39 research outputs found
The Maslov Gerbe
Let Lag(E) be the grassmannian of lagrangian subspaces of a complex
symplectic vector space E. We construct a Maslov class which generates the
second integral cohomology of Lag(E), and we show that its mod 2 reduction is
the characteristic class of a flat gerbe with structure group Z_2. We explain
the relation of this gerbe to the well-known flat Maslov line bundle with
structure group Z_4 over the real lagrangian grassmannian, whose characteristic
class is the mod 4 reduction of the real Maslov class.Comment: 8 page
Weak KAM for commuting Hamiltonians
For two commuting Tonelli Hamiltonians, we recover the commutation of the
Lax-Oleinik semi-groups, a result of Barles and Tourin ([BT01]), using a direct
geometrical method (Stoke's theorem). We also obtain a "generalization" of a
theorem of Maderna ([Mad02]). More precisely, we prove that if the phase space
is the cotangent of a compact manifold then the weak KAM solutions (or
viscosity solutions of the critical stationary Hamilton-Jacobi equation) for G
and for H are the same. As a corrolary we obtain the equality of the Aubry
sets, of the Peierls barrier and of flat parts of Mather's functions.
This is also related to works of Sorrentino ([Sor09]) and Bernard ([Ber07b]).Comment: 23 pages, accepted for publication in NonLinearity (january 29th
2010). Minor corrections, fifth part added on Mather's function (or
effective Hamiltonian
On the flow map for 2D Euler equations with unbounded vorticity
In Part I, we construct a class of examples of initial velocities for which
the unique solution to the Euler equations in the plane has an associated flow
map that lies in no Holder space of positive exponent for any positive time. In
Part II, we explore inverse problems that arise in attempting to construct an
example of an initial velocity producing an arbitrarily poor modulus of
continuity of the flow map.Comment: http://iopscience.iop.org/0951-7715/24/9/013/ for published versio
Critical Decay at Higher-Order Glass-Transition Singularities
Within the mode-coupling theory for the evolution of structural relaxation in
glass-forming systems, it is shown that the correlation functions for density
fluctuations for states at A_3- and A_4-glass-transition singularities can be
presented as an asymptotic series in increasing inverse powers of the logarithm
of the time t: , where
with p_n denoting some polynomial and x=ln (t/t_0). The results are
demonstrated for schematic models describing the system by solely one or two
correlators and also for a colloid model with a square-well-interaction
potential.Comment: 26 pages, 7 figures, Proceedings of "Structural Arrest Transitions in
Colloidal Systems with Short-Range Attractions", Messina, Italy, December
2003 (submitted
A Nonperturbative Eliasson's Reducibility Theorem
This paper is concerned with discrete, one-dimensional Schr\"odinger
operators with real analytic potentials and one Diophantine frequency. Using
localization and duality we show that almost every point in the spectrum admits
a quasi-periodic Bloch wave if the potential is smaller than a certain constant
which does not depend on the precise Diophantine conditions. The associated
first-order system, a quasi-periodic skew-product, is shown to be reducible for
almost all values of the energy. This is a partial nonperturbative
generalization of a reducibility theorem by Eliasson. We also extend
nonperturbatively the genericity of Cantor spectrum for these Schr\"odinger
operators. Finally we prove that in our setting, Cantor spectrum implies the
existence of a -set of energies whose Schr\"odinger cocycle is not
reducible to constant coefficients
Current preventive strategies and management of Epstein-Barr virus-related post-transplant lymphoproliferative disease in solid organ transplantation in Europe. Results of the ESGICH Questionnaire-based Cross-sectional Survey
There is limited clinical evidence on the utility of the monitoring of Epstein-Barr virus (EBV) DNAemia in the pre-emptive management of post-transplant lymphoproliferative disease (PTLD) in solid organ transplant (SOT) recipients. We investigated current preventive measures against EBV-related PTLD through a web-based questionnaire sent to 669 SOT programmes in 35 European countries. This study was performed on behalf of the ESGICH study group from the European Society of Clinical Microbiology and Infectious Diseases. A total of 71 SOT programmes from 15 European countries participated in the study. EBV serostatus of the recipient is routinely obtained in 69/71 centres (97%) and 64 (90%) have access to EBV DNAemia assays. EBV monitoring is routinely used in 85.9% of the programmes and 77.4% reported performing pre-emptive treatment for patients with significant EBV DNAemia levels. Pre-emptive treatment for EBV DNAemia included reduction of immunosuppression in 50.9%, switch to mammalian target of rapamycin inhibitors in 30.9%, and use of rituximab in 14.5% of programmes. Imaging by whole-body 18-fluoro-deoxyglucose positron emission tomography (FDG-PET) is used in 60.9% of centres to rule out PTLD and complemented computer tomography is used in 50%. In 10.9% of centres, FDG-PET is included in the first-line diagnostic workup in patients with high-risk EBV DNAemia. Despite the lack of definitive evidence, EBV load measurements are frequently used in Europe to guide diagnostic workup and pre-emptive reduction of immunosuppression. We need prospective and controlled studies to define the impact of EBV monitoring in reducing the risk of PTLD in SOT recipients
Recovery of dialysis patients with COVID-19 : health outcomes 3 months after diagnosis in ERACODA
Background. Coronavirus disease 2019 (COVID-19)-related short-term mortality is high in dialysis patients, but longer-term outcomes are largely unknown. We therefore assessed patient recovery in a large cohort of dialysis patients 3 months after their COVID-19 diagnosis. Methods. We analyzed data on dialysis patients diagnosed with COVID-19 from 1 February 2020 to 31 March 2021 from the European Renal Association COVID-19 Database (ERACODA). The outcomes studied were patient survival, residence and functional and mental health status (estimated by their treating physician) 3 months after COVID-19 diagnosis. Complete follow-up data were available for 854 surviving patients. Patient characteristics associated with recovery were analyzed using logistic regression. Results. In 2449 hemodialysis patients (mean ± SD age 67.5 ± 14.4 years, 62% male), survival probabilities at 3 months after COVID-19 diagnosis were 90% for nonhospitalized patients (n = 1087), 73% for patients admitted to the hospital but not to an intensive care unit (ICU) (n = 1165) and 40% for those admitted to an ICU (n = 197). Patient survival hardly decreased between 28 days and 3 months after COVID-19 diagnosis. At 3 months, 87% functioned at their pre-existent functional and 94% at their pre-existent mental level. Only few of the surviving patients were still admitted to the hospital (0.8-6.3%) or a nursing home (∼5%). A higher age and frailty score at presentation and ICU admission were associated with worse functional outcome. Conclusions. Mortality between 28 days and 3 months after COVID-19 diagnosis was low and the majority of patients who survived COVID-19 recovered to their pre-existent functional and mental health level at 3 months after diagnosis