716 research outputs found
Symmetries of modules of differential operators
Let be the space of tensor densities of degree (or
weight) on the circle . The space of -th order linear differential operators from
to is a natural module over
, the diffeomorphism group of . We determine the
algebra of symmetries of the modules , i.e.,
the linear maps on commuting with the
-action. We also solve the same problem in the case of
straight line (instead of ) 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
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
-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 -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 -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
-algebra), their projective realizations and their Hamiltonian pencil. We
generalize both structures to -dimensions and we prove that they are
Poisson. We define explicitly the -dimensional generalization of the planar
evolution (the discretization of the -algebra) and prove that it is
completely integrable, providing also its projective realization
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
Synaptic Remodeling Depends on Signaling between Serotonin Receptors and the Extracellular Matrix
Rewiring of synaptic circuitry pertinent to memory formation has been associated with morphological changes in dendritic spines and with extracellular matrix (ECM) remodeling. Here, we mechanistically link these processes by uncovering a signaling pathway involving the serotonin 5-HT7 receptor (5-HT7R), matrix metalloproteinase 9 (MMP-9), the hyaluronan receptor CD44, and the small GTPase Cdc42. We highlight a physical interaction between 5-HT7R and CD44 (identified as an MMP-9 substrate in neurons) and find that 5-HT7R stimulation increases local MMP-9 activity, triggering dendritic spine remodeling, synaptic pruning, and impairment of long-term potentiation (LTP). The underlying molecular machinery involves 5-HT7R-mediated activation of MMP-9, which leads to CD44 cleavage followed by Cdc42 activation. One important physiological consequence of this interaction includes an increase in neuronal outgrowth and elongation of dendritic spines, which might have a positive effect on complex neuronal processes (e.g., reversal learning and neuronal regeneration)
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
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
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
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