Publications related to Additive Envelopes of Continuous Functions

Universal Approximation Property of Hamiltonian Deep Neural Networks

Giancarlo Ferrari Trecate, Muhammad Zakwan

This letter investigates the universal approximation capabilities of Hamiltonian Deep Neural Networks (HDNNs) that arise from the discretization of Hamiltonian Neural Ordinary Differential Equations. Recently, it has been shown that HDNNs enjoy, by design, ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

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

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

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

Geometric ergodicity for some space-time max-stable Markov chains

Erwan Fabrice Koch

Max-stable processes are central models for spatial extremes. In this paper, we focus on some space-time max-stable models introduced in Embrechts et al. (2016). The processes considered induce discrete-time Markov chains taking values in the space of cont ...

ELSEVIER SCIENCE BV2019

Log Barriers for Safe Non-convex Black-box Optimization

Maryam Kamgarpour, Andreas Krause, Ilnura Usmanova

We address the problem of minimizing a smooth function f0(x) over a compact set D defined by smooth functional constraints fi(x)≤0, i=1,…,m given noisy value measurements of fi(x). This problem arises in safety-critical applications, where certain paramete ...

2019

Quantitative estimate on singularities in isoperimetric clusters

Maria Colombo

We prove a quantitative estimate on the number of certain singularities in almost minimizing clusters. In particular, we consider the singular points belonging to the lowest stratum of the Federer-Almgren stratification (namely, where each tangent cone doe ...

2019

Sign-Changing Solutions for a Class of Zero Mass Nonlocal Schrodinger Equations

We consider the following class of fractional Schrodinger equations: (-Delta)(alpha)u + V(x)u = K(x)f(u) in R-N, where alpha is an element of (0, 1), N > 2 alpha, (-Delta)(alpha) is the fractional Laplacian, V and K are positive continuous functions which ...

2019

Regularity of solutions for a fourth-order elliptic system via Conservation law

Changyu Guo

In this paper, we obtain interior Holder continuity for solutions of the fourth-order elliptic system Delta(2)u = Delta(V center dot del u) + div(w del u) + W center dot del u formulated by Lamm and Riviere [Comm. Partial Differential Equations 33 (2008) 2 ...

2019

Additive Envelopes of Continuous Functions

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Universal Approximation Property of Hamiltonian Deep Neural Networks

Localization errors of the stochastic heat equation

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

A combinatorial proof of a sumset conjecture of Furstenberg

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

Geometric ergodicity for some space-time max-stable Markov chains

Log Barriers for Safe Non-convex Black-box Optimization

Quantitative estimate on singularities in isoperimetric clusters

Sign-Changing Solutions for a Class of Zero Mass Nonlocal Schrodinger Equations

Regularity of solutions for a fourth-order elliptic system via Conservation law

Geometric ergodicity for some space-time max-stable Markov chains

Localization errors of the stochastic heat equation

A combinatorial proof of a sumset conjecture of Furstenberg

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

Universal Approximation Property of Hamiltonian Deep Neural Networks

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

Sign-Changing Solutions for a Class of Zero Mass Nonlocal Schrodinger Equations

Regularity of solutions for a fourth-order elliptic system via Conservation law

Log Barriers for Safe Non-convex Black-box Optimization

Quantitative estimate on singularities in isoperimetric clusters