In this paper we presented a lattice Boltzmann with square grid for compressible flow problems. Triple level velocity is considered for each cell. Migration step use discrete velocity but continuous parameters are utilized to calculate density, velocity, and energy. So, we called this semi-discrete method. To evaluate the performance of the method the well-known shock tube problem is solved, us...

The restricted Boltzmann machine is a graphical model for binary random variables. Based on a complete bipartite graph separating hidden and observed variables, it is the binary analog to the factor analysis model. We study this graphical model from the perspectives of algebraic statistics and tropical geometry, starting with the observation that its Zariski closure is a Hadamard power of the f...

The restricted Boltzmann machine is a graphical model for binary random variables. Based on a complete bipartite graph separating hidden and observed variables, it is the binary analog to the factor analysis model. We study this graphical model from the perspectives of algebraic statistics and tropical geometry, starting with the observation that its Zariski closure is a Hadamard power of the f...

Automatic extraction of distinctive features from a visual information stream is challenging due to the large amount of information contained in most image data. In recent years deep neural networks (DNNs) have gained outstanding popularity for solving visual information processing tasks. This study reports novel contributions, including a new DNN architecture and training method, which increas...

The covariant Boltzmann equation for a relativistic gas mixture is used to formulate a theory of relativistic irreversible thermodynamics. The modified moment method is applied to derive various evolution equations for macroscopic variables from the covariant Boltzmann equation. The method rigorously yields the entropy differential which is not an exact differential if

Although the fast spectral method has been established for solving the Boltzmann equation for single-species monatomic gases, its extension to gas mixtures is not easy because of the non-unitary mass ratio between the di↵erent molecular species. The conventional spectral method can solve the Boltzmann collision operator for binary gas mixtures but with a computational cost of the order m