Generation of Universal Linear Optics by Any Beamsplitter

In 1994, Reck et al. showed how to realize any unitary transformation on a single photon using a product of beamsplitters and phaseshifters. Here we show that any single beamsplitter that nontrivially mixes two modes, also densely generates the set of unitary transformations (or orthogonal transformations, in the real case) on the single-photon subspace with m>=3 modes. (We prove the same result for any two-mode real optical gate, and for any two-mode optical gate combined with a generic phaseshifter.) Experimentally, this means that one does not need tunable beamsplitters or phaseshifters for universality: any nontrivial beamsplitter is universal for linear optics. Theoretically, it means that one cannot produce "intermediate" models of linear optical computation (analogous to the Clifford group for qubits) by restricting the allowed beamsplitters and phaseshifters: there is a dichotomy; one either gets a trivial set or else a universal set. No similar classification theorem for gates acting on qubits is currently known. We leave open the problem of classifying optical gates that act on three or more modes.Comment: 14 pages; edited Lemma 3.3 and updated references. Results are unchange

Nonlinear Filtering for Stochastic Volatility Models with Heavy Tails and Leverage

This paper develops a computationally efficient filtering based procedure for the estimation of the heavy tailed SV model with leverage. While there are many accepted techniques for the estimation of standard SV models, incorporating these effects into an SV framework is difficult. Simulation evidence provided in this paper indicates that the proposed procedure outperforms competing approaches in terms of the accuracy of parameter estimation. In an empirical setting, it is shown how the individual effects of heavy tails and leverage can be isolated using standard likelihood ratio tests.

Validity proof of Lazard's method for CAD construction

In 1994 Lazard proposed an improved method for cylindrical algebraic decomposition (CAD). The method comprised a simplified projection operation together with a generalized cell lifting (that is, stack construction) technique. For the proof of the method's validity Lazard introduced a new notion of valuation of a multivariate polynomial at a point. However a gap in one of the key supporting results for his proof was subsequently noticed. In the present paper we provide a complete validity proof of Lazard's method. Our proof is based on the classical parametrized version of Puiseux's theorem and basic properties of Lazard's valuation. This result is significant because Lazard's method can be applied to any finite family of polynomials, without any assumption on the system of coordinates. It therefore has wider applicability and may be more efficient than other projection and lifting schemes for CAD.Comment: 21 page

Family, Unvalued: Discrimination, Denial, and the Fate of Binational Same-Sex Couples under U.S. Law

"Family, Unvalued" documents the crippling barriers same-sex binational couples face in pursuing a goal enshrined in America's founding document -- happiness. One fact sets them apart from other binational families. A heterosexual couple where one partner is foreign, one a U.S. citizen, can claim the right to enter the U.S. with a few strokes of a pen. But a lesbian or gay couple's relationship -- even if they have lived together for decades, even if their commitment is incontrovertible--is irrelevant. Instead they face a long limbo of legal indifference, harassment, and fear. Delays, bureaucracy, inconsistency, and injustice make the U.S. immigration system a nightmare for millions. Debate over that system is intensifying. Family, Unvalued shows how its failures affect, and sometimes destroy, families which prejudice has deprived of any legal protection. This report reveals how today's discrimination grows from a long history of anti-immigrant campaigns. Most of all, Family, Unvalued lets the reader hear the sometimes horrifying, always enlightening testimony of lesbian and gay families: people simply seeking to build a better future ... together

Search for Long-Lived Parents of the Z Boson

We present the results of a search for new particles with long lifetime that decay to a Z boson. A long-lived parent of the Z is predicted by several models in addition to being an experimentally clean channel. We vertex dimuons with invariant mass near the Z peak and study the decay length distribution. No evidence of a long-lived component is found, and cross-section limits are presented on a fourth generation quark model.Comment: Proceedings for the American Physical Society's 2004 Meeting of the Division of Particles and Field

The 2-Factor Polynomial Detects Even Perfect Matchings

In this paper, we prove that the 2-factor polynomial, an invariant of a planar trivalent graph with a perfect matching, counts the number of 2- factors that contain the the perfect matching as a subgraph. Consequently, we show that the polynomial detects even perfect matchings.Comment: 16 pages, 17 figure