Embedding Four-directional Paths on Convex Point Sets

A directed path whose edges are assigned labels "up", "down", "right", or "left" is called \emph{four-directional}, and \emph{three-directional} if at most three out of the four labels are used. A \emph{direction-consistent embedding} of an \mbox{$n$-vertex} four-directional path $P$ on a set $S$ of $n$ points in the plane is a straight-line drawing of $P$ where each vertex of $P$ is mapped to a distinct point of $S$ and every edge points to the direction specified by its label. We study planar direction-consistent embeddings of three- and four-directional paths and provide a complete picture of the problem for convex point sets.Comment: 11 pages, full conference version including all proof

Known Unknowns: Novelty Detection in Condition Monitoring

Abstract. In time-series analysis it is often assumed that observed data can be modelled as being derived from a number of regimes of dynamics, as e.g. in a Switching Kalman Filter (SKF) [8, 2]. However, it may not be possible to model all of the regimes, and in this case it can be useful to represent explicitly a ‘novel ’ regime. We apply this idea to the Factorial Switching Kalman Filter (FSKF) by introducing an extra factor (the ‘Xfactor’) to account for the unmodelled variation. We apply our method to physiological monitoring data from premature infants receiving intensive care, and demonstrate that the model is effective in detecting abnormal sequences of observations that are not modelled by the known regimes.

Shift invariant preduals of ℓ₁(ℤ)

The Banach space ℓ<sub>1</sub>(ℤ) admits many non-isomorphic preduals, for example, C(K) for any compact countable space K, along with many more exotic Banach spaces. In this paper, we impose an extra condition: the predual must make the bilateral shift on ℓ<sub>1</sub>(ℤ) weak<sup>*</sup>-continuous. This is equivalent to making the natural convolution multiplication on ℓ<sub>1</sub>(ℤ) separately weak*-continuous and so turning ℓ<sub>1</sub>(ℤ) into a dual Banach algebra. We call such preduals <i>shift-invariant</i>. It is known that the only shift-invariant predual arising from the standard duality between C<sub>0</sub>(K) (for countable locally compact K) and ℓ<sub>1</sub>(ℤ) is c<sub>0</sub>(ℤ). We provide an explicit construction of an uncountable family of distinct preduals which do make the bilateral shift weak<sup>*</sup>-continuous. Using Szlenk index arguments, we show that merely as Banach spaces, these are all isomorphic to c<sub>0</sub>. We then build some theory to study such preduals, showing that they arise from certain semigroup compactifications of ℤ. This allows us to produce a large number of other examples, including non-isometric preduals, and preduals which are not Banach space isomorphic to c<sub>0</sub>

A comparison of variational and Markov chain Monte Carlo methods for inference in partially observed stochastic dynamic systems

In recent work we have developed a novel variational inference method for partially observed systems governed by stochastic differential equations. In this paper we provide a comparison of the Variational Gaussian Process Smoother with an exact solution computed using a Hybrid Monte Carlo approach to path sampling, applied to a stochastic double well potential model. It is demonstrated that the variational smoother provides us a very accurate estimate of mean path while conditional variance is slightly underestimated. We conclude with some remarks as to the advantages and disadvantages of the variational smoother. © 2008 Springer Science + Business Media LLC

Genetic parameters for sugar content in an interspecific pear population

Fruit quality and flavour are important targets in all pear breeding programmes. Perceived sweetness is directly influenced by the amount and type of sugar accumulated in fruit. Limited information is available on sugar composition in pear fruit and published studies have been completed using cultivars rather than breeding populations. The objective of this research was to determine the quantitative genetic parameters of sugar content in fruit of interspecific hybrids from families making up a pear breeding population. Glucose, fructose, sucrose and sorbitol contents were measured in mature fruit. Most of the sugars, except for sorbitol, showed genetic variability and a relatively high (i.e., > 0.5) ratio between the estimated additive genetic variance and the total variance. Sorbitol showed a high negative genetic correlation (–0.65) with fructose. It could be suggested that the main product of sorbitol conversion was fructose. Sucrose showed a negative genetic correlation with glucose (–0.37) and fructose (–0.16), which would be expected given that sucrose is metabolised into fructose and glucose. Two parents with 100 % European parentage showed the highest empirical breeding values (eBV)s for fructose and total sugars. The parent with 100 % Asian parentage showed the lowest eBV for sorbitol. The mean percentages of the sugars across the entire population were: glucose 13 %, fructose 59 %, sucrose 8 % and sorbitol 20 %, indicating fructose was the main sugar with sucrose less prominent