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

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

Future broadband access network challenges

Copyright @ 2010 IEEEThe optical and wireless communication systems convergence will activate the potential capacity of photonic technology for providing the expected growth in interactive video, voice communication and data traffic services that are cost effective and a green communication service. The last decade growth of the broadband internet projects the number of active users will grow to over 2 billion globally by the end of 2014. Enabling the abandoned capacity of photonic signal processing is the promising solution for seamless transportation of the future consumer traffic demand. In this paper, the future traffic growth of the internet, wireless worldwide subscribers, and the end-users during the last and next decades is investigated. The challenges of the traditional access networks and Radio over Fiber solution are presented

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

Higher Equations of Motion in N = 1 SUSY Liouville Field Theory

Similarly to the ordinary bosonic Liouville field theory, in its N=1 supersymmetric version an infinite set of operator valued relations, the ``higher equations of motions'', holds. Equations are in one to one correspondence with the singular representations of the super Virasoro algebra and enumerated by a couple of natural numbers $(m,n)$. We demonstrate explicitly these equations in the classical case, where the equations of type $(1,n)$ survive and can be interpreted directly as relations for classical fields. General form of the higher equations of motion is established in the quantum case, both for the Neveu-Schwarz and Ramond series.Comment: Two references adde

Numerical solution of the two-dimensional Helmholtz equation with variable coefficients by the radial integration boundary integral and integro-differential equation methods

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2012 Taylor & Francis.This paper presents new formulations of the boundary–domain integral equation (BDIE) and the boundary–domain integro-differential equation (BDIDE) methods for the numerical solution of the two-dimensional Helmholtz equation with variable coefficients. When the material parameters are variable (with constant or variable wave number), a parametrix is adopted to reduce the Helmholtz equation to a BDIE or BDIDE. However, when material parameters are constant (with variable wave number), the standard fundamental solution for the Laplace equation is used in the formulation. The radial integration method is then employed to convert the domain integrals arising in both BDIE and BDIDE methods into equivalent boundary integrals. The resulting formulations lead to pure boundary integral and integro-differential equations with no domain integrals. Numerical examples are presented for several simple problems, for which exact solutions are available, to demonstrate the efficiency of the proposed methods