Normalized Gaussian path integrals

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This thesis explores the innovative potential of active acoustic metamaterials in the manipulation of sound waves through dynamic control and topological principles. Traditional acoustic metamaterials, while capable of achieving remarkable feats such as ne ...

We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations partial derivative( t)u + u center dot del u = Delta u - del p + sigma + xi, u(0, center dot ) = u(0),div (u) = 0, driven by additive space-time white noi ...

While classical in many theoretical settings-and in particular in statistical physics-inspired works-the assumption of Gaussian i.i.d. input data is often perceived as a strong limitation in the context of statistics and machine learning. In this study, we ...

The probability of detecting technosignatures (i.e., evidence of technological activity beyond Earth) increases with their longevity, or the time interval over which they manifest. Therefore, the assumed distribution of longevities has some bearing on the ...

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 ...

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...

Networks of tryptophan (Trp)& horbar;an aromatic amino acid with strong fluorescence response & horbar;are ubiquitous in biological systems, forming diverse architectures in transmembrane proteins, cytoskeletal filaments, subneuronal elements, photorecepto ...

There is a bias in the inference pipeline of most diffusion models. This bias arises from a signal leak whose distribution deviates from the noise distribution, creating a discrepancy between training and inference processes. We demonstrate that this signa ...

The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...

Thin-laminate composites with thicknesses below 200 mu m hold significant promise for future, larger, and lighter deployable structures. This paper presents a study of the time-dependent failure behavior of thin carbon-fiber laminates under bending, focusi ...

The concept of soliton gas was introduced in 1971 by Zakharov as an infinite collection of weakly interacting solitons in the framework of Korteweg-de Vries (KdV) equation. In this theoretical construction of a diluted (rarefied) soliton gas, solitons with ...

We propose a local, non -intrusive model order reduction technique to accurately approximate the solution of coupled multi -component parametrized systems governed by partial differential equations. Our approach is based on the approximation of the boundar ...

We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive (d-6)\documentclass[12pt]{minimal} \usepackage{ ...

Decentralized learning is appealing as it enables the scalable usage of large amounts of distributed data and resources (without resorting to any central entity), while promoting privacy since every user minimizes the direct exposure of their data. Yet, wi ...

This article describes a field-based analytical model of single-sided linear induction motors (SLIMs) that explicitly considers the following effects altogether: finite motor length, magnetomotive force mmf space harmonics, slot effect, edge effect, and ta ...

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 ...

In various robotics applications, the selection of function approximation methods greatly influences the feasibility and computational efficiency of algorithms. Tensor Networks (TNs), also referred to as tensor decomposition techniques, present a versatile ...

Realand imaginary -time quantum state evolutions are crucial in physics and chemistry for exploring quantum dynamics, preparing ground states, and computing thermodynamic observables. On near -term devices, variational quantum time evolution is a promising ...

Normalized Gaussian path integrals

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Active Acoustic Metamaterials: A New Way to Understand Nonlinear and Topological Phenomena

Global existence for perturbations of the 2D stochastic Navier-Stokes equations with space-time white noise

Gaussian universality of perceptrons with random labels

Technosignatures Longevity and Lindy's Law

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

From low-rank retractions to dynamical low-rank approximation and back

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

Ultraviolet Superradiance from Mega-Networks of Tryptophan in Biological Architectures

Exploiting the Signal-Leak Bias in Diffusion Models

Anomalous dissipation and other non-smooth phenomena in fluids

Experimental characterization and stochastic models for time-dependent rupture of thin-ply composite laminates

Soliton gas: Theory, numerics, and experiments

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

Hitting with Probability One for Stochastic Heat Equations with Additive Noise

The Privacy Power of Correlated Noise in Decentralized Learning

Analytical Model of Single-Sided Linear Induction Motors for High-Speed Applications

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Robot Learning using Tensor Networks

Variational quantum time evolution without the quantum geometric tensor