Cohomology Groups of Deformations of Line Bundles on Complex Tori

The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative deformations of complex tori. Our analysis interpolates between two extreme cases. The first case is a calculation of the space of (cohomological) theta functions for line bundles over constant, commutative deformations. The second case is a calculation of the cohomologies of non-commutative deformations of degree-zero line bundles.Comment: 24 pages, exposition improved, typos fixe

Electrochemical performances and post-operational characterization of a segmented sofc operated under load for 15k hours

In the frame of the ENDURANCE FCH-JU-FP7 project (2014-2017) a segmented cell (20 segments regularly distributed from fuel inlet to fuel outlet) was operated for 15k hours in co-flow at 750\ub0C (average temperature) in hydrogen under load. Each segment was carefully monitored during operation by periodically acquiring the impedance spectra and constantly checking the voltage under current load. After 15k hours of operation the test was stopped and the cell used for further investigations in order to compare the cell evolution with the segment degradation. The overall observation in cross section of the cell has shown a good stability, however some differences were observed in the electrodes that might be related to the local operating conditions: temperature, H2 /H2O ratio in the fuel stream. The gathered results will contribute to increase the understanding the evolution of a SOFC in real operating conditions. Evidences of the effect of temperature, time and fuel pollutants were found

Calibrated cycles and T-duality

For Hitchin's generalised geometries we introduce and analyse the concept of a structured submanifold which encapsulates the classical notion of a calibrated submanifold. Under a suitable integrability condition on the ambient geometry, these generalised calibrated cycles minimise a functional occurring as D-brane energy in type II string theories, involving both so-called NS-NS- and R-R-fields. Further, we investigate the behaviour of calibrated cycles under T-duality and construct non-trivial examples.Comment: 43 pages. v4: formalism and T-duality part considerably expande

Fredholm Modules on P.C.F. Self-Similar Fractals and their Conformal Geometry

The aim of the present work is to show how, using the differential calculus associated to Dirichlet forms, it is possible to construct Fredholm modules on post critically finite fractals by regular harmonic structures. The modules are d-summable, the summability exponent d coinciding with the spectral dimension of the generalized laplacian operator associated with the regular harmonic structures. The characteristic tools of the noncommutative infinitesimal calculus allow to define a d-energy functional which is shown to be a self-similar conformal invariant.Comment: 16 page

Mirror duality and noncommutative tori

In this paper, we study a mirror duality on a generalized complex torus and a noncommutative complex torus. First, we derive a symplectic version of Riemann condition using mirror duality on ordinary complex tori. Based on this we will find a mirror correspondence on generalized complex tori and generalize the mirror duality on complex tori to the case of noncommutative complex tori.Comment: 22pages, no figure

Supersymmetric D-branes and calibrations on general N=1 backgrounds

We study the conditions to have supersymmetric D-branes on general {\cal N}=1 backgrounds with Ramond-Ramond fluxes. These conditions can be written in terms of the two pure spinors associated to the SU(3)\times SU(3) structure on T_M\oplus T^\star_M, and can be split into two parts each involving a different pure spinor. The first involves the integrable pure spinor and requires the D-brane to wrap a generalised complex submanifold with respect to the generalised complex structure associated to it. The second contains the non-integrable pure spinor and is related to the stability of the brane. The two conditions can be rephrased as a generalised calibration condition for the brane. The results preserve the generalised mirror symmetry relating the type IIA and IIB backgrounds considered, giving further evidence for this duality.Comment: 23 pages. Some improvements and clarifications, typos corrected and references added. v3: Version published in JHE

Towards mirror symmetry \`a la SYZ for generalized Calabi-Yau manifolds

Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal six-manifold M with static SU(2) structure and mirror \hat{M}, it is argued that the product M x \hat{M} is doubly fibered by supersymmetric three-tori, with both sets of fibers transverse to M and \hat{M}. The mirror map is then realized by T-dualizing the fibers. Mirror-symmetric properties of the fluxes, both geometric and non-geometric, are shown to agree with previous conjectures based on the requirement of mirror symmetry for Killing prepotentials. The fibers are conjectured to be destabilized by fluxes on generic SU(3)xSU(3) backgrounds, though they may survive at type-jumping points. T-dualizing the surviving fibers ensures the exchange of pure spinors under mirror symmetry.Comment: 30 pages, 3 figures, LaTeX; v2: references adde

Strategies for Understanding and Reducing the Plasmodium vivax and Plasmodium ovale Hypnozoite Reservoir in Papua New Guinean Children: A Randomised Placebo-Controlled Trial and Mathematical Model

The undetectable hypnozoite reservoir for relapsing Plasmodium vivax and P. ovale malarias presents a major challenge for malaria control and elimination in endemic countries. This study aims to directly determine the contribution of relapses to the burden of P. vivax and P. ovale infection, illness, and transmission in Papua New Guinean children.; From 17 August 2009 to 20 May 2010, 524 children aged 5-10 y from East Sepik Province in Papua New Guinea (PNG) participated in a randomised double-blind placebo-controlled trial of blood- plus liver-stage drugs (chloroquine [CQ], 3 d; artemether-lumefantrine [AL], 3 d; and primaquine [PQ], 20 d, 10 mg/kg total dose) (261 children) or blood-stage drugs only (CQ, 3 d; AL, 3 d; and placebo [PL], 20 d) (263 children). Participants, study staff, and investigators were blinded to the treatment allocation. Twenty children were excluded during the treatment phase (PQ arm: 14, PL arm: 6), and 504 were followed actively for 9 mo. During the follow-up time, 18 children (PQ arm: 7, PL arm: 11) were lost to follow-up. Main primary and secondary outcome measures were time to first P. vivax infection (by qPCR), time to first clinical episode, force of infection, gametocyte positivity, and time to first P. ovale infection (by PCR). A basic stochastic transmission model was developed to estimate the potential effect of mass drug administration (MDA) for the prevention of recurrent P. vivax infections. Targeting hypnozoites through PQ treatment reduced the risk of having at least one qPCR-detectable P. vivax or P. ovale infection during 8 mo of follow-up (P. vivax: PQ arm 0.63/y versus PL arm 2.62/y, HR = 0.18 [95% CI 0.14, 0.25], p < 0.001; P. ovale: 0.06 versus 0.14, HR = 0.31 [95% CI 0.13, 0.77], p = 0.011) and the risk of having at least one clinical P. vivax episode (HR = 0.25 [95% CI 0.11, 0.61], p = 0.002). PQ also reduced the molecular force of P. vivax blood-stage infection in the first 3 mo of follow-up (PQ arm 1.90/y versus PL arm 7.75/y, incidence rate ratio [IRR] = 0.21 [95% CI 0.15, 0.28], p < 0.001). Children who received PQ were less likely to carry P. vivax gametocytes (IRR = 0.27 [95% CI 0.19, 0.38], p < 0.001). PQ had a comparable effect irrespective of the presence of P. vivax blood-stage infection at the time of treatment (p = 0.14). Modelling revealed that mass screening and treatment with highly sensitive quantitative real-time PCR, or MDA with blood-stage treatment alone, would have only a transient effect on P. vivax transmission levels, while MDA that includes liver-stage treatment is predicted to be a highly effective strategy for P. vivax elimination. The inclusion of a directly observed 20-d treatment regime maximises the efficiency of hypnozoite clearance but limits the generalisability of results to real-world MDA programmes.; These results suggest that relapses cause approximately four of every five P. vivax infections and at least three of every five P. ovale infections in PNG children and are important in sustaining transmission. MDA campaigns combining blood- and liver-stage treatment are predicted to be a highly efficacious intervention for reducing P. vivax and P. ovale transmission.; ClinicalTrials.gov NCT02143934

From non-symmetric particle systems to non-linear PDEs on fractals

We present new results and challenges in obtaining hydrodynamic limits for non-symmetric (weakly asymmetric) particle systems (exclusion processes on pre-fractal graphs) converging to a non-linear heat equation. We discuss a joint density-current law of large numbers and a corresponding large deviations principle.Comment: v2: 10 pages, 1 figure. To appear in the proceedings for the 2016 conference "Stochastic Partial Differential Equations & Related Fields" in honor of Michael R\"ockner's 60th birthday, Bielefel