Publications related to The loop group and the cobar construction

Cochains are all you need

In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...

EPFL2024

Distributed Lossy Computation with Structured Codes: From Discrete to Continuous Sources

Michael Christoph Gastpar, Sung Hoon Lim, Adriano Pastore, Chen Feng

This paper considers the problem of distributed lossy compression where the goal is to recover one or more linear combinations of the sources at the decoder, subject to distortion constraints. For certain configurations, it is known that codes with algebra ...

2023

A Hopf algebra model for Dwyer's tame spaces

Haoqing Wu

In this thesis, we give a modern treatment of Dwyer's tame homotopy theory using the language of

\infty

-categories.We introduce the notion of tame spectra and show it has a concrete algebraic description.We then carry out a study of

\infty

-operads and ...

EPFL2022

Improving First-Order Threshold Implementations of SKINNY

Andrea Felice Caforio, Daniel Patrick Collins, Subhadeep Banik, Ognjen Glamocanin

Threshold Implementations have become a popular generic technique to construct circuits resilient against power analysis attacks.In this paper, we look to devise efficient threshold circuits for the lightweight block cipher family SKINNY. The only threshol ...

Springer, Cham2021

A Computational Comparison Between Isogeometric Analysis and Spectral Element Methods: Accuracy and Spectral Properties

Alfio Quarteroni, Ondine Gabrielle Chanon

In this paper, we carry out a systematic comparison between the theoretical properties of Spectral Element Methods and NURBS-based Isogeometric Analysis in its basic form, that is in the framework of the Galerkin method, for the approximation of the Poisso ...

SPRINGER/PLENUM PUBLISHERS2020

Applications of one-point extensions to compute the A∞-(co)module structure of several Ext (resp., Tor) groups

Let A be a nonnegatively graded connected algebra over a noncommutative separable k-algebra K, and let M be a bounded below graded right A-module. If we denote by T the -coalgebra , we know that there exists an -comodule structure on over T. The structure ...

2019

On The Move: Localization With Kinetic Euclidean Distance Matrices

Martin Vetterli, Ivan Dokmanic, Puoya Tabaghi

In this paper, we propose kinetic Euclidean distance matrices (KEDMs) a new algebraic tool for localization of moving points from spatio temporal distance measurements. KEDMs are inspired by the well-known Euclidean distance matrices (EDM) which model stat ...

IEEE2019

Unique decomposition of homogeneous languages and application to isothetic regions

Nicolas René Jean Ninin

A language is said to be homogeneous when all its words have the same length. Homogeneous languages thus form a monoid under concatenation. It becomes freely commutative under the simultaneous actions of every permutation group G(n) on the collection of ho ...

2019

Using torsion theory to compute the algebraic structure of Hochschild (co)homology

The aim of this article is to provide explicit formulas for the cup product on the Hochschild cohomology of any nonnegatively graded connected algebra and for the cap products on the Hochschild homology of with coefficients in any graded bimodule at the le ...

2018

A higher homotopic extension of persistent (co)homology

Our objective is to show a possibly interesting structure of homotopic nature appearing in persistent (co)homology. Assuming that the filtration of a simplicial set embedded in induces a multiplicative filtration on the dg algebra of simplicial cochains, w ...

2018

The loop group and the cobar construction

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Cochains are all you need

Distributed Lossy Computation with Structured Codes: From Discrete to Continuous Sources

A Hopf algebra model for Dwyer's tame spaces

Improving First-Order Threshold Implementations of SKINNY

A Computational Comparison Between Isogeometric Analysis and Spectral Element Methods: Accuracy and Spectral Properties

Applications of one-point extensions to compute the A∞-(co)module structure of several Ext (resp., Tor) groups

On The Move: Localization With Kinetic Euclidean Distance Matrices

Unique decomposition of homogeneous languages and application to isothetic regions

Using torsion theory to compute the algebraic structure of Hochschild (co)homology

A higher homotopic extension of persistent (co)homology

Using torsion theory to compute the algebraic structure of Hochschild (co)homology

Distributed Lossy Computation with Structured Codes: From Discrete to Continuous Sources

Cochains are all you need

Applications of one-point extensions to compute the A∞-(co)module structure of several Ext (resp., Tor) groups

On The Move: Localization With Kinetic Euclidean Distance Matrices

A Computational Comparison Between Isogeometric Analysis and Spectral Element Methods: Accuracy and Spectral Properties

Unique decomposition of homogeneous languages and application to isothetic regions

A higher homotopic extension of persistent (co)homology

A Hopf algebra model for Dwyer's tame spaces

Improving First-Order Threshold Implementations of SKINNY