In earlier work with Gabor Lugosi, we introduced a method to select a smoothing factor for kernel density estimation such that, for all densities in all dimensions, the L1 error of the corresponding kernel estimate is not larger than 3 + e times the error of the estimate with the optimal smoothing factor plus a constant times Ov~--~-n/n, where n is the sample size, and the constant only depends...

The tame kernel of the K2 of a number field F is the kernel of some explicit map K2F → ⊕ k∗ v , where the product runs over all finite primes v of F and kv is the residue class field at v. When S is a set of primes of F , containing the infinite ones, we can consider the S-unit group US of F . Then US ⊗ US has a natural image in K2F . The tame kernel is contained in this image if S contains all...

The Pearcey kernel is a classical and universal arising from random matrix theory, which describes the local statistics of eigenvalues when limiting mean eigenvalue density exhibits cusp-like singularity. It appears in variety statistical physics models beyond as well. We consider Fredholm determinant trace class operator acting on $L^2\left(-s, s\right)$ with kernel. Based steepest descent ana...

Kernel based machine learning methods like support vector machines or gaussian processes have gained increasing attention for QSAR modelling in recent years. One of the most interesting aspects of this method is the analogy between the kernel and a similarity measure. Each similarity measure that fulfils the kernel properties can be used as a kernel. But despite the possibility to incorporate s...

Abstract In 2018, Bai, Fujita and Zhang [Discrete Math. 341 (2018), no. 6, 1523–1533] introduced the concept of a kernel by rainbow paths (for short, RP-kernel) an arc-coloured digraph D D , which is subset S S vertices such that ( a ) there exists no path for any pair distinct b ...

Object-oriented operating systems, as well as conventional O/S designs, present an overly restrictive level of abstraction to the programmer. Models of objects, processes, concurrency, etc., are embedded within the system in such a way that they are di cult to extend or replace. SPACE is an extensible operating system being developed for research into object-oriented and distributed systems des...

The integral ∫ L 0 e iνφ(s,t)f (s) ds with a highly oscillatory kernel (large ν, ν is up to 2000) is considered. This integral is accurately evaluated with an improved trapezoidal rule and effectively transcribed using local Fourier basis and adaptive multiscale local Fourier basis. The representation of the oscillatory kernel in these bases is sparse. The coefficients after the application of ...

The operator-valued Schur-class is defined to be the set of holomorphic functions S mapping the unit disk into the space of contraction operators between two Hilbert spaces. There are a number of alternate characterizations: the operator of multiplication by S defines a contraction operator between two Hardy Hilbert spaces, S satisfies a von Neumann inequality, a certain operator-valued kernel ...