Detection of Patches of Outliers in Stochastic Volatility Processes.

Because the volatility of nancial asset returns tends to arrive in clusters, it is quite likely that outliers appear in patches. In this case, most of the statistical tests developed to detect outliers have low power. We propose to use the posterior distribution of the size of the outlier and of the probability of the presence of an outlier at each observation to detect and estimate the outlier. This sampling algorithm is an adapted version of the algorithm proposed by Justel et al. (2001) for autoregressive time-series models. Our proposed sampling procedure is applied to a simulated sample according to the stochastic volatility, a sample of the New York Stock Exchange daily returns, and a sample of the Brazilian S~ao Paulo Stock Exchange daily returns.Because the volatility of nancial asset returns tends to arrive in clusters, it is quite likely that outliers appear in patches. In this case, most of the statistical tests developed to detect outliers have low power. We propose to use the posterior distribution of the size of the outlier and of the probability of the presence of an outlier at each observation to detect and estimate the outlier. This sampling algorithm is an adapted version of the algorithm proposed by Justel et al. (2001) for autoregressive time-series models. Our proposed sampling procedure is applied to a simulated sample according to the stochastic volatility, a sample of the New York Stock Exchange daily returns, and a sample of the Brazilian S~ao Paulo Stock Exchange daily returns

Boulware state and semiclassical thermodynamics of black holes in a cavity

A black hole, surrounded by a reflecting shell, acts as an effective star-like object with respect to the outer region that leads to vacuum polarization outside, where the quantum fields are in the Boulware state. We find the quantum correction to the Hawking temperature, taking into account this circumstance. It is proportional to the integral of the trace of the total quantum stress-energy tensor over the whole space from the horizon to infinity. For the shell, sufficiently close to the horizon, the leading term comes from the boundary contribution of the Boulware state.Comment: 7 pages. To appear in Phys. Rev.

Vacuum polarization in the spacetime of charged nonlinear black hole

Building on general formulas obtained from the approximate renormalized effective action, the approximate stress-energy tensor of the quantized massive scalar field with arbitrary curvature coupling in the spacetime of charged black hole being a solution of coupled equations of nonlinear electrodynamics and general relativity is constructed and analysed. It is shown that in a few limiting cases, the analytical expressions relating obtained tensor to the general renormalized stress-energy tensor evaluated in the geometry of the Reissner-Nordstr\"{o}m black hole could be derived. A detailed numerical analysis with special emphasis put on the minimal coupling is presented and the results are compared with those obtained earlier for the conformally coupled field. Some novel features of the renormalized stress-energy tensor are discussed

Spatial Patterns Induced Purely by Dichotomous Disorder

We study conditions under which spatially extended systems with coupling a la Swift-Hohenberg exhibit spatial patterns induced purely by the presence of quenched dichotomous disorder. Complementing the theoretical results based on a generalized mean-field approximation, we also present numerical simulations of particular dynamical systems that exhibit the proposed phenomenology

Theory of High \tc Ferromagnetism in SrB6SrB_6 family: A case of Doped Spin-1 Mott insulator in a Valence Bond Solid Phase

Doped divalent hexaborides such as $Sr_{1-x}La_xB_6$ exhibit high \tc ferromagnetism. We isolate a degenerate pair of $2p$-orbitals of boron with two valence electrons, invoke electron correlation and Hund coupling, to suggest that the undoped state is better viewed as a spin-1 Mott insulator; it is predicted to be a type of 3d Haldane gap phase with a spin gap $\sim 0.1 eV$, much smaller than the charge gap of $> 1.0 eV$ seen in ARPES. The experimentally seen high \tc `ferromagnetism' is argued to be a complex magnetic order in disguise - either a canted 6-sublattice AFM ($\approx 120^0$) order or its quantum melted version, a chiral spin liquid state, arising from a type of double exchange mechanism.Comment: 4 pages, 2 figures; minor corrections, references adde

Adaptive Mesh Refinement for Characteristic Grids

I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when numerically solving partial differential equations with wave-like solutions, using characteristic (double-null) grids. Such AMR algorithms are naturally recursive, and the best-known past Berger-Oliger characteristic AMR algorithm, that of Pretorius & Lehner (J. Comp. Phys. 198 (2004), 10), recurses on individual "diamond" characteristic grid cells. This leads to the use of fine-grained memory management, with individual grid cells kept in 2-dimensional linked lists at each refinement level. This complicates the implementation and adds overhead in both space and time. Here I describe a Berger-Oliger characteristic AMR algorithm which instead recurses on null \emph{slices}. This algorithm is very similar to the usual Cauchy Berger-Oliger algorithm, and uses relatively coarse-grained memory management, allowing entire null slices to be stored in contiguous arrays in memory. The algorithm is very efficient in both space and time. I describe discretizations yielding both 2nd and 4th order global accuracy. My code implementing the algorithm described here is included in the electronic supplementary materials accompanying this paper, and is freely available to other researchers under the terms of the GNU general public license.Comment: 37 pages, 15 figures (40 eps figure files, 8 of them color; all are viewable ok in black-and-white), 1 mpeg movie, uses Springer-Verlag svjour3 document class, includes C++ source code. Changes from v1: revised in response to referee comments: many references added, new figure added to better explain the algorithm, other small changes, C++ code updated to latest versio

A deep search for faint Chandra X-ray sources, radio sources, and optical counterparts in NGC 6752

We report the results of a deep search for faint Chandra X-ray sources, radio sources, and optical counterparts in the nearby, core-collapsed globular cluster, NGC 6752. We combined new and archival Chandra imaging to detect 51 X-ray sources (12 of which are new) within the 1.9 arcmin half-light radius. Three radio sources in deep ATCA 5 and 9 GHz radio images match with Chandra sources. We have searched for optical identifications for the expanded Chandra source list using deep Hubble Space Telescope photometry in B435, R625, H α, UV275, and U336. Among the entire sample of 51 Chandra sources, we identify 18 cataclysmic variables (CVs), 9 chromospherically active binaries (ABs), 3 red giants (RGs), 3 galaxies (GLXs), and 6 active galactic nuclei (AGNs). Three of the sources are associated with millisecond pulsars (MSPs). As in our previous study of NGC 6752, we find that the brightest CVs appear to be more centrally concentrated than the faintest CVs, although the effect is no longer statistically significant as a consequence of the inclusion in the faint group of two intermediate brightness CVs. This possible difference in the radial distributions of the bright and faint CV groups appears to indicate that mass segregation has separated them. We note that photometric incompleteness in the crowded central region of the cluster may also play a role. Both groups of CVs have an inferred mass above that of the main-sequence turnoff stars. We discuss the implications for the masses of the CV components