Showing papers on "Gaussian published in 1989"

Universal Gaussian basis sets for an optimum representation of Rydberg and continuum wavefunctions

Abstract: A universal Gaussian basis set concept for the calculation of Rydberg and continuum states by pure L2 methods is presented It is based on the generation of optimised sequences of Gaussian exponents by maximising the overlap with a series of Slater-type functions characterised by a constant exponent and a variable principal quantum number In this way linear combinations of Gaussian basis functions can be found which are ideally suited to imitate Laguerre-Slater functions It is thus possible to obtain optimum representations of Rydberg orbitals or of complete orthonormal systems of Laguerre functions playing an important role in the L2 expansion of continuum functions The basis sets are tested with the hydrogen atom The effectiveness of the basis is illustrated by the calculation of quantum defects associated with the s, p and d Rydberg series of the alkali metal atoms Li and Na The phaseshifts determined in the ionisation continuat of these systems nicely fit the series below the ionisation limit as is finally demonstrated by an Edlen plot

Parametric generalized Gaussian density estimation

Abstract: The primary objective of this paper is to compare the large‐sample as well as the small‐sample properties of different methods for estimating the parameters of a three‐parameter generalized Gaussian distribution. Three estimators, namely, the moment method (MM), the maximum‐likelihood (ML), and the moment/Newton‐step (MNS) estimators, are considered. The applicability of general asymptotic optimality results of the efficient ML and MNS estimation techniques is studied in the generalized Gaussian context. The asymptotic normal distributions of the estimators are obtained. The asymptotic relative superiority of the ML estimator or its variant, the MNS estimator, over the moment method is studied in terms of asymptotic relative efficiency. Based on this study, it is concluded that deviations from normality in the underlying distribution of the data necessitate the use of the efficient ML or MNS methods. In the small‐sample case, a detailed comparative study of the estimators is made possible by extensive Monte Carlo simulations. From this study, it is concluded that the maximum‐likelihood method is found to be significantly superior for heavy‐tailed distributions. In a region of the parameter space corresponding to the vicinity of the Gaussian distribution, the moment method compares well with the other methods. Further, the MNS estimator is shown to perform best for light‐tailed distributions. The simulation results are shown to lend support to analytically derived asymptotic results for each of the methods.

Gaussian influence diagrams

Abstract: An influence diagram is a network representation of probabilistic inference and decision analysis models. The nodes correspond to variables that can be either constants, uncertain quantities, decisions, or objectives. The arcs reveal probabilistic dependence of the uncertain quantities and information available at the time of the decisions. The influence diagram focuses attention on relationships among the variables. As a result, it is increasingly popular for eliciting and communicating the structure of a decision or probabilistic model. This paper develops the framework for assessment and analysis of linear-quadratic-Gaussian models within the influence diagram representation. The "Gaussian influence diagram" exploits conditional independence in a model to simplify elicitation of parameters for the multivariate normal distribution. It is straightforward to assess and maintain a positive semi-definite covariance matrix. Problems of inference and decision making can be analyzed using simple transformations to the assessed model, and these procedures have attractive numerical properties. Algorithms are also provided to translate between the Gaussian influence diagram and covariance matrix representations for the normal distribution.

Continuous hidden Markov modeling for speaker-independent word spotting

Abstract: A word-spotting system using Gaussian hidden Markov models is presented. Several aspects of this problem are investigated. Specifically, results are reported on the use of various signal processing and feature transformation techniques. The authors have observed that performance can be greatly affected by the choice of features used, the covariance structure of the Gaussian models, and transformations based on energy and feature distributions. Due to the open-set nature of the problem, the specific techniques for modeling out-of-vocabulary speech and the choice of scoring metric can have a significant effect on performance. >

Gaussian feedback capacity

Abstract: The capacity of time-varying additive Gaussian noise channels with feedback is characterized. Toward this end, an asymptotic equipartition theorem for nonstationary Gaussian processes is proved. Then, with the aid of certain matrix inequalities, it is proved that the feedback capacity C/sub FB/ in bits per transmission and the nonfeedback capacity C satisfy C >

The capacity region of the symbol-asynchronous Gaussian multiple-access channel

Abstract: An equivalent discrete-time Gaussian channel parametrized by the signal cross-correlations is derived to obtain an equivalent channel model with discrete-time outputs. The main feature introduced by the lack of symbol synchronism is that the channel has memory. This is due to the overlap of each symbol transmitted by a user with two consecutive symbols transmitted by the other user. It is shown that if the transmitters are assigned the same waveform, symbol asynchronism has no effect on the two-user capacity region of the white Gaussian channel which is equal to the Cover-Syner pentagon, whereas if the assigned waveforms are different (e.g., code division multiple access), the symbol-asynchronous capacity region is no longer a pentagon. An alternative representation of the capacity region which results in a particularly compact characterization of the fundamental limits of the multiple-access channel in the region of signal-to-noise ratios is also considered. >

A generalized Poincaré inequality for Gaussian measures

Abstract: New inequalities are obtained which interpolate in a sharp way between the Poincaré inequality and the logarithmic Sobolev inequality for both Gaussian measure and spherical surface measure. The classical Poincaré inequality provides an estimate for the first nontrivial eigenvalue of a positive self-adjoint operator that annihilates constants. For the Gaussian measure dp = T\k(2n)~{'2e~({l2)Xkdxk and the generator of the Ornstein-Uhlenbeck process N = -A + x • V, the Poincaré inequality is simply the estimate (1) ¡\f\2dp-[j fdp)

Extremal properties of orthogonal parallelepipeds and their applications to the geometry of banach spaces

Abstract: It is proved that the distribution function for the maximum of the modulus of a set of jointly Gaussian random variables with given variance and zero mean is minimal if these variables are independent. For let As a corollary of the result mentioned, the precise orders of the constants are computed (), and various improvements of these inequalities are obtained. The estimates are used in particular to construct lacunary analogues of the Rudin-Shapiro trigonometric polynomials.Bibliography: 24 titles.

Relative proper motions and the stellar velocity dispersion of the open cluster M67

Abstract: Relative proper motions for 663 stars in the field of the old open cluster M67 have been determined using 44 Yerkes 40-in refractor plates. The resulting proper-motion marginal distributions have been fit with a two-component model representing the sum of a cluster distribution and a much wider field distribution, both of which are assumed to be intrinsically Gaussian in form. The observed marginal distributions are actually quite non-Gaussian due to the effects of the proper-motion measurement errors, and thus a modeling procedure that realistically includes the measurement errors has been devised. The procedure yields excellent fits to the observed distributions, and thus allows reliable cluster-membership probabilities to be calculated. The cluster's intrinsic velocity dispersion is estimated from the proper motions of the about 80 brightest cluster stars to be 0.81 + or - 0.10 km/s. This is marginally higher than a dispersion estimate based on published radial-velocity measurements of a similar sample of cluster members. 16 refs.

Analytical gradient of the linear combination of Gaussian‐type orbitals—local spin density energy

Abstract: An expression has been derived for the analytical evaluation of the energy gradient within the linear combination of Gaussian‐type orbitals—local spin density method. This expression is valid for any exchange‐correlation energy functional which can be represented in a density gradient expansion. In practice, because the exchange‐correlation terms are fitted with auxiliary functions, one has to introduce an approximation. Results are reported of tests on diatomics that show that it is possible to attain a typical accuracy of ±0.01 a.u. on equilibrium distances, relative to the energy minimum. The formulas for molecular integral derivatives that we implemented are based on the highly efficient recurrence formulas of Obara and Saika. We report here an additional formula for angular momentum transfer which is very useful for efficient programming of the gradient. In all cases studied, the time required to compute the gradient is a fraction of the time spent to solve the self‐consistent‐field Kohn–Sham equations.

Rough surfaces: gaussian or exponential statistics?

Abstract: The authors make use of a numerical method for generating random rough surfaces to study the effects of sampling interval on measured surface correlation functions. This numerical investigation avoids some of the complications present in experimental studies of the effects of this parameter, such as instrument resolution and measurement reproducibility. The numerical technique is used to generate surfaces with exponential correlation functions and surfaces with gaussian correlations. The short-wavelength fluctuations on the exponential surfaces are clearly seen, these arising from the high-frequency tail in the surface power spectrum. The authors are able to quantify the sampling interval necessary to record this short-range surface behaviour. They conclude that the sampling interval must be at least as small as one tenth of the surface correlation length, for these high-frequency variations to be recorded and hence for the inherent exponential nature of the surface to be measured.

The Laplacian-of-Gaussian kernel: a formal analysis and design procedure for fast, accurate convolution and full-frame output

Abstract: An LoG of space constant σ can be decomposed into the product of a Gaussian and an LoG mask (Chen, Huertas, and Medioni, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 1987, 584–590). The resulting LoG has space constant σ1

Gaussian basis sets for calculation of spin densities in first-row atoms

Abstract: The suitability of Gaussian basis sets for ab initio calculation of Fermi contact spin densities is established by application to the prototype first-row atoms B-F having open shell p electrons. Small multiconfiguration self-consistent-field wave functions are used to describe relevant spin and orbital polarization effects. Basis sets are evaluated by comparing the results to highly precise numerical grid calculations previously carried out with the same wave function models. It is found that modest contracted Gaussian basis sets developed primarily for Hartree-Fock calculations can give semiquantitative results if augmented by diffuse functions and if further uncontracted in the outer core-inner valence region.

Mixture reduction algorithms for target tracking

Abstract: The paper is concerned with the development of practical filters for tracking a target when the origin of sensor measurements is uncertain. The full Bayesian solution to this problem gives rise to mixture distributions. From knowledge of the mixture distribution, in principle, an optimal estimate of the state vector for any criteria may be obtained. Also, if the problem is linear and Gaussian, the distribution becomes a Gaussian mixture in which each component probability density function is given by a Kalman filter. The author only considers this case. The methods presented are based on the premise that the number of mixture components should be minimized without modifying the 'structure' of the distribution beyond a specified limit. The techniques operate by merging similar components in such a way that the approximation preserves the mean and covariance of the original mixture. Also to allow the tracking filter to be implemented as a bank of Kalman filters, it is required that the approximated distribution is itself a Gaussian mixture.

Combinatorial optimization with Gaussian machines

Abstract: An artificial neuron model, called the Gaussian machine, is introduced. Gaussian machines have graded output responses, as well as stochastic behavior caused by random noise added to the input of each neuron. The Gaussian machine model includes the McCulloch-Pitts model, the Hopfield machine, and the Boltzmann machine as special cases. To demonstrate the efficiency of Gaussian machines, a solution of the traveling salesperson problem (TSP) is presented. Gaussian machines show an ability to solve combinatorial optimization problems better than either Hopfield or Boltzmann machines. The excellent performance of this model is also confirmed for the n-Queen's problem and the polyamino puzzle. >

Statistical evaluation of cell kinetic data from DNA flow cytometry (FCM) by the EM algorithm.

Abstract: Flow cytometric DNA measurements yield the amount of DNA for each of a large number of cells. A DNA histogram normally consists of a mixture of one or more constellations of G0/G1-, S-, G2/M-phase cells, together with internal standards, debris, background noise, and one or more populations of clumped cells. We have modelled typical DNA histograms as a mixed distribution with Gaussian densities for the G0/G1 and G2/M phases, an S-phase density, assumed to be uniform between the G0/G1 and G2/M peaks, observed with a Gaussian error, and with Gaussian densities for standards of chicken and trout red blood cells. The debris is modelled as a truncated exponential distribution, and we also have included a uniform background noise distribution over the whole observation interval. We have explored a new approach for maximum-likelihood analyses of complex DNA histograms by the application of the EM algorithm. This algorithm was used for four observed DNA histograms of varying complexity. Our results show that the algorithm works very well, and it converges to reasonable values for all parameters. In simulations from the estimated models, we have investigated bias, variance, and correlations of the estimates.

Nonparametric time series analysis for periodically correlated processes

Abstract: Correlation functions of continuous-time periodically correlated processes can be represented by a Fourier series with coefficient functions. It is shown that the usual estimator for stationary covariances, formed from a single sample path of the process, can be simply modified to provide a consistent (in quadratic mean) estimator for any of the coefficient functions resulting from the aforementioned representation. It is shown that, if the process is Gaussian and B/sub k/( tau ) is a Fourier integral with respect to a density function g/sub k/( lambda ), a two-dimensional periodogram, formed from a single sample function, can be smoothed along a line of constant difference frequency to provide a consistent estimator for g/sub k/( lambda ). This natural extension of the well-known procedure for stationary processes provides a method for nonparametric spectral analysis of periodically correlated processes. >

Comparison of adaptive and robust receivers for signal detection in ambient underwater noise

Abstract: Three receivers are compared for the detection of a known signal in additive ambient underwater noise of seagoing merchant vessels. These receivers are: the matched filter, which is the classical linear receiver based on a Gaussian assumption; the correlation-limiter, which is the Neyman-Pearson minimax robust receiver when the noise uncertainty is modeled as a mixture process with a Gaussian nominal; and the Gaussian-Gaussian mixture likelihood ratio receiver. This last receiver is adaptive in the sense that it is based on a parametric model whose parameters are computed from the actual data. The principal results of this study are that, in terms of the receiving operating curves, the adaptive receiver performs better than the linear one which, in turn, performs slightly better than the robust correlator-limiter. This study illustrates, for one particular noise sample, the merit of the simple mixture model in adaptive processing for signal detection purposes. >

Robust Principal Components

Abstract: This paper proposes a new algorithm to obtain an eigenvalue decomposition for the sample covariance matrix of a multivariate dataset. The algorithm is based on the rotation technique employed by Ammann and Van Ness (1988a,b) to obtain a robust solution to an errors-in-variables problem. When this rotation technique is combined with an iterative reweighting of the data, a robust eigenvalue decomposition is obtained. This robust eigenvalue decomposition has important applications to principal component analysis. Monte Carlo simulations are performed to compare ordinary principal component analysis using the standard eigenvalue decomposition with this algorithm, referred to as ROPRC. It is seen that ROPRC is reasonably efficient compared to an eigenvalue decomposition when Gaussian data is available, and that ROPRC is much better than the eigenvalue decomposition if outliers are present or if the data has a heavy-tailed distribution. The algorithm returns useful numerical diagnostic information in the form o...

Systematic study of fields due to extended apertures by Gaussian beam discretization

Abstract: Gaussian beams are used as basis elements in field representations. To gain insight into how the choice of beam parameters affects the final representation, a systematic study for the simple test case of a one-dimensional linearly phased cosine-aperture distribution has been undertaken. By successively adding individual displaced and/or tilted beams with large, narrow, or matched waists, one can assess how the elements in various portions of the lattice contribute to the build-up of the actual field in the aperture, near zone, and far zone. Adding enough beams always guarantees homing in on the exact solution, as is verified here by independent comparison. Different beam choices imply different modeling of the radiation process. The understanding gained thereby is helpful for selecting beam parameters in subsequent applications where it is necessary to balance requirements of good convergence, ease of computation, and ability to track the beams through perturbing environments like a radome. Indications are that the narrow beams provide the most robust and versatile formulation to deal with these generalized conditions. >

Universal shape ratios for open and closed random walks: exact results for all d

Abstract: The mean asphericities (Ad) of open and closed Gaussian polymer chains are computed exactly and analytically (up to simple quadratures) for arbitrary space dimensions d. Excellent agreement is found with existing simulation data for d=2, 3, and 4. The authors' technique can also be used to compute other averages of ratios of fluctuating variables as well as extended to include the effects of self-avoiding walk interactions.

Efficient estimation of parameters for non-Gaussian autoregressive processes

Abstract: The problem of estimating the parameters of a non-Gaussian autoregressive process is addressed. Departure of the driving noise from Gaussianity is shown to have the potential for improving their accuracy of the estimation of the parameters. While the standard linear prediction techniques are computationally efficient, they show a substantial loss of efficiency when applied to non-Gaussian processes. A maximum-likelihood estimator is proposed for more precise estimation of the parameters of these processes coupled with a realistic non-Gaussian model for the driving noise. The performance is compared to that of the linear prediction estimator and, as expected, the maximum-likelihood estimator displays a marked improvement. >

Propagation of a Gaussian beam in a nonhomogeneous plasma

Abstract: The asymptotic theory of Choudhary and Felsen [IEEE Trans. Antennas Propag. AP‐21, 827 (1973)] on the propagation of scalar inhomogeneous waves in two‐dimensional isotropic media is extended to the case of three‐dimensional vector fields. The theory is applied to the propagation of Gaussian beams in nonhomogeneous media. The wave trajectory equations are then reformulated for anisotropic media and used for tracking a Gaussian beam in a tokamak plasma.