Upon the existence of short-time approximations of any polynomial order for the computation of density matrices by path integral methods

In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and bounded from below potentials. While for Theorem 2, which is ``experimental'', I only provide a ``physicist's'' proof, I believe the present development is mathematically sound. As a verification, I explicitly construct two short-time approximations to the density matrix having convergence orders 3 and 4, respectively. Furthermore, in the Appendix, I derive the convergence constant for the trapezoidal Trotter path integral technique. The convergence orders and constants are then verified by numerical simulations. While the two short-time approximations constructed are of sure interest to physicists and chemists involved in Monte Carlo path integral simulations, the present article is also aimed at the mathematical community, who might find the results interesting and worth exploring. I conclude the paper by discussing the implications of the present findings with respect to the solvability of the dynamical sign problem appearing in real-time Feynman path integral simulations.Comment: 19 pages, 4 figures; the discrete short-time approximations are now treated as independent from their continuous version; new examples of discrete short-time approximations of order three and four are given; a new appendix containing a short review on Brownian motion has been added; also, some additional explanations are provided here and there; this is the last version; to appear in Phys. Rev.

The role of winding numbers in quantum Monte Carlo simulations

We discuss the effects of fixing the winding number in quantum Monte Carlo simulations. We present a simple geometrical argument as well as strong numerical evidence that one can obtain exact ground state results for periodic boundary conditions without changing the winding number. However, for very small systems the temperature has to be considerably lower than in simulations with fluctuating winding numbers. The relative deviation of a calculated observable from the exact ground state result typically scales as $T^{\gamma}$, where the exponent $\gamma$ is model and observable dependent and the prefactor decreases with increasing system size. Analytic results for a quantum rotor model further support our claim.Comment: 5 pages, 5 figure

Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model

A quantum Monte Carlo algorithm is constructed starting from the standard perturbation expansion in the interaction representation. The resulting configuration space is strongly related to that of the Stochastic Series Expansion (SSE) method, which is based on a direct power series expansion of exp(-beta*H). Sampling procedures previously developed for the SSE method can therefore be used also in the interaction representation formulation. The new method is first tested on the S=1/2 Heisenberg chain. Then, as an application to a model of great current interest, a Heisenberg chain including phonon degrees of freedom is studied. Einstein phonons are coupled to the spins via a linear modulation of the nearest-neighbor exchange. The simulation algorithm is implemented in the phonon occupation number basis, without Hilbert space truncations, and is exact. Results are presented for the magnetic properties of the system in a wide temperature regime, including the T-->0 limit where the chain undergoes a spin-Peierls transition. Some aspects of the phonon dynamics are also discussed. The results suggest that the effects of dynamic phonons in spin-Peierls compounds such as GeCuO3 and NaV2O5 must be included in order to obtain a correct quantitative description of their magnetic properties, both above and below the dimerization temperature.Comment: 23 pages, Revtex, 11 PostScript figure

Inhibition of activin/nodal signalling is necessary for pancreatic differentiation of human pluripotent stem cells

Peer reviewedPublisher PD

Pneumococcal carriage in sub-Saharan Africa--a systematic review.

BACKGROUND: Pneumococcal epidemiology varies geographically and few data are available from the African continent. We assess pneumococcal carriage from studies conducted in sub-Saharan Africa (sSA) before and after the pneumococcal conjugate vaccine (PCV) era. METHODS: A search for pneumococcal carriage studies published before 2012 was conducted to describe carriage in sSA. The review also describes pneumococcal serotypes and assesses the impact of vaccination on carriage in this region. RESULTS: Fifty-seven studies were included in this review with the majority (40.3%) from South Africa. There was considerable variability in the prevalence of carriage between studies (I-squared statistic = 99%). Carriage was higher in children and decreased with increasing age, 63.2% (95% CI: 55.6-70.8) in children less than 5 years, 42.6% (95% CI: 29.9-55.4) in children 5-15 years and 28.0% (95% CI: 19.0-37.0) in adults older than 15 years. There was no difference in the prevalence of carriage between males and females in 9/11 studies. Serotypes 19F, 6B, 6A, 14 and 23F were the five most common isolates. A meta-analysis of four randomized trials of PCV vaccination in children aged 9-24 months showed that carriage of vaccine type (VT) serotypes decreased with PCV vaccination; however, overall carriage remained the same because of a concomitant increase in non-vaccine type (NVT) serotypes. CONCLUSION: Pneumococcal carriage is generally high in the African continent, particularly in young children. The five most common serotypes in sSA are among the top seven serotypes that cause invasive pneumococcal disease in children globally. These serotypes are covered by the two PCVs recommended for routine childhood immunization by the WHO. The distribution of serotypes found in the nasopharynx is altered by PCV vaccination

The Index-Based Subgraph Matching Algorithm (ISMA): Fast Subgraph Enumeration in Large Networks Using Optimized Search Trees

Subgraph matching algorithms are designed to find all instances of predefined subgraphs in a large graph or network and play an important role in the discovery and analysis of so-called network motifs, subgraph patterns which occur more often than expected by chance. We present the index-based subgraph matching algorithm (ISMA), a novel tree-based algorithm. ISMA realizes a speedup compared to existing algorithms by carefully selecting the order in which the nodes of a query subgraph are investigated. In order to achieve this, we developed a number of data structures and maximally exploited symmetry characteristics of the subgraph. We compared ISMA to a naive recursive tree-based algorithm and to a number of well-known subgraph matching algorithms. Our algorithm outperforms the other algorithms, especially on large networks and with large query subgraphs. An implementation of ISMA in Java is freely available at http://sourceforge.net/projects/isma

Reprogramming of Escherichia coli K-12 Metabolism during the Initial Phase of Transition from an Anaerobic to a Micro-Aerobic Environment

Background: Many bacteria undergo transitions between environments with differing O2 availabilities as part of their natural lifestyles and during biotechnological processes. However, the dynamics of adaptation when bacteria experience changes in O2 availability are understudied. The model bacterium and facultative anaerobe Escherichia coli K-12 provides an ideal system for exploring this process. Methods and Findings: Time-resolved transcript profiles of E. coli K-12 during the initial phase of transition from anaerobic to micro-aerobic conditions revealed a reprogramming of gene expression consistent with a switch from fermentative to respiratory metabolism. The changes in transcript abundance were matched by changes in the abundances of selected central metabolic proteins. A probabilistic state space model was used to infer the activities of two key regulators, FNR (O2 sensing) and PdhR (pyruvate sensing). The model implied that both regulators were rapidly inactivated during the transition from an anaerobic to a micro-aerobic environment. Analysis of the external metabolome and protein levels suggested that the cultures transit through different physiological states during the process of adaptation, characterized by the rapid inactivation of pyruvate formate-lyase (PFL), a slower induction of pyruvate dehydrogenase complex (PDHC) activity and transient excretion of pyruvate, consistent with the predicted inactivation of PdhR and FNR. Conclusion: Perturbation of anaerobic steady-state cultures by introduction of a limited supply of O2 combined with time-resolved transcript, protein and metabolite profiling, and probabilistic modeling has revealed that pyruvate (sensed by PdhR) is a key metabolic signal in coordinating the reprogramming of E. coli K-12 gene expression by working alongside the O2 sensor FNR during transition from anaerobic to micro-aerobic conditions

Utilisation of an operative difficulty grading scale for laparoscopic cholecystectomy

Background A reliable system for grading operative difficulty of laparoscopic cholecystectomy would standardise description of findings and reporting of outcomes. The aim of this study was to validate a difficulty grading system (Nassar scale), testing its applicability and consistency in two large prospective datasets. Methods Patient and disease-related variables and 30-day outcomes were identified in two prospective cholecystectomy databases: the multi-centre prospective cohort of 8820 patients from the recent CholeS Study and the single-surgeon series containing 4089 patients. Operative data and patient outcomes were correlated with Nassar operative difficultly scale, using Kendall’s tau for dichotomous variables, or Jonckheere–Terpstra tests for continuous variables. A ROC curve analysis was performed, to quantify the predictive accuracy of the scale for each outcome, with continuous outcomes dichotomised, prior to analysis. Results A higher operative difficulty grade was consistently associated with worse outcomes for the patients in both the reference and CholeS cohorts. The median length of stay increased from 0 to 4 days, and the 30-day complication rate from 7.6 to 24.4% as the difficulty grade increased from 1 to 4/5 (both p < 0.001). In the CholeS cohort, a higher difficulty grade was found to be most strongly associated with conversion to open and 30-day mortality (AUROC = 0.903, 0.822, respectively). On multivariable analysis, the Nassar operative difficultly scale was found to be a significant independent predictor of operative duration, conversion to open surgery, 30-day complications and 30-day reintervention (all p < 0.001). Conclusion We have shown that an operative difficulty scale can standardise the description of operative findings by multiple grades of surgeons to facilitate audit, training assessment and research. It provides a tool for reporting operative findings, disease severity and technical difficulty and can be utilised in future research to reliably compare outcomes according to case mix and intra-operative difficulty

Variability and Diversity of Nasopharyngeal Microbiota in Children: A Metagenomic Analysis

The nasopharynx is the ecological niche for many commensal bacteria and for potential respiratory or invasive pathogens like Streptococcus pneumoniae, Haemophilus influenzae, and Neisseria meningitidis. Disturbance of a balanced nasopharyngeal (NP) microbiome might be involved in the onset of symptomatic infections with these pathogens, which occurs primarily in fall and winter. It is unknown whether seasonal infection patterns are associated with concomitant changes in NP microbiota. As young children are generally prone to respiratory and invasive infections, we characterized the NP microbiota of 96 healthy children by barcoded pyrosequencing of the V5–V6 hypervariable region of the 16S-rRNA gene, and compared microbiota composition between children sampled in winter/fall with children sampled in spring. The approximately 1000000 sequences generated represented 13 taxonomic phyla and approximately 250 species-level phyla types (OTUs). The 5 most predominant phyla were Proteobacteria (64%), Firmicutes (21%), Bacteroidetes (11%), Actinobacteria (3%) and Fusobacteria (1,4%) with Moraxella, Haemophilus, Streptococcus, Flavobacteria, Dolosigranulum, Corynebacterium and Neisseria as predominant genera. The inter-individual variability was that high that on OTU level a core microbiome could not be defined. Microbiota profiles varied strongly with season, with in fall/winter a predominance of Proteobacteria (relative abundance (% of all sequences): 75% versus 51% in spring) and Fusobacteria (absolute abundance (% of children): 14% versus 2% in spring), and in spring a predominance of Bacteroidetes (relative abundance: 19% versus 3% in fall/winter, absolute abundance: 91% versus 54% in fall/winter), and Firmicutes. The latter increase is mainly due to (Brevi)bacillus and Lactobacillus species (absolute abundance: 96% versus 10% in fall/winter) which are like Bacteroidetes species generally related to healthy ecosystems. The observed seasonal effects could not be attributed to recent antibiotics or viral co-infection

Calculation of the relative metastabilities of proteins in subcellular compartments of Saccharomyces cerevisiae

[abridged] Background: The distribution of chemical species in an open system at metastable equilibrium can be expressed as a function of environmental variables which can include temperature, oxidation-reduction potential and others. Calculations of metastable equilibrium for various model systems were used to characterize chemical transformations among proteins and groups of proteins found in different compartments of yeast cells. Results: With increasing oxygen fugacity, the relative metastability fields of model proteins for major subcellular compartments go as mitochondrion, endoplasmic reticulum, cytoplasm, nucleus. In a metastable equilibrium setting at relatively high oxygen fugacity, proteins making up actin are predominant, but those constituting the microtubule occur with a low chemical activity. A reaction sequence involving the microtubule and spindle pole proteins was predicted by combining the known intercompartmental interactions with a hypothetical program of oxygen fugacity changes in the local environment. In further calculations, the most-abundant proteins within compartments generally occur in relative abundances that only weakly correspond to a metastable equilibrium distribution. However, physiological populations of proteins that form complexes often show an overall positive or negative correlation with the relative abundances of proteins in metastable assemblages. Conclusions: This study explored the outlines of a thermodynamic description of chemical transformations among interacting proteins in yeast cells. The results suggest that these methods can be used to measure the degree of departure of a natural biochemical process or population from a local minimum in Gibbs energy.Comment: 32 pages, 7 figures; supporting information is available at http://www.chnosz.net/yeas