We study the problem of detecting and locating change points in high-dimensional Vector Autoregressive (VAR) models, whose transition matrices exhibit low rank plus sparse structure. first address a single point using an exhaustive search algorithm establish finite sample error bound for its accuracy. Next, we extend results to case multiple that can grow as function size. Their detection is ba...

We study a plug in least squares estimator for the change point parameter where is mean of high dimensional random vector under subgaussian or subexponential distributions. obtain sufficient conditions which this possesses adaptivity against estimates parameters order to yield an optimal rate convergence $O_{p}(\xi ^{-2})$ integer scale. This preserved while allowing dimensionality as well pote...

The Maier-Saupe hard-sphere fluid is one of the simplest models that accounts for the isotropic-nematic transition characteristic of liquid crystal phases. At low temperatures the model is known to present a gas-liquid-like transition with a large difference between the densities of the coexistence phases, whereas at higher temperature the transition becomes a weak first-order transition resemb...