A fixed point theorem for the infinite-dimensional simplex

We define the infinite dimensional simplex to be the closure of the convex hull of the standard basis vectors in R^infinity, and prove that this space has the 'fixed point property': any continuous function from the space into itself has a fixed point. Our proof is constructive, in the sense that it can be used to find an approximate fixed point; the proof relies on elementary analysis and Sperner's lemma. The fixed point theorem is shown to imply Schauder's fixed point theorem on infinite-dimensional compact convex subsets of normed spaces.Comment: 8 pages; related work at http://www.math.hmc.edu/~su/papers.htm

Detecting abnormalities in aircraft flight data and ranking their impact on the flight

To the best of the author’s knowledge, this is one of the first times that a large quantity of flight data has been studied in order to improve safety. A two phase novelty detection approach to locating abnormalities in the descent phase of aircraft flight data is presented. It has the ability to model normal time series data by analysing snapshots at chosen heights in the descent, weight individual abnormalities and quantitatively assess the overall level of abnormality of a flight during the descent. The approach expands on a recommendation by the UK Air Accident Investigation Branch to the UK Civil Aviation Authority. The first phase identifies and quantifies abnormalities at certain heights in a flight. The second phase ranks all flights to identify the most abnormal; each phase using a one class classifier. For both the first and second phases, the Support Vector Machine (SVM), the Mixture of Gaussians and the K-means one class classifiers are compared. The method is tested using a dataset containing manually labelled abnormal flights. The results show that the SVM provides the best detection rates and that the approach identifies unseen abnormalities with a high rate of accuracy. Furthermore, the method outperforms the event based approach currently in use. The feature selection tool F-score is used to identify differences between the abnormal and normal datasets. It identifies the heights where the discrimination between the two sets is largest and the aircraft parameters most responsible for these variations.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Formulation of an Optimum Winter Food-Patch Mix for Bobwhite Quail

Many state game agencies are seeking to improve winter quail food and habitat by means of artificial food-patch plantings. The objective of such plantings is to increase the limited supplies of nutrients available to quail in late winter. Desirable qualities of food species included in the seeding mixture are: low seeding cost, high nutrient and energy content, persistent seeds, and cultivation ease. Presently used mixtures have been formulated in the absence of detailed nutritional analysis and cost-minimization techniques. This paper seeks to demonstrate the utility of modern operations-research technology in such decisions by outlining the procedures for determining the composition of an optimum food-patch mix. This mix will meet nutrient and cultivation requirements at a least-possible cost per acre of food planting. Although a solution is presented, the emphasis of the paper is on the method for obtaining such a solution

Comparison of machine learning classifier models for bathing water quality exceedances in UK

The revised Bathing Water Directive (rBWD) (2006/7/EC) of the European Parliament requires monitoring of bathing water quality and, if early-warnings are provided to the public, it is permissible to discount a percentage of exceedance events from the monitoring process. This paper describes the development and implementation of both Decision Tree (DT) and Artificial Neural Network (ANN) based machine learning models for 8 beaches in south-west England, UK, as bases for early warning systems (EWS) and compares their performance for one beach. Weekly bacteria-count samples were gathered by the Environment Agency of England (EA) over a 12-year period from 2000-2011 during the 20-week bathing season and this data is used to calibrate and test the models. Daily sampling data were also collected at 5 of the beaches during the 2012 season to provide more robust validation of the models. As a benchmark, models are also compared with use of simple thresholds of antecedent rainfall to classify water quality exceedances. Evolutionary Algorithm-based optimisation of the ANN models is employed using single-objective approach using area under the Receiver Operating Characteristic (ROC) curve as fitness function. The optimum operating point is established using a weighting factor for the relative importance placed on false positives (passes) and false negatives (exceedances). The models use a number of input factors, including antecedent rainfall for the catchment adjacent to each bathing beach. A possible technique for automating selection of inputs is also discussed.Environment Agency (SW

Screening of Non- Saccharomyces cerevisiae Strains for Tolerance to Formic Acid in Bioethanol Fermentation.

Formic acid is one of the major inhibitory compounds present in hydrolysates derived from lignocellulosic materials, the presence of which can significantly hamper the efficiency of converting available sugars into bioethanol. This study investigated the potential for screening formic acid tolerance in non-Saccharomyces cerevisiae yeast strains, which could be used for the development of advanced generation bioethanol processes. Spot plate and phenotypic microarray methods were used to screen the formic acid tolerance of 7 non-Saccharomyces cerevisiae yeasts. S. kudriavzeii IFO1802 and S. arboricolus 2.3319 displayed a higher formic acid tolerance when compared to other strains in the study. Strain S. arboricolus 2.3319 was selected for further investigation due to its genetic variability among the Saccharomyces species as related to Saccharomyces cerevisiae and availability of two sibling strains: S. arboricolus 2.3317 and 2.3318 in the lab. The tolerance of S. arboricolus strains (2.3317, 2.3318 and 2.3319) to formic acid was further investigated by lab-scale fermentation analysis, and compared with S. cerevisiae NCYC2592. S. arboricolus 2.3319 demonstrated improved formic acid tolerance and a similar bioethanol synthesis capacity to S. cerevisiae NCYC2592, while S. arboricolus 2.3317 and 2.3318 exhibited an overall inferior performance. Metabolite analysis indicated that S. arboricolus strain 2.3319 accumulated comparatively high concentrations of glycerol and glycogen, which may have contributed to its ability to tolerate high levels of formic acid