A simple graph is said to be reflexive if its second largest eigenvalue does not exceed 2. The property λ2 ≤ 2 is a hereditary one, i.e. any induced subgraph of a reflexive graph preserves this property and that is why reflexive graphs are usually represented by maximal graphs within a given class. Bicyclic graphs whose two cycles have a common path are called θ-graphs. We consider classes of m...

In this paper, a sample estimator of the tangency portfolio (TP) weights is considered. The focus on situation where number observations smaller than assets in and returns are i.i.d. normally distributed. Under these assumptions, covariance matrix follows singular Wishart distribution and, therefore, regular inverse cannot be taken. bounds approximations for first two moments estimated TP deriv...

In this article children's musical improvisation is investigated through the "reflexive interaction" paradigm. We used a particular system, the MIROR-Impro, implemented in the framework of the MIROR project (EC-FP7), which is able to reply to the child playing a keyboard by a "reflexive" output, mirroring (with repetitions and variations) her/his inputs. The study was conducted in a public prim...