Publications related to Analysis

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Volkan Cevher, Grigorios Chrysos, Fanghui Liu

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

2024

On the Sums over Inverse Powers of Zeros of the Hurwitz Zeta Function and Some Related Properties of These Zeros

Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of the analytical function to find the sums over inverse powers of zeros for the incomplete gamma and Riemann zeta functions, polygamma functions, an ...

MDPI2024

BPS invariants from p-adic integrals

Dimitri Stelio Wyss, Francesca Carocci, Giulio Orecchia

We define p-adic BPS or pBPS invariants for moduli spaces M-beta,M-chi of one-dimensional sheaves on del Pezzo and K3 surfaces by means of integration over a non-archimedean local field F. Our definition relies on a canonical measure mu can on the F-analyt ...

Cambridge Univ Press2024

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Alfio Quarteroni, Francesco Regazzoni, Stefano Pagani

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

Nature Portfolio2024

Efficient Continual Finite-Sum Minimization

Volkan Cevher, Efstratios Panteleimon Skoulakis, Leello Tadesse Dadi

Given a sequence of functions

f_1,\ldots,f_n

with

f_i:\mathcal{D}\mapsto \mathbb{R}

, finite-sum minimization seeks a point

{x}^\star \in \mathcal{D}

minimizing

\sum_{j=1}^nf_j(x)/n

. In this work, we propose a key twist into the finite-sum minimizat ...

2024

Transportation-based functional ANOVA and PCA for covariance operators

Victor Panaretos, Yoav Zemel, Valentina Masarotto

We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...

Inst Mathematical Statistics-Ims2024

Robust mass lumping and outlier removal strategies in isogeometric analysis

Annalisa Buffa, Espen Sande, Yannis Dirk Voet

Mass lumping techniques are commonly employed in explicit time integration schemes for problems in structural dynamics and both avoid solving costly linear systems with the consistent mass matrix and increase the critical time step. In isogeometric analysi ...

2024

Null energy constraints on two-dimensional RG flows

Grégoire Olivier Mathys

We study applications of spectral positivity and the averaged null energy condition (ANEC) to renormalization group (RG) flows in two-dimensional quantum field theory. We find a succinct new proof of the Zamolodchikov c-theorem, and derive further independ ...

New York2024

Adaptive Finite Elements with Large Aspect Ratio. Application to Aluminium Electrolysis

Paride Passelli

The goal of this work is to use anisotropic adaptive finite elements for the numerical simulation of aluminium electrolysis. The anisotropic adaptive criteria are based on a posteriori error estimates derived for simplified problems. First, we consider an ...

EPFL2024

Stability of the Faber-Krahn inequality for the short-time Fourier transform

Joao Pedro Gonçalves Ramos

We prove a sharp quantitative version of the Faber–Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit which measures by how much the STFT of a function fails to be optimally concentrated on an arbitrary set of pos ...

Springer Heidelberg2024

Analysis

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Generalization of Scaled Deep ResNets in the Mean-Field Regime

On the Sums over Inverse Powers of Zeros of the Hurwitz Zeta Function and Some Related Properties of These Zeros

BPS invariants from p-adic integrals

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Efficient Continual Finite-Sum Minimization

Transportation-based functional ANOVA and PCA for covariance operators

Robust mass lumping and outlier removal strategies in isogeometric analysis

Null energy constraints on two-dimensional RG flows

Adaptive Finite Elements with Large Aspect Ratio. Application to Aluminium Electrolysis

Stability of the Faber-Krahn inequality for the short-time Fourier transform

On the Sums over Inverse Powers of Zeros of the Hurwitz Zeta Function and Some Related Properties of These Zeros

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Robust mass lumping and outlier removal strategies in isogeometric analysis

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Efficient Continual Finite-Sum Minimization

Transportation-based functional ANOVA and PCA for covariance operators

Null energy constraints on two-dimensional RG flows

BPS invariants from p-adic integrals

Adaptive Finite Elements with Large Aspect Ratio. Application to Aluminium Electrolysis

Stability of the Faber-Krahn inequality for the short-time Fourier transform