On the "Poisson Trick" and its Extensions for Fitting Multinomial Regression Models

This article is concerned with the fitting of multinomial regression models using the so-called "Poisson Trick". The work is motivated by Chen & Kuo (2001) and Malchow-M{\o}ller & Svarer (2003) which have been criticized for being computationally inefficient and sometimes producing nonsense results. We first discuss the case of independent data and offer a parsimonious fitting strategy when all covariates are categorical. We then propose a new approach for modelling correlated responses based on an extension of the Gamma-Poisson model, where the likelihood can be expressed in closed-form. The parameters are estimated via an Expectation/Conditional Maximization (ECM) algorithm, which can be implemented using functions for fitting generalized linear models readily available in standard statistical software packages. Compared to existing methods, our approach avoids the need to approximate the intractable integrals and thus the inference is exact with respect to the approximating Gamma-Poisson model. The proposed method is illustrated via a reanalysis of the yogurt data discussed by Chen & Kuo (2001)

Using LaX scintillator in a new low-background Compton telescope

The ability of Compton telescopes to perform imaging and spectroscopy in space depends directly on the speed and energy resolution of the calorimeter detectors in the telescope. The calorimeter detectors flown on space-borne or balloon-borne Compton telescopes have included NaI(Tl), CsI(Na), HPGe and liquid organic scintillator. By employing LaX scintillators for the calorimeter, one can take advantage of the unique speed and resolving power of the material to improve the instrument sensitivity and simultaneously enhance its spectroscopic performance and thus its imaging performance. We present a concept for a space-borne Compton telescope that employs LaX as a calorimeter and estimate the improvement in sensitivity over past realizations of Compton telescopes. With some preliminary laboratory measurements, we estimate that in key energy bands, typically corrupted with neutron-induced internal nuclear emissions, this design enjoys a twenty-fold improvement in background rejection

On a dissipative Gross-Pitaevskii-type model for exciton-polariton condensates

We study a generalized dissipative Gross-Pitaevskii-type model arising in the description of exciton-polariton condensates. We derive global in-time existence results and various a-priori estimates for this model posed on the one-dimensional torus. Moreover, we analyze in detail the long-time behavior of spatially homogenous solutions and their respective steady states and present numerical simulations in the case of more general initial data. We also study the convergence to the corresponding adiabatic regime, which results in a single damped-driven Gross-Pitaveskii equation.Comment: 25 pages, 11 figure

Gas micro-well track imaging detectors for gamma-ray astronomy

We describe our program to develop gas micro-well detectors (MWDs) as three-dimensional charged particle trackers for use in advanced gamma-ray telescope concepts. A micro-well detector consists of an array of individual micro-patterned gas proportional counters opposite a planar drift electrode. The well anodes and cathodes may be connected in X and Y strips, respectively, to provide two-dimensional imaging. When combined with transient digitizer electronics, which record the time signature of the charge collected in the wells of each strip, full three-dimensional reconstruction of charged-particle tracks in large gas volumes is possible. Such detectors hold great promise for advanced Compton telescope (ACT) and advanced pair telescope (APT) concepts due to the very precise measurement of charged particle momenta that is possible (Compton recoil electrons and electron-positron pairs, respectively). We present preliminary lab results, including detector fabrication, prototype electronics, and initial detector testing. We also discuss applications to the ACT and APT mission concepts, based on GEANT3 and GEANT4 simulations

Position Resolution in LaBr3 and LaCl3 Scintillators Using Position-Sensitive Photomultiplier Tubes

Advanced scintillator materials such as LaBr3:Ce and LaCl3:Ce hold great promise for future hard X-ray and gamma-ray astrophysics missions due to their high density, high light output, good linearity, and fast decay times. Of particular importance for future space-based imaging instruments, such as coded-aperture telescopes, is the precise spatial location of individual gamma-ray interactions. We have investigated the position and energy resolution achievable within monolithic (5 cm × 5 cm × 1 cm) LaBr3:Ce and LaCl3:Ce crystals using position-sensitive light readout devices, including a position-sensitive photomultiplier tube and a multi-anode photomultiplier tube. We present the results of these tests and discuss the applicability of such advanced scintillators to future high-energy imaging astrophysics missions

Synchronously-pumped OPO coherent Ising machine: benchmarking and prospects

The coherent Ising machine (CIM) is a network of optical parametric oscillators (OPOs) that solves for the ground state of Ising problems through OPO bifurcation dynamics. Here, we present experimental results comparing the performance of the CIM to quantum annealers (QAs) on two classes of NP-hard optimization problems: ground state calculation of the Sherrington-Kirkpatrick (SK) model and MAX-CUT. While the two machines perform comparably on sparsely-connected problems such as cubic MAX-CUT, on problems with dense connectivity, the QA shows an exponential performance penalty relative to CIMs. We attribute this to the embedding overhead required to map dense problems onto the sparse hardware architecture of the QA, a problem that can be overcome in photonic architectures such as the CIM

GRAPE: a balloon-borne gamma-ray polarimeter

The Gamma-RAy Polarimeter Experiment (GRAPE) is a concept for an astronomical hard X-ray Compton polarimeter operating in the 50 - 500 keV energy band. The instrument has been optimized for wide-field polarization measurements of transient outbursts from energetic astrophysical objects such as gamma-ray bursts and solar flares. The GRAPE instrument is composed of identical modules, each of which consists of an array of scintillator elements read out by a multi-anode photomultiplier tube (MAPMT). Incident photons Compton scatter in plastic scintillator elements and are subsequently absorbed in inorganic scintillator elements; a net polarization signal is revealed by a characteristic asymmetry in the azimuthal scattering angles. We have constructed a prototype GRAPE module that has been calibrated at a polarized hard X-ray beam and flown on an engineering balloon test flight. A full-scale scientific balloon payload, consisting of up to 36 modules, is currently under development. The first flight, a one-day flight scheduled for 2011, will verify the expected scientific performance with a pointed observation of the Crab Nebula. We will then propose long-duration balloon flights to observe gamma-ray bursts and solar flares