The domination number of a graph G = (V,E) is the minimum size of a dominating set U ⊆ V , which satisfies that every vertex in V \ U is adjacent to at least one vertex in U . The notion of a problem kernel refers to a polynomial time algorithm that achieves some provable reduction of the input size. Given a graph G whose domination number is k, the objective is to design a polynomial time algo...

The paper establishes the conditions under which the generalised least squares estimator of the regression parameters is equivalent to the weighted least squares estimator. The equivalence conditions have interesting applications in local polynomial regression and kernel smoothing. Specifically, they enable to derive the optimal kernel associated with a particular covariance structure of the me...

In all of these cases, one-dimensional coefficient swaths of the kernel are used, taking advantage of the ability to perform fast one-dimensional convolutions. Using multidimensional filters, however, has advantages. Filtering in multiple dimensions more easily addresses asymmetric nonlinearities that sometimes occur in practice. To generalize the division of the Volterra kernel to use multidim...

We investigate training and using Gaussian kernel SVMs by approximating the kernel with an explicit finitedimensional polynomial feature representation based on the Taylor expansion of the exponential. Although not as efficient as the recently-proposed random Fourier features [Rahimi and Recht, 2007] in terms of the number of features, we show how this polynomial representation can provide a be...

In this note, a new proof for the positivity of Dunkl’s intertwining operator in the crystallographic case is given. It is based on an asymptotic relationship between the Opdam-Cherednik kernel and the Dunkl kernel as recently observed by M. de Jeu, and on positivity results of S. Sahi for the Heckman-Opdam polynomials and their nonsymmetric counterparts. 2000 AMS Subject Classification: 33C52,...

We study the uniform approximation of the canonical conformal mapping, for a Jordan domain onto the unit disk, by polynomials generated from the partial sums of the Szegő kernel expansion. These polynomials converge to the conformal mapping uniformly on the closure of any Smirnov domain. We prove estimates for the rate of such convergence on domains with piecewise analytic boundaries, expressed...

----In statistical practices, difficulties of missing data are universal. Several techniques are used to handle this dilemma of missing data. They include both old approaches, which require only a small amount of mathematical computations and new approaches, which require additional difficult computations that are ever easier for social work researchers to carry out the statistical programming ...

As is well known the kernel of the orthogonal projector onto the polynomials of degree n in L2(wα,β , [−1, 1]) with wα,β(t) = (1−t) (1+t) can be written in terms of Jacobi polynomials. It is shown that if the coefficients in this kernel are smoothed out by sampling a C∞ function then the resulting function has nearly exponential (faster than any polynomial) rate of decay away from the main diag...

Computing the Dodgson Score of a candidate in an election is a hard computational problem, which has been analyzed using classical and parameterized analysis. In this paper we resolve two open problems regarding the parameterized complexity of DODGSON SCORE. We show that DODGSON SCORE parameterized by the target score value k has no polynomial kernel unless the polynomial hierarchy collapses to...

Treedepth-d modulator as a parameter Somnath Sikdar The recent kernelization algorithms in very general sparse graph classes such as graphs of bounded expansion use the structural parameter of a constant-treedepth modulator [1]. The parameter seems natural in these graph classes, but we have not yet investigated its full power also in general graphs. What natural problems admit a polynomial ker...