This note presents a concrete representation of stably compact spaces. This is used to give a simple, and predicative, description of the patch topology of a stably compact space (J. Pure Appl. Algebra, to appear). c © 2002 Elsevier B.V. All rights reserved.

A simple mathematical definition of the 4-port model for pure Prolog is given. The model combines the intuition of ports with a compact representation of execution state. Forward and backward derivation steps are possible. The model satisfies a modularity claim, making it suitable for formal reasoning.

We study the Gauss-Bonnet (GB) term as the leading higher-curvature correction to pure Einstein gravity. Assuming a tree-level ultraviolet completion free of ghosts or tachyons, we prove that the GB term has a nonnegative coefficient in dimensions greater than 4. Our result follows from unitarity of the spectral representation for a general ultraviolet completion of the GB term.

We present a general method for constructing pure-product-state representations for density operators of N quantum bits. If such a representation has nonnegative expansion coefficients, it provides an explicit separable ensemble for the density operator. We derive the condition for separability of a mixture of the GreenbergerHorne-Zeilinger state with the maximally mixed state.

It will be argued that among the known systems in three dimensions that have string like excitations periodic U(1) pure gauge theories are the most likely candidates to lead to a string representation of their universal properties. Some recent work with F. David will also be reviewed.

It is shown that the existence of a time operator in the Liouville space representation of both classical and quantum evolution provides a mechanism for effective entropy change of physical states. In particular, an initially effectively pure state can evolve under the usual unitary evolution to an effectively mixed state.

We consider the computational complexity of pure Nash equilibria in graphical games. It is known that the problem is NP-complete in general, but tractable (i.e., in P) for special classes of graphs such as those with bounded treewidth. It is then natural to ask: is it possible to characterize all tractable classes of graphs for this problem? In this work, we provide such a characterization for ...

A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method is obtained and a simple numerical example is provided.

This paper discusses the phenomenon of spontaneous symmetry breaking in the Schrödinger representation formulation of quantum field theory. The analysis is presented for three-dimensional space-time abelian gauge theories with either Maxwell, Maxwell-Chern-Simons, or pure Chern-Simons terms as the gauge field contribution to the action, each of which leads to a different form of mass generation...

Two experiments using embryonic and hatchling chickens examined how the representation of frequency along the basilar membrane changed during hearing development. In experiment 1, chicks were exposed to high intensity pure tones (500, 1,500, or 3,000 Hz) at one of three different ages. Analysis of hair cell degeneration indicated a discrete region of damage which systematically changed as a fun...