Cartesian closed categories of separable Scott domains

We classify all sub-cartesian closed categories of the category of separable Scott domains. The classification employs a notion of coherence degree determined by the possible inconsistency patterns of sets of finite elements of a domain. Using the classification, we determine all sub-cartesian closed categories of the category of separable Scott domains that contain a universal object. The separable Scott domain models of the λβ-calculus are then classified up to a retraction by their coherence degrees. Keywords

Game Refinement Relations and Metrics

We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose probability distributions over moves, rather than single moves. Given a goal, for example, reach a target state, the question of winning is thus a probabilistic one: what is the maximal probability of winning from a given state? On these game structures, two fundamental notions are those of equivalences and metrics. Given a set of winning conditions, two states are equivalent if the players can win the same games with the same probability from both states. Metrics provide a bound on the difference in the probabilities of winning across states, capturing a quantitative notion of state similarity. We introduce equivalences and metrics for two-player game structures, and we show that they characterize the difference in probability of winning games whose goals are expressed in the quantitative mu-calculus. The quantitative mu-calculus can express a large set of goals, including reachability, safety, and omega-regular properties. Thus, we claim that our relations and metrics provide the canonical extensions to games, of the classical notion of bisimulation for transition systems. We develop our results both for equivalences and metrics, which generalize bisimulation, and for asymmetrical versions, which generalize simulation

X-ray and Multiwavelength Insights into the Nature of Weak Emission-Line Quasars at Low Redshift

(Abridged) We report on the X-ray and multiwavelength properties of 11 radio-quiet quasars with weak or no emission lines identified by the Sloan Digital Sky Survey (SDSS) with redshift z=0.4-2.5. The distribution of relative X-ray brightness for our low-redshift weak-line quasar (WLQ) candidates is significantly different from that of typical radio-quiet quasars, having an excess of X-ray weak sources, but it is consistent with that of high-redshift WLQs. The X-ray weak sources generally show similar UV emission-line properties to those of the X-ray weak quasar PHL 1811; they may belong to the notable class of PHL 1811 analogs. The average X-ray spectrum of these sources is somewhat harder than that of typical radio-quiet quasars. Several other low-redshift WLQ candidates have normal ratios of X-ray-to-optical/UV flux, and their average X-ray spectral properties are also similar to those of typical radio-quiet quasars. The X-ray weak and X-ray normal WLQ candidates may belong to the same subset of quasars having high-ionization "shielding gas" covering most of the wind-dominated broad emission-line region, but be viewed at different inclinations. The mid-infrared-to-X-ray spectral energy distributions (SEDs) of these sources are generally consistent with those of typical SDSS quasars, showing that they are not likely to be BL Lac objects with relativistically boosted continua and diluted emission lines. However, one source in our X-ray observed sample is remarkably strong in X-rays, indicating that a small fraction of low-redshift WLQ candidates may actually be BL Lacs residing in the radio-faint tail of the BL Lac population. We also investigate universal selection criteria for WLQs over a wide range of redshift, finding that it is not possible to select WLQ candidates in a fully consistent way using different prominent emission lines as a function of redshift.Comment: ApJ in press; 26 pages, 11 figures and 7 tables. The full Table 3 is available upon reques

The Ultraviolet-to-Mid-Infrared Spectral Energy Distribution of Weak Emission Line Quasars

We present Spitzer Space Telescope photometry of 18 Sloan Digital Sky Survey (SDSS) quasars at 2.7 <= z <= 5.9 which have weak or undetectable high-ionization emission lines in their rest-frame ultraviolet (UV) spectra (hereafter weak-lined quasars, or WLQs). The Spitzer data are combined with SDSS spectra and ground-based, near-infrared (IR) photometry of these sources to produce a large inventory of spectral energy distributions (SEDs) of WLQs across the rest-frame ~0.1-5 mum spectral band. The SEDs of our sources are inconsistent with those of BL Lacertae objects which are dominated by synchrotron emission due to a jet aligned close to our line-of-sight, but are consistent with the SED of ordinary quasars with similar luminosities and redshifts that exhibit a near-to-mid-IR 'bump', characteristic of hot dust emission. This indicates that broad emission lines in WLQs are intrinsically weak, rather than suffering continuum dilution from a jet, and that such sources cannot be selected efficiently from traditional photometric surveys.Comment: 10 pages (emulateapj), 4 figures. Accepted for publication in Ap

Matching typed and untyped readability (Extended abstract)

AbstractRealizability interpretations of logics are given by saying what it means for computational objects of some kind to realize, logical formulae. The computational objects in question might be drawn from an untyped universe of computation, such as a partial combinatory algebra, or they might be typed objects such as terms of a PCF-style programming language. In some instances, one can show that a particular untyped realizability interpretation matches a particular typed one, in the sense that they give the same set of realizable formulae. In this case, we have a very good fit indeed between the typed language and the untyped realizability model–we refer to this condition as (constructive) logical full abstraction.,We give some examples of this situation for a variety of extensions of PCF. Of particular interest are some models that are logically fully abstract for typed languages including non-functional, features. Our results establish connections between what is computable in various programming languages, and what is true inside various realizability toposes. We consider some examples of logical formulae to illustrate these ideas, in particular their application to exact real-number computability.The present article summarizes the material I presented at the Domains IV workshop, plus a few subsequent developments; it is really an extended abstract for a projected journal paper. No proofs are included in the present version

On the completeness of order-theoretic models of the lambda-calculus

Scott discovered his domain-theoretic models of the \u3bb-calculus, isomorphic to their function space, in 1969. A natural completeness problem then arises: whether any two terms equal in all Scott models are convertible. There is also an analogous consistency problem: whether every equation between two terms, consistent with the \u3bb-calculus, has a Scott model. We consider such questions for wider sets of sentences and wider classes of models, the pointed (completely) partially ordered ones. A negative result for a set of sentences shows the impossibility of finding Scott models for that class; a positive result gives evidence that there might be enough Scott models. We find, for example, that the order-extensional pointed \u3c9-cpo models are complete for \u3a01-sentences with positive matrices, whereas the consistency question for \u3a31-sentences with equational matrices depends on the consistency of certain critical sentences asserting the existence of certain functions analogous to the generalized Mal'cev operators first considered in the context of the \u3bb-calculus by Selinger

Matching typed and untyped realizability

AbstractRealizability interpretations of logics are given by saying what it means for computational objects of some kind to realize logical formulae. The computational objects in question might be drawn from an untyped universe of computation, such as a partial combinatory algebra, or they might be typed objects such as terms of a PCF-style programming language. In some instances, one can show that a particular untyped realizability interpretation matches a particular typed one, in the sense that they give the same set of realizable formulae. In this case, we have a very good fit indeed between the typed language and the untyped realizability model — we refer to this condition as (constructive) logical full abstraction.We give some examples of this situation for a variety of extensions of PCF. Of particular interest are some models that are logically fully abstract for typed languages including non-functional features. Our results establish connections between what is computable in various programming languages and what is true inside various realizability toposes. We consider some examples of logical formulae to illustrate these ideas, in particular their application to exact real-number computability

Characterizing the Optical Variability of Bright Blazars: Variability-based Selection of Fermi Active Galactic Nuclei

We investigate the use of optical photometric variability to select and identify blazars in large-scale time-domain surveys, in part to aid in the identification of blazar counterparts to the ∼30% of γ -ray sources in the Fermi 2FGL catalog still lacking reliable associations. Using data from the optical LINEAR asteroid survey, we characterize the optical variability of blazars by fitting a damped random walk model to individual light curves with two main model parameters, the characteristic timescales of variability τ , and driving amplitudes on short timescales σ . Imposing cuts on minimum τ and σ allows for blazar selection with high efficiency E and completeness C. To test the efficacy of this approach, we apply this method to optically variable LINEAR objects that fall within the several arcminute error ellipses of γ -ray sources in the Fermi 2FGL catalog. Despite the extreme stellar contamination at the shallow depth of the LINEAR survey, we are able to recover previously associated optical counterparts to Fermi active galactic nuclei with E ≥ 88% and C = 88% in Fermi 95% confidence error ellipses having semimajor axis r < 8'. We find that the suggested radio counterpart to Fermi source 2FGL J1649.6+5238 has optical variability consistent with other γ -ray blazars and is likely to be the γ -ray source. Our results suggest that the variability of the non-thermal jet emission in blazars is stochastic in nature, with unique variability properties due to the effects of relativistic beaming. After correcting for beaming, we estimate that the characteristic timescale of blazar variability is ∼3 years in the rest frame of the jet, in contrast with the ∼320 day disk flux timescale observed in quasars. The variability-based selection method presented will be useful for blazar identification in time-domain optical surveys and is also a probe of jet physics