The Primary Pretenders

We call a composite number q such that there exists a positive integer b with b^p == b (mod q) a prime pretender to base b. The least prime pretender to base b is the primary pretender q_b. It is shown that there are only 132 distinct primary pretenders, and that q_b is a periodic function of b whose period is the 122-digit number 19568584333460072587245340037736278982017213829337604336734362- 294738647777395483196097971852999259921329236506842360439300.Comment: 7 page

Quantum Error Correction and Orthogonal Geometry

A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors, and 1 to 29 qubits correcting 5 errors.Comment: RevTex, 4 pages, no figures, submitted to Phys. Rev. Letters. We have changed the statement of Theorem 2 to correct it -- we now get worse rates than we previously claimed for our quantum codes. Minor changes have been made to the rest of the pape

Quantum Error Correction via Codes over GF(4)

The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.Comment: Latex, 46 pages. To appear in IEEE Transactions on Information Theory. Replaced Sept. 24, 1996, to correct a number of minor errors. Replaced Sept. 10, 1997. The second section has been completely rewritten, and should hopefully be much clearer. We have also added a new section discussing the developments of the past year. Finally, we again corrected a number of minor error

The PHASES Differential Astrometry Data Archive. I. Measurements and Description

The Palomar High-precision Astrometric Search for Exoplanet Systems (PHASES) monitored 51 sub-arcsecond binary systems to determine precision binary orbits, study the geometries of triple and quadruple star systems, and discover previously unknown faint astrometric companions as small as giant planets. PHASES measurements made with the Palomar Testbed Interferometer (PTI) from 2002 until PTI ceased normal operations in late 2008 are presented. Infrared differential photometry of several PHASES targets were measured with Keck Adaptive Optics and are presented.Comment: 33 pages emulateapj, Accepted to A

Masses, luminosities, and orbital coplanarities of the µ Orionis quadruple-star system from phases differential astrometry

μ Orionis was identified by spectroscopic studies as a quadruple-star system. Seventeen high-precision differential astrometry measurements of μ Ori have been collected by the Palomar High-precision Astrometric Search for Exoplanet Systems (PHASES). These show both the motion of the long-period binary orbit and short-period perturbations superimposed on that caused by each of the components in the long-period system being themselves binaries. The new measurements enable the orientations of the long-period binary and short-period subsystems to be determined. Recent theoretical work predicts the distribution of relative inclinations between inner and outer orbits of hierarchical systems to peak near 40 and 140 degrees. The degree of coplanarity of this complex system is determined, and the angle between the planes of the A–B and Aa–Ab orbits is found to be 136.7 ± 8.3 degrees, near the predicted distribution peak at 140 degrees; this result is discussed in the context of the handful of systems with established mutual inclinations. The system distance and masses for each component are obtained from a combined fit of the PHASES astrometry and archival radial velocity observations. The component masses have relative precisions of 5% (component Aa), 15% (Ab), and 1.4% (each of Ba and Bb). The median size of the minor axes of the uncertainty ellipses for the new measurements is 20 micro-arcseconds (μas). Updated orbits for δ Equulei, κ Pegasi, and V819 Herculis are also presented

Experimental Design for the Gemini Planet Imager

The Gemini Planet Imager (GPI) is a high performance adaptive optics system being designed and built for the Gemini Observatory. GPI is optimized for high contrast imaging, combining precise and accurate wavefront control, diffraction suppression, and a speckle-suppressing science camera with integral field and polarimetry capabilities. The primary science goal for GPI is the direct detection and characterization of young, Jovian-mass exoplanets. For plausible assumptions about the distribution of gas giant properties at large semi-major axes, GPI will be capable of detecting more than 10% of gas giants more massive than 0.5 M_J around stars younger than 100 Myr and nearer than 75 parsecs. For systems younger than 1 Gyr, gas giants more massive than 8 M_J and with semi-major axes greater than 15 AU are detected with completeness greater than 50%. A survey targeting young stars in the solar neighborhood will help determine the formation mechanism of gas giant planets by studying them at ages where planet brightness depends upon formation mechanism. Such a survey will also be sensitive to planets at semi-major axes comparable to the gas giants in our own solar system. In the simple, and idealized, situation in which planets formed by either the "hot-start" model of Burrows et al. (2003) or the core accretion model of Marley et al. (2007), a few tens of detected planets are sufficient to distinguish how planets form.Comment: 15 pages, 9 figures, revised after referee's comments and resubmitted to PAS

Survey of sediment quality in Sabine Lake, Texas and vicinity

The toxicity of sediments in Sabine Lake, Texas, and adjoining Intracoastal Waterway canals was determined as part of bioeffects assessment studies managed by NOAA’s National Status and Trends Program. The objectives of the survey were to determine: (1) the incidence and degree of toxicity of sediments throughout the study area; (2) the spatial patterns (or gradients) in chemical contamination and toxicity, if any, throughout the study area; (3) the spatial extent of chemical contamination and toxicity; and (4) the statistical relationships between measures of toxicity and concentrations of chemicals in the sediments. Surficial sediment samples were collected during August, 1995 from 66 randomly-chosen locations. Laboratory toxicity tests were performed as indicators of potential ecotoxicological effects in sediments. A battery of tests was performed to generate information from different phases (components) of the sediments. Tests were selected to represent a range in toxicological endpoints from acute to chronic sublethal responses. Toxicological tests were conducted to measure: reduced survival of adult amphipods exposed to solid-phase sediments; impaired fertilization success and abnormal morphological development in gametes and embryos, respectively, of sea urchins exposed to pore waters; reduced metabolic activity of a marine bioluminescent bacteria exposed to organic solvent extracts; and induction of a cytochrome P-450 reporter gene system in exposures to solvent extracts of the sediments. Chemical analyses were performed on portions of each sample to quantify the concentrations of trace metals, polynuclear aromatic hydrocarbons, and chlorinated organic compounds. Correlation analyses were conducted to determine the relationships between measures of toxicity and concentrations of potentially toxic substances in the samples. Based upon the compilation of results from chemical analyses and toxicity tests, the quality of sediments in Sabine Lake and vicinity did not appear to be severely degraded. Chemical concentrations rarely exceeded effects-based numerical guidelines, suggesting that toxicant-induced effects would not be expected in most areas. None of the samples was highly toxic in acute amphipod survival tests and a minority (23%) of samples were highly toxic in sublethal urchin fertilization tests. Although toxic responses occurred frequently (94% of samples) in urchin embryo development tests performed with 100% pore waters, toxicity diminished markedly in tests done with diluted pore waters. Microbial bioluminescent activity was not reduced to a great degree (no EC50 <0.06 mg/ml) and cytochrome P-450 activity was not highly induced (6 samples exceeded 37.1 ug/g benzo[a]pyrene equivalents) in tests done with organic solvent extracts. Urchin embryological development was highly correlated with concentrations of ammonia and many trace metals. Cytochrome P450 induction was highly correlated with concentrations of a number of classes of organic compounds (including the polynuclear aromatic hydrocarbons and chlorinated compounds). (PDF contains 51 pages

On the algebra of local unitary invariants of pure and mixed quantum states

We study the structure of the inverse limit of the graded algebras of local unitary invariant polynomials using its Hilbert series. For k subsystems, we conjecture that the inverse limit is a free algebra and the number of algebraically independent generators with homogenous degree 2m equals the number of conjugacy classes of index m subgroups in a free group on k-1 generators. Similarly, we conjecture that the inverse limit in the case of k-partite mixed state invariants is free and the number of algebraically independent generators with homogenous degree m equals the number of conjugacy classes of index m subgroups in a free group on k generators. The two conjectures are shown to be equivalent. To illustrate the equivalence, using the representation theory of the unitary groups, we obtain all invariants in the m=2 graded parts and express them in a simple form both in the case of mixed and pure states. The transformation between the two forms is also derived. Analogous invariants of higher degree are also introduced.Comment: 14 pages, no figure

Codes for the Quantum Erasure Channel

The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i. e., arbitrary errors at known positions. We show that four qubits are necessary and sufficient to encode one qubit and correct one erasure, in contrast to five qubits for unknown positions. Moreover, a family of quantum codes for the QEC, the quantum BCH codes, that can be efficiently decoded is introduced.Comment: 6 pages, RevTeX, no figures, submitted to Physical Review A, code extended to encode 2 qubits, references adde