Solution Map Analysis of a Multiscale Drift-Diffusion Model for Organic Solar Cells

In this article we address the theoretical study of a multiscale drift-diffusion (DD) model for the description of photoconversion mechanisms in organic solar cells. The multiscale nature of the formulation is based on the co-presence of light absorption, conversion and diffusion phenomena that occur in the three-dimensional material bulk, of charge photoconversion phenomena that occur at the two-dimensional material interface separating acceptor and donor material phases, and of charge separation and subsequent charge transport in each three-dimensional material phase to device terminals that are driven by drift and diffusion electrical forces. The model accounts for the nonlinear interaction among four species: excitons, polarons, electrons and holes, and allows to quantitatively predict the electrical current collected at the device contacts of the cell. Existence and uniqueness of weak solutions of the DD system, as well as nonnegativity of all species concentrations, are proved in the stationary regime via a solution map that is a variant of the Gummel iteration commonly used in the treatment of the DD model for inorganic semiconductors. The results are established upon assuming suitable restrictions on the data and some regularity property on the mixed boundary value problem for the Poisson equation. The theoretical conclusions are numerically validated on the simulation of three-dimensional problems characterized by realistic values of the physical parameters

Feature learning in feature-sample networks using multi-objective optimization

Data and knowledge representation are fundamental concepts in machine learning. The quality of the representation impacts the performance of the learning model directly. Feature learning transforms or enhances raw data to structures that are effectively exploited by those models. In recent years, several works have been using complex networks for data representation and analysis. However, no feature learning method has been proposed for such category of techniques. Here, we present an unsupervised feature learning mechanism that works on datasets with binary features. First, the dataset is mapped into a feature--sample network. Then, a multi-objective optimization process selects a set of new vertices to produce an enhanced version of the network. The new features depend on a nonlinear function of a combination of preexisting features. Effectively, the process projects the input data into a higher-dimensional space. To solve the optimization problem, we design two metaheuristics based on the lexicographic genetic algorithm and the improved strength Pareto evolutionary algorithm (SPEA2). We show that the enhanced network contains more information and can be exploited to improve the performance of machine learning methods. The advantages and disadvantages of each optimization strategy are discussed.Comment: 7 pages, 4 figure

A Regularized Method for Selecting Nested Groups of Relevant Genes from Microarray Data

Gene expression analysis aims at identifying the genes able to accurately predict biological parameters like, for example, disease subtyping or progression. While accurate prediction can be achieved by means of many different techniques, gene identification, due to gene correlation and the limited number of available samples, is a much more elusive problem. Small changes in the expression values often produce different gene lists, and solutions which are both sparse and stable are difficult to obtain. We propose a two-stage regularization method able to learn linear models characterized by a high prediction performance. By varying a suitable parameter these linear models allow to trade sparsity for the inclusion of correlated genes and to produce gene lists which are almost perfectly nested. Experimental results on synthetic and microarray data confirm the interesting properties of the proposed method and its potential as a starting point for further biological investigationsComment: 17 pages, 8 Post-script figure