Corrections to the Predicitions for Atmospheric Neutrino Observations

The theoretical Monte Carlo calculations of the production of neutrinos via cosmic rays incident upon the earth's atmosphere are examined. The calculations are sensitive to the assumed ratio of pi+ / pi- production cross sections; this ratio appears to be underestimated in the theory relative to the experimentally measured ratio. Since the neutrino detection cross section is three times larger than that for the antineutrino, the theoretical predicted detection ratio (nu_mu / nu_e) is correspondingly too large.Comment: 4 pages. HE.3.2.26 in 26th ICRC, 2, 147 (1999

Andragogy and the single session lecture: A critical reflection on the planning and delivery of a standalone postgraduate teaching event

This paper focuses on a lecture delivered each year to postgraduates within the Department of Information Science at City University. The teaching context is outlined at personal, institutional and national levels through which the challenges facing a visiting lecturer are illustrated. The relevance of andragogy to this piece is then introduced. These andragogical principles provide a framework in which to examine how the challenge of student engagement was resolved or exacerbated by the single lecture format, and how planning and delivery may also have contributed to this challenge. Engagement in the postgraduate context can be seen to depend on how well each of these principles is supported by the teaching methods used, and so realistic alterations which could be made in the future to promote deeper engagement are also considered

The limit configuration space integral for tangles and the Kontsevich integral

This article is the continuation of our first article (math/9901028). It shows how the zero-anomaly result of Yang implies the equality between the configuration space integral and the Kontsevich integral.Comment: 14 pages, 13 figure

On postcritically finite polynomials, part 1: critical portraits

We extend the work of Bielefeld, Fisher and Hubbard on Critical Portraits to the case of arbitrary postcritically finite polynomials. This determines an effective classification of postcritically finite polynomials as dynamical systems. This paper is the first in a series of two based on the author's thesis, which deals with the classification of postcritically finite polynomials. In this first part we conclude the study of critical portraits initiated by Fisher and continued by Bielefeld, Fisher and Hubbard

Quantum Mechanics Without Wavefunctions

We present a self-contained formulation of spin-free nonrelativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications - theoretical, computational, and interpretational - are discussed.Comment: 11 pages, accepted to appear in Journal of Chemical Physic

Quantum resistance standard accuracy close to the zero-dissipation state

We report on a comparison of four GaAs/AlGaAs-based quantum resistance standards using an original technique adapted from the well-known Wheatstone bridge. This work shows that the quantized Hall resistance at Landau level filling factor $\nu=2$ can be reproducible with a relative uncertainty of $32\times 10^{-12}$ in the dissipationless limit of the quantum Hall effect regime. In the presence of a very small dissipation characterized by a mean macroscopic longitudinal resistivity $\bar{R_{xx}(B)}$ of a few $\mu\Omega$, the discrepancy $\Delta R_{\mathrm{H}}(B)$ measured on the Hall plateau between quantum Hall resistors turns out to follow the so-called resistivity rule $\bar{R_{xx}(B)}=\alpha B\times d(\Delta R_{\mathrm{H}}(B))/dB$. While the dissipation increases with the measurement current value, the coefficient $\alpha$ stays constant in the range investigated ($40-120 \mathrm{\mu A}$). This result enlightens the impact of the dissipation emergence in the two-dimensional electron gas on the Hall resistance quantization, which is of major interest for the resistance metrology. The quantum Hall effect is used to realize a universal resistance standard only linked to the electron charge \emph{e} and the Planck's constant \emph{h} and it is known to play a central role in the upcoming revised \emph{Syst\`eme International} of units. There are therefore fundamental and practical benefits in testing the reproducibility property of the quantum Hall effect with better and better accuracy.Comment: 6 pages, 6 figure

Hyperbolic components in spaces of polynomial maps

We consider polynomial maps f:\C\to\C of degree $d\ge 2$, or more generally polynomial maps from a finite union of copies of \C to itself which have degree two or more on each copy. In any space \p^{S} of suitably normalized maps of this type, the post-critically bounded maps form a compact subset \cl^{S} called the connectedness locus, and the hyperbolic maps in \cl^{S} form an open set \hl^{S} called the hyperbolic connectedness locus. The various connected components H_\alpha\subset \hl^{S} are called hyperbolic components. It is shown that each hyperbolic component is a topological cell, containing a unique post-critically finite map which is called its center point. These hyperbolic components can be separated into finitely many distinct ``types'', each of which is characterized by a suitable reduced mapping schema $\bar S(f)$. This is a rather crude invariant, which depends only on the topology of $f$ restricted to the complement of the Julia set. Any two components with the same reduced mapping schema are canonically biholomorphic to each other. There are similar statements for real polynomial maps, or for maps with marked critical points.Comment: Main text by John W. Milnor, appendix by Alfredo Poirier. Fonts changed by arXiv admin to fix compilation problem (Dec2002

Bayesian variants of some classical semiparametric regression techniques

This paper develops new Bayesian methods for semiparametric inference in the partial linear Normal regression model: y=zβ+f(x)+var epsilon where f(.) is an unknown function. These methods draw solely on the Normal linear regression model with natural conjugate prior. Hence, posterior results are available which do not suffer from some problems which plague the existing literature such as computational complexity. Methods for testing parametric regression models against semiparametric alternatives are developed. We discuss how these methods can, at some cost in terms of computational complexity, be extended to other models (e.g. qualitative choice models or those involving censoring or truncation) and provide precise details for a semiparametric probit model. We show how the assumption of Normal errors can easily be relaxed

Inference on Breakdown Frontiers

Given a set of baseline assumptions, a breakdown frontier is the boundary between the set of assumptions which lead to a specific conclusion and those which do not. In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value (e.g., nonnegative) and second that the proportion of units who benefit from treatment is at least a specific value (e.g., at least 50\%). For these conclusions, we derive the breakdown frontier for two kinds of assumptions: one which indexes relaxations of the baseline random assignment of treatment assumption, and one which indexes relaxations of the baseline rank invariance assumption. These classes of assumptions nest both the point identifying assumptions of random assignment and rank invariance and the opposite end of no constraints on treatment selection or the dependence structure between potential outcomes. This frontier provides a quantitative measure of robustness of conclusions to relaxations of the baseline point identifying assumptions. We derive $\sqrt{N}$-consistent sample analog estimators for these frontiers. We then provide two asymptotically valid bootstrap procedures for constructing lower uniform confidence bands for the breakdown frontier. As a measure of robustness, estimated breakdown frontiers and their corresponding confidence bands can be presented alongside traditional point estimates and confidence intervals obtained under point identifying assumptions. We illustrate this approach in an empirical application to the effect of child soldiering on wages. We find that sufficiently weak conclusions are robust to simultaneous failures of rank invariance and random assignment, while some stronger conclusions are fairly robust to failures of rank invariance but not necessarily to relaxations of random assignment.Comment: 65 pages. 26 page supplemental appendi

Irregular Singularities in the H3+ WZW Model

We propose a definition of irregular vertex operators in the H3+ WZW model. Our definition is compatible with the duality [1] between the H3+ WZW model and Liouville theory, and we provide the explicit map between correlation functions of irregular vertex operators in the two conformal field theories. Our definition of irregular vertex operators is motivated by relations to partition functions of N=2 gauge theory and scattering amplitudes in N=4 gauge theoryComment: 31 pages, 2 figure