Evolving graphs: dynamical models, inverse problems and propagation

Applications such as neuroscience, telecommunication, online social networking, transport and retail trading give rise to connectivity patterns that change over time. In this work, we address the resulting need for network models and computational algorithms that deal with dynamic links. We introduce a new class of evolving range-dependent random graphs that gives a tractable framework for modelling and simulation. We develop a spectral algorithm for calibrating a set of edge ranges from a sequence of network snapshots and give a proof of principle illustration on some neuroscience data. We also show how the model can be used computationally and analytically to investigate the scenario where an evolutionary process, such as an epidemic, takes place on an evolving network. This allows us to study the cumulative effect of two distinct types of dynamics

Positioning systems in Minkowski space-time: Bifurcation problem and observational data

In the framework of relativistic positioning systems in Minkowski space-time, the determination of the inertial coordinates of a user involves the {\em bifurcation problem} (which is the indeterminate location of a pair of different events receiving the same emission coordinates). To solve it, in addition to the user emission coordinates and the emitter positions in inertial coordinates, it may happen that the user needs to know {\em independently} the orientation of its emission coordinates. Assuming that the user may observe the relative positions of the four emitters on its celestial sphere, an observational rule to determine this orientation is presented. The bifurcation problem is thus solved by applying this observational rule, and consequently, {\em all} of the parameters in the general expression of the coordinate transformation from emission coordinates to inertial ones may be computed from the data received by the user of the relativistic positioning system.Comment: 10 pages, 7 figures. The version published in PRD contains a misprint in the caption of Figure 3, which is here amende

Twelve experiments in restorative justice: the Jerry Lee program of randomized trials of restorative justice conferences

Objectives: We conducted and measured outcomes from the Jerry Lee Program of 12 randomized trials over two decades in Australia and the United Kingdom (UK), testing an identical method of restorative justice taught by the same trainers to hundreds of police officers and others who delivered it to 2231 offenders and 1179 victims in 1995–2004. The article provides a review of the scientific progress and policy effects of the program, as described in 75 publications and papers arising from it, including previously unpublished results of our ongoing analyses. Methods: After random assignment in four Australian tests diverting criminal or juvenile cases from prosecution to restorative justice conferences (RJCs), and eight UK tests of supplementing criminal or juvenile proceedings with RJCs, we followed intention-to-treat group differences between offenders for up to 18 years, and for victims up to 10 years. Results: We distil and modify prior research reports into 18 updated evidence-based conclusions about the effects of RJCs on both victims and offenders. Initial reductions in repeat offending among offenders assigned to RJCs (compared to controls) were found in 10 of our 12 tests. Nine of the ten successes were for crimes with personal victims who participated in the RJCs, with clear benefits in both short- and long-term measures, including less prevalence of post-traumatic stress symptoms. Moderator effects across and within experiments showed that RJCs work best for the most frequent and serious offenders for repeat offending outcomes, with other clear moderator effects for poly-drug use and offense seriousness. Conclusions: RJ conferences organized and led (most often) by specially-trained police produced substantial short-term, and some long-term, benefits for both crime victims and their offenders, across a range of offense types and stages of the criminal justice processes on two continents, but with important moderator effects. These conclusions are made possible by testing a new kind of justice on a programmatic basis that would allow prospective meta-analysis, rather than doing one experiment at a time. This finding provides evidence that funding agencies could get far more evidence for the same cost from programs of identical, but multiple, RCTs of the identical innovative methods, rather than funding one RCT at a time

On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators

This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrodinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so called quadratic projection method, in order to achieve convergence free from spectral pollution. We describe the theoretical foundations of the method in detail, and illustrate its effectiveness by several examples.Comment: 17 pages, 2 tables and 2 figure

EFFECT OF RESPIRATION DYNAMICS ON POSTURAL CONTROL FOLLOWING A 5K RUN

Research has shown postural control during upright stance can be diminished for up to twenty minutes following aerobic exercise of different types, intensities, and durations (Lepers et al., 1997; Nagy et al., 2002). Researchers have posited that this is caused by neuromuscular changes associated with aerobic exercise and fatigue such as the reduced excitability and central drive to peripheral muscles (Lepers et al., 2002), vestibular desensitization (Lepers et al., 1997), and peripheral somatosensory desensitization (Lepers et al., 1997). However, no research has measured or attempted to control for the influence that changes in respiration dynamics (e.g., rate and volume) alone might have on postural sway. The aim of the current study was to examine these effects in order decipher whether changes to postural control following intense aerobic exercise (a 5-kilometer run performed with maximal effort) can be attributed to effects of exercise and fatigue or simply changes in respiration

Products, coproducts and singular value decomposition

Products and coproducts may be recognized as morphisms in a monoidal tensor category of vector spaces. To gain invariant data of these morphisms, we can use singular value decomposition which attaches singular values, ie generalized eigenvalues, to these maps. We show, for the case of Grassmann and Clifford products, that twist maps significantly alter these data reducing degeneracies. Since non group like coproducts give rise to non classical behavior of the algebra of functions, ie make them noncommutative, we hope to be able to learn more about such geometries. Remarkably the coproduct for positive singular values of eigenvectors in $A$ yields directly corresponding eigenvectors in A\otimes A.Comment: 17 pages, three eps-figure

On the Matter of Time

Drawing on several disciplinary areas, this article considers diverse cultural concepts of time, space, and materiality. It explores historical shifts in ideas about time, observing that these have gone full circle, from visions in which time and space were conflated, through increasingly divergent linear understandings of the relationship between them, to their reunion in contemporary notions of space-time. Making use of long-term ethnographic research and explorations of the topic of Time at Durham University’s Institute of Advanced Study (2012–13), the article considers Aboriginal Australian ideas about relationality and the movement of matter through space and time. It asks why these earliest explanations of the cosmos, though couched in a wholly different idiom, seem to have more in common with the theories proposed by contemporary physicists than with the ideas that dominated the period between the Holocene and the Anthropocene. The analysis suggests that such unexpected resonance between these oldest and newest ideas about time and space may spring from the fact that they share an intense observational focus on material events. Comparing these vastly different but intriguingly compatible worldviews meets interdisciplinary aims in providing a fresh perspective on both of them

The Leeds Evaluation of Efficacy of Detoxification Study (LEEDS) project: An open-label pragmatic randomised control trial comparing the efficacy of differing therapeutic agents for primary care detoxification from either street heroin or methadone [ISRCTN07752728]

BACKGROUND: Heroin is a synthetic opioid with an extensive illicit market leading to large numbers of people becoming addicted. Heroin users often present to community treatment services requesting detoxification and in the UK various agents are used to control symptoms of withdrawal. Dissatisfaction with methadone detoxification [8] has lead to the use of clonidine, lofexidine, buprenorphine and dihydrocodeine; however, there remains limited evaluative research. In Leeds, a city of 700,000 people in the North of England, dihydrocodeine is the detoxification agent of choice. Sublingual buprenorphine, however, is being introduced. The comparative value of these two drugs for helping people successfully and comfortably withdraw from heroin has never been compared in a randomised trial. Additionally, there is a paucity of research evaluating interventions among drug users in the primary care setting. This study seeks to address this by randomising drug users presenting in primary care to receive either dihydrocodeine or buprenorphine. METHODS/DESIGN: The Leeds Evaluation of Efficacy of Detoxification Study (LEEDS) project is a pragmatic randomised trial which will compare the open use of buprenorphine with dihydrocodeine for illicit opiate detoxification, in the UK primary care setting. The LEEDS project will involve consenting adults and will be run in specialist general practice surgeries throughout Leeds. The primary outcome will be the results of a urine opiate screening at the end of the detoxification regimen. Adverse effects and limited data to three and six months will be acquired

Analytic, Group-Theoretic Density Profiles for Confined, Correlated N-Body Systems

Confined quantum systems involving $N$ identical interacting particles are to be found in many areas of physics, including condensed matter, atomic and chemical physics. A beyond-mean-field perturbation method that is applicable, in principle, to weakly, intermediate, and strongly-interacting systems has been set forth by the authors in a previous series of papers. Dimensional perturbation theory was used, and in conjunction with group theory, an analytic beyond-mean-field correlated wave function at lowest order for a system under spherical confinement with a general two-body interaction was derived. In the present paper, we use this analytic wave function to derive the corresponding lowest-order, analytic density profile and apply it to the example of a Bose-Einstein condensate.Comment: 15 pages, 2 figures, accepted by Physics Review A. This document was submitted after responding to a reviewer's comment

A simplicial gauge theory

We provide an action for gauge theories discretized on simplicial meshes, inspired by finite element methods. The action is discretely gauge invariant and we give a proof of consistency. A discrete Noether's theorem that can be applied to our setting, is also proved.Comment: 24 pages. v2: New version includes a longer introduction and a discrete Noether's theorem. v3: Section 4 on Noether's theorem has been expanded with Proposition 8, section 2 has been expanded with a paragraph on standard LGT. v4: Thorough revision with new introduction and more background materia