Lateral interaction by Laplacian‐based graph smoothing for deep neural networks

Lateral interaction in the biological brain is a key mechanism that underlies higher cognitive functions.Linear self‐organising map(SOM)introduces lateral interaction in a general form in which signals of any modality can be used.Some approaches directly incorporate SOM learning rules into neural networks,but incur complex operations and poor extendibility.The efficient way to implement lateral interaction in deep neural networks is not well established.The use of Laplacian Matrix‐based Smoothing(LS)regularisation is proposed for implementing lateral interaction in a concise form.The authors’derivation and experiments show that lateral interaction implemented by SOM model is a special case of LS‐regulated k‐means,and they both show the topology‐preserving capability.The authors also verify that LS‐regularisation can be used in conjunction with the end‐to‐end training paradigm in deep auto‐encoders.Additionally,the benefits of LS‐regularisation in relaxing the requirement of parameter initialisation in various models and improving the classification performance of prototype classifiers are evaluated.Furthermore,the topologically ordered structure introduced by LS‐regularisation in feature extractor can improve the generalisation performance on classification tasks.Overall,LS‐regularisation is an effective and efficient way to implement lateral interaction and can be easily extended to different models.

THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS

In this work,we study the linearized Landau equation with soft potentials and show that the smooth solution to the Cauchy problem with initial datum in L^(2)(ℝ^(3))enjoys an analytic regularization effect,and that the evolution of the analytic radius is the same as the heat equations.

An efficient non-iterative smoothed particle hydrodynamics fluid simulation method with variable smoothing length

In classical smoothed particle hydrodynamics(SPH)fluid simulation approaches,the smoothing length of Lagrangian particles is typically constant.One major disadvantage is the lack of adaptiveness,which may compromise accuracy in fluid regions such as splashes and surfaces.Attempts to address this problem used variable smoothing lengths.Yet the existing methods are computationally complex and non-efficient,because the smoothing length is typically calculated using iterative optimization.Here,we propose an efficient non-iterative SPH fluid simulation method with variable smoothing length(VSLSPH).VSLSPH correlates the smoothing length to the density change,and adaptively adjusts the smoothing length of particles with high accuracy and low computational cost,enabling large time steps.Our experimental results demonstrate the advantages of the VSLSPH approach in terms of its simulation accuracy and efficiency.

Structure-oriented edge-preserving smoothing based on accurate estimation of orientation and edges

In this paper, we present a new method for reducing seismic noise while preserving structural and stratigraphic discontinuities. Structure-oriented edge-preserving smoothing requires information such as the local orientation and edge of the reflections. The information is usually estimated from seismic data with full frequency bandwidth. When the data has a very low signal to noise ratio （SNR）, the noise usually reduces the estimation accuracy. For seismic data with extremely low SNR, the dominant frequency has higher SNR than other frequencies, so it can provide orientation and edge information more reliably than other frequencies. Orientation and edge are usually described in terms of apparent reflection dips and coherence differences, respectively. When frequency changes, both dip and coherence difference change more slowly than the seismogram itself. For this reason, dip and coherence estimated from dominant frequency data can approximately represent those of other frequency data. Ricker wavelet are widely used in seismic modeling. The Marr wavelet has the same shape as Ricker wavelets in both time and frequency domains, so the Marr wavelet transform is selected to divide seismic data into several frequency bands. Reflection apparent dip as well as the edge information can be obtained by scanning the dominant frequency data. This information can be used to selectively smooth the frequency bands （dominant, low, and high frequencies） separately by structure-oriented edge-preserving smoothing technology. The ultimate noise-suppressed seismic data is the combination of the smoothed frequency band data. Application to synthetic and real data shows the method can effectively reduce noise, preserve edges, improve trackable reflection continuity, and maintain useful information in seismic data.

Grey Smoothing Model for Predicting Mine Gas Emission

A grey smoothing model for predicting mine gas emission was presented by combining the grey system theory with the smoothing prediction technique. First of all, according to the variable sequence, GM(1,1) model was set up to predict the general development trend of variable as first fitted values, then the smoothing prediction technique was used to revise the fitted values so as to improve the accuracy of prediction. The results of application in the No.6 Coal Mine in Pingdingshan mining area show that the grey smoothing model has higher accuracy than that of GM(1,1) in predicting the variable sequence with strong fluctuation. The research provides a new scientific method for predicting mine gas emission.

An Enhanced Steepest Descent Method for Global Optimization-Based Mesh Smoothing

In order to speed up the global optimization-based mesh smoothing, an enhanced steepest descent method is presented in the paper. Numerical experiment results show that the method performs better than the steepest descent method in the global smoothing. We also presented a physically-based interpretation to explain why the method works better than the steepest descent method.

SMOOTHING NEWTON ALGORITHM FOR THE CIRCULAR CONE PROGRAMMING WITH A NONMONOTONE LINE SEARCH

In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.

Temporal Floorplanning Using Solution Space Smoothing Based on 3D-BSSG Structure

We develop a 3D bounded slice-surface grid （3D-BSSG） structure for representation and introduce the solution space smoothing technique to search for the optimal solution. Experiment results demonstrate that a 3D-BSSG structure based algorithm is very effective and efficient.

EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES

In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.

A novel coordinated control strategy considering power smoothing for a hybrid photovoltaic/battery energy storage system

This work presents a novel coordinated control strategy of a hybrid photovoltaic/battery energy storage(PV/BES) system. Different controller operation modes are simulated considering normal, high fluctuation and emergency conditions. When the system is grid-connected, BES regulates the fluctuated power output which ensures smooth net injected power from the PV/BES system. In islanded operation, BES system is transferred to single master operation during which the frequency and voltage of the islanded microgrid are regulated at the desired level. PSCAD/EMTDC simulation validates the proposed method and obtained favorable results on power set-point tracking strategies with very small deviations of net output power compared to the power set-point. The state-of-charge regulation scheme also very effective with SOC has been regulated between 32% and 79% range.

The most homogeneous dip-scanning method using edgepreserving smoothing for seismic noise attenuation

Highlighting and analyzing the geological features of faults and fractures in seismic data is particularly important for hydrocarbon exploration and exploitation since they are often essential for finding and delineating reservoirs. We apply edge-preserving smoothing （EPS） to seismic processing and propose a most homogeneous dip-scanning method. The method preserves the geological features, eliminate random noise efficiently, obtain dip information, and improve the accuracy of identifying the oil and gas traps.

Mesh Smoothing Method Based on Local Wave Analysis

As the mesh models usually contain noise data,it is necessary to eliminate the noises and smooth the mesh.But existed methods always lose geometric features during the smoothing process.Hence,the noise is considered as a kind of random signal with high frequency,and then the mesh model smoothing is operated with signal processing theory.Local wave analysis is used to deal with geometric signal,and then a novel mesh smoothing method based on the local wave is proposed.The proposed method includes following steps：Firstly,analyze the principle of local wave decomposition for 1D signal,and expand it to 2D signal and 3D spherical surface signal processing;Secondly,map the mesh to the spherical surface with parameterization,resample the spherical mesh and decompose the spherical signals by local wave analysis;Thirdly,propose the coordinate smoothing and radical radius smoothing methods,the former filters the mesh points＇ coordinates by local wave,and the latter filters the radical radius from their geometric center to mesh points by local wave;Finally,remove the high-frequency component of spherical signal,and obtain the smooth mesh model with inversely mapping from the spherical signal.Several mesh models with Gaussian noise are processed by local wave based method and other compared methods.The results show that local wave based method can obtain better smoothing performance,and reserve more original geometric features at the same time.

An Empirical Study of Good-Turing Smoothing for Language Models on Different Size Corpora of Chinese

Data sparseness has been an inherited issue of statistical language models and smoothing method is usually used to resolve the zero count problems. In this paper, we studied empirically and analyzed the well-known smoothing methods of Good-Turing and advanced Good-Turing for language models on large sizes Chinese corpus. In the paper, ten models are generated sequentially on various size of corpus, from 30 M to 300 M Chinese words of CGW corpus. In our experiments, the smoothing methods;Good-Turing and Advanced Good-Turing smoothing are evaluated on inside testing and outside testing. Based on experiments results, we analyzed further the trends of perplexity of smoothing methods, which are useful for employing the effective smoothing methods to alleviate the issue of data sparseness on various sizes of language models. Finally, some helpful observations are described in detail.

EXTENSION OF SMOOTHING FUNCTIONS TO SYMMETRIC CONE COMPLEMENTARITY PROBLEMS

The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity problems. Computable formulas for these functions and their Jacobians are derived. In addition, it is shown that these functions are Lipschitz continuous with respect to parameter # and continuously differentiable on J × J for any μ 〉 0.

ANALYTICAL SMOOTHING EFFECT OF SOLUTION FOR THE BOUSSINESQ EQUATIONS

In this article, we study the analytical smoothing effect of Cauchy problem for the incompressible Boussinesq equations. Precisely, we use the Fourier method to prove that the Sobolev H^1 -solution to the incompressible Boussinesq equations in periodic domain is analytic for any positive time. So the incompressible Boussinesq equations admit exactly same smoothing effect properties of incompressible Navier-Stokes equations.

Micro-Mechanism of Silicon-Based Waveguide Surface Smoothing in Hydrogen Annealing

The micro-mechanism of the silicon-based waveguide surface smoothing is investigated systematically to explore the effects of silicon-hydrogen bonds on high-temperature hydrogen annealing waveguides. The effect of silicon- hydrogen bonds on the surface migration movement of silicon atoms and the waveguide surface topography are revealed. The micro-migration from an upper state to a lower state of silicon atoms is driven by silicon- hydrogen bonding, which is the key to ameliorate the rough surface morphology of the silicon-based waveguide. The process of hydrogen annealing is experimentally validated based on the simulated parameters. The surface roughness declines from 1.523nm to 0.461 nm.

Visible and Near-Infrared Spectroscopy with Multi-Parameters Optimization of Savitzky-Golay Smoothing Applied to Rapid Analysis of Soil Cr Content of Pearl River Delta

Using visible and near-infrared (Vis-NIR) spectroscopy combined with partial least squares (PLS) regression, the rapid reagent-free analysis model for chromium (Cr) content in tideland reclamation soil in the Pearl River Delta, China was established. Based on Savitzky-Golay (SG) smoothing and PLS regression, a multi-parameters optimization platform (SG-PLS) covering 264 modes was constructed to select the appropriately spectral preprocessing mode. The optimal SG-PLS model was determined according to the prediction effect. The selected optimal parameters d, p, m and LV were 2, 6, 23 and 8, respectively. Using the validation samples that were not involved in modeling, the root mean square error (SEPV), relative root mean square error (R-SEPV) and correlation coefficients (RP, V) of prediction were 11.66 mg·kg-1, 10.7% and 0.722, respectively. The results indicated that the feasibility of using Vis-NIR spectroscopy combined with SG-PLS method to analyze soil Cr content. The constructed multi-parameters optimization platform with SG-PLS is expected to be applied to a wider field of analysis. The rapid detection method has important application values to large-scale agricultural production.

A Smoothing Neural Network Algorithm for Absolute Value Equations

In this paper, we give a smoothing neural network algorithm for absolute value equations (AVE). By using smoothing function, we reformulate the AVE as a differentiable unconstrained optimization and we establish a steep descent method to solve it. We prove the stability and the equilibrium state of the neural network to be a solution of the AVE. The numerical tests show the efficient of the proposed algorithm.

HAZARD REGRESSION WITH PENALIZED SPLINE:THE SMOOTHING PARAMETER CHOICE AND ASYMPTOTICS

In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.

NON-INTERIOR SMOOTHING ALGORITHM FOR FRICTIONAL CONTACT PROBLEMS

A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.