Within the framework of the two-Higgs Doublet Model (2HDM), we attempt to find some discrete, non-abelian flavour symmetry which could provide an explanation for the masses and mixing matrix elements of leptons. Unlike the Standard Model, currently there is no need for the flavour symmetry to be broken. With the GAP program we investigate all finite subgroups of the U3 group up to the order of 1025. Up to such an order there is no group for which it is possible to select free model parameters in order to match the masses of charged leptons, masses of neutrinos, and the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix elements in a satisfactory manner.

The structure of bonds in biomolecules, such as base pairs in RNA chains or native interactions in proteins, can be presented in the form of a chord diagram. A given biomolecule is then characterized by the genus of an auxiliary two-dimensional surface associated to such a diagram. In this work we introduce the notion of the genus trace, which describes dependence of genus on the choice of a subchain of a given backbone chain. We find that the genus trace encodes interesting physical and biological information about a given biomolecule and its three dimensional structural complexity; in particular it gives a way to quantify how much more complicated a biomolecule is than its nested secondary structure alone would indicate. We illustrate this statement in many examples, involving both RNA and protein chains. First, we conduct a survey of all published RNA structures with better than 3 Å resolution in the PDB database, and find that the genus of natural structural RNAs has roughly linear dependence on their length. Then, we show that the genus trace captures properties of various types of base pairs in RNA, and enables the identification of the domain structure of a ribosome. Furthermore, we find that not only does the genus trace detect a domain structure, but it also predicts a cooperative folding pattern in multi-domain proteins. The genus trace turns out to be a useful and versatile tool, with many potential applications.

The ‘Genus for biomolecules’ database (http://genus.fuw.edu.pl) collects information about topological structure and complexity of proteins and RNA chains, which is captured by the genus of a given chain and its subchains. For each biomolecule, this information is shown in the form of a genus trace plot, as well as a genus matrix diagram. We assemble such information for all and RNA structures deposited in the Protein Data Bank (PDB). This database presents also various statistics and extensive information about the biological function of the analyzed biomolecules. The database is regularly self-updating, once new structures are deposited in the PDB. Moreover, users can analyze their own structures.

From the new existing data with not vanishing θ 13 mixing angle we determine the possible shape of the Majorana neutrino mass matrix. We assume that CP symmetry is broken and all Dirac and Majorana phases are taken into account. Two possible approaches "bottom-up" and "top-down" are presented. The problem of unphysical phases is examined in detail.

The Standard Model does not explain the hierarchy problem. Before the discovery of nonzero lepton mixing angle θ 13 high hopes in explanation of the shape of the lepton mixing matrix were combined with non abelian symmetries. Nowadays, assuming one Higgs doublet, it is unlikely that this is still valid. Texture zeroes, that are combined with abelian symmetries, are intensively studied. The neutrino mass matrix is a natural way to study such symmetries.