Publications related to Finite group

Physical and unphysical regimes of self-consistent many-body perturbation theory

In the standard framework of self-consistent many-body perturbation theory, the skeleton series for the self-energy is truncated at a finite order N and plugged into the Dyson equation, which is then solved for the propagator G(N). We consider two examples ...

Scipost Foundation2024

Lattice packings through division algebras

Nihar Prakash Gargava

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

Positive Definite Completions and Continuous Graphical Models

Kartik Waghmare

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

ALMOST EVERYWHERE NONUNIQUENESS OF INTEGRAL CURVES FOR DIVERGENCE-FREE SOBOLEV VECTOR FIELDS

Massimo Sorella

We construct divergence-free Sobolev vector fields in C([0,1];W-1,W-r(T-d;Rd)) with r < d and d\geq 2 which simultaneously admit any finite number of distinct positive solutions to the continuity equation. These vector fields are then shown to have at leas ...

Siam Publications2023

Learning From Heterogeneous Data Based on Social Interactions Over Graphs

Ali H. Sayed, Virginia Bordignon, Stefan Vlaski

This work proposes a decentralized architecture, where individual agents aim at solving a classification problem while observing streaming features of different dimensions and arising from possibly different distributions. In the context of social learning ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

Positivity Of The Cm Line Bundle For K-Stable Log Fanos

Quentin Arthur Frantisek Posva

We prove the bigness of the Chow-Mumford line bundle associated to a Q-Gorenstein family of log Fano varieties of maximal variation with uniformly K-stable general geometric fibers. This result generalizes a theorem of Codogni and Patakfalvi to the logarit ...

2022

A finiteness result for p-adic families of Bianchi modular forms

Vlad Serban

We study p-adic families of cohomological automorphic forms for GL(2) over imaginary quadratic fields and prove that families interpolating a Zariski-dense set of classical cuspidal automorphic forms only occur under very restrictive conditions. We show ho ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Microscopic field theory for structure formation in systems of self-propelled particles with generic torques

Ignacio Pagonabarraga Mora, Elena Sesé Sansa

We derive a dynamical field theory for self-propelled particles subjected to generic torques and forces by explicitly coarse-graining their microscopic dynamics, described by a many-body Fokker-Planck equation. The model includes both intrinsic torques ind ...

AIP Publishing2022

Elimination of ringing artifacts by finite-element projection in FFT-based homogenization

Till Junge, Ali Falsafi, Martin Ladecký

Micromechanical homogenization is often carried out with Fourier-accelerated methods that are prone to ringing artifacts. We here generalize the compatibility projection introduced by Vond.rejc et al. (2014) [24] beyond the Fourier basis. In particular, we ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimization

Volkan Cevher, Kimon Antonakopoulos, Efstratios Panteleimon Skoulakis, Leello Tadesse Dadi, Ali Kavis

We propose an adaptive variance-reduction method, called AdaSpider, for minimization of L-smooth, non-convex functions with a finite-sum structure. In essence, AdaSpider combines an AdaGrad-inspired [Duchi et al., 2011, McMahan & Streeter, 2010], but a fai ...

2022

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Eva Vidlicková

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

EPFL2022

Variational Methods For Continuous-Domain Inverse Problems: the Quest for the Sparsest Solution

Thomas Jean Debarre

The goal of this thesis is to study continuous-domain inverse problems for the reconstruction of sparse signals and to develop efficient algorithms to solve such problems computationally. The task is to recover a signal of interest as a continuous function ...

EPFL2022

Structure-preserving approaches and data-driven closure modeling for model order reduction

Nicolò Ripamonti

In this thesis, we propose model order reduction techniques for high-dimensional PDEs that preserve structures of the original problems and develop a closure modeling framework leveraging the Mori-Zwanzig formalism and recurrent neural networks. Since high ...

EPFL2022

Remarks on the derived center of small quantum groups

Anna Lachowska

Let u(q)(g) be the small quantum group associated with a complex semisimple Lie algebra g and a primitive root of unity q, satisfying certain restrictions. We establish the equivalence between three different actions of g on the center of u(q)(g) and on th ...

SPRINGER INTERNATIONAL PUBLISHING AG2021

Positive moments for scattering amplitudes

Riccardo Rattazzi, Francesco Riva, Marc Riembau Saperas, Brando Bellazzini

We find the complete set of conditions satisfied by the forward 2 -> 2 scattering amplitude in unitary and causal theories. These are based on an infinite set of energy dependent quantities (the arcs) which are dispersively expressed as moments of a positi ...

American Physical Society2021

Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals

Michaël Unser, Shayan Aziznejad, Thomas Jean Debarre

We present a novel framework for the reconstruction of 1D composite signals assumed to be a mixture of two additive components, one sparse and the other smooth, given a finite number of linear measurements. We formulate the reconstruction problem as a cont ...

2021

Convex optimization in sums of Banach spaces

Michaël Unser, Shayan Aziznejad

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

2021

Robust Differentiable SVD

Pascal Fua, Mathieu Salzmann, Zheng Dang, Wei Wang, Yinlin Hu

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) ...

2021

The Solution of the Deep Boltzmann Machine on the Nishimori Line

Emanuele Mingione, Diego Alberici

The deep Boltzmann machine on the Nishimori line with a finite number of layers is exactly solved by a theorem that expresses its pressure through a finite dimensional variational problem of min-max type. In the absence of magnetic fields the order paramet ...

SPRINGER2021

A Large, Finite Permutation of Specific, Discrete Variants: Dan Graham's Children's Pavilion at Chambres d'Amis (1986)

Christophe van Gerrewey

In 1986, Dan Graham participated in Chambres d'Amis in Ghent, Belgium, curated by Jan Hoet as an art exhibition outside of the museum, in individual houses. With the help of a local architect, Graham constructed a glass and steel pavilion in a private gard ...

ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD2021