Linear response is an approximation method for Boltzmann machines based on mean field theory. It is known that in the absence of hidden units this method can learn the network quite accurately with the costs of only one matrix inversion. We show that adding a flat distribution to the target can decrease the classification error. We apply linear response learning to a real world data set of digi...

In ecology predictive models of the geographical distribution of certain species are widely used to capture the spatial diversity. Recently a method of Maxent based on Gibbs distribution is frequently employed to have reasonable accuracy of a target distribution of species at a site using environmental features such as temperature, precipitation, elevation and so on. It requires only presence d...

1639 the average frequency distribution H avg (s) := (1=N) N i=1 H(s; i): The behavior of the distributions for different values of K is discussed in Fig. 4. For M = 9 and K = 12; 16; 20; 24 the average frequency distribution Havg(s) (solid lines) and the approximation Happ(s) (dashed lines) are compared to the Maxwell–Boltzmann distribution H M-B (s) (dash-dotted lines). Here, the parameter is...

Mixed convection of Cu-Water nanofluid is studied numerically in a shallow inclined enclosure by applying lattice Boltzmann method. The D2Q9 lattice and internal energy distribution function based on the BGK collision operator are used in order to develop the thermal flow field. The enclosure's hot lid has the constant velocity of U0 while its cold lower wall has no motion. Moreover, sidewalls ...

this work is a primary achievement in studying the co2 and n2–oil systems. to predict gas-liquid relative permeability curves, a shan-chen type multicomponent multiphase lattice boltzmann model for two-phase flow through 2d porous media is developed. periodic and bounce back boundary conditions are applied to the model with the guo scheme for the external body force (i.e., the pressure gradient...

The Maxwell–Boltzmann distribution is a hallmark of statistical physics in thermodynamic equilibrium linking the probability density particle’s kinetic energies to temperature system that also determines its configurational fluctuations. This unique relation lost for Hot Brownian Motion, e.g., when particle constantly heated create an inhomogeneous surrounding liquid. While fluctuations this ca...

We study the possibility of modifying collisions in the lattice Boltzmann method to keep the proper entropy balance. We demonstrate that in the space of distributions operated on by lattice Boltzmann methods which respect a Boltzmann type H theorem, there exists a vicinity of the equilibrium where collisions with entropy balance are possible and, at the same time, there exists a region of noneq...