In this text, we will show the existence of lattice packings in a family of dimensions by employing division algebras. This construction is a generalization of Venkatesh's lattice packing result Venkatesh (Int Math Res Notices 2013(7): 1628-1642, 2013). In ...

SPRINGER HEIDELBERG2023

Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

Andreas Loukas, Nikolaos Karalias

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (I) not naturally amenable to gradient-based optimization, and (II) incompatible with deep lear ...

2022

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

Daniel Kressner, Stefano Massei, Alice Cortinovis

This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for performing low-rank up ...

SIAM PUBLICATIONS2022

Fast deterministic and randomized algorithms for low-rank approximation, matrix functions, and trace estimation

Alice Cortinovis

In this thesis we propose and analyze algorithms for some numerical linear algebra tasks: finding low-rank approximations of matrices, computing matrix functions, and estimating the trace of matrices. In the first part, we consider algorithms for building ...

EPFL2022

Functional Tucker Approximation Using Chebyshev Interpolation

Daniel Kressner, Christoph Max Strössner

This work is concerned with approximating a trivariate function defined on a tensor-product domain via function evaluations. Combining tensorized Chebyshev interpolation with a Tucker decomposition of low multilinear rank yields function approximations tha ...

SIAM PUBLICATIONS2021

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 ...

SPRINGER INTERNATIONAL PUBLISHING AG2021

Proving and Disproving Equivalence of Functional Programming Assignments

Viktor Kuncak, Dragana Milovancevic

We present an automated approach to verify the correctness of programming assignments, such as the ones that arise in a functional programming course. Our approach takes as input student submissions and reference solutions, and uses equivalence checking to ...

2023

Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

Daniel Kressner, Alice Cortinovis, Marcel Schweitzer

This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) when A is subject to low-rank modifications. It extends our previous work in this context on polynomial Krylov methods, for which we present a simplified conve ...

SIAM PUBLICATIONS2021

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

Fabio Nobile, Davide Pradovera

MATHICSE2020

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

Least-Squares Padé approximation of parametric and stochastic Helmholtz maps

Fabio Nobile, Davide Pradovera, Francesca Bonizzoni

The present work deals with rational model order reduction methods based on the single-point Least-Square (LS) Padé approximation techniques introduced in Bonizzoni et al. (ESAIM Math. Model. Numer. Anal., 52(4), 1261–1284 2018, Math. Comput. 89, 1229–1257 ...

2020

Distributed sampling for rational approximation of the acoustic scattering of an airfoil

Davide Pradovera, Francesca Bonizzoni

In this paper we compute a reduced order model for a time‐harmonic external acoustic scattering problem with parametric frequency. The employed technique is minimal rational interpolation, an explicit moment‐matching method for Hilbert space‐valued meromor ...

2019

A Hybrid Method for Spectral Translation Equivalent Boolean Functions

Giovanni De Micheli, Mathias Soeken, Eleonora Testa

The equivalence of Boolean functions with respect to five invariance (aka translation) operations has been well considered with respect to the Rademacher-Walsh spectral domain. In this paper, we introduce a hybrid approach that uses both the Reed-Muller an ...

IEEE2019

Presymplectic convexity and (ir)rational polytopes

Tudor Ratiu

In this paper, we extend the Atiyah-Guillemin-Sternberg convexity theorem and Delzant's classification of symplectic toric manifolds to presymplectic manifolds. We also define and study the Morita equivalence of presymplectic toric manifolds and of their c ...

2019

On the relation between linearity-generating processes and linear-rational models

Damir Filipovic, Martin Larsson

We review the notion of a linearity-generating (LG) process introduced by Gabaix and relate LG processes to linear-rational (LR) models studied by Filipović et al. We show that every LR model can be represented as an LG process and vice versa. We find that ...

2019

Moving on: Is Existenzminimum Still Relevant?

Bruno Marchand

In the inter-war period, progressive architects confronted the building of mass housing with an analogy with rational and functional workplaces. At the 2nd CIAM (Congres Internationaux d'Architecture Moderne), held in Frankfurt in 1929, this was tested aga ...

2019

Fourier interpolation on the real line

Maryna Viazovska

In this paper we construct an explicit interpolation formula for Schwartz functions on the real line. The formula expresses the value of a function at any given point in terms of the values of the function and its Fourier transform on the set {0,+/- 1,+/- ...

2019

Wearable System for Real-Time Sensing of Biomarkers in Human Sweat

Junrui Zhang

Wearable sweat sensing systems offer non-invasive and real-time bio-data streaming solutions. They open the possibility for continuous monitoring of biomarkers' concentrations as well as their variation in sweat, which is a complementary to current passive ...

EPFL2019

Low Frequency Sound Field Reconstruction in Non-rectangular Room: A Numerical Validation

Hervé Lissek, Etienne Thierry Jean-Luc Rivet, Vu Thach Pham

Characterization of sound fields in rooms has always been a challenging task. A faithful reconstruction of sound fields in rooms generally would require an impractically high number of microphones. At low frequencies, where sound field can be modeled as a ...

2018