Scaling level-spacing distribution functions in the “bulk of the spectrum” in random matrix models of N × N hermitian matrices and then going to the limit N → ∞, leads to the Fredholm determinant of the sine kernel sinπ(x− y)/π(x− y). Similarly a scaling limit at the “edge of the spectrum” leads to the Airy kernel [Ai(x)Ai′(y)−Ai′(x)Ai(y)] /(x − y). In this paper we derive analogues for this Ai...

A simple method for solving Prandtl's integro-differential equation is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. Compared with known investigations, its ...

β-mixing sequence Reproducing kernel Hilbert spaces ℓ 2-empirical covering number Capacity dependent error bounds a b s t r a c t We study learning algorithms for classification generated by regularization schemes in reproducing kernel Hilbert spaces associated with a general convex loss function in a non-i.i.d. process. Error analysis is studied and our main purpose is to provide an elaborate ...

By explicitly calculating and then analytically continuing the Fourier expansion of twisted double Eisenstein series $E_{s,k-s}^{*}(z,w; 1/2)$ Diamantis O'Sullivan, we prove a formula Petersson inner product Cohen's kernel one its twists, obtain rationality result. This extends result Kohnen Zagier.

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...

The paper investigates the eeective performance attainable for a speciic class of application programs on shared memory supercomputers. Speciically, we are to investigate how seismic data analysis applications behave on the Kendall Square Research Inc.'s KSR multiprocessors. The computational kernel of seismic computation algorithms is parallelized and its performance is analyzed. Three approac...

In this paper, we propose a two-step kernel learning method based on the support vector regression (SVR) for financial time series forecasting. Given a number of candidate kernels, our method learns a sparse linear combination of these kernels so that the resulting kernel can be used to predict well on future data. The L1-norm regularization approach is used to achieve kernel learning. Since th...

Kernel machine learning methods, such as the SNP-set kernel association test (SKAT), have been widely used to test associations between traits and genetic polymorphisms. In contrast to traditional single-SNP analysis methods, these methods are designed to examine the joint effect of a set of related SNPs (such as a group of SNPs within a gene or a pathway) and are able to identify sets of SNPs ...

Covariate shift is an 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 that of the test domain, such that classifiers computed on the former generalize well to the latter. Current approaches typically target on sample distributions in the input space, ho...

In these lecture notes, we combine recent homological methods of Kevin Whyte with older dynamical methods developed by Benson Farb and myself, to obtain a new quasiisometric rigidity theorem for the mapping class group MCG(S g ) of a once punctured surface S g : if K is a finitely generated group quasi-isometric to MCG(S g ) then there is a homomorphism K → MCG(S g ) with finite kernel and fini...