The Distribution of the first Eigenvalue Spacing at the Hard Edge of the Laguerre Unitary Ensemble

The distribution function for the first eigenvalue spacing in the Laguerre unitary ensemble of finite rank random matrices is found in terms of a Painlev\'e V system, and the solution of its associated linear isomonodromic system. In particular it is characterised by the polynomial solutions to the isomonodromic equations which are also orthogonal with respect to a deformation of the Laguerre weight. In the scaling to the hard edge regime we find an analogous situation where a certain Painlev\'e \IIId system and its associated linear isomonodromic system characterise the scaled distribution. We undertake extensive analytical studies of this system and use this knowledge to accurately compute the distribution and its moments for various values of the parameter $a$. In particular choosing $a=\pm 1/2$ allows the first eigenvalue spacing distribution for random real orthogonal matrices to be computed.Comment: 65 pages, 1 eps figure, typos and references correcte

Predicting Criminal Recidivism Using "Split Population" Survival Time Models

In this paper we develop a survival time model in which the probability of eventual failure is less than one, and in which both the probability of eventual failure and the timing of failure depend (separately) on individual characteristics. We apply this model to data on the tiring of return to prison for a sample of prison releasees, and we use it to make predictions of whether or not individuals return to prison. Our predictions are more accurate than previous predictions of criminal recidivism. The model we develop has potential applications in economics: far example, it could tie used to model the probability of default and the timing of default on loans.

Wind Ensemble

Kennesaw State University School of Music presents Wind Ensemble with special guests: Harrison High School Wind Ensemble.https://digitalcommons.kennesaw.edu/musicprograms/1703/thumbnail.jp

Wind Ensemble

Kennesaw State University School of Music presents Winder Ensemble.https://digitalcommons.kennesaw.edu/musicprograms/1770/thumbnail.jp

An Electron Target for Collision Experiments with Trapped Ions

Im Rahmen dieser Arbeit wurde ein Experiment zur Untersuchung von Elektronenstößen mit gespeicherten Molekülionen aufgebaut. Hierzu wird ein in einer Falle zwischen elektrostatischen Spiegeln gespeicherter Ionenstrahl mit einer kinetischen Energie von einigen keV im rechten Winkel mit einem niederenergetischen (5-50 eV) Elektronenstrahl gekreuzt. Damit kann zum einen eine Relaxation der inneren Anregungen der Molekülionen als auch ein effienter Fragmentnachweis gewährleistet werden. Ein weiterer Vorteil des Experimentes besteht darin, daß für die Ionenspeicherung sowie für die Erzeugung und Führung des Elektronenstrahls ausschließlich elektrostatische Felder benutzt werden. Daher besteht keine Beschränkung hinsichtlich der Masse der gespeicherten Ionen. Experimente an schweren Clustern werden zuganglich. Ausgehend von Simulationsberechnungen wurde ein Elektronentarget zur Erzeugung des erforderlichen Elektronenstrahls gefertigt, welches nach ersten Testmessungen in eine bestehende Ionenfalle am Weizmann Institute of Science eingebaut wurde. Nach Inbetriebnahme und Funktionstests wurden erste Messungen von Elektronenstoßen an positiven (Ar+ und CO+) sowie negative Ionen (C-, B- und C-2 ) vorgenommen, welche die Funktionsfähigkeit dieses neuartigen Experiments belegen

Sampling Errors and Confidence Intervals for Order Statistics: Implementing the Family Support Act

The Family Support Act allows states to reimburse child care costs up to the 75th percentile of local market price for child care. States must carry out surveys to estimate these 75th percentiles. This estimation problem raises two major statistical issues: (1) picking a sample design that will allow one to estimate the percentiles cheaply, efficiently and equitably; and (2) assessing the sampling variability of the estimates obtained. For Massa- chusetts, we developed a sampling design that equalized the standard errors of the estimated percentiles across 65 distinct local markets. This design was chosen because state administrators felt public day care providers and child advocates would find it equitable, thus limiting costly appeals. Estimation of standard errors for the sample 75th percentiles requires estimation of the density of the population at the 75th percentile. We implement and compare a number of parametric and nonparametric methods of density estimation. A kernel estimator provides the most reasonable estimates. On the basis of the mean integrated squared error criterion we selected the Epanechnikov kernel and the Sheather-Jones automatic bandwidth selection procedure. Because some of our sample sizes were too small to rely on asymptotics, we also constructed nonparametric confidence intervals using the hypergeometric distrition. For most of our samples, these confidence intervals were similar to those based on the asymptotic standard errors. Substantively we find wide variation in the price of child care, depending on the child's age, type of care and geographic location. For full-time care, the 75th percentiles ranged from $242 per week for infants in child care centers in Boston to$85 per week for family day care in western Massachusetts.