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We develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under polynomial trans ...
We present a technique for the approximation of a class of Hilbert space--valued maps which arise within the framework of model order reduction (MOR) for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR str ...
We propose a (epsilon, delta)-differentially private mechanism that, given an input graph G with n vertices and m edges, in polynomial time generates a synthetic graph G' approximating all cuts of the input graph up to an additive error of O (root mn/epsil ...
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi ...
The evaluation of small degree polynomials is critical for the computation of elementary functions. It has been extensively studied and is well documented. In this article, we evaluate existing methods for polynomial evaluation on superscalar architecture. ...
Given a level set E of an arbitrary multiplicative function f, we establish, by building on the fundamental work of Frantzikinakis and Host [14, 15], a structure theorem that gives a decomposition of 1E into an almost periodic and a pseudo-random part ...
Matrix (or operator) recovery from linear measurements is a well-studied problem. However, there are situations where only bilinear or quadratic measurements are available. A bilinear or quadratic problem can easily be transformed into a linear one, but it ...
We characterize the irreducible polynomials that occur as the characteristic polynomial of an automorphism of an even unimodular lattice of a given signature, generalizing a theorem of Gross and McMullen. As part of the proof, we give a general criterion i ...
A set R⊂N is called rational if it is well approximable by finite unions of arithmetic progressions, meaning that for every \unicode[STIX]x1D716>0 there exists a set B=⋃i=1raiN+bi, where $a_{1},\ldots ,a_ ...
A new approach is proposed to detect edges based on an artificial neural network (ANN). Some elementary continuous and discontinuous functions interpolated in the polynomial space and their continuity are used as the training sets to train a back propagati ...
