Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

Foundations of Black Hole Accretion Disk Theory

This review covers the main aspects of black hole accretion disk theory. We begin with the view that one of the main goals of the theory is to better understand the nature of black holes themselves. In this light we discuss how accretion disks might reveal some of the unique signatures of strong gravity: the event horizon, the innermost stable circular orbit, and the ergosphere. We then review, from a first-principles perspective, the physical processes at play in accretion disks. This leads us to the four primary accretion disk models that we review: Polish doughnuts (thick disks), Shakura-Sunyaev (thin) disks, slim disks, and advection-dominated accretion flows (ADAFs). After presenting the models we discuss issues of stability, oscillations, and jets. Following our review of the analytic work, we take a parallel approach in reviewing numerical studies of black hole accretion disks. We finish with a few select applications that highlight particular astrophysical applications: measurements of black hole mass and spin, black hole vs. neutron star accretion disks, black hole accretion disk spectral states, and quasi-periodic oscillations (QPOs).Comment: 91 pages, 23 figures, final published version available at http://www.livingreviews.org/lrr-2013-

Animal Perception of Seasonal Thresholds: Changes in Elephant Movement in Relation to Rainfall Patterns

Background: The identification of temporal thresholds or shifts in animal movement informs ecologists of changes in an animal\u2019s behaviour, which contributes to an understanding of species\u2019 responses in different environments. In African savannas, rainfall, temperature and primary productivity influence the movements of large herbivores and drive changes at different scales. Here, we developed a novel approach to define seasonal shifts in movement behaviour by examining the movements of a highly mobile herbivore (elephant; Loxodonta africana), in relation to local and regional rainfall patterns. Methodology/Principal Findings: We used speed to determine movement changes of between 8 and 14 GPS-collared elephant cows, grouped into five spatial clusters, in Kruger National Park, South Africa. To detect broad-scale patterns of movement, we ran a three-year daily time-series model for each individual (2007\u20132009). Piecewise regression models provided the best fit for elephant movement, which exhibited a segmented, waveform pattern over time. Major breakpoints in speed occurred at the end of the dry and wet seasons of each year. During the dry season, female elephant are constrained by limited forage and thus the distances they cover are shorter and less variable. Despite the inter-annual variability of rainfall, speed breakpoints were strongly correlated with both local and regional rainfall breakpoints across all three years. Thus, at a multi-year scale, rainfall patterns significantly affect the movements of elephant. The variability of both speed and rainfall breakpoints across different years highlights the need for an objective definition of seasonal boundaries. Conclusions/Significance: By using objective criteria to determine behavioural shifts, we identified a biologically meaningful indicator of major changes in animal behaviour in different years. We recommend the use of such criteria, from an animal\u2019s perspective, for delineating seasons or other extrinsic shifts in ecological studies, rather than arbitrarily fixed definitions based on convention or common practice

New Pharmacological Agents to Aid Smoking Cessation and Tobacco Harm Reduction: What has been Investigated and What is in the Pipeline?

A wide range of support is available to help smokers to quit and aid attempts at harm reduction, including three first-line smoking cessation medications: nicotine replacement therapy, varenicline and bupropion. Despite the efficacy of these, there is a continual need to diversify the range of medications so that the needs of tobacco users are met. This paper compares the first-line smoking cessation medications to: 1) two variants of these existing products: new galenic formulations of varenicline and novel nicotine delivery devices; and 2) twenty-four alternative products: cytisine (novel outside of central and eastern Europe), nortriptyline, other tricyclic antidepressants, electronic cigarettes, clonidine (an anxiolytic), other anxiolytics (e.g. buspirone), selective 5-hydroxytryptamine (5-HT) reuptake inhibitors, supplements (e.g. St John’s wort), silver acetate, nicobrevin, modafinil, venlafaxine, monoamine oxidase inhibitors (MAOI), opioid antagonist, nicotinic acetylcholine receptors (nAChR) antagonists, glucose tablets, selective cannabinoid type 1 receptor antagonists, nicotine vaccines, drugs that affect gamma-aminobutyric acid (GABA) transmission, drugs that affect N-methyl-D-aspartate receptors (NMDA), dopamine agonists (e.g. levodopa), pioglitazone (Actos; OMS405), noradrenaline reuptake inhibitors, and the weight management drug lorcaserin. Six criteria are used: relative efficacy, relative safety, relative cost, relative use (overall impact of effective medication use), relative scope (ability to serve new groups of patients), and relative ease of use (ESCUSE). Many of these products are in the early stages of clinical trials, however, cytisine looks most promising in having established efficacy and safety and being of low cost. Electronic cigarettes have become very popular, appear to be efficacious and are safer than smoking, but issues of continued dependence and possible harms need to be considered