Showing papers on "Gaussian published in 1990"

Layered neural networks with Gaussian hidden units as universal approximations

Abstract: A neural network with a single layer of hidden units of gaussian type is proved to be a universal approximator for real-valued maps defined on convex, compact sets of Rn.

Gaussian beam migration

Abstract: Just as synthetic seismic data can be created by expressing the wave field radiating from a seismic source as a set of Gaussian beams, recorded data can be downward continued by expressing the recorded wave field as a set of Gaussian beams emerging at the earth’s surface. In both cases, the Gaussian beam description of the seismic‐wave propagation can be advantageous when there are lateral variations in the seismic velocities. Gaussian‐beam downward continuation enables wave‐equation calculation of seismic propagation, while it retains the interpretive raypath description of this propagation. This paper describes a zero‐offset depth migration method that employs Gaussian beam downward continuation of the recorded wave field. The Gaussian‐beam migration method has advantages for imaging complex structures. Like finite‐difference migration, it is especially compatible with lateral variations in velocity, but Gaussian beam migration can image steeply dipping reflectors and will not produce unwanted reflectio...

Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers

Abstract: A description is given of a relatively simple derivation of the bit-error probability for a lightwave communications system using an amplitude-shift-keying (ASK) pulse modulation format and employing optical amplifiers such that amplified spontaneous emission noise dominates all other noise sources Mathematically, this noise is represented as a Fourier series expansion with Fourier coefficients that are assumed to be independent Gaussian random variables The bit-error probability is given in a closed analytical form that is derived by the approximate evaluation of several integrals appearing in the analysis The author uses the theory to derive the Gaussian approximation and finds that it overestimates the bit-error rate by one to two orders of magnitude >

Gaussian kernels have only Gaussian maximizers

Abstract: A Gaussian integral kernel G(x, y) on Rn x Rn is the exponential of a quadratic form in x and y; the Fourier transform kernel is an example. The problem addressed here is to find the sharp bound of G as an operator from L p(Rp) to L q(Rn) and to prove that the L P(Rn) functions that saturate the bound are necessarily Gaussians. This is accomplished generally for 1 q in some special cases. Besides greatly extending previous results in this area, the proof technique is also essentially different from earlier ones. A corollary of these results is a fully multidimensional, multilinear generalization of Young’s inequality.

The Gaussian-Type Orbitals Density-Functional Approach to Finite Systems

Abstract: The linear combination of Gaussian-type orbitals (LCGTO) approach to Xa and density functional theory is reviewed, with particular emphasis on applications to large molecules and clusters. Fitting the potential is central to the LCGTO approach, and efficient and accurate ways to do so are described. Model cluster calculations apply these methods to the adsorption of alkali atoms and carbon monoxide on transition metal surfaces as well as the problem of CO vibrational shifts upon alkali coadsorption.

On large deviations theory and asymptotically efficient Monte Carlo estimation

Abstract: It is shown how large-deviations theory can be applied to construct an asymptotically efficient simulation distribution for Monte Carlo simulation using the importance sampling technique. A sufficient and necessary condition is given for the asymptotic efficiency of the candidate simulation distributions. This is done in the multidimensional setting that is required by many practical simulation problems. The result obtained is applied primarily in two areas. First, the generalization of previous work dealing with functionals of Markov chains is discussed. A second area of application is the simulation of nonlinear systems with Gaussian inputs. As an example of a system with Gaussian inputs, the simulation of a digital communication channel with nonlinear ISI (intersymbol interference) characteristic of satellite data links is considered. In the case of linear ISI, the asymptotically efficient exponentially twisted distribution turns out to agree with a method previously proposed by D. Lu and K. Yao (1988). The large-deviations point of view provides some useful insight on how to extent the Lu and Yao method to nonlinear channels. >

Fourier description of digital phase-measuring interferometry

Abstract: A general description of phase measurement by digital heterodyne techniques is presented in which the heterodyning is explained as a filtering process in the frequency domain Examples of commonly used algorithms are given Special emphasis is given to the analysis of systematic errors Gaussian error propagation is used to derive equations for the random phase errors of common algorithms

Matching range images of human faces

Abstract: The problem of matching range images of human faces for the purpose of establishing a correspondence between similar features of two faces is addressed. Distinct facial features correspond to convex regions of the range image of the face, which is obtained by a segmentation of the range image based on the sign of the mean and Gaussian curvature at each point. Each convex region is represented by its extended Gaussian image, a 1-1 mapping between points of the region and points on the unit sphere that have the same normal. Several issues are examined that are associated with the difficult problem of interpolation of the values of the extended Gaussian image and its representation. A similarity measure between two regions is obtained by correlating their extended Gaussian images. To establish the optimal correspondence, a graph matching algorithm is applied. It uses the correlation matrix between convex regions of the two faces and incorporates additional relational constraints that account for the relative spatial locations of the convex regions in the domain of the range image. >

Mixture reduction algorithms for target tracking in clutter

Abstract: The Bayesian solution of the problem of tracking a target in random clutter gives rise to Gaussian mixture distributions, which are composed of an ever increasing number of components. To implement such a tracking filter, the growth of components must be controlled by approximating the mixture distribution. A popular and economical scheme is the Probabilistic Data Association Filter (PDAF), which reduces the mixture to a single Gaussian component at each time step. However this approximation may destroy valuable information, especially if several significant, well spaced components are present. In this paper, two new algorithms for reducing Gaussian mixture distributions are presented. These techniques preserve the mean and covariance of the mixture, and the fmal approximation is itself a Gaussian mixture. The reduction is achieved by successively merging pairs of components or groups of components until their number is reduced to some specified limit. Further reduction will then proceed while the approximation to the main features of the original distribution is still good. The performance of the most economical of these algorithms has been compared with that of the PDAF for the problem of tracking a single target which moves in a plane according to a second order model. A linear sensor which measures target position is corrupted by uniformly distributed clutter. Given a detection probability of unity and perfect knowledge of initial target position and velocity, this problem depends on only tw‡ non-dimensional parameters. Monte Carlo simulation has been employed to identify the region of this parameter space where significant performance improvement is obtained over the PDAF.© (1990) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Topology of microwave background fluctuations - Theory

Abstract: Topological measures are used to characterize the microwave background temperature fluctuations produced by 'standard' scenarios (Gaussian) and by cosmic strings (non-Gaussian). Three topological quantities: total area of the excursion regions, total length, and total curvature (genus) of the isotemperature contours, are studied for simulated Gaussian microwave background anisotropy maps and then compared with those of the non-Gaussian anisotropy pattern produced by cosmic strings. In general, the temperature gradient field shows the non-Gaussian behavior of the string map more distinctively than the temperature field for all topology measures. The total contour length and the genus are found to be more sensitive to the existence of a stringy pattern than the usual temperature histogram. Situations when instrumental noise is superposed on the map, are considered to find the critical signal-to-noise ratio for which strings can be detected.

Modeling and estimation of discrete-time Gaussian reciprocal processes

Abstract: Discrete-time Gaussian reciprocal processes are characterized in terms of a second-order two-point boundary-value nearest-neighbor model driven by a locally correlated noise whose correlation is specified by the model dynamics. This second-order model is the analog for reciprocal processes of the standard first-order state-space models for Markov processes. The model is used to obtain a solution to the smoothing problem for reciprocal processes. The resulting smoother obeys second-order equations whose structure is similar to that of the Kalman filter for Gauss-Markov processes. It is shown that the smoothing error is itself a reciprocal process. >

Training module for estimating mixture Gaussian densities for speech unit models in speech recognition systems

Abstract: A model-training module generates mixture Gaussian density models from speech training data for continuous, or isolated word speech recognition systems. Speech feature sequences are labeled into segments of states of speech units using Viterbi-decoding based optimized segmentation algorithm. Each segment is modeled by a Gaussian density, and the parameters are estimated by sample mean and sample covariance. A mixture Gaussian density is generated for each state of each speech unit by merging the Gaussian densities of all the segments with the same corresponding label. The resulting number of mixture components is proportional to the dispersion and sample size of the training data. A single, fully merged, Gaussian density is also generated for each state of each speech unit. The covariance matrices of the mixture components are selectively smoothed by a measure of relative sharpness of the Gaussian density and the smoothing can also be done blockwise. The weights of the mixture components are set uniformly initially, and are reestimated using a segmental-average procedure. The weighting coefficients, together with the Gaussian densities, then become the models of speech units for use in speech recognition.

Wave chaos in singular quantum billiard.

Abstract: We present a solvable singular quantum billiard which displays fully developed wave chaos. Its level statistics is investigated and proved to coincide with predictions of the Gaussian orthogonal ensemble of random matrices. The corresponding wave functions are shown to be well approximated by a Gaussian ransom variable.

On Series Representations of Infinitely Divisible Random Vectors

Abstract: General results on series representations, involving arrival times in a Poisson process, are established for infinitely divisible Banach space valued random vectors without Gaussian components. Applying these results, various generalizations of LePage's representation are obtained in a unified way. Certain conditionally Gaussian infinitely divisible random vectors are characterized and some problems related to a Gaussian randomization method are investigated.

Self‐avoiding walk between two fixed points as a tool to calculate reaction paths in large molecular systems

Abstract: A new computational technique is presented to calculate approximate reaction paths in complex molecules. The method is based on the Gaussian chain approach proposed by Elber and Karplus [1] but avoids some computational difficulties of this technique. It is also more than 10 times faster. The new formulation is quite general and enables empirical interpolation between two types of motions which differ considerably: trapped and ballistic (see also “Note Added in Proof”). We present test results for two model molecules: alanine dipeptide (AD) and isobutyryl-(ala)3-NH-methyl (IAN). The optimization of the chain is very stable and provides an approximate continuous path even if the initial guess is poor.

SPACES: A PC implementation of the stochastic theory of energy loss for narrow-resonance depth profiling☆

Abstract: The stochastic theory of charged-particle energy loss in matter has provided an accurate computational method for straggling calculations and for the simulation of excitation curves obtained in narrow-resonance depth profiling. We have developed Fortran programs that perform the autoconvolutions of the primary energy loss function, and the weighted summing of these autoconvolutions needed by the theory for both straggling and excitation curve calculations. In addition we have implemented Edgeworth's expansion to bridge the gap between highly asymmetrical straggling and the Gaussian limit. The relationship between the present algorithm and those based on the Vavilov limit are discussed.

A second‐order algorithm for the simulation of the Brownian dynamics of macromolecular models

Abstract: Most recent works on Brownian dynamics simulation employ a first‐order algorithm developed by Ermak and McCammon [J. Chem. Phys. 69, 1352 (1978)]. In this work we propose the use of a second‐order algorithm in which the step is a combination of two first‐order steps, like in the second‐order Runge–Kutta method for differential equations. Although the computer time per step is roughly doubled, the second‐order algorithm is more efficient than the previous one because a given accuracy in the results can be achieved with less than half the number of steps. The new algorithm also allows for longer time steps without divergence. The advantage of the new procedure is illustrated in the simulation of four macromolecular systems: A quasirigid dumbbell, a semiflexible trumbbell, a semiflexible hinged rod, and a Gaussian polymer chain.

Grad ø perturbations of massless Gaussian fields

Abstract: We investigate weak perturbations of the continuum massless Gaussian measure by a class of approximately local analytic functionals and use our general results to give a new proof that the pressure of the dilute dipole gas is analytic in the activity.

Nonparaxial Gaussian beams

Abstract: When the waist size of a Gaussian beam becomes of the order of the wavelength of light, the beam does not satisfy the paraxial condition in which it is derived. In this paper, we define the lower bound to the waist size by showing that a Gaussian beam whose waist size is larger than this bound safely satisfies the paraxial condition. A beam which is Gaussian in form but violates the paraxial condition is called a nonparaxial Gaussian beam. We clarify the range of the waist size for which the first-order correction to this beam is effective. It is shown that a distinct value of the waist size exists for which the paraxial approximation completely fails and the first-order correction never works.

Analysis and design of a signed regressor LMS algorithm for stationary and nonstationary adaptive filtering with correlated Gaussian data

Abstract: A least mean square (LMS) algorithm with clipped data is studied for use when updating the weights of an adaptive filter with correlated Gaussian input. Both stationary and nonstationary environments are considered. Three main contributions are presented. The first, corresponding to the stationary case, is a proof of the convergence of the algorithm in the case of a M-dependent sequence of correlated observation vectors. It is proven that the steady state mean square misalignment of the adaptive filter weights has an upper bound proportional to the algorithm step size mu . The second contribution, also belonging to the stationary case, is the derivation of the expressions of convergence time N/sub c/ and steady state mean square excess estimation error epsilon . It is shown that N/sub c/ is proportional to 1/( mu lambda ), with lambda being the minimum eigenvalue of the input covariance matrix. It is also shown that the product N/sub c/ epsilon is independent of mu . For a given epsilon , the convergence time increases with the eigenvalue spread of the input covariance matrix and the filter length, as well as its input noise power. The range of mu that achieves tolerable values of N/sub c/ and epsilon is determined. The third contribution is concerned with the nonstationary case. It is shown that the mean square excess estimation error is the sum of the two terms with opposite dependencies on mu . An optimum value of mu is derived. >

Biases of estimators in multivariate non‐gaussian autoregressions

Abstract: . Expressions for the bias of the least-squares and modified Yule-Walker estimators in a correctly specified multivariate autoregression of arbitrary order are obtained without assuming that the innovations are Gaussian. Instead, the innovations are assumed to form a martingale difference sequence which is stationary up to sixth order and which has finite sixth moments. The errors in the expressions are shown to be O(n-3/2), as the sample size n under some moment conditions. The expressions obtained are the same in the Gaussian and non-Gaussian cases.

On estimating noncausal nonminimum phase ARMA models of non-Gaussian processes

Abstract: 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. >

Gaussian‐based kernels

Abstract: We derive a class of higher-order kernels for estimation of densities and their derivatives, which can be viewed as an extension of the second-order Gaussian kernel. These kernels have some attractive properties such as smoothness, manageable convolution formulae, and Fourier transforms. One important application is the higher-order extension of exact calculations of the mean integrated squared error. The proposed kernels also have the advantage of simplifying computations of common window-width selection algorithms such as least-squares cross-validation. Efficiency calculations indicate that the Gaussian-based kernels perform almost as well as the optimal polynomial kernels when die order of the derivative being estimated is low.

Capacity of the Gaussian arbitrarily varying channel

Abstract: The Gaussian arbitrarily varying channel with input constraint Gamma and state constraint Lambda admits input sequences x=(x/sub 1/,---,X/sub n/) of real numbers with Sigma x/sub i//sup 2/ >

Applications of the Schwinger multichannel method to electron-molecule collisions

Abstract: We discuss some recent developments in the implementation of the Schwinger multichannel method for electron-molecule collision calculations. The evaluation of matrix elements involving the operator VG^(+)_PV, previously accomplished by insertion of a Gaussian basis on either side of G^(+)_P, is now done by direct numerical quadrature. This approach avoids the necessity of very large Gaussian basis sets, allowing the size of the basis to reflect only the dynamical requirements of the scattering wave function. We find that the reduction in the required basis size results in improved efficiency, in spite of the additional numerical effort of performing the quadrature. Trial applications to electron-CH4 scattering in the static-exchange approximation and to electronic excitation of H_2 illustrate the excellent convergence characteristics of the procedure.