A Fast Algorithm for Computing the p-Curvature

We design an algorithm for computing the $p$-curvature of a differential system in positive characteristic $p$. For a system of dimension $r$ with coefficients of degree at most $d$, its complexity is \softO (p d r^\omega) operations in the ground field (where $\omega$ denotes the exponent of matrix multiplication), whereas the size of the output is about $p d r^2$. Our algorithm is then quasi-optimal assuming that matrix multiplication is (\emph{i.e.} $\omega = 2$). The main theoretical input we are using is the existence of a well-suited ring of series with divided powers for which an analogue of the Cauchy--Lipschitz Theorem holds.Comment: ISSAC 2015, Jul 2015, Bath, United Kingdo

Mesopelagic N-2 fixation related to organic matter composition in the Solomon and Bismarck Seas (Southwest Pacific)

Dinitrogen (N-2) fixation was investigated together with organic matter composition in the mesopelagic zone of the Bismarck (Transect 1) and Solomon (Transect 2) Seas (Southwest Pacific). Transparent exopolymer particles (TEP) and the presence of compounds sharing molecular formulae with saturated fatty acids and sugars, as well as dissolved organic matter (DOM) compounds containing nitrogen (N) and phosphorus (P) were higher on Transect 1 than on Transect 2, while oxygen concentrations showed an opposite pattern. N-2 fixation rates (up to similar to 1 nmol N L-1 d(-1)) were higher in Transect 1 than in Transect 2, and correlated positively with TEP, suggesting a dependence of diazotroph activity on organic matter. The scores of the multivariate ordination of DOM molecular formulae and their relative abundance correlated negatively with bacterial abundances and positively with N-2 fixation rates, suggesting an active bacterial exploitation of DOM and its use to sustain diazotrophic activity. Sequences of the nifH gene clustered with Alpha-, Beta-, Gamma- and Deltaproteobacteria, and included representatives from Clusters I, III and IV. A third of the clone library included sequences close to the potentially anaerobic Cluster III, suggesting that N-2 fixation was partially supported by presumably particle-attached diazotrophs. Quantitative polymerase chain reaction (qPCR) primer-probe sets were designed for three phylotypes and showed low abundances, with a phylotype within Cluster III at up to 10(3) nifH gene copies L-1. These results provide new insights into the ecology of non-cyanobacterial diazotrophs and suggest that organic matter sustains their activity in the mesopelagic ocean

Ice Formation on Kaolinite: Insights from Molecular Dynamics Simulations

The formation of ice affects many aspects of our everyday life as well as technologies such as cryotherapy and cryopreservation. Foreign substances almost always aid water freezing through heterogeneous ice nucleation, but the molecular details of this process remain largely unknown. In fact, insight into the microscopic mechanism of ice formation on different substrates is difficult to obtain even via state-of-the-art experimental techniques. At the same time, atomistic simulations of heterogeneous ice nucleation frequently face extraordinary challenges due to the complexity of the water-substrate interaction and the long timescales that characterize nucleation events. Here, we have investigated several aspects of molecular dynamics simulations of heterogeneous ice nucleation considering as a prototypical ice nucleating material the clay mineral kaolinite, which is of relevance in atmospheric science. We show via seeded molecular dynamics simulations that ice nucleation on the hydroxylated (001) face of kaolinite proceeds exclusively via the formation of the hexagonal ice polytype. The critical nucleus size is two times smaller than that obtained for homogeneous nucleation at the same supercooling. Previous findings suggested that the flexibility of the kaolinite surface can alter the time scale for ice nucleation within molecular dynamics simulations. However, we here demonstrate that equally flexible (or non flexible) kaolinite surfaces can lead to very different outcomes in terms of ice formation, according to whether or not the surface relaxation of the clay is taken into account. We show that very small structural changes upon relaxation dramatically alter the ability of kaolinite to provide a template for the formation of a hexagonal overlayer of water molecules at the water-kaolinite interface, and that this relaxation therefore determines the nucleation ability of this mineral

Good reductions of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic. Part I

We prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic $(0,p)$. As a first application we provide a smooth solution (answer) to a conjecture (question) of Langlands for Shimura varieties of Hodge type. As a second application we prove the existence in arbitrary unramified mixed characteristic $(0,p)$ of integral canonical models of projective Shimura varieties of Hodge type with respect to h--hyperspecial subgroups as pro-\'etale covers of N\'eron models; this forms progress towards the proof of conjectures of Milne and Reimann. Though the second application was known before in some cases, its proof is new and more of a principle.Comment: 87 pages. Final version, to appear in Mathematische Nachrichten (most alignment issues kept loose to match with the layout of the journal

Accessible digital ophthalmoscopy based on liquid-lens technology

Ophthalmoscopes have yet to capitalise on novel low-cost miniature optomechatronics, which could disrupt ophthalmic monitoring in rural areas. This paper demonstrates a new design integrating modern components for ophthalmoscopy. Simulations show that the optical elements can be reduced to just two lenses: an aspheric ophthalmoscopic lens and a commodity liquid-lens, leading to a compact prototype. Circularly polarised transpupilary illumination, with limited use so far for ophthalmoscopy, suppresses reflections, while autofocusing preserves image sharpness. Experiments with a human-eye model and cadaver porcine eyes demonstrate our prototype’s clinical value and its potential for accessible imaging when cost is a limiting factor

Subnanosecond spectral diffusion measurement using photon correlation

Spectral diffusion is a result of random spectral jumps of a narrow line as a result of a fluctuating environment. It is an important issue in spectroscopy, because the observed spectral broadening prevents access to the intrinsic line properties. However, its characteristic parameters provide local information on the environment of a light emitter embedded in a solid matrix, or moving within a fluid, leading to numerous applications in physics and biology. We present a new experimental technique for measuring spectral diffusion based on photon correlations within a spectral line. Autocorrelation on half of the line and cross-correlation between the two halves give a quantitative value of the spectral diffusion time, with a resolution only limited by the correlation set-up. We have measured spectral diffusion of the photoluminescence of a single light emitter with a time resolution of 90 ps, exceeding by four orders of magnitude the best resolution reported to date

Tunable Indistinguishable Photons From Remote Quantum Dots

Single semiconductor quantum dots have been widely studied within devices that can apply an electric field. In the most common system, the low energy offset between the InGaAs quantum dot and the surrounding GaAs material limits the magnitude of field that can be applied to tens of kVcm^-1, before carriers tunnel out of the dot. The Stark shift experienced by the emission line is typically 1 meV. We report that by embedding the quantum dots in a quantum well heterostructure the vertical field that can be applied is increased by over an order of magnitude whilst preserving the narrow linewidths, high internal quantum efficiencies and familiar emission spectra. Individual dots can then be continuously tuned to the same energy allowing for two-photon interference between remote, independent, quantum dots

Surface specific peptide immobilization on radiografted polymers as potential screening assays for antiangiogenic immunotherapy

International audienceAngiogenesis is a key process of cancer development and metastasis. It's inhibition is an important and promising strategy to block tumor growth and invasion. One of these approaches, based on antiangiogenic immunotherapy, is the recognition of a specific region of an angiogenic growth factor, called VEGF-A, by monoclonal antibodies. Thus, we aimed to design a novel assay to screen potential monoclonal antibodies directed against VEGF-A. In a first approach, we chose to perform covalent coupling of angiogenesis active cyclopeptides onto biocompatible thermoplastic transparent PVDF films and to fully characterize the chemical structure, the surface state and the biochemical properties of the synthesized devices. Electron beam radiation created radical sites on PVDF films without adding any toxic chemicals. These primary radicals and some induced peroxides were used as initiators for acrylic acid polymerization. Under our experimental conditions, surface grafting was favoured. Functionalization of PVDF-g-PAA films with peptides via a spacer arm was possible by performing two subsequent coupling reactions. EDC was used as coupling agent. Spacer arm saturation of the film surface was achieved for 25 mol% yield meaning that one spacer arm on four carboxylic acids were covalently bound. Peptide immobilization resulted in binding 10 times less leading to a final 3 mol% yield. Binding densities are governed by their individual space requirements. Each chemical step has been followed by FTIR in ATR mode, NMR using HR MAS technique and XPS. From XPS results, a layer of peptide covered PVDF-g-PAA film surface. The amounts of covalently immobilized peptide were determined using indirect UV spectroscopy on supernatant reaction solution. Yields were correlated with high resolution NMR results. The peptide/antibody recognition validated our system showing the conservation of peptide tridimensional structure with a positive response to specific antibodies. Because of the covalent protein linkage to PVDF films, a simple cleaning with immunoaffinity chromatography buffer allows the films to be reused