Level-spacing distributions of the Gaussian unitary random matrix ensemble

Level-spacing distributions of the Gaussian Unitary Ensemble (GUE) of random matrix theory are expressed in terms of solutions of coupled differential equations. Series solutions up to order 50 in the level spacing are obtained, thus providing a very good description of the small-spacing part of the level-spacing distribution, which can be used to make comparisons with experimental or numerical data. The level-spacing distributions can be obtained by solving the system of differential equations numerically.Comment: The series expansions discussed in this paper are available as Mathematica code at http://mcs.open.ac.uk/ugg2/RMT/LevelSpacingGUE.m (16kB

Habitat enhancing marine structures: Creating habitat in urban waters

Although maritime regions support a large portion of the world’s human population, their value as habitat for other species is overlooked. Urban structures that are built in the marine environment are not designed or managed for the habitat they provide, and are built without considering the communities of marine organisms that could colonize them (Clynick et al., 2008). However, the urban waterfront may be capable of supporting a significant proportion of regional aquatic biodiversity (Duffy-Anderson et al., 2003). While urban shorelines will never return to their original condition, some scientists think that the habitat quality of urban waterfronts could be significantly improved through further research and some design modifications, and that many opportunities exist to make these modifications (Russel et al., 1983, Goff, 2008). Habitat enhancing marine structures (or HEMS) are a potentially promising approach to address the impact of cities on marine organisms including habitat fragmentation and degradation. HEMS are a type of habitat improvement project that are ecologically engineered to improve the habitat quality of urban marine structures such as bulkheads and docks for marine organisms. More specifically, HEMS attempt to improve or enhance the physical habitat that organisms depend on for survival in the inter- and sub-tidal waterfronts of densely populated areas. HEMS projects are targeted at areas where human-made structures cannot be significantly altered or removed. While these techniques can be used in suburban or rural areas restoration or removal is preferred in these settings, and HEMS are resorted to only if removal of the human-made structure is not an option. Recent research supports the use of HEMS projects. Researchers have examined the communities found on urban structures including docks, bulkheads, and breakwaters. Complete community shifts have been observed where the natural shoreline was sandy, silty, or muddy. There is also evidence of declines in community composition, ecosystem functioning, and increases in non-native species abundances in assemblages on urban marine structures. Researchers have identified two key differences between these substrates including the slope (seawalls are vertical; rocky shores contain multiple slopes) and microhabitat availability (seawalls have very little; rocky shores contain many different types). In response, researchers have suggested designing and building seawalls with gentler slopes or a combination of horizontal and vertical surfaces. Researchers have also suggested incorporating microhabitat, including cavities designed to retain water during low tide, crevices, and other analogous features (Chapman, 2003; Moreira et al., 2006) (PDF contains 4 pages

Building new partnerships: changing institutional relations [excerpts: Changing roles and relationships at the University of Lincoln; Appendix E]

Discusses the role of Learning Advisers at the University of Lincoln. Their work represents the cornerstone of the relationship between Learning Support and the academic community

The changing staff experience [excerpt: University of Lincoln]

Describes Learning Support 1997 restructuring at the University of Lincoln in chapter on the changing staff experience

Heretical thoughts about science and society: Frederick S. Pardee distinguished lecture, November 1, 2005

A version of this essay was delivered in November 1, 2005 as the Frederick S. Pardee Distinguished Lecture at Boston University.Freeman Dyson illuminates the importance of having heretics to challenge assumptions, and gives six heretical predictions of his own. The first is that American hegemony will not last until the next century. The second is that global warming is not the enormous problem that people make it out to be, primarily because increasing topsoil can counteract the excess of carbon dioxide and also, our knowledge is still too limited to diagnose the situation. His third heresy is that the increase in carbon dioxide may take us back to that wettest and warmest point in the interglacial period when the Sahara Desert was wet, and that this may be a better climate overall, driving at the critical juncture between naturalists and humanists. The fourth heresy makes an analogy between the transition that computers made to become small and ubiquitous, and the direction that biotechnology perhaps ought to go. Number five elaborates on communal sharing of genes and a completely new path for biology and evolution, and his sixth is that rural poverty should be solved by increasing the productivity of rural activities using “green technology,” (based on biology) such that people are not forced to migrate to urban centers

Rigidity and Normal Modes in Random Matrix Spectra

We consider the Gaussian ensembles of random matrices and describe the normal modes of the eigenvalue spectrum, i.e., the correlated fluctuations of eigenvalues about their most probable values. The associated normal mode spectrum is linear, and for large matrices, the normal modes are found to be Chebyshev polynomials of the second kind. We contrast this with the behaviour of a sequence of uncorrelated levels, which has a quadratic normal mode spectrum. The difference in the rigidity of random matrix spectra and sequences of uncorrelated levels can be attributed to this difference in the normal mode spectra. We illustrate this by calculating the number variance in the two cases.Comment: 12 pages, 1 LaTeX fil

Long memory and non-linearity in Stock Markets

In this paper the long memory and non-linear properties of share prices in the UK’s Stock Exchange and AIM are explored. The results suggest that the most commonly traded shares exhibit long memory thus raising interesting issues about the validity of normal assumptions of market efficiencies

Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach

We determine the asymptotic level spacing distribution for the Laguerre Ensemble in a single scaled interval, $(0,s)$, containing no levels, E_{\bt}(0,s), via Dyson's Coulomb Fluid approach. For the $\alpha=0$ Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by both Edelman and Forrester, while for $\alpha\neq 0$, the leading terms of $E_{2}(0,s)$, found by Tracy and Widom, are reproduced without the use of the Bessel kernel and the associated Painlev\'e transcendent. In the same approximation, the next leading term, due to a ``finite temperature'' perturbation (\bt\neq 2), is found.Comment: 10pp, LaTe

Non-local image deconvolution by Cauchy sequence

We present the deconvolution between two smooth function vectors as a Cauchy sequence of weight functions. From this we develop a Taylor series expansion of the convolution problem that leads to a non-local approximation for the deconvolution in terms of continuous function spaces. Optimisation of this form against a given measure of error produces a theoretically more exact algorithm. The discretization of this formulation provides a deconvolution iteration that deconvolves images quicker than the Richardson-Lucy algorithm.Comment: 12 pages, 3 figure