Publications related to Boundary (topology)

A Shape Derivative Approach to Domain Simplification

Annalisa Buffa, Jochen Peter Hinz, Ondine Gabrielle Chanon, Alessandra Arrigoni

The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is maintained under control. ...

Elsevier Sci Ltd2023

From SU(2)5 to SU(2)3 Wess-Zumino-Witten transitions in a frustrated spin-52 chain

Frédéric Mila, Natalia Chepiga

We investigate the properties of a frustrated spin-5/2 chain with next-nearest-neighbor two- and three-site interactions, with two questions in mind: the nature of the transition into the dimerized phase induced by the three-site interaction, and the possi ...

2022

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Wulfram Gerstner, Clément Hongler, Johanni Michael Brea, Francesco Spadaro, Berfin Simsek, Arthur Jacot

We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at $ r_1^*! \c ...

2021

Induction of a chromatin boundary in vivo upon insertion of a tad border

Denis Duboule, Christopher Chase Bolt, Lucille Delisle, Edgardo Rodriguez Carballo, Marie-Laure Gadolini

Author summary During development, enhancer sequences tightly regulate the spatio-temporal expression of target genes often located hundreds of kilobases away. This complex process is made possible by the folding of chromatin into domains, which are separa ...

2021

A unifying framework for form-finding and topology-finding of tensegrity structures

Yafeng Wang

This paper presents a unifying framework for the form-finding and topology-finding of tensegrity structures. The novel computational framework is based on rank-constrained linear matrix inequalities. For form-finding, given the topology (i.e., member conne ...

PERGAMON-ELSEVIER SCIENCE LTD2021

Entanglement Entropy from Nonequilibrium Work

Jonathan D'Emidio

The Renyi entanglement entropy in quantum many-body systems can be viewed as the difference in free energy between partition functions with different trace topologies. We introduce an external field lambda that controls the partition function topology, all ...

AMER PHYSICAL SOC2020

Robust Fano resonance in a topological mechanical beam

Romain Christophe Rémy Fleury, Wei Wang

The advances in topological condensed matter physics enable the manipulation of classic waves in different ways, such as unidirectional propagation featuring the suppression of backscattering and the robustness against impurities and disorder, making it po ...

2020

Instability of Thin Concrete Walls with a Single Layer of Reinforcement under Cyclic Loading: Numerical Simulation and Improved Equivalent Boundary Element Model for Assessment

Katrin Beyer, João Saraiva Esteves Pacheco de Almeida, Angelica Rosso, Lisandro Arturo Jimenez Roa

Thin reinforced concrete walls may fail due to out-of-plane instability when subjected to seismic loading. While previous numerical studies on wall instability have focused on the behaviour of members with two layers of vertical reinforcement, this work ad ...

TAYLOR & FRANCIS LTD2022

On the Hardness of the Strongly Dependent Decision Problem

Martin Biely

We present necessary and sufficient conditions for solving the strongly dependent decision (SDD) problem in various distributed systems. Our main contribution is a novel characterization of the SDD problem based on point-set topology. For partially synchro ...

ASSOC COMPUTING MACHINERY2019

Detecting Anisotropic Inclusions Through EIT

Jan Cristina

We study the evolution equation where is the Dirichlet-Neumann operator of a decreasing family of Riemannian manifolds with boundary . We derive a lower bound for the solution of such an equation, and apply it to a quantitative density estimate for the res ...

Springer2017

On some algebraic and extremal problems in discrete geometry

Seyed Hossein Nassajianmojarrad

In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer

n\ge 3

, we define

e(n)

to be the minimum positive integer such that an ...

EPFL2017

Calculus of Variations for Differential Forms

Swarnendu Sil

In this thesis we study calculus of variations for differential forms. In the first part we develop the framework of direct methods of calculus of variations in the context of minimization problems for functionals of one or several differential forms of th ...

EPFL2016

A real-time multi-aperture omnidirectional visual sensor with interconnected network of smart cameras

Hossein Afshari

A novel omnidirectional visual sensor called the Panoptic camera is introduced. The Panoptic camera is an omnidirectional multi-aperture visual system which is realized by mounting multiple camera sensors on a hemispherical frame. The introduced visual sen ...

EPFL2013

A result on flip-graph connectivity

Lionel Pournin

A polyhedral subdivision of a d-dimensional point configuration A is k-regular if it is projected from the boundary complex of a polytope with dimension at most d+k. Call γk(A) the subgraph induced by k-regular triangulations in the flip-graph of A. Gel’fa ...

Walter de Gruyter2012

Erdos-Szekeres-type theorems for monotone paths and convex bodies

János Pach

For any sequence of positive integers j(1)< j(2)= 2 and q >= 2, what is the s ...

London Math Soc2012

Weakly regular subdivisions

Lionel Pournin

It is shown that 2-dimensional subdivisions can be made regular by moving their vertices within parallel 1-dimensional spaces. As a consequence, any 2-dimensional subdivision is projected from the boundary complex of a 4-polytope. ...

Springer-Verlag2012

Contour parallel milling tool path generation for arbitrary pocket shape using a fast marching method

Paul Xirouchakis, Sandeep Dhanik

Contour parallel tool paths are among the most widely used tool paths for planer milling operations. A number of exact as well as approximate methods are available for offsetting a closed boundary in order to generate a contour parallel tool path; however, ...

Springer-Verlag2010

Multiplicities of simple closed geodesics and hypersurfaces in Teichmuller space

Hugo Parlier

Using geodesic length functions, we define a natural family of real codimension 1 subvarieties of Teichmuller space, namely the subsets where the lengths of two distinct simple closed geodesics are of equal length. We investigate the point set topology of ...

2008

Points surrounding the origin

János Pach, Andreas Fukami Holmsen

Suppose d > 2, n > d+1, and we have a set P of n points in d-dimensional Euclidean space. Then P contains a subset Q of d points such that for any p ∈ P, the convex hull of Q∪{p} does not contain the origin in its interior. We also show that for non-emp ...

2008