1,182 research outputs found
Nonlinear stability of the Taub-NUT soliton in 6+1 dimensions
Using mixed numerical and analytical methods we give evidence that the 6+1
dimensional Taub-NUT soliton is asymptotically nonlinearly stable against small
perturbations preserving biaxial Bianchi IX symmetry. We also show that for
sufficiently strong perturbations the soliton collapses to a warped black hole.
Since this black hole solution is not known in closed form, for completeness of
the exposition we prove its existence and determine its properties. In
particular, the mass of the black hole is computed.Comment: 19 pages, 5 figure
Geometric invariance of mass-like asymptotic invariants
We study coordinate-invariance of some asymptotic invariants such as the ADM
mass or the Chru\'sciel-Herzlich momentum, given by an integral over a
"boundary at infinity". When changing the coordinates at infinity, some terms
in the change of integrand do not decay fast enough to have a vanishing
integral at infinity; but they may be gathered in a divergence, thus having
vanishing integral over any closed hypersurface. This fact could only be
checked after direct calculation (and was called a "curious cancellation"). We
give a conceptual explanation thereof.Comment: 13 page
A Metric for Gradient RG Flow of the Worldsheet Sigma Model Beyond First Order
Tseytlin has recently proposed that an action functional exists whose
gradient generates to all orders in perturbation theory the Renormalization
Group (RG) flow of the target space metric in the worldsheet sigma model. The
gradient is defined with respect to a metric on the space of coupling constants
which is explicitly known only to leading order in perturbation theory, but at
that order is positive semi-definite, as follows from Perelman's work on the
Ricci flow. This gives rise to a monotonicity formula for the flow which is
expected to fail only if the beta function perturbation series fails to
converge, which can happen if curvatures or their derivatives grow large. We
test the validity of the monotonicity formula at next-to-leading order in
perturbation theory by explicitly computing the second-order terms in the
metric on the space of coupling constants. At this order, this metric is found
not to be positive semi-definite. In situations where this might spoil
monotonicity, derivatives of curvature become large enough for higher order
perturbative corrections to be significant.Comment: 15 pages; Erroneous sentence in footnote 14 removed; this version
therefore supersedes the published version (our thanks to Dezhong Chen for
the correction
On the Bartnik extension problem for the static vacuum Einstein equations
We develop a framework for understanding the existence of asymptotically flat
solutions to the static vacuum Einstein equations with prescribed boundary data
consisting of the induced metric and mean curvature on a 2-sphere. A partial
existence result is obtained, giving a partial resolution of a conjecture of
Bartnik on such static vacuum extensions. The existence and uniqueness of such
extensions is closely related to Bartnik's definition of quasi-local mass.Comment: 33 pages, 1 figure. Minor revision of v2. Final version, to appear in
Class. Quantum Gravit
Clustering Time-Series Gene Expression Data Using Smoothing Spline Derivatives
Microarray data acquired during time-course experiments allow the temporal variations in gene expression to be monitored. An original postprandial fasting experiment was conducted in the mouse and the expression of 200 genes was monitored with a dedicated macroarray at 11 time points between 0 and 72 hours of fasting. The aim of this study was to provide a relevant clustering of gene expression temporal profiles. This was achieved by focusing on the shapes of the curves rather than on the absolute level of expression. Actually, we combined spline smoothing and first derivative computation with hierarchical and partitioning clustering. A heuristic approach was proposed to tune the spline smoothing parameter using both statistical and biological considerations. Clusters are illustrated a posteriori through principal component analysis and heatmap visualization. Most results were found to be in agreement with the literature on the effects of fasting on the mouse liver and provide promising directions for future biological investigations
On vacuum gravitational collapse in nine dimensions
We consider the vacuum gravitational collapse for cohomogeneity-two solutions
of the nine dimensional Einstein equations. Using combined numerical and
analytical methods we give evidence that within this model the
Schwarzschild-Tangherlini black hole is asymptotically stable. In addition, we
briefly discuss the critical behavior at the threshold of black hole formation.Comment: 4 pages, 4 figure
A Barren Landscape?
We consider the generation of a non-perturbative superpotential in F-theory
compactifications with flux. We derive a necessary condition for the generation
of such a superpotential in F-theory. For models with a single volume modulus,
we show that the volume modulus is never stabilized by either abelian
instantons or gaugino condensation. We then comment on how our analysis extends
to a larger class of compactifications. From our results, it appears that among
large volume string compactifications, metastable de Sitter vacua (should any
exist) are non-generic.Comment: 14 pages, comments adde
Platelet-activating factor acetylhydrolase and haemophagocytosis in the sepsis syndrome.
Sepsis syndrome (SS) is associated with depressed PAF acetylhydrolase, the enzyme responsible for the degradation of platelet activating factor. PAF acetylhydrolase is in a large part produced by macrophages, whose inadequate activation with haemophagocytosis is frequent in patients with SS. The aim of this study was to test the hypothesis that PAF acetylhydrolase levels could be affected in these critically ill patients, because of the large amounts produced by activated macrophages in vitro and in vivo in animal models. The levels of serum PAF acetylhydrolase were assessed in 90 SS patients, who were divided into three groups: patients with (n = 34) or without haemophagocytosis (n = 31), and patients without thrombocytopenia (n = 25) who were used as a control group. The number of organ dysfunctions was matched between patients with haemophagocytosis and controls. Normal reference values were obtained in 59 randomly selected blood donors. Circulating levels of PAF acetylhydrolase were significantly (p = 0.0001) decreased in patients with SS (57+/-3 nmol/ml/min, n = 90) when compared with healthy subjects (69+/-3 nmol/ml/min, n = 59). PAF acetylhydrolase levels were greater in the presence of a haemophagocytosis but without statistical significance (64.2+/-6.5 vs. 50.1+/-2.8:p = 0.25). Despite the fact that macrophagic activation stimulates the in vitro release of PAF acetylhydrolase, no difference was found between patients with or without haemophagocytosis. The mechanism and the role of the PAF acetylhydrolase reduction in SS patients remain to be determined
On the stability and spectrum of non-supersymmetric AdS(5) solutions of M-theory compactified on Kahler-Einstein spaces
Eleven-dimensional supergravity admits non-supersymmetric solutions of the
form AdS(5)xM(6) where M(6) is a positive Kahler-Einstein space. We show that
the necessary and sufficient condition for such solutions to be stable against
linearized bosonic supergravity perturbations can be expressed as a condition
on the spectrum of the Laplacian acting on (1,1)-forms on M(6). For M(6)=CP(3),
this condition is satisfied, although there are scalars saturating the
Breitenlohner-Freedman bound. If M(6) is a product S(2)xM(4) (where M(4) is
Kahler-Einstein) then there is an instability if M(4) has a continuous
isometry. We show that a potential non-perturbative instability due to 5-brane
nucleation does not occur. The bosonic Kaluza-Klein spectrum is determined in
terms of eigenvalues of operators on M(6).Comment: 21 pages. v2: Includes SU(4) quantum numbers for CP3 case, typos
fixed, refs adde
On the global structure of conformal gradient solitons with nonnegative Ricci tensor
In this paper we prove that any complete conformal gradient soliton with
nonnegative Ricci tensor is either isometric to a direct product
, or globally conformally equivalent to the Euclidean
space or to the round sphere . In particular,
we show that any complete, noncompact, gradient Yamabe-type soliton with
positive Ricci tensor is rotationally symmetric, whenever the potential
function is nonconstant.Comment: Minor correction
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