Publications associées à Computation and visualization of ideal knot shapes

Spherical Convolutionnal Neural Networks: Empirical Analysis of SCNNs

Convolutional neural networks (CNNs) are powerful tools in Deep Learning mainly due to their ability to exploit the translational symmetry present in images, as they are equivariant to translations. Other datasets present different types of symmetries (e.g ...

2019

Periodic Motion of Sedimenting Flexible Knots

Giovanni Dietler, Krishnan Thyagarajan, Andrzej Stasiak

We study the dynamics of knotted deformable closed chains sedimenting in a viscous fluid. We show experimentally that trefoil and other torus knots often attain a remarkably regular horizontal toroidal structure while sedimenting, with a number of intertwi ...

APS2018

Concentration compactness for critical radial wave maps

Joachim Krieger, Elisabetta Chiodaroli

We consider radially symmetric, energy critical wave maps from (1 + 2)-dimensional Minkowski space into the unit sphere

\mathbf{S}^m

, m≥1, and prove global regularity and scattering for classical smooth data of finite energy. In addition, we establish a ...

2018

On chirality of toroidal embeddings of polyhedral graphs

Senja Dominique Barthel

We investigate properties of spatial graphs on the standard torus. It is known that nontrivial embeddings of planar graphs in the torus contain a nontrivial knot or a non-split link due to [2, 3]. Building on this and using the chirality of torus knots and ...

World Scientific Publishing2017

DETERMINING POSITIONS OF TRANSDUCERS FOR RECEIVING AND/OR TRANSMITTING WAVE SIGNALS

Paul Hurley, Matthieu Martin Jean-André Simeoni, Nezihe Merve Gürel

The invention is notably directed to a method for determining positions {pi}i=1,..., N of transducers {Ai}i=1,..., N of an apparatus. The transducers are assumed to be configured for receiving wave signals from and/or transmitting wave signals to one or mo ...

2017

Methods and apparatuses for versatile beamforming

Paul Hurley, Matthieu Martin Jean-André Simeoni, Giovanni Cherubini

The present invention is directed to methods and apparatuses for beamforming signals or compute beamformed signals. The present approach is to determine a series of beams from or for a set of devices configured for receiving signals from and/or transmittin ...

2017

Localization Genus

Jérôme Scherer

Which spaces look like an n-sphere through the eyes of the n-th Postnikov section functor and the n-connected cover functor? The answer is what we call the Postnikov genus of the n-sphere. We define in fact the notion of localization genus for any homotopi ...

Univ Autonoma Barcelona2017

Tuning knot abundance in semiflexible chains with crowders of different sizes: a Monte Carlo study of DNA chains

Giovanni Dietler

We use stochastic simulation techniques to sample the conformational space of linear semiflexible polymers in a crowded medium and study how the knotting properties depend on the crowder size and concentration. The abundance of physical knots in the chains ...

Royal Society of Chemistry2016

Stability of stationary wave maps from a curved background to a sphere

Sohrab Mirshams Shahshahani

We study time and space equivariant wave maps from

M \times \mathbb{R} \rightarrow S^2

, where

M

is dieomorphic to a two dimensional sphere and admits an action of

SO(2)

by isometries. We assume that metric on

M

can be written as $dr^2+f^2(r)d\theta ...

2016

Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots

Pedro Miguel Nunes Pereira de Almeida Reis

We combine experiments and theory to study the mechanics of overhand knots in slender elastic rods under tension. The equilibrium shape of the knot is governed by an interplay between topology, friction, and bending. We use precision model experiments to q ...

American Physical Society2015

Computation and visualization of ideal knot shapes

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Spherical Convolutionnal Neural Networks: Empirical Analysis of SCNNs

Periodic Motion of Sedimenting Flexible Knots

Concentration compactness for critical radial wave maps

On chirality of toroidal embeddings of polyhedral graphs

DETERMINING POSITIONS OF TRANSDUCERS FOR RECEIVING AND/OR TRANSMITTING WAVE SIGNALS

Methods and apparatuses for versatile beamforming

Localization Genus

Tuning knot abundance in semiflexible chains with crowders of different sizes: a Monte Carlo study of DNA chains

Stability of stationary wave maps from a curved background to a sphere

Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots

Localization Genus

On chirality of toroidal embeddings of polyhedral graphs

Periodic Motion of Sedimenting Flexible Knots

Spherical Convolutionnal Neural Networks: Empirical Analysis of SCNNs

Concentration compactness for critical radial wave maps

Methods and apparatuses for versatile beamforming

Tuning knot abundance in semiflexible chains with crowders of different sizes: a Monte Carlo study of DNA chains

Stability of stationary wave maps from a curved background to a sphere

Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots

DETERMINING POSITIONS OF TRANSDUCERS FOR RECEIVING AND/OR TRANSMITTING WAVE SIGNALS