Bridging boolean and quantitative synthesis using smoothed proof search

We present a new technique for parameter synthesis under boolean and quantitative objectives. The input to the technique is a "sketch" --- a program with missing numerical parameters --- and a probabilistic assumption about the program's inputs. The goal is to automatically synthesize values for the parameters such that the resulting program satisfies: (1) a {boolean specification}, which states that the program must meet certain assertions, and (2) a {quantitative specification}, which assigns a real valued rating to every program and which the synthesizer is expected to optimize. Our method --- called smoothed proof search --- reduces this task to a sequence of unconstrained smooth optimization problems that are then solved numerically. By iteratively solving these problems, we obtain parameter values that get closer and closer to meeting the boolean specification; at the limit, we obtain values that provably meet the specification. The approximations are computed using a new notion of smoothing for program abstractions, where an abstract transformer is approximated by a function that is continuous according to a metric over abstract states. We present a prototype implementation of our synthesis procedure, and experimental results on two benchmarks from the embedded control domain. The experiments demonstrate the benefits of smoothed proof search over an approach that does not meet the boolean and quantitative synthesis goals simultaneously.National Science Foundation (U.S.) (NSF Award #1162076

Complexity of checking whether two automata are synchronized by the same language

A deterministic finite automaton is said to be synchronizing if it has a reset word, i.e. a word that brings all states of the automaton to a particular one. We prove that it is a PSPACE-complete problem to check whether the language of reset words for a given automaton coincides with the language of reset words for some particular automaton.Comment: 12 pages, 4 figure

Vector bundles on the projective line and finite domination of chain complexes

Finitely dominated chain complexes over a Laurent polynomial ring in one indeterminate are characterised by vanishing of their Novikov homology. We present an algebro-geometric approach to this result, based on extension of chain complexes to sheaves on the projective line. We also discuss the K-theoretical obstruction to extension.Comment: v1: 11 page

Ownership and control in a competitive industry

We study a differentiated product market in which an investor initially owns a controlling stake in one of two competing firms and may acquire a non-controlling or a controlling stake in a competitor, either directly using her own assets, or indirectly via the controlled firm. While industry profits are maximized within a symmetric two product monopoly, the investor attains this only in exceptional cases. Instead, she sometimes acquires a noncontrolling stake. Or she invests asymmetrically rather than pursuing a full takeover if she acquires a controlling one. Generally, she invests indirectly if she only wants to affect the product market outcome, and directly if acquiring shares is profitable per se. --differentiated products,separation of ownership and control,private benefits of control

Early inhaled budesonide for the prevention of bronchopulmonary dysplasia

BACKGROUND Systemic glucocorticoids reduce the incidence of bronchopulmonary dysplasia among extremely preterm infants, but they may compromise brain development. The effects of inhaled glucocorticoids on outcomes in these infants are unclear. METHODS We randomly assigned 863 infants (gestational age, 23 weeks 0 days to 27 weeks 6 days) to early (within 24 hours after birth) inhaled budesonide or placebo until they no longer required oxygen and positive-pressure support or until they reached a postmenstrual age of 32 weeks 0 days. The primary outcome was death or bronchopulmonary dysplasia, confirmed by means of standardized oxygen-saturation monitoring, at a postmenstrual age of 36 weeks. RESULTS A total of 175 of 437 infants assigned to budesonide for whom adequate data were available (40.0%), as compared with 194 of 419 infants assigned to placebo for whom adequate data were available (46.3%), died or had bronchopulmonary dysplasia (relative risk, stratified according to gestational age, 0.86; 95% confidence interval [CI], 0.75 to 1.00; P = 0.05). The incidence of bronchopulmonary dysplasia was 27.8% in the budesonide group versus 38.0% in the placebo group (relative risk, stratified according to gestational age, 0.74; 95% CI, 0.60 to 0.91; P = 0.004); death occurred in 16.9% and 13.6% of the patients, respectively (relative risk, stratified according to gestational age, 1.24; 95% CI, 0.91 to 1.69; P = 0.17). The proportion of infants who required surgical closure of a patent ductus arteriosus was lower in the budesonide group than in the placebo group (relative risk, stratified according to gestational age, 0.55; 95% CI, 0.36 to 0.83; P = 0.004), as was the proportion of infants who required reintubation (relative risk, stratified according to gestational age, 0.58; 95% CI, 0.35 to 0.96; P = 0.03). Rates of other neonatal illnesses and adverse events were similar in the two groups. CONCLUSIONS Among extremely preterm infants, the incidence of bronchopulmonary dysplasia was lower among those who received early inhaled budesonide than among those who received placebo, but the advantage may have been gained at the expense of increased mortality

The circumstellar envelope of the C-rich post-AGB star HD 56126

We present a detailed study of the circumstellar envelope of the post-asymptotic giant branch ``21 micron object'' HD 56126. We build a detailed dust radiative transfer model of the circumstellar envelope in order to derive the dust composition and mass, and the mass-loss history of the star. To model the emission of the dust we use amorphous carbon, hydrogenated amorphous carbon, magnesium sulfide and titanium carbide. We present a detailed parametrisation of the optical properties of hydrogenated amorphous carbon as a function of H/C content. The mid-infrared imaging and spectroscopy is best reproduced by a single dust shell from 1.2 to 2.6 arcsec radius around the central star. This shell originates from a short period during which the mass-loss rate exceeded 10^(-4) M_sun/yr. We find that the strength of the ``21'' micron feature poses a problem for the TiC identification. The low abundance of Ti requires very high absorption cross-sections in the ultraviolet and visible wavelength range to explain the strength of the feature. Other nano-crystalline metal carbides should be considered as well. We find that hydrogenated amorphous carbon in radiative equilibrium with the local radiation field does not reach a high enough temperature to explain the strength of the 3.3-3.4 and 6-9 micron hydrocarbon features relative to the 11-17 micron hydrocarbon features. We propose that the carriers of these hydrocarbon features are not in radiative equilibrium but are transiently heated to high temperature. We find that 2 per cent of the dust mass is required to explain the strength of the ``30'' micron feature, which fits well within the measured atmospheric abundance of Mg and S. This further strengthens the MgS identification of the ``30'' micron feature.Comment: 20 Pages, 10 Figures, accepted for publication in Astronomy and Astrophysic