Publications related to A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation

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

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

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

Weak nonlinearity for strong non-normality

François Gallaire, Edouard Boujo, Yves-Marie François Ducimetière

We propose a theoretical approach to derive amplitude equations governing the weakly nonlinear evolution of non-normal dynamical systems, when they experience transient growth or respond to harmonic forcing. This approach reconciles the non-modal nature of ...

2022

Spectral Hypergraph Sparsifiers of Nearly Linear Size

Mikhail Kapralov, Jakab Tardos

Graph sparsification has been studied extensively over the past two decades, culminating in spectral sparsifiers of optimal size (up to constant factors). Spectral hypergraph sparsification is a natural analogue of this problem, for which optimal bounds on ...

IEEE COMPUTER SOC2022

Automated identification of local contamination in remote atmospheric composition time series

Julia Schmale, Andrea Baccarini, Jian Wang, Ivo Fabio Beck, Hélène Paule Angot, Lubna Dada

A common challenge of atmospheric measurements in remote environments is to identify pollution from nearby activities that interfere with the purpose of the observations. Pollution, particularly from combustion, typically reveals itself in enhanced particl ...

2022

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, partial derivative/partial derivative t u(t, x) = partial derivative(2)/partial derivative x(2) u(t, x) + sigma (u(t, ...

INST MATHEMATICAL STATISTICS-IMS2021

Global bifurcation at isolated singular points of the Hadamard derivative

Charles Stuart

Consider F is an element of C(RxX,Y) such that F(lambda, 0) = 0 for all lambda is an element of R, where X and Y are Banach spaces. Bifurcation from the line Rx{0} of trivial solutions is investigated in cases where F(lambda, center dot ) need not be Frech ...

2021

Automatic locking of a parametrically resonating, base-excited, nonlinear beam

Amit Yedidia Dolev

Described is a closed-loop control scheme capable of stabilizing a parametrically excited nonlinear structure in several vibration modes. By setting the relative phase between the spatially filtered response and the excitation, the open-loop unstable solut ...

SPRINGER2021

The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations

Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod

Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreten ess of the set of eigenvalues of the transmission problem and studied their locations. In this paper, we establish ...

2021

A first-order primal-dual method with adaptivity to local smoothness

Volkan Cevher, Maria-Luiza Vladarean

We consider the problem of finding a saddle point for the convex-concave objective

\min_x \max_y f(x) + \langle Ax, y\rangle - g^*(y)

, where

f

is a convex function with locally Lipschitz gradient and

g

is convex and possibly non-smooth. We propose an ...

2021

A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation

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

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

Weak nonlinearity for strong non-normality

Spectral Hypergraph Sparsifiers of Nearly Linear Size

Automated identification of local contamination in remote atmospheric composition time series

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

Global bifurcation at isolated singular points of the Hadamard derivative

Automatic locking of a parametrically resonating, base-excited, nonlinear beam

The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations

A first-order primal-dual method with adaptivity to local smoothness

Spectral Hypergraph Sparsifiers of Nearly Linear Size

Global bifurcation at isolated singular points of the Hadamard derivative

The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations

Weak nonlinearity for strong non-normality

Automated identification of local contamination in remote atmospheric composition time series

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

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

Automatic locking of a parametrically resonating, base-excited, nonlinear beam

A first-order primal-dual method with adaptivity to local smoothness

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