Turing computability with neural nets

This paper shows the existence of a finite neural network, made up of sigmoidal neurons, which simulates a universal Turing machine. It is composed of less than 10⁵ synchronously evolving processors, interconnected linearly. High-order connections are not required.     

Calculation of the propagator for a time-dependent damped,forced harmonic oscillator using the Schwinger action principle

A calculation of the quantum mechanical propagator for a general time-dependent one-dimensional damped, forced harmonic oscillator based on a direct application of the Schwinger action principle is presented. Contact with an earlier general method of calculation is made and in particular two previously found results are recovered from our general expression. The apparent dependence of one of them upon some unphysical parameters is clarified. The method presented here can be applied to any system described by a quadratic Hamiltonian and is an immediate extension of the calculation for the propagator of a simple harmonic oscillator with constant frequency.     

Perturbation theory without wave function for multidimensional systems

A new method to obtain perturbation corrections to the eigenvalues of multidimensional quantummechanical models is developed. It consists of rearranging the Rayleigh-Schrodinger perturbation theory so that any coefficient of the perturbation series is obtained from a simple and compact recursion relationship. The Zeeman effect in hydrogen and the hydrogen molecule-ion are used to illustrate the procedure.     

Robust discretizations versus increase of the time step for the Lorenz system

When continuous systems are discretized, their solutions depend on the time step chosen a priori. Such solutions are not necessarily spurious in the sense that they can still correspond to a solution of the differential equations but with a displacement in the parameter space. Consequently, it is of great interest to obtain discrete equations which are robust even when the discretization time step is large. In this paper, different discretizations of the Lorenz system are discussed versus the values of the discretization time step. It is shown that the sets of difference equations proposed are more robust versus increases of the time step than conventional discretizations built with standard schemes such as the forward Euler, backward Euler, or centered finite difference schemes. The nonstandard schemes used here are Mickens' scheme and Monaco and Normand-Cyrot's scheme.     

Melting of the nanocrystalline vortex matter in highly anisotropic high-temperature superconductors

Multilevel Monte Carlo simulations of the vortex matter in the highly anisotropic high-temperature superconductor Bi2Sr2CaCu2O8 were performed. We introduced low concentration of columnar defects satisfying Bphi < or = B. Both the electromagnetic and Josephson interactions among pancake vortices were included. The nanocrystalline, nanoliquid, and homogeneous liquid phases were identified in agreement with experiments. We observed the two-step melting process and also noted an enhancement of the structure factor just prior to the melting transition. A proposed theoretical model is in agreement with our findings.     

An inorganic iron complex that inhibits wild-type and an isoniazid-resistant mutant 2-trans-enoyl-ACP (CoA) reductase from Mycobacterium tuberculosis

The in vitro kinetics of inactivation of both wild-type and I21V InhA enzymes by [FeII(CN)5(INH)]3- indicate that this process requires no activation by KatG, and no need for the presence of NADH. This inorganic complex may represent a new class of lead compounds to the development of anti-tubercular agents aiming at inhibition of a validated target.