Binary words avoiding xx^Rx and strongly unimodal sequences

In previous work, Currie and Rampersad showed that the growth of the number of binary words avoiding the pattern xxx^R was intermediate between polynomial and exponential. We now show that the same holds for the growth of the number of binary words avoiding the pattern xx^Rx. Curiously, the analysis for xx^Rx is much simpler than that for xxx^R. We derive our results by giving a bijection between the set of binary words avoiding xx^Rx and a class of sequences closely related to the class of "strongly unimodal sequences."Comment: 4 page

Mean field analysis of Williams-Bjerknes type growth

We investigate a class of stochastic growth models involving competition between two phases in which one of the phases has a competitive advantage. The equilibrium populations of the competing phases are calculated using a mean field analysis. Regression probabilities for the extinction of the advantaged phase are calculated in a leading order approximation. The results of the calculations are in good agreement with simulations carried out on a square lattice with periodic boundaries. The class of models are variants of the Williams- Bjerknes model for the growth of tumours in the basal layer of an epithelium. In the limit in which only one of the phases is unstable the class of models reduces to the well known variants of the Eden model.Comment: 21 pages, Latex2e, Elsevier style, 5 figure

Investigating Trajectories of Social Recovery in Individuals with First Episode Psychosis:A Latent Class Growth Analysis

Background Social disability is a hallmark of severe mental illness yet individual differences and factors predicting outcome are largely unknown. Aim To explore trajectories and predictors of social recovery following a first episode of psychosis (FEP). Method A sample of 764 individuals with FEP were assessed on entry into early intervention in psychosis (EIP) services and followed up over 12 months. Social recovery profiles were examined using latent class growth analysis. Results Three types of social recovery profile were identified: Low Stable (66%), Moderate-Increasing (27%), and High-Decreasing (7%). Poor social recovery was predicted by male gender, ethnic minority status, younger age at onset of psychosis, increased negative symptoms, and poor premorbid adjustment. Conclusions Social disability is prevalent in FEP, although distinct recovery profiles are evident. Where social disability is present on entry into EIP services it can remain stable, highlighting a need for targeted intervention. Declaration of interest Non

Diffusion Limited Aggregation with Power-Law Pinning

Using stochastic conformal mapping techniques we study the patterns emerging from Laplacian growth with a power-law decaying threshold for growth $R_N^{-\gamma}$ (where $R_N$ is the radius of the $N-$ particle cluster). For $\gamma > 1$ the growth pattern is in the same universality class as diffusion limited aggregation (DLA) growth, while for $\gamma < 1$ the resulting patterns have a lower fractal dimension $D(\gamma)$ than a DLA cluster due to the enhancement of growth at the hot tips of the developing pattern. Our results indicate that a pinning transition occurs at $\gamma = 1/2$, significantly smaller than might be expected from the lower bound $\alpha_{min} \simeq 0.67$ of multifractal spectrum of DLA. This limiting case shows that the most singular tips in the pruned cluster now correspond to those expected for a purely one-dimensional line. Using multifractal analysis, analytic expressions are established for $D(\gamma)$ both close to the breakdown of DLA universality class, i.e., $\gamma \lesssim 1$, and close to the pinning transition, i.e., $\gamma \gtrsim 1/2$.Comment: 5 pages, e figures, submitted to Phys. Rev.

Linearity-Generating Processes: A Modelling Tool Yielding Closed Forms for Asset Prices

This methodological paper presents a class of stochastic processes with appealing properties for theoretical or empirical work in finance and macroeconomics, the "linearity-generating" class. Its key property is that it yields simple exact closed-form expressions for stocks and bonds, with an arbitrary number of factors. It operates in discrete and continuous time. It has a number of economic modeling applications. These include macroeconomic situations with changing trend growth rates, or stochastic probability of disaster, asset pricing with stochastic risk premia or stochastic dividend growth rates, and yield curve analysis that allows flexibility and transparency. Many research questions may be addressed more simply and in closed form by using the linearity-generating class.

Business Employment Dynamics: Tabulations by Employer Size

The gross job gains and gross job loss statistics from the BLS Business Employment Dynamics (BED) program measure the large gross job flows that underlie the quarterly net change in employment. In the fourth quarter of 2004, employment grew by 869,000 jobs. This growth is the sum of 8.1 million gross job gains from opening and expanding establishments, and 7.2 million gross job losses from contracting and closing establishments. The new BED data have captured the attention of economists and policymakers across the country, and these data are becoming a major contributor to our understanding of employment growth and business cycles in the U.S. economy. Following the initial release of the BED data in September 2003, the BED data series expanded in May 2004 with the release of industry statistics. The BLS then began work on tabulations by size class. The production of size-class statistics is a complex task involving several economic and statistical issues. Although it is trivial to classify a business into a size class in any given quarter, it is difficult to classify a business into a size class for a longitudinal analysis of employment growth. Several different classifications exist, and many of these possible classifications have appealing theoretical and statistical properties. Furthermore, these alternative classification methodologies result in sharply different portraits of employment growth by size class. In this article, we discuss the alternative statistical methodologies that the BLS considered for creating size class tabulations from the Business Employment Dynamics data. Our primary focus is on four methodologies: quarterly base-sizing, annual base-sizing, mean-sizing, and dynamic-sizing. We discuss the evaluation criteria that BLS considered for choosing its official size class methodology.gross job gains; gross job losses; business employment dynamics; size-class statistics; dynamic-sizing