Class Of Kernel Research Articles

Trend to equilibrium solution for the discrete Safronov–Dubovskiĭ aggregation equation with forcing

We consider the discrete Safronov-Dubovskiĭ aggregation equation associated with the physical condition, where particle injection and extraction take place in the dynamical system. In application, this model is used to describe the aggregation of particle-monomers in combination with sedimentation of particle-clusters. More precisely, we prove well-posedness of the considered model for a large class of aggregation kernel with source and efflux coefficients. Furthermore, over a long time period, we prove that the dynamical model attains a unique equilibrium solution with an exponential rate under a suitable condition on the forcing coefficient.

A New full-newton step infeasible interior-point method for P∗(κ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_*(\\kappa )$$\\end{document}-linear Complementarity problem

In this paper, we suggest a new infeasible interior-point method (IIPM) for P∗(κ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{*}(\\kappa )$$\\end{document}-linear complementarity problem (P∗(κ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{*}(\\kappa )$$\\end{document}-LCP) based on a new class of kernel functions with full-Newton steps. Each iteration of the algorithm consists of a feasible step and a few centering steps. The feasible step is defined by the newly proposed kernel functions, while the centering step is determined by using Newton’s method. New class of kernel functions includes a logarithmic kernel function in Roos (SIAM J Optim 16:1110–1136, 2006) and a trigonometric kernel function in Moslemi and Kheirfam (Optim Lett 13:127–157, 2019), Kheirfam and Haghighi (Commun Comb Optim 3:51–70, 2018), Fathi-Hafshejani et al. (J Appl Math Comput 48:111–128, 2015) as special cases. And we show that the proposed algorithm has the best known complexity for P∗(κ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_*(\\kappa )$$\\end{document}-LCP for such a method and present some numerical results.

Positive definite kernels on the set of integers, stability, some properties and applications

"We define and investigate a class of positive de nite kernel so called equivalent-kernel. We formulate and prove an analogous of Paley-Wiener theorem in the context of positive definite kernel. The main ingredient in the proof is Kolmogorov decomposition. Finally, some applications to stochastic processes are given."

Kernel L‐Ideals and L‐Congruence on a Subclass of Ockham Algebras

In this paper, we study L‐congruences and their kernel in a subclass of the variety of Ockham algebras A. We prove that the class of kernel L‐ideals of an Ockham algebra forms a complete Heyting algebra. Moreover, for a given kernel L‐ideal ξ on A, we obtain the least and the largest L‐congruences on A having ξ as its kernel.

IMPLEMENTASI SUPPORT VECTOR MACHINE DALAM MEMPREDIKSI HARGA RUMAH PADA PERUMAHAN DI KOTA BANDAR LAMPUNG

Machine Learning has been widely used in terms of predictions for analyzing datasets. One method of Machine Learning is Support Vector Machine (SVM). The house has an important role in the survival of human beings. With the times, many developers are competing to build housing. The purpose of this study is to predicted the housing cost using Support Vector Machine. The data in this research used the data of house in Bandar lampung, the price, the location and the building specification. The amount of data used 51 datas and 33 variables with regression and classification, also used 3 kernels and it's model, 12 times first trial and next 6 experiments done with fitur selection. The trial result was kernel regression polynomial model reached the highest R 2 that was 95,99% linear kernel and gaussian kernel reached R 2 90,99% and 81,43% each. While in accuration classification model trial is obtained in 8 class of gaussian kernel as big as 91,18%, and linear kernel and polynimonal kernel get an accuracy of 90,20% and 89,90%.

Specification Testing for Nonlinear Cointegrating Regression

We provide a limit theory for a general class of kernel smoothed U statistics that may be used for specification testing in time series regression with nonstationary data. The framework allows for linear and nonlinear models of cointegration and regressors that have autoregressive unit roots or near unit roots. The limit theory for the specification test depends on the self intersection local time of a Gaussian process. A new weak convergence result is developed for certain partial sums of functions involving nonstationary time series that converges to the intersection local time process. This result is of independent interest and useful in other applications.

A new general decay result for abstract evolution equation with time-dependent nonlinear dissipation

The following abstract problem: $$\begin{aligned} u_{tt}(t)+A u(t)-\int _{0}^{t}g(t-s)A u(s)ds+\eta (t)h(u_t)=\nabla F (u(t)) \end{aligned}$$ of second order evolution equation with time-dependent dissipation is considered. We prove, under a very general and wide class of kernel, a decay result. We establish optimal explicit and general decay rate results, using the multiplier method and some properties of the convex functions. Our result improves and generalizes many other results in the literature.

RETRACTED ARTICLE: Application of combined kernel function artificial intelligence algorithm in mobile communication network security authentication mechanism

Security threats, security requirements, and adopted security policies in the new mobile environment have changed. As a key issue in the development of mobile communication, the mobile communication network security authentication mechanism has attracted the attention of academic circles and industry, and research on its security has become a research hotspot. Firstly, aiming at the security threats and security requirements in the heterogeneous mobile communication network environment, the architecture of the security authentication mechanism in this mobile environment is proposed. The security architecture consists of three layers (transport layer, service layer, application layer) and four domains (user domain, access domain, network domain, and application domain), and defined security features. The security architecture includes functional entities such as public key infrastructure and application servers and defines new security features for security threats in the application domain and user domain, so that the security architecture can meet the heterogeneous mobile communication network environment. Security needs. Secondly, a linear combination kernel function is used to construct a new class of kernel functions with different characteristics in a linear combination and satisfy the Mercer theorem. The combined kernel function has both global kernel function and local kernel. The advantages function and their weight on the combined kernel function can be adjusted by the weight coefficient factor, and a better comprehensive prediction effect is obtained in the support vector machine model. Finally, the experimental results also show that the support vector regression machine model based on combined kernel function can achieve higher learning precision.

On the Lyapunov Matrix for Integral Delay Systems with a Class of General Kernel

We study integral delay systems with exponential kernel. The computation of the Lyapunov matrix is shown to reduce to an auxiliary system of differential equations with boundary conditions of mixed type. We prove that the solution of the auxiliary system exist and is unique if the integral delay system satisfies the Lyapunov condition.

A fully discrete Galerkin method for Abel-type integral equations

In this paper, we present a Galerkin method for Abel-type integral equation with a general class of kernel. Stability and quasi-optimal convergence estimates are derived in fractional-order Sobolev norms. The fully-discrete Galerkin method is defined by employing simple tensor-Gauss quadrature. We develop a corresponding perturbation analysis which allows to keep the number of quadrature points small. Numerical experiments have been performed which illustrate the sharpness of the theoretical estimates and the sensitivity of the solution with respect to some parameters in the equation.

A large-update primal–dual interior-point algorithm for second-order cone optimization based on a new proximity function

In this paper, we propose a large-update primal–dual interior-point algorithm for second-order cone optimization (SOCO) based on a class of kernel functions consisting of a trigonometric barrier term. The algorithm starts from a strictly feasible point and generates a sequence of points converging to an optimal solution of the problem. Using a simple analysis, we show that the algorithm has worst case iteration complexity for large-update primal–dual interior point methods which coincides with the so far best-known iteration bound for SOCO.

A class of kernel based real-time elastography algorithms

In this paper, a novel real-time kernel-based and gradient-based Phase Root Seeking (PRS) algorithm for ultrasound elastography is proposed. The signal-to-noise ratio of the strain image resulting from this method is improved by minimizing the cross-correlation discrepancy between the pre- and post-compression radio frequency signals with an adaptive temporal stretching method and employing built-in smoothing through an exponentially weighted neighborhood kernel in the displacement calculation. Unlike conventional PRS algorithms, displacement due to tissue compression is estimated from the root of the weighted average of the zero-lag cross-correlation phases of the pair of corresponding analytic pre- and post-compression windows in the neighborhood kernel. In addition to the proposed one, the other time- and frequency-domain elastography algorithms (Ara et al., 2013; Hussain et al., 2012; Hasan et al., 2012) proposed by our group are also implemented in real-time using Java where the computations are serially executed or parallely executed in multiple processors with efficient memory management. Simulation results using finite element modeling simulation phantom show that the proposed method significantly improves the strain image quality in terms of elastographic signal-to-noise ratio (SNRe), elastographic contrast-to-noise ratio (CNRe) and mean structural similarity (MSSIM) for strains as high as 4% as compared to other reported techniques in the literature. Strain images obtained for the experimental phantom as well as in vivo breast data of malignant or benign masses also show the efficacy of our proposed method over the other reported techniques in the literature.

Integral invariants for space motion trajectory matching and recognition

Motion trajectories provide a key and informative clue in motion characterization of humans, robots and moving objects. In this paper, we propose some new integral invariants for space motion trajectories, which benefit effective motion trajectory matching and recognition. Integral invariants are defined as the line integrals of a class of kernel functions along a motion trajectory. A robust estimation of the integral invariants is formulated based on the blurred segment of noisy discrete curve. Then a non-linear distance of the integral invariants is defined to measure the similarity for trajectory matching and recognition. Such integral invariants, in addition to being invariant to transformation groups, have some desirable properties such as noise insensitivity, computational locality, and uniqueness of representation. Experimental results on trajectory matching and sign recognition show the effectiveness and robustness of the proposed integral invariants in motion trajectory matching and recognition.

Generalizing the Mahalanobis distance via density kernels

The Mahalanobis distance (MD) is a distance widely used in Statistics, Machine Learning and Pattern Recognition. When the data come from a Gaussian distribution, the MD uses the covariance matrix to evaluate the distance between a data point and the distribution mean. In this paper, we generalize the MD for general unimodal distributions, introducing a particular class of Mercer kernel, the density kernel, based on the underlying data density. Density kernels induce distances that generalize the MD and that are useful when data do not fit to the Gaussian distribution. We study the theoretical properties of the proposed distance and show its performance on a variety of artificial and real data analysis problems.

STRONGLY ORTHODOX CONGRUENCES ON AN -INVERSIVE SEMIGROUP

AbstractIn this paper we investigate some subclasses of strongly regular congruences on an $E$-inversive semigroup $S$. We describe the minimum and the maximum strongly orthodox congruences on $S$ whose characteristic trace coincides with the characteristic trace of given congruences and, in each case, we present an alternative characterization for them. A description of all strongly orthodox congruences on $S$ with characteristic trace $\tau $ is given. Further, we investigate the kernel relation of strongly orthodox congruences on an $E$-inversive semigroup and give the least and the greatest element in the class of the same kernel with a given congruence.

3-Col problem modelling using simple kernel P systems

This paper presents the newly introduced class of (simple) kernel P systems ((s)kP systems) and investigates through a 3-colouring problem case study the expressive power and efficiency of kernel P systems. It describes two skP systems that model the problem and analyses them in terms of efficiency and complexity. The skP models prove to be more succinct (in terms of number of rules, objects, number of cells and execution steps) than the corresponding tissue P system, available in the literature, that solves the same problem, at the expense of a greater length of the rules.

A specification test for nonlinear nonstationary models

We provide a limit theory for a general class of kernel smoothed U-statistics that may be used for specification testing in time series regression with nonstationary data. The test framework allows for linear and nonlinear models with endogenous regressors that have autoregressive unit roots or near unit roots. The limit theory for the specification test depends on the self-intersection local time of a Gaussian process. A new weak convergence result is developed for certain partial sums of functions involving nonstationary time series that converges to the intersection local time process. This result is of independent interest and is useful in other applications. Simulations examine the finite sample performance of the test.

A class of new large-update primal-dual interior-point algorithms for P *(κ) nonlinear complementarity problems

In this paper we propose a class of new large-update primal-dual interior-point algorithms for P *(κ) nonlinear complementarity problem (NCP), which are based on a class of kernel functions investigated by Bai et al. in their recent work for linear optimization (LO). The arguments for the algorithms are followed as Peng et al.’s for P *(κ) complementarity problem based on the self-regular functions [Peng, J., Roos, C., Terlaky, T.: Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms, Princeton University Press, Princeton, 2002]. It is worth mentioning that since this class of kernel functions includes a class of non-self-regular functions as special case, so our algorithms are different from Peng et al.’s and the corresponding analysis is simpler than theirs. The ultimate goal of the paper is to show that the algorithms based on these functions have favorable polynomial complexity.

Interior point algorithm for [formula omitted] nonlinear complementarity problems

In this paper, we propose a new large-update primal–dual interior point algorithm for P ∗ complementarity problems (CPs). Different from most interior point methods which are based on the logarithmic kernel function, the new method is based on a class of kernel functions ψ ( t ) = ( t p + 1 − 1 ) / ( p + 1 ) + ( t − q − 1 ) / q , p ∈ [ 0 , 1 ] , q > 0 . We show that if a strictly feasible starting point is available and the undertaken problem satisfies some conditions, then the new large-update primal–dual interior point algorithm for P ∗ CPs has O ( ( 1 + 2 κ ) n log n log ( n μ 0 / ε ) ) iteration complexity which is currently the best known result for such methods with p = 1 and q = ( log n ) / 2 − 1 .

Uniform $l^1$ Behavior of a Time Discretization Method for a Volterra Integrodifferential Equation with Convex Kernel; Stability

We study stability of a numerical method in which the backward Euler method is combined with order one convolution quadrature for approximating the integral term of the linear Volterra integrodifferential equation $\mathbf{u}'(t)+\int_{0}^{t}\beta(t-s)\mathbf{Au}(s)\,ds=0$, $t\geq0$, $\mathbf{u}(0)=\mathbf{u}_{0}$, which arises in the theory of linear viscoelasticity. Here $\mathbf{A}$ is a positive self-adjoint densely defined linear operator in a real Hilbert space, and $\beta(t)$ is locally integrable, nonnegative, nonincreasing, convex, and $-\beta'(t)$ is convex. We establish stability of the method under these hypotheses on $\beta(t)$. Thus, the method is stable for a wider class of kernel functions $\beta(t)$ than was previously known. We also extend the class of operators $\mathbf{A}$ for which the method is stable.