Publications related to C*-algebra

Positive Definite Completions and Continuous Graphical Models

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

On the Grothendieck-Serre conjecture for classical groups

Eva Bayer Fluckiger

We prove some new cases of the Grothendieck-Serre conjecture for classical groups. This is based on a new construction of the Gersten-Witt complex for Witt groups of Azumaya algebras with involution on regular semilocal rings, with explicit second residue ...

WILEY2022

Multiplicity-free representations of algebraic groups II

Donna Testerman, Martin W. Liebeck

We continue our work, started in [9], on the program of classifying triples (X, Y, V), where X, Yare simple algebraic groups over an algebraically closed field of characteristic zero with X < Y, and Vis an irreducible module for Y such that the restriction ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

On the stress tensor light-ray operator algebra

Grégoire Olivier Mathys, Matthew Thomas Walters, Alexandre Mathieu Frédéric Belin

We study correlation functions involving generalized ANEC operators of the form integral dx-x-n+2T--x -> in four dimensions. We compute two, three, and ...

Springer Nature2021

Linear Lipschitz and C-1 extension operators through random projection

Federico Stra

We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and C-1 functions. This way we prove more directly a result by Lee and Naor [5] and we generalize the C-l extension theorem by ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

The algebra of Boolean matrices, correspondence functors, and simplicity

Jacques Thévenaz, Serge Bouc

We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a simple correspondence ...

2020

The uniform symbolic topology property for diagonally F-regular algebras

Javier Alonso Carvajal Rojas

Let k be a field of positive characteristic. Building on the work of the second named author, we define a new class of k-algebras, called diagonally F-regular algebras, for which the so-called Uniform. Symbolic Topology Property (USTP) holds effectively. W ...

2020

A multiphase CMAQ version 5.0 adjoint

Athanasios Nenes

We present the development of a multiphase adjoint for the Community Multiscale Air Quality (CMAQ) model, a widely used chemical transport model. The adjoint model provides location- and time-specific gradients that can be used in various applications such ...

2020

Machine-Learning of Atomic-Scale Properties Based on Physical Principles

Michele Ceriotti, Michael John Willatt

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train from linear fun ...

Springer International Publishing2020

An effective proof of the Cartan formula: The even prime

Anibal Maximiliano Medina Mardones

The Cartan formula encodes the relationship between the cup product and the action of the Steenrod algebra in F-p-cohomology. In this work, we present an effective proof of the Cartan formula at the cochain level when the field is F-2. More explicitly, for ...

2020

Beyond Wiener's Lemma: Nuclear Convolution Algebras and the Inversion of Digital Filters

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

A convolution algebra is a topological vector space X that is closed under the convolution operation. It is said to be inverse-closed if each element of X whose spectrum is bounded away from zero has a convolution inverse that is also part of the algebra. ...

SPRINGER BIRKHAUSER2019

Finally, a Polymorphic Linear Algebra Language

Amir Shaikhha, Lionel Emile Vincent Parreaux

Many different data analytics tasks boil down to linear algebra primitives. In practice, for each different type of workload, data scientists use a particular specialised library. In this paper, we present Pilatus, a polymorphic iterative linear algebra la ...

2019

Geometric spects A of Similarity Problems

Peter Clemens Schlicht

This article presents a geometric approach to some similarity problems involving metric arguments in the non-positively curved space of positive invertible operators of an operator algebra and the canonical isometric action by invertible elements on the co ...

OXFORD UNIV PRESS2018

On quadratic matrix equations with infinite size coefficients encountered in QBD stochastic processes

Stefano Massei

Matrix equations of the kind A(1)X(2)+A(0)X+A(-1)=X, where both the matrix coefficients and the unknown are semi-infinite matrices belonging to a Banach algebra, are considered. These equations, where coefficients are quasi-Toeplitz matrices, are encounter ...

WILEY2018

GlobalBioIm: A Unifying Computational Framework for Solving Inverse Problems

Michaël Unser, Laurène Donati, Michael Thompson McCann, Emmanuel Emilien Louis Soubies, Ferréol Arnaud Marie Soulez

We present a unifying framework for the development of state-of-the-art reconstruction algorithms in computational optics with a clear separation between the physical (forward model) and signal-related (regularization, incorporation of prior constraints) a ...

OSA2017

On the -Betti numbers of universal quantum groups

Sven Raum

We show that the first -Betti number of the duals of the free unitary quantum groups is one, and that all -Betti numbers vanish for the duals of the quantum automorphism groups of full matrix algebras. ...

Springer Heidelberg2017

SETS OF p-UNIQUENESS ON NONCOMMUTATIVE LOCALLY COMPACT GROUPS

Antoine Derighetti

We prove that a closed subgroup H of a locally compact group G is a set of p-uniqueness (1 < p < infinity) if and only if H is locally negligible. We also obtain the inverse projection theorem for sets of p-uniqueness. ...

Ars Polona-Ruch2017

The algebra of essential relations on a finite set

Jacques Thévenaz, Serge Bouc

Let X be a finite set and let k be a commutative ring. We consider the k-algebra of the monoid of all relations on X, modulo the ideal generated by the relations factorizing through a set of cardinality strictly smaller than Card(X), called inessential rel ...

Walter de Gruyter2016

The monoid algebra of all relations on a finite set

Jacques Thévenaz, Serge Bouc

We classify all the simple modules for the algebra of relations on a finite set, give their dimension, and find the dimension of the Jacobson radical of the algebra. ...

2015

Equivalences between blocks of cohomological Mackey algebras

Baptiste Thierry Pierre Rognerud

Let G be a finite group and (K, O, k) be a p-modular system “large enough”. Let R = O or k. There is a bijection between the blocks of the group algebra RG and the central primitive idempotents (the blocks) of the so-called cohomological Mackey algebra coμ ...

Springer Verlag2015