The relationship between parental education and children's schooling in a time of economic turmoil: The case of East Zimbabwe, 2001 to 2011.

Using data collected from 1998 to 2011 in a general population cohort study in eastern Zimbabwe, we describe education trends and the relationship between parental education and children's schooling during the Zimbabwean economic collapse of the 2000s. During this period, the previously-rising trend in education stalled, with girls suffering disproportionately; however, female enrolment increased as the economy began to recover. Throughout the period, children with more educated parents continued to have better outcomes such that, at the population level, an underlying increase in the proportion of children with more educated parents may have helped to maintain the upwards education trend

Randomized Rounding for the Largest Simplex Problem

The maximum volume $j$-simplex problem asks to compute the $j$-dimensional simplex of maximum volume inside the convex hull of a given set of $n$ points in $\mathbb{Q}^d$. We give a deterministic approximation algorithm for this problem which achieves an approximation ratio of $e^{j/2 + o(j)}$. The problem is known to be $\mathrm{NP}$-hard to approximate within a factor of $c^{j}$ for some constant $c > 1$. Our algorithm also gives a factor $e^{j + o(j)}$ approximation for the problem of finding the principal $j\times j$ submatrix of a rank $d$ positive semidefinite matrix with the largest determinant. We achieve our approximation by rounding solutions to a generalization of the $D$-optimal design problem, or, equivalently, the dual of an appropriate smallest enclosing ellipsoid problem. Our arguments give a short and simple proof of a restricted invertibility principle for determinants

qq-Trinomial identities

We obtain connection coefficients between $q$-binomial and $q$-trinomial coefficients. Using these, one can transform $q$-binomial identities into a $q$-trinomial identities and back again. To demonstrate the usefulness of this procedure we rederive some known trinomial identities related to partition theory and prove many of the conjectures of Berkovich, McCoy and Pearce, which have recently arisen in their study of the $\phi_{2,1}$ and $\phi_{1,5}$ perturbations of minimal conformal field theory.Comment: 21 pages, AMSLate

Rogers-Szego polynomials and Hall-Littlewood symmetric functions

We use Rogers-Szego polynomials to unify some well-known identities for Hall-Littlewood symmetric functions due to Macdonald and Kawanaka.Comment: 18 page

Optimizing local protocols implementing nonlocal quantum gates

We present a method of optimizing recently designed protocols for implementing an arbitrary nonlocal unitary gate acting on a bipartite system. These protocols use only local operations and classical communication with the assistance of entanglement, and are deterministic while also being "one-shot", in that they use only one copy of an entangled resource state. The optimization is in the sense of minimizing the amount of entanglement used, and it is often the case that less entanglement is needed than with an alternative protocol using two-way teleportation.Comment: 11 pages, 1 figure. This is a companion paper to arXiv:1001.546

A non-symmetric Yang-Baxter Algebra for the Quantum Nonlinear Schr\"odinger Model

We study certain non-symmetric wavefunctions associated to the quantum nonlinear Schr\"odinger model, introduced by Komori and Hikami using Gutkin's propagation operator, which involves representations of the degenerate affine Hecke algebra. We highlight how these functions can be generated using a vertex-type operator formalism similar to the recursion defining the symmetric (Bethe) wavefunction in the quantum inverse scattering method. Furthermore, some of the commutation relations encoded in the Yang-Baxter equation for the relevant monodromy matrix are generalized to the non-symmetric case.Comment: 31 pages; added some references; minor corrections throughou

Synchronization of chaotic networks with time-delayed couplings: An analytic study

Networks of nonlinear units with time-delayed couplings can synchronize to a common chaotic trajectory. Although the delay time may be very large, the units can synchronize completely without time shift. For networks of coupled Bernoulli maps, analytic results are derived for the stability of the chaotic synchronization manifold. For a single delay time, chaos synchronization is related to the spectral gap of the coupling matrix. For networks with multiple delay times, analytic results are obtained from the theory of polynomials. Finally, the analytic results are compared with networks of iterated tent maps and Lang-Kobayashi equations which imitate the behaviour of networks of semiconductor lasers

Precise calculation of transition frequencies of hydrogen and deuterium based on a least-squares analysis

We combine a limited number of accurately measured transition frequencies in hydrogen and deuterium, recent quantum electrodynamics (QED) calculations, and, as an essential additional ingredient, a generalized least-squares analysis, to obtain precise and optimal predictions for hydrogen and deuterium transition frequencies. Some of the predicted transition frequencies have relative uncertainties more than an order of magnitude smaller than that of the g-factor of the electron, which was previously the most accurate prediction of QED.Comment: 4 pages, RevTe

FlaA1, a New Bifunctional UDP-GlcNAc C6Dehydratase/ C4 Reductase from Helicobacter pylori

FlaA1 is a small soluble protein of unknown function in Helicobacter pylori. It has homologues that are essential for the virulence of numerous medically relevant bacteria. FlaA1 was overexpressed as a histidine-tagged protein and purified to homogeneity by nickel chelation and cation exchange chromatography. Spectrophotometric assays, capillary electrophoresis, and mass spectrometry analyses showed that FlaA1 is a novel bifunctional C(6) dehydratase/C(4) reductase specific for UDP-GlcNAc. It converts UDP-GlcNAc into a UDP-4-keto-6-methyl-GlcNAc intermediate, which is stereospecifically reduced into UDP-QuiNAc. Substrate conversions as high as 80% were obtained at equilibrium. The K(m) and V(max) for UDP-GlcNAc were 159 microm and 65 pmol/min, respectively. No exogenous cofactor was required to obtain full activity of FlaA1. Additional NADH was only used with poor efficiency for the reduction step. The biochemical characterization of FlaA1 is important for the elucidation of biosynthetic pathways that lead to the formation of 2,6-deoxysugars in medically relevant bacteria. It establishes unambiguously the first step of the pathway and provides the means of preparing the substrate UDP-QuiNAc, which is necessary for the study of downstream enzymes