Additive Entropies of degree-q and the Tsallis Entropy

The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are derived. Notions of additivity, extensivity and homogeneity are clarified. The relation between mean code lengths in coding theory and various expressions for average entropies is discussed.Comment: 13 page

Chlamydia diagnosis rate in England in 2012: an ecological study of local authorities

Objectives Local authorities (LAs) in England commission chlamydia screening as part of the National Chlamydia Screening Programme. It is recommended that LAs achieve a chlamydia diagnosis rate of ≥2300 cases per 100 000 population aged 15–24. We describe national patterns in attainment of the chlamydia diagnosis rate recommendation and possible implications of using it to measure LA-level performance. Methods We used publicly available data sets from England (2012) to explore the association between LAs attaining the recommended chlamydia diagnosis rate and population size, socioeconomic deprivation, test setting and sex. Results We used data from 1 197 121 recorded chlamydia tests in females and 564 117 in males. The chlamydia diagnosis rate recommendation was achieved by 22% (72/324) of LAs overall (43% female population; 8% male population). LAs in the highest deprivation quintile were more likely to reach the recommendation than those in the least-deprived quintile for both sexes (women: unadjusted prevalence ratio (UPR) 7.43, 95% CI 3.65 to 15.11; men: UPR 7.00, 95% CI 1.66 to 29.58). The proportion of tests performed in genitourinary medicine clinics was negatively associated with attainment of the recommended diagnosis rate (UPR 0.95, 0.93 to 0.97). Conclusions Chlamydia diagnosis rate recommendations that reflect local area deprivation (as a proxy for disease burden) may be more appropriate than a single national target if the aim is to reduce health inequalities nationally. We suggest LAs monitor their chlamydia diagnosis rate, test coverage and test positivity across a range of measures (including setting and sex) and pre/post changes to commissioned services. Critical evaluation of performance against the recommendation should be reflected in local commissioning decisions

Tadpole renormalization and relativistic corrections in lattice NRQCD

We make a comparison of two tadpole renormalization schemes in the context of the quarkonium hyperfine splittings in lattice NRQCD. Improved gauge-field and NRQCD actions are analyzed using the mean-link $u_{0,L}$ in Landau gauge, and using the fourth root of the average plaquette $u_{0,P}$. Simulations are done for $c\bar c$, $b\bar c$, and $b\bar b$ systems. The hyperfine splittings are computed both at leading and at next-to-leading order in the relativistic expansion. Results are obtained at lattice spacings in the range of about 0.14~fm to 0.38~fm. A number of features emerge, all of which favor tadpole renormalization using $u_{0,L}$. This includes much better scaling behavior of the hyperfine splittings in the three quarkonium systems when $u_{0,L}$ is used. We also find that relativistic corrections to the spin splittings are smaller when $u_{0,L}$ is used, particularly for the $c\bar c$ and $b\bar c$ systems. We also see signs of a breakdown in the NRQCD expansion when the bare quark mass falls below about one in lattice units. Simulations with $u_{0,L}$ also appear to be better behaved in this context: the bare quark masses turn out to be larger when $u_{0,L}$ is used, compared to when $u_{0,P}$ is used on lattices with comparable spacings. These results also demonstrate the need to go beyond tree-level tadpole improvement for precision simulations.Comment: 14 pages, 7 figures (minor changes to some phraseology and references

Quarkonium spin structure in lattice NRQCD

Numerical simulations of the quarkonium spin splittings are done in the framework of lattice nonrelativistic quantum chromodynamics (NRQCD). At leading order in the velocity expansion the spin splittings are of $O(M_Q v^4)$, where $M_Q$ is the renormalized quark mass and $v^2$ is the mean squared quark velocity. A systematic analysis is done of all next-to-leading order corrections. This includes the addition of $O(M_Q v^6)$ relativistic interactions, and the removal of $O(a^2 M_Q v^4)$ discretization errors in the leading-order interactions. Simulations are done for both S- and P-wave mesons, with a variety of heavy quark actions and over a wide range of lattice spacings. Two prescriptions for the tadpole improvement of the action are also studied in detail: one using the measured value of the average plaquette, the other using the mean link measured in Landau gauge. Next-to-leading order interactions result in a very large reduction in the charmonium splittings, down by about 60% from their values at leading order. There are further indications that the velocity expansion may be poorly convergent for charmonium. Prelimary results show a small correction to the hyperfine splitting in the Upsilon system.Comment: 16 pages, REVTEX v3.1, 5 postscript figures include

Environment Induced Entanglement in Markovian Dissipative Dynamics

We show that two, non interacting 2-level systems, immersed in a common bath, can become mutually entangled when evolving according to a Markovian, completely positive reduced dynamics.Comment: 4 pages, LaTex, no figures, added reference

Constrained Curve Fitting

We survey techniques for constrained curve fitting, based upon Bayesian statistics, that offer significant advantages over conventional techniques used by lattice field theorists.Comment: Lattice2001(plenary); plenary talk given by G.P. Lepage at Lattice 2001 (Berlin); 9 pages, 5 figures (postscript specials