A Simulation Estimator for Testing the Time Homogeneity of Credit Rating Transition

The measurement of credit quality is at the heart of the models designed to assess the reserves and capital needed to support the risks of both individual credits and portfolios of credit instruments. A popular specification for credit- rating transitions is the simple, time-homogeneous Markov model. While the Markov specification cannot really describe processes in the long run, it may be useful for adequately describing short-run changes in portfolio risk. In this specification, the entire stochastic process can be characterized in terms of estimated transition probabilities. However, the simple homogeneous Markovian transition framework is restrictive. We propose a test of the null hypotheses of time-homogeneity that can be performed on the sorts of data often reported. We apply the tests to 4 data sets, on commercial paper, sovereign debt, municipal bonds and S&P Corporates. The results indicate that commercial paper looks Markovian on a 30-day time scale for up to 6 months; sovereign debt also looks Markovian (perhaps due to a small sample size); municipals are well-modeled by the Markov specification for up to 5 years, but could probably benefit from frequent updating of the estimated transition matrix or from more sophisticated modeling, and S&P Corporate ratings are approximately Markov over 3 transitions but not 4.

Evaluating some computer enhancement algorithms that improve the visibility of cometary morphology

The observed morphology of cometary comae is determined by ejection circumstances and the interaction of the ejected material with the local environment. Anisotropic emission can provide useful information on such things as orientation of the nucleus, location of active areas on the nucleus, and the formation of ion structure near the nucleus. However, discrete coma features are usually diffuse, of low amplitude, and superimposed on a steep intensity gradient radial to the nucleus. To improve the visibility of these features, a variety of digital enhancement algorithms were employed with varying degrees of success. They usually produce some degree of spatial filtering, and are chosen to optimize visibility of certain detail. Since information in the image is altered, it is important to understand the effects of parameter selection and processing artifacts can have on subsequent interpretation. Using the criteria that the ideal algorithm must enhance low contrast features while not introducing misleading artifacts (or features that cannot be seen in the stretched, unprocessed image), the suitability of various algorithms that aid cometary studies were assessed. The strong and weak points of each are identified in the context of maintaining positional integrity of features at the expense of photometric information

Specification and Informational Issues in Credit Scoring

Lenders use rating and scoring models to rank credit applicants on their expected performance. The models and approaches are numerous. We explore the possibility that estimates generated by models developed with data drawn solely from extended loans are less valuable than they should be because of selectivity bias. We investigate the value of "reject inference"--methods that use a rejected applicant's characteristics, rather than loan performance data, in scoring model development. In the course of making this investigation, we also discuss the advantages of using parametric as well as nonparametric modeling. These issues are discussed and illustrated in the context of a simple stylized model.

Gravitational Radiation from Black Hole Binaries in Globular Clusters

A populations of stellar mass black hole binaries may exist in globular clusters. The dynamics of globular cluster evolution imply that there may be at most one black hole binary is a globular cluster. The population of binaries are expected to have orbital periods greater than a few hours and to have a thermal distribution of eccentricities. In the LISA band, the gravitational wave signal from these binaries will consist of several of the higher harmonics of the orbital frequency. A Monte Carlo simulation of the galactic globular cluster system indicates that LISA will detect binaries in 10 % of the clusters with an angular resolution sufficient to identify the host cluster of the binary.Comment: 7 pages, 2 eps figures, uses iopart styl

Effects of anode material on arcjet performance

Anodes fabricated from four different materials were tested in a modular arcjet thruster at 1 kW power level on nitrogen/hydrogen mixtures. A two-percent thoriated tungsten anode served as the control. Graphite was chosen for its ease in fabrication, but experienced severe erosion in the constrictor and diverging side. Hafnium carbide and lanthanum hexaboride were chosen for their low work functions but failed due to thermal stress and reacted with the propellant. When compared to the thoriated tungsten nozzle, thruster performance was significantly lower for the lanthanum hexaboride insert and the graphite nozzle, but was slightly higher for the hafnium carbide nozzle. Both the lanthanum hexaboride and hafnium carbide nozzle operated at higher voltages. An attempt was made to duplicate higher performance hafnium carbide results, but repeated attempts at machining a second anode insert were unsuccessful. Graphite, hafnium carbide, and lanthanum hexaboride do not appear viable anode materials for low power arcjet thrusters

Self-Similar Graphs

For any graph $G$ on $n$ vertices and for any {\em symmetric} subgraph $J$ of $K_{n,n}$, we construct an infinite sequence of graphs based on the pair $(G,J)$. The First graph in the sequence is $G$, then at each stage replacing every vertex of the previous graph by a copy of $G$ and every edge of the previous graph by a copy of $J$ the new graph is constructed. We call these graphs {\em self-similar} graphs. We are interested in delineating those pairs $(G,J)$ for which the chromatic numbers of the graphs in the sequence are bounded. Here we have some partial results. When $G$ is a complete graph and $J$ is a special matching we show that every graph in the resulting sequence is an {\em expander} graph.Comment: 13 pages, 1 tabl

Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses

We test for the existence of a spin-glass phase transition, the de Almeida-Thouless line, in an externally-applied (random) magnetic field by performing Monte Carlo simulations on a power-law diluted one-dimensional Ising spin glass for very large system sizes. We find that an Almeida-Thouless line only occurs in the mean field regime, which corresponds, for a short-range spin glass, to dimension d larger than 6.Comment: 4 pages, 2 figures, 1 tabl

On the rotating wave approximation in the adiabatic limit

I revisit a longstanding question in quantum optics; When is the rotating wave approximation justified? In terms of the Jaynes-Cummings and Rabi models I demonstrate that the approximation in general breaks down in the adiabatic limit regardless of system parameters. This is explicitly shown by comparing Berry phases of the two models, where it is found that this geometrical phase is strictly zero in the Rabi model contrary to the non-trivial Berry phase of the Jaynes-Cummings model. The source of this surprising result is traced back to different topologies in the two models.Comment: 8 pages, 3 figure

Dilute gas of ultracold two-level atoms inside a cavity; generalized Dicke model

We consider a gas of ultracold two-level atoms confined in a cavity, taking into account for atomic center-of-mass motion and cavity mode variations. We use the generalized Dicke model, and analyze separately the cases of a Gaussian, and a standing wave mode shape. Owing to the interplay between external motional energies of the atoms and internal atomic and field energies, the phase-diagrams exhibit novel features not encountered in the standard Dicke model, such as the existence of first and second order phase transitions between normal and superradiant phases. Due to the quantum description of atomic motion, internal and external atomic degrees of freedom are highly correlated leading to modified normal and superradiant phases.Comment: 10 pages, 7 figure