Contractibility results for certain spaces of Riemannian metrics on the disc

We provide a general contractibility criterion for subsets of Riemannian metrics on the disc. For instance, this result applies to the space of metrics that have positive Gauss curvature and make the boundary circle convex (or geodesic). The same conclusion is not known in any dimension $n\geq 3$, and (by analogy with the closed case) is actually expected to be false for many values of $n\geq 4$.Comment: Final pre-print version; to appear in Mathematical Research Letter

Multifunctional Conductive Paths Obtained by Laser Processing of Non-Conductive Carbon Nanotube/Polypropylene Composites

Functional materials are promising candidates for application in structural health monitoring/self-healing composites, wearable systems (smart textiles), robotics, and next-generation electronics. Any improvement in these topics would be of great relevance to industry, environment, and global needs for energy sustainability. Taking into consideration all these aspects, low-cost fabrication of electrical functionalities on the outer surface of carbon-nanotube/polypropylene composites is presented in this paper. Electrical-responsive regions and conductive tracks, made of an accumulation layer of carbon nanotubes without the use of metals, have been obtained by the laser irradiation process, leading to confined polymer melting/vaporization with consequent local increase of the nanotube concentration over the electrical percolation threshold. Interestingly, by combining different investigation methods, including thermogravimetric analyses (TGA), X-ray diffraction (XRD) measurements, scanning electron and atomic force microscopies (SEM, AFM), and Raman spectroscopy, the electrical properties of multi-walled carbon nanotube/polypropylene (MWCNT/PP) composites have been elucidated to unfold their potentials under static and dynamic conditions. More interestingly, prototypes made of simple components and electronic circuits (resistor, touch-sensitive devices), where conventional components have been substituted by the carbon nanotube networks, are shown. The results contribute to enabling the direct integration of carbon conductive paths in conventional electronics and next-generation platforms for low-power electronics, sensors, and devices

Improving discrimination of Raman spectra by optimising preprocessing strategies on the basis of the ability to refine the relationship between variance components

Discrimination of the samples into predefined groups is the issue at hand in many fields, such as medicine, environmental and forensic studies, etc. Its success strongly depends on the effectiveness of groups separation, which is optimal when the group means are much more distant than the data within the groups, i.e. the variation of the group means is greater than the variation of the data averaged over all groups. The task is particularly demanding for signals (e.g. spectra) as a lot of effort is required to prepare them in a way to uncover interesting features and turn them into more meaningful information that better fits for the purpose of data analysis. The solution can be adequately handled by using preprocessing strategies which should highlight the features relevant for further analysis (e.g. discrimination) by removing unwanted variation, deteriorating effects, such as noise or baseline drift, and standardising the signals. The aim of the research was to develop an automated procedure for optimising the choice of the preprocessing strategy to make it most suitable for discrimination purposes. The authors propose a novel concept to assess the goodness of the preprocessing strategy using the ratio of the between-groups to within-groups variance on the first latent variable derived from regularised MANOVA that is capable of exposing the groups differences for highly multidimensional data. The quest for the best preprocessing strategy was carried out using the grid search and much more efficient genetic algorithm. The adequacy of this novel concept, that remarkably supports the discrimination analysis, was verified through the assessment of the capability of solving two forensic comparison problems - discrimination between differently-aged bloodstains and various car paints described by Raman spectra - using likelihood ratio framework, as a recommended tool for discriminating samples in the forensics