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Euclidean geometry

Related publications (27)

The topology of a chaotic attractor in the Kuramoto-Sivashinsky equation

Tobias Schneider, Pierre Beck

The Birman-Williams theorem gives a connection between the collection of unstable periodic orbits (UPOs) contained within a chaotic attractor and the topology of that attractor, for three-dimensional systems. In certain cases, the fractal dimension of a ch ...

2025

On the boundedness of n-folds with κ(X) = n - 1

Stefano Filipazzi

In this note, we study certain sufficient conditions for a set of minimal klt pairs ( X, triangle) with kappa ( X, triangle) = dim( X ) - 1 to be bounded. ...

European Mathematical Soc-Ems2024

A Note on Lenses in Arrangements of Pairwise Intersecting Circles in the Plane

Rom Pinchasi

Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...

Electronic Journal Of Combinatorics2024

Reach For the Arcs: Reconstructing Surfaces from SDFs via Tangent Points

Yingying Ren

We introduce an algorithm to reconstruct a mesh from discrete samples of a shape's Signed Distance Function (SDF). A simple geometric reinterpretation of the SDF lets us formulate the problem through a point cloud, from which a surface can be extracted wit ...

Association for Computing Machinery2024

Incommensurate phases

Gervais Chapuis

Incommensurately modulated crystalline phases are part of a more general family called aperiodic crystals. Their symmetry is treated within the theoretical framework of superspace groups that is a generalization of the 3D space groups that are used for con ...

Academic Press2024

Stable cones in the thin one-phase problem

Xavier Fernandez-Real Girona

The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one -phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions n >= 3 is completely open. In this context, axial ...

Johns Hopkins Univ Press2024

Additive and geometric transversality of fractal sets in the integers

Florian Karl Richter

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

2024

Reactive collision-free motion generation in joint space via dynamical systems and sampling-based MPC

Aude Billard, Nadia Barbara Figueroa Fernandez, Mikhail Koptev

Dynamical system (DS) based motion planning offers collision-free motion, with closed-loop reactivity thanks to their analytical expression. It ensures that obstacles are not penetrated by reshaping a nominal DS through matrix modulation, which is construc ...

Sage Publications Ltd2024

Anomalous and Chern topological waves in hyperbolic networks

Romain Christophe Rémy Fleury, Haoye Qin, Zhe Zhang, Aleksi Antoine Bossart, Zhechen Zhang

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental ...

Nature Research2024

Into the ice: Exploration and data capturing in glacial moulins by a tethered robot

Josephine Anna Eleanor Hughes, Max Mirko Polzin

Glacial moulins (cylindrical meltwater drainage shafts) provide valuable insights into glacier dynamics, but are inaccessible and hazardous environments for humans to study. Exploring them using passive sensor probes has revealed their complex geometry, wh ...

Wiley2024

Digital Twins of Stone Masonry Buildings for Damage Assessment

Katrin Beyer, Radhakrishna Achanta, Bryan German Pantoja Rosero

Digital twins are virtual models of physical objects or systems that enable real-time monitoring and analysis. In the ﬁeld of stone masonry buildings, digital twins can be used to assess damage, predict maintenance needs, and opti- mize building performanc ...

Springer2024

Enhancement of brain atlases with region-specific coordinate systems: flatmaps and barrel column annotations

Felix Schürmann, Michael Reimann, Armando Romani, Huanxiang Lu, Sirio Bolaños Puchet, Juan Bautista Hernando Vieites, Aleksandra Zuzanna Teska

Digital brain atlases define a hierarchy of brain regions and their locations in three-dimensional space. They provide a standard coordinate system in which diverse datasets can be integrated for visualization and analysis. They also enable building of dat ...

2024

Grand canonical Brownian dynamics simulations of adsorption and self-assembly of SAS-6 rings on a surface

Pierre Gönczy, Niccolo Banterle

The Spindle Assembly Abnormal Protein 6 (SAS-6) forms dimers, which then self-assemble into rings that are critical for the nine-fold symmetry of the centriole organelle. It has recently been shown experimentally that the self-assembly of SAS-6 rings is st ...

AIP Publishing2023

Well-posedness Issues For the Half-Wave Maps Equation With Hyperbolic And Spherical Targets

Yang Liu

This thesis is a study of the global well-posedness of the Cauchy problems for half-wave maps from the Minkowski space of dimension n+1 to the 2-dimensional sphere and the hyperbolic plane. The work is mainly based on the results from Krieger-Sire 17' in ...

EPFL2023

Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions

Fabrizio Minganti

Finite simplex lattice models are used in different branches of science, e.g., in condensed-matter physics, when studying frustrated magnetic systems and non-Hermitian localization phenomena; or in chemistry, when describing experiments with mixtures. An n ...

Amer Physical Soc2023

One-Dimensional "Ghost Imaging" in Electron Microscopy of Inelastically Scattered Electrons

Fabrizio Carbone, Ivan Madan, Giovanni Maria Vanacore, Simone Gargiulo

Entanglement and correlation are at the basis of quantummechanicsand have been used in optics to create a framework for "ghostimaging". We propose that a similar scheme can be used in anelectron microscope to exploit the correlation of electrons with theco ...

2023

Region Extraction in Mesh Intersection

Annalisa Buffa, Pablo Antolin Sanchez, Emiliano Cirillo

Region extraction is a very common task in both Computer Science and Engineering with several applications in object recognition and motion analysis, among others. Most of the literature focuses on regions delimited by straight lines, often in the special ...

2023

Learning Linearized Degradation of Health Indicators using Deep Koopman Operator Approach

Olga Fink, Sergei Garmaev

With the current trend of increasing complexity of industrial systems, the construction and monitoring of health indicators becomes even more challenging. Given that health indicators are commonly employed to predict the end of life, a crucial criterion fo ...

Research Publishing2023

Chromatin organization in red triangles

Elisa Oricchio

This journal club by Elisa Oricchio highlights two studies published in 2012, which used chromatin conformation capture methods to detect the formation of self-interacting chromatin regions, known as topologically associating domains (TADs). ...

NATURE PORTFOLIO2023

A geometric optimal control approach for imitation and generalization of manipulation skills

Sylvain Calinon, Amirreza Razmjoo Fard

Daily manipulation tasks are characterized by regular features associated with the task structure, which can be described by multiple geometric primitives related to actions and object shapes. Only using Cartesian coordinate systems cannot fully represent ...

Elsevier2023