Ramanujan and Extensions and Contractions of Continued Fractions

If a continued fraction $K_{n=1}^{\infty} a_{n}/b_{n}$ is known to converge but its limit is not easy to determine, it may be easier to use an extension of $K_{n=1}^{\infty}a_{n}/b_{n}$ to find the limit. By an extension of $K_{n=1}^{\infty} a_{n}/b_{n}$ we mean a continued fraction $K_{n=1}^{\infty} c_{n}/d_{n}$ whose odd or even part is $K_{n=1}^{\infty} a_{n}/b_{n}$. One can then possibly find the limit in one of three ways: (i) Prove the extension converges and find its limit; (ii) Prove the extension converges and find the limit of the other contraction (for example, the odd part, if $K_{n=1}^{\infty}a_{n}/b_{n}$ is the even part); (ii) Find the limit of the other contraction and show that the odd and even parts of the extension tend to the same limit. We apply these ideas to derive new proofs of certain continued fraction identities of Ramanujan and to prove a generalization of an identity involving the Rogers-Ramanujan continued fraction, which was conjectured by Blecksmith and Brillhart.Comment: 16 page

Measuring Strategic Uncertainty in Coordination Games

Lecture on the first SFB/TR 15 meeting, Gummersbach, July, 18 - 20, 2004This paper explores predictability of behavior in coordination games with multiple equilibria. In a laboratory experiment we measure subjects' certainty equivalents for three coordination games and one lottery. Attitudes towards strategic uncertainty in coordination games are related to risk aversion, experience seeking, gender and age. From the distribution of certainty equivalents among participating students we estimate probabilities for successful coordination in a wide range of coordination games. For many games success of coordination is predictable with a reasonable error rate. The best response of a risk neutral player is close to the global-game solution. Comparing choices in coordination games with revealed risk aversion, we estimate subjective probabilities for successful coordination. In games with a low coordination requirement, most subjects underestimate the probability of success. In games with a high coordination requirement, most subjects overestimate this probability. Data indicate that subjects have probabilistic beliefs about success or failure of coordination rather than beliefs about individual behavior of other players

Carcinoid Tumour of the Appendix: An Analysis of 1,485 Consecutive Emergency Appendectomies

Aim: The aim of this study is to conduct a retrospective analysis of the incidence and long-term results of carcinoid tumours of the appendix in emergency appendectomies. Methods: A retrospective review of 1,485 appendectomies was performed in two centres from January 2000 until January 2006. Demographic data, clinical presentation, histopathology, operative reports and survival were scored and compared with the literature. Results: In three women and four men, carcinoid tumours were identified (0.47%). The mean age was 32.7 years (range, 20-59 years). The clinical presentation was resembling the symptoms of acute appendicitis in all cases. Laparoscopic appendectomy was the treatment of choice in five patients; in one of these patients, a conversion to laparotomy was necessary. The other two patients underwent primary open appendectomy. Five patients underwent additional surgery after the pathology report became available. Four patients underwent ileocecal resection; one other patient underwent right hemicolectomy. In none of the re-operation specimens was residual carcinoid tumour detected. After a mean follow-up of 65 months (range, 25-92), all patients were alive and disease- and symptom-free. Conclusion: Carcinoid tumours of the appendix most often present as acute appendicitis. It also emphasises the value of histopathological analysis of every removed appendix. The long-term prognosis of incidentally found carcinoids of the appendix is good

Clinical and operational value of the extensively drug-resistant tuberculosis definition.

Currently, no information is available on the effect of resistance/susceptibility to first-line drugs different from isoniazid and rifampicin in determining the outcome of extensively drug-resistant tuberculosis (XDR-TB) patients, and whether being XDR-TB is a more accurate indicator of poor clinical outcome than being resistant to all first-line anti-tuberculosis (TB) drugs. To investigate this issue, a large series of multidrug-resistant TB (MDR-TB) and XDR-TB cases diagnosed in Estonia, Germany, Italy and the Russian Federation during the period 1999-2006 were analysed. Drug-susceptibility testing for first- and second-line anti-TB drugs, quality assurance and treatment delivery was performed according to World Health Organization recommendations in all study sites. Out of 4,583 culture-positive TB cases analysed, 361 (7.9%) were MDR and 64 (1.4%) were XDR. XDR-TB cases had a relative risk (RR) of 1.58 to have an unfavourable outcome compared with MDR-TB cases resistant to all first-line drugs (isoniazid, rifampicin ethambutol, streptomycin and, when tested, pyrazinamide), and an RR of 2.61 compared with "other" MDR-TB cases (those susceptible to at least one first-line anti-TB drug among ethambutol, pyrazinamide and streptomycin, regardless of resistance to the second-line drugs not defining XDR-TB). The emergence of extensively drug-resistant tuberculosis confirms that problems in tuberculosis management are still present in Europe. While waiting for new tools which will facilitate management of extensively drug-resistant tuberculosis, accessibility to quality diagnostic and treatment services should be urgently ensured and adequate public health policies should be rapidly implemented to prevent further development of drug resistance

Observation of discrete time-crystalline order in a disordered dipolar many-body system

Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. It is well known that out-of-equilibrium systems can display a rich array of phenomena, ranging from self-organized synchronization to dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter. As a particularly striking example, the interplay of periodic driving, disorder, and strong interactions has recently been predicted to result in exotic "time-crystalline" phases, which spontaneously break the discrete time-translation symmetry of the underlying drive. Here, we report the experimental observation of such discrete time-crystalline order in a driven, disordered ensemble of $\sim 10^6$ dipolar spin impurities in diamond at room-temperature. We observe long-lived temporal correlations at integer multiples of the fundamental driving period, experimentally identify the phase boundary and find that the temporal order is protected by strong interactions; this order is remarkably stable against perturbations, even in the presence of slow thermalization. Our work opens the door to exploring dynamical phases of matter and controlling interacting, disordered many-body systems.Comment: 6 + 3 pages, 4 figure

Single-inhaler triple therapy fluticasone furoate/umeclidinium/vilanterol versus fluticasone furoate/vilanterol and umeclidinium/vilanterol in patients with COPD: results on cardiovascular safety from the IMPACT trial

BACKGROUND: This analysis of the IMPACT study assessed the cardiovascular (CV) safety of single-inhaler triple therapy with fluticasone furoate/umeclidinium/vilanterol (FF/UMEC/VI) versus FF/VI and UMEC/VI dual therapy. METHODS: IMPACT was a 52-week, randomized, double-blind, multicenter Phase III study comparing the efficacy and safety of FF/UMEC/VI 100/62.5/25 mcg with FF/VI 100/25 mcg or UMEC/VI 62.5/25 mcg in patients ≥40 years of age with symptomatic chronic obstructive pulmonary disease (COPD) and ≥1 moderate/severe exacerbation in the previous year. The inclusion criteria for the study were intentionally designed to permit the enrollment of patients with significant concurrent CV disease/risk. CV safety assessments included proportion of patients with and exposure-adjusted rates of on-treatment CV adverse events of special interest (CVAESI) and major adverse cardiac events (MACE), as well as time-to-first (TTF) CVAESI, and TTF CVAESI resulting in hospitalization/prolonged hospitalization or death. RESULTS: Baseline CV risk factors were similar across treatment groups. Overall, 68% of patients (n = 7012) had ≥1 CV risk factor and 40% (n = 4127) had ≥2. At baseline, 29% of patients reported a current/past cardiac disorder and 58% reported a current/past vascular disorder. The proportion of patients with on-treatment CVAESI was 11% for both FF/UMEC/VI and UMEC/VI, and 10% for FF/VI. There was no statistical difference for FF/UMEC/VI versus FF/VI or UMEC/VI in TTF CVAESI (hazard ratio [HR]: 0.98, 95% confidence interval [CI]: 0.85, 1.11; p = 0.711 and HR: 0.92, 95% CI: 0.78, 1.08; p = 0.317, respectively) nor TTF CVAESI leading to hospitalization/prolonged hospitalization or death (HR: 1.19, 95% CI: 0.93, 1.51; p = 0.167 and HR: 0.96, 95% CI: 0.72, 1.27; p = 0.760, respectively). On-treatment MACE occurred in ≤3% of patients across treatment groups, with similar prevalence and rates between treatments. CONCLUSIONS: In a symptomatic COPD population with a history of exacerbations and a high rate of CV disease/risk, the proportion of patients with CVAESI and MACE was 10-11% and 1-3%, respectively, across treatment arms, and the risk of CVAESI was low and similar across treatment arms. There was no statistically significant increased CV risk associated with the use of FF/UMEC/VI versus FF/VI or UMEC/VI, and UMEC/VI versus FF/VI. TRIAL REGISTRATION: NCT02164513 (GSK study number CTT116855)

Synovitis in osteoarthritis: current understanding with therapeutic implications

Modern concepts of osteoarthritis (OA) have been forever changed by modern imaging phenotypes demonstrating complex and multi-tissue pathologies involving cartilage, subchondral bone and (increasingly recognized) inflammation of the synovium. The synovium may show significant changes, even before visible cartilage degeneration has occurred, with infiltration of mononuclear cells, thickening of the synovial lining layer and production of inflammatory cytokines. The combination of sensitive imaging modalities and tissue examination has confirmed a high prevalence of synovial inflammation in all stages of OA, with a number of studies demonstrating that synovitis is related to pain, poor function and may even be an independent driver of radiographic OA onset and structural progression. Treating key aspects of synovial inflammation therefore holds great promise for analgesia and also for structure modification. This article will review current knowledge on the prevalence of synovitis in OA and its role in symptoms and structural progression, and explore lessons learnt from targeting synovitis therapeutically

Theoretical and Phenomenological Constraints on Form Factors for Radiative and Semi-Leptonic B-Meson Decays

We study transition form factors for radiative and rare semi-leptonic B-meson decays into light pseudoscalar or vector mesons, combining theoretical constraints and phenomenological information from Lattice QCD, light-cone sum rules, and dispersive bounds. We pay particular attention to form factor parameterisations which are based on the so-called series expansion, and study the related systematic uncertainties on a quantitative level. In this context, we also provide the NLO corrections to the correlation function between two flavour-changing tensor currents, which enters the unitarity constraints for the coefficients in the series expansion.Comment: 52 pages; v2: normalization error in (29ff.) corrected, conclusion about relevance of unitarity bounds modified; form factor fits unaffected; references added; v3: discussion on truncation of series expansion added, matches version to be published in JHEP; v4: corrected typos in Tables 5 and

Evolutionary relationships between Rhynchosporium lolii sp. nov. and other Rhynchosporium species on grass.

Copyright: 2013 King et al. 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 creditedThe fungal genus Rhynchosporium (causative agent of leaf blotch) contains several host-specialised species, including R. commune (colonising barley and brome-grass), R. agropyri (couch-grass), R. secalis (rye and triticale) and the more distantly related R. orthosporum (cocksfoot). This study used molecular fingerprinting, multilocus DNA sequence data, conidial morphology, host range tests and scanning electron microscopy to investigate the relationship between Rhynchosporium species on ryegrasses, both economically important forage grasses and common wild grasses in many cereal growing areas, and other plant species. Two different types of Rhynchosporium were found on ryegrasses in the UK. Firstly, there were isolates of R. commune that were pathogenic to both barley and Italian ryegrass. Secondly, there were isolates of a new species, here named R. lolii, that were pathogenic only to ryegrass species. R. lolii was most closely related to R. orthosporum, but exhibited clear molecular, morphological and host range differences. The species was estimated to have diverged from R. orthosporum ca. 5735 years before the present. The colonisation strategy of all of the different Rhynchosporium species involved extensive hyphal growth in the sub-cuticular regions of the leaves. Finally, new species-specific PCR diagnostic tests were developed that could distinguish between these five closely related Rhynchosporium species.Peer reviewedFinal Published versio