Periodic Reordering

For many networks in nature, science and technology, it is possible to order the nodes so that most links are short-range, connecting near-neighbours, and relatively few long-range links, or shortcuts, are present. Given a network as a set of observed links (interactions), the task of finding an ordering of the nodes that reveals such a range-dependent structure is closely related to some sparse matrix reordering problems arising in scientific computation. The spectral, or Fiedler vector, approach for sparse matrix reordering has successfully been applied to biological data sets, revealing useful structures and subpatterns. In this work we argue that a periodic analogue of the standard reordering task is also highly relevant. Here, rather than encouraging nonzeros only to lie close to the diagonal of a suitably ordered adjacency matrix, we also allow them to inhabit the off-diagonal corners. Indeed, for the classic small-world model of Watts & Strogatz (1998, Collective dynamics of ‘small-world’ networks. Nature, 393, 440–442) this type of periodic structure is inherent. We therefore devise and test a new spectral algorithm for periodic reordering. By generalizing the range-dependent random graph class of Grindrod (2002, Range-dependent random graphs and their application to modeling large small-world proteome datasets. Phys. Rev. E, 66, 066702-1–066702-7) to the periodic case, we can also construct a computable likelihood ratio that suggests whether a given network is inherently linear or periodic. Tests on synthetic data show that the new algorithm can detect periodic structure, even in the presence of noise. Further experiments on real biological data sets then show that some networks are better regarded as periodic than linear. Hence, we find both qualitative (reordered networks plots) and quantitative (likelihood ratios) evidence of periodicity in biological networks.

Dipole modes on open periodic structures — an experimental study

An experimental study is made of the lower pass-band of waveguides built as necklaces of oblate spheroids. Short lengths of guide are tested in open resonators. The dominant mode is found to be a glow-wave dipole type having no low-frequency cut off. High Q factors indicate low attenuations. Perturbation measurements demonstrate this energy to be concentrated in the vicinity of the guide.

Decoupling EU farm support: Does the new single payment scheme fit within the green box?

Recent reform of the EU’s Common Agricultural Policy (CAP) has led to a further decoupling of farm support. The EU believes that the new Single Payment Scheme, which replaces the former system of area and headage payments to farmers, tied to production, will qualify for green-box status in the WTO. We examine this contention, particularly in light of the recent WTO panel report on upland cotton.

Implications for food production, land use and rural development of the European Union's Single Farm Payment: Indications from a survey of farmers' intentions in Germany, Portugal and the UK

The 2003 reform of the European Union's (EU) Common Agricultural Policy introduced a decoupled income support for farmers called the Single Farm Payment (SFP). Concerns were raised about possible future land use and production changes and their impact on rural communities. Here, such concerns are considered against the workings of the SFP in three EU Member States. Various quantitative studies that have determined the likely impact of the SFP within the EU and the study countries are reviewed. We present the results of a farm survey conducted in the study countries in which farmers' responses to a decoupling scenario similar to the SFP were sought. We found that little short-term change was proposed in the three, rather different, study countries with only 30% of the farmers stating that they would alter their mix of farm activities. Furthermore, less than 30% of all respondents in each country would idle any land under decoupling. Of those who would adopt a new activity, the most popular choices were forestry, woodland and non-food crops. (c) 2007 Elsevier Ltd. All rights reserved.

The periodic table: Molybdenum

Chemical & Engineering News celebrates the Periodic Table of the Elements on the magazine's 80th anniversary.

Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing

We study the numerical efficiency of solving the self-consistent field theory (SCFT) for periodic block-copolymer morphologies by combining the spectral method with Anderson mixing. Using AB diblock-copolymer melts as an example, we demonstrate that this approach can be orders of magnitude faster than competing methods, permitting precise calculations with relatively little computational cost. Moreover, our results raise significant doubts that the gyroid (G) phase extends to infinite $\chi N$. With the increased precision, we are also able to resolve subtle free-energy differences, allowing us to investigate the layer stacking in the perforated-lamellar (PL) phase and the lattice arrangement of the close-packed spherical (S$_{cp}$) phase. Furthermore, our study sheds light on the existence of the newly discovered Fddd (O$^{70}$) morphology, showing that conformational asymmetry has a significant effect on its stability.

On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities

We prove that all the eigenvalues of a certain highly non-self-adjoint Sturm–Liouville differential operator are real. The results presented are motivated by and extend those recently found by various authors (Benilov et al. (2003) [3], Davies (2007) [7] and Weir (2008) [18]) on the stability of a model describing small oscillations of a thin layer of fluid inside a rotating cylinder.

On a class of nonselfadjoint periodic boundary value problems with discrete real spectrum

In a previous paper (J. of Differential Equations, Vol. 249 (2010), 3081-3098) we examined a family of periodic Sturm-Liouville problems with boundary and interior singularities which are highly non-self-adjoint but have only real eigenvalues. We now establish Schatten class properties of the associated resolvent operator.

Steady periodic water waves with constant vorticity: regularity and local bifurcation

This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential equation for a periodic function of one variable. The new formulation leads to a regularity result and, by use of bifurcation theory, to the existence of waves of small amplitude even in the presence of stagnation points in the flow.