829 research outputs found
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
Determinants of outcome following surgery for oral squamous cell carcinoma
The recent changes in incidence and prevalence of oral squamous cell carcinoma in relation to gender and age mirror the changing patterns of exposure to tobacco and alcohol, the main etiological agents. Most cases of oral cancer are managed by surgery, often combined with radiotherapy. Histopathological assessment of the resection specimen provides information vital for postoperative management and prognosis. This review considers the full range of histological determinants of outcome in relation to the primary oral tumor and any metastatic involvement of the cervical lymphatic system, together with an outline of more general patient factors that may also impact on morbidity and mortality rates. </jats:p
A Bakry-\'Emery Almost Splitting Result With Applications to the Topology of Black Holes
The almost splitting theorem of Cheeger-Colding is established in the setting
of almost nonnegative generalized -Bakry-\'{E}mery Ricci curvature, in which
is positive and the associated vector field is not necessarily required to
be the gradient of a function. In this context it is shown that with a diameter
upper bound and volume lower bound the fundamental group of such manifolds is
almost abelian. Furthermore, extensions of well-known results concerning Ricci
curvature lower bounds are given for generalized -Bakry-\'{E}mery Ricci
curvature. These include: the first Betti number bound of Gromov and Gallot,
Anderson's finiteness of fundamental group isomorphism types, volume
comparison, the Abresch-Gromoll inequality, and a Cheng-Yau gradient estimate.
Finally, this analysis is applied to stationary vacuum black holes in higher
dimensions to find that low temperature horizons must have limited topology,
similar to the restrictions exhibited by (extreme) horizons of zero
temperature.Comment: Comm. Math. Phys., to appea
The Positivity of Energy for Asymptotically Anti-de Sitter Spacetimes
We use the formulation of asymptotically anti-de Sitter boundary conditions
given by Ashtekar and Magnon to obtain a coordinate expression for the general
asymptotically AdeS metric in a neighbourhood of infinity. From this, we are
able to compute the time delay of null curves propagating near infinity. If the
gravitational mass is negative, so will be the time delay (relative to null
geodesics at infinity) for certain null geodesics in the spacetime. Following
closely an argument given by Penrose, Sorkin, and Woolgar, who treated the
asymptotically flat case, we are then able to argue that a negative time delay
is inconsistent with non-negative matter-energies in spacetimes having good
causal properties. We thereby obtain a new positive mass theorem for these
spacetimes. The theorem may be applied even when the matter flux near the
boundary-at-infinity falls off so slowly that the mass changes, provided the
theorem is applied in a time-averaged sense. The theorem also applies in
certain spacetimes having local matter-energy that is sometimes negative, as
can be the case in semi-classical gravity.Comment: (Plain TeX - figures not included
The Cosmic Censor Forbids Naked Topology
For any asymptotically flat spacetime with a suitable causal structure
obeying (a weak form of) Penrose's cosmic censorship conjecture and satisfying
conditions guaranteeing focusing of complete null geodesics, we prove that
active topological censorship holds. We do not assume global hyperbolicity, and
therefore make no use of Cauchy surfaces and their topology. Instead, we
replace this with two underlying assumptions concerning the causal structure:
that no compact set can signal to arbitrarily small neighbourhoods of spatial
infinity (``-avoidance''), and that no future incomplete null geodesic is
visible from future null infinity. We show that these and the focusing
condition together imply that the domain of outer communications is simply
connected. Furthermore, we prove lemmas which have as a consequence that if a
future incomplete null geodesic were visible from infinity, then given our
-avoidance assumption, it would also be visible from points of spacetime
that can communicate with infinity, and so would signify a true naked
singularity.Comment: To appear in CQG, this improved version contains minor revisions to
incorporate referee's suggestions. Two revised references. Plain TeX, 12
page
Late disruption of central visual field disrupts peripheral perception of form and color.
Evidence from neuroimaging and brain stimulation studies suggest that visual information about objects in the periphery is fed back to foveal retinotopic cortex in a separate representation that is essential for peripheral perception. The characteristics of this phenomenon have important theoretical implications for the role fovea-specific feedback might play in perception. In this work, we employed a recently developed behavioral paradigm to explore whether late disruption to central visual space impaired perception of color. In the first experiment, participants performed a shape discrimination task on colored novel objects in the periphery while fixating centrally. Consistent with the results from previous work, a visual distractor presented at fixation ~100ms after presentation of the peripheral stimuli impaired sensitivity to differences in peripheral shapes more than a visual distractor presented at other stimulus onset asynchronies. In a second experiment, participants performed a color discrimination task on the same colored objects. In a third experiment, we further tested for this foveal distractor effect with stimuli restricted to a low-level feature by using homogenous color patches. These two latter experiments resulted in a similar pattern of behavior: a central distractor presented at the critical stimulus onset asynchrony impaired sensitivity to peripheral color differences, but, importantly, the magnitude of the effect was stronger when peripheral objects contained complex shape information. These results show a behavioral effect consistent with disrupting feedback to the fovea, in line with the foveal feedback suggested by previous neuroimaging studies
A uniqueness theorem for the adS soliton
The stability of physical systems depends on the existence of a state of
least energy. In gravity, this is guaranteed by the positive energy theorem.
For topological reasons this fails for nonsupersymmetric Kaluza-Klein
compactifications, which can decay to arbitrarily negative energy. For related
reasons, this also fails for the AdS soliton, a globally static, asymptotically
toroidal spacetime with negative mass. Nonetheless, arguing from
the AdS/CFT correspondence, Horowitz and Myers (hep-th/9808079) proposed a new
positive energy conjecture, which asserts that the AdS soliton is the unique
state of least energy in its asymptotic class. We give a new structure theorem
for static spacetimes and use it to prove uniqueness of the AdS
soliton. Our results offer significant support for the new positive energy
conjecture and add to the body of rigorous results inspired by the AdS/CFT
correspondence.Comment: Revtex, 4 pages; Matches published version. More detail in Abstract
and one equation corrected. For details of proofs and further results, see
hep-th/020408
The impact of frozen sections on final surgical margins in squamous cell carcinoma of the oral cavity and lips: a retrospective analysis over an 11 years period
Taking intraoperative frozen sections (FS) is a widely used procedure in oncologic surgery. However so far no evidence of an association of FS analysis and premalignant changes in the surgical margin exists. Therefore, the aim of this study was to evaluate the impact of FS on different categories of the final margins of squamous cell carcinoma (SCC) of the oral cavity and lips
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