Model-based clustering of probability density functions

Complex data such as those where each statistical unit under study is described not by a single observation (or vector variable), but by a unit-specific sample of several or even many observations, are becoming more and more popular. Reducing these sample data by summary statistics, like the average or the median, implies that most inherent information (about variability, skewness or multi-modality) gets lost. Full information is preserved only if each unit is described by a whole distribution. This new kind of data, a.k.a. “distribution-valued data”, require the development of adequate statistical methods. This paper presents a method to group a set of probability density functions (pdfs) into homogeneous clusters, provided that the pdfs have to be estimated nonparametrically from the unit-specific data. Since elements belonging to the same cluster are naturally thought of as samples from the same probability model, the idea is to tackle the clustering problem by defining and estimating a proper mixture model on the space of pdfs. The issue of model building is challenging here because of the infinite-dimensionality and the non-Euclidean geometry of the domain space. By adopting a wavelet-based representation for the elements in the space, the task is accomplished by using mixture models for hyper-spherical data. The proposed solution is illustrated through a simulation experiment and on two real data sets.     

Improving charge transport in poly(3‐hexylthiophene) transistors via blending with an alkyl‐substituted phenylene–thiophene–thiophene–phenylene molecule

A prototypical semiconducting bicomponent system consisting of a conjugated polymer, that is, poly(3‐hexylthiophene) (P3HT), blended with a small thiophene containing conjugated molecule, that is, an alkyl‐substituted bisphenyl‐bithiophene [phenylene–thiophene–thiophene–phenylene (PTTP)], has been used as an electroactive active layer in field‐effect transistors (FETs). The self‐assembly of this bicomponent system at surfaces has been studied at different length scales, from the nanoscale to the macroscale, and compared with the behavior of monocomponent films of PTTP and P3HT. The correlation between morphology and electric properties of the semiconducting material is explored by fabricating prototypes of FETs varying the relative concentrations of the two‐component blend. The maximum charge carrier mobility value, achieved with a few percent of PTTP component, is not simply due to a uniform dispersion of the molecules in the polymer matrix, but rather to the generation of very long percolation paths, whose composition and electrical properties can be tuned with the PTTP concentration. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Particle-vibration coupling: Recent advances in microscopic calculations with the Skyrme Hamiltonian

In this contribution, we report some recent progress in our understanding of particle-vibration coupling (PVC) in nuclei. In particular, we first review the formal development that has allowed some of us to deduce the PVC equations within the Green’s functionmethod. Applications are then discussed, both in the case of single-particle states and giant resonances in magic nuclei. We also present a new model that extends the PVC ansatz and is meant to account for the complete low-lying spectra of odd nuclei.