Fast recovery and approximation of hidden Cauchy structure

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Nonperturbative aspects of scattering amplitudes

Miguel Alexandre Ribeiro Correia

In this thesis we study how physical principles imposed on the S-matrix, such as Lorentz invariance, unitarity, crossing symmetry and analyticity constrain quantum field theories at the nonperturbative level. We start with a pedagogical introduction to the ...

EPFL2023

Quantum Field Theory in AdS Space instead of Lehmann-Symanzik-Zimmerman Axioms

Xiang Zhao

The boundary correlation functions for a quantum field theory (QFT) in a fixed anti-de Sitter (AdS) background should reduce to S-matrix elements in the flat-space limit. We consider this procedure in detail for four-point functions. With minimal assumptio ...

AMER PHYSICAL SOC2023

Estimating the Topology of Preferential Attachment Graphs Under Partial Observability

Ali H. Sayed

This work addresses the problem of learning the topology of a network from the signals emitted by the network nodes. These signals are generated over time through a linear diffusion process, where neighboring nodes exchange messages according to the underl ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

Bayesian reconstruction of memories stored in neural networks from their connectivity

Lenka Zdeborová, Florent Gérard Krzakala

The advent of comprehensive synaptic wiring diagrams of large neural circuits has created the field of connectomics and given rise to a number of open research questions. One such question is whether it is possible to reconstruct the information stored in ...

2023

Statistical limits of dictionary learning: Random matrix theory and the spectral replica method

Nicolas Macris, Jean François Emmanuel Barbier

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existin ...

AMER PHYSICAL SOC2022

Iterative refinement of Schur decompositions

Daniel Kressner, Zvonimir Bujanovic

The Schur decomposition of a square matrix A is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following task: Compute a (m ...

SPRINGER2023

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

IMPROVED VARIANTS OF THE HUTCH plus plus ALGORITHM FOR TRACE ESTIMATION

Daniel Kressner, Alice Cortinovis, Ulf David Persson

This paper is concerned with two improved variants of the Hutch++ algorithm for estimating the trace of a square matrix, implicitly given through matrix-vector products. Hutch++ combines randomized low-rank approximation in a first phase with stochastic tr ...

SIAM PUBLICATIONS2022

Harmonic decomposition of the trace of 1D transfer matrices in layered media

Antonio Joaquin Garcia Suarez

The Transfer Matrix formalism is ubiquitous when it comes to study wave propagation in various stratified media, applications ranging from Seismology to Quantum Mechanics. A relation between variables at two points in two different layers can be establishe ...

2022

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

Drops: Controlled crystallization of organic crystals and their use as matrix materials for encapsulation of volatiles

Aysu Ceren Okur

Encapsulation techniques open up new possibilities to control the kinetics and location of the release of active ingredients. Despite the progresses achieved to obtain a better control over the dimensions and composition of the capsules, the encapsulation ...

EPFL2022