Showing papers on "Gaussian published in 1978"

The Gaussian wire-tap channel

Abstract: Wyner's results for discrete memoryless wire-tap channels are extended to the Gaussian wire-tap channel. It is shown that the secrecy capacity Cs is the difference between the capacities of the main and wire.tap channels. It is further shown that Rd= Cs is the upper boundary of the achievable rate-equivocation region.

Gaussian approximation of the fundamental modes of graded-index fibers

Abstract: Direct numerical integration of the wave equation is used to establish the validity of approximating the fundamental mode of graded-index fibers by a Gaussian function. We show that the fundamental modes of fibers, whose index profile can be expressed as a power law, are indeed very nearly Gaussian in shape (that is probably also true for graded-index fibers with convex profiles other than a power law). Graphs and empirical analytical expressions are presented for the optimum Gaussian beam width parameter and for the propagation constant of the fundamental mode.

Gaussian Random Processes

Abstract: I Preliminaries.- I.1 Gaussian Probability Distribution in a Euclidean Space.- I.2 Gaussian Random Functions with Prescribed Probability Measure.- I.3 Lemmas on the Convergence of Gaussian Variables.- I.4 Gaussian Variables in a Hilbert Space.- I.5 Conditional Probability Distributions and Conditional Expectations.- I.6 Gaussian Stationary Processes and the Spectral Representation.- II The Structures of the Spaces H(T) and LT(F).- II. 1 Preliminaries.- II.2 The Spaces L+(F) and L-(F).- II.3 The Construction of Spaces LT(F) When T Is a Finite Interval.- II.4 The Projection of L+(F) on L-(F).- II.5 The Structure of the ?-algebra of Events U(T).- III Equivalent Gaussian Distributions and their Densities.- III.1 Preliminaries.- III.2 Some Conditions for Gaussian Measures to be Equivalent.- III.3 General Conditions for Equivalence and Formulas for Density of Equivalent Distributions.- III.4 Further Investigation of Equivalence Conditions.- IV Conditions for Regularity of Stationary Random Processes.- IV.1 Preliminaries.- IV.2 Regularity Conditions and Operators Bt.- IV.3 Conditions for Information Regularity.- IV.4 Conditions for Absolute Regularity and Processes with Discrete Time.- IV.5 Conditions for Absolute Regularity and Processes with Continuous Time.- V Complete Regularity and Processes with Discrete Time.- V.l Definitions and Preliminary Constructions with Examples.- V.2 The First Method of Study: Helson-Sarason's Theorem.- V.3 The Second Method of Study: Local Conditions.- V.4 Local Conditions (continued).- V.5 Corollaries to the Basic Theorems with Examples.- V.6 Intensive Mixing.- VI Complete Regularity and Processes with Continuous Time.- VI.1 Introduction.- VI.2 The Investigation of a Particular Function ?(T ).- VI.3 The Proof of the Basic Theorem on Necessity.- VI.4 The Behavior of the Spectral Density on the Entire Line.- VI.5 Sufficiency.- VI.6 A Special Class of Stationary Processes.- VII Filtering and Estimation of the Mean.- VII.1 Unbiased Estimates.- VII.2 Estimation of the Mean Value and the Method of Least Squares.- VII.3 Consistent Pseudo-Best Estimates.- VII.4 Estimation of Regression Coefficients.- References.

Correlation functions and masterequations of generalized (non-Markovian) Langevin equations

Abstract: For the statistical behavior of macrovariables described in terms of Langevin equations with a in general colored random force we deduce useful formulas which simplify the calculation of correlation functions. Utilizing these results and the stochastic properties of the random force we derive an exact time-convolutionless masterequation for the probability hereby showing the mathematical equivalence of the formally different approaches of a Langevin description and a masterequation description. We study in detail the class of time-instantaneous Langevin equations and the important class of retarded (Mori-type) Langevin equations with both, Gaussian and general colored random forces. Using the generalization of the nonlinear Langevin equation for continuous Markov processes with white Gaussian noise and white generalized Poisson noise we show that the resulting masterequation can be recast in the Kramers-Moyal form. Interpreting this Langevin equation in the Stratonovitch sense we deduce the fluctuation induced drift (spurious drift) which can be divided up into two parts, the well known part induced by white Gaussian noise and the one induced by white generalized Poisson noise.

On degraded Gaussian two-user channels (Corresp.)

Abstract: Several bounds to the capacity region of a degraded Gaussian channel are studied. An outer bound utilizing the capacity region of the corresponding broadcast channel is obtained. Two achievable regions obtained previously are compared, and a region including both is introduced by using frequency division multiplexing.

Study of the Random Vibration of Nonlinear Systems by the Gaussian Closure Technique

Abstract: A technique is developed to study random vibration of nonlinear systems. The method is based on the assumption that the joint probability density function of the response variables and input variables is Gaussian. It is shown that this method is more general than the statistical linearization technique in that it can handle non-Gaussian excitations and amplitude-limited responses. As an example a bilinear hysteretic system under white noise excitation is analyzed. The prediction of various response statistics by this technique is in good agreement with other available results.

Photoabsorption in carbon monoxide: Stieltjes–Tchebycheff calculations in the separated‐channel static‐exchange approximation

Abstract: Theoretical investigations of total and partial‐channel photoabsorption cross sections in carbon monoxide are reported employing the Stieltjes–Tchebycheff (S–T) technique and separated‐channel static‐exchange calculations. Pseudospectra of discrete transition frequencies and oscillator strengths appropriate for individual excitations of each of the six occupied molecular orbitals are constructed using Hartree–Fock core functions and normalizable Gaussian orbitals to describe the photoexcited and ejected electrons. Use of relatively large basis sets of compact and diffuse functions insures the presence of appropriate discrete Rydberg states in the calculations and provides sufficiently dense pseudospectra for the determination of convergent photoionization cross sections from the S–T technique. The calculated discrete vertical electronic excitation spectra are in very good agreement with measured band positions and intensities, and the partial‐channel photoionization cross sections are in correspondingly g...

On establishing reference values.

Abstract: In order to establish a range of reference values for any characteristic one can use Gaussian or nonparametric techniques, whichever are most appropriate One has the choice of calculating tolerance intervals or percentile intervals A tolerance interval is said to contain, say 95% of the population with probability, say 090 A percentile interval simply simply calculates the values between which 95% of the observations fall If the data can be said to have a Gaussian distribution, the same precision can be obtained with smaller sample sizes than using the nonparametric techniques In some cases, data which are not Gaussian can be transformed into a Gaussian form and hence make use of the more efficient Gaussian techniques In both cases, the data should be checked for outliers or rogue observations and these should be eliminated if the testing procedure fails to imply that they are an integral part of the data

Theory of separable processes with applications to the identification of nonlinear systems

Abstract: By considering the class of separable random processes, a generalised Wiener-Hopf equation is derived for systems under Gaussian excitation that can be described by a model consisting of a linear system in cascade with a static nonlinear element, followed by another linear system. This result, together with a similar relationship for the 2nd-order crosscorrelation function, is used to formulate an identification and structure testing algorithm for this class of nonlinear system. The results of a simulation study are included to illustrate the validity of the algorithm.

Consistent estimation on finite parameter sets with application to linear systems identification

Abstract: The consistency of maximum likelihood and related Bayesian estimates for a general class of observation sequences is treated, following a result by P. E. Caines. The condition for consistency is then interpreted in terms of the statistics associated with linear systems driven by white Gaussian inputs, to establish a verifiable condition for the identifiability of such systems on finite sets of mathematical representations.

Energy bands, Compton profile, and optical conductivity of vanadium

Abstract: A self-consistent calculations of energy bands in vanadium has been performed using the linear-combination-of-atomic-orbitals method. The basis contained 13 s-type, ten p-type, five d-type, and one f-type Gaussian orbitals. A local exchange potential of the Kohn-Sham form was included. Results are presented for the band structure, density of states, Compton profile, and optical conductivity.

Minimum error dispersion linear filtering of scalar symmetric stable processes

Abstract: The well-known Kalman-Bucy linear-filtering theory for Gaussian Markov processes is generalized to cover a particular class of non-Gaussian Markov processes, the scalar symmetric stable Markov processes. Results are presented only for discrete time because of certain pathologies that arise in the continuous-time analog (except in the Gaussian case). Attention is confined to the scalar case because of technical problems arising in characterizing multivariate stable distributions (except in the Gaussian case).

Equivalence and Singularity of Gaussian Measures and Applications

Abstract: Keywords: reproducing kernel Hilbert spaces;;; equivalence and singularity;;; Gaussian measures;;; expository paper;;; Feldman-Hajek dichotomy for Gaussian measures;;; stationary Gaussian processes;;; absolute continuity and singularity of probability measures Reference GPRO-CHAPTER-1978-003 Record created on 2010-05-25, modified on 2016-08-08

Perturbation calculation of molecular correlation energy using Gaussian-type geminals. Second-order pair energies of LiH and BH

Abstract: The second‐order pair energies of LiH and BH are calculated using Rayleigh–Schroedinger perturbation theory. The first‐order perturbed pair functions are expanded in terms of explicitly correlated Gaussian functions. The nonlinear parameters entering the Gaussian geminals are optimized with reference to crude SCF functions according to the method proposed previously. The final values of the second‐order pair energies are then calculated using accurate SCF orbitals. At this final stage only the linear parameters are reoptimized. The calculated second‐order correlation energies of LiH and BH are compared with recent diagrammatic many‐body perturbation theory results. The basis sets composed of two optimized Gaussian geminals for each spin‐adapted pair function are shown to give quite reliable second‐order correlation energies. The results obtained with four geminals for each pair function are superior to the most accurate many‐body perturbation theory data. It is stressed that the nonlinear parameters of Gaussian geminals can be given a simple physical interpretation which facilitates their reasonable guess. The first‐order pair functions represented in terms of Gaussian geminals have a very attractive compact and simple form. If properly optimized they can also provide highly accurate values of the second‐order molecular correlation energies.

Fast time-invariant implementations of Gaussian signal detectors

Abstract: A new implementation is presented for the optimum likelihood ratio detector for stationary Gaussian signals in white Gaussian noise that uses only two causal time-invariant filters. This solution also has the advantage that fast algorithms based on the Levinson and Chandrasekhar equations can he used for the determination of these time-invariant filters. By using a notion of "closeness to stationarity,' there is a natural extension of the above results for nonstationary signal processes.

Some consideration of decomposition of a time series

Abstract: SUMMARY Suppose that an observable Gaussian time series Z1 can be written as the sum of an unobservable signal component T1 and a white noise component e1. This paper proposes a

A Fake Process Approach to Data Compression

Abstract: The problem of designing a good decoder for a timeinvariant tree-coding data compression system is equivalent to that of finding a good low rate "fake process" for the original source, where the fake is produced by a time-invariant nonlinear filtering of an independent, identically distributed sequence of uniformly distributed discrete random variables and "goodness" is measured by the \bar{\rho} -distance between the fake and the original source. Several simple ad hoc techniques for obtaining such fake processes are introduced and shown by simulation to provide an improvement of typically 1-2 dB over optimum quantization, delta modulation, and predictive quantization for one-bit per symbol compression of Gaussian memoryless, autoregressive, and moving average sources. In addition, the fake process viewpoint provides a new intuitive explanation of why delta modulation and predictive quantization work as well as they do on Gaussian autoregressive sources.

Molecular electric polarizabilities

Abstract: The electric field variant (EFV) Gaussian basis sets of double-zeta (2-ζ) quality are used for the calculation of the electric dipole polarizabilities of diatomic molecules in the Hartree-Fock approximation. The explicit external electric field dependence of the GTO basis set, introduced according to the method described in Part I of this series, is shown to account for the major portion of the electric field induced deformation of the wavefunction. The Polarizabilities obtained in the present calculations are quite close to the best Hartree-Fock results. The deviations from near-Hartree-Fock values amount to 3–8 per cent for the parallel component and to 10–15 per cent for the perpendicular one. It was also shown that the same method leads simultaneously to a considerable improvement of the dipole moments.

Optimum detection of signals in non‐Gaussian noise

Abstract: The purpose of this paper is to derive optimum processing structures for use in the detection of signals in additive non‐Gaussian noise. The cases chosen for analysis are of particular interest in sonar detection problems since it has been reported that ambient oceannoise may, under sone conditions, deviate from the Gaussian model. The processing structures are considered to be models of the likelihood ratio which is an optimum test no matter what the signal and noise statistics, and optimum single channel and array processors are derived for the small signal‐to‐noise ratio cases where (1) the signal is completely known, and (2) the signal is a noiselike, not necessarily Gaussian, zero‐mean process. Expressions are derived which compare the performance of processors optimized for non‐Gaussian noise with those optimized for Gaussian noise for each of the two cases, with transfer functions for the required optimum nonlinear filters and the expected improvements in performance determined using some ’’typical’’ non‐Gaussian probability density functions. Justification of these particular density functions is beyond the scope of this paper except to note that very good agreement is obtained with some published experimental data. New results include the derivation of optimum array processors for the detection of plane wave signals when the array is steered at the signal arrival angle, in a non‐Gaussian noise field and the development of expressions to predict their performance for the case where the signal is a zero‐mean, noiselike process.

A Lower Bound for the Mass of a Random Gaussian Lattice

Abstract: We give a criterion that the two point function for a Gaussian lattice with random mass decay exponentially. The proof uses a random walk representation which may be of interest in other contexts.

Asymptotic properties of time domain gaussian estimators

Abstract: We consider a general non-linear multivariate time series model which can be parameterized by a finite and fixed number of parameters and which can be rewritten, if necessary, in a form such that the disturbances are stationary martingale differences. Given a series of discrete, equally spaced observations we prove the strong consistency and asymptotic normality of the Gaussian estimators of the parameters, the parameters possibly being subject to nonlinear constraints. Because the normal equations are usually highly non-linear it may be difficult to obtain explicit expressions for the Gaussian estimates. To overcome this problem we use a Gauss-Newton type algorithm to obtain a sequence of iterates which converge to, and have the same asymptotic properties as, the Gaussian estimates.