The asymptotics of an amplitude for the 4-simplex

An expression for the oscillatory part of an asymptotic formula for the relativistic spin network amplitude for a 4-simplex is given. The amplitude depends on specified areas for each two-dimensional face in the 4-simplex. The asymptotic formula has a contribution from each flat Euclidean metric on the 4-simplex which agrees with the given areas. The oscillatory part of each contribution is determined by the Regge calculus Einstein action for that geometry.Comment: 5 pages amstex, typos correcte

Tullio Regge's legacy: Regge calculus and discrete gravity

The review paper "Discrete Structures in Physics", written in 2000, describes how Regge's discretization of Einstein's theory has been applied in classical relativity and quantum gravity. Here, developments since 2000 are reviewed briefly, with particular emphasis on progress in quantum gravity through spin foam models and group field theories.Comment: 15 pages; a contribution to the forthcoming volume "Tullio Regge: an eclectic genius, from quantum gravity to computer play", Eds. L Castellani, A. Ceresole, R. D'Auria and P. Fr\`e (World Scientific); v2: added references to more relevant work, minor changes to the tex

A note on area variables in Regge calculus

We consider the possibility of setting up a new version of Regge calculus in four dimensions with areas of triangles as the basic variables rather than the edge-lengths. The difficulties and restrictions of this approach are discussed.Comment: 4 pages, amstex. Revision has minor changes and more precise conclusion

Constraints on Area Variables in Regge Calculus

We describe a general method of obtaining the constraints between area variables in one approach to area Regge calculus, and illustrate it with a simple example. The simplicial complex is the simplest tessellation of the 4-sphere. The number of independent constraints on the variations of the triangle areas is shown to equal the difference between the numbers of triangles and edges, and a general method of choosing independent constraints is described. The constraints chosen by using our method are shown to imply the Regge equations of motion in our example.Comment: Typographical errors correcte

The asymptotics of an amplitude for the 4-simplex

An expression for the oscillatory part of an asymptotic formula for the relativistic spin network amplitude for a 4-simplex is given. The amplitude depends on specified areas for each two-dimensional face in the 4-simplex. The asymptotic formula has a contribution from each flat Euclidean metric on the 4-simplex which agrees with the given areas. The oscillatory part of each contribution is determined by the Regge calculus Einstein action for that geometry

Couple’s Relationship With Diabetes: Means and Meanings for Management Success

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/102683/1/jmft322.pd

Area Regge Calculus and Discontinuous Metrics

Taking the triangle areas as independent variables in the theory of Regge calculus can lead to ambiguities in the edge lengths, which can be interpreted as discontinuities in the metric. We construct solutions to area Regge calculus using a triangulated lattice and find that on a spacelike hypersurface no such discontinuity can arise. On a null hypersurface however, we can have such a situation and the resulting metric can be interpreted as a so-called refractive wave.Comment: 18 pages, 1 figur

Fabrication of free standing collagen membranes by pulsed-electrophoretic deposition.

This work reports an important new development in the production of collagen membranes, based on pulsed electrophoretic deposition (P-EPD), suitable for a wide range of biomedical applications. Collagen membranes are of great interest as a biomaterial and in a range of other industries, though current production techniques suffer from limitations with scaling up, homogeneity, and complex shapes. P-EPD can be used to rapidly create detachable, large-area, homogeneous products with controlled thickness in a wide variety of shapes. We provide a new understanding of the influence of a range of parameters (pulse width, voltage, duty cycle, solvent additions) and their effects on membrane structure. Characterisation by AFM, SEM, and cryoSEM revealed the ability to produce dense, structurally defect-free membranes, and significantly, we show and discuss the ability to produce thicker membranes by sequential deposition without seeing a corresponding increase in cell electrical resistance. We anticipate this novel, rapid, and controllable method for the production of collagen membranes to be of interest for a wide range of fields.The authors wish to acknowledge the support of theEngineering and Physical Sciences Research Council(EPSRC)grants EP/K503009/1, EP/J500380/1, EP/L504920/1, EP/M506485/1, and EP/M508007/1,Geistlich Pharma AG, and the European ResearchCouncil(ERC)Advanced Grant 320598 3D-

Discrete structures in gravity

Discrete approaches to gravity, both classical and quantum, are reviewed briefly, with emphasis on the method using piecewise-linear spaces. Models of 3-dimensional quantum gravity involving 6j-symbols are then described, and progress in generalising these models to four dimensions is discussed, as is the relationship of these models in both three and four dimensions to topological theories. Finally, the repercussions of the generalisations are explored for the original formulation of discrete gravity using edge-length variables.Comment: 30 pages, 4 figure

Landmark Models for Optimizing the Use of Repeated Measurements of Risk Factors in Electronic Health Records to Predict Future Disease Risk.

The benefits of using electronic health records (EHRs) for disease risk screening and personalized health-care decisions are being increasingly recognized. Here we present a computationally feasible statistical approach with which to address the methodological challenges involved in utilizing historical repeat measures of multiple risk factors recorded in EHRs to systematically identify patients at high risk of future disease. The approach is principally based on a 2-stage dynamic landmark model. The first stage estimates current risk factor values from all available historical repeat risk factor measurements via landmark-age-specific multivariate linear mixed-effects models with correlated random intercepts, which account for sporadically recorded repeat measures, unobserved data, and measurement errors. The second stage predicts future disease risk from a sex-stratified Cox proportional hazards model, with estimated current risk factor values from the first stage. We exemplify these methods by developing and validating a dynamic 10-year cardiovascular disease risk prediction model using primary-care EHRs for age, diabetes status, hypertension treatment, smoking status, systolic blood pressure, total cholesterol, and high-density lipoprotein cholesterol in 41,373 persons from 10 primary-care practices in England and Wales contributing to The Health Improvement Network (1997-2016). Using cross-validation, the model was well-calibrated (Brier score = 0.041, 95% confidence interval: 0.039, 0.042) and had good discrimination (C-index = 0.768, 95% confidence interval: 0.759, 0.777)