chow groups of projective varieties of very small degree see 12 5 and the references given there these facts together with various conjectures on the cohomology and chow groups of algebraic varieties suggest that the chow groups of x might satisfy chl x q chl pk q q for l 1 compare with remark 5 6 and corollary 5 7 this is explicitly formulated by v srinivas and k paranjape in 16 conjecture 1 8 the chain of reasoning goes roughly as follows suppose x is smooth one expects a good filtration 0 f j 1 f j f 0 ch x x q whose graded pieces f f l 1 are controlled by h2j l x x see 10 according to grothendieck s generalized conjecture 8 the groups h x should be generated by the image under the gysin morphism of the homology of a codimension subset together with the classes coming from p applying this to the diagonal in x x should then force the triviality of the chow groups in the desired range for zero cycles the conjecture follows from roitman s theorem see 17 and 18

on the energy spectrum and parameter spaces of classicalcp n models it is known that a large class of smooth solutions ofcpn models can be constructed starting from holomorphic maps of an algebraic curve into complex projective spaces here we apply results from algebraic geometry to describe the energy spectrum and the parameter spaces for such models

parabolic manifolds in the scattering map and direct quantum processes we analyse the quantum effects of parabolic manifolds in jung s iterated scattering map for this purpose we consider the classical map proposed previously to be the exact classical analogue of rydberg molecules calculated with the approximations relevant to the multichannel quantum defect theory for energies above the ionization threshold the part corresponding to positive electron energies can be viewed as a jung scattering map without the trivial direct processes this map contains a parabolic manifold of fixed points which gives rise to a regular series of quantum states which behave very much like eigenchannels that miss the target

autoregressive spectral analysis when observations are missing a new missing data algorithm arfil gives good results in spectral estimation the log likelihood of a multivariate gaussian random variable can always be written as a sum of conditional log likelihoods for a complete set of autoregressive ar p data the best predictor in the likelihood requires only p previous observations if observations are missing the best ar predictor in the likelihood will in general include all previous observations using only those observations that fall within a finite time interval will approximate this likelihood the resulting non linear estimation algorithm requires no user provided starting values in various simulations the spectral accuracy of robust maximum likelihood methods was much better than the accuracy of other spectral estimates for randomly missing data

lms like ar modeling in the case of missing observations this paper presents a new recursive algorithm for the time domain reconstruction and spectral estimation of uniformly sampled signals with missing observations an autoregressive ar modeling approach is adopted the ar parameters are estimated by optimizing a mean square error criterion the optimum is reached by means of a gradient method adapted to the nonperiodic sampling the time domain reconstruction is based on the signal prediction using the estimated model the power spectral density is obtained using the estimated ar parameters the development of the different steps of the algorithm is discussed in detail and several examples are presented to demonstrate the practical results that can be obtained the spectral estimates are compared with those obtained by known ar estimators applied to the same signals sampled periodically we note that this algorithm can also be used in the case of nonstationary signals

on periodic pulse interval analysis with outliers and missing observations analysis of periodic pulse trains based on time of arrival is considered with perhaps very many missing observations and contaminated data a period estimator is developed based on a modified euclidean algorithm this algorithm is a computationally simple robust method for estimating the greatest common divisor of a noisy contaminated data set the resulting estimate although it is not maximum likelihood is used as initialization in a three step algorithm that achieves the cramer rao bound crb for moderate noise levels as shown by comparing monte carlo results with the crbs this approach solves linear regression problems with missing observations and outliers comparisons with a periodogram approach based on a point process model are shown an extension using multiple independent data records is also developed that overcomes high levels of contamination

impact of localization on dyson s circular ensemble a wide variety of complex physical systems described by unitary matrices have been shown numerically to satisfy level statistics predicted by dyson s circular ensemble we argue that the impact of localization in such systems is to impose certain restrictions on the eigenvalues we consider a solvable model which takes into account such restrictions qualitatively and find that within the model a gap is created in the spectrum and there is a transition from the universal wigner distribution towards a poisson distribution with increasing localization

generalized method of moments estimation of location parameters application to blind phase acquisition in this paper we address the problem of location parameter estimation via a generalized method of moments gmm approach the general framework for the gmm estimation requires the minimization of a suitable generally nonconvex elliptic norm here we show that if the estimandum is a shift parameter for a suitable statistic of the observations a fast dft based computationally efficient procedure can be employed to perform the estimation besides we discuss the relation between the gmm estimation and the maximum likelihood ml estimation showing that the gmm estimation rule provides a closed form ml estimator for shift parameters when the observations are multinomially distributed as a case study we analyze a gmm blind phase offset estimator for general quadrature amplitude modulation constellations simulation results and theoretical performance analysis show that the gmm estimator outperforms selected state of the art estimators approaching the cramer rao lower bound for a wide range of signal to noise ratio values

poincare map for scattering states for scattering states in classical mechanics a map is constructed which is an analogue to the poincare map for bound state trajectories iteration of this map indicates which parts of the phase space are filled by unstable trajectories that are sensitive to small changes in the initial conditions and which regions are filled by stable trajectories examples for this map are given by numerical calculations for scattering off a simple two dimensional model potential

quantum signatures of an integrable system with a chaotic scattering map a rather simple completely integrable hamiltonian with a chaotic classical scattering map is analysed in quantum mechanics after the analytical computation of the s matrix we investigate numerically the distribution of scattering phases giving the nearest neighbour distribution the number variance and the fourier transform of the spectrum we find fair agreement with the random matrix prediction for the circular orthogonal ensemble coe as appropriate for the time reversal invariant system with a chaotic scattering map this example confirms that coe properties of the s matrix do not necessarily indicate topological chaos in the flow generated by the classical hamiltonian

reduced dimension blind space time 2 d rake receivers for ds cdma communication systems blind space time rake receivers for classical ds cdma that cancel strong multiuser access interference while optimally combining the desired user s multipath are presented the delay spread is assumed to be fraction of a symbol interval as in the is 95 cdma standard the post correlation symbol interval is segmented into that which encompasses the rake fingers and that away from the rake fingers the signal plus interference and interference alone space time correlation matrices are estimated during the former and latter respectively reduced dimension space time rake receivers are investigated for alleviation of the computational burden of computing the largest generalized eigenvector of the resulting matrix pencil theoretical analysis and supporting simulations reveal that if the space and time compressing transformations are designed judiciously reduced dimension two dimensional 2 d rake receivers offer faster convergence at the expense of only a slight loss in asymptotic signal to interference plus noise ratio sinr relative to the full dimension space time rake receiver applications to the is 95 uplink are also presented along with supporting simulations

nonemptiness of symmetric degeneracy loci let v be a rank n vector bundle on a d dimensional complex projective scheme x assume that v is equipped with a quadratic form with values in a line bundle l and that s 2 v l is ample suppose that the maximum rank of the quadratic form at any point of x is r 0 the main result of this paper is that if d n r the locus of points where the rank of the quadratic form is at most r 1 is nonempty we give some applications to subschemes of matrices and to degeneracy loci associated to embeddings in projective space the paper concludes with an appendix on gysin maps the main result of the appendix which may be of independent interest identifies a gysin map with the natural map from ordinary to relative cohomology

modifications of the euclidean algorithm for isolating periodicities from a sparse set of noisy measurements modifications of the euclidean algorithm are presented for determining the period from a sparse set of noisy measurements the elements of the set are the noisy occurrence times of a periodic event with perhaps very many missing measurements this problem arises in radar pulse repetition interval pri analysis in bit synchronization in communications and in other scenarios the proposed algorithms are computationally straightforward and converge quickly a robust version is developed that is stable despite the presence of arbitrary outliers the euclidean algorithm approach is justified by a theorem that shows that for a set of randomly chosen positive integers the probability that they do not all share a common prime factor approaches one quickly as the cardinality of the set increases in the noise free case this implies that the algorithm produces the correct answer with only 10 data samples independent of the percentage of missing measurements in the case of noisy data simulation results show for example good estimation of the period from 100 data samples with 50 of the measurements missing and 25 of the data samples being arbitrary outliers

limit linear series basic theory in this paper we introduce techniques for handling the degeneration of linear series on smooth curves as the curves degenerate to a certain type of reducible curves curves of compact type the technically much simpler special case of 1 dimensional series was developed by beauville 2 knudsen 21 23 harris and mumford 17 in the guise of admissible covers it has proved very useful for studying the moduli space of curves the above papers and harris 16 and the simplest sorts of weierstrass points diaz 4 with our extended tools we are able to prove for example that in this paper we present the basic theory of limit linear series necessary for proving these results the results themselves will be taken up in our forthcoming papers 8 12 simpler applications not requiring the tools developed in this paper but perhaps clarified by them have already been given in our papers 5 7

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

iterated scattering map for rearrangement scattering an iterated scattering map for three particle rearrangement scattering is constructed by forming sequences of scattering trajectories this map works in a similar way to the well known poincare map for bound trajectories it provides useful information for investigating the integrability properties of the system a numerical example is shown for the calogero moser system with hyperbolic potential functions

connection between conserved quantities of the hamiltonian and of the s matrix a conserved quantity k of a hamiltonian h implies a conserved quantity j of the s matrix only if the forward and the backward asymptotic limits of k are equal a conserved quantity j of s implies a conserved quantity of h only if j is also a conserved quantity of the free hamiltonian h0 therefore the integrability or chaoticity of s does not necessarily decide the integrability of h

arma spectral estimation of time series with missing observations the problem of estimating the power spectral density of stationary time series when the measurements are not contiguous is considered a new autoregressive moving average arma method is proposed for this problem based on nonlinear optimization of a weighted squared error criterion the method can handle either regularly or randomly missing observations as a special case the method can handle the problem of missing sample covariances the computational complexity is modest compared to exact maximum likelihood estimation of the same parameters the performance of the algorithm is illustrated by some numerical examples and is shown to be statistically efficient in these cases

spectral fluctuation properties of hamiltonian systems the transition region between order and chaos the authors study numerically the classical dynamical behaviour and the spectral fluctuation properties of a class of hamiltonian systems with two degrees of freedom the quantum mechanical properties of these systems are monotonic but non universal functions of the fraction of classical phase space filled by chaotic trajectories it is found that the observed spectral fluctuation measures can be reproduced by a random matrix model which depends on one parameter only

system parameter estimation with input output noisy data and missing measurements an investigation is undertaken to examine the parameter estimation problem of linear systems when some of the measurements are unavailable i e missing data and the probability of occurrence of missing data is unknown a priori the system input and output data are also assumed to be corrupted by measurement noise and the knowledge of the noise distribution is unknown under the unknown noise distribution and missing measurements a consistent parameter estimation algorithm which is based on an l sub p norm iterative estimation algorithm iteratively reweighted least squares irls is proposed to estimate the system parameters we show that if the probability of missing measurement is less than one half the parameter estimates via the proposed estimation algorithm will converge to the true parameters as the number of data tends to infinity finally several simulation results are presented to illustrate the performance of the proposed l sub p norm iterative estimation algorithm simulation results indicate that under input output missing data and noise environment the proposed parameter estimation algorithm is an efficient approach toward the system parameter estimation problem

the second order moments of the sample covariances for time series with missing observations the estimation of the covariances of a stationary time series with missing observations is considered general formulas for the asymptotic second order moments of the sample covariances of such a time series are given for either random or deterministic patterns of misses closed form expressions are derived for the random bernoulli pattern and for the deterministic periodic pattern of missing observations and are explicitly evaluated for autoregressive moving average time series these results are useful for constructing and analyzing parameter or spectrum estimation algorithms based on the sample covariances for a stationary time series with missing observations

vanishing theorems for ample vector bundles the main result of this article is a general vanishing theorem for the cohomology of tensorial representations of an ample vector bundle on a smooth complex projective variety in particular we extend classical theorems of griffiths and le potier to the whole dolbeault cohomology prove a variant of an uncorrect conjecture of sommese and answer a question of demailly as an application we prove conjectures of debarre and kim for branched coverings of grassmannians and extend a well known barth lefschetz type theorem for branched covers of projective spaces due to lazarsfeld we also obtain new restriction theorems for certain degeneracy loci

optimal arma parameter estimation based on the sample covariances for data with missing observations the problem of spectral estimation through the autoregressive moving average arma modeling of stationary processes with missing observations is considered a class of estimators based on the sample covariances is presented and an asymptotically optimal estimator in this class is proposed the proposed algorithm is based on a nonlinear least squares fit of the sample covariances computed from the data to the true covariances of the assumed arma model the statistical properties of the algorithm are explored and used to show that it is asymptotically optimal in the sense of achieving the smallest possible asymptotic variance the performance of the algorithm is illustrated by some numerical examples

the surface c c on jacobi varieties and 2nd order theta functions preprint enviat per a la seva publicacio en una revista cientifica acta mathematica volume 157 1986 1 22 https projecteuclid org euclid acta 1485890436

semiclassical theory of spectral rigidity the spectral rigidity l of a set of quantal energy levels is the mean square deviation of the spectral staircase from the straight line that best fits it over a range of l mean level spacings in the semiclassical limit 0 formulae are obtained giving l as a sum over classical periodic orbits when l l max where l max n 1 for a system of n freedoms l is shown to display the following universal behaviour as a result of properties of very long classical orbits if the system is classically integrable all periodic orbits filling tori l 1 5 l as in an uncorrelated poisson eigenvalue sequence if the system is classically chaotic all periodic orbits isolated and unstable and has no symmetry l in l 2 2 d if 1 l l max as in the gaussian unitary ensemble of random matrix theory if the system is chaotic and has time reversal symmetry l in l 2 e if 1 l l max as in the gaussian orthogonal ensemble when l l max l saturates non universally at a value determined by short classical orbits of order n 1 for integrable systems and in 1 for chaotic systems these results are obtained by using the periodic orbit expansion for the spectral density together with classical sum rules for the intensities of long orbits and a semiclassical sum rule restricting the manner in which their contributions interfere for two examples l is studied in detail the rectangular billiard integrable and the riemann zeta function assuming its zeros to be the eigenvalues of an unknown quantum system whose unknown classical limit is chaotic

bounds on the accuracy of gaussian arma parameter estimation methods based on sample covariances the asymptotic accuracy of gaussian arma parameter estimation methods based on a fixed number of sample covariances is considered several key results are briefly reviewed including i a general asymptotic expression for the error covariance of the arma parameter estimates ii the fact that this error covariance is always greater than a certain lower bound iii the fact that this lower bound is strictly greater than the cramer rao bound iv an explicit arma estimation technique that asymptotically achieves the bound the key result of this note is a proof that this lower bound approaches the cramer rao bound as the number of sample covariances tends to infinity

algebraic cycles on prym varieties this article proposes a generalization of tautological rings introduced by beauville and moonen for jacobians the main result is that under certain hypotheses the special subvarieties of prym varieties are algebraically equivalent and their classes belong to the tautological ring

on the transition to chaotic scattering a classical scattering system is chaotic if it possesses a fractal set of trapped unstable orbits resulting in singular deflection functions a scattering system is regular if it supports only a countable set of trapped unstable orbits its deflection functions are piecewise smooth with at most a countable number of scattering singularities caused by the trapped orbits despite the simple structure of the deflection functions the poincare scattering mapping psm may be regular hyperbolic or display mixed dynamics thus the degree of chaoticity of the psm serves as a finer scale for the discussion of the transition to chaotic scattering in the classical domain in the quantum domain the authors show that the properties of the psm determine the statistics of the eigenphases of the s matrix and that if the psm is hyperbolic the eigenphases follow the statistics predicted by random matrix theory

variance constrained filtering for uncertain stochastic systems with missing measurements in this note we consider a new filtering problem for linear uncertain discrete time stochastic systems with missing measurements the parameter uncertainties are allowed to be norm bounded and enter into the state matrix the system measurements may be unavailable i e missing data at any sample time and the probability of the occurrence of missing data is assumed to be known the purpose of this problem is to design a linear filter such that for all admissible parameter uncertainties and all possible incomplete observations the error state of the filtering process is mean square bounded and the steady state variance of the estimation error of each state is not more than the individual prescribed upper bound it is shown that the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic riccati like inequalities or linear matrix inequalities the explicit expression of the desired robust filters is parameterized and an illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach

limit linear series and ranks of multiplication maps we develop a new technique for studying ranks of multiplication maps for linear series via limit linear series and degenerations to chains of genus 1 curves we use this approach to prove a purely elementary criterion for proving cases of the maximal rank conjecture and then apply the criterion to several ranges of cases giving a new proof of the case of quadrics and also treating several families in the case of cubics our proofs do not require restrictions on direction of approach so we recover new information on the locus in the moduli space of curves on which the maximal rank condition fails

the connectedness of symmetric and skew symmetric degeneracy loci even ranks a degeneracy locus is the set of points where a vector bundle map has rank at most a given integer such a set is symmetric or skew symmetric according as whether the vector bundle map is symmetric or skew symmetric we prove a connectedness result first conjectured by fulton and lazarsfeld for skew symmetric degeneracy loci and for symmetric degeneracy loci of even ranks

the asymptotic cramer rao bound for gaussian arma processes with periodically missing data corresp an asymptotic formula is derived for the cramer rao lower bound on unbiased estimates of the parameters of gaussian autoregressive moving average arma processes in the case where the measurements are not contiguous but follow a periodic pattern of misses the formula is then used to illustrate the behavior of the bound for some specific examples