Mother-to-child transmission of HIV: a simulation-based approach for the evaluation of intervention strategies

Mother-to-child transmission (MTCT) of HIV is the most significant source of HIV infection in children below the age of 15 years. In 2000 alone, about 600 000 new infections occurred, the vast majority from mothers living in developing countries who were not aware of their HIV-positive status. To date, at least 4.3 million children have died from AIDS. In this paper, we discuss the development of an operational model that can be used to evaluate intervention options for the prevention of MTCT of HIV. The problem was approached by defining suitable pregnancy risk groups, prevention options and the required model outputs to evaluate different intervention strategies. The method chosen to approach the problem was a discrete-event, three-phase simulation, built in Visual Basic, with a stochastic semi-Markov structure. The developed model takes individual pregnant women through each stage of their pregnancy, labour and birth. Different intervention strategies may be modelled at any time, including short-course antiretroviral drugs and cessation of breastfeeding. The model is demonstrated with data from Botswana, which has one of the highest HIV-infection rates in the world.     

Rational Points on the Sphere

Using only basic tools from the theory of modular forms, the rational points of bounded height on the sphere are counted and shown to be uniformly distributed. The more difficult case of points with a given height is also treated.     

Finite Hurwitz braid group actions for Artin groups

We prove that (with two possible exceptions) the Hurwitz braid group action on the sequence of standard generators of an irreducible Artin group has a finite orbit if and only if the Artin group is of finite type (i.e., the corresponding Coxeter group is finite).     

The spectral measure of a Jacobi matrix in terms of the Fourier transform of the perturbation

We study the spectral properties of Jacobi matrices. By combining Killip's technique [12] with the technique of Killip and Simon [13] we obtain a result relating the properties of the elements of Jacobi matrices and the corresponding spectral measures. This theorem is a natural extension of a recent result of Laptev-Naboko-Safronov [17]. The author thanks Sergei Naboko for useful discussions and Barry Simon for pointing out the conjecture.     

On the characterisation of paired monotone metrics

Hasegawa and Petz introduced the notion of paired monotone metrics. They also gave a characterisation theorem showing that Wigner-Yanase-Dyson metrics are the only members of the paired family. In this paper we show that the characterisation theorem holds true under hypotheses that are more general than those used in the above quoted references.     

Natural Operators Lifting Vector Fields to Bundles of Weil Contact Elements

Let A be a Weil algebra. The bijection between all natural operators lifting vector fields from m-manifolds to the bundle functor K ^A of Weil contact elements and the subalgebra of fixed elements SA of the Weil algebra A is determined and the bijection between all natural affinors on K ^A and SA is deduced. Furthermore, the rigidity of the functor K ^A is proved. Requisite results about the structure of SA are obtained by a purely algebraic approach, namely the existence of nontrivial SA is discussed.     

Ab initio study of sodium intercalation into metal oxides

Using the full-potential linearized augmented plane wave (FP-LAPW) method, we have studied the effect of chemistry on the average intercalation voltage (AIV) caused by the Na ions intercalating into transition metal oxides. The effect of transition metal was systematically studied by varying M=Co, Ni and Mn in NaMO₂ and fixing the α-NaFeO₂ layered structure. The effect of the guest atoms into the host material is discussed in terms of the structural and electronic properties. Comparatively to Li intercalation, a significant electron transfer towards transition metal was found. This observation suggests that the transition metal contribute to the AIV determination and confirms the common assumption that intercalated electron reduces M⁴⁺ to M³⁺.