Publications related to On linear and quadratic Lipschitz bounds for twice continuously differentiable functions

Seeking the new, learning from the unexpected: Computational models of surprise and novelty in the brain

Human babies have a natural desire to interact with new toys and objects, through which they learn how the world around them works, e.g., that glass shatters when dropped, but a rubber ball does not. When their predictions are proven incorrect, such as whe ...

EPFL2024

Stable parameterization of continuous and piecewise-linear functions

Michaël Unser, Alexis Marie Frederic Goujon, Joaquim Gonçalves Garcia Barreto Campos

Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...

2023

IMPROVED REGULARITY OF SECOND DERIVATIVES FOR SUBHARMONIC FUNCTIONS

Xavier Fernandez-Real Girona, Riccardo Tione

In this note, we prove that if a subharmonic function Delta u >= 0 has pure second derivatives partial derivative(ii)u that are signed measures, then their negative part (partial derivative(ii)u)- belongs to L-1 (in particular, it is not singular). We then ...

Providence2023

Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022

Spectral analysis for transmission eigenvalue problems with and without the complementing conditions

Jean Louis-Alexandre Fornerod

The interior transmission eigenvalue problem is a system of partial differential equations equipped with Cauchy data on the boundary: the transmission conditions. This problem appears in the inverse scattering theory for inhomogeneous media when, for some ...

EPFL2022

Compact, Spatial-mode-interaction-free, Ultralow-loss, Nonlinear photonic integrated circuits

Tobias Kippenberg, Rui Ning Wang, Xinru Ji, Zheru Qiu, Junqiu Liu, Jijun He

We implement Euler bends to build compact high-Q Si3N4 racetrack microresonators, featuring a small footprint of only 0.21 mm(2) for 19.8 GHz FSR. We demonstrate that these multi-mode microresonators can be operated in the single-mode regime and generate a ...

IEEE2022

Explaining multiple patches of aquatic vegetation through linear stability analysis

Giulio Calvani

Aquatic vegetation is ubiquitous in lowland rivers, and it is typically present in the shape of spatial self-organized patches of biomass. In this work, we mathematically define the threshold conditions for the incipient formation of self-organized vegetat ...

2022

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

Nicolas Henri Bernard Flammarion

We consider the problem of sampling from a density of the form p(x) ? exp(-f (x) - g(x)), where f : Rd-+ R is a smooth function and g : R-d-+ R is a convex and Lipschitz function. We propose a new algorithm based on the Metropolis-Hastings framework. Under ...

MICROTOME PUBL2022

A combinatorial proof of a sumset conjecture of Furstenberg

Florian Karl Richter

We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if

\log r / \log s

is irrational and

X

and

Y

are

\times r

- and

\times s

-invariant subsets of

[0,1]

, respectively, then $\dim_\text{ ...

2021

Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

Maria Carola Colombo, Silja Noëmi Aline Haffter

We consider the SQG equation with dissipation given by a fractional Laplacian of order α

2021

On linear and quadratic Lipschitz bounds for twice continuously differentiable functions

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Seeking the new, learning from the unexpected: Computational models of surprise and novelty in the brain

Stable parameterization of continuous and piecewise-linear functions

IMPROVED REGULARITY OF SECOND DERIVATIVES FOR SUBHARMONIC FUNCTIONS

Localization errors of the stochastic heat equation

Spectral analysis for transmission eigenvalue problems with and without the complementing conditions

Compact, Spatial-mode-interaction-free, Ultralow-loss, Nonlinear photonic integrated circuits

Explaining multiple patches of aquatic vegetation through linear stability analysis

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

A combinatorial proof of a sumset conjecture of Furstenberg

Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

Seeking the new, learning from the unexpected: Computational models of surprise and novelty in the brain

Stable parameterization of continuous and piecewise-linear functions

Localization errors of the stochastic heat equation

A combinatorial proof of a sumset conjecture of Furstenberg

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

Explaining multiple patches of aquatic vegetation through linear stability analysis

Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

Compact, Spatial-mode-interaction-free, Ultralow-loss, Nonlinear photonic integrated circuits

Spectral analysis for transmission eigenvalue problems with and without the complementing conditions

IMPROVED REGULARITY OF SECOND DERIVATIVES FOR SUBHARMONIC FUNCTIONS