Dynamic Transition Theory for Thermohaline Circulation

The main objective of this and its accompanying articles is to derive a mathematical theory associated with the thermohaline circulations (THC). This article provides a general transition and stability theory for the Boussinesq system, governing the motion and states of the large-scale ocean circulation. First, it is shown that the first transition is either to multiple steady states or to oscillations (periodic solutions), determined by the sign of a nondimensional parameter $K$, depending on the geometry of the physical domain and the thermal and saline Rayleigh numbers. Second, for both the multiple equilibria and periodic solutions transitions, both Type-I (continuous) and Type-II (jump) transitions can occur, and precise criteria are derived in terms of two computable nondimensional parameters $b_1$ and $b_2$. Associated with Type-II transitions are the hysteresis phenomena, and the physical reality is represented by either metastable states or by a local attractor away from the basic solution, showing more complex dynamical behavior. Third, a convection scale law is introduced, leading to an introduction of proper friction terms in the model in order to derive the correct circulation length scale. In particular, the dynamic transitions of the model with the derived friction terms suggest that the THC favors the continuous transitions to stable multiple equilibria. Applications of the theoretical analysis and results to different flow regimes will be explored in the accompanying articles

Thinking outside the curve, part I: modeling birthweight distribution

<p>Abstract</p> <p>Background</p> <p>Greater epidemiologic understanding of the relationships among fetal-infant mortality and its prognostic factors, including birthweight, could have vast public health implications. A key step toward that understanding is a realistic and tractable framework for analyzing birthweight distributions and fetal-infant mortality. The present paper is the first of a two-part series that introduces such a framework.</p> <p>Methods</p> <p>We propose describing a birthweight distribution via a normal mixture model in which the number of components is determined from the data using a model selection criterion rather than fixed <it>a priori</it>.</p> <p>Results</p> <p>We address a number of methodological issues, including how the number of components selected depends on the sample size, how the choice of model selection criterion influences the results, and how estimates of mixture model parameters based on multiple samples from the same population can be combined to produce confidence intervals. As an illustration, we find that a 4-component normal mixture model reasonably describes the birthweight distribution for a population of white singleton infants born to heavily smoking mothers. We also compare this 4-component normal mixture model to two competitors from the existing literature: a contaminated normal model and a 2-component normal mixture model. In a second illustration, we discover that a 6-component normal mixture model may be more appropriate than a 4-component normal mixture model for a general population of black singletons.</p> <p>Conclusions</p> <p>The framework developed in this paper avoids assuming the existence of an interval of birthweights over which there are no compromised pregnancies and does not constrain birthweights within compromised pregnancies to be normally distributed. Thus, the present framework can reveal heterogeneity in birthweight that is undetectable via a contaminated normal model or a 2-component normal mixture model.</p

Unique TCR beta-subunit variable gene haplotypes in Africans.

This study investigated polymorphisms of genes in two regions of the T-cell antigen receptor beta-subunit (TCRB) locus, including BV9S2P, and BV6S7 in a 5' linkage group, and BV8S3, BV24S1, BV25S1, BV18S1, BV2S1, BV15S1 and BV3S1 in a 3' linkage group. These loci have been genotyped in individuals from five regions in Africa, including The Gambia, Nigeria, Cameroon, Tanzania, and Zambia, and in individuals from northern Britain, northern India, and Papua New Guinea (PNG). In the 3' linkage group, 11 unique haplotypes were identified in the combined African populations; two equally frequent haplotypes represent the majority of African chromosomes. One haplotype was found in all four regions studied. This is the most frequent haplotype in the northern British, northern Indian and PNG populations. Although present, it is infrequent in the African populations. A North-South gradient in the frequency of a common African haplotype was observed. The distribution did not represent that of a known disease. Evidence suggests that malaria is not responsible for selection of these haplotypes. Overall, this study highlights large differences in the genetic constitution of the TCRB locus between Africans and other populations