The application of Gaussian distribution deconvolution method to separate the overlapping signals in the 2D NMR map

The 2D NMR(T_(1)-T_(2))mapping technique,which can be used to separate different proton populations from various sources(hydroxyls,solid organic matter,free water,and free HC)has gained attention in petroleum industry.To separate proton contributions,a fixed straight line is commonly employed to separate different regions representing proton sources on the map.However,some of these regions(Region 1 and 2)might overlap which makes extracting the NMR signal amplitude from these regions inaccurate.In order to solve this issue,in this study,we applied the Gaussian distribution deconvolution method to separate the T_(1)and T_(2)relaxation distributions and then derived the signal amplitude of each region instead of following the common fixed line approach.Next,we employed this method to analyze several shale samples from the literature and compared the results following both methods to verify our methodology.Finally,samples from the Bakken Shale were studied to separate signals from Region 1 and Region 2 and corelated the results with geochemical properties that were obtained from programmed(Rock Eval)pyrolysis.Results demonstrated an improvement in their relation when our approach is employed compared to the fixed line technique to differentiate signal from overlapping regions.This means the Gaussian distribution deconvolution method can be used with confidence to provide us with more accurate petrophysical and geochemical understanding of complex formations.

Estimation of Hourly and Daily Global Solar Radiation at Clear Days Using an Approach Based on Modified Version of Gaussian Distribution

The performance of two models,Jam and Baig,based on the modified version of Gaussian distribution function in estimating the daily total of global solar radiation and its distribution through the hours of the day from sunrise to sunset al any clear day is evaluated with our own measured data in the period from June 1992 to May 1993 in Qena Egypt The results show a high relative deviation of calculated values from measured ones,especially for Jain model,in the most hours of the day,except for those near to local noon.This misfit behavior is quite obvious in the early morning and late afternoon A new approach has been proposed in this paper to estimate the daily and hourly global solar radiation This model performs with very high accuracy on the recorded data in our region.The validity of this approach was verified with new measurements in some clear days in June and August 1994.The resultant very low relative deviation of the calculated values of global solar radiation from the measured ones confirms the high performance of the approach proposed in this work

Deterministic quantum key distribution based on Gaussian-modulated EPR correlations

This paper proposes a deterministic quantum key distribution scheme based on Gaussian-modulated continuous variable EPR correlations. This scheme can implement fast and efficient key distribution. The security is guaranteed by continuous variable EPR entanglement correlations produced by nondegenerate optical parametric amplifier. For general beam splitter eavesdropping strategy, the secret information rate ΔI = I（α, β）-I（α, ε） is calculated in view of Shannon information theory. Finally the security analysis is presented.

Derivation of Gaussian Probability Distribution: A New Approach

The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbersome as it relies heavily on many lemmas and theorems. This paper invented an alternative and less rigorous method of deriving Gaussian distribution from basic random experiment conditional on some assumptions.

Mechanical properties of double-stranded DNA biofilm with Gaussian distribution

In microcantilever-based label-free biodetection technologies, deflection changes induced by adsorptions of double-stranded DNA （dsDNA） molecules on Au-layer surface are greatly affected by the mechanical, thermal and electrical properties of DNA biofilm. In this paper, the elastic properties of dsDNA biofilm are studied. First, the Parsegian＇s empirical potential based on a mesoscopic liq- uid crystal theory is employed to describe the interaction energy among coarse-grained DNA cylinders. Then, con- sidering a Gaussian distribution of DNA interaxial distance, the thought experiment method is used to derive an analyti- cal expression for Young＇s modulus of DNA biofilm with a stochastic packing pattern for the first time. Results show that Young＇s modulus of DNA biofilm is on the order of 10 MPa. These findings could provide a simple and effective method to evaluate the mechanical properties of soft biofilm on snbstrate.

Deterministic Quantum Key Distribution Using Gaussian-Modulated Squeezed States

A continuous variable ping-pong scheme,which is utilized to generate deterministic private key,is proposed. The proposed scheme is implemented physically by using Gaussian-modulated squeezed states.The deterministic characteristic, i.e.,no basis reconciliation between two parties,leads a nearly two-time efficiency comparing to the standard quantum key distribution schemes.Especially,the separate control mode does not need in the proposed scheme so that it is simpler and more available than previous ping-pong schemes.The attacker may be detected easily through the fidelity of the transmitted signal,and may not be successful in the beam splitter attack strategy.

Gaussian process assisted coevolutionary estimation of distribution algorithm for computationally expensive problems

In order to reduce the computation of complex problems, a new surrogate-assisted estimation of distribution algorithm with Gaussian process was proposed. Coevolution was used in dual populations which evolved in parallel. The search space was projected into multiple subspaces and searched by sub-populations. Also, the whole space was exploited by the other population which exchanges information with the sub-populations. In order to make the evolutionary course efficient, multivariate Gaussian model and Gaussian mixture model were used in both populations separately to estimate the distribution of individuals and reproduce new generations. For the surrogate model, Gaussian process was combined with the algorithm which predicted variance of the predictions. The results on six benchmark functions show that the new algorithm performs better than other surrogate-model based algorithms and the computation complexity is only 10% of the original estimation of distribution algorithm.

Investigation of the inhomogeneous barrier height of an Au/Bi_4Ti_3O_(12)/n-Si structure through Gaussian distribution of barrier height

A Au/Bi4Ti3O12/n-Si structure is fabricated in order to investigate its current voltage （IV） characteristics in a temperature range of 300 K-400 K. Obtained I-V data are evaluated by the thermionic emission （TE） theory. Zero-bias barrier height （Ф0） and ideality factor （n） calculated from I-V characteristics, are found to be temperature-dependent such that ФB0 increases with temperature increasing, whereas n decreases. The obtained temperature dependence of ФB0 and linearity in ФB0 versus the n plot, together with a lower barrier height and Richardson constant values obtained from the Richardson plot, indicate that the barrier height of the structure is inhomogeneous in nature. Therefore, I-V characteristics are explained on the basis of Caussian distribution of barrier height.

Cluster-Based Distributed Algorithms for Very Large Linear Equations

In many applications such as computational fluid dynamics and weather prediction, as well as image processing and state of Markov chain etc., the grade of matrix n is often very large, and any serial algorithm cannot solve the problems. A distributed cluster-based solution for very large linear equations is discussed, it includes the definitions of notations, partition of matrix, communication mechanism, and a master-slaver algorithm etc., the computing cost is O（n^3/N）, the memory cost is O（n^2/N）, the I/O cost is O（n^2/N）, and the com- munication cost is O（Nn ）, here, N is the number of computing nodes or processes. Some tests show that the solution could solve the double type of matrix under 10^6 × 10^6 effectively.

What Is the Difference between Gamma and Gaussian Distributions?

An inequality describing the difference between Gamma and Gaussian distributions is derived. The asymptotic bound is much better than by existing uniform bound from Berry-Esseen inequality.

Heavy-Tailed Distributions Generated by Randomly Sampled Gaussian, Exponential and Power-Law Functions

A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a radially uniform sampling scheme produces heavy-tailed distributions. For two-dimensional Gaussians and one-dimensional exponential functions, exact power-laws with exponent –1 are obtained. In other cases, densities with an approximate power-law behaviour close to the origin arise. These densities are analyzed using Padé approximants in order to show the approximate power-law behaviour. If the sampled function itself follows a power-law with exponent –α, random sampling leads to densities that also follow an exact power-law, with exponent -n/a – 1. The presented mechanism shows that power-laws can arise in generic situations different from previously considered specialized systems such as multi-particle systems close to phase transitions, dynamical systems at bifurcation points or systems displaying self-organized criticality. Thus, the presented mechanism may serve as an alternative hypothesis in system identification problems.

Oversampling Method Based on Gaussian Distribution and K-Means Clustering

Learning from imbalanced data is one of the greatest challenging problems in binary classification,and this problem has gained more importance in recent years.When the class distribution is imbalanced,classical machine learning algorithms tend to move strongly towards the majority class and disregard the minority.Therefore,the accuracy may be high,but the model cannot recognize data instances in the minority class to classify them,leading to many misclassifications.Different methods have been proposed in the literature to handle the imbalance problem,but most are complicated and tend to simulate unnecessary noise.In this paper,we propose a simple oversampling method based on Multivariate Gaussian distribution and K-means clustering,called GK-Means.The new method aims to avoid generating noise and control imbalances between and within classes.Various experiments have been carried out with six classifiers and four oversampling methods.Experimental results on different imbalanced datasets show that the proposed GK-Means outperforms other oversampling methods and improves classification performance as measured by F1-score and Accuracy.

A Normal Weighted Inverse Gaussian Distribution for Skewed and Heavy-Tailed Data

High frequency financial data is characterized by non-normality: asymmetric, leptokurtic and fat-tailed behaviour. The normal distribution is therefore inadequate in capturing these characteristics. To this end, various flexible distributions have been proposed. It is well known that mixture distributions produce flexible models with good statistical and probabilistic properties. In this work, a finite mixture of two special cases of Generalized Inverse Gaussian distribution has been constructed. Using this finite mixture as a mixing distribution to the Normal Variance Mean Mixture we get a Normal Weighted Inverse Gaussian (NWIG) distribution. The second objective, therefore, is to construct and obtain properties of the NWIG distribution. The maximum likelihood parameter estimates of the proposed model are estimated via EM algorithm and three data sets are used for application. The result shows that the proposed model is flexible and fits the data well.

Space Charge Effect of Bunched Beam With Gaussian Distribution

The nonlinear space charge effect of a bunched beam with Gaussian distribu-tion in the longitudinal direction is discussed.Some useful formulae are derived for cal-culating the potential induced by a cylinder model of space charge in the waveguide of alinac with different combinations of density distribution:Gaussian distribution in thelongitudinal direction versus Kapchinskij Vladimirskij,waterbag,parabolic andGaussian distribution in the transverse direction,rcspectively.

Analytical Evaluation of Non-Elementary Integrals Involving Some Exponential, Hyperbolic and Trigonometric Elementary Functions and Derivation of New Probability Measures Generalizing the Gamma-Type and Gaussian-Type Distributions

The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, and where α,η and β are real or complex constants are evaluated in terms of the confluent hypergeometric function 1F1 and the hypergeometric function 1F2. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions 1F1 and 1F2. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (x2) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.

Design of the Quantization Matrix in the Distributed Compressed Sensing Video Coding*

In the frame of compressed sensing distributed video coding, the design of the quantization matrix directly affects the reconstruction quality of the receiving terminal of the video. In this article, we present a new design method of the Gaussian quantization matrix adapting to the compressed sensing coding, for that the distribution of the parameters of the image is featured of the characteristic of approximately normal distribution after measured by compressive sensing. By this way, the parameters of a certain quantity of the image frames depending on the video sequences generated by the Gaussian quantization matrix possess certain adaptive capacity. By comparison with the plan of the traditional quantization, the quantization matrix presented in this article would improve the reconstruction quality of the video.

Free Energy and Emittance Growth Caused by Bunched Beam With Gaussian Distribution in Longitudinal Direction in Linac

The nonlinear space charge effect of bunched beam in linac is one of the important factors thatinduces the emittance growth due to the conversion of the field energy to kinetic energy.In this paper,us-ing a cylinder model of space charge in linac,we derived the internal energy for a bunched beam withsome nonuniform space charge distributions,such as longitudinal Gaussian distribution combined withKapchinskij-Vladimirski1,waterbag,parabolic or Gaussian transverse distribution.And the emittancegrowth caused by the above distributions is worked out.

The retrieval of the nonlinear random waves from the non-Gaussian characteristics of the sea surface elevation distribution

In this paper, without recourse to the nonlinear dynamical equations of the waves, the nonlinear random waves are retrieved from the non-Gaussian characteristic of the sea surface elevation distribution. The question of coincidence of the nonlinear wave profile, spectrum and its distributions of maximum (or minimum) values of the sea surface elevation with results derived from some existing nonlinear theories is expounded under the narrow-band spectrum condition. Taking the shoaling sea wave as an example, the nonlinear random wave process and its spectrum in shallow water are retrieved from both the non-Gaussian characteristics of the sea surface elevation distribution in shallow water and the normal sea waves in deep water and compared with the values actually measured. Results show that they can coincide with the actually measured values quite well, thus, this can confirm that the method proposed in this paper is feasible.

Technique for Multi-Pass Turning Optimization Based on Gaussian Quantum-Behaved Bat Algorithm

The multi-pass turning operation is one of the most commonly used machining methods in manufacturing field.The main objective of this operation is to minimize the unit production cost.This paper proposes a Gaussian quantum-behaved bat algorithm(GQBA)to solve the problem of multi-pass turning operation.The proposed algorithm mainly includes the following two improvements.The first improvement is to incorporate the current optimal positions of quantum bats and the global best position into the stochastic attractor to facilitate population diversification.The second improvement is to use a Gaussian distribution instead of the uniform distribution to update the positions of the quantum-behaved bats,thus performing a more accurate search and avoiding premature convergence.The performance of the presented GQBA is demonstrated through numerical benchmark functions and amulti-pass turning operation problem.Thirteen classical benchmark functions are utilized in the comparison experiments,and the experimental results for accuracy and convergence speed demonstrate that,in most cases,the GQBA can provide a better search capability than other algorithms.Furthermore,GQBA is applied to an optimization problem formulti-pass turning,which is designed tominimize the production cost while considering many practical machining constraints in the machining process.The experimental results indicate that the GQBA outperforms other comparison algorithms in terms of cost reduction,which proves the effectiveness of the GQBA.