Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given n samples, the time and space complexity of computing the KRR estimate scale as O(n) and O(n) respectively, and so is prohibitive in many cases. We propose approximations of KRR based on m-dimensional randomized sketches of the kernel matrix, and study how sm...

The Riemannian metric on the manifold of positive definite matrices is defined by a kernel function φ in the form K D(H,K) = ∑ i,j φ(λi, λj) −1TrPiHPjK when ∑ i λiPi is the spectral decomposition of the foot point D and the Hermitian matrices H,K are tangent vectors. For such kernel metrics the tangent space has an orthogonal decomposition. The pull-back of a kernel metric under a mapping D 7→ ...

We present an algorithm for the computation of the discrete logarithm in logarithmic `-Class Groups. This is applied to the calculation to the `-rank of the wild kernel WK2 of a number field F and in the determination of generators of the `-part of WK2(F ).

The initial analyses of the next-to-leading logarithmic corrections to the BFKL kernel were very discouraging. Encouraged by the success of new methods in the analysis of the BFKL equation at full NLL accuracy we demonstrate in this talk how some of the initial conclusions were based on a breakdown of the tools used in the analysis rather than the framework itself.

By means of the weight functions, the technique of real analysis and Hermite-Hadamard's inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered.

In present paper we elaborated the numerical schemes of iterative methods for an approximate solution of weak singular integral equations with logarithmic Kernel. The equation is examined in a pair of spaces. The results obtained could be used for any pair of the functional spaces where the problem of finding the solution of weak singular integral equations is correctly formulated problem by Ti...

The problem of the contact of two elastic bodies of arbitrary shape with a kernel in the form of a logarithmic function—which is investigated fromHertz problem—is reduced to an integral equation. A numerical method is adapted to determine the pressure between the two surfaces under certain conditions.

We present an algorithm for computing the 2-group e C` res F of narrow logarithmic divisor classes of degree 0 for number fields F . As an application, we compute in some cases the 2-rank of the wild kernel WK2(F ) and the 2-rank of its subgroup K ∞ 2 (F ) := ∩n≥1K 2 (F ) of infinite height elements in K2(F ).