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

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

Optimised Fabry-Perot (AlGa)As quantum well lasers tunable over 105 nm

Uncoated, Fabry-Perot (AlGa)As semiconductor lasers are tuned over 105nm in a grating-coupled external cavity. Broadband tunability is achieved by optimising the resonator loss so as to invoke lasing from both the first and second quantised states of the single quantum well active region

Additional diagnostic value of implantable loop recorder for differentiating syncope from non-syncopal forms of transient loss of consciousness

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Evidence of strong stabilizing effects on the evolution of boreoeutherian (Mammalia) dental proportions.

The dentition is an extremely important organ in mammals with variation in timing and sequence of eruption, crown morphology, and tooth size enabling a range of behavioral, dietary, and functional adaptations across the class. Within this suite of variable mammalian dental phenotypes, relative sizes of teeth reflect variation in the underlying genetic and developmental mechanisms. Two ratios of postcanine tooth lengths capture the relative size of premolars to molars (premolar-molar module, PMM), and among the three molars (molar module component, MMC), and are known to be heritable, independent of body size, and to vary significantly across primates. Here, we explore how these dental traits vary across mammals more broadly, focusing on terrestrial taxa in the clade of Boreoeutheria (Euarchontoglires and Laurasiatheria). We measured the postcanine teeth of N = 1,523 boreoeutherian mammals spanning six orders, 14 families, 36 genera, and 49 species to test hypotheses about associations between dental proportions and phylogenetic relatedness, diet, and life history in mammals. Boreoeutherian postcanine dental proportions sampled in this study carry conserved phylogenetic signal and are not associated with variation in diet. The incorporation of paleontological data provides further evidence that dental proportions may be slower to change than is dietary specialization. These results have implications for our understanding of dental variation and dietary adaptation in mammals

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

Geometric observation for the Bures fidelity between two states of a qubit

In this Brief Report, we present a geometric observation for the Bures fidelity between two states of a qubit.Comment: 4 pages, 1 figure, RevTex, Accepted by Phys. Rev.

Expert-Augmented Machine Learning

Machine Learning is proving invaluable across disciplines. However, its success is often limited by the quality and quantity of available data, while its adoption by the level of trust that models afford users. Human vs. machine performance is commonly compared empirically to decide whether a certain task should be performed by a computer or an expert. In reality, the optimal learning strategy may involve combining the complementary strengths of man and machine. Here we present Expert-Augmented Machine Learning (EAML), an automated method that guides the extraction of expert knowledge and its integration into machine-learned models. We use a large dataset of intensive care patient data to predict mortality and show that we can extract expert knowledge using an online platform, help reveal hidden confounders, improve generalizability on a different population and learn using less data. EAML presents a novel framework for high performance and dependable machine learning in critical applications

Lorentz transformation and vector field flows

The parameter changes resulting from a combination of Lorentz transformation are shown to form vector field flows. The exact, finite Thomas rotation angle is determined and interpreted intuitively. Using phase portraits, the parameters evolution can be clearly visualized. In addition to identifying the fixed points, we obtain an analytic invariant, which correlates the evolution of parameters.Comment: 11 pages, 3 figures. Section IV revised and title change