A new Q-matrix in the Eight-Vertex Model

We construct a $Q$-matrix for the eight-vertex model at roots of unity for crossing parameter $\eta=2mK/L$ with odd $L$, a case for which the existing constructions do not work. The new $Q$-matrix \Q depends as usual on the spectral parameter and also on a free parameter $t$. For $t=0$ \Q has the standard properties. For $t\neq 0$, however, it does not commute with the operator $S$ and not with itself for different values of the spectral parameter. We show that the six-vertex limit of \Q(v,t=iK'/2) exists.Comment: 10 pages section on quasiperiodicity added, typo corrected, published versio

Exploring the impact of varying definitions of exacerbations of chronic obstructive pulmonary disease in routinely collected electronic medical records

Background: Validity of exposure and outcome measures in electronic medical records is vital to ensure robust, comparable study findings however, despite validation studies, definitions of variables used often differ. Using exacerbations of chronic obstructive pulmonary disease (COPD) as an example, we investigated the impact of potential misclassification of different definitions commonly used in publications on study findings. Methods: A retrospective cohort study was performed. English primary care data from the Clinical Practice Research Datalink Aurum database with linked secondary care data were used to define a population of COPD patients ≥40 years old registered at a general practice. Index date was the date eligibility criteria were met and end of follow-up was 30/12/19, death or end of data collection. Exacerbations were defined using 6 algorithms based on definitions commonly used in the literature, including one validated definition. For each algorithm, the proportion of frequent exacerbators (≥2 exacerbations/year) and exacerbation rates were described. Cox proportional hazard regression was used to investigate each algorithm on the association between heart failure and risk of COPD exacerbation. Findings: A total of 315,184 patients were included. Baseline proportion of frequent exacerbators varied from 2.7% to 15.3% depending on the algorithm. Rates of exacerbations over follow-up varied from 19.3 to 66.6 events/100 person-years. The adjusted hazard ratio for the association between heart failure and exacerbation varied from 1.45, 95% confidence intervals 1.42–1.49, to 1.01, 0.98–1.04. Interpretation: The use of high validity definitions and standardisation of definitions in electronic medical records is crucial to generating high quality, robust evidence

Coordinate-invariant Path Integral Methods in Conformal Field Theory

We present a coordinate-invariant approach, based on a Pauli-Villars measure, to the definition of the path integral in two-dimensional conformal field theory. We discuss some advantages of this approach compared to the operator formalism and alternative path integral approaches. We show that our path integral measure is invariant under conformal transformations and field reparametrizations, in contrast to the measure used in the Fujikawa calculation, and we show the agreement, despite different origins, of the conformal anomaly in the two approaches. The natural energy-momentum in the Pauli-Villars approach is a true coordinate-invariant tensor quantity, and we discuss its nontrivial relationship to the corresponding non-tensor object arising in the operator formalism, thus providing a novel explanation within a path integral context for the anomalous Ward identities of the latter. We provide a direct calculation of the nontrivial contact terms arising in expectation values of certain energy-momentum products, and we use these to perform a simple consistency check confirming the validity of the change of variables formula for the path integral. Finally, we review the relationship between the conformal anomaly and the energy-momentum two-point functions in our formalism.Comment: Corrected minor typos. To appear in International Journal of Modern Physics

Harmonic Maa{\ss}-Jacobi forms of degree 1 with higher rank indices

We define and investigate real analytic weak Jacobi forms of degree 1 and arbitrary rank. En route we calculate the Casimir operator associated to the maximal central extension of the real Jacobi group, which for rank exceeding 1 is of order 4. In ranks exceeding 1, the notions of H-harmonicity and semi-holomorphicity are the same.Comment: 28 page

Statistical mechanics of an ideal Bose gas in a confined geometry

We study the behaviour of an ideal non-relativistic Bose gas in a three-dimensional space where one of the dimensions is compactified to form a circle. In this case there is no phase transition like that for the case of an infinite volume, nevertheless Bose-Einstein condensation signified by a sudden buildup of particles in the ground state can occur. We use the grand canonical ensemble to study this problem. In particular, the specific heat is evaluated numerically, as well as analytically in certain limits. We show analytically how the familiar result for the specific heat is recovered as we let the size of the circle become large so that the infinite volume limit is approached. We also examine in detail the behaviour of the chemical potential and establish the precise manner in which it approaches zero as the volume becomes large.Comment: 13 pages, 2 eps figures, revtex

Challenges and Pitfalls of Using Repeat Spirometry Recordings in Routine Primary Care Data to Measure FEV1 Decline in a COPD Population.

BACKGROUND: Electronic healthcare records (EHR) are increasingly used in epidemiological studies but are often viewed as lacking quality compared to randomised control trials and prospective cohorts. Studies of patients with chronic obstructive pulmonary disease (COPD) often use the rate of forced expiratory volume in 1 second (FEV1) decline as an outcome; however, its definition and robustness in EHR have not been investigated. We aimed to investigate how the rate of FEV1 decline differs by the criteria used in an EHR database. METHODS: Clinical Practice Research Datalink and Hospital Episode Statistics were used. Patient populations were defined using 8 sets of criteria around repeated FEV1 measurements. At a minimum, patients had a diagnosis of COPD, were ≥35 years old, were current or ex-smokers, and had data recorded from 2004. FEV1 measurements recorded during follow-up were identified. Thereafter, eight populations were defined based on criteria around: i) the exclusion of patients or individual measurements with potential measurement error; ii) minimum number of FEV1 measurements; iii) minimum time interval between measurements; iv) specific timing of measurements; v) minimum follow-up time; and vi) the use of linked data. For each population, the rate of FEV1 decline was estimated using mixed linear regression. RESULTS: For 7/8 patient populations, rates of FEV1 decline (age and sex adjusted) were similar and ranged from -18.7mL/year (95% CI -19.2 to -18.2) to -16.5mL/year (95% CI -17.3 to -15.7). Rates of FEV1 decline in populations that excluded patients with potential measurement error ranged from -79.4mL/year (95% CI -80.7 to -78.2) to -46.8mL/year (95% CI -47.6 to -46.0). CONCLUSION: FEV1 decline remained similar in a COPD population regardless of number of FEV1 measurements, time intervals between measurements, follow-up period, exclusion of specific FEV1 measurements, and linkage to HES. However, exclusion of individuals with questionable data led to selection bias and faster rates of decline

Family memories in the home: contrasting physical and digital mementos

We carried out fieldwork to characterise and compare physical and digital mementos in the home. Physical mementos are highly valued, heterogeneous and support different types of recollection. Contrary to expectations, we found physical mementos are not purely representational, and can involve appropriating common objects and more idiosyncratic forms. In contrast, digital mementos were initially perceived as less valuable, although participants later reconsidered this. Digital mementos were somewhat limited in function and expression, largely involving representational photos and videos, and infrequently accessed. We explain these digital limitations and conclude with design guidelines for digital mementos, including better techniques for accessing and integrating these into everyday life, allowing them to acquire the symbolic associations and lasting value that characterise their physical counterparts