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Criteria for the existence of a potential well

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We investigate how probability tools can be useful to study representations of non-amenable groups. A suitable notion of "probabilistic subgroup" is proposed for locally compact groups, and is valuable to induction of representations. Nonamenable groups ad ...

EPFL2017

Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization

Volkan Cevher, Jonathan Mark Scarlett, Ilija Bogunovic

In this paper, we consider the problem of sequentially optimizing a black-box function

f

based on noisy samples and bandit feedback. We assume that

f

is smooth in the sense of having a bounded norm in some reproducing kernel Hilbert space (RKHS), yield ...

2017

We analyse the existence of multiple critical points for an even functional J : H -> R in the following context: the Hilbert space H can be split into an orthogonal sum H = Y circle plus Z in such a way that inf{J(u) : u is an element of Z and parallel to ...

Springer Heidelberg2016

On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

Daniel Kressner, André Uschmajew

Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems and eigenvalue p ...

Elsevier Science Inc2016

Bifurcation at isolated singular points for a degenerate elliptic eigenvalue problem

Charles Stuart

We consider bifurcation from the line of trivial solutions for a nonlinear eigenvalue problem on a bounded open subset, Omega, of R-N with N >= 3, containing 0. The leading term is a degenerate elliptic operator of the form L(u) = del . A del u where A is ...

Pergamon-Elsevier Science Ltd2015

Asymptotic bifurcation and second order elliptic equations on R-N

Charles Stuart

This paper deals with asymptotic bifurcation, first in the abstract setting of an equation G(u) = lambda u, where G acts between real Hilbert spaces and lambda is an element of R, and then for square-integrable solutions of a second order non-linear ellipt ...

Elsevier Science Bv2015

Renormalized solutions to the continuity equation with an integrable damping term

Maria Colombo

We consider the continuity equation with a nonsmooth vector field and a damping term. In their fundamental paper, DiPerna and Lions (Invent Math 98:511-547, 1989) proved that, when the damping term is bounded in space and time, the equation is well posed i ...

2015

Bifurcation without Frechet differentiability at the trivial solution

Charles Stuart

Criteria for the bifurcation of small solutions of an equation F(lambda,u) = 0 from a line {(lambda,0): lambda is an element of R} of trivial solutions are usually based on properties of the DuF(lambda,0) at the trivial solutions, where the partial derivat ...

Wiley-Blackwell2015

Estimation in Functional Lagged Regression

Lukasz Kidzinski

The paper introduces a functional time series (lagged) regression model. The impulse-response coefficients in such a model are operators acting on a separable Hilbert space, which is the function space L-2 in applications. A spectral approach to the estima ...

Wiley-Blackwell2015

Homogeneous Sobolev Metric of Order One on Diffeomorphism Groups on Real Line

Martins Bruveris, Martin Bauer

In this article we study Sobolev metrics of order one on diffeomorphism groups on the real line. We prove that the space equipped with the homogeneous Sobolev metric of order one is a flat space in the sense of Riemannian geometry, as it is isometric to an ...

Springer Verlag2014

Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization

Volkan Cevher, Jonathan Mark Scarlett, Ilija Bogunovic

In this paper, we consider the problem of sequentially optimizing a black-box function

f

based on noisy samples and bandit feedback. We assume that

f

is smooth in the sense of having a bounded norm in some reproducing kernel Hilbert space (RKHS), yield ...

2017