An impact of integration over the paths of the Lévy flights on the quantum mechanical kernel has been studied. Analytical expression for a free particle kernel has been obtained in terms of the Fox Hfunction. A new equation for the kernel of a partical in the box has been found. New general results include the well known quantum formulae for a free particle kernel and particle in box kernel. PA...

This is the supplementary material for the paper entitled “On-line Reinforcement Learning Using Incremental Kernel-Based Stochastic Factorization” [2]. It contains the details of our theoretical developments that could not be included in the paper due to space constraints. This material should be read in conjunction with the main paper. 1 Preliminaries • Similarly to Ormoneit and Sen [3], we de...

Let D be a digraph. Let k be a natural number with k 2. A set J ⊆ V (D) will be called a k-kernel of the digraph D iff: 1) For each x, x′ ∈ J , x = x′ we have dD(x, x′) k and 2) For each y ∈ V (D) − J , there exists x ∈ J such that dD(y, x) ≤ k − 1. In [4], for any digraph D we constructed a digraph s(S) such that D has a k-kernel iff s(S) has a k-kernel. In this paper we prove that the number ...

We give an improved local partitioning algorithm using heat kernel pagerank, a modified version of PageRank. For a subset S with Cheeger ratio (or conductance) h, we show that there are at least a quarter of the vertices in S that can serve as seeds for heat kernel pagerank which lead to local cuts with Cheeger ratio at most O( √ h), improving the previously bound by a factor of p log |S|.

If V is a vector space over some field F, then we have the well known exact sequence 0 → Λ2(V ) T2(V S2(V 0, where first map given by x∧y x⊗y−y⊗x and second x⊗y 7→ xy. The obvious generalization, an sequence, Λk(V T

In this paper, we study the numerical integration of continuous functions on d-dimensional spheres S ⊆ R by equally weighted quadrature rules based at N ≥ 1 points on S which minimize a generalized energy functional. Examples of such points are configurations, which minimize energies for the Riesz kernel ‖x− y‖−s 0 < s ≤ d and logarithmic kernel − log ‖x− y‖. We deduce that extremal point confi...

To resolve the online detection difficulty of some important state variables in fermentation process with traditional instruments, a soft sensing modeling method based on relevance vector machine (RVM) with a hybrid kernel function is presented. Based on the characteristic analysis of two commonly-used kernel functions, that is, local Gaussian kernel function and global polynomial kernel functi...

In parameterized complexity each problem instance comes with a parameter k and the parameterized problem is said to admit a polynomial kernel if there are polynomial time preprocessing rules that reduce the input instance down to an instance with size polynomial in k. Many problems have been shown to admit polynomial kernels, but it is only recently that a framework for showing the non-existenc...

The idea of using logic in computer programs to perform systematic diagnosis was introduced early in computation history. There are several systems using punch-cards and rulers described as early as the mid 1950’s. Within the area of applied artificial intelligence the problem of diagnosis made its definite appearance in the form of expert systems during the 1970’s. This research eventually int...