non-Gaussian Type Research Articles

Direct Integration of Nanoscale Conventional and Slot Waveguides

Slot waveguides can provide high optical confinement in a nanoscale low-index layer. While a conventional waveguide has a Gaussian-like Eigenmode profile, the Eigenmode profile of a slot waveguide is quite non-Gaussian type, due to the large discontinuity of refractive indices and thus the transverse electric field component between the high and low index layers of a slot waveguide. Although the field profiles of the two types of waveguides seem different, here we show that direct integration of conventional and slot waveguides yields efficient coupling of light into and out of slot waveguides using the rigorous finite-difference time domain method. The proposed direct coupling method has comparable performance to recently proposed taper based coupling methods, while having advantages in easier integration with conventional waveguide optics and higher integration density. We also show that coupling efficiency is not sensitive to the symmetricity of the slot waveguide, resulting in good manufacturing tolerance. The proposed direct coupler may have a number of applications in lightwave interconnects, sensing and data storage.

On the optimality of the spherical Mexican hat wavelet estimator for the primordial non-Gaussianity

We study the spherical Mexican hat wavelet (SMHW) as a detector of primordial non-Gaussianity of the local type on the Cosmic Microwave Background (CMB) anisotropies. For this purpose we define third order statistics based on the wavelet coefficient maps and the original map. We find the dependence of these statistics in terms of the non-linear coupling parameter fnl and the bispectrum of this type of non-Gaussianity. We compare the analytical values for these statistics with the results obtained with non-Gaussian simulations for an ideal full-sky CMB experiment without noise. We study the power of this method to detect fnl, i. e. the variance of this parameter, and compare it with the variance obtained from the primary bispectrum for the same experiment. Finally we apply our wavelet based estimator on WMAP-like maps with incomplete sky and inhomogeneous noise and compare with the optimal bispectrum estimator. The results show that the wavelet cubic statistics are as efficient as the bispectrum as optimal detectors of this type of primordial non-Gaussianity.

Nongaussian Features from Inflationary Particle Production

The inflaton field can be expected to couple to a number of additional fields whose energy density does not play any significant role in driving inflation. Such couplings may lead to isolated bursts of particle production during inflation, for example via parametric resonance or a phase transition, and leave observable imprints in the cosmological fluctuations. I illustrate this effect for a simple prototype interaction g2(ϕ − ϕ0)2χ between the inflaton, ϕ, and iso-inflaton, χ. Using both classical lattice simulations and analytical quantum field theory computations, I show that this mechanism generates localized bump-like features in the power spectrum and also a completely new type of nongaussianity. Observations are consistent with relatively large features of this type and the nongaussianity from particle production may be observable in future missions.

Application of the Kurtosis Statistic to the Evaluation of the Risk of Hearing Loss in Workers Exposed to High-Level Complex Noise

Develop dose-response relations for two groups of industrial workers exposed to Gaussian or non-Gaussian (complex) types of continuous noises and to investigate what role, if any, the kurtosis statistic can play in the evaluation of industrial noise-induced hearing loss (NIHL). Audiometric and noise exposure data were acquired on a population (N = 195) of screened workers from a textile manufacturing plant and a metal fabrication facility located in Henan province of China. Thirty-two of the subjects were exposed to non-Gaussian (non-G) noise and 163 were exposed to a Gaussian (G) continuous noise. Each subject was given a general physical and an otologic examination. Hearing threshold levels (0.5-8.0 kHz) were age adjusted (ISI-1999) and the prevalence of NIHL at 3, 4, or 6 kHz was determined. The kurtosis metric, which is sensitive to the peak and temporal characteristics of a noise, was introduced into the calculation of the cumulative noise exposure metric. Using the prevalence of hearing loss and the cumulative noise exposure metric, a dose-response relation for the G and non-G noise-exposed groups was constructed. An analysis of the noise environments in the two plants showed that the noise exposures in the textile plant were of a Gaussian type with an Leq(A)8hr that varied from 96 to 105 dB whereas the exposures in the metal fabrication facility with an Leq(A)8hr = 95 dB were of a non-G type containing high levels (up to 125 dB peak SPL) of impact noise. The kurtosis statistic was used to quantify the deviation of the non-G noise environment from the Gaussian. The dose-response relation for the non-G noise-exposed subjects showed a higher prevalence of hearing loss for a comparable cumulative noise exposure than did the G noise-exposed subjects. By introducing the kurtosis variable into the temporal component of the cumulative noise exposure calculation, the two dose-response curves could be made to overlap, essentially yielding an equivalent noise-induced effect for the two study groups. For the same exposure level, the prevalence of NIHL is greater in workers exposed to non-G noise environments than for workers exposed to G noise. The kurtosis metric may be a reasonable candidate for use in modifying exposure level calculations that are used to estimate the risk of NIHL from any type of noise exposure environment. However, studies involving a large number of workers with well-documented exposures are needed before a relation between a metric such as the kurtosis and the risk of hearing loss can be refined.

Scale dependence of halo bispectrum from non-Gaussian initial conditions in cosmological N-body simulations

We study the halo bispectrum from non-Gaussian initial conditions. Based on a set of large N-body simulations starting from initial density fields with local type non-Gaussianity, we find that the halo bispectrum exhibits a strong dependence on the shape and scale of Fourier space triangles near squeezed configurations at large scales. The amplitude of the halo bispectrum roughly scales as fNL2. The resultant scaling on the triangular shape is consistent with that predicted by Jeong & Komatsu based on perturbation theory. We systematically investigate this dependence with varying redshifts and halo mass thresholds. It is shown that the fNL dependence of the halo bispectrum is stronger for more massive haloes at higher redshifts. This feature can be a useful discriminator of inflation scenarios in future deep and wide galaxy redshift surveys.

Primordial non-Gaussianity estimator: The inhomogeneous noise effect

Since the inhomogeneous instrument noise can produce extra non-Gaussianity in the cosmic microwave background (CMB) anisotropy, its effect should be carefully subtracted in the primordial non-Gaussianity estimation. We calculate the probability distribution function of the CMB anisotropy for a local type of non-Gaussianity, from which the optimal estimator in the general case (inhomogeneous noise and cut sky) is obtained. The new estimator obtained here is different from the popular one, since the inhomogeneous noise and cut sky effects are completely accounted for. The CMB anisotropy in the new estimator is noise weighted. The noise weight is different from that used by the WMAP Collaboration in their 5-year data analysis. Although it is still difficult to calculate the new estimator rigorously, for the case of the slightly inhomogeneous noise, there exists a series expansion method to compute the new estimator. Each order in the series is suppressed by two factors, (({sigma}{sup 2}/{sigma}{sub i}{sup 2})-1) and (C{sub l}/C{sub l}{sup tot}), which make the method feasible. Through the Edgeworth expansion we can generalize our discussion to other types of non-Gaussianity.

Estimators for local non-Gaussianities

We study the Likelihood function of data givenfNL forthe so-called local type of non-Gaussianity. In this case the curvature perturbation is a non-linearfunction, local in real space, of a Gaussian random field. We compute the Cramer–Rao bound forfNL and show thatfor small values of fNL the three-point function estimator saturates the bound and is equivalent tocalculating the full Likelihood of the data. However, for sufficiently largefNL, the naive three-point function estimator has a much larger variance than previously thought. Inthe limit in which the departure from Gaussianity is detected with high confidence, error bars onfNL onlydecrease as 1/lnNpix rather than Npix−1/2 as the size of the data set increases. We identify the physical origin of this behaviour andexplain why it only affects the local type of non-Gaussianity, where the contributionof the first multipoles is always relevant. We find a simple improvement to thethree-point function estimator that makes the square root of its variance decrease asNpix−1/2 evenfor large fNL, asymptotically approaching the Cramer–Rao bound. We show that using themodified estimator is practically equivalent to computing the full Likelihood offNL given the data. Thus other statistics of the data, such as the four-pointfunction and Minkowski functionals, contain no additional information onfNL. In particular, we explicitly show that the recent claims about the relevance of thefour-point function are not correct. By direct inspection of the Likelihood, we show thatthe data do not contain enough information for any statistic to be able to constrain higherorder terms in the relation between the Gaussian field and the curvature perturbation,unless these are orders of magnitude larger than the size suggested by the current limits onfNL. As our main focusis the scaling with Npix of the various quantities, calculations are done in flat sky approximation and without theradiation transfer function.

A principle of fractal-stochastic dualism and Gompertzian dynamics of growth and self-organization

The emergence of Gompertzian dynamics at the macroscopic, tissue level during growth and self-organization is determined by the existence of fractal-stochastic dualism at the microscopic level of supramolecular, cellular system. On one hand, Gompertzian dynamics results from the complex coupling of at least two antagonistic, stochastic processes at the molecular cellular level. It is shown that the Gompertz function is a probability function, its derivative is a probability density function, and the Gompertzian distribution of probability is of non-Gaussian type. On the other hand, the Gompertz function is a contraction mapping and defines fractal dynamics in time-space; a prerequisite condition for the coupling of processes. Furthermore, the Gompertz function is a solution of the operator differential equation with the Morse-like anharmonic potential. This relationship indicates that distribution of intrasystemic forces is both non-linear and asymmetric. The anharmonic potential is a measure of the intrasystemic interactions. It attains a point of the minimum ( U 0, t 0) along with a change of both complexity and connectivity during growth and self-organization. It can also be modified by certain factors, such as retinoids.

Non‐Gaussian Features of Transmitted Flux of QSOs' Lyα Absorption: Intermittent Exponent

Recently, it has been found that the field traced by QSOs' Lyα forests is intermittent on small scales. Intermittent behavior is essential for understanding the statistics and dynamics of cosmic gravitational clustering in the nonlinear regime. The most effective method of describing intermittency uses the structure functions and the intermittent exponent, which measure the scale and order dependencies of the ratio between the higher order and second-order moments of the field. These properties can be used not only to confirm the non-Gaussianity of fields but also to detect the type of non-Gaussianity. In this paper, we calculate the structure function and intermittent exponent of (1) Keck data, which consists of 28 high-resolution, high signal-to-noise ratio QSO Lyα absorption spectra, and (2) Lyα forest simulation samples produced via the pseudohydrodynamic scheme for the low-density cold dark matter model and warm dark matter (WDM) model with particle mass mW = 300, 600, 800, and 1000 eV. Aside from the WDM model with mW = 300 eV, the simulation samples are in agreement with observations in the context of the power spectrum. We find, however, that the intermittent behavior of all the simulation samples is substantially inconsistent, both quantitatively and qualitatively, with the Keck data. Specifically, (1) the structure functions of the simulation samples are significantly larger than that of Keck data on scales k ≥ 0.1 km-1 s; (2) the intermittent exponents of the simulation samples are more negative than that of Keck data on all redshifts considered; and (3) the order dependence of the structure functions of simulation samples is closer to the intermittency of hierarchical clustering on all scales, while the Keck data are closer to a lognormal field on small scales. These differences are independent of noise and show that the intermittent evolution modeled by the pseudohydrodynamic simulation is substantially different from observations, even though they are in good agreement with each other in terms of second- and lower order statistics. This result also shows that weakly clustered samples, such as the high-resolution Lyα absorption spectrum, are effective in testing dynamical models of structure formation if their intermittent features are considered.

Image recognition in the presence of non-Gaussian noise with unknown statistics

We design receivers to detect a known pattern or a reference signal in the presence of very general and non-Gaussian types of noise. Three sources of input-noise degradation are considered: additive, multiplicative, and disjoint background. The detection process involves two steps: (1) estimation of the relevant noise parameters within the framework of hypothesis testing and (2) maximizing a certain metric that measures the likelihood of the target being at a given location. The parameter estimation portion is carried out by moment-matching techniques. Because of the number of unknown parameters and the fact that various types of input-noise processes are non-Gaussian, the methods that are used to estimate these parameters differ from the standard methods of maximizing the likelihood function. To verify the existence of the target at a certain location, we use l(p)-norm metric for p > or = 0 to measure the likelihood of the target being present at the location of interest. Computer simulations are used to show that for the images tested here, the receivers designed herein perform better than some existing receivers.

Off-Diagonal Bounds of Non-Gaussian Type for the Dirichlet Heat Kernel

The paper considers the heat kernel KΩ(t, x, y) of the operator −Δ on a proper Euclidean domain Ω, with Dirichlet boundary conditions. A general pointwise lower bound for KΩ, which is valid for t larger than a suitable t0(x,y), is proved (the short-time behaviour being well understood). The resulting non-Gaussian bounds describe simultaneously both the case of bounded domains and the case, modelled on the half-space example, of domains which satisfy a twisted infinite internal cone condition. Bounds for the Green's function are given as well.

An Expert Correlator Receiver

Design of an expert receiver has been investigated which can decide about its front end nonlinearity from a look up table. Considerations have been given for operability of this receiver in Gaussian and non-Gaussian both types of channel noise environments. The experimently estimated probability density function of the incoming noise is closely approximated with that of an ideal generalized Gaussian noise. Three distinct measures have been investigated for closed form approximation. Effect of increasing the dimension of slope error vector on the design of the receiver has been discussed.

Applicability of Kalman Filter Based on Equivalence Transformation to Standard Gaussian Type in State Estimation Problems of Non-Gaussian Type

Applicability of Kalman Filter Based on Equivalence Transformation to Standard Gaussian Type in State Estimation Problems of Non-Gaussian Type

An extended evaluation method of non-Gaussian type sound environment utilizing the generalized capability in the parallel information processing of neural network and fuzzy probability

An extended evaluation method of non-Gaussian type sound environment utilizing the generalized capability in the parallel information processing of neural network and fuzzy probability

A stochastic evaluation method based on the least entropy criterion for room with arbitrary environmental noise excitation.

As one of evaluation methods for the room sound fluctuation, a new trial to predict the probability distribution of the response sound fluctuation in the room excited by arbitrary type environmental noise input is proposed by emphasizing its methodological viewpoint. The response sound intensity of the room can be naturally expressed as a total sum on intensity scale of each frequency response component and its modelling error caused by the quantized error and/or the observation noise. Owing to the non-Gaussian property of intensity variable and modelling error, the well-known system identification method is too difficult to be directly applied to the present case. So, in this paper, first by newly introducing some kind of information measure in a form of mutual entropy quantity between input and output and maximizing it, a new estimation algorithm of acoustic characteristic parameters of the room is derived by applying a stochastic approximation method to the above extremal condition with using a general expression form of the Gram-Charier series expansion type non-Gaussian probability distribution. In the room excited by an arbitrary environmental noise input fluctuating in non-Gaussian type probability distribution form, the probability distribution of response sound fluctuation for an overall frequency range and each frequency band component can be predicted by using the above identified system model. The proposed method is applied to the room simulating the actual living acoustic situation and its justification and usefulness is experimentally confirmed, too.

An evaluation method of Leq for noise fluctuation of non-Gaussian and nonstationary types.

An Leq is usually calculated through an averaging operation of anti-logarithm of the measured instantaneous level value in a decibel scale. Considering the nonlinear transformation of level observation, there seems to remain a principal problem that the average energy can not be exactly obtained owing to the inequality of quantization width in an energy scale differing from the equality of quantization width in a level scale. In this paper, the averaged sound energy is estimated on the basis of level statistics with help of the moment generating function of sound level by considering the fundamental relationship between the sound level and its energy. Then, an evaluation method of Leq is derived in the series expansion form reflecting the stationary and Gaussian properties as the first expansion term and the correction term for the deviation from these statistical properties as the higher order expansion terms. Finally, the proposed estimation method is experimentally confirmed by applying it to the actual noise environment inside and outside a room.

Two kinds of parameter estimation methods based on the information theory and an application to the acoustical measurement.

In this paper, two kinds of parameter estimation methods for overcoming the obstruction of the background noise co-existing in many actual acoustical or vibrational measurements are studied. As it is very important in an estimation problem for the measurement with the background noise of non-Gaussian type to grasp first the statistical properties of noise from all viewpoints as precise as possible, two kinds of information quantities which enable us to evaluate the distance between two different types of distribution forms or the uncertainty between two random physical quantities (e. g., the input and the output of the acoustical system) are newly introduced as the estimation criteria, and two kinds of sequential estimation algorithms which can be applied to the estimation for the general non-linear acoustical system with the background noise of arbitrary distribution type are explicitly derived. Furthermore, the legitimacy and the effectiveness of these algorithms are confirmed by applying to the actual parameter estimation problem of the reverberation room under the background noise from an acoustical viewpoint.