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Fixed points and amenability in non-positive curvature

Related publications (57)

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Training DNNs with Hybrid Block Floating Point

Babak Falsafi, Martin Jaggi, Tao Lin, Mario Paulo Drumond Lages De Oliveira

The wide adoption of DNNs has given birth to unrelenting computing requirements, forcing datacenter operators to adopt domain-specific accelerators to train them. These accelerators typically employ densely packed full-precision floating-point arithmetic t ...

2018

Geometry-aware Deep Network for Single-Image Novel View Synthesis

Mathieu Salzmann

This paper tackles the problem of novel view synthesis from a single image. In particular, we target real-world scenes with rich geometric structure, a challenging task due to the large appearance variations of such scenes and the lack of simple 3D models ...

IEEE2018

Representing groups against all odds

Maxime Gheysens

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

Fixed Points For Bounded Orbits In Hilbert Spaces

Nicolas Monod, Maxime Gheysens

Consider the following property of a topological group G: every continuous affine G-action on a Hilbert space with a bounded orbit has a fixed point. We prove that this property characterizes amenability for locally compact a-compact groups (e.g., countabl ...

Elsevier2017

An upper bound for the Tarski numbers of nonamenable groups of piecewise projective homeomorphisms

Yash Lodha

The Tarski number of a nonamenable group is the smallest number of pieces needed for a paradoxical decomposition of the group. Nonamenable groups of piecewise projective homeomorphisms were introduced in [N. Monod, Groups of piecewise projective homeomorph ...

World Scientific Publ Co Pte Ltd2017

The size of the sync basin revisited

Philippe René Joseph Jacquod, Robin Delabays

In dynamical systems, the full stability of fixed point solutions is determined by their basins of attraction. Characterizing the structure of these basins is, in general, a complicated task, especially in high dimensionality. Recent works have advocated t ...

Amer Inst Physics2017

Secure numerical and logical multi party operations

Bin Lu

We derive algorithms for efficient secure numerical and logical operations in the semi-honest model ensuring statistical or perfect security for secure multi-party computation (MPC). To derive our algorithms for trigonometric functions, we use basic mathem ...

Elsevier Science Bv2017

Variations on a theme by Higman

Nicolas Monod

We propose elementary and explicit presentations of groups that have no amenable quotients and yet are SQ-universal. Examples include groups with a finite K (pi,1), no Kazhdan subgroups and no Haagerup quotients. ...

Elsevier2017

Extreme points in non-positive curvature

Nicolas Monod

A natural analogue of the Krein-Milman theorem is shown to fail for CAT(0) spaces. ...

Polish Acad Sciences Inst Mathematics-Impan2016

A parametric augmented Lagrangian algorithm for real-time economic NMPC

Colin Neil Jones, Jean-Hubert Hours, Harsh Ambarishkumar Shukla

In this paper, a novel optimality-tracking algorithm for solving Economic Nonlinear Model Predictive Control (ENMPC) problems in real-time is presented. Developing online schemes for ENMPC is challenging, since it is unclear how convexity of the Quadratic ...

IEEE2016