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

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

Probability Aggregation in Time-Series: Dynamic Hierarchical Modeling of Sparse Expert Beliefs

Most subjective probability aggregation procedures use a single probability judgment from each expert, even though it is common for experts studying real problems to update their probability estimates over time. This paper advances into unexplored areas of probability aggregation by considering a dynamic context in which experts can update their beliefs at random intervals. The updates occur very infrequently, resulting in a sparse data set that cannot be modeled by standard time-series procedures. In response to the lack of appropriate methodology, this paper presents a hierarchical model that takes into account the expert’s level of self-reported expertise and produces aggregate probabilities that are sharp and well calibrated both in- and outof-sample. The model is demonstrated on a real-world data set that includes over 2300 experts making multiple probability forecasts over two years on different subsets of 166 international political events

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

Thomas rotation and Thomas precession

Exact and simple calculation of Thomas rotation and Thomas precessions along a circular world line is presented in an absolute (coordinate-free) formulation of special relativity. Besides the simplicity of calculations the absolute treatment of spacetime allows us to gain a deeper insight into the phenomena of Thomas rotation and Thomas precession.Comment: 20 pages, to appear in Int. J. Theo. Phy

Quenched Narrow-Line Laser Cooling of 40Ca to Near the Photon Recoil Limit

We present a cooling method that should be generally applicable to atoms with narrow optical transitions. This technique uses velocity-selective pulses to drive atoms towards a zero-velocity dark state and then quenches the excited state to increase the cooling rate. We demonstrate this technique of quenched narrow-line cooling by reducing the 1-D temperature of a sample of neutral 40Ca atoms. We velocity select and cool with the 1S0(4s2) to 3P1(4s4p) 657 nm intercombination line and quench with the 3P1(4s4p) to 1S0(4s5s) intercombination line at 553 nm, which increases the cooling rate eight-fold. Limited only by available quenching laser power, we have transferred 18 % of the atoms from our initial 2 mK velocity distribution and achieved temperatures as low as 4 microK, corresponding to a vrms of 2.8 cm/s or 2 recoils at 657 nm. This cooling technique, which is closely related to Raman cooling, can be extended to three dimensions.Comment: 5 pages, 4 figures; Submitted to PRA Rapid Communication

Time on a Rotating Platform

Traditional clock synchronisation on a rotating platform is shown to be incompatible with the experimentally established transformation of time. The latter transformation leads directly to solve this problem through noninvariant one-way speed of light. The conventionality of some features of relativity theory allows full compatibility with existing experimental evidence.Comment: 12 pages, Latex, no figure. Copies available at [email protected] accepted for publication in Found. Phys. Let

Pattern formation in directional solidification under shear flow. I: Linear stability analysis and basic patterns

An asymptotic interface equation for directional solidification near the absolute stabiliy limit is extended by a nonlocal term describing a shear flow parallel to the interface. In the long-wave limit considered, the flow acts destabilizing on a planar interface. Moreover, linear stability analysis suggests that the morphology diagram is modified by the flow near the onset of the Mullins-Sekerka instability. Via numerical analysis, the bifurcation structure of the system is shown to change. Besides the known hexagonal cells, structures consisting of stripes arise. Due to its symmetry-breaking properties, the flow term induces a lateral drift of the whole pattern, once the instability has become active. The drift velocity is measured numerically and described analytically in the framework of a linear analysis. At large flow strength, the linear description breaks down, which is accompanied by a transition to flow-dominated morphologies, described in a companion paper. Small and intermediate flows lead to increased order in the lattice structure of the pattern, facilitating the elimination of defects. Locally oscillating structures appear closer to the instability threshold with flow than without.Comment: 20 pages, Latex, accepted for Physical Review

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