Publications associées à Ergodic Theory Meets Polarization I: A Foundation of Polarization Theory

Publications associées (23)

Geometric Learning: Leveraging differential geometry for learning and control

In this thesis, we concentrate on advancing high-level behavioral control policies for robotic systems within the framework of Dynamical Systems (DS). Throughout the course of this research, a unifying thread weaving through diverse fields emerges, and tha ...

EPFL2024

Seeking the new, learning from the unexpected: Computational models of surprise and novelty in the brain

Alireza Modirshanechi

Human babies have a natural desire to interact with new toys and objects, through which they learn how the world around them works, e.g., that glass shatters when dropped, but a rubber ball does not. When their predictions are proven incorrect, such as whe ...

EPFL2024

Deep Learning Meets Sparse Regularization

Rahul Parhi

Deep learning (DL) has been wildly successful in practice, and most of the state-of-the-art machine learning methods are based on neural networks (NNs). Lacking, however, is a rigorous mathematical theory that adequately explains the amazing performance of ...

2023

Fairness and Explainability in Clustering Problems

Xinrui Jia

In this thesis we present and analyze approximation algorithms for three different clustering problems. The formulations of these problems are motivated by fairness and explainability considerations, two issues that have recently received attention in the ...

EPFL2023

Parallel temporal signal processing enabled by polarization-multiplexed programmable THz metasurfaces

Romain Christophe Rémy Fleury, Ali Momeni

Under the trends of multifunctionality, tunability, and compactness in modern wave -based signal processors, in this paper, we propose a polarization-multiplexed graphene-based metasurface to realize distinct mathematical operators on the parallel time-dom ...

Optica Publishing Group2022

Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes

Alexis Arnaudon

Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model ...

NATURE PORTFOLIO2022

Forward-reflected-backward method with variance reduction

Volkan Cevher, Ahmet Alacaoglu

We propose a variance reduced algorithm for solving monotone variational inequalities. Without assuming strong monotonicity, cocoercivity, or boundedness of the domain, we prove almost sure convergence of the iterates generated by the algorithm to a soluti ...

2021

Programmable Logic Gates Based On Tunable Multistable Mechanisms

Simon Nessim Henein, Ilan Vardi, Hubert Pierre-Marie Benoît Schneegans, Mohamed Gamal Abdelrahman Ahmed Zanaty

Binary logic operations are the building blocks of computing machines. In this paper, we present a new programmable binary logic gate based on programmable multistable mechanisms (PMM), which are multistable structures whose stability behavior depends on m ...

AMER SOC MECHANICAL ENGINEERS2020

Asymptotically Optimal Contextual Bandit Algorithm Using Hierarchical Structures

We propose an online algorithm for sequential learning in the contextual multiarmed bandit setting. Our approach is to partition the context space and, then, optimally combine all of the possible mappings between the partition regions and the set of bandit ...

2019

Parallel integro-differential equation solving via multi-channel reciprocal bianisotropic metasurface augmented by normal susceptibilities

Karim Achouri, Ali Momeni

Analog optical signal processing has dramatically transcended the speed and energy limitations accompanied with its digital microelectronic counterparts. Motivated by recent metasurface?s evolution, the angular scattering diversity of a reciprocal passive ...

2019

An Ergodic Theory of Binary Operations-Part II: Applications to Polarization

Rajai Nasser

An open problem in polarization theory is to determine the binary operations that always lead to polarization (in the general multilevel sense) when they are used in Arikan style constructions. This paper, which is presented in two parts, solves this probl ...

Institute of Electrical and Electronics Engineers2017

Polarization and Channel Ordering: Characterizations and Topological Structures

Rajai Nasser

Information theory is the field in which we study the fundamental limitations of communication. Shannon proved in 1948 that there exists a maximum rate, called capacity, at which we can reliably communicate information through a given channel. However, Sha ...

EPFL2017

Polarization of photons emitted by decaying dark matter

Mikhail Chapochnikov, Anna Tokareva

Radiatively decaying dark matter may be searched through investigating the photon spectrum of galaxies and galaxy clusters. We explore whether the properties of dark matter can be constrained through the study of a polarization state of emitted photons. St ...

Elsevier2017

The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications

Alfio Quarteroni, Andrea Manzoni, Christian Vergara

Mathematical and numerical modelling of the cardiovascular system is a research topic that has attracted remarkable interest from the mathematical community because of its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseas ...

Cambridge Univ Press2017

An Ergodic Theory of Binary Operations-Part I: Key Properties

Rajai Nasser

An open problem in polarization theory is to determine the binary operations that always lead to polarization (in the general multilevel sense) when they are used in Arikan style constructions. This paper, which is presented in two parts, solves this probl ...

Ieee-Inst Electrical Electronics Engineers Inc2016

Binary Compressed Imaging

Michaël Unser, Aurélien Bourquard

Compressed sensing can substantially reduce the number of samples required for conventional signal acquisition at the expense of an additional reconstruction procedure. It also provides robust reconstruction when using quantized measurements, including in ...

Ieee-Inst Electrical Electronics Engineers Inc2013

CAT(0) Geometry for the Thompson Group

Dan Titus Salajan

We investigate Farley’s CAT(0) cubical model for Thompson’s group F (we adopt the classical language of F, using binary trees and piecewise linear maps, avoiding the one of diagram groups and pictures). Main results include: in general, Thompson’s group el ...

EPFL2012

An Efficient Algorithm for Level Set Method Preserving Distance Function

Jean-Philippe Thiran, Xavier Bresson, Dominique Zosso, Virginia Estellers Casas

The level set method is a popular technique for tracking moving interfaces in several disciplines including computer vision and fluid dynamics. However, despite its high flexibility, the original level set method is limited by two important numerical issue ...

Institute of Electrical and Electronics Engineers2012

A power-efficient, current-mode, binary-tree min / max circuit for Kohonen self-organizing feature maps and nonlinear filters

Rafal Tomasz Dlugosz

A novel current-mode, binary-tree Min / Max circuit for application in analog neural networks and filters has been presented. In the proposed circuit input currents are first converted to step signals with equal amplitudes and different delays that are pro ...

2010

Low power current-mode binary-tree asynchronous Min/Max circuit

Rafal Tomasz Dlugosz

A novel, current-mode, binary-tree, asynchronous Min/Max circuit for application in nonlinear filters as well as in analog artificial neural networks is proposed. The relatively high precision above 99% can be achieved by eliminating the copying of the inp ...

2010