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Upper bounds for the reach-avoid probability via robust optimization

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Approximating Functions On Stratified Sets

We investigate smooth approximations of functions, with prescribed gradient behavior on a distinguished stratified subset of the domain. As an application, we outline how our results yield important consequences for a recently introduced class of stochasti ...

Amer Mathematical Soc2015

Upper bounds for Euclidean minima of abelian number fields

Eva Bayer Fluckiger, Piotr Aleksander Maciak

Le but de cet article est de donner des bornes supérieures pour les minima euclidiens de corps abéliens, en particulier dans le cas des corps abéliens de conducteurs des puissances de nombres premiers. ...

2015

High order numerical approximation of the invariant measure of ergodic SDEs

Assyr Abdulle, Gilles Vilmart

We introduce new sufficient conditions for a numerical method to approximate with high order of accuracy the invariant measure of an ergodic system of stochastic differential equations, independently of the weak order of accuracy of the method. We then pre ...

Society for Industrial and Applied Mathematics2014

Torsion homology of arithmetic lattices and K-2 of imaginary fields

Vincent Emery

Let be a symmetric space of noncompact type. A result of Gelander provides exponential upper bounds in terms of the volume for the torsion homology of the noncompact arithmetic locally symmetric spaces . We show that under suitable assumptions on this resu ...

Springer Heidelberg2014

Single machine scheduling with scenarios

Ola Nils Anders Svensson

In the field of robust optimization, the goal is to provide solutions to combinatorial problems that hedge against variations of the numerical parameters. This constitutes an effort to design algorithms that are applicable in the presence of uncertainty in ...

2013

Explicit methods for stiff stochastic differential equations

Assyr Abdulle

Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...

Springer-Verlag Berlin2012

Reduced Models for Optimal Control, Shape Optimization and Inverse Problems in Haemodynamics

Andrea Manzoni

The objective of this thesis is to develop reduced models for the numerical solution of optimal control, shape optimization and inverse problems. In all these cases suitable functionals of state variables have to be minimized. State variables are solutions ...

EPFL2012

Reduction strategies for PDE-constrained optimization problems in haemodynamics

Gianluigi Rozza, Andrea Manzoni, Federico Negri

Solving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numeri ...

Vienna Technical University,2012

Explicit stabilized integration of stiff determinisitic or stochastic problems

Assyr Abdulle

Explicit stabilized methods for stiff ordinary differential equations have a long history. Proposed in the early 1960s and developed during 40 years for the integration of stiff ordinary differential equations, these methods have recently been extended to ...

Amer Inst Physics2012

Expected loss bounds for authentication in constrained channels

Serge Vaudenay, Christos Dimitrakakis, Aikaterini Mitrokotsa

We derive bounds on the expected loss for authenti-cation protocols in channels which are constrained due to noisyconditions and communication costs. This is motivated by anumber of authentication protocols, where at least some partof the authentication is ...

Ieee2012