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

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.

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.

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.

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.

Plasma current tomography for HL-2A based on Bayesian inference

An accurate plasma current profile has irreplaceable value for the steady-state operation of the plasma.In this study,plasma current tomography based on Bayesian inference is applied to an HL-2A device and used to reconstruct the plasma current profile.Two different Bayesian probability priors are tried,namely the Conditional Auto Regressive(CAR)prior and the Advanced Squared Exponential(ASE)kernel prior.Compared to the CAR prior,the ASE kernel prior adopts nonstationary hyperparameters and introduces the current profile of the reference discharge into the hyperparameters,which can make the shape of the current profile more flexible in space.The results indicate that the ASE prior couples more information,reduces the probability of unreasonable solutions,and achieves higher reconstruction accuracy.

Characteristics of Fallen Seed Distribution by Domestic and Imported Aerial Seeding Equipment

In order to explore the seed drop characteristics by aerial seeding equipment,taking aerial seeding for Pinus tabulaeformis as an example,the Gaussian curve fitting and chi-square goodness-of-fit test were carried out on the data of fallen seed distribution,and the seed distribution models of domestic FB-85 and imported PZLM-18 equipment were established.The seeding performance indexes of the two kinds of equipment were calculated and compared by using the model,the existing problems of domestic equipment and their causes are analyzed,and finally,some suggestions for equipment optimization were put forward.The results indicated that the seed drop of the two kinds of equipment showed the characteristics of dense distribution in the middle and sparse distribution on both sides,and followed the Gaussian distribution as a whole;compared with PZLM-18,FB-85 had better seeding performance,but it also had the problem of uneven seed distribution;in addition to the influence of aircraft flow field,the fishtail structure design of diffuser is another important reason for the uneven seed distribution of domestic equipment;without changing the fishtail structure design,it is suggested that the principle of cross-superposition of two seeding belts should be used to replace a single large-size diffuser with two small-size diffusers,which can reduce the number of seeds in the middle and increase the number of seeds on both sides,so as to improve the uniformity of seed distribution.

Stacking Ensemble Learning-Based Convolutional Gated Recurrent Neural Network for Diabetes Miletus

Diabetes mellitus is a metabolic disease in which blood glucose levels rise as a result of pancreatic insulin production failure.It causes hyperglycemia and chronic multiorgan dysfunction,including blindness,renal failure,and cardi-ovascular disease,if left untreated.One of the essential checks that are needed to be performed frequently in Type 1 Diabetes Mellitus is a blood test,this procedure involves extracting blood quite frequently,which leads to subject discomfort increasing the possibility of infection when the procedure is often recurring.Exist-ing methods used for diabetes classification have less classification accuracy and suffer from vanishing gradient problems,to overcome these issues,we proposed stacking ensemble learning-based convolutional gated recurrent neural network(CGRNN)Metamodel algorithm.Our proposed method initially performs outlier detection to remove outlier data,using the Gaussian distribution method,and the Box-cox method is used to correctly order the dataset.After the outliers’detec-tion,the missing values are replaced by the data’s mean rather than their elimina-tion.In the stacking ensemble base model,multiple machine learning algorithms like Naïve Bayes,Bagging with random forest,and Adaboost Decision tree have been employed.CGRNN Meta model uses two hidden layers Long-Short-Time Memory(LSTM)and Gated Recurrent Unit(GRU)to calculate the weight matrix for diabetes prediction.Finally,the calculated weight matrix is passed to the soft-max function in the output layer to produce the diabetes prediction results.By using LSTM-based CG-RNN,the mean square error(MSE)value is 0.016 and the obtained accuracy is 91.33%.

A Gaussian Noise-Based Algorithm for Enhancing Backdoor Attacks

Deep Neural Networks(DNNs)are integral to various aspects of modern life,enhancing work efficiency.Nonethe-less,their susceptibility to diverse attack methods,including backdoor attacks,raises security concerns.We aim to investigate backdoor attack methods for image categorization tasks,to promote the development of DNN towards higher security.Research on backdoor attacks currently faces significant challenges due to the distinct and abnormal data patterns of malicious samples,and the meticulous data screening by developers,hindering practical attack implementation.To overcome these challenges,this study proposes a Gaussian Noise-Targeted Universal Adversarial Perturbation(GN-TUAP)algorithm.This approach restricts the direction of perturbations and normalizes abnormal pixel values,ensuring that perturbations progress as much as possible in a direction perpendicular to the decision hyperplane in linear problems.This limits anomalies within the perturbations improves their visual stealthiness,and makes them more challenging for defense methods to detect.To verify the effectiveness,stealthiness,and robustness of GN-TUAP,we proposed a comprehensive threat model.Based on this model,extensive experiments were conducted using the CIFAR-10,CIFAR-100,GTSRB,and MNIST datasets,comparing our method with existing state-of-the-art attack methods.We also tested our perturbation triggers using various defense methods and further experimented on the robustness of the triggers against noise filtering techniques.The experimental outcomes demonstrate that backdoor attacks leveraging perturbations generated via our algorithm exhibit cross-model attack effectiveness and superior stealthiness.Furthermore,they possess robust anti-detection capabilities and maintain commendable performance when subjected to noise-filtering methods.

Variational quality control of non-Gaussian innovations and its parametric optimizations for the GRAPES m3DVAR system

The magnitude and distribution of observation innovations,which have an important impact on the analyzed accuracy,are critical variables in data assimilation.Variational quality control(VarQC)based on the contaminated Gaussian distribution(CGD)of observation innovations is now widely used in data assimilation,owing to the more reasonable representation of the probability density function of innovations that can sufficiently absorb observations by assigning different weights iteratively.However,the inaccurate parameters prevent VarQC from showing the advantages it should have in the GRAPES(Global/Regional Assimilation and PrEdiction System)m3DVAR system.Consequently,the parameter optimization methods are considerable critical studies to improve VarQC.In this paper,we describe two probable CGDs to include the non-Gaussian distribution of actual observation errors,Gaussian plus flat distribution and Huber norm distribution.The potential optimization methods of the parameters are introduced in detail for different VarQCs.With different parameter configurations,the optimization analysis shows that the Gaussian plus flat distribution and the Huber norm distribution are more consistent with the long-tail distribution of actual innovations compared to the Gaussian distribution.The VarQC’s cost and gradient functions with Huber norm distribution are more reasonable,while the VarQC’s cost function with Gaussian plus flat distribution may converge on different minimums due to its nonconcave properties.The weight functions of two VarQCs gradually decrease with the increase of innovation but show different shapes,and the VarQC with Huber norm distribution shows more elasticity to assimilate the observations with a high contamination rate.Moreover,we reveal a general derivation relationship between the CGDs and VarQCs.A novel schematic interpretation that classifies the assimilated data into three categories in VarQC is presented.They are conducive to the development of a new VarQC method in the future.

Numerical simulation of 3D-microstructures in solidification processes based on the CAFE method

It was analyzed that the finite element-cellular automaton （CAFE） method was used to simulate 3D-microstructures in solidification processes. Based on this method, the 3D-microstructure of 9SMn28 free-cutting steel was simulated in solidification processes and the simulation results are consistent with the experimental ones. In addition, the effects of Gaussian distribution parameters were also studied. The simulation results show that the higher the mean undercooling, the larger the columnar dendrite zones, and the larger the maximum nucleation density, the smaller the size of grains. The larger the standard deviation, the less the number of minimum grains is. However, the uniformity degree decreases first, and then increases gradually.

Coverage of communication-based sensor nodes deployed location and energy efficient clustering algorithm in WSN

An effective algorithm based on signal coverage of effective communication and local energy-consumption saving strategy is proposed for the application in wireless sensor networks.This algorithm consists of two sub-algorithms.One is the multi-hop partition subspaces clustering algorithm for ensuring local energybalanced consumption ascribed to the deployment from another algorithm of distributed locating deployment based on efficient communication coverage probability（DLD-ECCP）.DLD-ECCP makes use of the characteristics of Markov chain and probabilistic optimization to obtain the optimum topology and number of sensor nodes.Through simulation,the relative data demonstrate the advantages of the proposed approaches on saving hardware resources and energy consumption of networks.

COMPARISONS AMONG THE SOLUTIONS OF FIBER TEXTURE VECTOR

The texture vectors, as the fundatnental elements of the vector method (VM), are usually determined by the Durand's iterative method. In present paper, the texture vector is derived by two kinds of the maximum entropy method (MEM), which choose pole figure data (MEM(I)) and the series coefficients of pole figures (MEM(II)), respectively, as a constrained condition. The detailed comparisons, including the texture vector and residual vector in the pole figure and ODF, among the results obtained by different methods are given through the ideal fiber texture simulation with Gaussian distribution. It is demonstrated that, although both methods the good results in the ideal texture simulation, the solution on assumption of maximum entropy displays more attractive results. In order to compare the sensitivity of the different methods to the experimental errors, the stochastical errors in pole figures are introduced by the computer random processes (Monte-Carlo simulation). The Monte-Carlo simulation shows that the MEM with the series coefficients as a constrained condition is rather sensitive to the 'experimental' errors, however, inversely the conventional VM and MEM with pole figure data as a constrained condition.

Analysis of sand particles’ lift-off and incident velocities in wind-blown sand flux

In the research of windblown sand movement,the lift-off and incident velocities of saltating sand particles play a significant role in bridging the spatial and temporal scales from single sand particle＇s motion to windblown sand flux.In this paper,we achieved wind tunnel measurements of the movement of sand particles near sand bed through improving the wind tunnel experimental scheme of paticle image velocimetry（PIV） and data processing method.And then the influence of observation height on the probability distributions of lift-off and incident velocities of sand particles was analyzed.The results demonstrate that the observation height has no obvious influence on the distribution pattern of the lift-off and incident velocities of sand particles,i.e.,the probability distribution of horizontal and vertical velocities of lift-off and incident sand particles follow a Gaussian distribution and a negative exponential distribution,respectively.However,it influences the center of the Gaussian distribution,the decay constant and the amplitude of the negative exponential distribution.

An improved deconvolution method for X-ray coded imaging in inertial confinement fusion

In inertial confinement fusion （ICF）, X-ray coded imaging is considered as the most potential means to diagnose the compressed core. The traditional Richardson-Lucy （RL） method has a strong ability to deblur the image where the noise follows the Poisson distribution. However, it always suffers from over-fitting and noise amplification, especially when the signal-to-noise ratio of image is relatively low. In this paper, we propose an improved deconvolution method for X-ray coded imaging. We model the image data as a set of independent Gaussian distributions and derive the iterative solution with a maximum-likelihood scheme. The experimental results on X-ray coded imaging data demonstrate that this method is superior to the RL method in terms of anti-overfitting and noise suppression.

A MODEL FOR WHITE NOISE ANALYSIS IN P-ADIC NUMBER FIELDS

We propose a simple model for white noise analysis in the p-adic case based on the p-adic analogue of the space L(2)(R(infinity), d mu).

AN INVESTIGATION ON THE LOW TEMPERATURE RELAXATION OF POLYETHERETHERKETONE

The temperature spectra of internal friction of polyetheretherketone (PEEK) are investigated from 130K to 250K with a multi-function torsion pendulum in the frequency range of 0.1 Hz to 5 Hz. A relaxation process, γ relaxation, appears in the temperature range of the measurement. Its relaxation time distribution in terms of a Gaussian distribution, and the relation between molecular motion mechanism and the distribution characteristic are discussed. The element process of γ relaxation is found to be a disordering one.

An Advanced Probabilistic Neural Network for the Design of Breakwater Armor Blocks

In this study, an advanced probabilistic neural network （APNN） method is proposed to reflect the global probability density function （PDF） by summing up the heterogeneous local PDF which is automatically determined in the individual standard deviation of variables. The APNN is applied to predict the stability number of armor blocks of breakwaters using the experimental data of＇ van der Meet, and the estimated results of the APNN are compared with those of an empirical formula and a previous artificial neural network （ANN） model. The APNN shows better results in predicting the stability number of armor bilks of breakwater and it provided the promising probabilistic viewpoints by using the individual standard deviation in a variable.

Transverse effects in photorefractive two-wave mixing

In a biased photorefractive crystal, the process of two one-dimensional waves mixing, i.e., the dynamical evolution of both pump beam and signal beam, is traced by numerically solving the coupled-wave equation. Direct simulations show that the propagation and stability of the two beams are completely determined by the system parameters, such as the external bias field, the intensity and the beam waist of the pump beam. By adjusting these parameters, one can control the state of two Gaussian waves mixing. The numerical results are helpful for performing a two-wave mixing experiment.