40,960 research outputs found
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 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
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