A random walk version of Robbins' problem: small horizon

In Robbins' problem of minimizing the expected rank, a finite sequence of $n$ independent, identically distributed random variables are observed sequentially and the objective is to stop at such a time that the expected rank of the selected variable (among the sequence of all $n$ variables) is as small as possible. In this paper we consider an analogous problem in which the observed random variables are the steps of a symmetric random walk. Assuming continuously distributed step sizes, we describe the optimal stopping rules for the cases $n=2$ and $n=3$ in two versions of the problem: a "full information" version in which the actual steps of the random walk are disclosed to the decision maker; and a "partial information" version in which only the relative ranks of the positions taken by the random walk are observed. When $n=3$, the optimal rule and expected rank depend on the distribution of the step sizes. We give sharp bounds for the optimal expected rank in the partial information version, and fairly sharp bounds in the full information version.Comment: 18 pages, 2 table

Managing the circulation of banknotes

Issuing banknotes is one of the Bank of England’s best known and most recognisable functions. To maintain confidence in the physical currency, genuine notes must be available to meet public demand. This article explains how the note circulation is managed to maintain this confidence. The Bank’s role in this has changed considerably over the past 50 years with technological innovations and as the involvement of the commercial sector has grown. The Bank’s response to future developments will continue to be consistent with its objective of ensuring the availability of genuine notes of good quality in a balanced mix of denominations.

Charged Vortex Dynamics in Ginzburg-Landau Theory of the Fractional Quantum Hall Effect

We write a Ginzburg-Landau Hamiltonian for a charged order parameter interacting with a background electromagnetic field in 2+1 dimensions. Using the method of Lund we derive a collective coordinate action for vortex defects in the order parameter and demonstrate that the vortices are charged. We examine the classical dynamics of the vortices and then quantize their motion, demonstrating that their peculiar classical motion is a result of the fact that the quantum motion takes place in the lowest Landau level. The classical and quantum motion in two dimensional regions with boundaries is also investigated. The quantum theory is not invariant under magnetic translations. Magnetic translations add total time derivative terms to the collective action, but no extra constants of the motion result.Comment: 28 pages + 1 Figure, new phyzzx macro (included), MAD/TH-92-0

Prevalence and predictors of refractive error and spectacle coverage in Nakuru, Kenya: a cross-sectional, population-based study.

A cross-sectional study was undertaken in Nakuru, Kenya to assess the prevalence of refractive error and the spectacle coverage in a population aged ≥50 years. Of the 5,010 subjects who were eligible, 4,414 underwent examination (response rate 88.1 %). LogMAR visual acuity was assessed in all participants and refractive error was measured in both eyes using a Topcon auto refractor RM8800. Detailed interviews were undertaken and ownership of spectacles was assessed. Refractive error was responsible for 51.7 % of overall visual impairment (VI), 85.3 % (n = 191) of subjects with mild VI, 42.7 % (n = 152) of subjects with moderate VI, 16.7 % (n = 3) of subjects with severe VI and no cases of blindness. Myopia was more common than hyperopia affecting 59.5 % of those with refractive error compared to 27.4 % for hyperopia. High myopia (+5.0 DS). Of those who needed distance spectacles (spectacle coverage), 25.5 % owned spectacles. In conclusion, the oldest, most poor and least educated are most likely to have no spectacles and they should be specifically targeted when refractive services are put in place

High altitude climbers as ethnomethodologists making sense of cognitive dissonance: ethnographic insights from an attempt to scale Mt Everest

This ethnographic study examined how a group of high altitude climbers (N = 6)drew on ethnomethodological principles (the documentary method of interpretation, reflexivity, indexicality, and membership) to interpret their experiences of cognitive dissonance during an attempt to scale Mt. Everest. Data were collected via participant observation, interviews, and a field diary. Each data source was subjected to a content mode of analysis. Results revealed how cognitive dissonance reduction is accomplished from within the interaction between a pattern of self-justification and self-inconsistencies; how the reflexive nature of cognitive dissonance is experienced; how specific features of the setting are inextricably linked to the cognitive dissonance experience; and how climbers draw upon a shared stock of knowledge in their experiences with cognitive dissonance

Differences In Cultural Perception In Websites

The goal of this research was to determine what elements of websites are tied to the value of individualism and collectivism when viewed by two different national cultures. The research determined whether two participant groups (United States or Chinese) looked at the same or different website elements when experiencing the website. The Website Experience Analysis protocol was used to create a questionnaire that the students filled out as they experienced the website, allowing the researcher to determine what elements of the website they were experiencing when focusing on a particular cultural or organization-public relation value. This research found that culture did have an impact on how a public perceives a website. However, this impact was not the same as what other current research would imply. It also found that website elements may be used to counter this cultural bias, and provides insight into precisely what elements can be utilized to do so