1,561 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
Recherches sur lâĂ©tiologie de lâanĂ©mie infectieuse de la Truite
BossĂ© Philippe. Recherches sur lâĂ©tiologie de lâanĂ©mie infectieuse de la Truite. In: Bulletin de l'AcadĂ©mie VĂ©tĂ©rinaire de France tome 108 n°5, 1955. pp. 194-199
Epizootie de gangrĂšne gazeuse chez la Soffie (Chondrostoma toxostoma)
Besse P. Ăpizootie de gangrĂšne gazeuse chez la Soffie (Chondrostoma toxostoma). In: Bulletin de l'AcadĂ©mie VĂ©tĂ©rinaire de France tome 102 n°9, 1949. pp. 377-379
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
- âŠ