Fisher Hartwig determinants, conformal field theory and universality in generalised XX models

We discuss certain quadratic models of spinless fermions on a 1D lattice, and their corresponding spin chains. These were studied by Keating and Mezzadri in the context of their relation to the Haar measures of the classical compact groups. We show how these models correspond to translation invariant models on an infinite or semi-infinite chain, which in the simplest case reduce to the familiar XX model. We give physical context to mathematical results for the entanglement entropy, and calculate the spin-spin correlation functions using the Fisher-Hartwig conjecture. These calculations rigorously demonstrate universality in classes of these models. We show that these are in agreement with field theoretic and renormalization group arguments that we provide

Defining and describing what we do: Doctrinal legal research

What exactly is doctrinal legal research? And where does the doctrinal methodology ‘fit’ within the spectrum of scientific and social research methodologies undertaken in other disciplines? The practitioner lawyer of the past had little need to reflect on process. The doctrinal research methodology developed intuitively within the common law - a research method at the core of practice. There was no need to justify or classify it within a broader research framework. Modern academic lawyers are facing a different situation. At a time when competition for limited research funds is becoming more intense, and in which interdisciplinary work is highly valued and non-lawyers are involved in the assessment of grant applications, lawyer-applicants who engage in doctrinal research need to be able to explain their methodology more clearly. Doctrinal scholars need to be more open and articulate about their methods. These methods may be different in different contexts. This paper examines the legal research doctrinal method and its place in recent research dialogue. Some commentators are of the view that the doctrinal method is simply scholarship rather than a separate research methodology. Richard Posner even suggests that law is ‘not a field with a distinct methodology, but an amalgam of applied logic, rhetoric, economics and familiarity with a specialized vocabulary and a particular body of texts, practices, and institutions ..’. Therefore, academic lawyers are beginning to realise that the doctrinal research methodology needs clarification for those outside the legal profession and that a discussion about the standing and place of doctrinal research compared to other methodologies is required

Effects of temperature upon the collapse of a Bose-Einstein condensate in a gas with attractive interactions

We present a study of the effects of temperature upon the excitation frequencies of a Bose-Einstein condensate formed within a dilute gas with a weak attractive effective interaction between the atoms. We use the self-consistent Hartree-Fock Bogoliubov treatment within the Popov approximation and compare our results to previous zero temperature and Hartree-Fock calculations The metastability of the condensate is monitored by means of the $l=0$ excitation frequency. As the number of atoms in the condensate is increased, with $T$ held constant, this frequency goes to zero, signalling a phase transition to a dense collapsed state. The critical number for collapse is found to decrease as a function of temperature, the rate of decrease being greater than that obtained in previous Hartree-Fock calculations.Comment: 4 pages LaTeX, 3 eps figures. To appear as a letter in J. Phys.

Confounding Issues in the Deadweight Loss of Gift-Giving

When a gift is given, someone other than the final consumer makes the consumption choice. Thus there is a possibility that the gift will not match the preferences of the receiver, i.e., the gift will represent a wise use of the money given the gift-giver's tastes but not necessarily a wise use of money given the recipient's tastes. In other words, gift giving can result in a deadweight loss. This paper addresses and clarifies the discrepancy between Waldfogel's (1993) finding of a deadweight loss from gift giving and Solnick and Hemenway's (1996) finding of a deadweight gain from gift giving. It also builds on some of the concerns raised by Ruffle and Tykocinski (2000).

Review of modern concepts in the engineering interpretation of earthquake response spectra

The design response spectrum is typically the starting point of most codified seismic design and assessment procedures and is used predominantly to prescribe the applied inertia forces induced by earthquake ground motions. This paper introduces and reviews modern concepts related to the effective development and application of earthquake design response spectra, including the conventional acceleration response spectrum, the velocity spectrum, and the displacement spectrum. It further briefly reviews the concepts of the inelastic response spectrum and the capacity spectrum. A number of the ideas presented are targeted particularly at assisting practising engineers working in low- and moderate-seismicity environments. The principal purpose is to enlighten engineers to modern concepts in response spectra development, in order to subsequently facilitate the effective use of the information contained in an earthquake response spectrum for both analysis and design applications.published_or_final_versio

2017 McDonald diagnostic criteria: A review of the evidence

The diagnosis of Multiple Sclerosis (MS) has continuously evolved, allowing for an earlier and more accurate diagnosis of MS over time. The McDonald Criteria for diagnosis of MS were originally proposed in 2001, with previous revisions in both 2005 and 2010. The International Panel on Diagnosis in MS have recently reviewed the 2010 McDonald Criteria, and made recommendations for the revised 2017 McDonald Criteria. Any revisions made relied entirely on the available evidence, and not expert opinion. In this review, we provide an overview of the recent 2017 revisions to the McDonald Criteria, focusing in particular on the motivating evidence behind the recommendations made. We also review the existing research around misdiagnosis in MS, as well as areas considered to be high priorities of research, currently lacking in sufficient evidence, which may influence future diagnostic criteria in years to come. Finally, we illustrate some clinical examples, to demonstrate the impact of new diagnostic criteria on time to MS diagnosis in a real-world setting

Increased risk of HIV and other drug-related harms associated with injecting in public places: national bio-behavioural survey of people who inject drugs

Background: Whilst injecting drugs in public places is considered a proxy for high risk behaviour among people who inject drugs (PWID), studies quantifying its relationship with multiple drug-related harms are lacking and none have examined this in the context of an ongoing HIV outbreak (located in Glasgow, Scotland). We aimed to: 1) estimate the prevalence of public injecting in Scotland and associated risk factors; and 2) estimate the association between public injecting and HIV, current HCV, overdose, and skin and soft tissue infections (SSTI). Methods: Cross-sectional, bio-behavioural survey (including dried blood spot testing to determine HIV and HCV infection) of 1469 current PWID (injected in last 6 months) recruited by independent interviewers from 139 harm reduction services across Scotland during 2017–18. Primary outcomes were: injecting in a public place (yes/no); HIV infection; current HCV infection; self-reported overdose in the last year (yes/no) and SSTI the last year (yes/no). Multi-variable logistic regression was used to determine factors associated with public injecting and to estimate the association between public injecting and drug-related harms (HIV, current HCV, overdose and SSTI). Results: Prevalence of public injecting was 16% overall in Scotland and 47% in Glasgow city centre. Factors associated with increased odds of public injecting were: recruitment in Glasgow city centre (aOR=5.45, 95% CI 3.48–8.54, p<0.001), homelessness (aOR=3.68, 95% CI 2.61–5.19, p<0.001), high alcohol consumption (aOR=2.42, 95% CI 1.69–3.44, p<0.001), high injection frequency (≥4 per day) (aOR=3.16, 95% CI 1.93–5.18, p<0.001) and cocaine injecting (aOR=1.46, 95% CI 1.00 to 2.13, p = 0.046). Odds were lower for those receiving opiate substitution therapy (OST) (aOR=0.37, 95% CI 0.24 to 0.56, p<0.001) and older age (per year increase) (aOR=0.97, 95% CI 0.95 to 0.99, p = 0.013). Public injecting was associated with an increased risk of HIV infection (aOR=2.11, 95% CI 1.13–3.92, p = 0.019), current HCV infection (aOR=1.49, 95% CI 1.01–2.19, p = 0.043), overdose (aOR=1.59, 95% CI 1.27–2.01, p<0.001) and SSTI (aOR=1.42, 95% CI 1.17–1.73, p<0.001). Conclusions: These findings highlight the need to address the additional harms observed among people who inject in public places and provide evidence to inform proposals in the UK and elsewhere to introduce facilities that offer safer drug consumption environments