In this paper we present an explicit (rank one) function transform which contains several Jacobi-type function transforms and Hankel-type transforms as degenerate cases. The kernel of the transform, which is given explicitly in terms of basic hypergeometric series, thus generalizes the Jacobi function as well as the Bessel function. The kernel is named the Askey-Wilson function, since it provid...

Local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature. Their simplest version, the local constant estimator, can be easily extended to the errors-in-variables context by exploiting its similarity with the deconvolution kernel density estimator. The generalization of the higher order versions of the estimato...

The parameter identification for problems where losses arising from overestimation and underestimation are different and can be described by an asymmetrical and polynomial function, is investigated here. The Bayes decision rule allowing to minimize potential losses is used. Calculation algorithms are based on the nonparametric methodology of statistical kernel estimators, which frees the method...

We consider connectivity-augmentation problems in a setting where each potential new edge has a nonnegative cost associated with it, and the task is to achieve a certain connectivity target with at most p new edges of minimum total cost. The main result is that the minimum cost augmentation of edge-connectivity from k − 1 to k with at most p new edges is fixed-parameter tractable parameterized ...

PROBLEM SETTING Support vector machines (SVMs) are very popular tools for classification, regression and other problems. Due to the large choice of kernels they can be applied with, a large variety of data can be analysed using these tools. Machine learning thanks its popularity to the good performance of the resulting models. However, interpreting the models is far from obvious, especially whe...

Vertex Cover is one of the most well studied problems in the realm of parameterized algorithms and admits a kernel with O(`2) edges and 2` vertices. Here, ` denotes the size of a vertex cover we are seeking for. A natural question is whether Vertex Cover admits a polynomial kernel (or a parameterized algorithm) with respect to a parameter k, that is, provably smaller than the size of the vertex...

Abstract We investigate heat kernel estimates of the form p t ( x , ) ≥ c − α for large enough where and are positive reals may depend on manifolds having at least one end with a polynomial volume growth.

We demonstrate how a new data structure for sparse distributed polynomials in the Maple kernel significantly accelerates several key Maple library routines. The POLY data structure and its associated kernel operations (degree, coeff, subs, has, diff, eval, ...) are programmed for high scalability with very low overhead. This enables polynomial to have tens of millions of terms, increases parall...

Bessière et al. (AAAI’08) showed that several intractable global constraints can be efficiently propagated when certain natural problem parameters are small. In particular, the complete propagation of a global constraint is fixed-parameter tractable in k – the number of holes in domains – whenever bound consistency can be enforced in polynomial time; this applies to the global constraints ATMOS...

Volterra and Wiener series are perhaps the best-understood nonlinear system representations in signal processing. Although both approaches have enjoyed a certain popularity in the past, their application has been limited to rather low-dimensional and weakly nonlinear systems due to the exponential growth of the number of terms that have to be estimated. We show that Volterra and Wiener series c...