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

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

Investigating the use of an electronic hand hygiene monitoring and prompt device: influence and acceptability

Introduction: Hand hygiene (HH) prevents the transmission of healthcare-associated infections. Electronic HH monitoring and prompt devices have been developed to overcome problems with monitoring HH and to improve compliance. Devices monitor room entry and exit and soap use through communication between ceiling sensors and badges worn by practitioners and the badges sense alcohol rub. Objectives: To investigate (1) the impact of devices on HH compliance, (2) how devices influence behaviour and (3) the experience and opinions of practitioners on the use devices. Methods: HH compliance was monitored (before, during and after system installation) by observations and alcohol rub usage. Compliance during installation was also monitored by the device. Healthcare practitioner interviews (n = 12) explored how the device influenced behaviour and experiences and opinions of wearing the device. Results: HH compliance improved during the period the device was installed. Practitioners reported the device increased their awareness, enhancing their empathy for patients and encouraged patients and colleagues to prompt when HH was needed. Practitioners’ reported better HH, gaming the system and feelings of irritation. Conclusion: HH prompt and monitoring systems seem to improve compliance but improvements may be undermined by practitioner irritation and system gaming

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

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

A Quantum Many-body Problem in Two Dimensions: Ground State

We obtain the exact ground state for the Calogero-Sutherland problem in arbitrary dimensions. In the special case of two dimensions, we show that the problem is connected to the random matrix problem for complex matrices, provided the strength of the inverse-square interaction $g = 2$. In the thermodynamic limit, we obtain the ground state energy and the pair-correlation function and show that in this case there is no long-range order.Comment: Typos corrected. Note added on ODLRO. Version to appear in Phys Lett

Operational modes for a wave injection facility aboard spacelab and a sub-satellite

Various modes of operation are described for an orbiting wave injection facility planned to measure the properties of waves propagating in space plasma. Such a facility would cover a wide frequency range including MF and HF. Phase shift and Doppler shift measurements will yield more accurate measurements of echo time delay and the angle of arrival. Because Spacelab will involve some sub-satellites, some consideration is given to propagation between two vehicles both at HF and VHF