On Convergence of the Inexact Rayleigh Quotient Iteration with the Lanczos Method Used for Solving Linear Systems

For the Hermitian inexact Rayleigh quotient iteration (RQI), the author has established new local general convergence results, independent of iterative solvers for inner linear systems. The theory shows that the method locally converges quadratically under a new condition, called the uniform positiveness condition. In this paper we first consider the local convergence of the inexact RQI with the unpreconditioned Lanczos method for the linear systems. Some attractive properties are derived for the residuals, whose norms are $\xi_{k+1}$'s, of the linear systems obtained by the Lanczos method. Based on them and the new general convergence results, we make a refined analysis and establish new local convergence results. It is proved that the inexact RQI with Lanczos converges quadratically provided that $\xi_{k+1}\leq\xi$ with a constant $\xi\geq 1$. The method is guaranteed to converge linearly provided that $\xi_{k+1}$ is bounded by a small multiple of the reciprocal of the residual norm $\|r_k\|$ of the current approximate eigenpair. The results are fundamentally different from the existing convergence results that always require $\xi_{k+1}<1$, and they have a strong impact on effective implementations of the method. We extend the new theory to the inexact RQI with a tuned preconditioned Lanczos for the linear systems. Based on the new theory, we can design practical criteria to control $\xi_{k+1}$ to achieve quadratic convergence and implement the method more effectively than ever before. Numerical experiments confirm our theory.Comment: 20 pages, 8 figures. arXiv admin note: text overlap with arXiv:0906.223

Representation of Africa online: sourcing practice and frames of reference

The dominant perspective on the representation of Africa in the western media claims that western media coverage is bias and crisis orientated and the liberal perspective claims that the coverage of Africa is not as negative as is often assumed. However, there is a paucity of literature on the representation of Africa online. This research enquiry is relevant because literature claims that the Internet has the potential to resolve the journalistic predicament of representing other culture through political participation and deliberation. But this requires a re-orientation of the sourcing practice of news organization to embrace sensitivity to and knowledge of African cultures. Moreover, the journalistic predicament can be resolved or not depending on the news gathering approach adopted by the news organization. Literature has identified two approaches, that is, ‘gatekeeping’ used mainly by dominant traditional media and ‘gatewatching’ used by alternative media in their quest to counter mainstream ideology. This study examines the impacts of the ‘gatewatching’ approach adopted by Africa Have Your Say (AHYS) website on its representation and frames of reference of Africa. It uses on-site observation, in-depth interviews and textual analysis to gather data. The study found that although the sourcing practice at the AHYS is elaborate and complex, the ‘gatewatching’ approach makes its susceptible to second level agenda setting. Hence, its frame repeats the attributes and tone used by the mainstream traditional media. However, a minority of users did not use repeat this frame in their comments

The martyrdom effect : when pain and effort increase prosocial contributions

Most theories of motivation and behavior (and lay intuitions alike) consider pain and effort to be deterrents. In contrast to this widely held view, we provide evidence that the prospect of enduring pain and exerting effort for a prosocial cause can promote contributions to the cause. Specifically, we show that willingness to contribute to a charitable or collective cause increases when the contribution process is expected to be painful and effortful rather than easy and enjoyable. Across five experiments, we document this “martyrdom effect,” show that the observed patterns defy standard economic and psychological accounts, and identify a mediator and moderator of the effect. Experiment 1 showed that people are willing to donate more to charity when they anticipate having to suffer to raise money. Experiment 2 extended these findings to a non-charity laboratory context that involved real money and actual pain. Experiment 3 demonstrated that the martyrdom effect is not the result of an attribute substitution strategy (whereby people use the amount of pain and effort involved in fundraising to determine donation worthiness). Experiment 4 showed that perceptions of meaningfulness partially mediate the martyrdom effect. Finally, Experiment 5 demonstrated that the nature of the prosocial cause moderates the martyrdom effect: the effect is strongest for causes associated with human suffering. We propose that anticipated pain and effort lead people to ascribe greater meaning to their contributions and to the experience of contributing, thereby motivating higher prosocial contributions. We conclude by considering some implications of this puzzling phenomenon. Copyright © 2011 John Wiley & Sons, Ltd

THERMAL DENATURATION OF MONOMERIC AND TRIMERIC PHYCOCYANINS STUDIED BY STATIC AND SPECTROSCOPY POLARIZED TIME-RESOLVED FLUORESCENCE

C-Phycocyanin (PC) and allophycocyanin (APC). as well as the a-subunit of PC. have been isolated from the blue-green alga (cyanobacterium). Spirulina platensis. The effects of partial thermal denaturation of PC and of its state of aggregation have been studied by ps time-resolved, polarized fluorescence spectroscopy. All measurements have been performed under low photon fluxes (< 10’ ’ photonsipulse x cm’) to minimize singlet-singlet annihilation processes. A complex decay is obtained under most conditions, which can be fitted satisfactorily with a bi-exponential (7’ = 70400 ps. T? = 1000-3000 ps) for both the isotropic and the polarized part, but with different intensities and time constants for the two decay curves. The data are interpreted in the frameworkof the model first developed by Teak and Dale (Biochern. J. 116, 161 (1970)], which divides the spectroscopically different chromophores in (predominantly) sensitizing (s) and fluorescing U, ones. If one assumes temperature dependent losses in the energy transfer from the s to the f and between f chromophores. both the biexponential nature of the isotropic fluorescence decay and the polarization data can be rationalized. In the isotropic emission (corresponding to the population of excited states) the short lifetime is related to the s-,f transfer. the longer one to the “free“ decay of the final acceptor(s) (= f). The polarized part is dominated by an extremely short decay time. which is related to s+f transfer, as well as to resonance transfer between the f-chromophores

Mammography Facility Characteristics Associated With Interpretive Accuracy of Screening Mammography

BackgroundAlthough interpretive performance varies substantially among radiologists, such variation has not been examined among mammography facilities. Understanding sources of facility variation could become a foundation for improving interpretive performance.MethodsIn this cross-sectional study conducted between 1996 and 2002, we surveyed 53 facilities to evaluate associations between facility structure, interpretive process characteristics, and interpretive performance of screening mammography (ie, sensitivity, specificity, positive predictive value [PPV1], and the likelihood of cancer among women who were referred for biopsy [PPV2]). Measures of interpretive performance were ascertained prospectively from mammography interpretations and cancer data collected by the Breast Cancer Surveillance Consortium. Logistic regression and receiver operating characteristic (ROC) curve analyses estimated the association between facility characteristics and mammography interpretive performance or accuracy (area under the ROC curve [AUC]). All P values were two-sided.ResultsOf the 53 eligible facilities, data on 44 could be analyzed. These 44 facilities accounted for 484 463 screening mammograms performed on 237 669 women, of whom 2686 were diagnosed with breast cancer during follow-up. Among the 44 facilities, mean sensitivity was 79.6% (95% confidence interval [CI] = 74.3% to 84.9%), mean specificity was 90.2% (95% CI = 88.3% to 92.0%), mean PPV1 was 4.1% (95% CI = 3.5% to 4.7%), and mean PPV2 was 38.8% (95% CI = 32.6% to 45.0%). The facilities varied statistically significantly in specificity (P &lt; .001), PPV1 (P &lt; .001), and PPV2 (P = .002) but not in sensitivity (P = .99). AUC was higher among facilities that offered screening mammograms alone vs those that offered screening and diagnostic mammograms (0.943 vs 0.911, P = .006), had a breast imaging specialist interpreting mammograms vs not (0.932 vs 0.905, P = .004), did not perform double reading vs independent double reading vs consensus double reading (0.925 vs 0.915 vs 0.887, P = .034), or conducted audit reviews two or more times per year vs annually vs at an unknown frequency (0.929 vs 0.904 vs 0.900, P = .018).ConclusionMammography interpretive performance varies statistically significantly by facility