counterexamples to on estimating noncausal nonminimum phase arma models of non gaussian processes and reply in the above named work by giannakis and swami see ibid vol 38 no 3 p 478 1990 an order selection procedure was proposed for parameter estimation for noncausal nonminimum phase arma autoregressive moving average models of non gaussian processes the commenter argues that it has been derived under an erroneous assumption and he also gives a counterexample to show that it does not yield a consistent order estimate in general two linear approaches for parameter estimation were also presented in the above named work the commenter contends that an existing counterexample to an earlier version of one of the algorithms also applies to both the approaches of the above named work the authors reply is presented

identifiability of general arma processes using linear cumulant based estimators abstract cumulants of order greater than two may be used to estimate the parameters of non gaussian arma processes observed in additive colored gaussian noise the arma model may be causal or non causal mixed phase and have inherent all pass factors and repeated poles recent counterexamples to existing algorithms based on third order cumulants have given rise to questions of uniqueness and consistency of the parameter estimates two new order and parameter estimation algorithms are derived and consistency of the estimators is established these algorithms involve the solution of sets of linear equations and may be based on cumulants of any order greater than three it is demonstrated that the counterexamples do not apply to the new methods

cumulant based order determination of non gaussian arma models the objective is the order determination of non gaussian and nonminimum phase autoregressive moving average arma models using higher order cumulant statistics the two methods developed assume knowledge of upper bounds on the arma orders the first method performs a linear dependence search among the columns of a higher order statistics matrix by means of the gram schmidt orthogonalization procedure in the second method the order of the ar part is found as the rank of the matrix formed by the higher order statistics sequence for numerically robust rank determination the singular value decomposition approach is adopted the argument principle and samples of the polyspectral phase are used to obtain the relative degree of the arma model from which the order of the ma part can be determined statistical analysis is included for determining the correct ma order with high probability when estimates of third order cumulants are only available simulations are used to verify the performance of the methods and compare autocorrelation with cumulant based order determination approaches

olriv a new fast adaptive algorithm for rectangular block toeplitz systems in this paper we propose a new algorithm for solving overdetermined systems when they are rectangular block toeplitz the blocks can have more rows than columns it is based on the expression of the matrix of the system to solve as the intercorrelation between two vectorial processes namely the original and the instrumental processes the instrumental process has generally more components than the original one therefore it takes the overdetermined character of the system into consideration the proposed algorithm known as the overdetermined lattice recursive instrumental variable olriv belongs to the fast rls family and lies on a double lattice structure where one lattice performs the prediction of the original process and the other one the prediction of the instrumental process the geometric complete derivation of the proposed algorithm is given in the paper afterwards we show how olriv can be applied to perform blind adaptive identification of ar channels using high order statistics where the systems to solve are often overdetermined to ensure identifiability both the scalar and the vectorial cases are investigated simulation results are finally given to show the performances of olriv

hamilton jacobi skeleton on cortical surfaces in this paper we propose a new method to construct graphical representations of cortical folding patterns by computing skeletons on triangulated cortical surfaces in our approach a cortical surface is first partitioned into sulcal and gyral regions via the solution of a variational problem using graph cuts which can guarantee global optimality after that we extend the method of hamilton jacobi skeleton to subsets of triangulated surfaces together with a geometrically intuitive pruning process that can trade off between skeleton complexity and the completeness of representing folding patterns compared with previous work that uses skeletons of 3 d volumes to represent sulcal patterns the skeletons on cortical surfaces can be easily decomposed into branches and provide a simpler way to construct graphical representations of cortical morphometry in our experiments we demonstrate our method on two different cortical surface models its ability of capturing major sulcal patterns and its application to compute skeletons of gyral regions

fitting noncausal autoregressive signal plus noise models to noisy non gaussian linear processes the problem of estimating the parameters of a noncausal autoregressive signal model from noisy observations is considered the signal is assumed to be non gaussian the measurement noise is allowed to be non gaussian two techniques that use both autocorrelations and third order autocumulants of the data are presented for parameter estimation knowledge of the probability distribution of the driving noise is not required several simulation examples are presented to illustrate the two methods the problem of model order selection is also addressed

higher order spectrum estimation via noncausal autoregressive modeling and deconvolution a method for nonminimum phase finite impulse response fir system identification is introduced that is based on noncausal autoregressive ar modeling of the third moments of the output data the magnitude and phase response of the fir system are expressed in terms of the parameters of a noncausal ar model the set of ar parameters is obtained by solving an overdetermined linear system of equations that is formed using third moment estimates of the output data the performance of the method is illustrated with simulation examples

a unifying maximum likelihood view of cumulant and polyspectral measures for non gaussian signal classification and estimation classification and estimation of non gaussian signals observed in additive gaussian noise of unknown covariance are addressed using cumulants or polyspectra by integrating ideas from pattern recognition and model identification asymptotically optimum maximum likelihood classifiers and arma autoregressive moving average parameter estimators are derived without knowledge of the data distribution identifiability of noncausal and nonminimum phase arma models is established using a finite number of cumulant or polyspectral lags of any order greater than two a unifying view of cumulant and polyspectral discriminant measures utilizes these lags and provides a common framework for development and performance analysis of novel and existing estimation and classification algorithms tentative order determination and model validation tests for non gaussian arma processes are described briefly illustrative simulations are also presented

parameter estimation of cyclostationary am time series with application to missing observations time series with systematic misses occur often in practice and can be modeled as amplitude modulated arma processes with this as a motivating application modeling of cyclostationary amplitude modulated time series is addressed in the paper assuming that the modulating sequence is almost periodic parameter estimation algorithms are developed based on second and higher order cumulants of the resulting cyclostationary observations which may be corrupted by any additive stationary noise of unknown covariance if unknown the modulating sequence can be recovered even in the presence of additive perhaps nonstationary and colored gaussian or any symmetrically distributed noise if the arma process is nongaussian cyclic cumulants of order greater than three can identify non causal and non minimum phase models from partial noisy data simulation experiments corroborate the theoretical results

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

new family of tilings of three dimensional euclidean space by tetrahedra and octahedra abstract it is well known that two regular tetrahedra can be combined with a single regular octahedron to tile complete fill three dimensional euclidean space this structure was called the octet truss by buckminster fuller it was believed that such a tiling which is the delaunay tessellation of the face centered cubic fcc lattice and its closely related stacking variants are the only tessellations of that involve two different regular polyhedra here we identify and analyze a unique family comprised of a noncountably infinite number of periodic tilings of whose smallest repeat tiling unit consists of one regular octahedron and six smaller regular tetrahedra we first derive an extreme member of this unique tiling family by showing that the holes in the optimal lattice packing of octahedra obtained by minkowski over a century ago are congruent tetrahedra this tiling has 694 distinct concave i e nonconvex repeat units 24 of which possess central symmetry and hence is distinctly different and combinatorically richer than the fcc tetrahedra octahedra tiling which only has two distinct tiling units then we construct a one parameter family of octahedron packings that continuously spans from the fcc to the optimal lattice packing of octahedra we show that the holes in these packings except for the two extreme cases are tetrahedra of two sizes leading to a family of periodic tilings with units composed four small tetrahedra and two large tetrahedra that contact an octahedron these tilings generally possess 2 068 distinct concave tiling units 62 of which are centrally symmetric

recovering the poles from third order cumulants of system output the problem of identifying the poles of single input single output siso linear stochastic systems from the higher order statistics of noisy observations is considered it is assumed that the system is driven by an independent and identically distributed non gaussian process with nonzero third order cumulant function at zero lag there is no other restriction of the probability distribution of the driving noise the system is assumed to be of known order causal and exponentially stable but is not required to be minimum phase the system output is observed in additive possibly non gaussian noise it is shown that if there are no pole zero cancellations in the transfer function of the given system then it is necessary and sufficient for a block hankel matrix to have rank equal to the system order where the matrix is constructed from a partial set of third order cumulants of the noisy output sequence this fundamental result then leads to a linear solution to the problem of estimating the coefficients of the system characteristic polynomial from which the system poles can be found via root finding

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

parameter estimation for noncausal arma models of non gaussian signals via cumulant matching we consider the problem of estimating the parameters of a stable stationary scalar arma p q signal model driven by an i i d non gaussian sequence the driving noise sequence is not observed the signal is allowed to be nonminimum phase and or noncausal i e poles may lie both inside as well as outside the unit circle we address the problem of parameter identifiability given the higher order cumulants of the signal on a finite set of lags the sufficient set of lags required to achieve parameter identifiability is the smallest to date the sufficient conditions for parameter identifiability are also the least restrictive to date we also propose a frequency domain approach for time domain nonlinear optimization of a quadratic cumulant matching criterion illustrative computer simulation results are presented

multichannel arma processes parametric modeling of multichannel time series is accomplished by using higher than second order statistics hos of the observed nongaussian data cumulants of vector processes are defined using a kronecker product formulation and consistency of their sample estimators is addressed identifiability results in connection with the hos based parameter estimation of causal and noncausal multivariate arma processes are established estimates of the parameters of causal arma models are obtained as the solution to a set of linear equations whereas those of noncausal arma models are obtained as the solution to a cumulant matching algorithm conventional approaches based on second order statistics can identify a multichannel system only to within post multiplication by a unimodular matrix hos based methods yield solutions that are unique to within post multiplication by an extended permutation matrix additionally the multiminimum phase assumption can be relaxed and the observations may be contaminated with colored gaussian noise frequency domain methods for nonparametric system identification are discussed briefly simulations results validating the multichannel parameter estimation algorithms are provided

random sequential adsorption of oriented superdisks in this work we extend recent study of the properties of the dense packing of superdisks by y jiao phys rev lett 100 245504 2008 to the jammed state formed by these objects in random sequential adsorption the superdisks are two dimensional shapes bound by the curves of the form x 2p y 2p 1 with p 0 we use monte carlo simulations and theoretical arguments to establish that p 1 2 is a special point at which the jamming density rhoj p has a discontinuous derivative as a function of p the existence of this point can be also argued for by a phenomenological excluded area argument

on the identifiability of non gaussian arma models using cumulants a fixed set of output cumulants of order greater than two guarantees unique identification of known order causal arma autoregressive moving average models which are driven by unobservable non gaussian i i d noise the models are allowed to be non minimum phase and their outputs may be corrupted by additive colored gaussian noise of unknown covariance the arma parameters can be estimated either by means of linear equations and closed form expressions or by minimizing quadratic cumulant matching criteria the latter approach requires computation of cumulants in terms of the arma parameters which is carried out in the state space using kronecker products

on estimating noncausal nonminimum phase arma models of non gaussian processes the authors address the problem of estimating the parameters of non gaussian arma autoregressive moving average processes using only the cumulants of the noisy observation the measurement noise is allowed to be colored gaussian or independent and identically non gaussian distributed the arma model is not restricted to be causal or minimum phase and may even contain all pass factors the unique parameter estimates of both the ma and ar parts are obtained by linear equations the structure of the proposed algorithm facilitates asymptotic performance evaluation of the parameter estimators and model order selection using cumulant statistics the method is computationally simple and can be viewed as the least squares solution to a quadratic model fitting of a sampled cumulant sequence identifiability issues are addressed simulations are presented to illustrate the proposed algorithm

noncausal nonminimum phase arma modeling of non gaussian processes a method is presented for the estimation of the parameters of a noncausal nonminimum phase arma model for non gaussian random processes using certain higher order cepstra slices the fourier phases of two intermediate sequences h sub min n and h sub max n can be computed where h sub min n is composed of the minimum phase parts of the ar and ma models and h sub max n of the corresponding maximum phase parts under the condition that there are no zero pole cancellations in the arma model these two sequences can be estimated from their phases only and lead to the reconstruction of the ar and ma parameters within a scalar and a time shift the ar and ma orders do not have to be estimated separately but they are by product of the parameter estimation procedure through simulations it is shown that unlike existing methods the estimation procedure is fairly robust if a small order mismatch occurs since the robustness of the method in the presence of additive noise depends on the accuracy of the estimated phases of h sub min n and h sub max n the phase errors due to finite length data are studied and their statistics are derived

automatic and robust computation of 3d medial models incorporating object variability this paper presents a novel processing scheme for the automatic and robust computation of a medial shape model which represents an object population with shape variability the sensitivity of medial descriptions to object variations and small boundary perturbations are fundamental problems of any skeletonization technique these problems are approached with the computation of a model with common medial branching topology and grid sampling this model is then used for a medial shape description of individual objects via a constrained model fit the process starts from parametric 3d boundary representations with existing point to point homology between objects the voronoi skeleton of each sampled object boundary is partitioned into non branching medial sheets and simplified by a novel pruning algorithm using a volumetric contribution criterion using the surface homology medial sheets are combined to form a common medial branching topology finally the medial sheets are sampled and represented as meshes of medial primitives results on populations of up to 184 biological objects clearly demonstrate that the common medial branching topology can be described by a small number of medial sheets and that even a coarse sampling leads to a close approximation of individual objects

image modeling using inverse filtering criteria with application to textures statistical approaches to image modeling have largely relied upon random models that characterize the 2 d process in terms of its first and second order statistics and therefore cannot completely capture phase properties of random fields that are non gaussian this constrains the parameters of noncausal image models to be symmetric and therefore the underlying random field to be spatially reversible research indicates that this assumption may not be always valid for texture images in this paper higher than second order statistics are used to derive and implement two classes of inverse filtering criteria for parameter estimation of asymmetric noncausal autoregressive moving average arma image models with known orders contrary to existing approaches fir inverse filters are employed and image models with zeros on the unit bicircle can be handled one of the criteria defines the smallest set of cumulant lags necessary for identifiability of these models to date consistency of these estimators is established and their performance is evaluated with monte carlo simulations as well as texture classification and synthesis experiments

exact results for the jammed state of binary mixtures of superdisks on the plane abstract by analytical and numerical methods we investigate the late stage deposition of binary mixtures of oriented superdisks on a plane superdisks are objects bounded by lame curves x 2 p y 2 p 1 where deformation parameter p controls their size and shape for deposition of single type superdisks the maximum packing and jamming densities are known to be nonanalytic at p 0 5 for binary mixtures of superdisks we discover that nonanalyticities form a locus of points separating phase diagram of shape combinations into regions with different excluded area constructions an analytical expression for this phase boundary and exact constructions of the excluded areas are presented the corresponding saturation coverages are obtained by extensive numerical monte carlo simulations

random sequential addition of hard spheres in high euclidean dimensions sphere packings in high dimensions have been the subject of recent theoretical interest employing numerical and theoretical methods we investigate the structural characteristics of random sequential addition rsa of congruent spheres in d dimensional euclidean space mathbb r d in the infinite time or saturation limit for the first six space dimensions 1 ensuremath le d ensuremath le 6 specifically we determine the saturation density pair correlation function cumulative coordination number and the structure factor in each of these dimensions we find that for 2 ensuremath le d ensuremath le 6 the saturation density ensuremath phi s scales with dimension as ensuremath phi s c 1 2 d c 2 d 2 d where c 1 0 202 phantom rule 0 2em 0ex 048 and c 2 0 973 phantom rule 0 2em 0ex 872 we also show analytically that the same density scaling is expected to persist in the high dimensional limit albeit with different coefficients a byproduct of this high dimensional analysis is a relatively sharp lower bound on the saturation density for any d given by ensuremath phi s ensuremath ge d 2 1 ensuremath s 0 2 d 1 where s 0 0 1 is the structure factor at k 0 i e infinite wavelength number variance in the high dimensional limit we demonstrate that a pal asti type conjecture the saturation density in mathbb r d is equal to that of the one dimensional problem raised to the d th power cannot be true for rsa hyperspheres we show that the structure factor s k must be analytic at k 0 and that rsa packings for 1 ensuremath le d ensuremath le 6 are nearly hyperuniform consistent with the recent decorrelation principle we find that pair correlations markedly diminish as the space dimension increases up to six we also obtain kissing contact number statistics for saturated rsa configurations on the surface of a d dimensional sphere for dimensions 2 ensuremath le d ensuremath le 5 and compare to the maximal kissing numbers in these dimensions we determine the structure factor exactly for the related ghost rsa packing in mathbb r d and demonstrate that its distance from hyperuniformity increases as the space dimension increases approaching a constant asymptotic value of 1 2 our work has implications for the possible existence of disordered classical ground states for some continuous potentials in sufficiently high dimensions