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

LNCS

We define the model-measuring problem: given a model M and specification φ, what is the maximal distance ρ such that all models M′ within distance ρ from M satisfy (or violate) φ. The model measuring problem presupposes a distance function on models. We concentrate on automatic distance functions, which are defined by weighted automata. The model-measuring problem subsumes several generalizations of the classical model-checking problem, in particular, quantitative model-checking problems that measure the degree of satisfaction of a specification, and robustness problems that measure how much a model can be perturbed without violating the specification. We show that for automatic distance functions, and ω-regular linear-time and branching-time specifications, the model-measuring problem can be solved. We use automata-theoretic model-checking methods for model measuring, replacing the emptiness question for standard word and tree automata by the optimal-weight question for the weighted versions of these automata. We consider weighted automata that accumulate weights by maximizing, summing, discounting, and limit averaging. We give several examples of using the model-measuring problem to compute various notions of robustness and quantitative satisfaction for temporal specifications

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

Chemical composition of gahnite and degree of pegmatitic fractionation in the Borborema Pegmatitic Province, northeastern Brazil

Gahnite electron probe microanalyses from three pegmatites (Mirador, Capoeira and Quintos) of the Borborema Pegmatitic Province in northeastern Brazil allowed to determine molar compositions ranging from 86.22 to 95.41 mol% gahnite (ZnAl2O4), 1.51 to 6.62 mol% hercynite (Fe2+Al2O4), 0.11 to 5.89 mol% spinel (MgAl2O4), 1.48 to 2.74 mol% galaxite (MnAl2O4), and Zn/FeTotal atomic ratios ranging from 11.53 to 60.87. These data compared with gahnite compositions from albite subtype pegmatites from Cap de Creus, Spain (Zn/FeTotal between 10 and 60) and from the source granite of the Separation Rapids pegmatite field, Ontario, Canada (Zn/FeTotal =3.5) indicate a high degree of fractionation of the studied pegmatites. This interpretation agrees with conclusions based on compositional data of tourmaline (vacancy in X-site 0.42 to 0.49), white mica (K/Rb between 8 and 33), feldspar (K/Rb between 8 and 109), garnet (Mn/(Mn+Fe2+)between 0.93 and 0.97) and in Nb-Ta oxides (Mn/(Mn+Fe2+)>0.5) in the same pegmatites.<br>Análises via microssonda eletrônica de gahnita de três pegmatitos (Mirador, Capoeira e Quintos) da Província Pegmatítica da Borborema, no Nordeste do Brasil, permitiram estabelecer uma composição molar variando entre 86,22 e 95,41 mol% de gahnita (ZnAl2O4), 1,51 e 6,62 mol% de hercinita (Fe2+Al2O4), 0,11 e 5,89 mol% de espinélio (MgAl2O4), 1,48 e 2,74 mol% de galaxita (MnAl2O4) e relação Zn/FeTotal variando entre 11,53 e 60,87. Estes dados comparados com os de gahnita dos pegmatitos subtipo albita de Cap de Creus, Espanha (Zn/FeTotal variando entre 10 e 60) e gahnita de fonte granítica do campo pegmatítico Separation Rapids, Ontário, Canadá (Zn/FeTotal = 3,5) indicam um alto grau de fracionamento dos pegmatitos estudados. Esta interpretação está de acordo com conclusões baseadas em dados de turmalina (vacância no sítio X variando entre 0,42 a 0,49), mica clara (K/Rb variando entre 8 e 33), feldspato (K/Rb variando entre 8 e 109), granada (Mn/(Mn+Fe2+)variando entre 0,93 e 0,97) e óxidos de Nb-Ta (Mn/(Mn+Fe2+)> 0, 5), nos mesmos pegmatitos