevant quantities of the solution such as its energy can be expressed through certain holomorphic integrals on the curve this allows for a classification of finite gap solutions analogous to the general solution of strings in flat space the role of fermions in the context of the algebraic curve is clarified finally we derive a set of integral equations which reformulates the algebraic curve as a riemann hilbert problem they agree with the planar one loop open image in new window supersymmetric gauge theory proving the complete agreement of spectra in this approximation

performance of discrete time predictors of continuous time stationary processes the asymptotic performance of linear predictors of continuous time stationary processes is studied from observations at n sampling instants on a fixed observation interval both optimal and simpler choices of predictor coefficients are considered using uniform sampling as well as nonuniform sampling tailored to the statistics of the process under prediction the focus is on stationary processes with rational spectral densities and the asymptotic performance for cases with and without a quadratic mean derivatives is obtained the analytical results are supplemented by numerical examples depicting small and large sample size performance

asymptotic analysis of multidimensional jittered sampling we study a class of random matrices that appear in several communication and signal processing applications and whose asymptotic eigenvalue distribution is closely related to the reconstruction error of an irregularly sampled bandlimited signal we focus on the case where the random variables characterizing these matrices are d dimensional vectors independent and quasi equally spaced i e they have an arbitrary distribution and their averages are vertices of a d dimensional grid although a closed form expression of the eigenvalue distribution is still unknown under these conditions we are able i to derive the distribution moments as the matrix size grows to infinity while its aspect ratio is kept constant and ii to show that the eigenvalue distribution tends to the marc enko pastur law as d these results can find application in several fields as an example we show how they can be used for the estimation of the mean square error provided by linear reconstruction techniques

fine quantization in signal detection and estimation the performance lost to data quantization in signal detection and estimation procedures is considered the performance is measured by f divergences which are useful indices of discrimination information between statistical hypotheses some properties of the f divergences are briefly discussed and a general result for the loss in divergence due to uniform data quantization is obtained several applications of this result in specific problems of signal detection and estimation being developed and some numerical results that illustrate the asymptotic behavior of the divergence in these applications are given the divergence lost to finite nonuniform quantization through the use of a companding model is considered and the asymptotically optimum nonuniform quantizer within this class is derived some interesting problems that remain open are discussed

some properties of matrix variate laplace transforms and matrix variate whittaker functions abstract some results on scalar variable laplace transforms are generalized to the matrix variate case then a matrix variate function is defined which can be interpreted as a matrix variate analogue of the univariate whittaker function several properties of this function which generalize the corresponding properties of univariate whittaker function are established an application of this function to statistical distribution theory is also given

on the uniqueness of best 0 1 approximation by piecewise polynomials with variable breakpoints in this paper a sufficient condition for the uniqueness of best l2 0 1 approximation by piecewise polynomials of order k with variable breakpoints is generalized from that of order 2 other extensions included here are nonuniqueness and eventual uniqueness results

asymptotic behavior of random vandermonde matrices with entries on the unit circle analytical methods for finding moments of random vandermonde matrices with entries on the unit circle are developed vandermonde matrices play an important role in signal processing and wireless applications such as direction of arrival estimation precoding and sparse sampling theory just to name a few within this framework we extend classical freeness results on random matrices with independent and identically distributed i i d entries and show that vandermonde structured matrices can be treated in the same vein with different tools we focus on various types of matrices such as vandermonde matrices with and without uniform phase distributions as well as generalized vandermonde matrices in each case we provide explicit expressions of the moments of the associated gram matrix as well as more advanced models involving the vandermonde matrix comparisons with classical i i d random matrix theory are provided and deconvolution results are discussed we review some applications of the results to the fields of signal processing and wireless communications

estimating random integrals from noisy observations sampling designs and their performance the problem of estimating a weighted average of a random process from noisy observations at a finite number of sampling points is considered the performance of sampling designs with optimal or suboptimal but easily computable estimator coefficients is studied several examples and special cases are studied including additive independent noise nonlinear distortion with noise and quantization noise

decentralized detection with censoring sensors in the censoring approach to decentralized detection sensors transmit real valued functions of their observations when informative and save energy by not transmitting otherwise we address several practical issues in the design of censoring sensor networks including the joint dependence of sensor decision rules randomization of decision strategies and partially known distributions in canonical decentralized detection problems involving quantization of sensor observations joint optimization of the sensor quantizers is necessary we show that under a send no send constraint on each sensor and when the fusion center has its own observations the sensor decision rules can be determined independently in terms of design and particularly for adaptive systems the independence of sensor decision rules implies that minimal communication is required we address the uncertainty in the distribution of the observations typically encountered in practice by determining the optimal sensor decision rules and fusion rule for three formulations a robust formulation generalized likelihood ratio tests and a locally optimum formulation examples are provided to illustrate the independence of sensor decision rules and to evaluate the partially known formulations

sampling designs for the detection of signals in noise sampling designs for the detection of sure signals in gaussian noise are considered both deterministic and random sampling schemes using optimal and nonoptimal detectors are presented and their performance is studied the analytical results are supplemented by comparison of performance for small and large sample size for some representative processes including the gauss markov and wiener processes

optimal measurement scheduling for prediction and estimation a general theory of optimal measurement scheduling for least squares estimation is developed the theory is based on the assumption that the cost of a measurement is inversely proportional to the variance of measurement noise and that it is possible to distribute the total measurement cost arbitrarily among a set of measurements the theory leads to a nonquadratic minimization problem an effective algorithm for solving this problem is developed the theory is applied to the prediction of a discrete time integrated wiener process from noisy past samples

near optimal sensor placements in gaussian processes theory efficient algorithms and empirical studies when monitoring spatial phenomena which can often be modeled as gaussian processes gps choosing sensor locations is a fundamental task there are several common strategies to address this task for example geometry or disk models placing sensors at the points of highest entropy variance in the gp model and a d or e optimal design in this paper we tackle the combinatorial optimization problem of maximizing the mutual information between the chosen locations and the locations which are not selected we prove that the problem of finding the configuration that maximizes mutual information is np complete to address this issue we describe a polynomial time approximation that is within 1 1 e of the optimum by exploiting the submodularity of mutual information we also show how submodularity can be used to obtain online bounds and design branch and bound search procedures we then extend our algorithm to exploit lazy evaluations and local structure in the gp yielding significant speedups we also extend our approach to find placements which are robust against node failures and uncertainties in the model these extensions are again associated with rigorous theoretical approximation guarantees exploiting the submodularity of the objective function we demonstrate the advantages of our approach towards optimizing mutual information in a very extensive empirical study on two real world data sets

cubature of random fields by product type integration rules abstract cubature of random functions with multivariate domains by means of product type integration rules is examined bounds for the approximation error with respect to the l p norm and in terms of the levy distance are established and an additional error bound involving the spectral measure is derived for homogeneous random fields

performance of space time codes for a large number of antennas we study the asymptotic behavior of space time codes when the number of transmit and receive antennas grows to infinity specifically we determine the behavior of pairwise error probabilities with maximum likelihood ml decoding and with three types of receiver interfaces the ml interface the linear zero forcing zf interface and the linear minimum mean square error mmse interface two situations are studied when the number of receiving antennas grows to infinity while the number of transmitting antennas is finite and when both numbers grow to infinity but their ratio remains constant we show that with ml or linear interfaces the asymptotic performance of space time codes is determined by the euclidean distances between codewords moreover with the two linear interfaces examined here the number r of receive antennas must be much larger than the number t of transmit antennas to avoid a sizeable loss of performance on the other hand when r spl gt t the performance of these linear interfaces comes close to that of ml the dependence of error probabilities on euclidean distance is valid for intermediate signal to noise ratios snrs even when the number of antennas is small simulations validate our theoretical findings and show how asymptotic results may be substantially valid even in a nonasymptotic regime thus even for few antennas off the shelf codes may outperform space time codes designed ad hoc

event detection in wireless sensor networks in random spatial sensors deployments we develop a new class of event detection algorithms in wireless sensor networks where the sensors are randomly deployed spatially we formulate the detection problem as a binary hypothesis testing problem and design the optimal decision rules for two scenarios namely the poisson point process and binomial point process random deployments to calculate the intractable marginal likelihood density we develop three types of series expansion methods which are based on an askey orthogonal polynomials in addition we develop a novel framework to provide guidance on which series expansion is most suitable i e most accurate to use for different system parameters extensive monte carlo simulations are carried out to illustrate the benefits of this framework as well as the quality of the series expansion methods and the impacts that different parameters have on detection performance via the receiver operating curves roc

locally lattice sampling designs for isotropic random fields for predicting g v x z x dx where v is a fixed known function and z is a stationary random field a good sampling design should have a greater density of observations where v is relatively large in absolute value designs using this idea when g 0 1 have been studied for some time for g a region in two dimensions very little is known about the statistical properties of cubature rules based on designs with varying density this work proposes a class of designs that are locally parallelogram lattices but whose densities can vary the asymptotic variance of the cubature error for these designs is obtained for a class of isotropic random fields and an asymptotically optimal sequence of cubature rules within this class is found i conjecture that this sequence of cubature rules is asymptotically optimal with respect to all cubature rules

sampling and reconstruction of signals with finite rate of innovation in the presence of noise recently it was shown that it is possible to develop exact sampling schemes for a large class of parametric nonbandlimited signals namely certain signals of finite rate of innovation a common feature of such signals is that they have a finite number of degrees of freedom per unit of time and can be reconstructed from a finite number of uniform samples in order to prove sampling theorems vetterli et al considered the case of deterministic noiseless signals and developed algebraic methods that lead to perfect reconstruction however when noise is present many of those schemes can become ill conditioned in this paper we revisit the problem of sampling and reconstruction of signals with finite rate of innovation and propose improved more robust methods that have better numerical conditioning in the presence of noise and yield more accurate reconstruction we analyze in detail a signal made up of a stream of diracs and develop algorithmic tools that will be used as a basis in all constructions while some of the techniques have been already encountered in the spectral estimation framework we further explore preconditioning methods that lead to improved resolution performance in the case when the signal contains closely spaced components for classes of periodic signals such as piecewise polynomials and nonuniform splines we propose novel algebraic approaches that solve the sampling problem in the laplace domain after appropriate windowing building on the results for periodic signals we extend our analysis to finite length signals and develop schemes based on a gaussian kernel which avoid the problem of ill conditioning by proper weighting of the data matrix our methods use structured linear systems and robust algorithmic solutions which we show through simulation results

efficient numerical methods in non uniform sampling theory summary we present a new second generation reconstruction algorithm for irregular sampling i e for the problem of recovering a band limited function from its non uniformly sampled values the efficient new method is a combination of the adaptive weights method which was developed by the two first named authors and the method of conjugate gradients for the solution of positive definite linear systems the choice of adaptive weights can be seen as a simple but very efficient method of preconditioning further substantial acceleration is achieved by utilizing the toeplitztype structure of the system matrix this new algorithm can handle problems of much larger dimension and condition number than have been accessible so far furthermore if some gaps between samples are large then the algorithm can still be used as a very efficient extrapolation method across the gaps

optimal periodic transmission power schedules for remote estimation of arma processes we consider periodic sensor transmission power allocation with an average energy constraint the sensor sends its kalman filter based state estimate to the remote estimator through an unreliable link dropout probabilities depend on the power level used to encompass applications where the estimator needs to attend to multiple tasks we allow for irregular sampling following a periodic pattern using properties of an underlying markov chain model we derive an explicit expression for the estimation error covariance the results are then used to study optimal sensor power scheduling which minimizes the average error covariance

predicting integrals of random fields using observations on a lattice for a stationary random field z on r d this work studies the asymptotic behavior of predictors of v x z x dx based on observations on a lattice as the distance between neighbors in the lattice tends to 0 under a mild condition on the spectral density of z an asymptotic expression for the mean squared error of a predictor of v x z x dx based on observations on an infinite lattice is derived for predicting integrals over the unit cube a simple predictor based just on observations in the unit cube is shown to be asymptotically optimal if v is sufficiently smooth and z is not too smooth modified predictors extend this result to smoother processes

a simple class of asymptotically optimal quantizers a simple class of quantizers is introduced which are asymptotically optimal as the number of quantization levels increases to infinity with respect to a mean r th power absolute error distortion measure these asymptotically optimal quantizers are very easy to compute their performance is evaluated for several distributions and compares favorably with the performance of the optimal quantizers in all cases for which the latter have been computed in addition their asymptotic robustness is studied under location scale and shape mismatch for several families of distributions

energy efficient signal detection in sensor networks using ordered transmissions signal detection is one application for which dedicated sensor networks have been proposed joint signal processing and communication design of such networks has been of great interest recently we consider new approaches where transmissions can be ordered and halted when sufficient evidence is accumulated we demonstrate that these approaches require on average fewer sensor transmissions and that the savings can be significant in cases of interest we describe a highly efficient approach which saves transmissions over either the optimum unconstrained energy approach or censoring while achieving the same error probability as these approaches the average number of transmissions saved ants is lower bounded by a quantity proportional to the number of sensors employed provided a well behaved distance measure between the sensor distributions is sufficiently large for such cases the ants over the optimum unconstrained energy approach is shown to be larger than half the number of sensors employed numerical results for a mean shift hypothesis testing problem with gaussian noise show significant savings even for smaller values of the distance measure

reconstruction of irregularly sampled discrete time bandlimited signals with unknown sampling locations the purpose of this paper is to develop methods that can reconstruct a bandlimited discrete time signal from an irregular set of samples at unknown locations we define a solution to the problem using first a geometric and then an algebraic point of view we find the locations of the irregular set of samples by treating the problem as a combinatorial optimization problem we employ an exhaustive method and two descent methods the random search and cyclic coordinate methods the numerical simulations were made on three types of irregular sets of locations random sets sets with jitter around a uniform set and periodic nonuniform sets furthermore for the periodic nonuniform set of locations we develop a fast scheme that reduces the computational complexity of the problem by exploiting the periodic nonuniform structure of the sample locations in the dft

asymptotic optimality of regular sequence designs we study linear estimators for the weighted integral of a stochastic process the process may only be observed on a finite sampling design the error is defined in a mean square sense and the process is assumed to satisfy sacks ylvisaker regularity conditions of order r n o we show that sampling at the quantiles of a particular density already yields asymptotically optimal estimators hereby we extend the results of sacks and ylvisaker for regularity r o or 1 and we confirm a conjecture by eubank smith and smith

uniqueness and eventual uniqueness of optimal designs in some time series models abstract earlier results on the uniqueness and eventual uniqueness of optimal designs for certain time series models are extended to a wider class of processes which includes those with covariance structures such as that of multiple integrals of brownian motion and brownian bridge processes the relationship between the problems of regression design for time series and piecewise polynomial approximation with free breakpoints is discussed and consequently asymptotic results obtained by sacks and ylvisaker 1970 are seen to hold under weaker assumptions for these processes

irregular sampling toeplitz matrices and the approximation of entire functions of exponential type in many applications one seeks to recover an entire function of exponential type from its non uniformly spaced samples whereas the mathematical theory usually addresses the question of when such a function in l 2 r can be recovered numerical methods operate with a finite dimensional model the numerical reconstruction or approximation of the original function amounts to the solution of a large linear system we show that the solutions of a particularly efficient discrete model in which the data are fit by trigonometric polynomials converge to the solution of the original infinite dimensional reconstruction problem this legitimatizes the numerical computations and explains why the algorithms employed produce reasonable results the main mathematical result is a new type of approximation theorem for entire functions of exponential type from a finite number of values from another point of view our approach provides a new method for proving sampling theorems

algebraic curve for the so 6 sector of ads cft we construct the general algebraic curve of degree four solving the classical sigma model on s 5 up to two loops it coincides with the algebraic curve for the dual sector of scalar operators in open image in new window sym also constructed here

sparse sensing for distributed detection an offline sampling design problem for distributed detection is considered in this paper to reduce the sensing storage transmission and processing costs the natural choice for the sampler is the sparsest one that results in a desired global error probability since the numerical optimization of the error probabilities is difficult we adopt simpler costs related to distance measures between the conditional distributions of the sensor observations we design sparse samplers for the bayesian as well as the neyman pearson setting the developed theory can be applied to sensor placement selection sample selection and fully decentralized data compression for conditionally independent observations we give an explicit solution which is optimal in terms of the error exponents more specifically the best subset of sensors is the one with the smallest local average root likelihood ratio and largest local average log likelihood ratio in the bayesian and neyman pearson setting respectively we supplement the proposed framework with a thorough analysis for gaussian observations including the case when the sensors are conditionally dependent and also provide examples for other observation distributions one of the results shows that for nonidentical gaussian sensor observations with uncommon means and common covariances under both hypotheses the number of sensors required to achieve a desired detection performance reduces significantly as the sensors become more coherent

methods for numerical integration of high dimensional posterior densities with application to statistical image models numerical computation with bayesian posterior densities has recently received much attention both in the applied statistics and image processing communities this paper surveys previous literature and presents efficient methods for computing marginal density values for image models that have been widely considered in computer vision and image processing the particular models chosen are a markov random field mrf formulation implicit polynomial surface models and parametric polynomial surface models the computations can be used to make a variety of statistically based decisions such as assessing region homogeneity for segmentation or performing model selection detailed descriptions of the methods are provided along with demonstrative experiments on real imagery

convolution operations arising from vandermonde matrices different types of convolution operations involving large vandermonde matrices are considered the convolutions parallel those of large gaussian matrices and additive and multiplicative free convolution and include additive and multiplicative convolution of vandermonde matrices and deterministic diagonal matrices and cases where two independent vandermonde matrices are involved it is also shown that the convergence of any combination of vandermonde matrices is almost sure the convolutions are divided into two types those which depend on the phase distribution of the vandermonde matrices and those which depend only on the spectra of the matrices a general criterion is presented to find which type applies for any given convolution a simulation is presented verifying the results implementations of the presented convolutions are provided and discussed the implementation is based on the technique of fourier motzkin elimination and is quite general as it can be applied to virtually any combination of vandermonde matrices connections with related matrices such as toeplitz and hankel matrices are also discussed

the effect of quantization on the performance of sampling designs the most common form of quantization is rounding off which occurs in all digital systems a general quantizer approximates an observed value by the nearest among a finite number of representative values in estimating weighted integrals of a time series with no quadratic mean derivatives by means of samples at discrete times it is known that the rate of convergence of the mean square error is reduced from n sup 2 to n sup 1 5 when the samples are quantized for smoother time series with k 1 2 quadratic mean derivatives it is now shown that the rate of convergence is reduced from n sup 2k 2 to n sup 2 when the samples are quantized which is a very significant reduction the interplay between sampling and quantization is also studied leading to asymptotically optimal allocation between the number of samples and the number of levels of quantization

on bandlimited signal reconstruction from the distribution of unknown sampling locations in remote sensing with a large array of spatially distributed sensors localization of individual sensor nodes could be difficult motivated by the smart dust paradigm this work addresses the reconstruction of spatially bandlimited fields from samples taken at unknown but statistically distributed sampling locations periodic one dimensional bandlimited fields are considered for sampling samples of the field at uniform independent and identically distributed locations are obtained the statistical realization of the sampling locations is not known first it is shown that a bandlimited field cannot be uniquely determined with samples taken at uniformly distributed but unknown locations even if the number of samples is infinite next it is assumed that the order of sample locations is known with order information on sample locations consistent bandlimited field estimates are designed and analyzed for mean squared error the proposed estimates are analyzed for mean squared error for two cases when the field measurements are noiseless and when the field measurements are affected by additive independent noise process with finite variance finally a central limit is established for the field estimate in the case where field measurements are noiseless