Orthonormal Polynomials on the Unit Circle and Spatially Discrete Painlev\'e II Equation

We consider the polynomials $\phi_n(z)= \kappa_n (z^n+ b_{n-1} z^{n-1}+ >...)$ orthonormal with respect to the weight $\exp(\sqrt{\lambda} (z+ 1/z)) dz/2 \pi i z$ on the unit circle in the complex plane. The leading coefficient $\kappa_n$ is found to satisfy a difference-differential (spatially discrete) equation which is further proved to approach a third order differential equation by double scaling. The third order differential equation is equivalent to the Painlev\'e II equation. The leading coefficient and second leading coefficient of $\phi_n(z)$ can be expressed asymptotically in terms of the Painlev\'e II function.Comment: 16 page

Differential Equations for Dyson Processes

We call "Dyson process" any process on ensembles of matrices in which the entries undergo diffusion. We are interested in the distribution of the eigenvalues (or singular values) of such matrices. In the original Dyson process it was the ensemble of n by n Hermitian matrices, and the eigenvalues describe n curves. Given sets X_1,...,X_m the probability that for each k no curve passes through X_k at time \tau_k is given by the Fredholm determinant of a certain matrix kernel, the extended Hermite kernel. For this reason we call this Dyson process the Hermite process. Similarly, when the entries of a complex matrix undergo diffusion we call the evolution of its singular values the Laguerre process, for which there is a corresponding extended Laguerre kernel. Scaling the Hermite process at the edge leads to the Airy process and in the bulk to the sine process; scaling the Laguerre process at the edge leads to the Bessel process. Generalizing and strengthening earlier work, we assume that each X_k is a finite union of intervals and find for the Airy process a system of partial differential equations, with the end-points of the intervals of the X_k as independent variables, whose solution determines the probability that for each k no curve passes through X_k at time \tau_k. Then we find the analogous systems for the Hermite process (which is more complicated) and also for the sine process. Finally we find an analogous system of PDEs for the Bessel process, which is the most difficult.Comment: 36 pages, LaTeX. Version 3 corrects an error in the earlier version

The distribution of trimoraic syllables in German and English as evidence for the phonological word

In the present article I discuss the distribution of trimoraic syllables in German and English. The reason I have chosen to analyze these two languages together is that the data in both languages are strikingly similar. However, although the basic generalization in (1) holds for both German and English, we will see below that trimoraic syllabIes do not have an identical distribution in both languages. In the present study I make the following theoretical claims. First, I argue that the three environments in (1) have a property in common: they all describe the right edge of a phonological word (or prosodic word; henceforth pword). From a formal point of view, I argue that a constraint I dub the THIRD MORA RESTRICTION (henceforth TMR), which ensures that trimoraic syllables surface at the end of a pword, is active in German and English. According to my proposal trimoraic syllables cannot occur morpheme-internally because monomorphemic grammatical words like garden are parsed as single pwords. Second, I argue that the TMR refers crucially to moraic structure. In particular, underlined strings like the ones in (1) will be shown to be trimoraic; neither skeletal positions nor the subsyllabic constituent rhyme are necessary. Third, the TMR will be shown to be violated in certain (predictable) pword-internal cases, as in Monde and chamber; I account for such facts in an OptimalityTheoretic analysis (henceforth OT; Prince & Smolensky 1993) by ranking various markedness constraints among themselves or by ranking them ahead of the TMR. Fourth, I hold that the TMR describes a concrete level of grammar, which I refer to below as the 'surface' representation. In this respect, my treatment differs significantly from the one proposed for English by Borowsky (1986, 1989), in which the English facts are captured in a Lexical Phonology model by ordering the relevant constraint at level 1 in the lexicon

Rethinking High School: An Introduction to New York City's Experience

Provides a review of the small school movement in New York City and highlights the early successes achieved at Marble Hill School for International Studies, located in the Bronx

On ASEP with Step Bernoulli Initial Condition

This paper extends results of earlier work on ASEP to the case of step Bernoulli initial condition. The main results are a representation in terms of a Fredholm determinant for the probability distribution of a fixed particle, and asymptotic results which in particular establish KPZ universality for this probability in one regime. (And, as a corollary, for the current fluctuations.)Comment: 16 pages. Revised version adds references and expands the introductio

Talking Trash: Valuing Household Preferences for Garbage and Recycling Services Bundles Using a Discrete Choice Experiment

Facing increasing costs for tipping fees and worker salaries, many smaller municipalities have begun to explore ways to adopt mechanized pay-as-you throw container garbage collection and changes to the basket of currently provided services, such as the addition of curbside recycling. Choice-experiments, while used widely in marketing, have not often been applied to environmental policy issues such as municipal waste. Using a discrete choice experiment offers a new way to examine the basket of services cities provide in waste collection given limited budgets and often vocal opposition to change among residents. A discrete choice model is developed to test household preferences for municipal waste services in Stillwater, Oklahoma. In addition, the study compares the willingness to pay estimates for adding curbside recycling service from the discrete choice model ($1.98/household/month) with results from an embedded contingent valuation question ($1.35/household/month). The survey shows that residents are willing give up one of two weekly garbage days to obtain weekly curbside recyclable collection. Furthermore, women are willing to willing to pay more than men for curbside collection of recyclables.Consumer/Household Economics,

A Red Tide Monitoring Program for Texas Coastal Waters

This is the final report for the red tide monitoring project conducted at The University of Texas at Austin Marine Science Institute (UTMSI) and covers the period from 1 Nov. 1998 to 10 April 2000. The study was designed to examine the seasonal dynamics of the toxic red tide dinoflagellate Karenia brevis (Davis) G. Hansen and Moestrup at 5 locations off the Texas coast. The work was conducted in collaboration with the Texas Parks and Wildlife Department (TPWD) utilizing bimonthly finfish surveys (Coastal Fisheries Division) to collect samples. The samples were shipped to UTMSI for chl a, nutrient, and cell count analyses. Significant interannual variability occurred in the temperature and salinity fields. Temperature was lowest in Jan.-Feb. of each year and increased. In general, the 5 stations showed little concordance with each other. There was no annual pattern in nutrient distributions. Individual stations appeared to reflect local inputs, rather than coast wide events. The only exception was a generalized silicate increase noted in Feb-April 2001 at all stations except Brazos Santiago near Brownsville. Karenia brevis was observed sporadically along the coast during the winter and most observations were limited to the summer/fall months. The sporadic occurrences and numerous "no cells" observations do not support the hypothesis that a year round resident red tide population exists in the Texas coastal zone. It appears that are transported into the area by large scale oceanographic features. The mechanism for this remains unknown. A minor red tide occurred along South Padre Island in Oct./Nov 1999. The bloom advected south into Mexico, and no further fish kills were noted in 1999. However, K. brevis occurred sporadically along the coast during this time. These events suggest that K. brevis may be seeded into the area from further offshore regularly at very low levels. Until fish-killing populations develop, it likely remains undetected. One major red tide event occurred during 2000 that affected the entire Texas coast. A small red tide occurred along South Padre Island in July, 2000 but disappeared after moving north to Padre Island National Seashore. Fish-killing concentrations of K. brevis were first detected in mid August off Sabine Pass in the north and moved south along the coast over the following months. However, low level occurrences of K. brevis were found at intermediate stations well before the main red tide advected into the region, and were nearly coincident with the initial observations off Sabine Pass. It is impossible from this data to determine if the July bloom in south Texas was related to the events off Sabine, but there is a possibility that offshore continental shelf currents may well be transporting cells north from Mexico into northern Texas waters. Another toxic species closely related to K. brevis has been seen at reasonably high abundance. This species, Karenia mikimotoi, is toxic to fish and has been reported to co-occur with K. brevis in blooms. Maximum abundance of this species was 6000 cells L-1, and appeared to exhibit a distinct increase and decline in population levels at 3 different stations.Marine Scienc

Correlation Functions, Cluster Functions and Spacing Distributions for Random Matrices

The usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants. From this representation one can deduce formulas for spacing probabilities in terms of Fredholm determinants of matrix-valued kernels. The derivations of the various formulas are somewhat involved. In this article we present a direct approach which leads immediately to scalar kernels for unitary ensembles and matrix kernels for the orthogonal and symplectic ensembles, and the representations of the correlation functions, cluster functions and spacing distributions in terms of them.Comment: 22 pages. LaTeX file. Minor correctio