Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian

We consider Hamilton Jacobi Bellman equations in an inifinite dimensional Hilbert space, with quadratic (respectively superquadratic) hamiltonian and with continuous (respectively lipschitz continuous) final conditions. This allows to study stochastic optimal control problems for suitable controlled Ornstein Uhlenbeck process with unbounded control processes

Invariant and polynomial identities for higher rank matrices

We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct discriminants and the determinant as the discriminant of order $d$, where $d$ is the dimension of the matrix. The characteristic polynomials and the Cayley--Hamilton theorem for higher rank matrices are obtained there from

A bipartite class of entanglement monotones for N-qubit pure states

We construct a class of algebraic invariants for N-qubit pure states based on bipartite decompositions of the system. We show that they are entanglement monotones, and that they differ from the well know linear entropies of the sub-systems. They therefore capture new information on the non-local properties of multipartite systems.Comment: 6 page

The invariant-comb approach and its relation to the balancedness of multipartite entangled states

The invariant-comb approach is a method to construct entanglement measures for multipartite systems of qubits. The essential step is the construction of an antilinear operator that we call {\em comb} in reference to the {\em hairy-ball theorem}. An appealing feature of this approach is that for qubits (or spins 1/2) the combs are automatically invariant under SL(2,\CC), which implies that the obtained invariants are entanglement monotones by construction. By asking which property of a state determines whether or not it is detected by a polynomial SL(2,\CC) invariant we find that it is the presence of a {\em balanced part} that persists under local unitary transformations. We present a detailed analysis for the maximally entangled states detected by such polynomial invariants, which leads to the concept of {\em irreducibly balanced} states. The latter indicates a tight connection with SLOCC classifications of qubit entanglement. \\ Combs may also help to define measures for multipartite entanglement of higher-dimensional subsystems. However, for higher spins there are many independent combs such that it is non-trivial to find an invariant one. By restricting the allowed local operations to rotations of the coordinate system (i.e. again to the SL(2,\CC)) we manage to define a unique extension of the concurrence to general half-integer spin with an analytic convex-roof expression for mixed states.Comment: 17 pages, revtex4. Substantially extended manuscript (e.g. proofs have been added); title and abstract modified

Multipartite entanglement in 2 x 2 x n quantum systems

We classify multipartite entangled states in the 2 x 2 x n (n >= 4) quantum system, for example the 4-qubit system distributed over 3 parties, under local filtering operations. We show that there exist nine essentially different classes of states, and they give rise to a five-graded partially ordered structure, including the celebrated Greenberger-Horne-Zeilinger (GHZ) and W classes of 3 qubits. In particular, all 2 x 2 x n-states can be deterministically prepared from one maximally entangled state, and some applications like entanglement swapping are discussed.Comment: 9 pages, 3 eps figure

Analytical solution of a model for complex food webs

We investigate numerically and analytically a recently proposed model for food webs [Nature {\bf 404}, 180 (2000)] in the limit of large web sizes and sparse interaction matrices. We obtain analytical expressions for several quantities with ecological interest, in particular the probability distributions for the number of prey and the number of predators. We find that these distributions have fast-decaying exponential and Gaussian tails, respectively. We also find that our analytical expressions are robust to changes in the details of the model.Comment: 4 pages (RevTeX). Final versio

Hematological Changes in Women and Infants Exposed to an AZT-Containing Regimen for Prevention of Mother-to-child-transmission of HIV in Tanzania.

Tanzanian guidelines for prevention of mother-to-child-transmission of HIV (PMTCT) recommend an antiretroviral combination regimen involving zidovudine (AZT) during pregnancy, single-dosed nevirapine at labor onset, AZT plus Lamivudine (3TC) during delivery, and AZT/3TC for 1-4 weeks postpartum. As drug toxicities are a relevant concern, we assessed hematological alterations in AZT-exposed women and their infants. A cohort of HIV-positive women, either with AZT intake (n = 82, group 1) or without AZT intake (n = 62, group 2) for PMTCT during pregnancy, was established at Kyela District Hospital, Tanzania. The cohort also included the infants of group 1 with an in-utero AZT exposure ≥4 weeks, receiving AZT for 1 week postpartum (n = 41), and infants of group 2 without in-utero AZT exposure, receiving a prolonged 4-week AZT tail (n = 58). Complete blood counts were evaluated during pregnancy, birth, weeks 4-6 and 12. For women of group 1 with antenatal AZT intake, we found a statistically significant decrease in hemoglobin level, red blood cells, white blood cells, granulocytes, as well as an increase in red cell distribution width and platelet count. At delivery, the median red blood cell count was significantly lower and the median platelet count was significantly higher in women of group 1 compared to group 2. At birth, infants from group 1 showed a lower median hemoglobin level and granulocyte count and a higher frequency of anemia and granulocytopenia. At 4-6 weeks postpartum, the mean neutrophil granulocyte count was significantly lower and neutropenia was significantly more frequent in infants of group 2. AZT exposure during pregnancy as well as after birth resulted in significant hematological alterations for women and their newborns, although these changes were mostly mild and transient in nature. Research involving larger cohorts is needed to further analyze the impact of AZT-containing regimens on maternal and infant health

First-phase ejection fraction by CMR predicts outcomes in aortic stenosis

BACKGROUND: First-phase ejection fraction (EF1; the ejection fraction measured during active systole up to the time of maximal aortic flow) measured by transthoracic echocardiography (TTE) is a powerful predictor of outcomes in patients with aortic stenosis. We aimed to assess whether cardiovascular magnetic resonance (CMR) might provide more precise measurements of EF1 than TTE and to examine the correlation of CMR EF1 with measures of fibrosis. METHODS: In 141 patients with at least mild aortic stenosis, we measured CMR EF1 from a short-axis 3D stack and compared its variability with TTE EF1, and its associations with myocardial fibrosis and clinical outcome (aortic valve replacement (AVR) or death). RESULTS: Intra- and inter-observer variation of CMR EF1 (standard deviations of differences within and between observers of 2.3% and 2.5% units respectively) was approximately 50% that of TTE EF1. CMR EF1 was strongly predictive of AVR or death. On multivariable Cox proportional hazards analysis, the hazard ratio for CMR EF1 was 0.93 (95% confidence interval 0.89–0.97, p = 0.001) per % change in EF1 and, apart from aortic valve gradient, CMR EF1 was the only imaging or biochemical measure independently predictive of outcome. Indexed extracellular volume was associated with AVR or death, but not after adjusting for EF1. CONCLUSIONS: EF1 is a simple robust marker of early left ventricular impairment that can be precisely measured by CMR and predicts outcome in aortic stenosis. Its measurement by CMR is more reproducible than that by TTE and may facilitate left ventricular structure–function analysis

Relativistic Calculation of two-Electron one-Photon and Hypersatellite Transition Energies for 12≤Z≤3012\leq Z\leq30 Elements

Energies of two-electron one-photon transitions from initial double K-hole states were computed using the Dirac-Fock model. The transition energies of competing processes, the K$\alpha$ hypersatellites, were also computed. The results are compared to experiment and to other theoretical calculations.Comment: accepted versio

Extended Classical Over-Barrier Model for Collisions of Highly Charged Ions with Conducting and Insulating Surfaces

We have extended the classical over-barrier model to simulate the neutralization dynamics of highly charged ions interacting under grazing incidence with conducting and insulating surfaces. Our calculations are based on simple model rates for resonant and Auger transitions. We include effects caused by the dielectric response of the target and, for insulators, localized surface charges. Characteristic deviations regarding the charge transfer processes from conducting and insulating targets to the ion are discussed. We find good agreement with previously published experimental data for the image energy gain of a variety of highly charged ions impinging on Au, Al, LiF and KI crystals.Comment: 32 pages http://pikp28.uni-muenster.de/~ducree