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

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

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