In this paper we study the AdS/CFT correspondence for N = 4 SYM with gauge group U(N), compactified on S in four dimensions using Monte-Carlo techniques. The simulation is based on a particular reduction of degrees of freedom to commuting matrices of constant fields, and in particular, we can write the wave functions of these degrees of freedom exactly. The square of the wave function is equiva...

This paper summarizes theory, experimental techniques, and the reported data pertaining to the zeta potential of silica and silicon with attention to use as microfluidic substrate materials, particularly for microchip chemical separations. Dependence on cation concentration, buffer and cation type, pH, cation valency, and temperature are discussed. The Debye-Hückel limit, which is often correct...

Thermodynamical and magnetic properties of the half-filled, two-site Hubbard model have been discussed within the framework of the Tsallis nonextensive statistics, in which the entropic index q plays an important role, the conventional Boltzman-Gibbs statistics being recovered in the limit of q = 1. The temperature dependence of the entropy, specific heat and magnetic susceptibility, and the ma...

The freeze out of the expanding systems, created in relativistic heavy ion collisions, is discussed. We combine Bjorken scenario with earlier developed freeze out equations into a unified model. The important feature of the proposed model is that physical freeze out is completely finished in a finite time, which can be varied from 0 (freeze out hypersurface) to ∞. The dependence of the post fre...

We report a quasi-exact power law behavior for Ising critical temperatures on hypercubes. It reads J/kBTc = K0[(1 − 1/d)(q − 1)] a where K0 = 0.6260356, a = 0.8633747, d is the space dimension, q the coordination number (q = 2d), J the coupling constant, kB the Boltzman constant and Tc the critical temperature. Absolute errors from available exact estimates (d = 2 up to d = 7) are always less t...

We consider d× d tensors A(x) that are symmetric, positive semi-definite, and whose rowdivergence vanishes identically. We establish sharp inequalities for the integral of (detA) 1 d−1 . We apply them to models of compressible inviscid fluids: Euler equations, Euler–Fourier, relativistic Euler, Boltzman, BGK, etc... We deduce an a priori estimate for a new quantity, namely the space-time integr...

Horizontal contaminant transport through unsaturated soil been demonstrated both analytically and experimentally. The water and solute transport equations were solved using the Boltzman transformation, to convert the partial differential equations to ordinary differential equations. The resulted mathematical model was verified using experimental data. A laboratory scale column system was constr...

We give an algorithm that learns a representation of data through compression. The algorithm 1) predicts bits sequentially from those previously seen and 2) has a structure and a number of computations similar to an autoencoder. The likelihood under the model can be calculated exactly, and arithmetic coding can be used directly for compression. When training on digits the algorithm learns filte...

Restricted Boltzman Machines (RBMs) have been successfully used in recommender systems. However, as with most of other collaborative filtering techniques, it cannot solve cold start problems for there is no rating for a new item. In this paper, we first apply conditional RBM (CRBM) which could take extra information into account and show that CRBM could solve cold start problem very well, espec...