Portfolios and the market geometry

A geometric analysis of the time series of returns has been performed in the past and it implied that the most of the systematic information of the market is contained in a space of small dimension. Here we have explored subspaces of this space to find out the relative performance of portfolios formed from the companies that have the largest projections in each one of the subspaces. It was found that the best performance portfolios are associated to some of the small eigenvalue subspaces and not to the dominant directions in the distances matrix. This occurs in such a systematic fashion over an extended period (1990-2008) that it may not be a statistical accident.Comment: 13 pages 12 figure

A theorem regarding families of topologically non-trivial fermionic systems

We introduce a Hamiltonian for fermions on a lattice and prove a theorem regarding its topological properties. We identify the topological criterion as a $\mathbb{Z}_2-$ topological invariant $p(\textbf{k})$ (the Pfaffian polynomial). The topological invariant is not only the first Chern number, but also the sign of the Pfaffian polynomial coming from a notion of duality. Such Hamiltonian can describe non-trivial Chern insulators, single band superconductors or multiorbital superconductors. The topological features of these families are completely determined as a consequence of our theorem. Some specific model examples are explicitly worked out, with the computation of different possible topological invariants.Comment: 6 page

Vescalagin and castalagin present bactericidal activity toward methicillin-resistant bacteria

"Published online 17 February 2021"Polyphenols have been extensively exploited in the biomedical field because of their wide range of bioactive properties and historical use as traditional medicines. They typically present antioxidant, antimicrobial, antiamyloidogenic, and/or antitumor activities. In particular, cork water extracts and their components, have been previously reported to present antioxidant and antiamyloidogenic properties. On the basis of this knowledge, we tested cork water extract (CWE), cork water enriched extract (CWE-E), vescalagin/castalagin (two of the main polyphenols present in CWE and CWE-E) for their antibacterial activity against four bacterial strains, namely, methicillin-resistant Staphylococcus epidermidis (MRSE), Staphylococcus aureus (SA), methicillin-resistant Staphylococcus aureus (MRSA), and Pseudomonas aeruginosa (PA). Vescalagin and castalagin presented bactericidal activity against all the tested bacterial strains, in particular toward the methicillin-resistant ones, i.e., MRSA and MRSE, as well as the ability to inhibit the formation of biofilms and to disrupt preformed ones. Moreover, vescalagin/castalagin seem to modulate the normal assembly of the peptidoglycans at the bacteria surface, promoting the disruption of their cell wall, leading to bacterial cell death. We also demonstrate that vescalagin/castalagin can be loaded into alginate hydrogels to generate antibacterial biomaterials that are not toxic to eukaryotic cells.We acknowledge the financial support from the EC (FORECAST 668983 and MEPHOS 872648). A.R.A. acknowledges the “Programa Operacional Regional do Norte”, “Fundo Social Europeu”, and Norte2020 TERM&SC, for her PhD grant (NORTE-08-5369-FSE-000044)