Random Graph Models with Hidden Color

We demonstrate how to generalize two of the most well-known random graph models, the classic random graph, and random graphs with a given degree distribution, by the introduction of hidden variables in the form of extra degrees of freedom, color, applied to vertices or stubs (half-edges). The color is assumed unobservable, but is allowed to affect edge probabilities. This serves as a convenient method to define very general classes of models within a common unifying formalism, and allowing for a non-trivial edge correlation structure.Comment: 17 pages, 2 figures; contrib. to the Workshop on Random Geometry in Krakow, May 200

Radio and X-ray Observations of the Type Ic SN 2007gr Reveal an Ordinary, Non-relativistic Explosion

We present extensive radio and X-ray observations of the nearby Type Ic SN 2007gr in NGC 1058 obtained with the Very Large Array and the Chandra X-ray Observatory and spanning 5 to 150 days after explosion. Through our detailed modeling of these data, we estimate the properties of the blastwave and the circumstellar environment. We find evidence for a freely-expanding and non-relativistic explosion with an average blastwave velocity, v~0.2c, and a total internal energy for the radio emitting material of E ~ 2 x 10^46 erg assuming equipartition of energy between electrons and magnetic fields (epsilon_e=epsilon_B=0.1). The temporal and spectral evolution of the radio emission points to a stellar wind-blown environment shaped by a steady progenitor mass loss rate of Mdot ~ 6 x 10^-7 solar masses per year (wind velocity, v_w=10^3 km/s). These parameters are fully consistent with those inferred for other SNe Ibc and are in line with the expectations for an ordinary, homologous SN explosion. Our results are at odds with those of Paragi et al. (2010) who recently reported evidence for a relativistic blastwave in SN 2007gr based on their claim that the radio emission was resolved away in a low signal-to-noise Very Long Baseline Interferometry (VLBI) observation. Here we show that the exotic physical scenarios required to explain the claimed relativistic velocity -- extreme departures from equipartition and/or a highly collimated outflow -- are excluded by our detailed Very Large Array radio observations. Moreover, we present an independent analysis of the VLBI data and propose that a modest loss of phase coherence provides a more natural explanation for the apparent flux density loss which is evident on both short and long baselines. We conclude that SN 2007gr is an ordinary Type Ibc supernova.Comment: 14 pages, 6 figures, submitted to Ap

Deterministic Annealing and Nonlinear Assignment

For combinatorial optimization problems that can be formulated as Ising or Potts spin systems, the Mean Field (MF) approximation yields a versatile and simple ANN heuristic, Deterministic Annealing. For assignment problems the situation is more complex -- the natural analog of the MF approximation lacks the simplicity present in the Potts and Ising cases. In this article the difficulties associated with this issue are investigated, and the options for solving them discussed. Improvements to existing Potts-based MF-inspired heuristics are suggested, and the possibilities for defining a proper variational approach are scrutinized.Comment: 15 pages, 3 figure

The Unique Signature of Shell Curvature in Gamma-Ray Bursts

As a result of spherical kinematics, temporal evolution of received gamma-ray emission should demonstrate signatures of curvature from the emitting shell. Specifically, the shape of the pulse decay must bear a strict dependence on the degree of curvature of the gamma-ray emitting surface. We compare the spectral evolution of the decay of individual GRB pulses to the evolution as expected from curvature. In particular, we examine the relationship between photon flux intensity (I) and the peak of the \nu F\nu distribution (E_{peak}) as predicted by colliding shells. Kinematics necessitate that E_{peak} demonstrate a power-law relationship with I described roughly as: I=E_{peak}^{(1-\zeta)} where \zeta represents a weighted average of the low and high energy spectral indices. Data analyses of 24 BATSE gamma-ray burst pulses provide evidence that there exists a robust relationship between E_{peak} and I in the decay phase. Simulation results, however, show that a sizable fraction of observed pulses evolve faster than kinematics allow. Regardless of kinematic parameters, we found that the existence of curvature demands that the I - E_{peak} function decay be defined by \sim (1-\zeta). Efforts were employed to break this curvature dependency within simulations through a number of scenarios such as anisotropic emission (jets) with angular dependencies, thickness values for the colliding shells, and various cooling mechanisms. Of these, the only method successful in dominating curvature effects was a slow cooling model. As a result, GRB models must confront the fact that observed pulses do not evolve in the manner which curvature demands.Comment: 3 pages, To appear in Proc. from the 2nd Workshop on Gamma-Ray Bursts in the Afterglow Er

The Lund Fragmentation Process for a Multi-gluon String According to the Area Law

The Lund Area Law describes the probability for the production of a set of colourless hadrons from an initial set of partons, in the Lund string fragmentation model. In this paper we will present a general method to implement the Area Law for a multi-gluon string state. The partonic states are in general given by a perturbative QCD cascade and are consequently defined only down to a cutoff in the energy momentum fluctuations. We will show that our method defines the states down to the hadronic mass scale inside an analytically calculable scenario. We will then show that there is a differential version of our process which is closely related to the generalised rapidity range \lambda, which has been used as a measure on the partonic states. We identify \lambda as the area spanned between the directrix curve (the curve given by the parton energy momentum vectors laid out in colour order, which determines the string surface) and the average curve (to be called the P-curve) of the stochastic X-curves (curves obtained when the hadronic energy-momentum vectors are laid out in rank order). Finally we show that from the X-curve corresponding to a particular stochastic fragmentation situation it is possible to reproduce the directrix curve (up to one starting vector and a set of sign choices, one for each hadron).Comment: 1 title page + 36 pages, 20 figure

SN 2007bg: The Complex Circumstellar Environment Around One of the Most Radio-Luminous Broad-Lined Type Ic Supernovae

In this paper we present the results of the radio light curve and X-ray observations of broad-lined Type Ic SN 2007bg. The light curve shows three distinct phases of spectral and temporal evolution, implying that the SNe shock likely encountered at least 3 different circumstellar medium regimes. We interpret this as the progenitor of SN 2007bg having at least two distinct mass-loss episodes (i.e., phases 1 and 3) during its final stages of evolution, yielding a highly-stratified circumstellar medium. Modelling the phase 1 light curve as a freely-expanding, synchrotron-emitting shell, self-absorbed by its own radiating electrons, requires a progenitor mass-loss rate of \dot{M}~1.9x10^{-6}(v_{w}/1000 km s^{-1}) Solar masses per year for the last t~20(v_{w}/1000 km s^{-1}) yr before explosion, and a total energy of the radio emitting ejecta of E\sim1x10^{48} erg after 10 days from explosion. This places SN 2007bg among the most energetic Type Ib/c events. We interpret the second phase as a sparser "gap" region between the two winds stages. Phase 3 shows a second absorption turn-on before rising to a peak luminosity 2.6 times higher than in phase 1. Assuming this luminosity jump is due to a circumstellar medium density enhancement from a faster previous mass-loss episode, we estimate that the phase 3 mass-loss rate could be as high as \dot{M}<~4.3x10^{-4}(v_{w}/1000 km s^{-1}) Solar masses per year. The phase 3 wind would have transitioned directly into the phase 1 wind for a wind speed difference of ~2. In summary, the radio light curve provides robust evidence for dramatic global changes in at least some Ic-BL progenitors just prior (~10-1000 yr) to explosion. The observed luminosity of this SN is the highest observed for a non-gamma-ray-burst broad-lined Type Ic SN, reaching L_{8.46 GHz}~1x10^{29} erg Hz^{-1} s^{-1}, ~567 days after explosion.Comment: 11 pages, 5 figures, accepted for publication in MNRA

ArgoNeuT: A Liquid Argon Time Projection Chamber Test in the NuMI Beamline

Liquid Argon Time Projection Chamber detectors are ideally suited for studying neutrino interactions and probing the parameters that characterize neutrino oscillations. The ability to drift ionization particles over long distances in purified argon and to trigger on abundant scintillation light allows for excellent particle identification and triggering capability. In these proceedings the details of the ArgoNeuT test-beam project will be presented after a brief introduction to the detector technique. ArgoNeuT is a 175 liter detector exposed to Fermilab's NuMI neutrino beamline. The first neutrino interactions observed in ArgoNeuT will be presented, along with discussion of the various physics analyses to be performed on this data sample.Comment: To be published in the proceedings of DPF-2009, Detroit, MI, July 2009, eConf C09072