Algebraic damping in the one-dimensional Vlasov equation

We investigate the asymptotic behavior of a perturbation around a spatially non homogeneous stable stationary state of a one-dimensional Vlasov equation. Under general hypotheses, after transient exponential Landau damping, a perturbation evolving according to the linearized Vlasov equation decays algebraically with the exponent -2 and a well defined frequency. The theoretical results are successfully tested against numerical $N$-body simulations, corresponding to the full Vlasov dynamics in the large $N$ limit, in the case of the Hamiltonian mean-field model. For this purpose, we use a weighted particles code, which allows us to reduce finite size fluctuations and to observe the asymptotic decay in the $N$-body simulations.Comment: 26 pages, 8 figures; text slightly modified, references added, typos correcte

Convergent Validity of a Single Question with Multiple Classification Options for Depression Screening in Medical Settings

The purpose of this study was to assess the convergent validity of a single depression question with multiple classification options for depression screening. Participants were 40 medical inpatients. The age range of our sample was 18 to 85 years (M = 56.15, SD = 17.66). A clinical interview and the BDI-II were administered. The correlation between patients’ self-rating classification of depression and their BDI-II classification was significant, rs(38) = .90, p < .01. Follow-up repeated-measures chi-square revealed a statistically significant association between BDI-II classification and patients’ self-rating classification, χ2(9, N = 40) = 47.79, p < .005. Significant positive standardized residuals revealed a clear linear relationship between BDI-II and patient self-rating classifications. Our data support the use of a single depression question with multiple classification options as a useful and valid means of quickly screening for the presence of depression by frontline health care professionals

Bootstrap current for the edge pedestal plasma in a diverted tokamak geometry

The edge bootstrap current plays a critical role in the equilibrium and stability of the steep edge pedestal plasma. The pedestal plasma has an unconventional and difficult neoclassical property, as compared with the core plasma. It has a narrow passing particle region in velocity space that can be easily modified or destroyed by Coulomb collisions. At the same time, the edge pedestal plasma has steep pressure and electrostatic potential gradients whose scale-lengths are comparable with the ion banana width, and includes a magnetic separatrix surface, across which the topological properties of the magnetic field and particle orbits change abruptly. A driftkinetic particle code XGC0, equipped with a mass-momentum-energy conserving collision operator, is used to study the edge bootstrap current in a realistic diverted magnetic field geometry with a self-consistent radial electric field. When the edge electrons are in the weakly collisional banana regime, surprisingly, the present kinetic simulation confirms that the existing analytic expressions [represented by O. Sauter et al. , Phys. Plasmas 6 , 2834 (1999)] are still valid in this unconventional region, except in a thin radial layer in contact with the magnetic separatrix. The agreement arises from the dominance of the electron contribution to the bootstrap current compared with ion contribution and from a reasonable separation of the trapped-passing dynamics without a strong collisional mixing. However, when the pedestal electrons are in plateau-collisional regime, there is significant deviation of numerical results from the existing analytic formulas, mainly due to large effective collisionality of the passing and the boundary layer trapped particles in edge region. In a conventional aspect ratio tokamak, the edge bootstrap current from kinetic simulation can be significantly less than that from the Sauter formula if the electron collisionality is high. On the other hand, when the aspect ratio is close to unity, the collisional edge bootstrap current can be significantly greater than that from the Sauter formula. Rapid toroidal rotation of the magnetic field lines at the high field side of a tight aspect-ratio tokamak is believed to be the cause of the different behavior. A new analytic fitting formula, as a simple modification to the Sauter formula, is obtained to bring the analytic expression to a better agreement with the edge kinetic simulation result

Patient-reported outcome measures for cancer caregivers: a systematic review

Purpose Informal caregivers provide invaluable help and support to people with cancer. As treatments extend survival and the potential burdens on carers increase, there is a need to assess the impact of the role. This systematic review identified instruments that measure the impact of caregiving, evaluated their psychometric performance specifically in cancer and appraised the content. Methods A 2-stage search strategy was employed to: 1. identify instruments that measure the impact of caregiving, 2. run individual searches on each measure to identify publications evaluating psychometric performance in the target population. Searches were conducted in Medline, Embase, CINAHL and Psychinfo and restricted to English for instrument used and article language. Psychometric performance was evaluated for content and construct validity, internal consistency, test-retest reliability, precision, responsiveness and acceptability. Individual scale items were extracted and systematically categorised into conceptual domains. Results 10 papers were included reporting on the psychometric properties of 8 measures. Although construct validity and internal consistency were most frequently evaluated, no study comprehensively evaluated all relevant properties. Few studies met our inclusion criteria so it was not possible to consider the psychometric performance of the measures across a group of studies. Content analysis resulted in 16 domains with 5 overarching themes: lifestyle disruption; wellbeing; health of the caregiver; managing the situation and relationships. Conclusions Few measures of caregiver impact have been subject to psychometric evaluation in cancer caregivers. Those that have do not capture well changes in roles and responsibilities within the family and career, indicating the need for a new instrument

A Racial/Ethnic Performance Disparity on the Facial Recognition Test

The Facial Recognition Test is a widely used psychometric instrument for assessing visuoperceptual functioning. Only two prior studies have examined the effects of race/ethnicity on this test. Given that the United States has become more culturally diverse since the creation of the test, it is important to re-visit the effects of this demographic variable on performance. Participants were 75 males and 75 females between the ages of 18 and 43 years (M = 21.91, SD = 5.33). Racial/ethnic categories utilized by the U.S. Census Bureau were equally represented. No gender differences were observed. The race/ethnicity main effect was significant. The gender x race/ethnicity interaction was not significant. The data revealed a clear racial/ethnic performance disparity on the Facial Recognition Test

Toward a first-principles integrated simulation of tokamak edge plasmas

Performance of the ITER is anticipated to be highly sensitive to the edge plasma condition. The edge pedestal in ITER needs to be predicted from an integrated simulation of the necessary first-principles, multi-scale physics codes. The mission of the SciDAC Fusion Simulation Project (FSP) Prototype Center for Plasma Edge Simulation (CPES) is to deliver such a code integration framework by (1) building new kinetic codes XGC0 and XGC1, which can simulate the edge pedestal buildup; (2) using and improving the existing MHD codes ELITE, M3D-OMP, M3D-MPP and NIMROD, for study of large-scale edge instabilities called Edge Localized Modes (ELMs); and (3) integrating the codes into a framework using cutting-edge computer science technology. Collaborative effort among physics, computer science, and applied mathematics within CPES has created the first working version of the End-to-end Framework for Fusion Integrated Simulation (EFFIS), which can be used to study the pedestal-ELM cycles

Mathematical practice, crowdsourcing, and social machines

The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. Crowdsourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated for humans to comprehend. Mathematical practice is an emerging interdisciplinary field which draws on philosophy and social science to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice - for example the community question answering system {\it mathoverflow} contains around 40,000 mathematical conversations, and {\it polymath} collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of "soft" aspects such as analogy and creativity, alongside deduction and proof, in the production of mathematics, and have given us new ways to think about the roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal. Crowdsourced mathematical activity is an example of a "social machine", a new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathematics, and to transform the reach, pace, and impact of mathematics research.Comment: To appear, Springer LNCS, Proceedings of Conferences on Intelligent Computer Mathematics, CICM 2013, July 2013 Bath, U

Psi-Series Solution of Fractional Ginzburg-Landau Equation

One-dimensional Ginzburg-Landau equations with derivatives of noninteger order are considered. Using psi-series with fractional powers, the solution of the fractional Ginzburg-Landau (FGL) equation is derived. The leading-order behaviours of solutions about an arbitrary singularity, as well as their resonance structures, have been obtained. It was proved that fractional equations of order $alpha$ with polynomial nonlinearity of order $s$ have the noninteger power-like behavior of order $\alpha/(1-s)$ near the singularity.Comment: LaTeX, 19 pages, 2 figure