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

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

The distribution of school quality: Do schools serving mostly white and high-SES children produce the most learning?

Item does not contain fulltextWhat is schools' role in the stratification system? One view is that schools are an important mechanism for perpetuating inequality because children from advantaged backgrounds (white and high socioeconomic) enjoy better school learning environments than their disadvantaged peers. But it is difficult to know this with confidence because children's development is a product of both school and nonschool factors, making it a challenge to isolate school’s role. A novel approach for isolating school effects is to estimate the difference in learning when school is in versus out, what is called impact. Scholars employing this strategy have come to a remarkable conclusion - that schools serving disadvantaged children produce as much learning as those serving advantaged children. The empirical basis for this position is modest, however, and so we address several shortcomings of the previous research by analyzing a nationally representative sample of about 3,500 children in 270 schools from the Early Childhood Longitudinal Study-Kindergarten Cohort of 2011. With more comprehensive data and better scales, we also find no difference in impact on reading scores across schools serving poor or black children versus those serving nonpoor or white children. These patterns challenge the view that differences in school quality play an important role shaping achievement gaps and prompt us to reconsider theoretical positions regarding schools and inequality.18 p

Socioeconomic, ethnic, racial, and gender gaps in children's social/behavioral skills: Do they grow faster in school or out?

Contains fulltext : 212677.pdf (publisher's version ) (Open Access)Children's social and behavioral skills vary considerably by socioeconomic status (SES), race and/or ethnicity, and gender, yet it is unclear to what degree these differences are due to school or nonschool factors. We observe how gaps in social and behavioral skills change during school and nonschool (summer) periods from the start of kindergarten entry until the end of second grade in a recent and nationally representative sample of more than 16,000 children (the Early Childhood Longitudinal Study Kindergarten Class of 2010-11). We find that large gaps in social and behavioral skills exist at the start of kindergarten entry, and these gaps favor high-SES, white, and female children. Over the next three years, we observed that the gaps grow no faster when school is in than when school is out. In the case of social and behavioral skills, it appears that schools neither exacerbate inequality nor reduce it.21 p

Number of siblings in childhood, social outcomes in adulthood

Contains fulltext : 213695.pdf (Publisher’s version ) (Closed access)In many parts of the world, fertility has declined in important ways in the past century. What are the consequences of this demographic change? Our study expands the empirical basis for understanding the relationship between number of siblings in childhood and social outcomes among adults. An important recent study found that for each additional sibling an individual grows up with, the likelihood of divorce as an adult declines by 3%. We expand this work by (a) determining whether the original pattern replicates in the National Longitudinal Study of Adolescent to Adult Health and (b) extending the analysis beyond divorce to consider whether growing up with siblings is related to prosocial adult behaviors (relationships with parents, friends, and views on conflict management with one’s partner). Our results confirm a negative association between number of siblings and divorce in adulthood. We find mixed results related to other prosocial adult behaviors.23 p

Schools as a relatively standardizing institution: The case of gender gaps in cognitive skills

Growing evidence suggests that contrary to popular belief, schools mostly do not generate achievement gaps in cognitive skills but, rather, reflect the inequalities that already exist. In the case of socioeconomic status, exposure to school often reduces gaps. Surprisingly little is known, however, about whether this pattern extends to gender gaps in cognitive skills. We compare how gender gaps in math and reading change when children are in school versus out (in the summer) among over 900,000 U.S. children. We find that girls learn faster than boys when school is out (in both reading and math), but this advantage is completely eliminated when school is in session. Compared to the family environment, schools act as a relatively standardizing institution, producing more similar gendered patterns in learning