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Markov processes are used in a wide range of disciplines including finance.The transition densities of these processes are often unknown. However, the conditionalcharacteristic functions are more like...
Multivariate hypergeometric functions associated with toric varieties were introduced by Gel'fand, Kapranov and Zelevinsky. Singularities of such functions are discriminants, that is, divisors project...
In the present paper we use the Wannier function basis to construct lattice approximations of the nonlinear Schrödinger equation with a periodic potential. We show that the nonlinear Schrödi...
Using a time-dependent linear (Rabi) coupling between the components of a weakly interacting multicomponent Bose-Einstein condensate (BEC), we propose a protocol for transferring the wave function of ...
We prove a large deviation principle for the expectation of macroscopic observables in quantum (and classical) Gibbs states. Our proof is based on Ruelle-Lanford functions [20, 34] and direct subaddit...
We describe the structure of all codimension-2 lattice configurations A which admit a stable rational A-hypergeometric function, that is a rational function F all the partial derivatives of which are ...
For copulas whose partial derivatives are not continuous everywhere on the interior of the unit cube, the empirical copula process does not converge weakly with respect to the supremum distance. This ...
Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of conf...
In this contribution we describe an approach to evolve composite covariance functions for Gaussian processes using genetic programming. A critical aspect of Gaussian processes and similar kernel-based...
In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we mak...
In this paper, we study the generalization properties of online learning based stochastic methods for supervised learning problems where the loss function is dependent on more than one training sample...
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regul...
Power law generalized covariance functions provide a simple model for describing the local behavior of an isotropic random field. This work seeks to extend this class of covariance functions to spatia...
The paper considers probability distribution, density, conditional distribution and density and conditional moments as well as their kernel estimators in spaces of generalized functions. This approach...
We present a system that enables rapid model experimentation for tera-scale machine learning with trillions of non-zero features, billions of training examples, and millions of parameters. Our contrib...

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