QCD sum rules involving mixed inverse moment integration kernels are used in order to determine the running charm-quark mass in the MS scheme. Both the high and the low energy expansion of the vector current correlator are involved in this determination. The optimal integration kernel turns out to be of the form p(s) = 1 − (s0/s) , where s0 is the onset of perturbative QCD. This kernel enhances...

We use the gradient flow on the path space to obtain estimates on the heat kernel k(t, x, y) on a complete Riemannian manifold. This approach gives a sharp formula for the small-time asymptotics of k(t, x, y) and an upper bound for all time for pairs x and y are not conjugate. It also gives a theorem about convolutions of heat kernels that makes precise the intuition that heat flows in packets ...

Covariate shift is a unconventional learning scenario in which training and testing data have different distributions. A general principle to solve the problem is to make the training data distribution similar to the test one, such that classifiers computed on the former generalizes well to the latter. Current approaches typically target on the sample distribution in the input space, however, f...

Here Index(D) is the Fredholm index of the Dirac operator acting on smooth sections of the spinor bundle S over an even dimensional compact Riemannian spin manifold M , e−tD 2 is the solution operator for the heat equation ∂s ∂t+D s = 0 for D, and Trs is the supertrace. The goal of this essay is to explicitly compute the righthand side in terms of local information on M , thereby proving the At...

Multivariate kernel regression is an important tool for investigating the relationship between a response and a set of explanatory variables. It is generally accepted that the performance of a kernel regression estimator largely depends on the choice of bandwidth rather than the kernel function. This nonparametric technique has been employed in a number of empirical studies including the state-...

Guilherme França∗ and Joshua T. Vogelstein† Johns Hopkins University Abstract Energy statistics was proposed by Székely in the 80’s inspired by the Newtonian gravitational potential from classical mechanics, and it provides a hypothesis test for equality of distributions. It was further generalized from Euclidean spaces to metric spaces of strong negative type, and more recently, a connection w...

In the `-Component Order Connectivity problem (` ∈ N), we are given a graph G on n vertices, m edges and a non-negative integer k and asks whether there exists a set of vertices S ⊆ V (G) such that |S| ≤ k and the size of the largest connected component in G−S is at most `. In this paper, we give a kernel for `-Component Order Connectivity with at most 2`k vertices that takes nO(`) time for eve...

Let X be a graph and let C be a class of X-maps (that is, of continuous maps from X into itself). A map f ∈ C is said to have full periodicity if Per (f) = N (here, Per (f) denotes the set of periods of all periodic points of f and N the set of positive integers). The set K ⊆ N is a full periodicity kernel of C if it satisfies the following two conditions: (i) If f ∈ C and K ⊆ Per (f) then f ha...

This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular, we try to extend this concept and prove some related theorems. Moreover, we focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular, we extend reproducing kernels to relative reproducing kernels an...