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

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, 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

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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