Externally definable sets and dependent pairs

We prove that externally definable sets in first order NIP theories have honest definitions, giving a new proof of Shelah's expansion theorem. Also we discuss a weak notion of stable embeddedness true in this context. Those results are then used to prove a general theorem on dependent pairs, which in particular answers a question of Baldwin and Benedikt on naming an indiscernible sequence.Comment: 17 pages, some typos and mistakes corrected, overall presentation improved, more details for the examples are give

Generation of photon pairs using polarization-dependent two-photon absorption

We propose a new method for generating photon pairs from coherent light using polarization-dependent two-photon absorption. We study the photon statistics of two orthogonally polarized modes by solving a master equation, and show that when we prepare a coherent state in one polarization mode, photon pairs are created in the other mode. The photon pairs have the same frequency as that of the incident light.Comment: 4 pages, 3 figures, submitted to PR

Dynamic generation of orbital quasiparticle entanglement in mesoscopic conductors

We propose a scheme for dynamically creating orbitally entangled electron-hole pairs through a time-dependent variation of the electrical potential in a mesoscopic conductor. The time-dependent potential generates a superposition of electron-hole pairs in two different orbital regions of the conductor, a Mach-Zehnder interferometer in the quantum Hall regime. The orbital entanglement is detected via violation of a Bell inequality, formulated in terms of zero-frequency current noise. Adiabatic cycling of the potential, both in the weak and strong amplitude limit, is considered.Comment: 4 pages, 2 figures; references update

Parallel inferencing method and apparatus for rule-based expert systems

The invention analyzes areas of conditions with an expert knowledge base of rules using plural separate nodes which fire respective rules of said knowledge base, each of said rules upon being fired altering certain of said conditions predicated upon the existence of other said conditions. The invention operates by constructing a P representation of all pairs of said rules which are input dependent or output dependent; constructing a C representation of all pairs of said rules which are communication dependent or input dependent; determining which of the rules are ready to fire by matching the predicate conditions of each rule with the conditions of said set; enabling said node means to simultaneously fire those of the rules ready to fire which are defined by said P representation as being free of input and output dependencies; and communicating from each node enabled by said enabling step the alteration of conditions by the corresponding rule to other nodes whose rules are defined by said C matrix means as being input or communication dependent upon the rule of said enabled node