Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)

We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel interpolation. The SKI framework clarifies how the quality of an inducing point approach depends on the number of inducing (aka interpolation) points, interpolation strategy, and GP covariance kernel. SKI also provides a mechanism to create new scalable kernel methods, through choosing different kernel interpolation strategies. Using SKI, with local cubic kernel interpolation, we introduce KISS-GP, which is 1) more scalable than inducing point alternatives, 2) naturally enables Kronecker and Toeplitz algebra for substantial additional gains in scalability, without requiring any grid data, and 3) can be used for fast and expressive kernel learning. KISS-GP costs O(n) time and storage for GP inference. We evaluate KISS-GP for kernel matrix approximation, kernel learning, and natural sound modelling.Comment: 19 pages, 4 figure

Environmental effects of the Manganui ski field, Mt Taranaki/Egmont

During May 2012, the environmental effects of the Manganui ski field were examined. Permanent quadrats first established in 1974 to monitor vegetation changes were re-measured, vegetation mapping was conducted, modifications to ground form and drainage were identified, soil compaction was examined, and stream water from the ski field catchment was tested for nutrient enrichment. This report focusses primarily on the lower Manganui ski field, as the upper Manganui ski field consists mostly of unmodified herbfield or gravelfield, protected by a sufficient snow base over the winter months. The lower Manganui ski field has a long history of modification spanning from the early 1900s. Vegetation types mapped on the lower field included unmown tussockfield, mown tussock-herbfield, shrubland and exotics. The re-measurement of vegetation in permanent quadrats on the lower field suggests that since the last re-measurement in 1994, several exotic species have increased in cover, including Carex ovalis, Poa annua, and Agrostis capillaris (percentage cover increases of up to 46.6%, 42.0% and 20.7% respectively). Vegetation mapping and historic photographs indicate that the lower ski field sits within the elevational belt of shrubland vegetation, little of which remains due to regular mowing conducted on the field since 1947. Shrubs which have been largely excluded from the field through mowing include Brachyglottis elaeagnifolius, Hebe odora, Ozothamnus vauvilliersii, Dracophyllum filifolium, Pseudopanax colensoi, Raukaua simplex and Hebe stricta var. egmontiana. Areas of the ski field dominated by exotic vegetation were predominantly associated with historic culvert construction and rock dynamiting. Compaction by machinery was confined to the sensitive mossfield area at the base of the lower field

Physics of Skiing: The Ideal-Carving Equation and Its Applications

Ideal carving occurs when a snowboarder or skier, equipped with a snowboard or carving skis, describes a perfect carved turn in which the edges of the ski alone, not the ski surface, describe the trajectory followed by the skier, without any slipping or skidding. In this article, we derive the "ideal-carving" equation which describes the physics of a carved turn under ideal conditions. The laws of Newtonian classical mechanics are applied. The parameters of the ideal-carving equation are the inclination of the ski slope, the acceleration of gravity, and the sidecut radius of the ski. The variables of the ideal-carving equation are the velocity of the skier, the angle between the trajectory of the skier and the horizontal, and the instantaneous curvature radius of the skier's trajectory. Relations between the slope inclination and the velocity range suited for nearly ideal carving are discussed, as well as implications for the design of carving skis and snowboards.Comment: 13 pages, 9 figures, LaTeX; to appear in Can. J. Phy

Warming winters and New Hampshire’s lost ski areas: An integrated case study

New Hampshire’s mountains and winter climate support a ski industry that contributes substantially to the state economy. Through more than 70 years of history, this industry has adapted and changed with its host society. The climate itself has changed during this period too, in ways that influenced the ski industry’s development. During the 20th century, New Hampshire’s mean winter temperature warmed about 2.1° C (3.8° F). Much of that change occurred since 1970. The mult‐decadal variations in New Hampshire winters follow global temperature trends. Snowfall exhibits a downward trend, strongest in southern New Hampshire, and also correlates with the North Atlantic Oscillation. Many small ski areas opened during the early years while winters were cold and snowy. As winters warmed, areas in southern or lowelevation locations faced a critical disadvantage. Under pressure from both climate and competition, the number of small ski areas leveled off and then fell steeply after 1970. The number of larger, chairliftoperating ski areas began falling too after 1980. Aprolonged warming period increased the importance of geographic advantages, and also of capital investment in snowmaking, grooming and economic diversification. The consolidation trend continues today. Most of the surviving ski areas are located in the northern mountains. Elsewhere around the state, one can find the remains of “lost” ski areas in places that now rarely have snow suitable for downhill skiing. This case study demonstrates a general approach for conducting integrated empirical research on the human dimensions of climate change

From 2-Dimensional Surfaces to Cosmological Solutions

We construct perfect fluid metrics corresponding to spacelike surfaces invariant under a 1-dimensional group of isometries in 3-dimensional Minkowski space. Under additional assumptions we obtain new cosmological solutions of Bianchi type II, VI_0 and VII_0. The solutions depend on an arbitrary function of time, which can be specified in order to satisfy an equation of state.Comment: 12 pages, no figures, LaTeX2e, to be published in Class. Quant. Gra