Causal Dependence Tree Approximations of Joint Distributions for Multiple Random Processes

We investigate approximating joint distributions of random processes with causal dependence tree distributions. Such distributions are particularly useful in providing parsimonious representation when there exists causal dynamics among processes. By extending the results by Chow and Liu on dependence tree approximations, we show that the best causal dependence tree approximation is the one which maximizes the sum of directed informations on its edges, where best is defined in terms of minimizing the KL-divergence between the original and the approximate distribution. Moreover, we describe a low-complexity algorithm to efficiently pick this approximate distribution.Comment: 9 pages, 15 figure

Neutrino Fluxes from Active Galaxies: a Model-Independent Analysis

There are tantalizing hints that jets, powered by supermassive black holes at the center of active galaxies, are true cosmic proton accelerators. They produce photons of TeV energy, possible higher, and may be the enigmatic source of the highest energy cosmic rays. Photoproduction of neutral pions by accelerated protons on UV light is the source of the highest energy photons, in which most of the bolometric luminosity of the galaxy may be emitted. The case that proton beams power active galaxies is, however, far from conclusive. Neutrinos from the decay of charged pions represent an uncontrovertible signature for the proton induced cascades. We show that their flux can be estimated by model-independent methods, based on dimensional analysis and textbook particle physics. Our calculations also demonstrate why different models for the proton blazar yield very similar results for the neutrino flux, consistent with the ones obtained here.Comment: Latex 2.09 with epsf.sty. 12 pages, 2 postscript figures. Compressed postscript version of paper with figures also available soon at http://phenom.physics.wisc.edu/pub/preprints/1997/madph-97-982.ps.Z or at ftp://phenom.physics.wisc.edu/pub/preprints/1997/madph-97-982.ps.

Spectropolarimetry of the Type Ia SN 2007sr Two Months After Maximum Light

We present late time spectropolarimetric observations of SN 2007sr, obtained with the VLT telescope at ESO Paranal Observatory when the object was 63 days after maximum light. The late time spectrum displays strong line polarization in the CaII absorption features. SN 2007sr adds to the case of some normal Type Ia SNe that show high line polarization or repolarization at late times, a fact that might be connected with the presence of high velocity features at early times

A spectropolarimetric view on the nature of the peculiar Type I SN 2005hk

We report two spectropolarimetric observations of SN 2005hk, which is a close copy of the "very peculiar" SN 2002cx, showing low peak luminosity, slow decline, high ionization near peak and an unusually low expansion velocity of only about 7,000 km s^-1. Further to the data presented by Chornock et al., (2006), at -4 days before maximum, we present data of this object taken on 9 November 2005 (near maximum) and 23 November (+ two weeks) that show the continuum and most of the spectral lines to be polarized at levels of about 0.2-0.3%. At both epochs the data corresponds to the Spectropolarimetric Type D1. The general low level of line polarization suggests that the line forming regions for most species observed in the spectrum have a similar shape to that of the photosphere, which deviates from a spherical symmetry by <10%. In comparison with spectropolarimetry of Type Ia and Core-collapse SNe at similar epochs, we find that the properties of SN 2005hk are most similar to those of Type Ia SNe. In particular, we find the low levels of continuum and line polarization to indicate that the explosion mechanism is approximately spherical, with homogeneous ejecta (unlike the chemically segregated ejecta of CCSNe). We discuss the possibility that SN 2005hk was the result of the pure deflagration of a white dwarf and note the issues concerning this interpretation.Comment: ApJ accepted, uses emulateapj, 16 pages, 10 figures, figures 3 and 4 update

Evidence for massive bulk Dirac Fermions in Pb1−x_{1-x}Snx_xSe from Nernst and thermopower experiments

The lead chalcogenides (Pb,Sn)Te and (Pb,Sn)Se are the first examples of topological crystalline insulators (TCI) predicted \cite{Fu,Hsieh} (and confirmed \cite{Hasan,Story,Takahashi}) to display topological surface Dirac states (SDS) that are protected by mirror symmetry. A starting premise \cite{Hsieh} is that the SDS arise from bulk states describable as massive Dirac states \cite{Wallis,Svane}, but this assumption is untested. Here we show that the thermoelectric response of the bulk states display features specific to the Dirac spectrum. We show that, in the quantum limit, the lowest Landau Level (LL) is singly spin-degenerate, whereas higher levels are doubly degenerate. The abrupt change in spin degeneracy leads to a large step-decrease in the thermopower $S_{xx}$. In the lowest LL, $S_{xx}$ displays a striking linear increase vs. magnetic field. In addition, the Nernst signal undergoes an anomalous sign change when the bulk gap inverts at 180 K.Comment: 16 pages, 8 figure

Rapid Formation of Supermassive Black Hole Binaries in Galaxy Mergers with Gas

Supermassive black holes (SMBHs) are a ubiquitous component of the nuclei of galaxies. It is normally assumed that, following the merger of two massive galaxies, a SMBH binary will form, shrink due to stellar or gas dynamical processes and ultimately coalesce by emitting a burst of gravitational waves. However, so far it has not been possible to show how two SMBHs bind during a galaxy merger with gas due to the difficulty of modeling a wide range of spatial scales. Here we report hydrodynamical simulations that track the formation of a SMBH binary down to scales of a few light years following the collision between two spiral galaxies. A massive, turbulent nuclear gaseous disk arises as a result of the galaxy merger. The black holes form an eccentric binary in the disk in less than a million years as a result of the gravitational drag from the gas rather than from the stars.Comment: Accepted for publication in Science, 40 pages, 7 figures, Supplementary Information include