Surface embedding, topology and dualization for spin networks

Spin networks are graphs derived from 3nj symbols of angular momentum. The surface embedding, the topology and dualization of these networks are considered. Embeddings into compact surfaces include the orientable sphere S^2 and the torus T, and the not orientable projective space P^2 and Klein's bottle K. Two families of 3nj graphs admit embeddings of minimal genus into S^2 and P^2. Their dual 2-skeletons are shown to be triangulations of these surfaces.Comment: LaTeX 17 pages, 6 eps figures (late submission to arxiv.org

Semiclassical short strings in AdS_5 x S^5

We present results for the one-loop correction to the energy of a class of string solutions in AdS_5 x S^5 in the short string limit. The computation is based on the observation that, as for rigid spinning string elliptic solutions, the fluctuation operators can be put into the single-gap Lame' form. Our computation reveals a remarkable universality of the form of the energy of short semiclassical strings. This may help to understand better the structure of the strong coupling expansion of the anomalous dimensions of dual gauge theory operators.Comment: 12 pages, one pdf figure. Invited Talk at 'Nonlinear Physics. Theory and Experiment VI', Gallipoli (Italy) - June 23 - July 3, 201

Quantum mechanics of lattice gas automata. I. One particle plane waves and potentials

Classical lattice gas automata effectively simulate physical processes such as diffusion and fluid flow (in certain parameter regimes) despite their simplicity at the microscale. Motivated by current interest in quantum computation we recently defined quantum lattice gas automata; in this paper we initiate a project to analyze which physical processes these models can effectively simulate. Studying the single particle sector of a one dimensional quantum lattice gas we find discrete analogues of plane waves and wave packets, and then investigate their behaviour in the presence of inhomogeneous potentials.Comment: 19 pages, plain TeX, 14 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages), two additional large figures available upon reques

Statistical mechanics of voting

Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system from the agents' preferences and a voting rule. The dynamics form a one dimensional statistical mechanics model; this suggests the use of the topological entropy to quantify the complexity of the system. We formulate natural political/social questions about the expected complexity of a voting rule and degree of cohesion/diversity among agents in terms of random matrix models---ensembles of statistical mechanics models---and compute quantitative answers in some representative cases.Comment: 9 pages, plain TeX, 2 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages

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

A class of elementary particle models without any adjustable real parameters

Conventional particle theories such as the Standard Model have a number of freely adjustable coupling constants and mass parameters, depending on the symmetry algebra of the local gauge group and the representations chosen for the spinor and scalar fields. There seems to be no physical principle to determine these parameters as long as they stay within certain domains dictated by the renormalization group. Here however, reasons are given to demand that, when gravity is coupled to the system, local conformal invariance should be a spontaneously broken exact symmetry. The argument has to do with the requirement that black holes obey a complementarity principle relating ingoing observers to outside observers, or equivalently, initial states to final states. This condition fixes all parameters, including masses and the cosmological constant. We suspect that only examples can be found where these are all of order one in Planck units, but the values depend on the algebra chosen. This paper combines findings reported in two previous preprints, and puts these in a clearer perspective by shifting the emphasis towards the implications for particle models.Comment: 28 pages (incl. title page), no figure

From quantum cellular automata to quantum lattice gases

A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, in this paper we begin an investigation of exactly unitary cellular automata. After proving that there can be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in one dimension, we weaken the homogeneity condition and show that there are nontrivial, exactly unitary, partitioning cellular automata. We find a one parameter family of evolution rules which are best interpreted as those for a one particle quantum automaton. This model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the Dirac equation. We describe two generalizations of this automaton, the second of which, to multiple interacting particles, is the correct definition of a quantum lattice gas.Comment: 22 pages, plain TeX, 9 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages); minor typographical corrections and journal reference adde

Microalbuminuria among Type 1 and Type 2 diabetic patients of African origin in Dar Es Salaam, Tanzania

BACKGROUND: The prevalences and risk factors of microalbuminuria are not full described among black African diabetic patients. This study aimed at determining the prevalence of microalbuminuria among African diabetes patients in Dar es Salaam, Tanzania, and relate to socio-demographic features as well as clinical parameters. METHODS: Cross sectional study on 91 Type 1 and 153 Type 2 diabetic patients. Two overnight urine samples per patient were analysed. Albumin concentration was measured by an automated immunoturbidity assay. Average albumin excretion rate (AER) was used and were categorised as normalbuminuria (AER < 20 ug/min), microalbuminuria (AER 20–200 ug/min), and macroalbuminuria (AER > 200 ug/min). Information obtained also included age, diabetes duration, sex, body mass index, blood pressure, serum total cholesterol, high-density and low-density lipoprotein cholesterol, triglycerides, serum creatinine, and glycated hemoglobin A(1c). RESULTS: Overall prevalence of microalbuminuria was 10.7% and macroalbuminuria 4.9%. In Type 1 patients microalbuminuria was 12% and macroalbuminuria 1%. Among Type 2 patients, 9.8% had microalbuminuria, and 7.2% had macroalbuminuria. Type 2 patients with abnormal albumin excretion rate had significantly longer diabetes duration 7.5 (0.2–24 yrs) than those with normal albumin excretion rate 3 (0–25 yrs), p < 0.001. Systolic and diastolic blood pressure among Type 2 patients with abnormal albumin excretion rate were significantly higher than in those with normal albumin excretion rate, (p < 0.001). No significant differences in body mass index, glycaemic control, and cholesterol levels was found among patients with normal compared with those with elevated albumin excretion rate either in Type 1 or Type 2 patients. A stepwise multiple linear regression analysis among Type 2 patients, revealed AER (natural log AER) as the dependent variable to be predicted by [odds ratio (95% confidence interval)] diabetes duration 0.090 (0.049, 0.131), p < 0.0001, systolic blood pressure 0.012 (0.003–0.021), p < 0.010 and serum creatinine 0.021 (0.012, 0.030). CONCLUSION: The prevalence of micro and macroalbuminuria is higher among African Type 1 patients with relatively short diabetes duration compared with prevalences among Caucasians. In Type 2 patients, the prevalence is in accordance with findings in Caucasians. The present study detects, however, a much lower prevalence than previously demonstrated in studies from sub-Saharan Africa. Abnormal AER was significantly related to diabetes duration and systolic blood pressure