Kernel Type Research Articles

Convexity, monotonicity, and positivity results for sequential fractional nabla difference operators with discrete exponential kernels

We consider positivity, monotonicity, and convexity results for discrete fractional operators with exponential kernels. Our results cover both the sequential and nonsequential cases, and we demonstrate both similarities and dissimilarities between the exponential kernel case and fractional differences with other types of kernels. This shows that the qualitative information gleaned in the exponential kernel case is not precisely the same as in other cases.

Global Plemelj Formula of Slice Dirac Operator in Octonions with Complex Spine

Slice analysis is generalized to the setting of octonions with new book structure whose spine consists of a complex plane instead of the real axis. The theory leads to the study of the slice Dirac operator. The associated Cauchy type kernel turns out to be operator-valued rather than function-valued, in contrast to the associative case. The global Plemelj jump formula is established on the boundary of any axially symmetric domain of octonions.

Prediction of Unknown Fault of Induction Motor using SVM following Decision-Directed Acyclic Graph

Prediction of unknown fault of induction motor is an important task to prevent it from unscheduled shutdown. Here, an unknown fault of induction motor has been classified and authenticated from other type of faults using multiclass support vector machine (SVM) following decision-directed acyclic graph (DDAG). Three phase current data samples are collected from induction motors with different known type of fault conditions and one induction motor with unknown type fault condition. Experiment has been performed for motor fault current signature analysis (MFCSA) to identify the type of unknown fault among the mixture of various type of faults. A feature extraction and dimensions reduction process called principal component analysis (PCA) is used to extract the information from fault current signature of each faulty motor and two eigenvalues of stator currents which are called principal components are effective fault features of the motors are captured with the help of PCA transformation. One vs one (OVO) SVM algorithm is applied to separate each pair of classes out of six classes nonlinearly by RBF type kernel assigning the unknown test sample to the class. The multiple PC values of each phase of each faulty induction motor are considered as one class. The OVO-SVM constructs n (n-1)/2 no of classifiers for n class problem of each phase and DDAG technique is used to create a directed acyclic graph using the classifiers to take accurate decision about the classification of the unknown fault. The unknown fault is classified for each phase among different type of faults depending on maximum membership count generated by classifiers and the fault is also authenticated from the results of DDAG of three phases.

Approximation methods for system of nonlinear Fredholm–Hammerstein integral equations

In this article, we apply projection methods and their iterated versions to approximate the solution of system of Fredholm–Hammerstein integral equations with both smooth and weakly singular kernels of algebraic and logarithmic type using the piecewise polynomial basis functions. We show that the iterated Galerkin approximate solution converges to the exact solution faster than the Galerkin approximate solution for both smooth and weakly singular algebraic and logarithmic type kernels. We improve these results further in iterated multi-Galerkin method. Numerical results are provided for the illustration of the theoretical results.

A generalized integro-differential theory of nonlocal elasticity of n-Helmholtz type: part I—analytical formulation and thermodynamic framework

A generalized theory of nonlocal elasticity is elaborated. The proposed integral type nonlocal formulation is based on attenuation functions being assumed as the convolution product of n first order (Eringen type) kernels. The theory stems from a generalized higher-order constitutive relation between the nonlocal stress and the local strain. Inspired by the Eringen two-phase local/nonlocal integral model, this theory can also be thought of as the constitutive relation for an (n + 1)-phase material, in which one phase has local elastic behavior, and the remaining n phases comply with nonlocal elasticity of higher order. The theory is supported by a suitable thermodynamic framework. In the spirit of Eringen’s 1983 paper, the particular family of attenuation functions adopted are the Green functions associated with generalized Helmholtz type differential operators of order n —which suggests denoting this model as a generalized nonlocal elasticity theory of n-Helmholtz type. Besides the integral type nonlocal formulation, elegant and compact expressions for the differential and integro-differential counterpart are derived. For n = 1 this formulation straightforwardly leads to the Aifantis 2003 implicit gradient elasticity theory with simultaneous stress gradients and strain gradients, which was postulated to eliminate stress and strain singularities from crack tips and dislocation lines. For n = 2 an implicit gradient elasticity formulation with bi-Helmholtz type stress and strain gradients is obtained. The paper is complemented by a companion Part II on the particularization of the generalized theory of nonlocal elasticity for the one-dimensional case, along with some applications in statics and dynamics.

Efficient Processing of Sparse Tensor Decomposition via Unified Abstraction and PE-Interactive Architecture

We propose a novel architecture to efficiently perform sparse tensor decomposition/completion. As the generalization of vectors and matrices, tensors are widely used to process high-dimensional data. Sparse tensor decomposition (SpTD) is not only an emerging tensor analysis technique but also an effective tool to reduce the storage and computation costs of tensors. However, conventional general-purpose processors are inefficient to perform SpTD, mainly due to: i) variable sparsity degree and flexible buffer size requirement; ii) difficulties of fusing multiple execution kernels to pursue better performance. For domain-specific accelerator designers on the other hand, the diversity of decomposition algorithms is also an important problem that must be considered. To solve these challenges, we propose a unified abstraction for SpTD algorithms and design a specialized accelerator. First, we formulate two types of core kernels (SpLrMM and LrSampling) that serve as a standard form to fit a broad range of SpTD algorithms. Second, we design a sparse tensor engine (STE) to efficiently perform SpTD. STE uses a processing element (PE)-interactive architecture where PEs can be flexibly grouped together via Network-on-Chip (NoC) to share the buffer capacity, bandwidth, and compute resources. We evaluate our accelerator with extensive experiments, and it can achieve an average speedup of 45× over CPU and 29× over GPU.

Mathematical analysis of tuberculosis control model using nonsingular kernel type Caputo derivative

This research work investigates some theoretical and semi-analytical results for the mathematical model of tuberculosis disease via derivative due to Caputo and Fabrizio. The concerned derivative involves exponential kernel and very recently it has been adapted for various applied problems. The required results are established by using some fixed point approach of Krasnoselskii and Banach. Further, by the use of iterative tools of Adomian decomposition and Laplace, the semi-analytical results are studied. Some graphical results are given with discussion.

Improving the sorting efficiency of maize haploid kernels using an NMR-based method with oil content double thresholds

BackgroundMaize haploid breeding technology can be used to rapidly develop homozygous lines, significantly shorten the breeding cycle and improve breeding efficiency. Rapid and accurate sorting haploid kernels is a prerequisite for the large-scale application of this technology. At present, the automatic haploid sorting based on nuclear magnetic resonance (NMR) using a single threshold method has been realized. However, embryo-aborted (EmA) kernels are usually produced during in vivo haploid induction, and both haploids and EmA kernels have lower oil content and are separated together using a single threshold method based on NMR. This leads to a higher haploid false discrimination rate (FDR) and requires secondary manual sorting to select the haploid kernels from the mixtures, which increases the sorting cost and decreases the haploid sorting efficiency. In order to improve the correct discrimination rate (CDR) in sorting haploids, a method to distinguish EmA kernels is required.ResultsSingle kernel weight and oil content were measured for the diploid, haploid, and EmA kernels derived from three maize hybrids and nine inbred lines by in vivo induction. The results showed that the distribution of oil content showed defined boundaries between the three types of kernels, while the single kernel weight didn't. According to the distribution of oil content in the three types of kernels, a double-threshold method was proposed to distinguish the embryo-aborted kernels, haploid and diploid kernels based on NMR and their oil content. The double thresholds were set based on the minimum oil content of diploid kernels and the maximum content of EmA kernels as the upper and lower boundary values, respectively. The CDR of EmA kernels in different maize materials was > 97.8%, and the average FDR was reduced by 27.9 percent.ConclusionsThe oil content is an appropriate indicator to discriminate diploid, haploid and EmA kernels. An oil content double-threshold method based on NMR was first developed in this study to identify the three types of kernels. This methodology could reduce the FDR of haploids and improve the sorting efficiency of automated sorting system. Thus, this technique represents a potentially efficient method for haploid sorting and provides a reference for the process of automated sorting of haploid kernels with high efficiency using NMR.

Study on variability in resistance to barley yellow dwarf virus (BYDV-PAV) among Ethiopian barley (Hordeum vulgare L.) landraces

Ethiopian barley landraces are recognized as an important genetic resource with which a search for tolerance to biotic stresses is of worth. In present study, 585 barley (Hordeum vulgare L.) landraces collected from 13 barley producing zones of Ethiopia were evaluated along with 10 improved checks for resistance to BYDV serotype PAV under field conditions at Sinana and Goba during 2018 and 2019 cropping seasons. The trial was laid out in an augmented design consisting of six blocks. Data on disease incidence, severity and some agronomic traits were recorded. The result of analysis showed highly significant variations among landraces for disease incidence, severity and agronomic traits. The BYDV incidence and severity varied from 0.90 to 45.3% and 12.0 to 58.0%, respectively. Similarly, significant variations in terms of regions of origin, altitude classes and kernel row number were observed among landraces. Landraces originated from Arsi, Gojam, Bale and Gonder had significantly lower disease incidence and severity levels than others. Furthermore, landraces collected from altitude class IV (above 2500 m) and those with 6-row and irregular kernel type had lower disease severity. Segregation in infection was observed in some landraces due to a reduction of disease severity and 68 landraces showing lowest disease severity were selected. The resistant landraces identified in the present investigation can be utilized as good resource for barley improvement program targeting BYDV, which subsequently will help to incorporate the resistant genes into several elite backgrounds of barley.

Parameter Optimization of Support Vector Regression Using Harris Hawks Optimization

Abstract Support Vector Regression (SVR) is often used in forecasting. Adjustment of parameters in the SVR affects the results of forecasting. This study aims to analyze the SVR method that is optimized using Harris Hawks Optimization (HHO), hereinafter referred to as HHO-SVR. The HHO-SVR was evaluated using five benchmark datasets to determine the performance of this method. The HHO process is also compared based on the type of kernel and other metaheuristic algorithms. The results showed that the HHO-SVR has almost the same performance as other methods but is less efficient in terms of time. In addition, the type of kernel also affects the process and results.

Numerical simulation of the fractal-fractional reaction diffusion equations with general nonlinear

<abstract> In this paper a new approach to the use of kernel operators derived from fractional order differential equations is proposed. Three different types of kernels are used, power law, exponential decay and Mittag-Leffler kernels. The kernel's fractional order and fractal dimension are the key parameters for these operators. The main objective of this paper is to study the effect of the fractal-fractional derivative order and the order of the nonlinear term, $ 1 &lt; q &lt; 2 $, in the equation on the behavior of numerical solutions of fractal-fractional reaction diffusion equations (FFRDE). Iterative approximations to the solutions of these equations are constructed by applying the theory of fractional calculus with the help of Lagrange polynomial functions. In key parameter regimes, all these iterative solutions based on a power kernel, an exponential kernel and a generalized Mittag-Leffler kernel are very close. Hence, iterative solutions obtained using one of these kernels are compared with full numerical solutions of the FFRDE and excellent agreement is found. All numerical solutions in this paper were obtained using Mathematica. </abstract>

Support vector machine in predicting epoxy glass powder mixed cement concrete

An experimental study is carried out on the utilization of epoxy glass powder (EGP) as a percentage replacement of fine aggregate in concrete, which is a by-product of E-waste obtained after removal of metals from it. The specimens of concrete with and without EGP as fine aggregate are cured in a standard condition using the membrane to obtain mechanical properties and to exhibit a good strength. Results show that the weight of concrete is reduced in the range of 3% to 9% when it is replaced by EGP from 10% to 50%, respectively. For the constant water-cement ratio of 0.4, the workability of concrete is increased as the EGP increases. But the compressive strength of concrete is decreased as the EGP increases. The compressive strength of concrete identified with EGP squander more by 10% strength with 10% EGP, and the remaining mix is lesser in examination with control blend solid specimen, but it is in the required range of M20 grade. The Support Vector Machine (SVM) method, which is a unique specific loss function and kernel type, is applied to experimental data. SVM with different kernel functions is performed, among them, erbf kernel function gives higher CC 0.9623 and lower RMSE 1.0939 for test data, respectively, as compared to other functions. The predicted test compressive strengths are closed to observed values.

Separation of Empty Kernels Using the Physical Properties of Short-Grain Rough Rice

Highlights Physical properties of whole rough rice and empty kernels of five short-grain rice varieties were measured. Geometric traits of kernels could not be used for the separation of empty kernels from whole kernels. Separation of kernels can be achieved based on weight difference between whole and empty kernels. Air velocity in pre-cleaners should be set between the terminal velocities of whole and empty kernels. Abstract . The key factors required to separate empty kernels (EKs) from whole kernels (WKs) were investigated in rough rice varieties. The geometric properties and 1000-grain weight of rough rice WKs and EKs of five varieties of short-grain rice with varying moisture content were measured. The terminal velocities for floating and dropping of WKs and EKs were tested in a vertical air column to identify the aerodynamic separation characteristics. The separation of EKs from WKs based on kernel geometric characteristics was not possible because of insignificant differences between WKs and EKs in terms of length, width, roundness, and other geometric characteristics. The 1000-grain weight of WKs and EKs ranged from 23.7 to 29.2 g and from 3.9 to 8.5 g, respectively. Linear regression equations were used to determine the relationship between terminal velocity and moisture content in both floating and dropping phase. The allowable floating and dropping terminal velocity range for separating WKs and EKs ranged from 5.0 to 7.6 m s-1 and from 2.1 to 4.1 m s-1, respectively. Moisture content, and especially, kernel type and terminal velocity type had significant effects on the terminal velocity. Keywords: Empty kernel, Physical property, Rough rice, Separating, Terminal velocity.

Applying Synthetic Minority Over-sampling Technique and Support Vector Machine to Develop a Classifier for Parkinson’s disease

As the number of Parkinson’s disease patients increases in the elderly population, it has become a critical issue to understand the early characteristics of Parkinson’s disease and to detect Parkinson’s disease as soon as possible during normal aging. This study minimized the imbalance issue by employing Synthetic Minority Over-sampling Technique (SMOTE), developed eight Support Vector Machine (SVM) models for predicting Parkinson’s disease using different kernel types {(C-SVM or Nu-SVM)×(Gaussian kernel, linear, polynomial, or sigmoid algorithm)}, and compared the accuracy, sensitivity, and specificity of the developed models. This study evaluated 76 senior citizens with Parkinson’s disease (32 males and 44 females) and 285 healthy senior citizens without Parkinson’s disease (148 males and 137 females). The analysis results showed that the liner kernel-based Nu-SVM had the highest sensitivity (62.0%), specificity (81.6%), and overall accuracy (71.3%). The major negative relationship factors of the Parkinson’s disease prediction model were MMSE-K, Stroop Test, Rey Complex Figure Test (RCFT), verbal memory test, ADL, IADL, 70 years old or older, middle school graduation or below, and women. When the influence of variables was compared using “functional weight”, RCFT was identified as the most influential variable in the model for distinguishing Parkinson’s disease from healthy elderly. The results of this study implied that developing a prediction model by using linear kernel-based Nu-SVM would be more accurate than other kernel-based SVM models for handling imbalanced disease data.

Hybrid Sooty Tern Optimization and Differential Evolution for Feature Selection

In this paper, a hybrid model based on sooty tern optimization algorithm (STOA) is proposed to optimize the parameters of the support vector machine (SVM) and identify the best feature sets simultaneously. Feature selection is an essential process of data preprocessing, and it aims to find the most relevant subset of features. In recent years, it has been applied in many practical domains of intelligent systems. The application of SVM in many fields has proved its effectiveness in classification tasks of various types. Its performance is mainly determined by the kernel type and its parameters. One of the most challenging process in machine learning is feature selection, intending to select effective and representative features. The main disadvantages of feature selection processes included in classical optimization algorithm are local optimal stagnation and slow convergence. Therefore, the hybrid model proposed in this paper merges the STOA and differential evolution (DE) to improve the search efficiency and convergence rate. A series of experiments are conducted on 12 datasets from the UCI repository to comprehensively and objectively evaluate the performance of the proposed method. The superiority of the proposed method is illustrated from different aspects, such as the classification accuracy, convergence performance, reduced feature dimensionality, standard deviation (STD), and computation time.

Trimmed extreme value estimators for censored heavy-tailed data

We consider estimation of the extreme value index and extreme quantiles for heavy–tailed data that are right-censored. We study a general procedure of removing low importance observations in tail estimators. This trimming procedure is applied to the state-of-the-art estimators for randomly right-censored tail estimators. Through an averaging procedure over the amount of trimming we derive new kernel type estimators. Extensive simulation suggests that one of the new considered kernels leads to a highly competitive estimator against virtually any other available alternative in this framework. Moreover we propose an adaptive selection method for the amount of top data used in estimation based on the trimming procedure minimizing the asymptotic mean squared error. We also provide an illustration of this approach to simulated as well as to real-world MTPL insurance data.

Asymptotic normality of conditional density and conditional mode in the functional single index model

The main objective of this paper is to investigate the nonparametric estimation of the conditional density of a scalar response variable Y, given the explanatory variable X taking value in a Hilbert space when the sample of observations is considered as an independent random variables with identical distribution (i.i.d) and are linked with a single functional index structure. First of all, a kernel type estimator for the conditional density function (cond-df) is introduced. Afterwards, the asymptotic properties are stated for a conditional density estimator when the observations are linked with a single-index structure from which one derives a central limit theorem (CLT) of the conditional density estimator to show the asymptotic normality of the kernel estimate of this model. As an application the conditional mode in functional single-index model is presented, and the asymptotic (1 – ζ) confidence interval of the conditional mode function is given for 0

Formation of sets of independent components of a multidimensional random variable based on a nonparametric pattern recognition algorithm

The possibility of circumventing the problem of decomposition of the range of values of random variables when testing various hypotheses is considered. A brief review of the literature on this problem is given. A method for forming sets of independent components of a multidimensional random variable is proposed, based on hypotheses testing about the independence of paired combinations of components of a multidimensional random variable. The method uses a two-dimensional non-parametric algorithm for pattern recognition of the kernel type, corresponding to the criterion of maximum likelihood. In contrast to the traditional method based on the application of the Pearson criterion, the proposed approach avoids the problem of decomposing the range of values of random variables into multidimensional intervals. The results of computational experiments performed according to the method of forming sets of independent random variables are presented. Using the information obtained, an information graph is constructed, the vertices of which correspond to the components of a multidimensional random variable, and the edges determine their independence. Then the vertices of the complete subgraphs correspond to groups of independent components of a random variable. The obtained results form the basis for the synthesis of a multi-level nonparametric large volume data processing system, each level of which corresponds to a specific set of independent random variables.

An analysis for Klein–Gordon equation using fractional derivative having Mittag–Leffler‐type kernel

Within this paper, we present an analysis of the fractional model of the Klein–Gordon (K‐G) equation. K‐G equation is considered as one of the significant equations in mathematical physics that describe the interaction of soliton in a collision less plasma. In a novel aspect of this work, we have used the latest form of fractional derivative (FCs), which contains the Mittag–Leffler type of kernel. The homotopy analysis transform method (HATM) is being taken to solve the fractional model of the K‐G equation. A convergence study of HATM has been studied. The existence and uniqueness of the solution for the fractional K‐G equation are presented. For verifying the obtained numerical outcomes regarding accuracy and competency, we have given different graphical presentations. Figures are reflecting that a novel form of the technique is a good organization in respect of proficiency and accurateness to solve the mentioned fractional problem.

Non parametric bias reduction of diffusion coefficient in integrated diffusion processes

In this paper, we propose a non parametric functional estimator for diffusion coefficient in integrated stochastic diffusion process. The asymptotic bias of the kernel type estimator and the new proposed non parametric estimator for diffusion coefficient are developed when the time span is fixed, and we can see that the new non parametric estimator has a smaller asymptotic bias than the kernel estimator. Moreover, the consistency and the asymptotic normality of the new proposed non parametric estimator are explored under some mild conditions.