Parametric Constructive Kripke-Semantics for Standard Multi-Agent Belief and Knowledge (Knowledge As Unbiased Belief)

We propose parametric constructive Kripke-semantics for multi-agent KD45-belief and S5-knowledge in terms of elementary set-theoretic constructions of two basic functional building blocks, namely bias (or viewpoint) and visibility, functioning also as the parameters of the doxastic and epistemic accessibility relation. The doxastic accessibility relates two possible worlds whenever the application of the composition of bias with visibility to the first world is equal to the application of visibility to the second world. The epistemic accessibility is the transitive closure of the union of our doxastic accessibility and its converse. Therefrom, accessibility relations for common and distributed belief and knowledge can be constructed in a standard way. As a result, we obtain a general definition of knowledge in terms of belief that enables us to view S5-knowledge as accurate (unbiased and thus true) KD45-belief, negation-complete belief and knowledge as exact KD45-belief and S5-knowledge, respectively, and perfect S5-knowledge as precise (exact and accurate) KD45-belief, and all this generically for arbitrary functions of bias and visibility. Our results can be seen as a semantic complement to previous foundational results by Halpern et al. about the (un)definability and (non-)reducibility of knowledge in terms of and to belief, respectively

Segue 1: An Unevolved Fossil Galaxy from the Early Universe

We present Magellan/MIKE and Keck/HIRES high-resolution spectra of six red giant stars in the dwarf galaxy Segue 1. Including one additional Segue 1 star observed by Norris et al. (2010), high-resolution spectra have now been obtained for every red giant in Segue 1. Remarkably, three of these seven stars have metallicities below [Fe/H] = -3.5, suggesting that Segue 1 is the least chemically evolved galaxy known. We confirm previous medium-resolution analyses demonstrating that Segue 1 stars span a metallicity range of more than 2 dex, from [Fe/H] = -1.4 to [Fe/H] = -3.8. All of the Segue 1 stars are alpha-enhanced, with [alpha/Fe] ~ 0.5. High alpha-element abundances are typical for metal-poor stars, but in every previously studied galaxy [alpha/Fe] declines for more metal-rich stars, which is typically interpreted as iron enrichment from supernova Ia. The absence of this signature in Segue 1 indicates that it was enriched exclusively by massive stars. Other light element abundance ratios in Segue 1, including carbon-enhancement in the three most metal-poor stars, closely resemble those of metal-poor halo stars. Finally, we classify the most metal-rich star as a CH star given its large overabundances of carbon and s-process elements. The other six stars show remarkably low neutron-capture element abundances of [Sr/H] < -4.9 and [Ba/H] < -4.2, which are comparable to the lowest levels ever detected in halo stars. This suggests minimal neutron-capture enrichment, perhaps limited to a single r-process or weak s-process synthesizing event. Altogether, the chemical abundances of Segue 1 indicate no substantial chemical evolution, supporting the idea that it may be a surviving first galaxy that experienced only one burst of star formation.Comment: ApJ, accepted, 20 pages (emulateapj), 9 figure

Orbital Circularization of Hot and Cool Kepler Eclipsing Binaries

The rate of tidal circularization is predicted to be faster for relatively cool stars with convective outer layers, compared to hotter stars with radiative outer layers. Observing this effect is challenging, because it requires large and well-characterized samples including both hot and cool stars. Here we seek evidence for the predicted dependence of circularization upon stellar type, using a sample of 945 eclipsing binaries observed by Kepler. This sample complements earlier studies of this effect, which employed smaller samples of better-characterized stars. For each Kepler binary we measure $e\cos\omega$ based on the relative timing of the primary and secondary eclipses. We examine the distribution of $e\cos\omega$ as a function of period for binaries composed of hot stars, cool stars, and mixtures of the two types. At the shortest periods, hot-hot binaries are most likely to be eccentric; for periods shorter than 4 days, significant eccentricities occur frequently for hot-hot binaries, but not for hot-cool or cool-cool binaries. This is in qualitative agreement with theoretical expectations based on the slower dissipation rates of hot stars. However, the interpretation of our results is complicated by the largely unknown ages and evolutionary states of the stars in our sample.Comment: Accepted for publication in Ap

The geometry of the generic line complex

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1995.Includes bibliographical references (leaves 27-28).by Joshua S. Sher.Ph.D

Execution Models for Choreographies and Cryptoprotocols

A choreography describes a transaction in which several principals interact. Since choreographies frequently describe business processes affecting substantial assets, we need a security infrastructure in order to implement them safely. As part of a line of work devoted to generating cryptoprotocols from choreographies, we focus here on the execution models suited to the two levels. We give a strand-style semantics for choreographies, and propose a special execution model in which choreography-level messages are faithfully delivered exactly once. We adapt this model to handle multiparty protocols in which some participants may be compromised. At level of cryptoprotocols, we use the standard Dolev-Yao execution model, with one alteration. Since many implementations use a "nonce cache" to discard multiply delivered messages, we provide a semantics for at-most-once delivery

Spectroscopic Confirmation of the Dwarf Galaxies Hydra II and Pisces II and the Globular Cluster Laevens 1

We present Keck/DEIMOS spectroscopy of stars in the recently discovered Milky Way satellites Hydra II, Pisces II, and Laevens 1. We measured a velocity dispersion of 5.4 (+3.6 -2.4) km/s for Pisces II, but we did not resolve the velocity dispersions of Hydra II or Laevens 1. We marginally resolved the metallicity dispersions of Hydra II and Pisces II but not Laevens 1. Furthermore, Hydra II and Pisces II obey the luminosity-metallicity relation for Milky Way dwarf galaxies ( = -2.02 +/- 0.08 and -2.45 +/- 0.07, respectively), whereas Laevens 1 does not ( = -1.68 +/- 0.05). The kinematic and chemical properties suggest that Hydra II and Pisces II are dwarf galaxies, and Laevens 1 is a globular cluster. We determined that two of the previously observed blue stars near the center of Laevens 1 are not members of the cluster. A third blue star has ambiguous membership. Hydra II has a radial velocity = 303.1 +/- 1.4 km/s, similar to the leading arm of the Magellanic stream. The mass-to-light ratio for Pisces II is 370 (+310 -240) M_sun/L_sun. It is not among the most dark matter-dominated dwarf galaxies, but it is still worthy of inclusion in the search for gamma rays from dark matter self-annihilation.Comment: Accepted to ApJ. v2 has been revised in response to the referee's repor