The low-frequency response in the surface superconducting state of ZrB12_{12} single crystal}

The large nonlinear response of a single crystal ZrB$_{12}$ to an ac field (frequency 40 - 2500 Hz) for $H_0>H_{c2}$ has been observed. Direct measurements of the ac wave form and the exact numerical solution of the Ginzburg-Landau equations, as well as phenomenological relaxation equation, permit the study of the surface superconducting states dynamics. It is shown, that the low frequency response is defined by transitions between the metastable superconducting states under the action of an ac field. The relaxation rate which determines such transitions dynamics, is found.Comment: 7 pages, 11 figure

Star Formation Efficiency in the Central 1 kpc Region of Early-Type Spiral Galaxies

It has been reported recently that there are some early-type spiral (Sa--Sab) galaxies having evident star-forming regions which concentrate in their own central 1-kpc. In such central region, is the mechanism of the star formation distinct from that in disks of spiral galaxies? To reveal this, we estimate the star formation efficiency (SFE) in this central 1-kpc star-forming region of some early-type spiral galaxies, taking account of the condition for this 1-kpc region to be self-gravitating. Using two indicators of present star formation rate (H$\alpha$ and infrared luminosity), we estimate the SFE to be a few percents. This is equivalent to the observational SFE in the disks of late-type spiral (Sb--) galaxies. This coincidence may support the universality of the mean SFE of spiral galaxies reported in the recent studies. That is, we find no evidence of distinct mechanism of the star formation in the central 1-kpc region of early-type galaxies. Also, we examine the structure of the central star-forming region, and discuss a method for estimating the mass of star-forming regions.Comment: accepted by A

Gauge covariances and nonlinear optical responses

The formalism of the reduced density matrix is pursued in both length and velocity gauges of the perturbation to the crystal Hamiltonian. The covariant derivative is introduced as a convenient representation of the position operator. This allow us to write compact expressions for the reduced density matrix in any order of the perturbation which simplifies the calculations of nonlinear optical responses; as an example, we compute the first and third order contributions of the monolayer graphene. Expressions obtained in both gauges share the same formal structure, allowing a comparison of the effects of truncation to a finite set of bands. This truncation breaks the equivalence between the two approaches: its proper implementation can be done directly in the expressions derived in the length gauge, but require a revision of the equations of motion of the reduced density matrix in the velocity gauge.The work of G.B.V. and D.J.P. is supported by Fundação para a Ciência e Tecnologia (FCT) under the Grants No. PD/BI/129220/2017 and No. PD/BD/135019/2017, respectively. N.M.R.P. acknowledges funding from the European Commission within the project "Graphene-Driven Revolutions in ICT and Beyond" (Ref. No. 696656) and the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Financing Grant No. UID/FIS/04650/2013.info:eu-repo/semantics/publishedVersio

Simultaneous Analysis of All SNPs in Genome-Wide and Re-Sequencing Association Studies

Testing one SNP at a time does not fully realise the potential of genome-wide association studies to identify multiple causal variants, which is a plausible scenario for many complex diseases. We show that simultaneous analysis of the entire set of SNPs from a genome-wide study to identify the subset that best predicts disease outcome is now feasible, thanks to developments in stochastic search methods. We used a Bayesian-inspired penalised maximum likelihood approach in which every SNP can be considered for additive, dominant, and recessive contributions to disease risk. Posterior mode estimates were obtained for regression coefficients that were each assigned a prior with a sharp mode at zero. A non-zero coefficient estimate was interpreted as corresponding to a significant SNP. We investigated two prior distributions and show that the normal-exponential-gamma prior leads to improved SNP selection in comparison with single-SNP tests. We also derived an explicit approximation for type-I error that avoids the need to use permutation procedures. As well as genome-wide analyses, our method is well-suited to fine mapping with very dense SNP sets obtained from re-sequencing and/or imputation. It can accommodate quantitative as well as case-control phenotypes, covariate adjustment, and can be extended to search for interactions. Here, we demonstrate the power and empirical type-I error of our approach using simulated case-control data sets of up to 500 K SNPs, a real genome-wide data set of 300 K SNPs, and a sequence-based dataset, each of which can be analysed in a few hours on a desktop workstation

Fixed points approach to clustering

Fixed points, Hierarchical clustering, Graph-theoretic clustering, Conceptual clustering, Overlapping clusters,