The Hahn Quantum Variational Calculus

We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann's direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems. To illustrate the results, we provide several examples and discuss a quantum version of the well known Ramsey model of economics.Comment: Submitted: 3/March/2010; 4th revision: 9/June/2010; accepted: 18/June/2010; for publication in Journal of Optimization Theory and Application

Professionalism, Golf Coaching and a Master of Science Degree: A commentary

As a point of reference I congratulate Simon Jenkins on tackling the issue of professionalism in coaching. As he points out coaching is not a profession, but this does not mean that coaching would not benefit from going through a professionalization process. As things stand I find that the stimulus article unpacks some critically important issues of professionalism, broadly within the context of golf coaching. However, I am not sure enough is made of understanding what professional (golf) coaching actually is nor how the development of a professional golf coach can be facilitated by a Master of Science Degree (M.Sc.). I will focus my commentary on these two issues

Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

The <i>Castalia</i> mission to Main Belt Comet 133P/Elst-Pizarro

We describe Castalia, a proposed mission to rendezvous with a Main Belt Comet (MBC), 133P/Elst-Pizarro. MBCs are a recently discovered population of apparently icy bodies within the main asteroid belt between Mars and Jupiter, which may represent the remnants of the population which supplied the early Earth with water. Castalia will perform the first exploration of this population by characterising 133P in detail, solving the puzzle of the MBC’s activity, and making the first in situ measurements of water in the asteroid belt. In many ways a successor to ESA’s highly successful Rosetta mission, Castalia will allow direct comparison between very different classes of comet, including measuring critical isotope ratios, plasma and dust properties. It will also feature the first radar system to visit a minor body, mapping the ice in the interior. Castalia was proposed, in slightly different versions, to the ESA M4 and M5 calls within the Cosmic Vision programme. We describe the science motivation for the mission, the measurements required to achieve the scientific goals, and the proposed instrument payload and spacecraft to achieve these

The exposure of the hybrid detector of the Pierre Auger Observatory

The Pierre Auger Observatory is a detector for ultra-high energy cosmic rays. It consists of a surface array to measure secondary particles at ground level and a fluorescence detector to measure the development of air showers in the atmosphere above the array. The "hybrid" detection mode combines the information from the two subsystems. We describe the determination of the hybrid exposure for events observed by the fluorescence telescopes in coincidence with at least one water-Cherenkov detector of the surface array. A detailed knowledge of the time dependence of the detection operations is crucial for an accurate evaluation of the exposure. We discuss the relevance of monitoring data collected during operations, such as the status of the fluorescence detector, background light and atmospheric conditions, that are used in both simulation and reconstruction.Comment: Paper accepted by Astroparticle Physic

Customer emotions in service failure and recovery encounters

Emotions play a significant role in the workplace, and considerable attention has been given to the study of employee emotions. Customers also play a central function in organizations, but much less is known about customer emotions. This chapter reviews the growing literature on customer emotions in employee–customer interfaces with a focus on service failure and recovery encounters, where emotions are heightened. It highlights emerging themes and key findings, addresses the measurement, modeling, and management of customer emotions, and identifies future research streams. Attention is given to emotional contagion, relationships between affective and cognitive processes, customer anger, customer rage, and individual differences

Techniques for measuring aerosol attenuation using the Central Laser Facility at the Pierre Auger Observatory

The Pierre Auger Observatory in Malargüe, Argentina, is designed to study the properties of ultra-high energy cosmic rays with energies above 10(18) eV. It is a hybrid facility that employs a Fluorescence Detector to perform nearly calorimetric measurements of Extensive Air Shower energies. To obtain reliable calorimetric information from the FD, the atmospheric conditions at the observatory need to be continuously monitored during data acquisition. In particular, light attenuation due to aerosols is an important atmospheric correction. The aerosol concentration is highly variable, so that the aerosol attenuation needs to be evaluated hourly. We use light from the Central Laser Facility, located near the center of the observatory site, having an optical signature comparable to that of the highest energy showers detected by the FD. This paper presents two procedures developed to retrieve the aerosol attenuation of fluorescence light from CLF laser shots. Cross checks between the two methods demonstrate that results from both analyses are compatible, and that the uncertainties are well understood. The measurements of the aerosol attenuation provided by the two procedures are currently used at the Pierre Auger Observatory to reconstruct air shower data

The rapid atmospheric monitoring system of the Pierre Auger Observatory

The Pierre Auger Observatory is a facility built to detect air showers produced by cosmic rays above 10(17) eV. During clear nights with a low illuminated moon fraction, the UV fluorescence light produced by air showers is recorded by optical telescopes at the Observatory. To correct the observations for variations in atmospheric conditions, atmospheric monitoring is performed at regular intervals ranging from several minutes (for cloud identification) to several hours (for aerosol conditions) to several days (for vertical profiles of temperature, pressure, and humidity). In 2009, the monitoring program was upgraded to allow for additional targeted measurements of atmospheric conditions shortly after the detection of air showers of special interest, e. g., showers produced by very high-energy cosmic rays or showers with atypical longitudinal profiles. The former events are of particular importance for the determination of the energy scale of the Observatory, and the latter are characteristic of unusual air shower physics or exotic primary particle types. The purpose of targeted (or 'rapid') monitoring is to improve the resolution of the atmospheric measurements for such events. In this paper, we report on the implementation of the rapid monitoring program and its current status. The rapid monitoring data have been analyzed and applied to the reconstruction of air showers of high interest, and indicate that the air fluorescence measurements affected by clouds and aerosols are effectively corrected using measurements from the regular atmospheric monitoring program. We find that the rapid monitoring program has potential for supporting dedicated physics analyses beyond the standard event reconstruction

Comprehensive analysis of epigenetic clocks reveals associations between disproportionate biological ageing and hippocampal volume

The concept of age acceleration, the difference between biological age and chronological age, is of growing interest, particularly with respect to age-related disorders, such as Alzheimer’s Disease (AD). Whilst studies have reported associations with AD risk and related phenotypes, there remains a lack of consensus on these associations. Here we aimed to comprehensively investigate the relationship between five recognised measures of age acceleration, based on DNA methylation patterns (DNAm age), and cross-sectional and longitudinal cognition and AD-related neuroimaging phenotypes (volumetric MRI and Amyloid-β PET) in the Australian Imaging, Biomarkers and Lifestyle (AIBL) and the Alzheimer’s Disease Neuroimaging Initiative (ADNI). Significant associations were observed between age acceleration using the Hannum epigenetic clock and cross-sectional hippocampal volume in AIBL and replicated in ADNI. In AIBL, several other findings were observed cross-sectionally, including a significant association between hippocampal volume and the Hannum and Phenoage epigenetic clocks. Further, significant associations were also observed between hippocampal volume and the Zhang and Phenoage epigenetic clocks within Amyloid-β positive individuals. However, these were not validated within the ADNI cohort. No associations between age acceleration and other Alzheimer’s disease-related phenotypes, including measures of cognition or brain Amyloid-β burden, were observed, and there was no association with longitudinal change in any phenotype. This study presents a link between age acceleration, as determined using DNA methylation, and hippocampal volume that was statistically significant across two highly characterised cohorts. The results presented in this study contribute to a growing literature that supports the role of epigenetic modifications in ageing and AD-related phenotypes