The strength of Ramsey Theorem for coloring relatively large sets

We characterize the computational content and the proof-theoretic strength of a Ramsey-type theorem for bi-colorings of so-called {\em exactly large} sets. An {\it exactly large} set is a set X\subset\Nat such that \card(X)=\min(X)+1. The theorem we analyze is as follows. For every infinite subset $M$ of \Nat, for every coloring $C$ of the exactly large subsets of $M$ in two colors, there exists and infinite subset $L$ of $M$ such that $C$ is constant on all exactly large subsets of $L$. This theorem is essentially due to Pudl\`ak and R\"odl and independently to Farmaki. We prove that --- over Computable Mathematics --- this theorem is equivalent to closure under the $\omega$ Turing jump (i.e., under arithmetical truth). Natural combinatorial theorems at this level of complexity are rare. Our results give a complete characterization of the theorem from the point of view of Computable Mathematics and of the Proof Theory of Arithmetic. This nicely extends the current knowledge about the strength of Ramsey Theorem. We also show that analogous results hold for a related principle based on the Regressive Ramsey Theorem. In addition we give a further characterization in terms of truth predicates over Peano Arithmetic. We conjecture that analogous results hold for larger ordinals

The Doping Effect of Fluorinated Aromatic Solvent on the Rate of Ruthenium Catalysed Olefin Metathesis

A study concerning the effect of using a fluorinated aromatic solvent as the medium for olefin metathesis reactions catalysed by ruthenium complexes bearing N-heterocyclic carbene ligands is presented. The use of fluorinated aromatic hydrocarbons (FAH) as solvents for olefin metathesis reactions catalysed by standard commercially available ruthenium pre-catalysts allows substantially higher yields of the desired products to be obtained,especially in the case of demanding polyfunctional molecules, including natural and biologically active compounds. Interactions between the FAH and the second-generation ruthenium catalysts, which apparently improve the efficiency of the olefin metathesis transformation, have been studied by X-ray structure analysis and computations, as well as by carrying out a number of metathesis experiments. The optimisation of reaction conditions by using an FAH can be regarded as a complementary approach for the design of new improved ruthenium catalysts. Fluorinated aromatic solvents are an attractive alternative medium for promoting challenging olefin metathesis reactions

An avian influenza H5N1 virus vaccine candidate based on the extracellular domain produced in yeast system as subviral particles protects chickens from lethal challenge

AbstractHighly pathogenic avian influenza is an on-going problem in poultry and a potential human pandemic threat. Pandemics occur suddenly and vaccine production must be fast and effective to be of value in controlling the spread of the virus. In this study we evaluated the potential of a recombinant protein from the extracellular domain of an H5 hemagglutinin protein produced in a yeast expression system to act as an effective vaccine. Protein production was efficient, with up to 200 mg purified from 1 L of culture medium. We showed that the deletion of the multibasic cleavage site from the protein improves oligomerization and, consequentially, its immunogenicity. We also showed that immunization with this deleted protein protected chickens from challenge with a highly pathogenic avian influenza H5N1 virus. Our results suggest that this recombinant protein produced in yeast may be an effective vaccine against H5N1 virus in poultry

Modeling of Dolichol Mass Spectra Isotopic Envelopes as a Tool to Monitor Isoprenoid Biosynthesis1

The cooperation of the mevalonate (MVA) and methylerythritol phosphate (MEP) pathways, operating in parallel in plants to generate isoprenoid precursors, has been studied extensively. Elucidation of the isoprenoid metabolic pathways is indispensable for the rational design of plant and microbial systems for the production of industrially valuable terpenoids. Here, we describe a new method, based on numerical modeling of mass spectra of metabolically labeled dolichols (Dols), designed to quantitatively follow the cooperation of MVA and MEP reprogrammed upon osmotic stress (sorbitol treatment) in Arabidopsis (Arabidopsis thaliana). The contribution of the MEP pathway increased significantly (reaching 100%) exclusively for the dominating Dols, while for long-chain Dols, the relative input of the MEP and MVA pathways remained unchanged, suggesting divergent sites of synthesis for dominating and long-chain Dols. The analysis of numerically modeled Dol mass spectra is a novel method to follow modulation of the concomitant activity of isoprenoid-generating pathways in plant cells; additionally, it suggests an exchange of isoprenoid intermediates between plastids and peroxisomes

Status Update and Interim Results from the Asymptomatic Carotid Surgery Trial-2 (ACST-2)

Objectives: ACST-2 is currently the largest trial ever conducted to compare carotid artery stenting (CAS) with carotid endarterectomy (CEA) in patients with severe asymptomatic carotid stenosis requiring revascularization. Methods: Patients are entered into ACST-2 when revascularization is felt to be clearly indicated, when CEA and CAS are both possible, but where there is substantial uncertainty as to which is most appropriate. Trial surgeons and interventionalists are expected to use their usual techniques and CE-approved devices. We report baseline characteristics and blinded combined interim results for 30-day mortality and major morbidity for 986 patients in the ongoing trial up to September 2012. Results: A total of 986 patients (687 men, 299 women), mean age 68.7 years (SD ± 8.1) were randomized equally to CEA or CAS. Most (96%) had ipsilateral stenosis of 70-99% (median 80%) with contralateral stenoses of 50-99% in 30% and contralateral occlusion in 8%. Patients were on appropriate medical treatment. For 691 patients undergoing intervention with at least 1-month follow-up and Rankin scoring at 6 months for any stroke, the overall serious cardiovascular event rate of periprocedural (within 30 days) disabling stroke, fatal myocardial infarction, and death at 30 days was 1.0%. Conclusions: Early ACST-2 results suggest contemporary carotid intervention for asymptomatic stenosis has a low risk of serious morbidity and mortality, on par with other recent trials. The trial continues to recruit, to monitor periprocedural events and all types of stroke, aiming to randomize up to 5,000 patients to determine any differential outcomes between interventions. Clinical trial: ISRCTN21144362. © 2013 European Society for Vascular Surgery. Published by Elsevier Ltd. All rights reserved

Second asymptomatic carotid surgery trial (ACST-2): a randomised comparison of carotid artery stenting versus carotid endarterectomy

Background: Among asymptomatic patients with severe carotid artery stenosis but no recent stroke or transient cerebral ischaemia, either carotid artery stenting (CAS) or carotid endarterectomy (CEA) can restore patency and reduce long-term stroke risks. However, from recent national registry data, each option causes about 1% procedural risk of disabling stroke or death. Comparison of their long-term protective effects requires large-scale randomised evidence. Methods: ACST-2 is an international multicentre randomised trial of CAS versus CEA among asymptomatic patients with severe stenosis thought to require intervention, interpreted with all other relevant trials. Patients were eligible if they had severe unilateral or bilateral carotid artery stenosis and both doctor and patient agreed that a carotid procedure should be undertaken, but they were substantially uncertain which one to choose. Patients were randomly allocated to CAS or CEA and followed up at 1 month and then annually, for a mean 5 years. Procedural events were those within 30 days of the intervention. Intention-to-treat analyses are provided. Analyses including procedural hazards use tabular methods. Analyses and meta-analyses of non-procedural strokes use Kaplan-Meier and log-rank methods. The trial is registered with the ISRCTN registry, ISRCTN21144362. Findings: Between Jan 15, 2008, and Dec 31, 2020, 3625 patients in 130 centres were randomly allocated, 1811 to CAS and 1814 to CEA, with good compliance, good medical therapy and a mean 5 years of follow-up. Overall, 1% had disabling stroke or death procedurally (15 allocated to CAS and 18 to CEA) and 2% had non-disabling procedural stroke (48 allocated to CAS and 29 to CEA). Kaplan-Meier estimates of 5-year non-procedural stroke were 2·5% in each group for fatal or disabling stroke, and 5·3% with CAS versus 4·5% with CEA for any stroke (rate ratio [RR] 1·16, 95% CI 0·86–1·57; p=0·33). Combining RRs for any non-procedural stroke in all CAS versus CEA trials, the RR was similar in symptomatic and asymptomatic patients (overall RR 1·11, 95% CI 0·91–1·32; p=0·21). Interpretation: Serious complications are similarly uncommon after competent CAS and CEA, and the long-term effects of these two carotid artery procedures on fatal or disabling stroke are comparable. Funding: UK Medical Research Council and Health Technology Assessment Programme

THE STRENGTH OF RAMSEY’S THEOREM FOR COLORING RELATIVELY LARGE SETS

We characterize the effective content and the proof-theoretic strength of a Ramsey-type theorem for bi-colorings of so-called exactly large sets. The theorem we analyze is as follows. For every infinite subset M of N, for every coloring C of the exactly large subsets of M in two colors, there exists and infinite subset L of M such that C is constant on all exactly large subsets of L. This theorem is essentially due to Pudlák and Rödl and independently to Farmaki. We prove that—over RCA0 —this theorem is equivalent to closure under the ωth Turing jump (i.e., under arithmetical truth). Natural combinatorial theorems at this level of complexity are rare. In terms of Reverse Mathematics we give the first Ramsey-theoretic characterization of ACA0+. Our results give a complete characterization of the theorem from the point of view of Computability Theory and of the Proof Theory of Arithmetic. This nicely extends the current knowledge about the strength of Ramsey’s Theorem. We also show that analogous results hold for a related principle based on the Regressive Ramsey’s Theorem. We conjecture that analogous results hold for larger ordinals

A note on Ramsey theorems and Turing jumps

We give a new treatment of the relations between Ramsey's Theorem, ACA 0 and ACA′ 0. First we combine a result by Girard with a colouring used by Loebl and Nešetril for the analysis of the Paris-Harrington principle to obtain a short combinatorial proof of ACA 0 from Ramsey Theorem for triples. We then extend this approach to ACA′ 0 using a characterization of this system in terms of preservation of well-orderings due to Marcone and Montalbán. We finally discuss how to apply this method to ACA 0 + using an extension of Ramsey's Theorem for colouring relatively large sets due to Pudlàk and Rödl and independently to Farmaki. © 2012 Springer-Verlag