Measure based metrics for aggregated data

Aggregated data arises commonly from surveys and censuses where groups of individuals are studied as coherent entities. The aggregated data can take many forms including sets, intervals, distributions and histograms. The data analyst needs to measure the similarity between such aggregated data items and a range of metrics are reported in the literature to achieve this (e.g. the Jaccard metric for sets and the Wasserstein metric for histograms). In this paper, a unifying theory based on measure theory is developed that establishes not only that known metrics are essentially similar but also suggests new metrics

Hypergrammars: An extension of macrogrammars

A new class of generative grammars called hypergrammars is introduced. They are described as a natural extension of Fischer's macrogrammars. Three modes of derivation, inside-out, outside-in, and unrestricted are considered, and the classes of languages so defined are compared with other known classes. It is shown that the outside-in hyper-languages are the same as the outside-in macrolanguages but that inside-out hyperlanguages are the same as Fischer's quoted languages. Various closure properties are considered as well as generalizations of the original definitions. Three new hierarchies of languages each embedded in the class of quoted languages are discovered. It is claimed that this new approach to Fischer's work is more understandable and also mathematically elegant

Sedation for Gastrointestinal Endoscopic Procedures in the Elderly: Getting Safer but Still Not Nearly Safe Enough

Previously published UK reports showed that excessively large doses of benzodiazepines and opiates were being commonly used to sedate elderly patients for gastrointestinal (GI) endoscopy. This unsafe practice has lead to avoidable morbidity and mortality. We have taken the opportunity provided by recent reports to examine whether GI endoscopy sedation practice in the elderly has improved in the light of this evidence and the publication of guidelines in which specific recommendations on sedation dosage are given

Jamming Model for the Extremal Optimization Heuristic

Extremal Optimization, a recently introduced meta-heuristic for hard optimization problems, is analyzed on a simple model of jamming. The model is motivated first by the problem of finding lowest energy configurations for a disordered spin system on a fixed-valence graph. The numerical results for the spin system exhibit the same phenomena found in all earlier studies of extremal optimization, and our analytical results for the model reproduce many of these features.Comment: 9 pages, RevTex4, 7 ps-figures included, as to appear in J. Phys. A, related papers available at http://www.physics.emory.edu/faculty/boettcher

Polynomial-time approximation schemes for scheduling problems with time lags

We identify two classes of machine scheduling problems with time lags that possess Polynomial-Time Approximation Schemes (PTASs). These classes together, one for minimizing makespan and one for minimizing total completion time, include many well-studied time lag scheduling problems. The running times of these approximation schemes are polynomial in the number of jobs, but exponential in the number of machines and the ratio between the largest time lag and the smallest positive operation time. These classes constitute the first PTAS results for scheduling problems with time lags