Publications related to Geometric topology

Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups

We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring g ...

SPRINGER HEIDELBERG2023

Arithmetic and geometric deformations of threefolds

Stefano Filipazzi, Fabio Bernasconi

We show that mixed-characteristic and equicharacteristic small deformations of 3-dimensional canonical (resp., terminal) singularities with perfect residue field of characteristic p>5 are canonical (resp., terminal). We discuss applications to arithmetic a ...

Wiley2023

Computational Exploration of Multistable Elastic Knots

Mark Pauly, Michele Vidulis, Yingying Ren

We present an algorithmic approach to discover, study, and design multistable elastic knots. Elastic knots are physical realizations of closed curves embedded in 3-space. When endowed with the material thickness and bending resistance of a physical wire, t ...

2023

Seeding and Emergence of Composite Skyrmions in a van der Waals Magnet

Klaus Kern, Marko Burghard, Lukas Powalla

Topological charge plays a significant role in a range of physical systems. In particular, observations of real-space topological objects in magnetic materials have been largely limited to skyrmions - states with a unitary topological charge. Recently, mor ...

Wiley-V C H Verlag Gmbh2023

From Trees to Barcodes and Back Again: A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

Adélie Eliane Garin

In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view. Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B invol ...

EPFL2022

Incompleteness of graph neural networks for points clouds in three dimensions

Michele Ceriotti, Sergey Pozdnyakov

Graph neural networks (GNN) are very popular methods in machine learning and have been applied very successfully to the prediction of the properties of molecules and materials. First-order GNNs are well known to be incomplete, i.e. there exist graphs that ...

IOP Publishing Ltd2022

Efficient implementation of atom-density representations

Michele Ceriotti, Guillaume André Jean Fraux, Till Junge, Félix Benedito Clément Musil, Michael John Willatt, Max David Veit, Alexander Jan Goscinski

Physically motivated and mathematically robust atom-centered representations of molecular structures are key to the success of modern atomistic machine learning. They lie at the foundation of a wide range of methods to predict the properties of both materi ...

2021

A stability theory beyond the co-rotational setting for critical wave maps blow up

Joachim Krieger, Shuang Miao

We exhibit non-equivariant perturbations of the blowup solutions constructed in [18] for energy critical wave maps into

\mathbb{S}^2

. Our admissible class of perturbations is an open set in some sufficiently smooth topology and vanishes near the light co ...

2020

Optimum design of low environmental impact structures through component reuse

Jan Friedrich Georg Brütting

Load-bearing systems (structures) in buildings and infrastructure contribute to a significant share of adverse environmental impacts (EI) because of resource- and energy-intensive fabrication. A currently overlooked circular economy strategy to reduce EI i ...

EPFL2020

Kernel Density Estimation through Density Constrained Near Neighbor Search

Mikhail Kapralov, Navid Nouri

In this paper we revisit the kernel density estimation problem: given a kernel K(x, y) and a dataset of n points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query q, a (1 + epsilon)-approximation to mu := ...

IEEE2020

Exact Synthesis of LTL Properties from Traces

Heinz Riener

We present an exact approach to synthesize temporal-logic formulas in linear temporal logic (LTL) from a set of given positive and negative example traces. Our approach uses topology structures, in particular partial DAGs, to partition the search space int ...

IEEE2019

Efficient geometric integrators for nonadiabatic quantum dynamics. II. The diabatic representation

Jiri Vanicek, Seonghoon Choi, Julien Roulet

Exact nonadiabatic quantum evolution preserves many geometric properties of the molecular Hilbert space. In the first paper of this series ["Paper I," S. Choi and J. Vaníček, J. Chem. Phys. 150, 204112 (2019)], we presented numerical integrators of arbitra ...

2019

Pattern formation in thin liquid films: from coating-flow instabilities to microfluidic droplets

Gioele Mariano Nicolò Balestra

Nature and technical applications abound with thin viscous flows, ranging from the lava flow on volcanoes to the lubricating layer around confined bubbles in the microchannels of Lab-on-a-Chip devices. Countless are the examples where coating flows arise i ...

EPFL2018

Dynamics of falling films on the outside of a vertical rotating cylinder: waves, rivulets and dripping transitions

François Gallaire, Nicolas Igor Jacques Kofman

Falling liquid films on the underside of a plate or on the outside of a rotating cylinder are subject to a destabilizing body force. The evolution of the film topology is determined by interactions between the Kapitza and the Rayleigh-Taylor instability, l ...

Cambridge University Press2017

Understanding the mixing process in 3D microfluidic nozzle/diffuser systems: simulations and experiments

Martinus Gijs, Abdeljalil Sayah

We characterise computationally and experimentally a three-dimensional (3D) microfluidic passive mixer for various Reynolds numbers ranging from 1 to 100, corresponding to primary flow rates of 10-870 mu l min(-1). The 3D mixing channel is composed of mult ...

Iop Publishing Ltd2016

Muscle Moment-Arms: A Key Element in Muscle-Force Estimation

Alexandre Terrier, Philippe Müllhaupt, Alain Farron, Christoph Anselm Engelhardt, David Ingram

A clear and rigorous definition of muscle moment-arms in the context of musculoskeletal systems modelling is presented, using classical mechanics and screw theory. The definition provides an alternative to the tendon excursion method, which can lead to inc ...

Taylor & Francis2015

A link between short-range and long-range properties of random sphere packings

Daniele Mari, Gérard Gremaud, Arnaud Comment, Riccardo Balzan, Alessandro Luigi Sellerio

We present a high precision particle-by-particle 3D reconstruction of granular systems composed of monodispersed spheres (sphere packings); the experimental approach is based on magnetic resonance imaging techniques. Our measurements revealed a strong corr ...

Springer Berlin Heidelberg2013

Capacities, Systoles and Jacobians of Riemann Surfaces

Björn Mützel

To any compact Riemann surface of genus g one may assign a principally polarized abelian variety (PPAV) of dimension g, the Jacobian of the Riemann surface. The Jacobian is a complex torus and we call a Gram matrix of the lattice of a Jacobian a period Gra ...

EPFL2011

The geometric structure of complex fluids

Tudor Ratiu, François Gay-Balmaz

This paper develops the theory of affine Euler-Poincare and affine Lie-Poisson reductions and applies these processes to various examples of complex fluids, including Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids, spin glasses, microf ...

Elsevier2009

Parallel mesh adaptive techniques for complex flow simulation

Angelo Casagrande

Dynamic mesh adaptation on unstructured grids, by localised refinement and derefinement, is a very efficient tool for enhancing solution accuracy and optimise computational time. One of the major drawbacks however resides in the projection of the new nodes ...

EPFL2008