The AF structure of non commutative toroidal Z/4Z orbifolds

For any irrational theta and rational number p/q such that q|qtheta-p|<1, a projection e of trace q|qtheta-p| is constructed in the the irrational rotation algebra A_theta that is invariant under the Fourier transform. (The latter is the order four automorphism U mapped to V, V mapped to U^{-1}, where U, V are the canonical unitaries generating A_theta.) Further, the projection e is approximately central, the cut down algebra eA_theta e contains a Fourier invariant q x q matrix algebra whose unit is e, and the cut downs eUe, eVe are approximately inside the matrix algebra. (In particular, there are Fourier invariant projections of trace k|qtheta-p| for k=1,...,q.) It is also shown that for all theta the crossed product A_theta rtimes Z_4 satisfies the Universal Coefficient Theorem. (Z_4 := Z/4Z.) As a consequence, using the Classification Theorem of G. Elliott and G. Gong for AH-algebras, a theorem of M. Rieffel, and by recent results of H. Lin, we show that A_theta rtimes Z_4 is an AF-algebra for all irrational theta in a dense G_delta.Comment: 35 page

Black Hole Entropy, Topological Entropy and the Baum-Connes Conjecture in K-Theory

We shall try to exhibit a relation between black hole entropy and topological entropy using the famous Baum-Connes conjecture for foliated manifolds which are particular examples of noncommutative spaces. Our argument is qualitative and it is based on the microscopic origin of the Beckenstein-Hawking area-entropy formula for black holes, provided by superstring theory, in the more general noncommutative geometric context of M-Theory following the Connes- Douglas-Schwarz article.Comment: 17 pages, Latex, contains an important paragraph in section 2 which gives a better understandin

The Broad Absorption Line Tidal Disruption Event iPTF15af: Optical and Ultraviolet Evolution

We present multi-wavelength observations of the tidal disruption event (TDE) iPTF15af, discovered by the intermediate Palomar Transient Factory (iPTF) survey at redshift $z=0.07897$. The optical and ultraviolet (UV) light curves of the transient show a slow decay over five months, in agreement with previous optically discovered TDEs. It also has a comparable black-body peak luminosity of $L_{\rm{peak}} \approx 1.5 \times 10^{44}$ erg/s. The inferred temperature from the optical and UV data shows a value of (3$-$5) $\times 10^4$ K. The transient is not detected in X-rays up to $L_X < 3 \times 10^{42}$erg/s within the first five months after discovery. The optical spectra exhibit two distinct broad emission lines in the He II region, and at later times also H$\alpha$ emission. Additionally, emission from [N III] and [O III] is detected, likely produced by the Bowen fluorescence effect. UV spectra reveal broad emission and absorption lines associated with high-ionization states of N V, C IV, Si IV, and possibly P V. These features, analogous to those of broad absorption line quasars (BAL QSOs), require an absorber with column densities $N_{\rm{H}} > 10^{23}$ cm$^{-2}$. This optically thick gas would also explain the non-detection in soft X-rays. The profile of the absorption lines with the highest column density material at the largest velocity is opposite that of BAL QSOs. We suggest that radiation pressure generated by the TDE flare at early times could have provided the initial acceleration mechanism for this gas. Spectral UV line monitoring of future TDEs could test this proposal.Comment: 20 pages, 12 figures, published in Ap

On the arithmetic sums of Cantor sets

Let C_\la and C_\ga be two affine Cantor sets in $\mathbb{R}$ with similarity dimensions d_\la and d_\ga, respectively. We define an analog of the Bandt-Graf condition for self-similar systems and use it to give necessary and sufficient conditions for having \Ha^{d_\la+d_\ga}(C_\la + C_\ga)>0 where C_\la + C_\ga denotes the arithmetic sum of the sets. We use this result to analyze the orthogonal projection properties of sets of the form C_\la \times C_\ga. We prove that for Lebesgue almost all directions $\theta$ for which the projection is not one-to-one, the projection has zero (d_\la + d_\ga)-dimensional Hausdorff measure. We demonstrate the results on the case when C_\la and C_\ga are the middle-(1-2\la) and middle-(1-2\ga) sets

Explorations in anatomy: the remains from Royal London Hospital

This paper considers the faunal remains from recent excavations at the Royal London Hospital. The remains date to the beginning of the 19th century and offer an insight into the life of the hospital's patients and practices of the attached medical school. Many of the animal remains consist of partially dissected skeletons, including the unique finds of Hermann's tortoise (Testudo hermanni) and Cercopithecus monkey. The hospital diet and developments in comparative anatomy are discussed by integrating the results with documentary research. They show that zooarchaeological study of later post-medieval material can significantly enhance our understanding of the exploitation of animals in this perio

Nonconventional Large Deviations Theorems

We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation

Galaxy Zoo Supernovae

This paper presents the first results from a new citizen science project: Galaxy Zoo Supernovae. This proof of concept project uses members of the public to identify supernova candidates from the latest generation of wide-field imaging transient surveys. We describe the Galaxy Zoo Supernovae operations and scoring model, and demonstrate the effectiveness of this novel method using imaging data and transients from the Palomar Transient Factory (PTF). We examine the results collected over the period April-July 2010, during which nearly 14,000 supernova candidates from PTF were classified by more than 2,500 individuals within a few hours of data collection. We compare the transients selected by the citizen scientists to those identified by experienced PTF scanners, and find the agreement to be remarkable - Galaxy Zoo Supernovae performs comparably to the PTF scanners, and identified as transients 93% of the ~130 spectroscopically confirmed SNe that PTF located during the trial period (with no false positive identifications). Further analysis shows that only a small fraction of the lowest signal-to-noise SN detections (r > 19.5) are given low scores: Galaxy Zoo Supernovae correctly identifies all SNe with > 8{\sigma} detections in the PTF imaging data. The Galaxy Zoo Supernovae project has direct applicability to future transient searches such as the Large Synoptic Survey Telescope, by both rapidly identifying candidate transient events, and via the training and improvement of existing machine classifier algorithms.Comment: 13 pages, 10 figures, accepted MNRA

Graded and Binary Responses in Stochastic Gene Expression

Recently, several theoretical and experimental studies have been undertaken to probe the effect of stochasticity on gene expression (GE). In experiments, the GE response to an inducing signal in a cell, measured by the amount of mRNAs/proteins synthesized, is found to be either graded or binary. The latter type of response gives rise to a bimodal distribution in protein levels in an ensemble of cells. One possible origin of binary response is cellular bistability achieved through positive feedback or autoregulation. In this paper, we study a simple, stochastic model of GE and show that the origin of binary response lies exclusively in stochasticity. The transitions between the active and inactive states of the gene are random in nature. Graded and binary responses occur in the model depending on the relative stability of the activated and deactivated gene states with respect to that of mRNAs/proteins.The theoretical results on binary response provide a good description of the ``all-or-none'' phenomenon observed in an eukaryotic system.Comment: to be published in Physical Biolog