In this paper we present a generic primal-dual interior-point algorithm for linear optimization in which the search direction depends on a univariate kernel function which is also used as proximity measure in the analysis of the algorithm. We present some powerful tools for the analysis of the algorithm under the assumption that the kernel function satisfies three easy to check and mild conditi...

We show global and interior higher-order log-Hölder regularity estimates for solutions of Dirichlet integral equations where the operator has a nonintegrable kernel with singularity at origin that is weaker than any fractional Laplacian. As consequence, under mild assumptions on right hand side, we existence classical problems involving logarithmic Laplacian Schrödinger operator.

In this paper we show how the generation of documents can be thought of as a k-stage Markov process, which leads to a Fisher kernel from which the n-gram and string kernels can be reconstructed. The Fisher kernel view gives a more exible insight into the string kernel and suggests how it can be parametrised in a way that re-ects the statistics of the training corpus. Furthermore, the prob-abili...

In this paper we show how the generation of documents can be thought of as a k-stage Markov process, which leads to a Fisher kernel from which the n-gram and string kernels can be re-constructed. The Fisher kernel view gives a more flexible insight into the string kernel and suggests how it can be parametrised in a way that reflects the statistics of the training corpus. Furthermore, the probab...

In this note, we give some applications of projective logarithmic potentials. First introduce the notions energy and capacity associated to kernel. We compare quantitatively with complex Monge-Ampère on space deduce that set zero is zero. Further, define transfinite diameter a compact show it coincides capacity. Finally there an analogous classical Evans's theorem.

We prove several new results of Ax-Lindemann type for semiabelian varieties over the algebraic closure K of C(t), making heavy use of the Galois theory of logarithmic differential equations. Using related techniques, we also give a generalization of the theorem of the kernel for abelian varieties over K. This paper is a continuation of [7] as well as an elaboration on the methods of Galois desc...

We used function theoretic method to solve a singular integral equation with logarithmic kernel in two disjoint finite intervals where the unknown function satisfying the integral equation may be bounded or unbounded at the nonzero finite endpoints of the interval concerned. An appropriate solution of this integral equation is then applied to solve the problem of scattering of time harmonic sur...

Here, the solution in one, two and three dimensional for the Volterra–Fredholm integral equation of the first kind is obtained in the space L2ðXÞ C1⁄20; T , T < 1. Using a numerical method the integral equation of Volterra–Fredholm becomes a linear system of Fredholm integral equation when that the kernel of Fredholm integral takes a logarithmic form, Carleman function, generalized potential fu...

I present a calculation of the one particle deep inelastic cross section in the target fragmentation region in (φ)6. The renormalized cross section gets a large logarithmic correction whose coefficient is precisely the scalar DGLAP kernel. The result is found to be consistent with an extended factorization hypothesis and with infrared power counting. To appear in the Proceedings of QCD Euroconf...

The paper [5] presented a bound on the generalisation error of classifiers learned through multiple kernel learning. The bound has (an improved) additive dependence on the number of kernels (with the same logarithmic dependence on this number). However, parts of the proof were incorrectly presented in that paper. This note remedies this weakness by restating the problem and giving a detailed pr...