Recurrent backpropagation and the dynamical approach to adaptive neural computation

Error backpropagation in feedforward neural network models is a popular learning algorithm that has its roots in nonlinear estimation and optimization. It is being used routinely to calculate error gradients in nonlinear systems with hundreds of thousands of parameters. However, the classical architecture for backpropagation has severe restrictions. The extension of backpropagation to networks with recurrent connections will be reviewed. It is now possible to efficiently compute the error gradients for networks that have temporal dynamics, which opens applications to a host of problems in systems identification and control

General Relativity as a Theory of Two Connections

We show in this paper that it is possible to formulate General Relativity in a phase space coordinatized by two $SO(3)$ connections. We analyze first the Husain-Kucha\v{r} model and find a two connection description for it. Introducing a suitable scalar constraint in this phase space we get a Hamiltonian formulation of gravity that is close to the Ashtekar one, from which it is derived, but has some interesting features of its own. Among them a possible mechanism for dealing with the degenerate metrics and a neat way of writing the constraints of General Relativity.Comment: 18 pages, LATEX, Preprint CGPG-93/09-

From Euclidean to Lorentzian General Relativity: The Real Way

We study in this paper a new approach to the problem of relating solutions to the Einstein field equations with Riemannian and Lorentzian signatures. The procedure can be thought of as a "real Wick rotation". We give a modified action for general relativity, depending on two real parameters, that can be used to control the signature of the solutions to the field equations. We show how this procedure works for the Schwarzschild metric and discuss some possible applications of the formalism in the context of signature change, the problem of time, black hole thermodynamics...Comment: 20 pages uuencoded gzipped tar format. Accepted in Phys. Rev. D. Some references adde

A Comment on the Degrees of Freedom in the Ashtekar Formulation for 2+1 Gravity

We show that the recent claim that the 2+1 dimensional Ashtekar formulation for General Relativity has a finite number of physical degrees of freedom is not correct.Comment: 6 pages LaTex, to appear in Classical and Quantum Gravit

The central density of R136 in 30 Doradus

The central density rho_0 of a stellar cluster is an important physical parameter for determining its evolutionary and dynamical state. How much mass segregation there is, or whether the cluster has undergone core collapse both depends on rho_0. We reanalyze the results of a previous paper that gives the mass density profile of R136 and combine them with both a conservative upper limit for the core parameter and a more uncertain recent measurement. We thus place a lower limit on rho_0 under reasonable and defensible assumptions about the IMF, finding rho_0 >~ 1.5x10^4 Msun/pc^3 for the conservative assumption a < 0.4 pc for the cluster core parameter. If we use the lower, but more uncertain value a = 0.025 pc, the central density estimate becomes greater than 10^7 Msun/pc^3. A mechanism based on the destruction of a large number of circumstellar disks is posited to explain the hitherto unexplained increase in reddening presented in that same work.Comment: 6 pages, 2 figure

Bessel Integrals and Fundamental Solutions for a Generalized Tricomi Operator

Partial Fourier transforms are used to find explicit formulas for two remarkable fundamental solutions for a generalized Tricomi operator. These fundamental solutions reflect clearly the mixed type of the operator. In order to prove these results, we establish explicit formulas for Fourier transforms of some type of Bessel functions

Statistical description of the black hole degeneracy spectrum

We use mathematical methods based on generating functions to study the statistical properties of the black hole degeneracy spectrum in loop quantum gravity. In particular we will study the persistence of the observed effective quantization of the entropy as a function of the horizon area. We will show that this quantization disappears as the area increases despite the existence of black hole configurations with a large degeneracy. The methods that we describe here can be adapted to the study of the statistical properties of the black hole degeneracy spectrum for all the existing proposals to define black hole entropy in loop quantum gravity.Comment: 41 pages, 12 figure