1,046 research outputs found
Late-time expansion in the semiclassical theory of the Hawking radiation
We give a detailed treatment of the back-reaction effects on the Hawking
spectrum in the late-time expansion within the semiclassical approach to the
Hawking radiation. We find that the boundary value problem defining the action
of the modes which are regular at the horizon admits in general the presence of
caustics. We show that for radii less that a certain critical value no
caustic occurs for all values of the wave number and time and we give a
rigorous lower bound on such a critical value. We solve the exact system of non
linear equations defining the motion, by an iterative procedure rigorously
convergent at late times. The first two terms of such an expansion give the
correction to the Hawking spectrum.Comment: 17 pages, 1 figure, LaTex, typos corrected, one intermediate formula
adde
The Digital Flynn Effect: Complexity of Posts on Social Media Increases over Time
Parents and teachers often express concern about the extensive use of social
media by youngsters. Some of them see emoticons, undecipherable initialisms and
loose grammar typical for social media as evidence of language degradation. In
this paper, we use a simple measure of text complexity to investigate how the
complexity of public posts on a popular social networking site changes over
time. We analyze a unique dataset that contains texts posted by 942, 336 users
from a large European city across nine years. We show that the chosen
complexity measure is correlated with the academic performance of users: users
from high-performing schools produce more complex texts than users from
low-performing schools. We also find that complexity of posts increases with
age. Finally, we demonstrate that overall language complexity of posts on the
social networking site is constantly increasing. We call this phenomenon the
digital Flynn effect. Our results may suggest that the worries about language
degradation are not warranted
Menelaus relation and Fay's trisecant formula are associativity equations
It is shown that the celebrated Menelaus relation and Fay's trisecant formula
similar to the WDVV equation are associativity conditions for structure
constants of certain three-dimensional algebra.Comment: Talk given at the Conference " Mathematics and Physics of Solitons
and Integrable Systems", Dijon, 28.6-2.7, 2009. Minor misprints correcte
Gunning-Narasimhan's theorem with a growth condition
Given a compact Riemann surface X and a point x_0 in X, we construct a
holomorphic function without critical points on the punctured Riemann surface R
= X - x_0 which is of finite order at the point x_0. This complements the
result of Gunning and Narasimhan from 1967 who constructed a noncritical
holomorphic function on every open Riemann surface, but without imposing any
growth condition. On the other hand, if the genus of X is at least one, then we
show that every algebraic function on R admits a critical point. Our proof also
shows that every cohomology class in H^1(X;C) is represented as a de Rham class
by a nowhere vanishing holomorphic one-form of finite order on the punctured
surface X-x_0.Comment: J. Geom. Anal., in pres
Residue currents associated with weakly holomorphic functions
We construct Coleff-Herrera products and Bochner-Martinelli type residue
currents associated with a tuple of weakly holomorphic functions, and show
that these currents satisfy basic properties from the (strongly) holomorphic
case, as the transformation law, the Poincar\'e-Lelong formula and the
equivalence of the Coleff-Herrera product and the Bochner-Martinelli type
residue current associated with when defines a complete intersection.Comment: 28 pages. Updated with some corrections from the revision process. In
particular, corrected and clarified some things in Section 5 and 6 regarding
products of weakly holomorphic functions and currents, and the definition of
the Bochner-Martinelli type current
Recurrent De Novo NAHR Reciprocal Duplications in the ATAD3 Gene Cluster Cause a Neurogenetic Trait with Perturbed Cholesterol and Mitochondrial Metabolism.
Recent studies have identified both recessive and dominant forms of mitochondrial disease that result from ATAD3A variants. The recessive form includes subjects with biallelic deletions mediated by non-allelic homologous recombination. We report five unrelated neonates with a lethal metabolic disorder characterized by cardiomyopathy, corneal opacities, encephalopathy, hypotonia, and seizures in whom a monoallelic reciprocal duplication at the ATAD3 locus was identified. Analysis of the breakpoint junction fragment indicated that these 67 kb heterozygous duplications were likely mediated by non-allelic homologous recombination at regions of high sequence identity in ATAD3A exon 11 and ATAD3C exon 7. At the recombinant junction, the duplication allele produces a fusion gene derived from ATAD3A and ATAD3C, the protein product of which lacks key functional residues. Analysis of fibroblasts derived from two affected individuals shows that the fusion gene product is expressed and stable. These cells display perturbed cholesterol and mitochondrial DNA organization similar to that observed for individuals with severe ATAD3A deficiency. We hypothesize that the fusion protein acts through a dominant-negative mechanism to cause this fatal mitochondrial disorder. Our data delineate a molecular diagnosis for this disorder, extend the clinical spectrum associated with structural variation at the ATAD3 locus, and identify a third mutational mechanism for ATAD3 gene cluster variants. These results further affirm structural variant mutagenesis mechanisms in sporadic disease traits, emphasize the importance of copy number analysis in molecular genomic diagnosis, and highlight some of the challenges of detecting and interpreting clinically relevant rare gene rearrangements from next-generation sequencing data
Optimising background-limited observing during bright-moon phases and twilight
For the majority of optical observing programs, the sky brightness provides
the fundamental limit to signal detection such that the scientific feasibility
is largely dictated by the moon phase. Since most observatories do not have the
resources to build expensive high-resolution or infrared instruments, they are
increasingly at a loss as to how to exploit bright time. We show that, with due
consideration of the field and moon position, it is possible to undertake `dark
time' observing programs under `bright time' conditions. Our recommendations
are particularly appropriate to all-sky survey programs.
In certain instances, there are gains in observing efficiency with the use of
a polariser, which can significantly reduce the moonlight (or twilight)
sky-background flux relative to an extraterrestrial flux. These gains are
possible in background-limited cases because the sky background can be highly
polarised, due to scattering, around ninety degrees away from the moon (or
sun). To take advantage of this, only minor modifications to existing
instruments are needed.Comment: 5 pages, 4 figures, accepted by MNRA
Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I
We define the partition and -point correlation functions for a vertex
operator superalgebra on a genus two Riemann surface formed by sewing two tori
together. For the free fermion vertex operator superalgebra we obtain a closed
formula for the genus two continuous orbifold partition function in terms of an
infinite dimensional determinant with entries arising from torus Szeg\"o
kernels. We prove that the partition function is holomorphic in the sewing
parameters on a given suitable domain and describe its modular properties.
Using the bosonized formalism, a new genus two Jacobi product identity is
described for the Riemann theta series. We compute and discuss the modular
properties of the generating function for all -point functions in terms of a
genus two Szeg\"o kernel determinant. We also show that the Virasoro vector one
point function satisfies a genus two Ward identity.Comment: A number of typos have been corrected, 39 pages. To appear in Commun.
Math. Phy
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