Publications related to Lefschetz fixed-point theorem

Nonlocally-resonant metamaterials

In this thesis, we unveil a third design path to manipulate elastic waves within architected media, distinct from the traditional phononic crystal and locally-resonant metamaterial concepts. The core innovation lies in the concept of nonlocal resonances, d ...

EPFL2023

Data-driven Methods for Control: from Linear to Lifting

Yingzhao Lian

The progress towards intelligent systems and digitalization relies heavily on the use of automation technology. However, the growing diversity of control objects presents significant challenges for traditional control approaches, as they are highly depende ...

EPFL2023

Invariant integrals on topological groups

Vasco Schiavo

We generalize the fixed-point property for discrete groups acting on convex cones given by Monod in [23] to topological groups. At first, we focus on describing this fixed-point property from a functional point of view, and then we look at the class of gro ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

The Jordan property for local fundamental groups

Stefano Filipazzi, Roberto Svaldi

We show the Jordan property for regional fundamental groups of klt singularities of fixed dimension. Furthermore, we prove the existence of effective simultaneous index 1 covers for n-dimensional klt singularities. We give an application to the study of lo ...

2022

Wind farm layout and unconstrained hub height optimization using genetic algorithms applied to different power densities

Fernando Porté Agel, Nicolas Otto Kirchner Bossi

LES and wind tunnel studies have shown significant benefit when allowing turbines (T) in a wind farm to adopt different heights. This work presents two new genetic algorithms (GA) that perform wind farm layout optimization (WFLO) involving continuous and t ...

2022

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Victor Panaretos, Matthieu Martin Jean-André Simeoni, Julien René Pierre Fageot, Alessia Caponera

We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...

2022

Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations

Espen Sande

We show that isogeometric Galerkin discretizations of eigenvalue problems related to the Laplace operator subject to any standard type of homogeneous boundary conditions have no outliers in certain optimal spline subspaces. Roughly speaking, these optimal ...

2022

Spectral Coarse Spaces for the Substructured Parallel Schwarz Method

Tommaso Vanzan

The parallel Schwarz method (PSM) is an overlapping domain decomposition (DD) method to solve partial differential equations (PDEs). Similarly to classical nonoverlapping DD methods, the PSM admits a substructured formulation, that is, it can be formulated ...

2022

Visual Focus of Attention Estimation in 3D Scene with an Arbitrary Number of Targets

Jean-Marc Odobez, Rémy Alain Siegfried

Visual Focus of Attention (VFOA) estimation in conversation is challenging as it relies on difficult to estimate information (gaze) combined with scene features like target positions and other contextual information (speaking status) allowing to disambigua ...

IEEE COMPUTER SOC2021

Global bifurcation at isolated singular points of the Hadamard derivative

Charles Stuart

Consider F is an element of C(RxX,Y) such that F(lambda, 0) = 0 for all lambda is an element of R, where X and Y are Banach spaces. Bifurcation from the line Rx{0} of trivial solutions is investigated in cases where F(lambda, center dot ) need not be Frech ...

2021

Masksembles for Uncertainty Estimation

Pascal Fua, Pierre Bruno Baqué, Nikita Durasov, Timur Bagautdinov

Deep neural networks have amply demonstrated their prowess but estimating the reliability of their predictions remains challenging. Deep Ensembles are widely considered as being one of the best methods for generating uncertainty estimates but are very expe ...

2021

Invariant Integrals on Topological Groups and Applications

Vasco Schiavo

We study a fixed point property for linear actions of discrete groups on weakly complete convex proper cones in locally convex topological vector spaces. We search to understand the class of discrete groups which enjoys this property and we try to generali ...

EPFL2021

Fourier Interpolation From Spheres

Martin Peter Stoller

In every dimension d >= 2, we give an explicit formula that expresses the values of any Schwartz function on R-d only in terms of its restrictions, and the restrictions of its Fourier transform, to all origin-centered spheres whose radius is the square roo ...

2021

Sparsely Observed Functional Time Series: Theory and Applications

Tomas Rubin

Functional time series is a temporally ordered sequence of not necessarily independent random curves. While the statistical analysis of such data has been traditionally carried out under the assumption of completely observed functional data, it may well ha ...

EPFL2021

Numerical methods for structural anomaly detection using model order reduction and data-driven techniques

Caterina Bigoni

The objective of this thesis is to provide a mathematical and computational framework for the proactive maintenance of complex systems with a particular application to structural health monitoring (SHM). SHM techniques rely primarily on sensor responses to ...

EPFL2020

Fast Transformers with Clustered Attention

François Fleuret, Angelos Katharopoulos, Apoorv Vyas

Transformers have been proven a successful model for a variety of tasks in sequence modeling. However, computing the attention matrix, which is their key component, has quadratic complexity with respect to the sequence length, thus making them prohibitivel ...

2020

Efficient Treatment of Correlation Energies at the Basis-Set Limit by Monte Carlo Summation of Continuum States

Ursula Röthlisberger, Justin Villard, Martin Peter Bircher

The calculation of electron correlation is vital for the description of atomistic phenomena in physics, chemistry, and biology. However, accurate wavefunction-based methods exhibit steep scaling and often sluggish convergence with respect to the basis set ...

AMER CHEMICAL SOC2020

Structural Properties Of Dendrite Groups

Nicolas Monod

Let G be the homeomorphism group of a dendrite. We study the normal subgroups of G. For instance, there are uncountably many nonisomorphic such groups G that are simple groups. Moreover, these groups can be chosen so that any isometric G-action on any metr ...

AMER MATHEMATICAL SOC2019

On the Computational Complexity of Blind Detection of Binary Linear Codes

Alexios Konstantinos Balatsoukas Stimming, Aris Filos Ratsikas

In this work, we study the computational complexity of the Minimum Distance Code Detection problem. In this problem, we are given a set of noisy codeword observations and we wish to find a code in a set of linear codes C of a given dimension k, for which t ...

IEEE2019

Graph fragmentation problem: analysis and synthesis

Manuel Francesco Aprile, Pablo Romero Gómez

Vulnerability metrics play a key role in the understanding of cascading failures and target/random attacks to a network. The graph fragmentation problem (GFP) is the result of a worst-case analysis of a random attack. We can choose a fixed number of indivi ...

WILEY2019