Properties of canonical determinants and a test of fugacity expansion for finite density lattice QCD with Wilson fermions

We analyze canonical determinants, i.e., grand canonical determinants projected to a fixed net quark number. The canonical determinants are the coefficients in a fugacity expansion of the grand canonical determinant and we evaluate them as the Fourier moments of the grand canonical determinant with respect to imaginary chemical potential, using a dimensional reduction technique. The analysis is done for two mass-degenerate flavors of Wilson fermions at several temperatures below and above the confinement/deconfinement crossover. We discuss various properties of the canonical determinants and analyse the convergence of the fugacity series for different temperatures.Comment: Typo removed, paragraph added in the discussion. Version to appear in Phys. Rev.

Hadron Spectroscopy with Dynamical Chirally Improved Fermions

We simulate two dynamical, mass degenerate light quarks on 16^3x32 lattices with a spatial extent of 2.4 fm using the Chirally Improved Dirac operator. The simulation method, the implementation of the action and signals of equilibration are discussed in detail. Based on the eigenvalues of the Dirac operator we discuss some qualitative features of our approach. Results for ground state masses of pseudoscalar and vector mesons as well as for the nucleon and delta baryons are presented.Comment: 26 pages, 17 figures, 10 table

Coloring translates and homothets of a convex body

We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of finite families of translates and homothets of a convex body in \RR^n.Comment: 11 pages, 2 figure

Topology and confinement

These lectures contain an introduction to instantons, calorons and dyons of the Yang--Mills gauge theory. Since we are interested in the mechanism of confinement and of the deconfinement phase transition at some critical temperature, the Yang--Mills theory is formulated and studied at nonzero temperatures. We introduce ``calorons with a nontrivial holonomy'' that are generalizations of instantons and can be viewed as ``made of'' constituent dyons. The quantum weight with which these calorons contribute to the Yang--Mills partition function is considered, and the ensuing statistical mechanics of the ensemble of interacting dyons is discussed. We argue that a simple semiclassical picture based on dyons satisfies all known criteria of confinement and explains the confinement-deconfinement phase transition. This refers not only to the SU(N) gauge groups where dyons lead to the expected behaviour of the observables with N, but also to the exceptional G(2) group whose group center, unlike SU(N), is trivial. Despite being centerless, the G(2) gauge group possesses confinement at low temperatures, and a 1st order deconfinement transition, according to several latest lattice simulations, indicating that confinement-deconfinement is not related to the group center. Dyons, however, reproduce this behaviour.Comment: Lectures at the ITEP Winter School (February 2009, Moscow) and Schladming Winter School (March 2009, Schladming, Austria), 42 pages, 16 figure

The local atomic quasicrystal structure of the icosahedral Mg25Y11Zn64 alloy

A local and medium range atomic structure model for the face centred icosahedral (fci) Mg25Y11Zn64 alloy has been established in a sphere of r = 27 A. The model was refined by least squares techniques using the atomic pair distribution (PDF) function obtained from synchrotron powder diffraction. Three hierarchies of the atomic arrangement can be found: (i) five types of local coordination polyhedra for the single atoms, four of which are of Frank-Kasper type. In turn, they (ii) form a three-shell (Bergman) cluster containing 104 atoms, which is condensed sharing its outer shell with its neighbouring clusters and (iii) a cluster connecting scheme corresponding to a three-dimensional tiling leaving space for few glue atoms. Inside adjacent clusters, Y8-cubes are tilted with respect to each other and thus allow for overall icosahedral symmetry. It is shown that the title compound is essentially isomorphic to its holmium analogue. Therefore fci-Mg-Y-Zn can be seen as the representative structure type for the other rare earth analogues fci-Mg-Zn-RE (RE = Dy, Er, Ho, Tb) reported in the literature.Comment: 12 pages, 8 figures, 2 table

Improving statistical inference on pathogen densities estimated by quantitative molecular methods: malaria gametocytaemia as a case study

BACKGROUND: Quantitative molecular methods (QMMs) such as quantitative real-time polymerase chain reaction (q-PCR), reverse-transcriptase PCR (qRT-PCR) and quantitative nucleic acid sequence-based amplification (QT-NASBA) are increasingly used to estimate pathogen density in a variety of clinical and epidemiological contexts. These methods are often classified as semi-quantitative, yet estimates of reliability or sensitivity are seldom reported. Here, a statistical framework is developed for assessing the reliability (uncertainty) of pathogen densities estimated using QMMs and the associated diagnostic sensitivity. The method is illustrated with quantification of Plasmodium falciparum gametocytaemia by QT-NASBA. RESULTS: The reliability of pathogen (e.g. gametocyte) densities, and the accompanying diagnostic sensitivity, estimated by two contrasting statistical calibration techniques, are compared; a traditional method and a mixed model Bayesian approach. The latter accounts for statistical dependence of QMM assays run under identical laboratory protocols and permits structural modelling of experimental measurements, allowing precision to vary with pathogen density. Traditional calibration cannot account for inter-assay variability arising from imperfect QMMs and generates estimates of pathogen density that have poor reliability, are variable among assays and inaccurately reflect diagnostic sensitivity. The Bayesian mixed model approach assimilates information from replica QMM assays, improving reliability and inter-assay homogeneity, providing an accurate appraisal of quantitative and diagnostic performance. CONCLUSIONS: Bayesian mixed model statistical calibration supersedes traditional techniques in the context of QMM-derived estimates of pathogen density, offering the potential to improve substantially the depth and quality of clinical and epidemiological inference for a wide variety of pathogens

The strong thirteen spheres problem

The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on a enumeration of the so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag

The sign problem across the QCD phase transition

The average phase factor of the QCD fermion determinant signals the strength of the QCD sign problem. We compute the average phase factor as a function of temperature and baryon chemical potential using a two-flavor NJL model. This allows us to study the strength of the sign problem at and above the chiral transition. It is discussed how the $U_A(1)$ anomaly affects the sign problem. Finally, we study the interplay between the sign problem and the endpoint of the chiral transition.Comment: 9 pages and 9 fig

The Fermat-Torricelli problem in normed planes and spaces

We investigate the Fermat-Torricelli problem in d-dimensional real normed spaces or Minkowski spaces, mainly for d=2. Our approach is to study the Fermat-Torricelli locus in a geometric way. We present many new results, as well as give an exposition of known results that are scattered in various sources, with proofs for some of them. Together, these results can be considered to be a minitheory of the Fermat-Torricelli problem in Minkowski spaces and especially in Minkowski planes. This demonstrates that substantial results about locational problems valid for all norms can be found using a geometric approach

Human cytomegalovirus immediate-early 1 protein rewires upstream STAT3 to downstream STAT1 signaling switching an IL6-type to an IFNγ-like response

MN and CP were supported by the Wellcome Trust (www.wellcome.ac.uk) Institutional Strategic Support Fund and CP was supported by the Deutsche Forschungsgemeinschaft (PA 815/2-1; www.dfg.de).The human cytomegalovirus (hCMV) major immediate-early 1 protein (IE1) is best known for activating transcription to facilitate viral replication. Here we present transcriptome data indicating that IE1 is as significant a repressor as it is an activator of host gene expression. Human cells induced to express IE1 exhibit global repression of IL6- and oncostatin M-responsive STAT3 target genes. This repression is followed by STAT1 phosphorylation and activation of STAT1 target genes normally induced by IFNγ. The observed repression and subsequent activation are both mediated through the same region (amino acids 410 to 445) in the C-terminal domain of IE1, and this region serves as a binding site for STAT3. Depletion of STAT3 phenocopies the STAT1-dependent IFNγ-like response to IE1. In contrast, depletion of the IL6 receptor (IL6ST) or the STAT kinase JAK1 prevents this response. Accordingly, treatment with IL6 leads to prolonged STAT1 instead of STAT3 activation in wild-type IE1 expressing cells, but not in cells expressing a mutant protein (IE1dl410-420) deficient for STAT3 binding. A very similar STAT1-directed response to IL6 is also present in cells infected with a wild-type or revertant hCMV, but not an IE1dl410-420 mutant virus, and this response results in restricted viral replication. We conclude that IE1 is sufficient and necessary to rewire upstream IL6-type to downstream IFNγ-like signaling, two pathways linked to opposing actions, resulting in repressed STAT3- and activated STAT1-responsive genes. These findings relate transcriptional repressor and activator functions of IE1 and suggest unexpected outcomes relevant to viral pathogenesis in response to cytokines or growth factors that signal through the IL6ST-JAK1-STAT3 axis in hCMV-infected cells. Our results also reveal that IE1, a protein considered to be a key activator of the hCMV productive cycle, has an unanticipated role in tempering viral replication.Publisher PDFPeer reviewe