Multiple scattering of polarized light in disordered media exhibiting short-range structural correlations

We develop a model based on a multiple scattering theory to describe the diffusion of polarized light in disordered media exhibiting short-range structural correlations. Starting from exact expressions of the average field and the field spatial correlation function, we derive a radiative transfer equation for the polarization-resolved specific intensity that is valid for weak disorder and we solve it analytically in the diffusion limit. A decomposition of the specific intensity in terms of polarization eigenmodes reveals how structural correlations, represented via the standard anisotropic scattering parameter $g$, affect the diffusion of polarized light. More specifically, we find that propagation through each polarization eigenchannel is described by its own transport mean free path that depends on $g$ in a specific and non-trivial way

Transport in quenched disorder: light diffusion in strongly heterogeneous turbid media

We present a theoretical and experimental study of light transport in disordered media with strongly heterogeneous distribution of scatterers formed via non-scattering regions. Step correlations induced by quenched disorder are found to prevent diffusivity from diverging with increasing heterogeneity scale, contrary to expectations from annealed models. Spectral diffusivity is measured for a porous ceramic where nanopores act as scatterers and macropores render their distribution heterogeneous. Results agree well with Monte Carlo simulations and a proposed analytical model.Comment: 12 pages, 9 figures (significant amount of supplemental information

Weak localization of light in superdiffusive random systems

L\'evy flights constitute a broad class of random walks that occur in many fields of research, from animal foraging in biology, to economy to geophysics. The recent advent of L\'evy glasses allows to study L\'evy flights in controlled way using light waves. This raises several questions about the influence of superdiffusion on optical interference effects like weak and strong localization. Super diffusive structures have the extraordinary property that all points are connected via direct jumps, meaning that finite-size effects become an essential part of the physical problem. Here we report on the experimental observation of weak localization in L\'evy glasses and compare results with recently developed optical transport theory in the superdiffusive regime. Experimental results are in good agreement with theory and allow to unveil how light propagates inside a finite-size superdiffusive system

A unified censored normal regression model for qPCR differential gene expression analysis

Reverse transcription quantitative polymerase chain reaction (RT-qPCR) is considered as the gold standard for accurate, sensitive, and fast measurement of gene expression. Prior to downstream statistical analysis, RT-qPCR fluorescence amplification curves are summarized into one single value, the quantification cycle (Cq). When RT-qPCR does not reach the limit of detection, the Cq is labeled as undetermined . Current state of the art qPCR data analysis pipelines acknowledge the importance of normalization for removing non-biological sample to sample variation in the Cq values. However, their strategies for handling undetermined Cq values are very ad hoc. We show that popular methods for handling undetermined values can have a severe impact on the downstream differential expression analysis. They introduce a considerable bias and suffer from a lower precision. We propose a novel method that unites preprocessing and differential expression analysis in a single statistical model that provides a rigorous way for handling undetermined Cq values. We compare our method with existing approaches in a simulation study and on published microRNA and mRNA gene expression datasets. We show that our method outperforms traditional RT-qPCR differential expression analysis pipelines in the presence of undetermined values, both in terms of accuracy and precision