Eigenvalue Separation in Some Random Matrix Models

The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large N limit a single eigenvalue will separate from the support of the Wigner semi-circle provided c > 1. In this study, using an asymptotic analysis of the secular equation for the eigenvalue condition, we compare this effect to analogous effects occurring in general variance Wishart matrices and matrices from the shifted mean chiral ensemble. We undertake an analogous comparative study of eigenvalue separation properties when the size of the matrices are fixed and c goes to infinity, and higher rank analogues of this setting. This is done using exact expressions for eigenvalue probability densities in terms of generalized hypergeometric functions, and using the interpretation of the latter as a Green function in the Dyson Brownian motion model. For the shifted mean Gaussian unitary ensemble and its analogues an alternative approach is to use exact expressions for the correlation functions in terms of classical orthogonal polynomials and associated multiple generalizations. By using these exact expressions to compute and plot the eigenvalue density, illustrations of the various eigenvalue separation effects are obtained.Comment: 25 pages, 9 figures include

Species Abundance Patterns in Complex Evolutionary Dynamics

An analytic theory of species abundance patterns (SAPs) in biological networks is presented. The theory is based on multispecies replicator dynamics equivalent to the Lotka-Volterra equation, with diverse interspecies interactions. Various SAPs observed in nature are derived from a single parameter. The abundance distribution is formed like a widely observed left-skewed lognormal distribution. As the model has a general form, the result can be applied to similar patterns in other complex biological networks, e.g. gene expression.Comment: 4 pages, 3 figures. Physical Review Letters, in pres

Subband Engineering Even-Denominator Quantum Hall States

Proposed even-denominator fractional quantum Hall effect (FQHE) states suggest the possibility of excitations with non-Abelian braid statistics. Recent experiments on wide square quantum wells observe even-denominator FQHE even under electrostatic tilt. We theoretically analyze these structures and develop a procedure to accurately test proposed quantum Hall wavefunctions. We find that tilted wells favor partial subband polarization to yield Abelian even-denominator states. Our results show that tilting quantum wells effectively engineers different interaction potentials allowing exploration of a wide variety of even-denominator states

Secondary literacy across the curriculum: Challenges and possibilities

This paper discusses the challenges and possibilities attendant upon successfully implementing literacy across the curriculum initiatives – or ‘school language policies’ as they have come to be known - particularly at the secondary or high school level. It provides a theoretical background to these issues, exploring previous academic discussions of school language policies, and highlights key areas of concern as well as opportunity with respect to school implementation of such policies. As such, it provides a necessary conceptual background to the subsequent papers in this special issue, which focus upon the Secondary Schools’ Literacy Initiative (SSLI) – a New Zealand funded programme that aims to establish cross-curricular language and literacy policies in secondary schools

From neurons to epidemics: How trophic coherence affects spreading processes

Trophic coherence, a measure of the extent to which the nodes of a directed network are organised in levels, has recently been shown to be closely related to many structural and dynamical aspects of complex systems, including graph eigenspectra, the prevalence or absence of feed-back cycles, and linear stability. Furthermore, non-trivial trophic structures have been observed in networks of neurons, species, genes, metabolites, cellular signalling, concatenated words, P2P users, and world trade. Here we consider two simple yet apparently quite different dynamical models -- one a Susceptible-Infected-Susceptible (SIS) epidemic model adapted to include complex contagion, the other an Amari-Hopfield neural network -- and show that in both cases the related spreading processes are modulated in similar ways by the trophic coherence of the underlying networks. To do this, we propose a network assembly model which can generate structures with tunable trophic coherence, limiting in either perfectly stratified networks or random graphs. We find that trophic coherence can exert a qualitative change in spreading behaviour, determining whether a pulse of activity will percolate through the entire network or remain confined to a subset of nodes, and whether such activity will quickly die out or endure indefinitely. These results could be important for our understanding of phenomena such as epidemics, rumours, shocks to ecosystems, neuronal avalanches, and many other spreading processes

Can virtual nature improve patient experiences and memories of dental treatment? A study protocol for a randomized controlled trial

Background Dental anxiety and anxiety-related avoidance of dental care create significant problems for patients and the dental profession. Distraction interventions are used in daily medical practice to help patients cope with unpleasant procedures. There is evidence that exposure to natural scenery is beneficial for patients and that the use of virtual reality (VR) distraction is more effective than other distraction interventions, such as watching television. The main aim of this randomized controlled trial is to determine whether the use of VR during dental treatment can improve the overall dental experience and recollections of treatment for patients, breaking the negative cycle of memories of anxiety leading to further anxiety, and avoidance of future dental appointments. Additionally, the aim is to test whether VR benefits dental patients with all levels of dental anxiety or whether it could be especially beneficial for patients suffering from higher levels of dental anxiety. The third aim is to test whether the content of the VR distraction can make a difference for its effectiveness by comparing two types of virtual environments, a natural environment and an urban environment. Methods/design The effectiveness of VR distraction will be examined in patients 18 years or older who are scheduled to undergo dental treatment for fillings and/or extractions, with a maximum length of 30 minutes. Patients will be randomly allocated into one of three groups. The first group will be exposed to a VR of a natural environment. The second group will be exposed to a VR of an urban environment. A third group consists of patients who receive standard care (control group). Primary outcomes relate to patients’ memories of the dental treatment one week after treatment: (a) remembered pain, (b) intrusive thoughts and (c) vividness of memories. Other measures of interest are the dental experience, the treatment experience and the VR experience. Trial registration Current Controlled Trials ISRCTN4144280

Rethinking the patient: using Burden of Treatment Theory to understand the changing dynamics of illness

<b>Background</b> In this article we outline Burden of Treatment Theory, a new model of the relationship between sick people, their social networks, and healthcare services. Health services face the challenge of growing populations with long-term and life-limiting conditions, they have responded to this by delegating to sick people and their networks routine work aimed at managing symptoms, and at retarding - and sometimes preventing - disease progression. This is the new proactive work of patient-hood for which patients are increasingly accountable: founded on ideas about self-care, self-empowerment, and self-actualization, and on new technologies and treatment modalities which can be shifted from the clinic into the community. These place new demands on sick people, which they may experience as burdens of treatment.<p></p> <b>Discussion</b> As the burdens accumulate some patients are overwhelmed, and the consequences are likely to be poor healthcare outcomes for individual patients, increasing strain on caregivers, and rising demand and costs of healthcare services. In the face of these challenges we need to better understand the resources that patients draw upon as they respond to the demands of both burdens of illness and burdens of treatment, and the ways that resources interact with healthcare utilization.<p></p> <b>Summary</b> Burden of Treatment Theory is oriented to understanding how capacity for action interacts with the work that stems from healthcare. Burden of Treatment Theory is a structural model that focuses on the work that patients and their networks do. It thus helps us understand variations in healthcare utilization and adherence in different healthcare settings and clinical contexts