Height growth of solutions and a discrete Painlev\'e equation

Consider the discrete equation $$y_{n+1}+y_{n-1}=\frac{a_n+b_ny_n+c_ny_n^2}{1-y_n^2},$$ where the right side is of degree two in $y_n$ and where the coefficients $a_n$, $b_n$ and $c_n$ are rational functions of $n$ with rational coefficients. Suppose that there is a solution such that for all sufficiently large $n$, $y_n\in\mathbb{Q}$ and the height of $y_n$ dominates the height of the coefficient functions $a_n$, $b_n$ and $c_n$. We show that if the logarithmic height of $y_n$ grows no faster than a power of $n$ then either the equation is a well known discrete Painlev\'e equation ${\rm dP}_{\!\rm II}$ or its autonomous version or $y_n$ is also an admissible solution of a discrete Riccati equation. This provides further evidence that slow height growth is a good detector of integrability.Comment: 26 page

An investigation into international business collaboration in higher education organisations: a case study of international partnerships in four UK leading universities

Purpose - The purpose of this paper is to develop a comparative analysis of the main objectives of international institutional partnerships in four UK leading universities. Based on the presented case studies, the paper outlines a model for objectives and implementation of international partnership. Design/methodology/approach - Using a multiple case study approach, the paper employs three sources of data: templates of international partnerships, actual agreements of international partnerships and interviews with senior and very senior managers concerned with internationalisation at the four universities. The analysis includes inter-university comparative analysis and templates-agreements-interviews comparative analysis for each of the four universities separately. Findings - It is found that, for the four universities, the objectives of international partnerships are related to both students and staff with relative importance given to the student dimension. While the student dimension refers to any overseas partnerships where the core topic of the partnership is the student whether it is related to student exchange, collaborative programs, student recruitment, etc.; the staff dimension refers to any overseas partnerships that are more related to the staff topic, such as joint research, collaborative teaching, staff exchange, etc

A Numerical Test of a High-Penetrability Approximation for the One-Dimensional Penetrable-Square-Well Model

The one-dimensional penetrable-square-well fluid is studied using both analytical tools and specialized Monte Carlo simulations. The model consists of a penetrable core characterized by a finite repulsive energy combined with a short-range attractive well. This is a many-body one-dimensional problem, lacking an exact analytical solution, for which the usual van Hove theorem on the absence of phase transition does not apply. We determine a high-penetrability approximation complementing a similar low-penetrability approximation presented in previous work. This is shown to be equivalent to the usual Debye-H\"{u}ckel theory for simple charged fluids for which the virial and energy routes are identical. The internal thermodynamic consistency with the compressibility route and the validity of the approximation in describing the radial distribution function is assessed by a comparison against numerical simulations. The Fisher-Widom line separating the oscillatory and monotonic large-distance behavior of the radial distribution function is computed within the high-penetrability approximation and compared with the opposite regime, thus providing a strong indication of the location of the line in all possible regimes. The high-penetrability approximation predicts the existence of a critical point and a spinodal line, but this occurs outside the applicability domain of the theory. We investigate the possibility of a fluid-fluid transition by Gibbs ensemble Monte Carlo techniques, not finding any evidence of such a transition. Additional analytical arguments are given to support this claim. Finally, we find a clustering transition when Ruelle's stability criterion is not fulfilled. The consequences of these findings on the three-dimensional phase diagrams are also discussed.Comment: 17 pages, 12 figures; to be published in JC

RAPD PCR Confirms Absence of Genetic Variation Between Insecticide Resistant Variants of the Green Peach Aphid, \u3ci\u3eMyzus Persicae\u3c/i\u3e (Homoptera: Aphididae)

Previous allozyme analysis has revealed an apparent absence of enzyme variability in the green peach aphid, Myzus persicae (Sulzer). We are interested in determining the genetic relatedness of individual M persicae clones carrying different numbers of esterase 4 (E4) gene copies conferring resistance to insecticides, in order to determine how many times and in what geographic locations resistance via gene duplication may have evolved. We have therefore extended the analysis of genetic variability in M. persicae to the DNA level using random amplification of polymorphic DNA (RAPD) with single 10 mer oligonucleotide primers. Here we report a lack of variability be- tween resistant clones in Wisconsin populations even at the DNA level Further, \u27fast\u27 E4 (FE4) variants appear to be absent from Wisconsin populations, despite FE4 variants of moderate resistance (Rl) being the most common clones in the United Kingdom. These results suggest that resistance in M. persicae may have evolved a very few times and that North American populations may differ from those in Europe by founder effects

Consumer confidence indeces and short-term forecasting of consumption

Recently there has been growing interest in examining the potential shortterm link between survey-based confidence indicators and real economic activity, notably for macroeconomic policy making. This paper builds on previous studies to establish whether there is a short-term predictive relationship between measures of consumer confidence and actual consumption, that could be used for forecasting, in a range of major industrial countries. It then extends such previous analyses by assessing whether this relation has changed over time, and whether we can attribute any time-varying relation to structural developments in the economy, such as financial deepening and the increasing role of house prices in determination of consumption

Predicting protein function by machine learning on amino acid sequences – a critical evaluation

Copyright @ 2007 Al-Shahib et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Background: Predicting the function of newly discovered proteins by simply inspecting their amino acid sequence is one of the major challenges of post-genomic computational biology, especially when done without recourse to experimentation or homology information. Machine learning classifiers are able to discriminate between proteins belonging to different functional classes. Until now, however, it has been unclear if this ability would be transferable to proteins of unknown function, which may show distinct biases compared to experimentally more tractable proteins. Results: Here we show that proteins with known and unknown function do indeed differ significantly. We then show that proteins from different bacterial species also differ to an even larger and very surprising extent, but that functional classifiers nonetheless generalize successfully across species boundaries. We also show that in the case of highly specialized proteomes classifiers from a different, but more conventional, species may in fact outperform the endogenous species-specific classifier. Conclusion: We conclude that there is very good prospect of successfully predicting the function of yet uncharacterized proteins using machine learning classifiers trained on proteins of known function

Consumer confidence indices and short-term forecasting of consumption

Recently there has been growing interest in examining the potential shortterm link between survey-based confidence indicators and real economic activity, notably for macroeconomic policy making. This paper builds on previous studies to establish whether there is a short-term predictive relationship between measures of consumer confidence and actual consumption, that could be used for forecasting, in a range of major industrial countries. It then extends such previous analyses by assessing whether this relation has changed over time, and whether we can attribute any time-varying relation to structural developments in the economy, such as financial deepening and the increasing role of house prices in determination of consumption