Concept

Cauchy's integral formula

Related publications (32)

Mean value theorems for collections of lattices with a prescribed group of symmetries

Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...

EPFL2024

Hybrid Quadratic Programming - Pullback Bundle Dynamical Systems Control

Aude Billard, Bernardo Fichera

Dynamical System (DS)-based closed-loop control is a simple and effective way to generate reactive motion policies that well generalize to the robotic workspace, while retaining stability guarantees. Lately the formalism has been expanded in order to handl ...

SPRINGER INTERNATIONAL PUBLISHING AG2023

Asymptotic Errors for Teacher-Student Convex Generalized Linear Models (Or: How to Prove Kabashima’s Replica Formula)

Florent Gérard Krzakala, Alia Abbara

There has been a recent surge of interest in the study of asymptotic reconstruction performance in various cases of generalized linear estimation problems in the teacher-student setting, especially for the case of i.i.d standard normal matrices. Here, we g ...

2022

Stable high-order randomized cubature formulae in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure μ defined on a domain Γ⊆ℝ^d, in any dimension d. Each cubature formula is conceived to be exact on a given finite dim ...

2018

Conformal Mapping of Impedance Stability Models for System-Level Dynamics Assessments

Drazen Dujic, Francisco Daniel Freijedo Fernández, Uzair Javaid

Impedance stability methods are suitable for assessing the dynamics of power converters controllers, but also for ac/dc microgrids system level studies. This work proposes the combination of impedance modeling and conformal mapping for the identification o ...

2017

MATHICSE Technical Report : Bounds for the decay of the entries in inverses and Cauchy- Stieltjes functions of sparse, normal matrices

Marcel Schweitzer

It is known that in many functions of banded, and more generally, sparse Hermitian positive definite matrices, the entries exhibit a rapid decay away from the sparsity pattern. This is in particular true for the inverse, and based on results for the invers ...

MATHICSE2017

Fast recovery and approximation of hidden Cauchy structure

Robert Gerhard Jérôme Luce

We derive an algorithm of optimal complexity which determines whether a given matrix is a Cauchy matrix, and which exactly recovers the Cauchy points defining a Cauchy matrix from the matrix entries. Moreover, we study how to approximate a given matrix by ...

Elsevier Science Inc2016

Essays on Capital Calculation in Insurance

Mathieu Jacques David Cambou

In order to be able to bear the risk they are taking, insurance companies have to set aside a certain amount of cushion that can guarantee the payment of liabilities, up to a dened probability, and thus to remain solvent in case of bad events. This amount ...

EPFL2016

MATHICSE Technical Report: Fast recovery and approximation of hidden Cauchy structure

MATHICSE2015

Anderson localization of Bogoliubov excitations on quasi-1D strips

Pierre Lugan

Anderson localization of Bogoliubov excitations is studied for disordered lattice Bose gases in planar quasi-one-dimensional geometries. The inverse localization length is computed as function of energy by a numerical transfer-matrix scheme, for strips of ...

Wiley-V C H Verlag Gmbh2015

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