LS Penrose’s limit theorem: Tests by simulation

LS Penrose’s limit theorem (PLT) – which is implicit in Penrose [5, p. 72] and for which he gave no rigorous proof – says that, in simple weighted voting games, if the number of voters increases indefinitely while existing voters retain their weights and the relative quota is pegged, then – under certain conditions – the ratio between the voting powers of any two voters converges to the ratio between their weights. Lindner and Machover [3] prove some special cases of PLT; and conjecture that the theorem holds, under rather general conditions, for large classes of weighted voting games, various values of the quota, and with respect to several measures of voting power. We use simulation to test this conjecture. It is corroborated w.r.t. the Penrose–Banzhaf index for a quota of 50% but not for other values; w.r.t. the Shapley–Shubik index the conjecture is corroborated for all values of the quota (short of 100%).limit theorems, majority games, simulation, weighted voting games

Evolution of superconductivity in K2-xFe4+ySe5: Spectroscopic studies of X-ray absorption and emission.

This study investigates the evolution of superconductivity in K2-xFe4+ySe5 using temperature-dependent X-ray absorption and resonant inelastic X-ray scattering techniques. Magnetization measurements show that polycrystalline superconducting (SC) K1.9Fe4.2Se5 has a critical temperature (T c) of ∼31 K with a varying superconducting volume fraction, which strongly depends on its synthesis temperature. An increase in Fe-structural/vacancy disorder in SC samples with more Fe atoms occupying vacant 4d sites is found to be closely related to the decrease in the spin magnetic moment of Fe. Moreover, the nearest-neighbor Fe-Se bond length in SC samples exceeds that in the non-SC (NS) sample, K2Fe4Se5, which indicates a weaker hybridization between the Fe 3d and Se 4p states in SC samples. These results clearly demonstrate the correlations among the local electronic and atomic structures and the magnetic properties of K2-xFe4+ySe5 superconductors, providing deeper insight into the electron pairing mechanisms of superconductivity

Effect of a Normal-State Pseudogap on Optical Conductivity in Underdoped Cuprate Superconductors

We calculate the c-axis infrared conductivity $\sigma_c(\omega)$ in underdoped cuprate superconductors for spinfluctuation exchange scattering within the CuO$_2$-planes including a phenomenological d-wave pseudogap of amplitude $E_g$. For temperatures decreasing below a temperature $T^* \sim E_g/2$, a gap for $\omega < 2E_g$ develops in $\sigma_c(\omega)$ in the incoherent (diffuse) transmission limit. The resistivity shows 'semiconducting' behavior, i.e. it increases for low temperatures above the constant behavior for $E_g=0$. We find that the pseudogap structure in the in-plane optical conductivity is about twice as big as in the interplane conductivity $\sigma_c(\omega)$, in qualitative agreement with experiment. This is a consequence of the fact that the spinfluctuation exchange interaction is suppressed at low frequencies as a result of the opening of the pseudogap. While the c-axis conductivity in the underdoped regime is described best by incoherent transmission, in the overdoped regime coherent conductance gives a better description.Comment: to be published in Phys. Rev. B (November 1, 1999

Collective Modes and the Superconducting State Spectral Function of Bi2212

Photoemission spectra of the high temperature superconductor Bi2212 near (pi,0) show a dramatic change when cooling below Tc: the broad peak in the normal state turns into a sharp low energy peak followed by a higher binding energy hump. Recent experiments find that this low energy peak persists over a significant range in momentum space. We show in this paper that these data are well described by a simple model of electrons interacting with a collective mode which appears only below Tc.Comment: 4 pages, revtex, 4 encapsulated postscript figure

Bosonic Mode Mixing in the Superconducting State Spectral Function of Bi_2Sr_2CaCu_2O_{8+delta}

Photoemission spectra of Bi_2Sr_2CaCu_2O_{8+delta} below T_c show two features near the (pi,0) point of the zone: a sharp peak at low energy and a higher binding energy hump. We find that the sharp peak persists at low energy even as one moves towards (0,0), while the broad hump shows significant dispersion which correlates well with the normal state dispersion. We argue that these features are naturally explained by the mixing of electrons with a bosonic mode which appears only below T_c, and speculate that the latter may be related to the resonance seen in recent neutron data.Comment: 4 pages, revtex, 4 postscript figure

Increased HIV Incidence in Men Who Have Sex with Men Despite High Levels of ART-Induced Viral Suppression: Analysis of an Extensively Documented Epidemic

Background: There is interest in expanding ART to prevent HIV transmission, but in the group with the highest levels of ART use, men-who-have-sex-with-men (MSM), numbers of new infections diagnosed each year have not decreased as ART coverage has increased for reasons which remain unclear. Methods: We analysed data on the HIV-epidemic in MSM in the UK from a range of sources using an individual-based simulation model. Model runs using parameter sets found to result in good model fit were used to infer changes in HIV-incidence and risk behaviour. Results: HIV-incidence has increased (estimated mean incidence 0.30/100 person-years 1990–1997, 0.45/100 py 1998–2010), associated with a modest (26%) rise in condomless sex. We also explored counter-factual scenarios: had ART not been introduced, but the rise in condomless sex had still occurred, then incidence 2006–2010 was 68% higher; a policy of ART initiation in all diagnosed with HIV from 2001 resulted in 32% lower incidence; had levels of HIV testing been higher (68% tested/year instead of 25%) incidence was 25% lower; a combination of higher testing and ART at diagnosis resulted in 62% lower incidence; cessation of all condom use in 2000 resulted in a 424% increase in incidence. In 2010, we estimate that undiagnosed men, the majority in primary infection, accounted for 82% of new infections. Conclusion: A rise in HIV-incidence has occurred in MSM in the UK despite an only modest increase in levels of condomless sex and high coverage of ART. ART has almost certainly exerted a limiting effect on incidence. Much higher rates of HIV testing combined with initiation of ART at diagnosis would be likely to lead to substantial reductions in HIV incidence. Increased condom use should be promoted to avoid the erosion of the benefits of ART and to prevent other serious sexually transmitted infections

Which biomarker predicts benefit from EGFR-TKI treatment for patients with lung cancer?

Subsets of patients with non-small cell lung cancer respond remarkably well to small molecule tyrosine kinase inhibitors (TKI) specific for epidermal growth factor receptor (EGFR) such as gefitinib or erlotinib. In 2004, it was found that EGFR mutations occurring in the kinase domain are strongly associated with EGFR-TKI sensitivity. However, subsequent studies revealed that this relationship was not perfect and various predictive markers have been reported. These include EGFR gene copy numbers, status of ligands for EGFR, changes in other HER family genes or molecules downstream to EGFR including KRAS or AKT. In this review, we would like to review current knowledge of predictive factors for EGFR-TKI. As all but one phase III trials failed to show a survival advantage of the treatment arm involving EGFR-TKIs, it is necessary to select patients by these biomarkers in future clinical trials. Through these efforts, it would be possible to individualise EGFR-TKI treatment for patients suffering from lung cancer

Theory of Electric Transport in the Pseudogap State of High-Tc Cuprates

We theoretically investigate the electric transport in the pseudogap state of High-Tc cuprates. Starting from the repulsive Hubbard model, we perform the microscopic calculation to describe the pseudogap phenomena which are induced by the superconducting fluctuations. The single particle Green function, spin susceptibility and superconducting fluctuations are self-consistently determined by the SC-FLEX+T-matrix approximation. The longitudinal and transverse conductivities are calculated by using the Eliashberg and Kohno-Yamada formalism. The effects of the spin fluctuations and superconducting fluctuations are estimated, respectively. The vertex corrections arising from the two fluctuations are also calculated. The additional contribution from the Aslamazov-Larkin term is also estimated beyond the Eliashberg formalism. It is shown that the main effect of the superconducting fluctuations is the feedback effect through the spin fluctuations. The correct results are obtained by considering the superconducting fluctuations and the spin fluctuations simultaneously. The temperature and doping dependences of the resistivity and the Hall coefficient are well explained. We point out that the characteristic momentum dependence of the systems plays an essential role in this explanation.Comment: To appear in J. Phys. Soc. Jpn. Vol.71 No.1 (2002

Renormalized mean-field theory of the neutron scattering in cuprate superconductors

The magnetic excitation spectrum of the t-t'-J-model is studied in mean-field theory and compared to inelastic neutron-scattering (INS) experiments on YBCO and BSCCO superconductors. Within the slave-particle formulation the dynamical spin response is calculated from a renormalized Fermi liquid with an effective interaction ~J in the magnetic particle--hole channel. We obtain the so-called 41meV resonance at wave vector (pi,pi) as a collective spin-1 excitation in the d-wave superconducting state. It appears sharp (undamped), if the underlying Fermi surface is hole-like with a sufficient next-nearest-neighbor hopping t'<0. The double-layer structure of YBCO or BSCCO is not important for the resonance to form. The resonance energy \omega_{res} and spectral weight at optimal doping come out comparable to experiment. The observed qualitative behavior of \omega_{res} with hole filling is reproduced in the underdoped as well as overdoped regime. A second, much broader peak becomes visible in the magnetic excitation spectrum if the 2D wave-vector is integrated over. It is caused by excitations across the maximum gap, and in contrast to the resonance its energy is almost independent of doping. At energies above or below \omega_{res} the commensurate resonance splits into incommensurate peaks, located off (pi,pi). Below \omega_{res} the intensity pattern is of `parallel' type and the dispersion relation of incommensurate peaks has a negative curvature. This is in accordance with recent INS experiments on YBCO.Comment: 17pp including 14 figure

Two-Particle-Self-Consistent Approach for the Hubbard Model

Even at weak to intermediate coupling, the Hubbard model poses a formidable challenge. In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem. The Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem as well as particle conservation, the Pauli principle, the local moment and local charge sum rules. The self-energy formula does not assume a Migdal theorem. There is consistency between one- and two-particle quantities. Internal accuracy checks allow one to test the limits of validity of TPSC. Here I present a pedagogical review of TPSC along with a short summary of existing results and two case studies: a) the opening of a pseudogap in two dimensions when the correlation length is larger than the thermal de Broglie wavelength, and b) the conditions for the appearance of d-wave superconductivity in the two-dimensional Hubbard model.Comment: Chapter in "Theoretical methods for Strongly Correlated Systems", Edited by A. Avella and F. Mancini, Springer Verlag, (2011) 55 pages. Misprint in Eq.(23) corrected (thanks D. Bergeron