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

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

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

Degree of entanglement for two qubits

In this paper, we present a measure to quantify the degree of entanglement for two qubits in a pure state.Comment: 5 page

Chew-Bites, Jaw Movement Allocation and Bite Rate in Grazing Cattle as Identified by Acoustic Monitoring

Bite rate derives from the time budget of the biting and chewing processes of intake, which are both performed by jaw movements. A new type of jaw movement was revealed by acoustic monitoring in cattle - the chew-bite -which chews herbage already in the mouth and harvests fresh herbage with the same jaw movement (Laca et al., 1992). Chew-biting should enable the animal to reduce the total number of jaw movements performed per bite without reducing the number of chews per bite. We examined the variation among individuals in the allocation of jaw movements between the three types, and its relation to bite rate

The Importance of Patch Size in Estimating Steady-State Bite Rate in Grazing Cattle

Since the pioneering work of Black and Kenney (1984), various intake studies have been conducted at the spatial scale of a single feeding station ( patch ) to elucidate the processes that determine instantaneous intake rate (e.g. Laca et al., 1994). While these are well-suited for patch depletion studies, it is less clear how well they represent non-patchy and relatively homogeneous environments (Ungar & Griffiths, 2002). Clearly, grazing should be restricted to the upper grazing horizon (i.e. layer of bites), but sample duration may be insufficient to characterize steady-state behaviour, especially when grazing commences on an empty mouth. We examined the impact of feeding station size on bite rate and jaw movement allocation between bites and chews

Spatial Heterogeneity of Seasonal Grazing Pressure Created by Herd Movement Patterns on Hilly Rangelands Using GPS and GIS

The spatial heterogeneity of grazing pressure on extensive rangelands has management implications (Adler et al., 2001) but it has traditionally been difficult to quantify. Combination of technologies based on GPS (Global Positioning System) and GIS (Geographic Information Systems) is a quantum leap in our ability to address this issue. These tools were used to estimate the spatial heterogeneity of grazing pressure at a farm scale, and examine the relation between local landscape features and local grazing pressure

Development of a 2-Dimensional Video-Acoustic Tool for Monitoring Bite Placement

Studies of grazing behaviour conducted at the spatial scale of a feeding station demonstrate that intake rate declines with increasing depletion, a response attributed to an increase in bite overlap (Ginnett et al., 1999; Ungar et al., 2001). In order to understand the rules that govern bite placement, a methodology is required that can map the sequential placement of bites on the sward surface. We developed a video-acoustic tool to achieve this and report the findings of using the tool on small uniform patches of herbage

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.

The geometry of entanglement: metrics, connections and the geometric phase

Using the natural connection equivalent to the SU(2) Yang-Mills instanton on the quaternionic Hopf fibration of $S^7$ over the quaternionic projective space ${\bf HP}^1\simeq S^4$ with an $SU(2)\simeq S^3$ fiber the geometry of entanglement for two qubits is investigated. The relationship between base and fiber i.e. the twisting of the bundle corresponds to the entanglement of the qubits. The measure of entanglement can be related to the length of the shortest geodesic with respect to the Mannoury-Fubini-Study metric on ${\bf HP}^1$ between an arbitrary entangled state, and the separable state nearest to it. Using this result an interpretation of the standard Schmidt decomposition in geometric terms is given. Schmidt states are the nearest and furthest separable ones lying on, or the ones obtained by parallel transport along the geodesic passing through the entangled state. Some examples showing the correspondence between the anolonomy of the connection and entanglement via the geometric phase is shown. Connections with important notions like the Bures-metric, Uhlmann's connection, the hyperbolic structure for density matrices and anholonomic quantum computation are also pointed out.Comment: 42 page