Bayesian multiscale deconvolution applied to gamma-ray spectroscopy

A common task in gamma-ray astronomy is to extract spectral information, such as model constraints and incident photon spectrum estimates, given the measured energy deposited in a detector and the detector response. This is the classic problem of spectral “deconvolution” or spectral inversion. The methods of forward folding (i.e., parameter fitting) and maximum entropy “deconvolution” (i.e., estimating independent input photon rates for each individual energy bin) have been used successfully for gamma-ray solar flares (e.g., Rank, 1997; Share and Murphy, 1995). These methods have worked well under certain conditions but there are situations were they don’t apply. These are: 1) when no reasonable model (e.g., fewer parameters than data bins) is yet known, for forward folding; 2) when one expects a mixture of broad and narrow features (e.g., solar flares), for the maximum entropy method; and 3) low count rates and low signal-to-noise, for both. Low count rates are a problem because these methods (as they have been implemented) assume Gaussian statistics but Poisson are applicable. Background subtraction techniques often lead to negative count rates. For Poisson data the Maximum Likelihood Estimator (MLE) with a Poisson likelihood is appropriate. Without a regularization term, trying to estimate the “true” individual input photon rates per bin can be an ill-posed problem, even without including both broad and narrow features in the spectrum (i.e., amultiscale approach). One way to implement this regularization is through the use of a suitable Bayesian prior. Nowak and Kolaczyk (1999) have developed a fast, robust, technique using a Bayesian multiscale framework that addresses these problems with added algorithmic advantages. We outline this new approach and demonstrate its use with time resolved solar flare gamma-ray spectroscopy

A study of omega bands and Ps6 pulsations on the ground, at low altitude and at geostationary orbit

We investigate the electrodynamic coupling between auroral omega bands and the inner magnetosphere. The goal of this study is to determine the features to which omega bands map in the magnetosphere. To establish the auroral-magnetosphere connection, we appeal to the case study analysis of the data rich event of September 26, 1989. At 6 magnetic local time (MLT), two trains of Ps6 pulsations (ground magnetic signatures of omega bands) were observed to drift over the Canadian Auroral Network For the OPEN Program Unified Study (CANOPUS) chain. At the same time periodic ionospheric flow patterns moved through the collocated Bistatic Auroral Radar System (BARS) field of view. Similar coincident magnetic variations were observed by GOES 6, GOES 7 and SCATHA, all of which had magnetic foot points near the CANOPUS/BARS stations. SCATHA, which was located at 6 MLT, 0.5 RE earthward of GOES 7 observed the 10 min period pulsations, whereas GOES 7 did not. In addition, DMSP F6 and F8 were over-flying the region and observed characteristic precipitation and flow signatures. From this fortunate constellation of ground and space observations, we conclude that auroral omega bands are the electrodynamic signature of a corrugated current sheet (or some similar spatially localized magnetic structure) in the near-Earth geostationary magnetosphere

The Locations of Gamma-Ray Bursts Measured by COMPTEL

The COMPTEL instrument on the Compton Gamma Ray Observatory is used to measure the locations of gamma-ray bursts through direct imaging of MeV photons. In a comprehensive search, we have detected and localized 29 bursts observed between 1991 April 19 and 1995 May 31. The average location accuracy of these events is 1.25\arcdeg (1$\sigma$), including a systematic error of \sim0.5\arcdeg, which is verified through comparison with Interplanetary Network (IPN) timing annuli. The combination of COMPTEL and IPN measurements results in locations for 26 of the bursts with an average ``error box'' area of only $\sim$0.3 deg$^2$ (1$\sigma$). We find that the angular distribution of COMPTEL burst locations is consistent with large-scale isotropy and that there is no statistically significant evidence of small-angle auto-correlations. We conclude that there is no compelling evidence for burst repetition since no more than two of the events (or $\sim$7% of the 29 bursts) could possibly have come from the same source. We also find that there is no significant correlation between the burst locations and either Abell clusters of galaxies or radio-quiet quasars. Agreement between individual COMPTEL locations and IPN annuli places a lower limit of $\sim$100~AU (95% confidence) on the distance to the stronger bursts.Comment: Accepted for publication in the Astrophysical Journal, 1998 Jan. 1, Vol. 492. 33 pages, 9 figures, 5 table

Gauge Theory for the Rate Equations: Electrodynamics on a Network

Systems of coupled rate equations are ubiquitous in many areas of science, for example in the description of electronic transport through quantum dots and molecules. They can be understood as a continuity equation expressing the conservation of probability. It is shown that this conservation law can be implemented by constructing a gauge theory akin to classical electrodynamics on the network of possible states described by the rate equations. The properties of this gauge theory are analyzed. It turns out that the network is maximally connected with respect to the electromagnetic fields even if the allowed transitions form a sparse network. It is found that the numbers of degrees of freedom of the electric and magnetic fields are equal. The results shed light on the structure of classical abelian gauge theory beyond the particular motivation in terms of rate equations.Comment: 4 pages, 2 figures included, v2: minor revision, as publishe

Spectra of a recent bright burst measured by CGRO-COMPTEL: GRB 990123

CGRO-COMPTEL measures gamma-ray burst positions, time-histories and spectra in the 0.1–30 MeV energy range, in both imaging “telescope” and single detector “burst spectroscopy” mode. GRB 990123, one of the most recent bright bursts seen by COMPTEL, was caught in the optical while the gamma-ray emission was ongoing. The burst spectral shape can be characterized by a peak in ν−Fν just below 1 MeV and a power-law tail above(photon index∼−2.4,) and flattening below. There is also spectral evolution by downward movement of the peak and/or softening of the power laws. We present light-curves, time resolved spectra and an image map for this burst

Fundamental Differences Between Positive and Negative Tone Imaging

Abstract The reasons that imaging is tone-dependent come from two fundamental concepts: the aerial images of complimentary mask patterns for partially coherent projection systems are not complimentary, and the exposure reaction is highly non-linear in the concentration of the soluble species. Complimentary mask patterns are simply patterns of opposite tone. If m p (x) describes a positive mask pattern, then its complimentary mask pattern, m n (x), is given by m n (x) = 1 -m p (x). For incoherent imaging systems, complimentary mask patterns result in complimentary images; however, partially coherent imaging systems do not produce complimentary images. For a first order exposure reaction, the concentration of the photosensitive species is exponentially related to the exposure energy. However, the dependence of the concentration of developer-soluble species on exposure is different for positive and negative resist systems, resulting in different exposure properties. The net result is lithographic behavior which can vary significantly with resist tone

Pressure-driven instability in auroral images to create auroral patches

第3回極域科学シンポジウム/第36回極域宙空圏シンポジウム 11月27日（火） 国立極地研究所 2階大会議

Trace identities and their semiclassical implications

The compatibility of the semiclassical quantization of area-preserving maps with some exact identities which follow from the unitarity of the quantum evolution operator is discussed. The quantum identities involve relations between traces of powers of the evolution operator. For classically {\it integrable} maps, the semiclassical approximation is shown to be compatible with the trace identities. This is done by the identification of stationary phase manifolds which give the main contributions to the result. The same technique is not applicable for {\it chaotic} maps, and the compatibility of the semiclassical theory in this case remains unsettled. The compatibility of the semiclassical quantization with the trace identities demonstrates the crucial importance of non-diagonal contributions.Comment: LaTeX - IOP styl

The external benefits of higher education

The private market benefits of education are widely studied at the micro level, although the magnitude of their macroeconomic impact is disputed. However, there are additional benefits of education, which are less well understood. In this paper the macroeconomic effects of external benefits of higher education are estimated using the “micro-to-macro” simulation approach. Two types of externalities are explored: technology spillovers and productivity spillovers in the labour market. These links are illustrated and the results suggest they could be very large. However, this is qualified by the dearth of microeconomic evidence, for which we hope to encourage further work