Publications related to Second derivative

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 ...

Amer Mathematical Soc2023

The hunt for the Karman 'constant' revisited

Peter Monkewitz

The log law of the wall, joining the inner, near-wall mean velocity profile (MVP) in wall-bounded turbulent flows to the outer region, has been a permanent fixture of turbulence research for over hundred years, but there is still no general agreement on th ...

Cambridge University Press2023

Extension, validation, and optimization of Serpent/DYN3D/ATHLET code system for SFR applications

Vincenzo Anthony Di Nora

The sequence of codes Serpent/DYN3D has been developed by the Helmholtz-Zentrum Dresden-Rossendorf and successfully applied to core static and transient analyses of sodium-cooled fast reactors (SFRs). The successful application of the sequence to SFRs was ...

EPFL2023

Safe Zeroth-Order Convex Optimization Using Quadratic Local Approximations

Giancarlo Ferrari Trecate, Maryam Kamgarpour, Yuning Jiang, Baiwei Guo

We address black-box convex optimization problems, where the objective and constraint functions are not explicitly known but can be sampled within the feasible set. The challenge is thus to generate a sequence of feasible points converging towards an optim ...

IEEE2023

Pollution mask for the continuous corrected particle number concentration data in 1 min time resolution measured in the Swiss aerosol container using a whole air inlet during MOSAiC 2019/2020

Julia Schmale, Andrea Baccarini, Ivo Fabio Beck, Hélène Paule Angot

This dataset contains particle number concentrations and a pollution flag in 1 min time resolution. It is derived by the pollution detection algorithm (PDA, doi:10.5281/zenodo.5761101) based on the corrected particle number concentration data of the CPC377 ...

Zenodo2023

Stochastic derivative estimation for max-stable random fields

Erwan Fabrice Koch

We consider expected performances based on max-stable random fields and we are interested in their derivatives with respect to the spatial dependence parameters of those fields. Max-stable fields, such as the Brown-Resnick and Smith fields, are very popula ...

ELSEVIER2022

Learning of Continuous and Piecewise-Linear Functions With Hessian Total-Variation Regularization

Michaël Unser, Shayan Aziznejad, Joaquim Gonçalves Garcia Barreto Campos

We develop a novel 2D functional learning framework that employs a sparsity-promoting regularization based on second-order derivatives. Motivated by the nature of the regularizer, we restrict the search space to the span of piecewise-linear box splines shi ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Nicolas Boumal

We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...

SPRINGER HEIDELBERG2022

Pollution mask for the continuous corrected particle number concentration data in 1 min resolution, measured in the Swiss aerosol container during MOSAiC 2019/2020

Julia Schmale, Ivo Fabio Beck, Andrea Baccarini, Hélène Paule Angot

This dataset contains a pollution flag in 1 min time resolution. It is derived by the pollution detection algorithm (PDA) based on the corrected particle number concentration data (DOI upcoming) measured during the year long MOSAiC expedition from October ...

Zenodo2022

Polarity Of Almost All Points For Systems Of Nonlinear Stochastic Heat Equations In The Critical Dimension

Robert Dalang

We study vector-valued solutions u(t, x) is an element of R-d to systems of nonlinear stochastic heat equations with multiplicative noise, ...

INST MATHEMATICAL STATISTICS-IMS2021

Pollution Detection Algorithm (PDA)

Julia Schmale, Andrea Baccarini, Ivo Fabio Beck, Hélène Paule Angot

The Pollution Detection Algorithm (PDA) is an algorithm to identify and flag periods of primary polluted data in remote atmospheric time series in five steps. The first and most important step identifies polluted periods based on the gradient (time-derivat ...

Zenodo2021

Local Non-Rigid Structure-from-Motion from Locally Diffeomorphic Mappings

Pascal Fua, Mathieu Salzmann, Shaifali Parashar

We propose a new formulation to the non-rigid structure-from-motion problem that only requires the deforming surface to meaning that its differential structure is preserved. This is a much weaker assumption than the traditional ones of isometry or conforma ...

2020

Computation of "Best" Interpolants in the Lp Sense

Michaël Unser, Pakshal Narendra Bohra

We study a variant of the interpolation problem where the continuously defined solution is regularized by minimizing the L p -norm of its second-order derivative. For this continuous-domain problem, we propose an exact discretization scheme that restricts ...

2020

A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation

Charles Stuart

In an open, bounded subset Omega of R-N such that 0 is an element of Omega we consider the nonlinear eigenvalue problem -Sigma(N)(i,j,=1) partial derivative(i){A(ij)(x)partial derivative(j)u} + V(x)u + n(x,del u)+ g(x, u) = lambda u in Omega integral(Omega ...

2020

Linear Speedup In Saddle-Point Escape For Decentralized Non-Convex Optimization

Ali H. Sayed, Stefan Vlaski

Under appropriate cooperation protocols and parameter choices, fully decentralized solutions for stochastic optimization have been shown to match the performance of centralized solutions and result in linear speedup (in the number of agents) relative to no ...

IEEE2020

On design strategies for binary dielectric metasurfaces based on the Fourier modal method

Kévin Müller

Binary dielectric metasurfaces are arrays of sub-wavelength structures that act as a thin layer of artificial material. They are generally lossless and relatively simple to fabricate since only a single structuring step is required. By carefully designing ...

EPFL2020

A note on efficient computation of privileged directions in modifier adaptation

Dominique Bonvin, Martand Singhal, Timm Faulwasser, Alejandro Gabriel Marchetti

In the presence of plant-model mismatch, the estimation of plant gradients is key to the performance of measurement-based iterative optimization schemes. However, gradient estimation requires time-consuming experiments, wherein the plant is sequentially pe ...

PERGAMON-ELSEVIER SCIENCE LTD2020

Finding Second-Order Stationary Points in Constrained Minimization: A Feasible Direction Approach

Shaul Nadav Hallak

This paper introduces a method for computing points satisfying the second-order necessary optimality conditions for nonconvex minimization problems subject to a closed and convex constraint set. The method comprises two independent steps corresponding to t ...

SPRINGER/PLENUM PUBLISHERS2020

Radiative Backpropagation: An Adjoint Method for Lightning-Fast Differentiable Rendering

Wenzel Alban Jakob, Sébastien Nicolas Speierer, Merlin Eléazar Nimier-David

Physically based differentiable rendering has recently evolved into a powerful tool for solving inverse problems involving light. Methods in this area perform a differentiable simulation of the physical process of light transport and scattering to estimate ...

ASSOC COMPUTING MACHINERY2020

On the choice of metric in gradient-based theories of brain function

Wulfram Gerstner, Johanni Michael Brea, Jean-Pascal Théodor Pfister

The idea that the brain functions so as to minimize certain costs pervades theoretical neuroscience. Because a cost function by itself does not predict how the brain finds its minima, additional assumptions about the optimization method need to be made to ...

2020