A New Lower Bound on the Maximum Number of Satisfied Clauses in Max-SAT and its Algorithmic Applications

A pair of unit clauses is called conflicting if it is of the form $(x)$, $(\bar{x})$. A CNF formula is unit-conflict free (UCF) if it contains no pair of conflicting unit clauses. Lieberherr and Specker (J. ACM 28, 1981) showed that for each UCF CNF formula with $m$ clauses we can simultaneously satisfy at least \pp m clauses, where \pp =(\sqrt{5}-1)/2. We improve the Lieberherr-Specker bound by showing that for each UCF CNF formula $F$ with $m$ clauses we can find, in polynomial time, a subformula $F'$ with $m'$ clauses such that we can simultaneously satisfy at least \pp m+(1-\pp)m'+(2-3\pp)n"/2 clauses (in $F$), where $n"$ is the number of variables in $F$ which are not in $F'$. We consider two parameterized versions of MAX-SAT, where the parameter is the number of satisfied clauses above the bounds $m/2$ and $m(\sqrt{5}-1)/2$. The former bound is tight for general formulas, and the later is tight for UCF formulas. Mahajan and Raman (J. Algorithms 31, 1999) showed that every instance of the first parameterized problem can be transformed, in polynomial time, into an equivalent one with at most $6k+3$ variables and $10k$ clauses. We improve this to $4k$ variables and $(2\sqrt{5}+4)k$ clauses. Mahajan and Raman conjectured that the second parameterized problem is fixed-parameter tractable (FPT). We show that the problem is indeed FPT by describing a polynomial-time algorithm that transforms any problem instance into an equivalent one with at most $(7+3\sqrt{5})k$ variables. Our results are obtained using our improvement of the Lieberherr-Specker bound above

Blood pressure and metabolic effects of acetyl-L-carnitine in type 2 diabetes: DIABASI randomized controlled trial

Context: Acetyl-L-carnitine (ALC), a mitochondrial carrier involved in lipid oxidation and glucose metabolism, decreased systolic blood pressure (SBP), and ameliorated insulin sensitivity in hypertensive nondiabetic subjects at high cardiovascular risk. Objective: To assess the effects of ALC on SBP and glycemic and lipid control in patients with hypertension, type 2 diabetes mellitus (T2D), and dyslipidemia on background statin therapy. Design: After 4-week run-in period and stratification according to previous statin therapy, patients were randomized to 6-month, double-blind treatment with ALC or placebo added-on simvastatin. Setting: Five diabetology units and one clinical research center in Italy. Patients: Two hundred twenty-nine patients with hypertension and dyslipidemic T2D > 40 years with stable background antihypertensive, hypoglycemic, and statin therapy and serum creatinine < 1.5 mg/ dL. Interventions: Oral ALC 1000 mg or placebo twice daily on top of stable simvastatin therapy. Outcome and Measures: Primary outcome was SBP. Secondary outcomes included lipid and glycemic profiles. Total-body glucose disposal rate and glomerular filtration rate were measured in subgroups by hyperinsulinemic-euglycemic clamp and iohexol plasma clearance, respectively. Results: SBP did not significantly change after 6-month treatment with ALC compared with placebo (-2.09mmHg vs-3.57mmHg, P = 0.9539). Serum cholesterol, triglycerides, and lipoprotein(a), as well as blood glucose, glycated hemoglobin, fasting insulin levels, homeostatic model assessment of insulin resistance index, glucose disposal rate, and glomerular filtration rate did not significantly differ between treatments. Adverse events were comparable between groups. Conclusions: Six-month oral ALC supplementation did not affect blood pressure, lipid and glycemic control, insulin sensitivity and kidney function in hypertensive normoalbuminuric and microalbuminuric T2D patients on background statin therapy

Continuous population-level monitoring of SARS-CoV-2 seroprevalence in a large European metropolitan region.

Effective public health measures against SARS-CoV-2 require granular knowledge of population-level immune responses. We developed a Tripartite Automated Blood Immunoassay (TRABI) to assess the IgG response against three SARS-CoV-2 proteins. We used TRABI for continuous seromonitoring of hospital patients and blood donors (n = 72'250) in the canton of Zurich from December 2019 to December 2020 (pre-vaccine period). We found that antibodies waned with a half-life of 75 days, whereas the cumulative incidence rose from 2.3% in June 2020 to 12.2% in mid-December 2020. A follow-up health survey indicated that about 10% of patients infected with wildtype SARS-CoV-2 sustained some symptoms at least twelve months post COVID-19. Crucially, we found no evidence of a difference in long-term complications between those whose infection was symptomatic and those with asymptomatic acute infection. The cohort of asymptomatic SARS-CoV-2-infected subjects represents a resource for the study of chronic and possibly unexpected sequelae

Risk thresholds for alcohol consumption : combined analysis of individual-participant data for 599 912 current drinkers in 83 prospective studies

Background Low-risk limits recommended for alcohol consumption vary substantially across different national guidelines. To define thresholds associated with lowest risk for all-cause mortality and cardiovascular disease, we studied individual-participant data from 599 912 current drinkers without previous cardiovascular disease. Methods We did a combined analysis of individual-participant data from three large-scale data sources in 19 high-income countries (the Emerging Risk Factors Collaboration, EPIC-CVD, and the UK Biobank). We characterised dose-response associations and calculated hazard ratios (HRs) per 100 g per week of alcohol (12.5 units per week) across 83 prospective studies, adjusting at least for study or centre, age, sex, smoking, and diabetes. To be eligible for the analysis, participants had to have information recorded about their alcohol consumption amount and status (ie, non-drinker vs current drinker), plus age, sex, history of diabetes and smoking status, at least 1 year of follow-up after baseline, and no baseline history of cardiovascular disease. The main analyses focused on current drinkers, whose baseline alcohol consumption was categorised into eight predefined groups according to the amount in grams consumed per week. We assessed alcohol consumption in relation to all-cause mortality, total cardiovascular disease, and several cardiovascular disease subtypes. We corrected HRs for estimated long-term variability in alcohol consumption using 152 640 serial alcohol assessments obtained some years apart (median interval 5.6 years [5th-95th percentile 1.04-13.5]) from 71 011 participants from 37 studies. Findings In the 599 912 current drinkers included in the analysis, we recorded 40 310 deaths and 39 018 incident cardiovascular disease events during 5.4 million person-years of follow-up. For all-cause mortality, we recorded a positive and curvilinear association with the level of alcohol consumption, with the minimum mortality risk around or below 100 g per week. Alcohol consumption was roughly linearly associated with a higher risk of stroke (HR per 100 g per week higher consumption 1.14, 95% CI, 1.10-1.17), coronary disease excluding myocardial infarction (1.06, 1.00-1.11), heart failure (1.09, 1.03-1.15), fatal hypertensive disease (1.24, 1.15-1.33); and fatal aortic aneurysm (1.15, 1.03-1.28). By contrast, increased alcohol consumption was loglinearly associated with a lower risk of myocardial infarction (HR 0.94, 0.91-0.97). In comparison to those who reported drinking >0-100-200-350 g per week had lower life expectancy at age 40 years of approximately 6 months, 1-2 years, or 4-5 years, respectively. Interpretation In current drinkers of alcohol in high-income countries, the threshold for lowest risk of all-cause mortality was about 100 g/week. For cardiovascular disease subtypes other than myocardial infarction, there were no clear risk thresholds below which lower alcohol consumption stopped being associated with lower disease risk. These data support limits for alcohol consumption that are lower than those recommended in most current guidelines. Copyright (C) The Author(s). Published by Elsevier Ltd.Peer reviewe