Publications related to Vector-valued function

Stability: a search for structure

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

EPFL2024

ALMOST EVERYWHERE NONUNIQUENESS OF INTEGRAL CURVES FOR DIVERGENCE-FREE SOBOLEV VECTOR FIELDS

Massimo Sorella

We construct divergence-free Sobolev vector fields in C([0,1];W-1,W-r(T-d;Rd)) with r < d and d\geq 2 which simultaneously admit any finite number of distinct positive solutions to the continuity equation. These vector fields are then shown to have at leas ...

Siam Publications2023

Positive Definite Completions and Continuous Graphical Models

Kartik Waghmare

This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...

EPFL2023

Coarse graining and large-N behavior of the d-dimensional N-clock model

Matthias Ruf, Matthias Benjamin Ruf

We study the asymptotic behavior of the N-clock model, a nearest neighbors ferromagnetic spin model on the d-dimensional cubic epsilon-lattice in which the spin field is constrained to take values in a discretization S-N of the unit circle S-1 consisting o ...

2021

Collaborative Learning in the Jungle (Decentralized, Byzantine, Heterogeneous, Asynchronous and Nonconvex Learning)

Rachid Guerraoui, Sadegh Farhadkhani, El Mahdi El Mhamdi, Le Nguyen Hoang, Sébastien Louis Alexandre Rouault, Arsany Hany Abdelmessih Guirguis

We study Byzantine collaborative learning, where n nodes seek to collectively learn from each others' local data. The data distribution may vary from one node to another. No node is trusted, and f < n nodes can behave arbitrarily. We prove that collaborati ...

2021

A Spectral Algorithm for 3-valued Function Equivalence Classification

Mathias Soeken

Spectral techniques for Boolean and multiple-valued functions have been well studied and found to be useful in logic design and testing for conventional circuits. Spectral techniques also have potential application for reversible and quantum circuits. This ...

OLD CITY PUBLISHING INC2020

Locally supported tangential vector, n-vector, and tensor fields

Christopher Brandt

We introduce a construction of subspaces of the spaces of tangential vector, n-vector, and tensor fields on surfaces. The resulting subspaces can be used as the basis of fast approximation algorithms for design and processing problems that involve tangenti ...

2020

MATHICSE Technical Report : Frequency-domain non-intrusive greedy Model Order Reduction based on minimal rational approximation

Fabio Nobile, Davide Pradovera

We present a technique for Model Order Reduction (MOR) of frequency-domain problems relying on rational interpolation of vector-valued functions. The selection of the sample points is carried out adaptively according to a greedy procedure. We describe seve ...

MATHICSE2020

Multirotor UAV-based platform for the measurement of atmospheric turbulence: validation and signature detection of tip vortices of wind turbine blades

Fernando Porté Agel, Lionel Wilhelm, Fernando Carbajo Fuertes

The present study describes the development of a technique for the measurement of atmospheric turbulence and temperature at a point in space based on the integration of a fast-response multi-hole pressure probe and a thermocouple with an inertial measureme ...

2019

Extinction In Lower Hessenberg Branching Processes With Countably Many Types

Sophie Myriam Hautphenne

We consider a class of branching processes with countably many types which we refer to as Lower Hessenberg branching processes. These are multitype Galton-Watson processes with typeset X = {0, 1, 2,...}, in which individuals of type i may give birth to off ...

INST MATHEMATICAL STATISTICS2019

Convergence of the Exponentiated Gradient Method with Armijo Line Search

Volkan Cevher, Yen-Huan Li

Consider the problem of minimizing a convex differentiable function on the probability simplex, spectrahedron, or set of quantum density matrices. We prove that the expo-nentiated gradient method with Armijo line search always converges to the optimum, if ...

2019

Innovative measurement techniques for atmospheric turbulence and wind energy

Fernando Carbajo Fuertes

The measurement of different atmospheric flow quantities is of utmost importance for a correct understanding of most atmospheric phenomena. Researchers and industry in the fields of meteorology and wind engineering demand extensive and accurate measurement ...

EPFL2018

Exploiting sequence information for text-dependent Speaker Verification

Petr Motlicek, Subhadeep Dey

Model-based approaches to Speaker Verification (SV), such as Joint Factor Analysis (JFA), i-vector and relevance Maximum-a-Posteriori (MAP), have shown to provide state-of-the-art performance for text-dependent systems with fixed phrases. The performance o ...

Ieee2017

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Emrah Bostan

We propose new regularization models to solve inverse problems encountered in biomedical imaging applications. In formulating mathematical schemes, we base our approach on the sparse signal processing principles that have emerged as a central paradigm in t ...

EPFL2016

Bioluminescence for Assessing Drug Potency against Nonreplicating Mycobacterium tuberculosis

Stewart Cole, Neeraj Dhar, Claudia Sala, Ruben Hartkoorn, Ming Zhang, Benoit Lechartier, Anthony Vocat

Targeting dormant Mycobacterium tuberculosis represents a challenge to antituberculosis drug discovery programs. We previously reported and validated the use of the streptomycin (STR)-dependent M. tuberculosis 18b strain as a tool for assessing drug potenc ...

American Society for Microbiology2015

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that ...

2015

The inviscid, compressible and rotational, 2D isotropic Burgers and pressureless Euler-Coriolis fluids: Solvable models with illustrations

Philippe Choquard

The coupling between dilatation and vorticity, two coexisting and fundamental processes in fluid dynamics (Wu et al., 2006, pp. 3, 6) is investigated here, in the simplest cases of inviscid 2D isotropic Burgers and pressureless Euler Coriolis fluids respec ...

Elsevier Science Bv2014

Tensor optimisation for optical-interferometric imaging

Jean-Philippe Thiran, Yves Wiaux, Rafael Eduardo Carrillo Rangel, Anna Auria Rasclosa

Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bispectrum measurements. We reformulate this nonlin- ear problem as a linear problem for the supersymmetric rank-1 order-3 tensor ...

Oxford Univ Press2014

Accurate Directional Inference for Vector Parameters in Linear Exponential Families

Anthony Christopher Davison

We consider inference on a vector-valued parameter of interest in a linear exponential family, in the presence of a finite-dimensional nuisance parameter. Based on higher-order asymptotic theory for likelihood, we propose a directional test whose p-value i ...

American Statistical Association2014

Fourier Analysis of Functional Time Series, with Applications to DNA Dynamics

Shahin Tavakoli

This work is about time series of functional data (functional time series), and consists of three main parts. In the first part (Chapter 2), we develop a doubly spectral decomposition for functional time series that generalizes the Karhunen–Loève expansion ...

EPFL2014