This paper discusses modiications of the convolution type kernel regression estimator. One modiication uses kernel quantile estimators and is analyzed more detailed. This regression estimator combines advantages of local polynomial and kernel regression estimators and can be applied for small to large sample size. Its properties are illustrated by simulation results and asymptotic theory. Espec...

We evaluate three link functions (square root, logit, and copula) and Matérn kernel in the kernel-based estimation of reflectance spectra of the Munsell Matte collection in the 400-700 nm region. We estimate reflectance spectra from RGB camera responses in case of real and simulated responses and show that a combination of link function and a kernel regression model with a Matérn kernel decreas...

Abstract Given an elliptic curve E and a finite subgroup G, Vélu’s formulae concern to a separable isogeny IG : E → E ′ with kernel G. In particular, for a point P ∈ E these formulae express the first elementary symmetric polynomial on the abscissas of the points in the set P +G as the difference between the abscissa of IG(P ) and the first elementary symmetric polynomial on the abscissas of th...

Bleher and Kuijlaars, and Daems and Kuijlaars showed that the correlation functions of the eigenvalues of a random matrix from unitary ensemble with external source can be expressed in terms of the ChristoffelDarboux kernel for multiple orthogonal polynomials. We obtain a representation of this Christoffel-Darboux kernel in terms of the usual orthogonal polynomials.

We describe a data complexity approach to kernel selection based on the behavior of polynomial and Gaussian kernels. Our results show how the use of a Gaussian kernel produces a gram matrix with useful local information that has no equivalent counterpart in polynomial kernels. By exploiting neighborhood information embedded by data complexity measures, we are able to carry out a form of meta-ge...

In the Connected Dominating Set problem we are given as input a graph G and a positive integer k, and are asked if there is a set S of at most k vertices of G such that S is a dominating set of G and the subgraph induced by S is connected. This is a basic connectivity problem that is known to be NP-complete, and it has been extensively studied using several algorithmic approaches. In this paper...

The polynomial space H in the span of the integer translates of a box spline M admits a well-known characterization as the joint kernel of a set of homogeneous differential operators with constant coefficients. The dual space H∗ has a convenient representation by a polynomial space P, explicitly known, which plays an important role in box spline theory as well as in multivariate polynomial inte...

Abstract This study employed soft computing techniques, namely, support vector machine (SVM) and Gaussian process regression (GPR) to predict the properties of a scour hole [depth (ds) length (Ls)] in diversion channel flow system. The considered different geometries channels (angles bed widths) hydraulic conditions. Four kernel function models for each technique (polynomial function, normalize...

We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability, Nonmonotonic and Bayesian Reasoning under structural restrictions. All these problems involve two tasks: (i) identifying the structure in the input as required b...

Using the framework of kernelization we study whether efficient preprocessing schemes for the Treewidth problem can give provable bounds on the size of the processed instances. Assuming the ANDdistillation conjecture to hold, the standard parameterization of Treewidth does not have a kernel of polynomial size and thus instances (G, k) of the decision problem of Treewidth cannot be efficiently r...