Concept

Holonomic function

Related publications (11)

Stochastic Zeroth-Order Optimisation Algorithms with Variance Reduction

Introduction of optimisation problems in which the objective function is black box or obtaining the gradient is infeasible, has recently raised interest in zeroth-order optimisation methods. As an example finding adversarial examples for Deep Learning mode ...

2019

Analytic twists of modular forms and applications

Alexandre François Peyrot

We are interested in the study of non-correlation of Fourier coefficients of Maass forms against a wide class of real analytic functions. In particular, the class of functions we are interested in should be thought of as some archimedean analogs of Frobeni ...

EPFL2017

Sequences with Minimal Time-Frequency Uncertainty

Martin Vetterli, Reza Parhizkar, Yann Barbotin

A central problem in signal processing and communications is to design signals that are compact both in time and frequency. Heisenberg's uncertainty principle states that a given function cannot be arbitrarily compact both in time and frequency, defining a ...

Elsevier2015

On Counter-Example Complete Verification for Higher-Order Functions

Viktor Kuncak, Etienne Kneuss, Nicolas Charles Yves Voirol

We present a verification procedure for pure higher-order functional Scala programs with parametric types. We show that our procedure is sound for proofs, as well as sound and complete for counter-examples. The procedure reduces the analysis of higher-orde ...

2015

Computing with an SMT Solver

Tiark Rompf, Nada Amin

Satisfiability modulo theories (SMT) solvers that support quantifier instantiations via matching triggers can be programmed to give practical support for user-defined theories. Care must be taken to avoid so-called matching loops, which may prevent termina ...

2014

Sound Compilation of Reals

Viktor Kuncak, Eva Darulova

Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued implementation and sp ...

ACM2014

On Sound Compilation of Reals

Viktor Kuncak, Eva Darulova

2013

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

In this work we consider the random discrete

L^2

projection on polynomial spaces (hereafter RDP) for the approximation of scalar quantities of interest (QOIs) related to the solution of a partial differential equation model with random input parameters. ...

Siam Publications2013

Satisfiability Modulo Recursive Programs

Viktor Kuncak, Philippe Paul Henri Suter, Ali Sinan Köksal

We present a semi-decision procedure for checking satisfiability of expressive correctness properties of recursive first-order functional programs. In our approach, both properties and programs are expressed in the same language, a subset of Scala. We impl ...

Springer-Verlag Berlin2011

Quantitative Fourier Analysis of Approximation Techniques: Part II—Wavelets

Michaël Unser, Thierry Blu

In a previous paper, we proposed a general Fourier method which provides an accurate prediction of the approximation error, irrespective of the scaling properties of the approximating functions. Here, we apply our results when these functions satisfy the u ...

IEEE1999

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Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

In this work we consider the random discrete

L^2

Siam Publications2013