An Introduction to Hyperbolic Barycentric Coordinates and their Applications

Barycentric coordinates are commonly used in Euclidean geometry. The adaptation of barycentric coordinates for use in hyperbolic geometry gives rise to hyperbolic barycentric coordinates, known as gyrobarycentric coordinates. The aim of this article is to present the road from Einstein's velocity addition law of relativistically admissible velocities to hyperbolic barycentric coordinates along with applications.Comment: 66 pages, 3 figure

Thematic mapper studies band correlation analysis

Spectral data representative of thematic mapper candidate bands 1 and 3 to 7 were obtained by selecting appropriate combinations of bands from the JSC 24 channel multispectral scanner. Of all the bands assigned, only candidate bands 4 (.74 mu to .80 mu) and 5 (.80 mu to .91 mu) showed consistently high intercorrelation from region to region and time to time. This extremely high correlation persisted when looking at the composite data set in a multitemporal, multilocation domain. The GISS investigations lend positive confirmation to the hypothesis, that TM bands 4 and 5 are redundant

Gyrations: The Missing Link Between Classical Mechanics with its Underlying Euclidean Geometry and Relativistic Mechanics with its Underlying Hyperbolic Geometry

Being neither commutative nor associative, Einstein velocity addition of relativistically admissible velocities gives rise to gyrations. Gyrations, in turn, measure the extent to which Einstein addition deviates from commutativity and from associativity. Gyrations are geometric automorphisms abstracted from the relativistic mechanical effect known as Thomas precession

A Risk Comparison of Ordinary Least Squares vs Ridge Regression

We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component Analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that the risk of this ordinary least squares method is within a constant factor (namely 4) of the risk of ridge regression.Comment: Appearing in JMLR 14, June 201

Anterior Dental Microwear Texture Analysis of the Krapina Neandertals

Some Neandertal anterior teeth show unusual and excessive gross wear, commonly explained by non-dietary anterior tooth use, or using the anterior dentition as a tool, clamp, or third hand. This alternate use is inferred from aboriginal arctic populations, who used their front teeth in this manner. Here we examine anterior dental microwear textures of the Krapina Neandertals to test this hypothesis and further analyze tooth use in these hominins. Microwear textures from 17 Krapina Dental People were collected by white-light confocal profilometry using a 100x objective lens. Four adjacent scans were generated, totaling an area of 204x276 μm, and were analyzed using Toothfrax and SFrax SSFA software packages. The Neandertals were compared to six bioarchaeological/ethnographic samples with reported variation in diet, abrasive load, and non-dietary anterior tooth use. Results indicate that Krapina anterior teeth lack extreme microwear textures expected of hominins exposed to heavy abrasives or those that regularly generated high stresses associated with intense use of the front teeth as tools. Krapina hominins have microwear attributes in common with Coast Tsimshian, Aleut, and Puye Pueblo samples. Collectively, this suggests that the Krapina Neandertals faced moderate abrasive loads and only periodically used their anterior teeth as tools for non-diet related behaviors

Harmonic analysis on the Möbius gyrogroup

In this paper we propose to develop harmonic analysis on the Poincaré ball $B_t^n$, a model of the n-dimensional real hyperbolic space. The Poincaré ball $B_t^n$ is the open ball of the Euclidean n-space $R^n$ with radius $t>0$, centered at the origin of $R^n$ and equipped with Möbius addition, thus forming a Möbius gyrogroup where Möbius addition in the ball plays the role of vector addition in $\mathbb{R}^n$. For any $t>0$ and an arbitrary parameter $\sigma \in R$ we study the $(\sigma,t)$-translation, the $( \sigma,t)$-convolution, the eigenfunctions of the $(\sigma,t)$-Laplace-Beltrami operator, the $(\sigma,t)$-Helgason Fourier transform, its inverse transform and the associated Plancherel's Theorem, which represent counterparts of standard tools, thus, enabling an effective theory of hyperbolic harmonic analysis. Moreover, when $t \rightarrow +\infty$ the resulting hyperbolic harmonic analysis on $B_t^n$ tends to the standard Euclidean harmonic analysis on $R^n$, thus unifying hyperbolic and Euclidean harmonic analysis. As an application we construct diffusive wavelets on $B_t^n$

A multi-sensory interactive reading experience for visually impaired children; a user evaluation

© 2018 Springer-Verlag London Ltd., part of Springer Nature The children’s experience of reading is enhanced by visual displays, and through picture book experiences, young children expose themselves to develop socially, personally, intellectually, and culturally. While a sighted person’s mental imagining is constructed mostly through visual experiences, a visually impaired person’s mental images are a product of haptic, taste, smell, and sounds. In this paper, we are introducing a picture book with multi-sensory interactions for the visually impaired children. The key novelty in our concept is the integration of multi-sensory interactions (touch, sound, and smell) to create a new reading experience for visually impaired. Also, this concept is highlighting the lack of appropriately designed sensory reading experiences for visually impaired children. We have conducted a user study with 10 educators, and 25 children from a special school for visually impaired in Malaysia, and our evaluation revealed that this book is engaging and a novel experience of multi-sensory interactions to both children and educators

Cold collisions between atoms in optical lattices

We have simulated binary collisions between atoms in optical lattices during Sisyphus cooling. Our Monte Carlo Wave Function simulations show that the collisions selectively accelerate mainly the hotter atoms in the thermal ensemble, and thus affect the steady state which one would normally expect to reach in Sisyphus cooling without collisions.Comment: 4 pages, 1 figur

RELEASE: A High-level Paradigm for Reliable Large-scale Server Software

Erlang is a functional language with a much-emulated model for building reliable distributed systems. This paper outlines the RELEASE project, and describes the progress in the first six months. The project aim is to scale the Erlang’s radical concurrency-oriented programming paradigm to build reliable general-purpose software, such as server-based systems, on massively parallel machines. Currently Erlang has inherently scalable computation and reliability models, but in practice scalability is constrained by aspects of the language and virtual machine. We are working at three levels to address these challenges: evolving the Erlang virtual machine so that it can work effectively on large scale multicore systems; evolving the language to Scalable Distributed (SD) Erlang; developing a scalable Erlang infrastructure to integrate multiple, heterogeneous clusters. We are also developing state of the art tools that allow programmers to understand the behaviour of massively parallel SD Erlang programs. We will demonstrate the effectiveness of the RELEASE approach using demonstrators and two large case studies on a Blue Gene

Columbus IFHX Ammonia Leak Analysis

After the Columbus Moderate Temperature Loop (MTL) InterFace Heat eXchanger (IFHX) low temperature event of GMT 345-2013, NASA investigated relevant transient scenarios involving IFHX rupture after water freezing and subsequent thawing. NASA recommended development of a Fault Detection Isolation and Recovery (FDIR) plan that would, in the event of a heat exchanger freeze event, close the Water On/Off Valves (WOOVs) to isolate the heat exchanger and prevent ammonia from the external flow loops from spreading into the cabin. NASA performed a preliminary simplified analysis for the reference case of IFHX rupture, but for a deeper understanding TAS developed detailed SINDA-FLUINT models of the Columbus ITCS that were built and run through the SINAPS GUI. This allowed simulation of the ammonia leakage physics including the variation of environmental parameters, thus providing more accurate and specific input to the FDIR under development. The result was finalization of the IFHX WOOVs closure sequence and wait times to contain the ammonia propagation to Columbus and allow identification of the leaking IFHX. In addition, the analysis results provided reference pressure profiles to be used on console and by the Engineering as support for the telemetry data assessment in case of failure.This paper gives an overview on the issue and focuses on the analytical aspects of the multiphase fluid dynamics involved