Relativistic stable processes in quasiballistic heat conduction in semiconductors.

In this article, we show how relativistic α-stable processes can be used to explain quasiballistic heat conduction in semiconductors. This is a method that can fit experimental results of ultrafast laser heating in alloys. It also provides a connection to a rich literature on the Feynman-Kac formalism and random processes that transition from a stable Lévy process on short time and length scales to the Brownian motion at larger scales. This transition was captured by a heuristic truncated Lévy distribution in earlier papers. The rigorous Feynman-Kac approach is used to derive sharp bounds for the transition kernel. Future directions are briefly discussed.

Monte Carlo methods for light propagation in biological tissues.

Light propagation in turbid media is driven by the equation of radiative transfer. We give a formal probabilistic representation of its solution in the framework of biological tissues and we implement algorithms based on Monte Carlo methods in order to estimate the quantity of light that is received by a homogeneous tissue when emitted by an optic fiber. A variance reduction method is studied and implemented, as well as a Markov chain Monte Carlo method based on the Metropolis-Hastings algorithm. The resulting estimating methods are then compared to the so-called Wang-Prahl (or Wang) method. Finally, the formal representation allows to derive a non-linear optimization algorithm close to Levenberg-Marquardt that is used for the estimation of the scattering and absorption coefficients of the tissue from measurements.

Spectral features selection and classification for bimodal optical spectroscopy applied to bladder cancer in vivo diagnosis.

This paper describes an experimental study combining spatially resolved autofluorescence (AF) and diffuse reflectance (DR) fibred spectroscopies to discriminate in vivo between healthy and pathological tissues in a preclinical model of bladder cancer. Then, a detailed step-by-step analysis scheme is presented for the extraction and the selection of discriminative spectral features (correlation, linear discriminant, and logistic regression analysis), and for the spectroscopic data final classification algorithms (regularized discriminant analysis and support vector machines). Significant differences between healthy, inflammatory, and tumoral tissues were obtained by selecting a reasonable number of discriminant spectral features from AF, DR, and intrinsic fluorescence spectra, leading to improved sensitivity (87%) and specificity (77%) compared to monomodality (AF or DR alone).