An Embedded Split-Step method for solving the nonlinear Schrodinger equation in optics

International audienceIn optics the nonlinear Schrõdinger equation (NLSE) which modelizes wave propagation in an optical fiber is mostly solved by the Symmetric Split-Step method. The practical efficiency of the Symmetric Split-Step method is highly dependent on the computational grid points distribution along the fiber, therefore an efficient adaptive step-size control strategy is mandatory. The most common approach for step-size control is the ``step-doubling'' approach. It provides an estimation of the local error for an extra computational cost of around 50 %. Alternatively there exist in optics literature other approaches based on the observation along the propagation length of the behavior of a given optical quantity. The step-size at each computational step is set so as to guarantee that the known properties of the quantity are preserved. These approaches derived under specific physical assumptions are low cost but suffer from a lack of generality. In this paper we present a new method for estimating the local error in the Symmetric Split-Step method when solving the NLSE. It conciliates the advantages of the step-doubling approach in terms of generality without the drawback of requiring a significant extra computational cost. The method is related to Embedded Split-Step methods for nonlinear evolution problems

Optical properties of apple skin and flesh in the wavelength range from 350 to 2200 nm

Optical measurement of fruit quality is challenging due to the presence of a skin around the fruit flesh and the multiple scattering by the structured tissues. To gain insight in the light-tissue interaction, the optical properties of apple skin and flesh tissue are estimated in the 350-2200nm range for three cultivars. For this purpose, single integrating sphere measurements are combined with inverse adding- doubling. The observed absorption coefficient spectra are dominated by water in the near infrared and by pigments and chlorophyll in the visible region, whose concentrations are much higher in skin tissue. The scattering coefficient spectra show the monotonic decrease with increasing wavelength typical for biological tissues with skin tissue being approximately three times more scattering than flesh tissue. Comparison to the values from time-resolved spectroscopy reported in literature showed comparable profiles for the optical properties, but overestimation of the absorption coefficient values, due to light losses

Images IV: Strong evolution of the oxygen abundance in gaseous phases of intermediate mass galaxies since z=0.8

Intermediate mass galaxies (logM(Msun)>10) at z~0.6 are the likeliest progenitors of the present-day numerous population of spirals. There is growing evidence that they have evolved rapidly since the last 6 to 8 Gyr ago, and likely have formed a significant fraction of their stellar mass, often showing perturbed morphologies and kinematics. We have gathered a representative sample of 88 such galaxies and have provided robust estimates of their gas phase metallicity. For doing so, we have used moderate spectral resolution spectroscopy at VLT/FORS2 with unprecedented high S/N allowing to remove biases coming from interstellar absorption lines and extinction to establish robust values of R23=([OII]3727 + [OIII]4959,5007)/Hbeta. We definitively confirm that the predominant population of z~0.6 starbursts and luminous IR galaxies (LIRGs) are on average, two times less metal rich than the local galaxies at a given stellar mass. We do find that the metal abundance of the gaseous phase of galaxies is evolving linearly with time, from z=1 to z=0 and after comparing with other studies, from z=3 to z=0. Combining our results with the reported evolution of the Tully Fisher relation, we do find that such an evolution requires that ~30% of the stellar mass of local galaxies have been formed through an external supply of gas, thus excluding the close box model. Distant starbursts & LIRGs have properties (metal abundance, star formation efficiency & morphologies) similar to those of local LIRGs. Their underlying physics is likely dominated by gas infall probably through merging or interactions. Our study further supports the rapid evolution of z~0.4-1 galaxies. Gas exchanges between galaxies is likely the main cause of this evolution.Comment: 21 pages, 12 figures, A&A, In pres

TESTING THE NEG MODEL : FURTHER EVIDENCE FROM PANEL DATA

Local wage variations in the UK are explained by two non-nested rival hypotheses. The first derives from new economic geography theory, in which wages depend on market access. The second come from urban economics theory, giving a reduced form with wage rates dependent on employment density. The paper examines whether one of these rivals is encompassed by the other by fitting an artificial nesting model using three alternative panel data estimators. The estimates indicate that neither hypothesis is encompassed by its rival, suggesting a need for new, more comprehensive, theory.PANEL DATA, SPATIALLY CORRELATED ERROR COMPONENTS, MARKET ACCESS, NEW ECONOMIC GEOGRAPHY, SPATIAL ECONOMETRICS, NON-NESTED HYPOTHESIS

Convolutional Neural Fabrics

Despite the success of CNNs, selecting the optimal architecture for a given task remains an open problem. Instead of aiming to select a single optimal architecture, we propose a "fabric" that embeds an exponentially large number of architectures. The fabric consists of a 3D trellis that connects response maps at different layers, scales, and channels with a sparse homogeneous local connectivity pattern. The only hyper-parameters of a fabric are the number of channels and layers. While individual architectures can be recovered as paths, the fabric can in addition ensemble all embedded architectures together, sharing their weights where their paths overlap. Parameters can be learned using standard methods based on back-propagation, at a cost that scales linearly in the fabric size. We present benchmark results competitive with the state of the art for image classification on MNIST and CIFAR10, and for semantic segmentation on the Part Labels dataset.Comment: Corrected typos (In proceedings of NIPS16