Symmetries of modules of differential operators

Let ${\cal F}\_\lambda(S^1)$ be the space of tensor densities of degree (or weight) $\lambda$ on the circle $S^1$. The space ${\cal D}^k\_{\lambda,\mu}(S^1)$ of $k$-th order linear differential operators from ${\cal F}\_\lambda(S^1)$ to ${\cal F}\_\mu(S^1)$ is a natural module over $\mathrm{Diff}(S^1)$, the diffeomorphism group of $S^1$. We determine the algebra of symmetries of the modules ${\cal D}^k\_{\lambda,\mu}(S^1)$, i.e., the linear maps on ${\cal D}^k\_{\lambda,\mu}(S^1)$ commuting with the $\mathrm{Diff}(S^1)$-action. We also solve the same problem in the case of straight line $\mathbb{R}$ (instead of $S^1$) and compare the results in the compact and non-compact cases.Comment: 29 pages, LaTeX, 4 figure

Large Chiral Diffeomorphisms on Riemann Surfaces and W-algebras

The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a complex scalar field over a Riemann surface is presented in the paper under the name of large diffeomorphisms. After an heuristic approach, we show how a linear truncation in the Taylor expansion can generate an algebra of symmetry characterized by some structure functions. Such a linear truncation is explicitly realized by introducing the notion of Forsyth frame over the Riemann surface with the help of a conformally covariant algebraic differential equation. The large chiral diffeomorphism action is then implemented through a B.R.S. formulation (for a given order of truncation) leading to a more algebraic set up. In this context the ghost fields behave as holomorphically covariant jets. Subsequently, the link with the so called W-algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones. We give a general solution with the help of the structure functions pertaining to all the possible truncations lower or equal to the given order. This provides another contribution to the relationship between KdV flows and W-diffeomorphimsComment: LaTeX file, 31 pages, no figure. Version to appear in J. Math. Phys. Work partly supported by Region PACA and INF

Invariants of pseudogroup actions: Homological methods and Finiteness theorem

We study the equivalence problem of submanifolds with respect to a transitive pseudogroup action. The corresponding differential invariants are determined via formal theory and lead to the notions of k-variants and k-covariants, even in the case of non-integrable pseudogroup. Their calculation is based on the cohomological machinery: We introduce a complex for covariants, define their cohomology and prove the finiteness theorem. This implies the well-known Lie-Tresse theorem about differential invariants. We also generalize this theorem to the case of pseudogroup action on differential equations.Comment: v2: some remarks and references addee

Hamiltonian evolutions of twisted gons in \RP^n

In this paper we describe a well-chosen discrete moving frame and their associated invariants along projective polygons in \RP^n, and we use them to write explicit general expressions for invariant evolutions of projective $N$-gons. We then use a reduction process inspired by a discrete Drinfeld-Sokolov reduction to obtain a natural Hamiltonian structure on the space of projective invariants, and we establish a close relationship between the projective $N$-gon evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that {any} Hamiltonian evolution is induced on invariants by an evolution of $N$-gons - what we call a projective realization - and we give the direct connection. Finally, in the planar case we provide completely integrable evolutions (the Boussinesq lattice related to the lattice $W_3$-algebra), their projective realizations and their Hamiltonian pencil. We generalize both structures to $n$-dimensions and we prove that they are Poisson. We define explicitly the $n$-dimensional generalization of the planar evolution (the discretization of the $W_n$-algebra) and prove that it is completely integrable, providing also its projective realization

Freeze-out configuration properties in the 197Au + 197Au reaction at 23 AMeV

Data from the experiment on the 197Au + 197Au reaction at 23 AMeV are analyzed with an aim to find signatures of exotic nuclear configurations such as toroid-shaped objects. The experimental data are compared with predictions of the ETNA code dedicated to look for such configurations and with the QMD model. A novel criterion of selecting events possibly resulting from the formation of exotic freeze-out configurations, "the efficiency factor", is tested. Comparison between experimental data and model predictions may indicate for the formation of flat/toroidal nuclear systems

Further search for a neutral boson with a mass around 9 MeV/c2

Two dedicated experiments on internal pair conversion (IPC) of isoscalar M1 transitions were carried out in order to test a 9 MeV/c2 X-boson scenario. In the 7Li(p,e+e-)8Be reaction at 1.1 MeV proton energy to the predominantly T=0 level at 18.15 MeV, a significant deviation from IPC was observed at large pair correlation angles. In the 11B(d,n e+e-)12C reaction at 1.6 MeV, leading to the 12.71 MeV 1+ level with pure T=0 character, an anomaly was observed at 9 MeV/c2. The compatibility of the results with the scenario is discussed.Comment: 12 pages, 5 figures, 2 table

Safety, tolerability, and impact on allergic inflammation of autologous E.coli autovaccine in the treatment of house dust mite asthma - a prospective open clinical trial

Background: Asthma is increasing worldwide and results from a complex immunological interaction between genetic susceptibility and environmental factors. Autovaccination with E. coli induces a strong TH-1 immune response, thus offering an option for the treatment of allergic diseases. Methods: Prospective open trial on safety, tolerability, and impact on allergic inflammation of an autologous E.coli autovaccine in intermittent or mild persistent house dust mite asthma. Determination of exhaled nitric monoxide (eNO) before and after bronchial mite challenge initially and after nine months of autovaccination. Results: Median eNO increase after autovaccination was significantly smaller (from 27.3 to 33.8 ppb; p=0.334) compared to initial values (from 32.6 to 42.2 ppb; p=0.046) (p=0.034). In nine subjects and a total of 306 injections, we observed 101 episodes of local erythema (33.3%; median of maximal diameter 2.5 cm), 95 episodes of local swelling (31.1%; median of maximal diameter 3 cm), and 27 episodes of local pain (8.8%). Four subjects reported itching at the injection site with a total of 30 episodes (9.8%). We observed no serious adverse events. All organ functions (inclusive electrocardiogramm) and laboratory testing of the blood (clinical chemistry, hematology) and the urine (screening test, B-microglobuline) were within normal limits. Vital signs undulated within the physiological variability. Conclusion: The administration of autologous autovacine for the treatment of house dust mite asthma resulted in a reduction of the eNO increase upon bronchial mite challenge. In nine subjects and 306 injections, only a few mild local reactions and no systemic severe adverse events were observed. EudraCT Nr. 2005-005534-12 ClinicalTrials.gov ID NCT0067720

A cross-sectional study of the number and frequency of terms used to refer to knowledge translation in a body of health literature in 2006: a Tower of Babel?

<p/> <p>Background</p> <p>The study of implementing research findings into practice is rapidly growing and has acquired many competing names (<it>e.g</it>., dissemination, uptake, utilization, translation) and contributing disciplines. The use of multiple terms across disciplines pose barriers to communication and progress for applying research findings. We sought to establish an inventory of terms describing this field and how often authors use them in a collection of health literature published in 2006.</p> <p>Methods</p> <p>We refer to this field as knowledge translation (KT). Terms describing aspects of KT and their definitions were collected from literature, the internet, reports, textbooks, and contact with experts. We compiled a database of KT and other articles by reading 12 healthcare journals representing multiple disciplines. All articles published in these journals in 2006 were categorized as being KT or not. The KT articles (all KT) were further categorized, if possible, for whether they described KT projects or implementations (KT application articles), or presented the theoretical basis, models, tools, methods, or techniques of KT (KT theory articles). Accuracy was checked using duplicate reading. Custom designed software determined how often KT terms were used in the titles and abstracts of articles categorized as being KT.</p> <p>Results</p> <p>A total of 2,603 articles were assessed, and 581 were identified as KT articles. Of these, 201 described KT applications, and 153 included KT theory. Of the 100 KT terms collected, 46 were used by the authors in the titles or abstracts of articles categorized as being KT. For all 581 KT articles, eight terms or term variations used by authors were highly discriminating for separating KT and non-KT articles (p < 0.001): implementation, adoption, quality improvement, dissemination, complex intervention (with multiple endings), implementation (within three words of) research, and complex intervention. More KT terms were associated with KT application articles (n = 13) and KT theory articles (n = 18).</p> <p>Conclusions</p> <p>We collected 100 terms describing KT research. Authors used 46 of them in titles and abstracts of KT articles. Of these, approximately half discriminated between KT and non-KT articles. Thus, the need for consolidation and consistent use of fewer terms related to KT research is evident.</p