The algebra of the box spline

In this paper we want to revisit results of Dahmen and Micchelli on box-splines which we reinterpret and make more precise. We compare these ideas with the work of Brion, Szenes, Vergne and others on polytopes and partition functions.Comment: 69 page

Habituation to pain : a motivational-ethological perspective

Habituation to pain is mainly studied using external pain stimuli in healthy volunteers, often to identify the underlying brain mechanisms, or to investigate problems in habituation in specific forms of pain (eg, migraine). Although these studies provide insight, they do not address one pertinent question: Why do we habituate to pain? Pain is a warning signal that urges us to react. Habituation to pain may thus be dysfunctional: It could make us unresponsive in situations where sensitivity and swift response to bodily damage are essential. Early theories of habituation were well aware of this argument. Sokolov argued that responding to pain should not decrease, but rather increase with repeated exposure, a phenomenon he called “sensitization.” His position makes intuitive sense: Why would individuals respond less to pain that inherently signals bodily harm? In this topical review, we address this question from a motivational ethological perspective. First, we describe some core characteristics of habituation. Second, we discuss theories that explain how and when habituation occurs. Third, we introduce a motivational-ethological perspective on habituation and explain why habituation occurs. Finally, we discuss how a focus on habituation to pain introduces important methodological, theoretical, and clinical implications, otherwise overlooked

Divided Differences

Starting with a novel definition of divided differences, this essay derives and discusses the basic properties of, and facts about, (univariate) divided differences.Comment: 24 page

Using mirror and other internal surveys in order to improve student experience

This article is the first stage of a project which considers how best to use the data collected from mirror surveys and other internal student surveys to enhance the student experience, with a subsidiary aim of thereby enhancing National Student Survey (NSS) scores. The second stage, which is underway at present, combines the theoretical basis and debate explored in this article with detailed statistical analysis of internal and external survey results, to provide a greater evidential basis for decision-making and strategic planning. The research was supported as a 2011-12 Learning Development Project, at City University London, and is intended to inform educational discussion and strategy. The interim findings discussed below are readily transferable to other disciplines and other universities. Universities have put a great deal of effort into improving student satisfaction, but not always with measurable results. Throughout the existence of the NSS, universities have experienced significant variance between student satisfaction as represented by internal measures and the levels of satisfaction reported in the NSS. This has been the case even when the internal measures take the form of mirror surveys, i.e. surveys which mirror or closely resemble the questions on the current version of the NSS. Although general morale factors and events beyond a university’s control may play a strong role in the scores, they do not necessarily explain the differences, especially where the internal questions are based on those from the NSS. Both measures may be an accurate representation of student satisfaction but measuring subtly different factors, or other influences may be operating. By examining this issue, this project aims to enable better planning for the future and the development of appropriate, tailored responses to issues. The interim findings reflect examples of best practice and next steps for the strategic use of such data, including free-text comments

Constraining A General-Relativistic Frame-Dragging Model for Pulsed Radiation from a Population of Millisecond Pulsars in 47 Tucanae using GLAST/LAT

Although only 22 millisecond pulsars (MSPs) are currently known to exist in the globular cluster (GC) 47 Tucanae, this cluster may harbor 30-60 MSPs, or even up to ~200. In this Letter, we model the pulsed curvature radiation (CR) gamma-ray flux expected from a population of MSPs in 47 Tucanae. These MSPs produce gamma-rays in their magnetospheres via accelerated electron primaries which are moving along curved magnetic field lines. A GC like 47 Tucanae containing a large number of MSPs provides the opportunity to study a randomized set of pulsar geometries. Geometry-averaged spectra make the testing of the underlying pulsar model more reliable, since in this case the relative flux uncertainty is reduced by one order of magnitude relative to the variation expected for individual pulsars (if the number of visible pulsars N=100). Our predicted spectra violate the EGRET upper limit at 1 GeV, constraining the product of the number of visible pulsars N and the average integral flux above 1 GeV per pulsar. GLAST/LAT should place even more stringent constraints on this product, and may also limit the maximum average accelerating potential by probing the CR spectral tail. For N=22-200, a GLAST/LAT non-detection will lead to the constraints that the average integral flux per pulsar should be lower by factors 0.03-0.003 than current model predictions.Comment: 10 pages, 2 figures, to appear in the Astrophysical Journal Letter