Embeddings of integrable models in supergravity and their perturbative stability

We discuss the perturbative stability of an AdS 3 non-supersymmetric solution of the type-IIB supergravity, whose internal geometry is given by the direct product of a round three-sphere and two λ-deformed factors based on the coset CFTs SU(2)/U(1) and SL(2, ℝ)/SO(1,1). This solution admits a two-dimensional parametric space spanned by the inverse radius of the AdS 3 and the deformation parameter λ. Reality of the background imposes restrictions on the values of these parameters. Further limitations on the values of the inverse radius and the parameter λ arise after requiring the stability of the solution. Our approach relies on the study of scalar perturbations around the AdS 3 vacuum of a three-dimensional effective theory. This reveals the existence of a region in the parametric space where the Breitenlohner-Freedman bound is not violated.

Exceptional Points through Variation of Distances between Four Coaxial Dielectric Disks

By variation of a refractive index and aspect ratio of the isolated disk, we achieved exceptional points (EPs) at which the resonant frequencies and resonant modes coalesce. However, in practice, that kind of variation presents a technological problem. We considered the method to avoid the problem by substitution of two disk’s dimers. In each dimer, variation of the distance between disks was equivalent to a variation of the aspect ratio of the dimer. Moreover, the variation of the distance between dimers provides the second parameter that gives rise to a vast number of EPs. We recovered the initial resonant eigenmode by encircling multiple EPs two, three, and four times in the two-dimensional parametric space of distances.

Wavelet analysis algorithm for bi- and trivariate statistical distributions

We consider the task of detecting statistically significant patterns in a distribution of some astronomical objects. For this goal we use the wavelet analysis method in bi- or trivariate parametric space. The bivariate analysis algorithm is finished and released as an open-source C++ code of a stable version, while the trivariate algorithm is at an experimental stage.