Cohomology of Banach algebras of operators and geometry of Banach spaces.

In the paper we give an exposition of the major results concerning the relation between first order cohomology of Banach algebras of operators on a Banach space with coefficients in specified modules and the geometry of the underlying Banach space. In particular we shall compare the properties weak amenability and amenability for Banach algebras A(X), the approximable operators on a Banach space X. Whereas amenability is a local property of the Banach space X, weak amenability is often the consequence of properties of large scale geometry.

Juxtaposition and Non-Motion: Varese Bridges Modernism and Electroacoustic Music

Edgard Vare` se’s Poe` me e´ lectronique can be viewed as a bridge between early twentieth-century modernism and electroacoustic music. This connection to early modernism is most clearly seen in its use of musical juxtaposition, a favoured technique of early modernist composers, especially those active in Paris. Juxtaposition and non-motion are considered here, particularly in relationship to Smalley’s exposition of spectromorphology (Smalley 1986), which in its preoccupation with motion omits any significant consideration of non-motion. Juxtaposition and non-motion have an important history within twentieth-century music, and as an early classic of electroacoustic music, Poe` me e´ lectronique is a particularly striking example of a composition that is rich in juxtapositions similar to those found in passages of early modernist music. Examining Poe` me e´ lectronique through the lens of juxtaposition and non-motion reveals how the organisation of its juxtaposed sounds encourages the experience of sound structure suspended time.

Explicit argumentation as a supervisory tool for decision making in child protection cases involving human rights issues

This paper addresses the problems often faced by social workers and their supervisors in decision making where human rights considerations and child protection concerns collide. High profile court cases in the United Kingdom and Europe have consistently called for social workers to convey more clarity when justifying their reasons for interfering with human rights in child protection cases. The themes emerging from these case law decisions imply that social workers need to be better at giving reasons and evidence in more explicit ways to support any actions they propose which cause interference with Convention Rights. Toulmin (1958, 1985) offers a structured approach to argumentation which may have relevance to the supervision of child protection cases when social workers and managers are required to balance these human rights considerations. One of the key challenges in this balancing act is the need for decision makers to feel confident that any interventions resulting in the interference of human rights are both justified and proportionate. Toulmin’s work has already been shown to have relevance for assisting social workers navigate pathways through cases involving competing ethical and moral demands (Osmo and Landau, 2001) and more recently to human rights and decision making in child protection (Duffy et al, 2006). Toulmin’s model takes the practitioner through a series of stages where any argument or proposed recommendation (claim) is subjected to intense critical analysis involving exposition of its strengths and weaknesses. The author therefore proposes that explicit argumentation (Osmo and Landau, 2001) may help supervisors and practitioners towards safer and more confident decision making in child protection cases involving the interference of the human rights of children and parents. In addition to highlighting the broader context of human rights currently permeating child protection decision making, the paper will include case material to practically demonstrate the application of Toulmin’s model of argumentation to the supervision context. In this way the paper adopts a strong practice approach in helping to assist practitioners with the problems and dilemmas they may come up against in decision making in complex cases.

Maximum likelihood estimation of higher-order integer-valued autoregressive processes

In this article, we extend the earlier work of Freeland and McCabe [Journal of time Series Analysis (2004) Vol. 25, pp. 701–722] and develop a general framework for maximum likelihood (ML) analysis of higher-order integer-valued autoregressive processes. Our exposition includes the case where the innovation sequence has a Poisson distribution and the thinning is binomial. A recursive representation of the transition probability of the model is proposed. Based on this transition probability, we derive expressions for the score function and the Fisher information matrix, which form the basis for ML estimation and inference. Similar to the results in Freeland and McCabe (2004), we show that the score function and the Fisher information matrix can be neatly represented as conditional expectations. Using the INAR(2) speci?cation with binomial thinning and Poisson innovations, we examine both the asymptotic e?ciency and ?nite sample properties of the ML estimator in relation to the widely used conditional least
squares (CLS) and Yule–Walker (YW) estimators. We conclude that, if the Poisson assumption can be justi?ed, there are substantial gains to be had from using ML especially when the thinning parameters are large.

Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.