Positivity and lower bounds for the density of Wiener functionals

We consider a functional on the Wiener space which is smooth and not degenerated in Malliavin sense and we give a criterion of strict positivity of the density. We also give lower bounds for the density. These results are based on the representation of the density by means of the Riesz transform introduced by Malliavin and Thalmaier and on the estimates of the Riesz transform given Bally and Caramellino

Regularity of Wiener functionals under a H\"ormander type condition of order one

We study the local existence and regularity of the density of the law of a functional on the Wiener space which satisfies a criterion that generalizes the H\"ormander condition of order one (that is, involving the first order Lie brackets) for diffusion processes

Predicting Blood Glucose with an LSTM and Bi-LSTM Based Deep Neural Network

A deep learning network was used to predict future blood glucose levels, as this can permit diabetes patients to take action before imminent hyperglycaemia and hypoglycaemia. A sequential model with one long-short-term memory (LSTM) layer, one bidirectional LSTM layer and several fully connected layers was used to predict blood glucose levels for different prediction horizons. The method was trained and tested on 26 datasets from 20 real patients. The proposed network outperforms the baseline methods in terms of all evaluation criteria.Comment: 5 pages, submitted to 2018 14th Symposium on Neural Networks and Applications (NEUREL

Multi-step Richardson-Romberg Extrapolation: Remarks on Variance Control and complexity

We propose a multi-step Richardson-Romberg extrapolation method for the computation of expectations $E f(X_{_T})$ of a diffusion $(X_t)_{t\in [0,T]}$ when the weak time discretization error induced by the Euler scheme admits an expansion at an order $R\ge 2$. The complexity of the estimator grows as $R^2$ (instead of $2^R$) and its variance is asymptotically controlled by considering some consistent Brownian increments in the underlying Euler schemes. Some Monte carlo simulations carried with path-dependent options (lookback, barriers) which support the conjecture that their weak time discretization error also admits an expansion (in a different scale). Then an appropriate Richardson-Romberg extrapolation seems to outperform the Euler scheme with Brownian bridge.Comment: 28 pages, \`a para\^itre dans Monte Carlo Methods and Applications Journa

Non elliptic SPDEs and ambit fields: existence of densities

Relying on the method developed in [debusscheromito2014], we prove the existence of a density for two different examples of random fields indexed by (t,x)\in(0,T]\times \Rd. The first example consists of SPDEs with Lipschitz continuous coefficients driven by a Gaussian noise white in time and with a stationary spatial covariance, in the setting of [dalang1999]. The density exists on the set where the nonlinearity $\sigma$ of the noise does not vanish. This complements the results in [sanzsuess2015] where $\sigma$ is assumed to be bounded away from zero. The second example is an ambit field with a stochastic integral term having as integrator a L\'evy basis of pure-jump, stable-like type.Comment: 23 page

X-rays from HH210 in the Orion nebula

We report the detection during the Chandra Orion Ultradeep Project (COUP) of two soft, constant, and faint X-ray sources associated with the Herbig-Haro object HH210. HH210 is located at the tip of the NNE finger of the emission line system bursting out of the BN-KL complex, northwest of the Trapezium cluster in the OMC-1 molecular cloud. Using a recent Halpha image obtained with the ACS imager on board HST, and taking into account the known proper motions of HH210 emission knots, we show that the position of the brightest X-ray source, COUP703, coincides with the emission knot 154-040a of HH210, which is the emission knot of HH210 having the highest tangential velocity (425 km/s). The second X-ray source, COUP704, is located on the complicated emission tail of HH210 close to an emission line filament and has no obvious optical/infrared counterpart. Spectral fitting indicates for both sources a plasma temperature of ~0.8 MK and absorption-corrected X-ray luminosities of about 1E30 erg/s (0.5-2.0 keV). These X-ray sources are well explained by a model invoking a fast-moving, radiative bow shock in a neutral medium with a density of ~12000 cm^{-3}. The X-ray detection of COUP704 therefore reveals, in the complicated HH210 region, an energetic shock not yet identified at other wavelengths.Comment: 5 pages, 3 figures; accepted for publication in A&A Letter

The Australian mango breeding project

The Australian mango industry is currently dominated by Kensington Pride which comprises some 80 per cent of all plantings. This is in contrast to other countries with modern export industries such as South Africa, Israel and Mexico, which are based on three to five cultivars. A joint venture between Agriculture Western Australia, the Queensland Department of Primary Industries (DPI), the Northern Territory Department of Primary Industries and Fisheries (DPIF) and the CSIRO commenced six years ago to generate a wide range of promising new mango hybrids that can meet both domestic and export market requirements. There has been considerable success to date

Accurate seeing measurements with MASS and DIMM

Astronomical seeing is quantified by a single parameter, turbulence integral, in the framework of the Kolmogorov turbulence model. This parameter can be routinely measured by a Differential Image Motion Monitor, DIMM. A new instrument, Multi-Aperture Scintillation Sensor (MASS), permits to measure the seeing in the free atmosphere above ~0.5km and, together with a DIMM, to estimate the ground-layer seeing. The absolute accuracy of both methods is studied here using analytical theory, numerical simulation, and experiments. A modification of the MASS data processing to compensate for partially saturated scintillation is developed. We find that the DIMM can be severely biased by optical aberrations (e.g. defocus) and propagation. Seeing measurements with DIMM and MASS can reach absolute accuracy of ~10% when their biases are carefully controlled. Pushing this limit to 1% appears unrealistic because the seeing itself is just a model-dependent parameter of a non-stationary random process.Comment: 13 pages, 14 figures. Accepted for publication in MNRA