33 research outputs found
Relative Ruan and Gromov-Taubes Invariants of Symplectic 4-Manifolds
We define relative Ruan invariants that count embedded connected symplectic
submanifolds which contact a fixed stable symplectic hypersurface V in a
symplectic 4-manifold (X,w) at prescribed points with prescribed contact orders
(in addition to insertions on X\V) for stable V. We obtain invariants of the
deformation class of (X,V,w). Two large issues must be tackled to define such
invariants: (1) Curves lying in the hypersurface V and (2) genericity results
for almost complex structures constrained to make V pseudo-holomorphic (or
almost complex). Moreover, these invariants are refined to take into account
rim tori decompositions. In the latter part of the paper, we extend the
definition to disconnected submanifolds and construct relative Gromov-Taubes
invariants
Gauge transformations and symmetries of integrable systems
We analyze several integrable systems in zero-curvature form within the
framework of invariant gauge theory. In the Drienfeld-Sokolov gauge
we derive a two-parameter family of nonlinear evolution equations which as
special cases include the Kortweg-de Vries (KdV) and Harry Dym equations. We
find residual gauge transformations which lead to infinintesimal symmetries of
this family of equations. For KdV and Harry Dym equations we find an infinite
hierarchy of such symmetry transformations, and we investigate their relation
with local conservation laws, constants of the motion and the bi-Hamiltonian
structure of the equations. Applying successive gauge transformatinos of Miura
type we obtain a sequence of gauge equivalent integrable systems, among them
the modified KdV and Calogero KdV equations.Comment: 18pages, no figure Journal versio
Strong time operators associated with generalized Hamiltonians
Let the pair of operators, , satisfy the weak Weyl relation:
, where is self-adjoint and is closed
symmetric. Suppose that g is a realvalued Lebesgue measurable function on \RR
such that for some closed subset K \subset \RR with Lebesgue
measure zero. Then we can construct a closed symmetric operator such that
also obeys the weak Weyl relation.Comment: 10 page
Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice
`Umbral calculus' deals with representations of the canonical commutation
relations. We present a short exposition of it and discuss how this calculus
can be used to discretize continuum models and to construct representations of
Lie algebras on a lattice. Related ideas appeared in recent publications and we
show that the examples treated there are special cases of umbral calculus. This
observation then suggests various generalizations of these examples. A special
umbral representation of the canonical commutation relations given in terms of
the position and momentum operator on a lattice is investigated in detail.Comment: 19 pages, Late
Timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space
It is shown that timelike surfaces of constant mean curvature 1 in anti-de
Sitter 3-space can be constructed from a pair of Lorentz holomorphic and
Lorentz antiholomorphic null curves in PSL(2,R) via Bryant type representation
formulae. These formulae are used to investigate an explicit one-to-one
correspondence, the so-called Lawson correspondence, between timelike surfaces
of constant mean curvature 1 in anti-de Sitter 3-space and timelike minimal
surfaces in Minkowski 3-space. The hyperbolic Gauss map of timelike surfaces in
anti-de Sitter 3-space, which is a close analogue of the classical Gauss map is
considered. It is discussed that the hyperbolic Gauss map plays an important
role in the study of timelike surfaces of constant mean curvature 1 in anti-de
Sitter 3-space. In particular, the relationship between the Lorentz
holomorphicity of the hyperbolic Gauss map and timelike surfaces of constant
mean curvature 1 in anti-de Sitter 3-space is studied.Comment: 47 pages, 24 figures, references revised, Annals of Global Analysis
and Geometr
Berezin quantization of homogeneous bounded domains
We prove that a homogeneous bounded domain admits a Berezin quantization
Bezlotoxumab for Prevention of Recurrent Clostridium difficile Infection
BACKGROUND Clostridium difficile is the most common cause of infectious diarrhea in hospitalized patients. Recurrences are common after antibiotic therapy. Actoxumab and bezlotoxumab are human monoclonal antibodies against C. difficile toxins A and B, respectively. METHODS We conducted two double-blind, randomized, placebo-controlled, phase 3 trials, MODIFY I and MODIFY II, involving 2655 adults receiving oral standard-of-care antibiotics for primary or recurrent C. difficile infection. Participants received an infusion of bezlotoxumab (10 mg per kilogram of body weight), actoxumab plus bezlotoxumab (10 mg per kilogram each), or placebo; actoxumab alone (10 mg per kilogram) was given in MODIFY I but discontinued after a planned interim analysis. The primary end point was recurrent infection (new episode after initial clinical cure) within 12 weeks after infusion in the modified intention-to-treat population. RESULTS In both trials, the rate of recurrent C. difficile infection was significantly lower with bezlotoxumab alone than with placebo (MODIFY I: 17% [67 of 386] vs. 28% [109 of 395]; adjusted difference, −10.1 percentage points; 95% confidence interval [CI], −15.9 to −4.3; P<0.001; MODIFY II: 16% [62 of 395] vs. 26% [97 of 378]; adjusted difference, −9.9 percentage points; 95% CI, −15.5 to −4.3; P<0.001) and was significantly lower with actoxumab plus bezlotoxumab than with placebo (MODIFY I: 16% [61 of 383] vs. 28% [109 of 395]; adjusted difference, −11.6 percentage points; 95% CI, −17.4 to −5.9; P<0.001; MODIFY II: 15% [58 of 390] vs. 26% [97 of 378]; adjusted difference, −10.7 percentage points; 95% CI, −16.4 to −5.1; P<0.001). In prespecified subgroup analyses (combined data set), rates of recurrent infection were lower in both groups that received bezlotoxumab than in the placebo group in subpopulations at high risk for recurrent infection or for an adverse outcome. The rates of initial clinical cure were 80% with bezlotoxumab alone, 73% with actoxumab plus bezlotoxumab, and 80% with placebo; the rates of sustained cure (initial clinical cure without recurrent infection in 12 weeks) were 64%, 58%, and 54%, respectively. The rates of adverse events were similar among these groups; the most common events were diarrhea and nausea. CONCLUSIONS Among participants receiving antibiotic treatment for primary or recurrent C. difficile infection, bezlotoxumab was associated with a substantially lower rate of recurrent infection than placebo and had a safety profile similar to that of placebo. The addition of actoxumab did not improve efficacy. (Funded by Merck; MODIFY I and MODIFY II ClinicalTrials.gov numbers, NCT01241552 and NCT01513239.