Online gradient algorithm has been widely used as a learning algorithm for feedforward neural networks training. Penalty is a common and popular method for improving the generalization performance of networks. In this paper, a convergence theorem is proved for the online gradient learning algorithm with penalty, a term proportional to the magnitude of the weights. The monotonicity of the error ...

We propose a penalty-function method for constrained molecular dynamics simulation by defining a quadratic penalty function for the constraints. The simulation with such a method can be done by using a conventional, unconstrained solver only with the penalty parameter increased in an appropriate manner as the simulation proceeds. More specifically, we scale the constraints with their force cons...

The death penalty by lethal injection is a legal punishment in the United States. Sodium Thiopental, once used in the death penalty cocktail, is no longer available for use in the United States as a consequence of this association. Anesthesiologists possess knowledge of Sodium Thiopental and possible chemical alternatives. Further, lethal injection has the look and feel of a medical act thereby...

In this note we derive a geometric formulation for equality constrained problems of an ideal penalty function This di erentiable penalty function requires no parameter esti mation or adjustment has numerical conditioning similar to that of the target function from which it is constructed and also has the desirable property that the strict second order constrained minima of the target function a...

We give an error analysis of the finite element variable penalty method for Stokes equations. It is shown that the variable penalty method is of higher order than the standard penalty method.

a Criminal Justice Bill. Sir Hartley Shawcross Attorney-General, moved that the House should disagree with the Lords' amendment to delete Clause I (suspension of the death penalty for murder). He urged the merits of the Government's proposal to recognize two categories of murder?the capital and non-capital. He thought that juries would have no difficulty in deciding whether a murder came into o...

" In what sense can the death penalty be part of a justice system? " The idealised view of justice in the West is that it is blind. It does not recognise any difference between the rich and the poor, or the educated and the uneducated. A judge is obliged to give the same sentence to either, and therefore sees everyone as equal. The death penalty forces us to look at the problems of putting an i...