Eisenstein series for infinite-dimensional U-duality groups

We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E_n series of string duality groups, and in particular for the infinite-dimensional Kac-Moody groups E9, E10 and E11. We show that, remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains only a finite number of terms for particular choices of a parameter appearing in the definition of the series. This resonates with the idea that the constant term of the Eisenstein series encodes perturbative string corrections in BPS-protected sectors allowing only a finite number of corrections. We underpin our findings with an extensive discussion of physical degeneration limits in D<3 space-time dimensions.Comment: 69 pages. v2: Added references and small additions, to be published in JHE

Karhunen-Lo\`eve expansion for a generalization of Wiener bridge

We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.Comment: 25 pages, 1 figure. The appendix is extende

Sociodemographic characteristics determine dietary pattern adherence during pregnancy

OBJECTIVE:Sociodemographic factors may affect adherence to specific dietary patterns during pregnancy. The present study aimed to identify dietary patterns during pregnancy and associated factors among Brazilian pregnant women. DESIGN:A cross-sectional analysis. Dietary intake was evaluated with a semi-quantitative FFQ during the first postpartum week; the time frame included the second and third gestational trimesters. Principal component analysis was used to identify dietary patterns during pregnancy. Sociodemographic data were obtained using a structured questionnaire. Multiple linear regressions were applied to test the associations between the sociodemographic factors and dietary patterns. SETTING:Mesquita, Rio de Janeiro, Brazil, 2011. SUBJECTS:Postpartum women (n 327) who were 18-45 years of age and Mesquita residents. RESULTS:Three different dietary patterns were identified: 'healthy' (mainly comprising legumes, vegetables and fruits), 'mixed' (mainly comprising candy, butter and margarine, and snacks) and 'traditional' (mainly comprising beans and rice). Women with a higher monthly per capita family income (β=0·0006; 95% CI 0·0001, 0·001; P=0·011) and women of older age (β=0·021; 95% CI -0·001, 0·042; P=0·058) were more likely to adhere to the 'healthy' dietary pattern. Women with higher parity were less likely to adhere to the 'healthy' pattern (β=-0·097; 95% CI -0·184, -0·009; P=0·030) and were more likely to adhere to the 'traditional' pattern (β=0·098; 95% CI 0·021, 0·175; P=0·012). Although not statistically significant, older women were less likely to adhere to the 'mixed' (β=-0·017; 95% CI -0·037, 0·003; P=0·075) and 'traditional' (β=-0·018; 95% CI -0·037, 0·001; P=0·061) dietary patterns. CONCLUSIONS:Monthly per capita family income, parity and maternal age were factors associated with adherence to a healthy diet during pregnancy

Static Charges in the Low-Energy Theory of the S-Duality Twist

We continue the study of the low-energy limit of N=4 super Yang-Mills theory compactified on a circle with S-duality and R-symmetry twists that preserve N=6 supersymmetry in 2+1D. We introduce external static supersymmetric quark and anti-quark sources into the theory and calculate the Witten Index of the resulting Hilbert space of ground states on a torus. Using these results we compute the action of simple Wilson loops on the Hilbert space of ground states without sources. In some cases we find disagreement between our results for the Wilson loop eigenvalues and previous conjectures about a connection with Chern-Simons theory.Comment: 73 pages, two paragraphs added, one to the introduction and one to the discussio

Strings on Semisymmetric Superspaces

Several string backgrounds which arise in the AdS/CFT correspondence are described by integrable sigma-models. Their target space is always a Z(4) supercoset (a semi-symmetric superspace). Here we list all semi-symmetric cosets which have zero beta function and central charge c<=26 at one loop in perturbation theory.Comment: 25 pages, 1 figur

Spacelike Singularities and Hidden Symmetries of Gravity

We review the intimate connection between (super-)gravity close to a spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody algebras. We show that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly infinite) sequence of reflections, which are elements of a Lorentzian Coxeter group. Such Coxeter groups are the Weyl groups of infinite-dimensional Kac-Moody algebras, suggesting that these algebras yield symmetries of gravitational theories. Our presentation is aimed to be a self-contained and comprehensive treatment of the subject, with all the relevant mathematical background material introduced and explained in detail. We also review attempts at making the infinite-dimensional symmetries manifest, through the construction of a geodesic sigma model based on a Lorentzian Kac-Moody algebra. An explicit example is provided for the case of the hyperbolic algebra E10, which is conjectured to be an underlying symmetry of M-theory. Illustrations of this conjecture are also discussed in the context of cosmological solutions to eleven-dimensional supergravity.Comment: 228 pages. Typos corrected. References added. Subject index added. Published versio

Type 2 diabetes mellitus management among Ghanaian migrants resident in three European countries and their compatriots in rural and urban Ghana - The RODAM study

AIMS: To compare Type 2 Diabetes Mellitus (T2DM) awareness, treatment and control between Ghanaians resident in Ghana and Europe. // METHODS: Comparisons were made for the 530 participants of the Research on Obesity and Diabetes among African Migrants (RODAM) study with T2DM (25-70 years) living in Amsterdam, Berlin, London, urban Ghana and rural Ghana. We used logistic regression to assess disparities with adjustment for age, sex and education. // RESULTS: T2DM awareness was 51% in rural Ghana. This was lower than levels in Europe ranging from 73% in London (age-sex adjusted odds ratio (OR) = 2.7; 95%CI = 1.2-6.0) to 79% in Amsterdam (OR = 4.7; 95%CI = 2.3-9.6). T2DM treatment was also lower in rural Ghana (37%) than in urban Ghana (56%; OR = 2.6; 95%CI = 1.3-5.3) and European sites ranging from 67% in London (OR = 3.4; 95%CI = 1.5-7.5) to 73% in Berlin (OR = 6.9; 95%CI = 2.9-16.4). In contrast, T2DM control in rural Ghana (63%) was comparable to Amsterdam and Berlin, but higher than in London (40%; OR = 0.4; 95%CI = 0.2-0.9) and urban Ghana (28%; OR = 0.3; 95%CI = 0.1-0.6). // CONCLUSIONS: Our findings suggest that improved detection and treatment of T2DM in rural Ghana, and improved control for people with diagnosed T2DM in London and urban Ghana warrant prioritization. Further work is needed to understand the factors driving the differences

Adaptation to Aridity in the Malaria Mosquito Anopheles gambiae: Chromosomal Inversion Polymorphism and Body Size Influence Resistance to Desiccation

Chromosomal inversions are thought to confer a selective advantage in alternative habitats by protecting co-adapted alleles from recombination. The frequencies of two inversions (2La and 2Rb) of the afro-tropical malaria mosquito Anopheles gambiae change gradually along geographical clines, increasing in frequency with degree of aridity. Such clines can result from gene flow and local selection acting upon alternative karyotypes along the cline, suggesting that these inversions may be associated with tolerance to xeric conditions. Since water loss represents a major challenge in xeric habitats, it can be supposed that genes inside these inversions are involved in water homeostasis. To test this hypothesis, we compared the desiccation resistance of alternative karyotypes from a colonised 2Rb/2La polymorphic population of A. gambiae from Cameroon. The strain included only the molecular form S, one of the genetic units marking incipient speciation in this taxon. Day-old mosquitoes of both sexes were assayed individually for time to death in a dry environment and the karyotype of each was determined post-mortem using molecular diagnostic assays for each inversion. In agreement with expectations based on their eco-geographical distribution, we found that 2La homokaryotypes survived significantly longer (1.3 hours) than the other karyotypes. However, there was weak support for the effect of 2Rb on desiccation resistance. Larger mosquitoes survived longer than smaller ones. Median survival of females was greater than males, but the effect of sex on desiccation resistance was weakly supported, indicating that differential survival was correlated to differences between sexes in average size. We found weak evidence for a heterotic effect of 2La karyotype on size in females. These results support the notion that genes located inside the 2La inversion are involved in water balance, contributing towards local adaptation of A. gambiae to xeric habitats, beyond the adaptive value conferred by a larger body size