efficient high dimensional importance sampling the paper describes a simple generic and yet highly accurate efficient importance sampling eis monte carlo mc procedure for the evaluation of high dimensional numerical integrals eis is based upon a sequence of auxiliary weighted regressions which actually are linear under appropriate conditions it can be used to evaluate likelihood functions and byproducts thereof such as ml estimators for models which depend upon unobservable variables a dynamic stochastic volatility model and a logit panel data model with unobserved heterogeneity random effects in both dimensions are used to provide illustrations of eis high numerical accuracy even under small number of mc draws mc simulations are used to characterize the finite sample numerical and statistical properties of eis based ml estimators

optimal information bit decoding of linear block codes we consider the problem of decoding a linear block code used over a binary symmetric channel with crossover probability p when the goal of the decoding is to minimize the probability of an information bit error in general there will be several different decoding strategies each corresponding to the optimal rule over some range p spl isin p sub i 1 p sub i each of these strategies can be implemented by standard array with the appropriate choice of coset leaders that are not in general of minimum weight we give optimal rules for selecting coset leaders in the first region 0 p sub 1 and the region p sub max 1 2 for any linear mapping between information bits and codewords the determination of the optimal rule has been an open problem for small p the rule for p p sub max is important because for many codes when p is fixed the optimal rule for any coset corresponds to either the optimal rule for small p or the optimal rule for p near 1 2 the optimal decoding strategy varies with the generator matrix used in general but it is demonstrated that the optimal generator matrix is separable when d sup spl perp 2 the results are shown to extend in a natural way to the case where the goal is to minimize the probability that arbitrary collections of information bits are in error we examine some specific codes and compare the performance under optimal decoding to the performance of previously suggested strategies

on the coveting radius of extremal self dual codes it is known that every self dual binary code which is not doubly even is a child of a doubly even parent it will be shown that an n 2 n 2 2 child of an n n 2 d doubly even parent has covering radius geq d 1 every extremal doubly even 32 16 8 code has covering radius 6 and every extremal doubly even 48 24 12 code has covering radius 8 the complete coset weight distribution of the 32 16 8 quadratic residue code is given as well as bounds or exact values for the covering radii of all extremai doubly even codes of length less than or equal to 96

a new approach to the general minimum distance decoding problem the zero neighbors algorithm minimum distance decoding mdd for a general error correcting linear code is a hard computational problem that recently has been shown to be np hard the complexity of known decoding algorithms is determined by min 2 k 2 n k where n is the code length and k is the number of information digits two new algorithms are suggested that reduce substantially the complexity of mdd the algorithms use a new concept of zero neighbors a special set of codewords only these codewords which can be computed in advance should be stored and used in the decoding procedure the number of zero neighbors is shown to be very small compared with min 2 k 2 n k for n gg 1 and a wide range of code rates r k n for example for r approx 0 5 this number grows approximately as a square root of the number of codewords

a characterization of codes meeting the griesmer bound for any binary linear code of length n dimension k and minimum distance d the griesmer bound says that uif128 1 in this paper we completely characterize all codes which meet the griesmer bound with equality and for which d 2usuk 1 in particular we prove belov s conjecture

association schemes and coding theory this paper contains a survey of association scheme theory with its algebraic and analytical aspects and of its applications to coding theory in a wide sense it is mainly concerned with a class of subjects that involve the central notion of the distance distribution of a code special emphasis is put on the linear programming method inspired by the macwilliams transform this produces upper bounds for the size of a code with a given minimum distance and lower bounds for the size of a design with a given strength the most specific results are obtained in the case where the underlying association scheme satisfies certain well defined polynomial properties this leads one into the realm of orthogonal polynomial theory in particular some universal bounds are derived for codes and designs in polynomial type association schemes throughout the paper the main concepts methods and results are illustrated by two examples that are of major significance in classical coding theory namely the hamming scheme and the johnson scheme other topics that receive special attention are spherical codes and designs and additive codes in translation schemes including z sub 4 additive binary codes

jacobi polynomials for singly even self dual codes and the covering radius problems in this correspondence we develop a method to determine the complete coset weight distributions of the class of singly even self dual binary codes our basic tool is the jacobi polynomials for the code it describes and controls the coset weight enumerators as the results of our present method we give the complete coset weight distributions of some extremal singly even self dual codes of lengths 14 22 32 36 and 40 respectively we give the generator matrices of the used codes of lengths 36 and 40 respectively

generalization of the norse bounds to codes of higher strength the norse bounds state that all codes of strength 1 and length n have covering radius at most n 2 and all self complementary codes of strength 2 and length n have covering radius at most n square root n 2 this is generalized to arbitrary even values of strength still assuming self complementarity and to odd strengths without this hypothesis the proof techniques used are probabilistic

directions of arrival estimation through bayesian compressive sensing strategies the estimation of the directions of arrival doas of narrow band signals impinging on a linear antenna array is addressed within the bayesian compressive sensing bcs framework unlike several state of the art approaches the voltages at the output of the receiving sensors are directly used to determine the doas of the signals thus avoiding the computation of the correlation matrix towards this end the estimation problem is properly formulated to enforce the sparsity of the solution in the linear relationships between output voltages i e the problem data and the unknown doas customized implementations exploiting the measurements collected at a unique time instant single snapshot and multiple time instants multiple snapshots are presented and discussed the effectiveness of the proposed approaches is assessed through an extensive numerical analysis addressing different scenarios signal configurations and noise conditions comparisons with state of the art methods are reported as well

on covering radii and coset weight distributions of extremal binary self dual codes of length 56 we present a method to determine the complete coset weight distributions of doubly even binary self dual extremal 56 28 12 codes the most important steps are 1 to describe the shape of the basis for the linear space of rigid jacobi polynomials associated with such codes in each index i 2 to describe the basis polynomials for the coset weight enumerators of the assigned coset weight i by means of rigid jacobi polynomials of index i the multiplicity of the cosets of weight i have a connection with the frequency of the rigid reference binary vectors v of weight i for the jacobi polynomials this information is sufficient to determine the complete coset weight distributions determination of the covering radius of the codes is an immediate consequence of this method one important practical advantage of this method is that it is enough to get information on 8190 codewords of weight 12 minimal weight words in each such code for computing every necessary information

estimation of stochastic volatility models via monte carlo maximum likelihood this paper discusses the monte carlo maximum likelihood method of estimating stochastic volatility sv models the basic sv model can be expressed as a linear state space model with log chi square disturbances the likelihood function can be approximated arbitrarily accurately by decomposing it into a gaussian part constructed by the kalman filter and a remainder function whose expectation is evaluated by simulation no modifications of this estimation procedure are required when the basic sv model is extended in a number of directions likely to arise in applied empirical research this compares favorably with alternative approaches the finite sample performance of the new estimator is shown to be comparable to the monte carlo markov chain mcmc method

on the spatial bandwidth of scattered fields it is shown that the scattered fields are almost space bandlimited functions the effective bandwidth w is introduced and evaluated for a very general scattering system as well as the error made using functions bandlimited to w w for representing the scattered field the effective bandwidth is very simply related to the maximum dimension of the scattering system the error drops to negligible values for modest increases of w compared to w in the case of large scatterers important consequences of the above general results are finally stressed

particle efficient importance sampling abstract the efficient importance sampling eis method is a general principle for the numerical evaluation of high dimensional integrals that uses the sequential structure of target integrands to build variance minimising importance samplers despite a number of successful applications in high dimensions it is well known that importance sampling strategies are subject to an exponential growth in variance as the dimension of the integration increases we solve this problem by recognising that the eis framework has an offline sequential monte carlo interpretation the particle eis method is based on non standard resampling weights that take into account the construction of the importance sampler as a sequential approximation to the state smoothing density we apply the method for a range of univariate and bivariate stochastic volatility specifications we also develop a new application of the eis approach to state space models with student s t state innovations our results show that the particle eis method strongly outperforms both the standard eis method and particle filters for likelihood evaluation in high dimensions we illustrate the efficiency of the method for bayesian inference using the particle marginal metropolis hastings and importance sampling squared algorithms

on the interpolation of electromagnetic near field without prior knowledge of the radiating source a method is proposed to interpolate the electromagnetic near field when no information on the radiating source is available in the absence of a priori knowledge general properties of the electromagnetic field are exploited to estimate the field namely the minimum complexity of the field and the continuity of the first derivatives these properties are enforced by minimizing the nuclear norm and using the thin plate spline interpolation results respectively the proposed procedure is validated experimentally by interpolating the planar electrical near field radiated by three antennas the quality of the interpolation and its robustness to noise are investigated despite its simplicity the interpolation method is able to properly estimate the near field from a random coarse sampling of 2 lambda the quality of the near field interpolation is also confirmed by deriving the far field these promising results pave the way for the development of fast antenna measurement procedures

monte carlo methods for estimating smoothing and filtering one and two factor stochastic volatility models one and two factor stochastic volatility models are assessed over three sets of stock returns data sp the problem is to get the shape of the conditional returns distribution right none of the models come close to matching the tails of this distribution including a second factor provides only a relatively small improvement over the single factor models fitting this aspect of the data is important for option pricing and risk management

likelihood analysis of non gaussian measurement time series summary in this paper we provide methods for estimating non gaussian time series models these techniques rely on markov chain monte carlo to carry out simulation smoothing and bayesian posterior analysis of parameters and on importance sampling to estimate the likelihood function for classical inference the time series structure of the models is used to ensure that our simulation algorithms are efficient

weight distributions of cosets of two error correcting binary bch codes extended or not let b be the binary two error correcting bch code of length 2 sup m 1 and let b spl circ be the extended code of b we give formal expressions of weight distributions of the cosets of the codes b spl circ only depending on m we can then deduce the weight distributions of the cosets of b when m is odd it is well known that there are four distinct weight distributions for the cosets of b so our main result is about the even case camion courteau and montpetit see ibid vol 38 no 7 p 1353 1992 observe that for the lengths 15 63 and 255 there are eight distinct weight distributions we prove that this property holds for the codes b spl circ and b for all even m

representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples it is shown that the electromagnetic em field radiated or scattered by bounded sources can be accurately represented over a substantially arbitrary surface by a finite number of samples even when the observation domain is unbounded the number of required samples is nonredundant and essentially coincident with the number of degrees of freedom of the field this result relies on the extraction of a proper phase factor from the field expression and on the use of appropriate coordinates to parameterize the domain it is demonstrated that the number of degrees of freedom is independent of the observation domain and depends only on the source geometry the case of spheroidal sources and observation domains with rotational symmetry is analyzed in detail and the particular cases of spherical and planar sources are explicitly considered for these geometries precise and fast sampling algorithms of central type are presented which allow an efficient recovery of em fields from a nonredundant finite number of samples such algorithms are stable with respect to random errors affecting the data

an upper bound on the covering radius as a function of the dual distance p delsarte 1973 developed a method that gives an upper bound on the cardinality of a code as a function of its minimum distance it is shown that using a modification of that method one gets an upper bound on the covering radius of a code as a function of its dual distance as an interesting special case the covering radius of the dual of a bch code is considered

on the sampling of the electromagnetic field radiated by sparse sources the aim of this paper is to discuss the effectiveness of random sampling of the electromagnetic field in problems involving sparse radiating sources the method adopted in this paper uses an intuitive geometrical approach based on the johnson linderstrauss lemma applied to the epsilon net of the set of the fields radiated by the sparse source the paper shows that a proper non uniform random sampling nurs using some a priori information on the problem allows a significant reduction in the cardinality of the set of the measured data compared to uniform random sampling and to random sampling from a lambda 2 equispaced set of data it is also shown that there is a limiting number of data after which random sampling is not convenient in this case a deterministic sampling strategy called modified non uniform sampling mnus is proposed numerical results on linear sparse arrays confirm the effectiveness of nurs and mnus

modified bounds for covering codes the covering radius of binary codes is studied bounds on k n r the minimum cardinality of any binary code of length n and covering radius r are found modifications of the van wee lower bounds are proved for k n r the minimal number of codewords in any binary code of length n and covering radius r the first of the two van wee bounds is based on studying the hamming spheres of radius 1 centered at the points which have distance r to the code c the points covered by more than one codeword are divided into several classes and better estimates for some of these classes are obtained using a suitable averaging process the lower bound for k n r when r or 2 is improved the second van wee bound studies spheres of radius 2 centered at the points which have distance r 1 or r to the code c these points are divided essentially into two classes the points that are covered by only one codeword of c and the points that are covered by more than one codeword

the covering radius of the 2 15 16 reed muller code is at least 16276 two interesting cosets of the first order reed muller code of block length 2 15 are described they provide counterexamples to a conjecture on the covering radius

on the covering radius of binary linear codes meeting the griesmer bound let g k d sum i 0 k 1 lceil d 2 i rceil by the griesmer bound n geq g k d for any binary linear n k d code let s lceil d 2 k 1 rceil then s can be interpreted as the maximum number of occurrences of a column in the generator matrix of any code with parameters g k d k d let rho be the covering radius of a g k d k d code it will be shown that rho leq d lceil s 2 rceil moreover the existence of a g k d k d code with rho d lceil s 2 rceil is equivalent to the existence of a g k 1 d k 1 d code for s leq 2 all g k d k d codes with rho d lceil s 2 rceil are described while for s 2 a sufficient condition for their existence is formulated

perfect codes hardly exist the main lines of a partial proof of the perfect code theorem are presented the relevant part refers to the nonexistence of unknown t perfect codes over arbitrary alphabets for t not in 1 2 6 8 the details of the proof can be found in the author s ph d dissertation at the university of amsterdam

testing the assumptions behind importance sampling importance sampling is used in many areas of modern econometrics to approximate unsolvable integrals its reliable use requires the sampler to possess a variance for this guarantees a square root speed of convergence and asymptotic normality of the estimator of the integral however this assumption is seldom checked in this paper we use extreme value theory to empirically assess the appropriateness of this assumption our main application is the stochastic volatility model where importance sampling is commonly used for maximum likelihood estimation of the parameters of the model

on the covering radius of codes the covering radius r of a code is the maximal distance of any vector from the code this work gives a number of new results concerning t n k the minimal covering radius of any binary code of length n and dimension k for example t n 4 and t n 5 are determined exactly and reasonably tight bounds on t n k are obtained for any k when n is large these results are found by using several new constructions for codes with small covering radius one construction the amalgamated direct sum involves a quantity called the norm of a code codes with norm leq 2 r 1 are called normal and may be combined efficiently the paper concludes with a table giving bounds on t n k for n leq 64

minimum trace norm regularization mtnr in electromagnetic inverse problems this paper discusses a method to regularize linear problems in presence of incomplete and noisy data generated by partially or totally unknown sources the idea is to identify the simplest solution looking for the system having the minimum number of degrees of freedom ndf compatible with the available data it is shown that a normalized version of the trace norm known as 1 schatten norm in functional analysis is a good convex approximation of the ndf of the field this allows to use the trace norm as a convex surrogate of the ndf in the minimization process taking advantage of the recent literature on rank minimization examples regarding mimo beamforming from incomplete channel matrix field interpolation with no a priori information on the sources and land mine identification using the total field are discussed

the second order reed muller code of length 64 has covering radius 18 corresp the assertion of the title is proved by first showing that the covering radius of r 2 6 cannot exceed 18 and then constructing a weight 18 coset leader

monte carlo maximum likelihood estimation for non gaussian state space models state space models are considered for observations which have non gaussian distributions we obtain accurate approximations to the loglikelihood for such models by monte carlo simulation devices are introduced which improve the accuracy of the approximations and which increase computational efficiency the loglikelihood function is maximised numerically to obtain estimates of the unknown hyperparameters standard errors of the estimates due to simulation are calculated details are given for the important special cases where the observations come from an exponential family distribution and where the observation equation is linear but the observation errors are non gaussian the techniques are illustrated with a series for which the observations have a poisson distribution and a series for which the observation errors have a t distribution

new lower bounds for binary covering codes g d chen et al ibid vol it 32 p 680 94 1986 presented two new lower bounds for k n r where k n r denotes the minimum cardinality of a binary code of length n and covering radius r the author shows that a slight modification gives further improvements and some examples are given to confirm the argument codes that have a certain partitioning property are considered

synthesis of sparse arrays with focused or shaped beampattern via sequential convex optimizations an iterative procedure for the synthesis of sparse arrays radiating focused or shaped beampattern is presented the algorithm consists in solving a sequence of weighted l1 convex optimization problems the method can thus be readily implemented and efficiently solved in the optimization procedure the objective is the minimization of the number of radiating elements and the constraints correspond to the pattern requirements the method can be applied to synthesize either focused or shaped beampattern and there is no restriction regarding the array geometry and individual element patterns numerical comparisons with standard benchmark problems assess the efficiency of the proposed approach whose computation time is several orders of magnitude below those of so called global optimization algorithms

on the minimum distance of cyclic codes the main result is a new lower bound for the minimum distance of cyclic codes that includes earlier bounds i e bch bound ht bound roos bound this bound is related to a second method for bounding the minimum distance of a cyclic code which we call shifting this method can be even stronger than the first one for all binary cyclic codes of length with two exceptions we show that our methods yield the true minimum distance the two exceptions at the end of our list are a code and its even weight subcode we treat several examples of cyclic codes of length geq 63

on the peak to mean envelope power ratio of phase shifted binary codes the peak to mean envelope power ratio pmepr of a code employed in orthogonal frequency division multiplexing ofdm systems can be reduced by permuting its coordinates and by rotating each coordinate by a fixed phase shift motivated by some previous designs of phase shifts using suboptimal methods the following question is considered in this paper for a given binary code how much pmepr reduction can be achieved when the phase shifts are taken from a 2h ary phase shift keying 2h psk constellation a lower bound on the achievable pmepr is established which is related to the covering radius of the binary code generally speaking the achievable region of the pmepr shrinks as the covering radius of the binary code decreases the bound is then applied to some well understood codes including nonredundant bpsk signaling bch codes and their duals reed muller codes and convolutional codes it is demonstrated that most presumably not optimal phase shift designs from the literature attain or approach our bound

on the role of the number of degrees of freedom of the field in mimo channels the aim of this paper is to investigate the relationship between the effective number of degrees of freedom endf of a multiple input multiple output mimo channel and the number of degrees of freedom ndf of the field in particular the ndf of the field represents an upperbound for the endf of a mimo channel consequently the evaluation of the maximum endf can be carried out by adopting the literature on the ndf based on the spatial bandlimitation properties of the field this approach allows a simple and intuitive explanation of the maximum endf in a mimo channel based on a geometrical interpretation of the spatial channel in terms of spatial nyquist intervals

weight distribution of translates covering radius and perfect codes correcting errors of given weights let v bed binary linear n k code defined by a check matrix h and let h x be the characteristic function for the set of columns of h connections between the walsh transform of h x and the weight distributions of all translates of the code are obtained explicit formulas for the weight distributions of translates are given for small weights i i the computation of the weight distribution of all translates including the code itself for i requires at most 7 n k 2 n k additions and subtractions 6 cdot 2 n k multiplications and 2 n k l memory cells this method may be very effective if there is an analytic expression for h x a simple method for computing the covering radius of the code by the walsh transform of h x is described the implementation of this method requires for large n at most 2 n k n k log 2 n k arithmetical operations and 2 n k 1 memory cells we define the concept l perfect for codes where l is a set of weights after describing several linear and nonlinear l perfect codes necessary and sufficient conditions for a code to be l perfect in terms of the walsh transform of h x are established an analog of the lloyd theorem for such codes is proved

further results on the covering radius of codes a number of upper and lower bounds are obtained for k n r the minimal number of codewords in any binary code of length n and covering radius r several new constructions are used to derive the upper bounds including an amalgamated direct sum construction for nonlinear codes this construction works best when applied to normal codes and we give some new and stronger conditions which imply that a linear code is normal an upper bound is given for the density of a covering code over any alphabet and it is shown that k n 2 r 1 leq k n r holds for sufficiently large n

the covering radius of the leech lattice we investigate the points in 24 dimensional space that are at maximal distance from the leech lattice i e the deep holes in that lattice the distance of such a point from the leech lattice is 1 sqrt 2 times the minimal distance between the lattice points furthermore there are 23 inequivalent types of deep hole one for each of the 23 even unimodular 24 dimensional lattices found by niemeier

maximum likelihood estimation of partially observed diffusion models this paper develops a maximum likelihood ml method to estimate partially observed diffusion models based on data sampled at discrete times the method combines two techniques recently proposed in the literature in two separate steps in the first step the closed form approach of ait sahalia 2008 is used to obtain a highly accurate approximation to the joint transition probability density of the latent and the observed states in the second step the efficient importance sampling technique of richard and zhang 2007 is used to integrate out the latent states thereby yielding the likelihood function using both simulated and real data we show that the proposed ml method works better than alternative methods the new method does not require the underlying diffusion to have an affine structure and does not involve infill simulations therefore the method has a wide range of applicability and its computational cost is moderate

a new class of codes meeting the griesmer bound an infinite sequence of k dimensional binary linear block codes is constructed with parameters n 2 k 2 k 2 15 d 2 k 1 2 k 3 8 k geq 7 for k geq 8 these codes are unique while there are five nonisomorphic codes for k 7 by shortening these codes in an appropriate way one finds codes meeting the griesmer bound for 2 k 1 2 k 3 15 leq d leq 2 k 1 2 k 3 8 k geq 7

sphere packing bounds revisited for moderate block lengths the main reference of this paper is the sphere packing bound of 1967 sp67 derived by shannon gallager and berlekamp it offers a lower bound on the decoding error probability over a very large variety of channels if it has failed so far to provide any usable material in practical implementation of telecommunication systems it is due to an original focus on asymptotic results making it inapplicable for moderate code lengths and to the difficulty of the involved methods which makes the derivation of sp67 quite hermetic and uninspiring for further research the purpose of this paper is two fold 1 to stir up some renewed interest in the topic on which shannon concluded his career in information theory thanks to a qualitative rather than technical review of the derivation of sp67 introduced by a review of the simpler sphere packing bound derived by shannon in 1959 2 to prove the practical interest of sp67 by extending its field of application to continuous output channels and particularly the additive white gaussian noise awgn channel used with any particular modulation scheme and by improving its lower bound for the moderate code length case so that it becomes the best lower bound for most iteratively decodable codes turbo codes low density parity check ldpc codes repeat accumulate ra codes etc of usual lengths

the index calculus method using non smooth polynomials we study a generalized version of the index calculus method for the discrete logarithm problem in f q when q p n p is a small prime and n the database consists of the logarithms of all irreducible polynomials of degree between given bounds the original version of the algorithm uses lower bound equal to one we show theoretically that the algorithm has the same asymptotic running time as the original version the analysis shows that the best upper limit for the interval coincides with the one for the original version the lower limit for the interval remains a free variable of the process we provide experimental results that indicate practical values for that bound we also give heuristic arguments for the running time of the waterloo variant and of the coppersmith method with our generalized database

the covering radius of cyclic codes of length up to 31 corresp the covering radius is given for all binary cyclic codes of length less than or equal to 31 many of these codes are optimal in the sense of having the smallest possible covering radius of any linear code of that length and dimension

the complexity of computing the covering radius of a code the problem of finding the covering radius of a binary linear code is shown to be nondeterministic polynomial np hard in fact a problem that is complete for the class prod 2 p in the polynomial hierarchy is shown to be reducible to the covering radius problem so that finding the covering radius is strictly harder than any np complete problem unless the polynomial hierarchy collapses with np prod 2 p

variational multinomial logit gaussian process gaussian process prior with an appropriate likelihood function is a flexible non parametric model for a variety of learning tasks one important and standard task is multi class classification which is the categorization of an item into one of several fixed classes a usual likelihood function for this is the multinomial logistic likelihood function however exact inference with this model has proved to be difficult because high dimensional integrations are required in this paper we propose a variational approximation to this model and we describe the optimization of the variational parameters experiments have shown our approximation to be tight in addition we provide data independent bounds on the marginal likelihood of the model one of which is shown to be much tighter than the existing variational mean field bound in the experiments we also derive a proper lower bound on the predictive likelihood that involves the kullback leibler divergence between the approximating and the true posterior we combine our approach with a recently proposed sparse approximation to give a variational sparse approximation to the gaussian process multi class model we also derive criteria which can be used to select the inducing set and we show the effectiveness of these criteria over random selection in an experiment

voronoi regions of lattices second moments of polytopes and quantization if a point is picked at random inside a regular simplex octahedron 600 cell or other polytope what is its average squared distance from the centroid in n dimensional space what is the average squared distance of a random point from the closest point of the lattice a n or d n e n a n ast or d n ast the answers are given here together with a description of the voronoi or nearest neighbor regions of these lattices the results have applications to quantization and to the design of signals for the gaussian channel for example a quantizer based on the eight dimensional lattice e8 has a mean squared error per symbol of 0 0717 cdots when applied to uniformly distributed data compared with 0 08333 cdots for the best one dimensional quantizer

on the degrees of freedom of scattered fields starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities the degrees of freedom of the scattered field are introduced and then computed the degrees of freedom are shown to be practically equal to the nyquist number appropriate to the effective spatial bandwidth of the scattered field and to the extension of the observation domain accordingly a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error it is also shown that the field representation can be made in terms of field values and simple sampling functions provided that a marginal increase in the approximation error is tolerated the results not only completely justify the use of sampling interpolation for representing scattering fields but also demonstrate that such representation is practically an optimal one an algorithm for the reconstruction of scattered fields given the maximum allowed error is then produced

stochastic volatility in asset prices estimation with simulated maximum likelihood abstract the stochastic volatility model is used to estimate daily asset price dynamics the model is estimated by integrating latent volatility out of the joint density of prices and volatility to obtain the marginal density of prices due to high number of dimensions of the integral no conventional integration technique is applicable a monte carlo method called simulated maximum likelihood is used to obtain the marginal density where the latent variable is simulated conditional on available information the model is estimated by 2022 observations from the s p 500 index for comparison arch type models are estimated with the same data

on covering radii and coset weight distributions of extremal binary self dual codes of length 40 in the present paper we develop a method to determine the coset weight distributions and covering radius of doubly even self dual extremal binary codes of length 40 the method is algebraic in nature and largely eliminates necessary computations by electronic computers the method easily applies to longer codes e g self dual 56 28 12 binary codes or to non extremal codes

on the complete coset weight distribution of the extremal self dual 46 23 10 code it is known that there is a unique extremal self dual 46 23 10 code up to equivalence in this correspondence we give the complete coset weight distribution of the unique code

some new upper bounds on the covering radius of binary linear codes a griesmer like upper bound on the covering radius r is given to the author s knowledge this is the only upper bound which explicitly depends on all three parameters n k and d an upper bound on r for cyclic codes is then given which depends on the generator polynomial of the cyclic code and which in many cases leads to an improvement of the previous bound an upper bound on the irreducible generator polynomial cyclic codes is also given new interpretations and applications of the so called norse bounds and necessary and sufficient conditions to attain one of these bounds are provided generalizations of most of the results for codes over gf q are outlined

kuhn tucker likelihood ratio and wald tests for nonlinear models with inequality constraints on the parameters abstract this paper considers the problem of testing statistical hypothesis in nonlinear regression models with inequality constraints on the parameters first the kuhn tucker test procedure is defined next it is shown that the distribution of the kuhn tucker the likelihood ratio and the wald test statistics converges to the same mixture of chi square distributions under the null hypothesis to illustrate these results two examples are considered 1 the problem of testing that individual effects are missing in an error component model and 2 the problem of testing equilibrium for a model of markets in disequilibrium

a new method for avoiding the truncation error in near field antennas measurements a new method to avoid the truncation error in antenna near field measurements is presented the approach relies on the concept of information content of the field according to this point of view the truncation problem is solved by picking up the information that is lost due to the finite size of scanning area in points of the space reachable by the measurement system the method can be applied to any scanning geometry including the planar and cylindrical ones whenever the set up allows to vary the distance between the antenna under test and the probe during the scanning procedure application of the method to cylindrical near field scanning is numerically investigated assessing the effectiveness of the proposed technique

the multicovering radii of codes the covering radius of a code is the least r such that the set of balls of radius r around codewords covers the entire ambient space we introduce a generalization of the notion of covering radius the m covering radius of a code is the least radius such that the set of balls of that radius covers all m tuples of elements in the ambient space we investigate basic properties of m covering radii we investigate whether codes exist with given m covering radii not always we derive bounds on the size of the smallest code with a given m covering radius based on generalizations of the sphere bound and the method of counting excesses

on electromagnetics and information theory some connections are described between electromagnetic theory and information theory identifying some unavoidable limitations imposed by the laws of electromagnetism to communication systems starting from this result the role of the degrees of freedom of the field in radiating systems is investigated different classes of antennas use the available degrees of freedom in different ways in particular a multiple input multiple output antenna is a radiating system conveying statistically independent information on more than one degree of freedom of the field applications of the theory to antenna synthesis and antenna characterization in complex environments are shown

covering radius survey and recent results all known results on covering radius are presented as well as some new results there are a number of upper and lower bounds including asymptotic results a few exact determinations of covering radius some extensive relations with other aspects of coding theory through the reed muller codes and new results on the least covering radius of any linear n k code there is also a recent result on the complexity of computing the covering radius

bayesian inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

another upper bound on covering radius a new upper bound on the covering radius of binary linear codes improves on previously known bounds for some codes the bound is w 2 rho 2 where w is one of the weights occurring among the codewords and rho 2 is the covering radius of an associated code some comparisons with other bounds are made

estimating tails of probability distributions we study the asymptotic properties of estimators of the tail of a distribution based on the excesses over a threshold a key idea is the use of pickands generalised pareto distribution and its fitting in most cases by the method of maximum likelihood the results cover all three limiting types of extreme value theory we propose a new estimator for an index of regular variation and show that it often performs better than hill s estimator we give new results for estimating the endpoint of a distribution extending earlier work by hall and by smith and weissman finally we give detailed results for the domain of attraction of exp e x and show that in most cases our proposed estimator is more efficient than two others one based on the exponential distribution and the other due to davis and resnick we also touch briefly on the problem of large deviations from a statistical point of view the results make extensive use of existing work on rates of convergence

some results on the covering radii of reed muller codes let r r m be the rth order reed muller code of length 2 sup m and let rho r m be its covering radius r

monte carlo estimation for nonlinear non gaussian state space models we develop a proposal or importance density for state space models with a nonlinear non gaussian observation vector y p y and an unobserved linear gaussian signal vector p the proposal density is obtained from the laplace approximation of the smoothing density p y we present efficient algorithms to calculate the mode of p y and to sample from the proposal density the samples can be used for importance sampling and markov chain monte carlo methods the new results allow the application of these methods to state space models where the observation density p y is not log concave additional results are presented that lead to computationally efficient implementations we illustrate the methods for the stochastic volatility model with leverage

reduced lists of error patterns for maximum likelihood soft decoding a method whereby a substantially reduced family of error patterns called survivors may be created for maximum likelihood soft decoding is introduced the family of survivor depends on the received word a decoder based on this approach first forms the survivors then scores them rather than obtaining the survivors by online elimination of error patterns the use of predetermined lists that represent all families of survivors is proposed

lower bounds on the covering radius of the non binary and binary irreducible goppa codes new lower bounds on the covering radius for different subclasses of irreducible goppa codes are obtained

bayesian leave one out cross validation approximations for gaussian latent variable models the future predictive performance of a bayesian model can be estimated using bayesian cross validation in this article we consider gaussian latent variable models where the integration over the latent values is approximated using the laplace method or expectation propagation ep we study the properties of several bayesian leave one out loo cross validation approximations that in most cases can be computed with a small additional cost after forming the posterior approximation given the full data our main objective is to assess the accuracy of the approximative loo cross validation estimators that is for each method laplace and ep we compare the approximate fast computation with the exact brute force loo computation secondarily we evaluate the accuracy of the laplace and ep approximations themselves against a ground truth established through extensive markov chain monte carlo simulation our empirical results show that the approach based upon a gaussian approximation to the loo marginal distribution the so called cavity distribution gives the most accurate and reliable results among the fast methods

the covering radius of extremal self dual code d11 and its application d11 constructed by conway and sloane is an extremal self dual 56 28 12 code with weight enumerator 1 8190y sup 12 622314y sup 16 11699688y sup 20 we find that the covering radius of d11 is 10 this shows that the inequality r c sub 56 spl les 10 cannot be improved any more where r c sub 56 is the covering radius of any extremal doubly even 56 28 12 code c sub 56 and we use it to get ten new 58 29 10 codes

fast quantizing and decoding and algorithms for lattice quantizers and codes for each of the lattices a n n geq 1 d n n geq 2 e 6 e 7 e 8 and their duals a very fast algorithm is given for finding the closest lattice point to an arbitrary point if these lattices are used for vector quantizing of uniformly distributed data the algorithm finds the minimum distortion lattice point if the lattices are used as codes for a gaussian channel the algorithm performs maximum likelihood decoding

complex weight sparse linear array synthesis by bayesian compressive sampling an innovative method for the synthesis of maximally sparse linear arrays matching arbitrary reference patterns is proposed in the framework of sparseness constrained optimization the approach exploits the multi task mt bayesian compressive sensing bcs theory to enable the design of complex non hermitian layouts with arbitrary radiation and geometrical constraints by casting the pattern matching problem into a probabilistic formulation a relevance vector machine rvm technique is used as solution tool the numerical assessment points out the advances of the proposed implementation over the extension to complex patterns of and it gives some indications about the reliability flexibility and numerical efficiency of the mt bcs approach also in comparison with state of the art sparse arrays synthesis methods

generalized dynamic panel data models with random effects for cross section and time abstract an exact maximum likelihood method is developed for the estimation of parameters in a nonlinear non gaussian dynamic panel data model with unobserved random individual specific and time varying effects we propose an estimation procedure based on the importance sampling technique in particular a sequence of conditional importance densities is derived which integrates out all random effects from the joint distribution of endogenous variables we disentangle the integration over both the cross section and the time series dimensions the estimation method facilitates the modeling of large panels in both dimensions we evaluate the method in an extended monte carlo study for dynamic panel data models with observations from different non gaussian distributions we finally present three empirical illustrations for i union choice of young males using a binary panel ii crime rates of families using a binomial panel and iii economic growth modeling using a student s t panel