Picture offshore wind farm

Open Access research that is improving renewable energy technology...

Strathprints makes available scholarly Open Access content by researchers across the departments of Mechanical & Aerospace Engineering (MAE), Electronic & Electrical Engineering (EEE), and Naval Architecture, Ocean & Marine Engineering (NAOME), all of which are leading research into aspects of wind energy, the control of wind turbines and wind farms.

Researchers at EEE are examining the dynamic analysis of turbines, their modelling and simulation, control system design and their optimisation, along with resource assessment and condition monitoring issues. The Energy Systems Research Unit (ESRU) within MAE is producing research to achieve significant levels of energy efficiency using new and renewable energy systems. Meanwhile, researchers at NAOME are supporting the development of offshore wind, wave and tidal-current energy to assist in the provision of diverse energy sources and economic growth in the renewable energy sector.

Explore Open Access research by EEE, MAE and NAOME on renewable energy technologies. Or explore all of Strathclyde's Open Access research...

Periodic reordering

Grindrod, Peter and Higham, Desmond J. and Kalna, Gabriela (2010) Periodic reordering. IMA Journal of Numerical Analysis, 30 (1). pp. 195-207. ISSN 0272-4979

[img]
Preview
PDF (periodic.pdf)
periodic.pdf
Accepted Author Manuscript

Download (4MB) | Preview

Abstract

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 and Strogatz (Nature, 1998) 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 (Phys. Rev. E, 2002) 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 ofperiodicity in biological networks.