Exact Dimensionality Selection for Bayesian PCA

We present a Bayesian model selection approach to estimate the intrinsic dimensionality of a high-dimensional dataset. To this end, we introduce a novel formulation of the probabilisitic principal component analysis model based on a normal-gamma prior distribution. In this context, we exhibit a closed-form expression of the marginal likelihood which allows to infer an optimal number of components. We also propose a heuristic based on the expected shape of the marginal likelihood curve in order to choose the hyperparameters. In non-asymptotic frameworks, we show on simulated data that this exact dimensionality selection approach is competitive with both Bayesian and frequentist state-of-the-art methods

Stationary convection-diffusion between two co-axial cylinders

In this note, we examine the high Peclet number limit of the stationary extended Graetz problem for which two families of real and imaginary eigenvalues are associated, respectively, with a downstream convective relaxation and the upstream diffusive establishment. The asymptotic behavior of both families of eigenvalues is studied, in the limit of large Peclet number and thin wall, which bring to the fore a single parameter dependence, previously mentioned in the literature from numerical investigations [M.A. Cotton, J.D. Jackson, in: R.W. Lewis, K. Morgan (Eds.), Numerical Methods in Thermal Problems, vol. IV, Pineridge Press, Swansea, 1985, pp. 504–515]. The fully developed region is specifically studied thanks to the first eigenvalue dependence on the Peclet number, on the thermal conductivity coefficients and on the diameter ratio of the cylinders. The effective transport between the fluid and the solid is investigated through the evaluation of the fully developed Nusselt number and experimental measurements

Administering Systemic Risk vs. Administering Justice: What Can We Do Now that We Have Agreed to Pay Differences?

Professor Stout's brilliant concept of disagreement-based speculation (in "Risk, Speculation, and OTC Derivatives: An Inaugural Essay for Convivium") calls for further developments and studies concerning implications for stability and resilience of the financial system over time. Moreover, it also suggests rediscovering and situating the socio-economic function of finance (and financing) in the economy and society. To complement this approach, we recall the European acceptance of "paying differences" since late nineteenth century. Derivative assets were traded in Europe, but the underlying assets (stocks and bonds) on which derivatives are built were authorized beforehand. Marteau and Morand (2010) recently appealed for reintroducing an a priori authorization procedure before new derivative assets can be marketed: this view thus inherits a century-long tradition. Eventually, it seems that a priori authorization allows for administration of systemic risk while common law-inherited rejection of disagreement-based speculation is a strong foundation for both supervisory and legal (a posteriori) decisions.

Scattering of a cross-polarized linear wave by a soliton at an optical event horizon in a birefringent nanophotonic waveguide

The scattering of a linear wave on an optical event horizon, induced by a cross polarized soliton, is experimentally and numerically investigated in integrated structures. The experiments are performed in a dispersion-engineered birefringent silicon nanophotonic waveguide. In stark contrast with co-polarized waves, the large difference between the group velocity of the two cross-polarized waves enables a frequency conversion almost independent on the soliton wavelength. It is shown that the generated idler is only shifted by 10 nm around 1550 nm over a pump tuning range of 350 nm. Simulations using two coupled full vectorial nonlinear Schr\"odinger equations fully support the experimental results

Generation of ultra broadband coherent supercontinuum in tapered and dispersion managed silicon nanophotonic waveguides

Tapered and dispersion managed (DM) silicon nanophotonic waveguides are investigated for the generation of optimal ultra broadband supercontinuum (SC). DM waveguides are structures showing a longitudinally dependent group velocity dispersion that results from the variation of the waveguide width with the propagation distance. For the generation of optimal SC, a genetic algorithm has been used to find the best dispersion map. This allows for the generation of highly coherent supercontinuums that span over 1.14 octaves from 1300 nm to 2860 nm and 1.25 octaves from 1200 nm to 2870 nm at -20 dB level for the tapered and DM waveguides respectively, for a 2 $\mu$m, 200 fs and 6.4 pJ input pulse. The comparison of these two structures with the usually considered optimal fixed width waveguide shows that the SC is broader and flatter in the more elaborated DM waveguide, while the high coherence is ensured by the varying dispersion.Comment: arXiv admin note: substantial text overlap with arXiv:1610.0566

Are Firms That Received R&D Subsidies More Innovative?

This paper looks at the effectiveness of R&D grants for Canadian plants that already benefit from R&D tax credits. Using a non-parametric matching estimator, we find that firms that benefited from both policy measures introduced more new products than their counterparts that only benefited from R&D tax incentives. They also made more world-first product innovations and were more successful in commercializing their innovations.Innovations, R&D, Matching Estimators, Mahalanobis, Innovation Survey, Tax Credits, Grants