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 $r_c$ 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 $O(\omega/M)$ 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 $f$ 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 $f$ when $f$ 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 $n$-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 $n$-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