Hidden Markov models are well-known methods for image processing. They are used in many areas where 1D data are processed. In the case of 2D data, there appear some problems with application HMM. There are some solutions, but they convert input observation from 2D to 1D, or create parallel pseudo 2D HMM, which is set of 1D HMMs in fact. This paper describes authentic 2D HMM with two-dimensional...

We define a Mellin amplitude for CFT$_1$ four-point functions. Its analytical properties are inferred from physical requirements on the correlator. discuss analytic continuation that is necessary fully nonperturbative definition of transform. The resulting bounded, meromorphic function single complex variable used to derive an infinite set sum rules CFT data exchanged operators, which we test k...

There has been a huge amount of interest in perovskites recently and new structures hybrid are frequently reported. The classification unambiguous the discussion 3D layered 2D due to dimensional constraints. However, 1D perovskites, additional degrees freedom have resulted large number possible structural configurations. proposed notation aims classify these based on connectivity octahedra pero...

Recent experimental and theoretical work in strongly correlated electron system necessitates a formulation to deal with 1d to 2d dimensional crossover and raises several interesting questions. A particularly interesting question is what happens to the 1d Luttinger liquid, as we go from 1d to 2d? The issue of dimensional crossover in lower dimensional systems is of great general interest, in par...