Patterns theory and geodesic automatic structure for a class of groups

We introduce a theory of "patterns" in order to study geodesics in a certain class of group presentations. Using patterns we show that there does not exist a geodesic automatic structure for certain group presentations, and that certain group presentations are almost convex.Comment: Appeared in 2003. I am putting all my past papers on arxi

Analysis of filament reinforced metal-shell pressure vessels

Computer program analyzes design requirements and computes designs for metal-lined filament-wound pressure vessels with either geodesic /helical/ or in-plane filament winding patterns on the cylindrical portion and over the ends, reinforced by circumferential windings on the cylindrical portion

Temperature and Polarization Patterns in Anisotropic Cosmologies

We study the coherent temperature and polarization patterns produced in homogeneous but anisotropic cosmological models. We show results for all Bianchi types with a Friedman-Robertson-Walker limit (i.e. Types I, V, VII$_{0}$, VII$_{h}$ and IX) to illustrate the range of possible behaviour. We discuss the role of spatial curvature, shear and rotation in the geodesic equations for each model and establish some basic results concerning the symmetries of the patterns produced. We also give examples of the time-evolution of these patterns in terms of the Stokes parameters $I$, $Q$ and $U$.Comment: 24 pages, 7 Figures, submitted to JCAP. Revised version: numerous references added, text rewritten, and errors corrected

LCS Tool : A Computational Platform for Lagrangian Coherent Structures

We give an algorithmic introduction to Lagrangian coherent structures (LCSs) using a newly developed computational engine, LCS Tool. LCSs are most repelling, attracting and shearing material lines that form the centerpieces of observed tracer patterns in two-dimensional unsteady dynamical systems. LCS Tool implements the latest geodesic theory of LCSs for two-dimensional flows, uncovering key transport barriers in unsteady flow velocity data as explicit solutions of differential equations. After a review of the underlying theory, we explain the steps and numerical methods used by LCS Tool, and illustrate its capabilities on three unsteady fluid flow examples

On sphere-filling ropes

What is the longest rope on the unit sphere? Intuition tells us that the answer to this packing problem depends on the rope's thickness. For a countably infinite number of prescribed thickness values we construct and classify all solution curves. The simplest ones are similar to the seamlines of a tennis ball, others exhibit a striking resemblance to Turing patterns in chemistry, or to ordered phases of long elastic rods stuffed into spherical shells.Comment: 15 pages, 8 figure

Spherical clustering of users navigating 360{\deg} content

In Virtual Reality (VR) applications, understanding how users explore the omnidirectional content is important to optimize content creation, to develop user-centric services, or even to detect disorders in medical applications. Clustering users based on their common navigation patterns is a first direction to understand users behaviour. However, classical clustering techniques fail in identifying these common paths, since they are usually focused on minimizing a simple distance metric. In this paper, we argue that minimizing the distance metric does not necessarily guarantee to identify users that experience similar navigation path in the VR domain. Therefore, we propose a graph-based method to identify clusters of users who are attending the same portion of the spherical content over time. The proposed solution takes into account the spherical geometry of the content and aims at clustering users based on the actual overlap of displayed content among users. Our method is tested on real VR user navigation patterns. Results show that our solution leads to clusters in which at least 85% of the content displayed by one user is shared among the other users belonging to the same cluster.Comment: 5 pages, conference (Published in: ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)