182,126 research outputs found
Barcode Embeddings for Metric Graphs
Stable topological invariants are a cornerstone of persistence theory and
applied topology, but their discriminative properties are often
poorly-understood. In this paper we study a rich homology-based invariant first
defined by Dey, Shi, and Wang, which we think of as embedding a metric graph in
the barcode space. We prove that this invariant is locally injective on the
space of metric graphs and globally injective on a GH-dense subset. Moreover,
we show that is globally injective on a full measure subset of metric graphs,
in the appropriate sense.Comment: The newest draft clarifies the proofs in Sections 7 and 8, and
provides improved figures therein. It also includes a results section in the
introductio
Quantitative Analysis by the Point-Centered Quarter Method
This document is an introduction to the use of the point-centered quarter
method. It briefly outlines its history, its methodology, and some of the
practical issues (and modifications) that inevitably arise with its use in the
field. Additionally this paper shows how data collected using point-centered
quarter method sampling may be used to determine importance values of different
species of trees and describes and derives several methods of estimating plant
density and corresponding confidence intervals. New to this revision is an
appendix of R functions to carry out these calculations.Comment: 56 pages, 12 figures, 16 tables. Corrected typos. Expanded Appendix B
on Angle-Order Methods. Added Appendix D containing R functions to carry out
all calculations. Added references. Original version: 34 pages, 6 figures, 16
table
Casimir force between integrable and chaotic pistons
We have computed numerically the Casimir force between two identical pistons
inside a very long cylinder, considering different shapes for the pistons. The
pistons can be considered as quantum billiards, whose spectrum determines the
vacuum force. The smooth part of the spectrum fixes the force at short
distances, and depends only on geometric quantities like the area or perimeter
of the piston. However, correcting terms to the force, coming from the
oscillating part of the spectrum which is related to the classical dynamics of
the billiard, are qualitatively different for classically integrable or chaotic
systems. We have performed a detailed numerical analysis of the corresponding
Casimir force for pistons with regular and chaotic classical dynamics. For a
family of stadium billiards, we have found that the correcting part of the
Casimir force presents a sudden change in the transition from regular to
chaotic geometries.Comment: 13 pages, 10 figure
Cooperative Pursuit with Multi-Pursuer and One Faster Free-moving Evader
This paper addresses a multi-pursuer single-evader pursuit-evasion game where
the free-moving evader moves faster than the pursuers. Most of the existing
works impose constraints on the faster evader such as limited moving area and
moving direction. When the faster evader is allowed to move freely without any
constraint, the main issues are how to form an encirclement to trap the evader
into the capture domain, how to balance between forming an encirclement and
approaching the faster evader, and what conditions make the capture possible.
In this paper, a distributed pursuit algorithm is proposed to enable pursuers
to form an encirclement and approach the faster evader. An algorithm that
balances between forming an encirclement and approaching the faster evader is
proposed. Moreover, sufficient capture conditions are derived based on the
initial spatial distribution and the speed ratios of the pursuers and the
evader. Simulation and experimental results on ground robots validate the
effectiveness and practicability of the proposed method
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