Slepian functions and their use in 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 on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla

Measurement of the inclusive and dijet cross-sections of b-jets in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

The inclusive and dijet production cross-sections have been measured for jets containing b-hadrons (b-jets) in proton-proton collisions at a centre-of-mass energy of sqrt(s) = 7 TeV, using the ATLAS detector at the LHC. The measurements use data corresponding to an integrated luminosity of 34 pb^-1. The b-jets are identified using either a lifetime-based method, where secondary decay vertices of b-hadrons in jets are reconstructed using information from the tracking detectors, or a muon-based method where the presence of a muon is used to identify semileptonic decays of b-hadrons inside jets. The inclusive b-jet cross-section is measured as a function of transverse momentum in the range 20 < pT < 400 GeV and rapidity in the range |y| < 2.1. The bbbar-dijet cross-section is measured as a function of the dijet invariant mass in the range 110 < m_jj < 760 GeV, the azimuthal angle difference between the two jets and the angular variable chi in two dijet mass regions. The results are compared with next-to-leading-order QCD predictions. Good agreement is observed between the measured cross-sections and the predictions obtained using POWHEG + Pythia. MC@NLO + Herwig shows good agreement with the measured bbbar-dijet cross-section. However, it does not reproduce the measured inclusive cross-section well, particularly for central b-jets with large transverse momenta.Comment: 10 pages plus author list (21 pages total), 8 figures, 1 table, final version published in European Physical Journal

Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries

The determination of the energy spectra of small spin systems as for instance given by magnetic molecules is a demanding numerical problem. In this work we review numerical approaches to diagonalize the Heisenberg Hamiltonian that employ symmetries; in particular we focus on the spin-rotational symmetry SU(2) in combination with point-group symmetries. With these methods one is able to block-diagonalize the Hamiltonian and thus to treat spin systems of unprecedented size. In addition it provides a spectroscopic labeling by irreducible representations that is helpful when interpreting transitions induced by Electron Paramagnetic Resonance (EPR), Nuclear Magnetic Resonance (NMR) or Inelastic Neutron Scattering (INS). It is our aim to provide the reader with detailed knowledge on how to set up such a diagonalization scheme.Comment: 29 pages, many figure

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

Asteroseismology and Interferometry

Asteroseismology provides us with a unique opportunity to improve our understanding of stellar structure and evolution. Recent developments, including the first systematic studies of solar-like pulsators, have boosted the impact of this field of research within Astrophysics and have led to a significant increase in the size of the research community. In the present paper we start by reviewing the basic observational and theoretical properties of classical and solar-like pulsators and present results from some of the most recent and outstanding studies of these stars. We centre our review on those classes of pulsators for which interferometric studies are expected to provide a significant input. We discuss current limitations to asteroseismic studies, including difficulties in mode identification and in the accurate determination of global parameters of pulsating stars, and, after a brief review of those aspects of interferometry that are most relevant in this context, anticipate how interferometric observations may contribute to overcome these limitations. Moreover, we present results of recent pilot studies of pulsating stars involving both asteroseismic and interferometric constraints and look into the future, summarizing ongoing efforts concerning the development of future instruments and satellite missions which are expected to have an impact in this field of research.Comment: Version as published in The Astronomy and Astrophysics Review, Volume 14, Issue 3-4, pp. 217-36

Search for R-parity-violating supersymmetry in events with four or more leptons in sqrt(s) =7 TeV pp collisions with the ATLAS detector

A search for new phenomena in final states with four or more leptons (electrons or muons) is presented. The analysis is based on 4.7 fb−1 of $\sqrt{s}=7\;\mathrm{TeV}$ proton-proton collisions delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in two signal regions: one that requires moderate values of missing transverse momentum and another that requires large effective mass. The results are interpreted in a simplified model of R-parity-violating supersymmetry in which a 95% CL exclusion region is set for charged wino masses up to 540 GeV. In an R-parity-violating MSUGRA/CMSSM model, values of m 1/2 up to 820 GeV are excluded for 10 < tan β < 40

First report on dung beetles in intra-Amazonian savannahs in Roraima, Brazil

This is the first study to address the dung beetle (Coleoptera: Scarabaeidae: Scarabaeinae) diversity in intra-Amazonian savannahs in the state of Roraima, Brazil. Our aim was to survey the dung beetle fauna associated with these savannahs (regionally called 'lavrado'), since little is known about the dung beetles from this environment. We conducted three field samples using pitfall traps baited with human dung in savannah areas near the city of Boa Vista during the rainy seasons of 1996, 1997, and 2008. We collected 383 individuals from ten species, wherein six have no previous record in intra-Amazonian savannahs. The most abundant species were Ontherus appendiculatus (Mannerheim, 1829), Canthidium aff. humerale (Germar, 1813), Dichotomius nisus (Olivier, 1789), and Pseudocanthon aff. xanthurus (Blanchard, 1846). We believe that knowing the dung beetles diversity associated with the intra-Amazonian savannahs is ideal for understanding the occurrence and distribution of these organisms in a highly threatened environment, it thus being the first step towards conservation strategy development

Optimization of insect cell based protein production processes - online monitoring, expression systems, scale-up

Due to the increasing use of insect cell based expression systems in research and industrial recombinant protein production, the development of efficient and reproducible production processes remains a challenging task. In this context, the application of online monitoring techniques is intended to ensure high and reproducible product qualities already during the early phases of process development. In the following chapter, the most common transient and stable insect cell based expression systems are briefly introduced. Novel applications of insect cell based expression systems for the production of insect derived antimicrobial peptides/proteins (AMPs) are discussed using the example of G. mellonella derived gloverin. Suitable in situ sensor techniques for insect cell culture monitoring in disposable and common bioreactor systems are outlined with respect to optical and capacitive sensor concepts. Since scale-up of production processes is one of the most critical steps in process development, a conclusive overview is given about scale up aspects for industrial insect cell culture processes

Clinical risk factors associated with radiographic osteoarthritis progression among people with knee pain: a longitudinal study

Background: The aim of this study was to identify modifiable clinical factors associated with radiographic osteoarthritis progression over 1 to 2 years in people with painful medial knee osteoarthritis. Methods: A longitudinal study was conducted within a randomised controlled trial, the “Long-term Evaluation of Glucosamine Sulfate” (LEGS study). Recruitment occurred in 2007–2009, with 1- and 2-year follow-up assessments by blinded assessors. Community-dwelling people with chronic knee pain (≥4/10) and medial tibiofemoral narrowing (but retaining >2mm medial joint space width) on radiographs were recruited. From 605 participants, follow-up data were available for 498 (82%, mean [sd] age 60 [8] years). Risk factors evaluated at baseline were pain, physical function, use of non-steroidal anti-inflammatory drugs (NSAIDs), statin use, not meeting physical activity guidelines, presence of Heberden’s nodes, history of knee surgery/trauma, and manual occupation. Multivariable logistic regression analysis was conducted adjusting for age, sex, obesity, high blood pressure, allocation to glucosamine and chondroitin treatment, and baseline structural disease severity (Kellgren and Lawrence grade, joint space width, and varus alignment). Radiographic osteoarthritis progression was defined as joint space narrowing ≥0.5mm over 1 to 2 years (latest follow-up used where available). Results: Radiographic osteoarthritis progression occurred in 58 participants (12%). Clinical factors independently associated with radiographic progression were the use of NSAIDs, adjusted odds ratios (OR) and 95% confidence intervals (CI) 2.05 (95% CI 1.1 to 3.8), and not meeting physical activity guidelines, OR 2.07 (95% CI 0.9 to 4.7). Conclusions: Among people with mild radiographic knee osteoarthritis, people who use NSAIDs and/or do not meet physical activity guidelines have a greater risk of radiographic osteoarthritis progression. Trial registration: ClinicalTrials.gov, NCT00513422. This original study trial was registered a priori, on August 8, 2007. The current study hypothesis arose before inspection of the data