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 In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem.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

Snout Shape in Extant Ruminants

Copyright: © 2014 Tennant, MacLeod. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. [4.0 license]. The attached file is the published version of the article

Protease-Sensitive Conformers in Broad Spectrum of Distinct PrPSc Structures in Sporadic Creutzfeldt-Jakob Disease Are Indicator of Progression Rate

The origin, range, and structure of prions causing the most common human prion disease, sporadic Creutzfeldt-Jakob disease (sCJD), are largely unknown. To investigate the molecular mechanism responsible for the broad phenotypic variability of sCJD, we analyzed the conformational characteristics of protease-sensitive and protease-resistant fractions of the pathogenic prion protein (PrPSc) using novel conformational methods derived from a conformation-dependent immunoassay (CDI). In 46 brains of patients homozygous for polymorphisms in the PRNP gene and exhibiting either Type 1 or Type 2 western blot pattern of the PrPSc, we identified an extensive array of PrPSc structures that differ in protease sensitivity, display of critical domains, and conformational stability. Surprisingly, in sCJD cases homozygous for methionine or valine at codon 129 of the PRNP gene, the concentration and stability of protease-sensitive conformers of PrPSc correlated with progression rate of the disease. These data indicate that sCJD brains exhibit a wide spectrum of PrPSc structural states, and accordingly argue for a broad spectrum of prion strains coding for different phenotypes. The link between disease duration, levels, and stability of protease-sensitive conformers of PrPSc suggests that these conformers play an important role in the pathogenesis of sCJD

Functional correlates of skull shape in Chiroptera: feeding and echolocation adaptations.

Morphological, functional and behavioural adaptations of bats are among the most diverse within mammals. A strong association between bat skull morphology and feeding behaviour has been suggested previously. However, morphological variation related to other drivers of adaptation, in particular echolocation, remains understudied. We assessed variation in skull morphology with respect to ecology (diet and emission type) and function (bite force, masticatory muscles and echolocation characteristics) using geometric morphometrics and comparative methods. Our study suggests that variation in skull shape of 10 bat families is the result of adaptations to broad dietary categories and sound emission types (oral or nasal). Skull shape correlates with echolocation parameters only in a subsample of insectivorous species, possibly because they (almost) entirely rely on this sensory system for locating and capturing prey. Insectivores emitting low frequencies are characterised by a ventrally tilted rostrum, a trait not associated with feeding parameters. This result questions the validity of a trade-off between feeding and echolocation function. Our study advances understanding of the relationship between skull morphology and specific features of echolocation and suggests that evolutionary constraints due to echolocation may differ between different groups within the Chiroptera