Relations and Equivalences Between Circuit Lower Bounds and Karp-Lipton Theorems

A frontier open problem in circuit complexity is to prove P^{NP} is not in SIZE[n^k] for all k; this is a necessary intermediate step towards NP is not in P_{/poly}. Previously, for several classes containing P^{NP}, including NP^{NP}, ZPP^{NP}, and S_2 P, such lower bounds have been proved via Karp-Lipton-style Theorems: to prove C is not in SIZE[n^k] for all k, we show that C subset P_{/poly} implies a "collapse" D = C for some larger class D, where we already know D is not in SIZE[n^k] for all k. It seems obvious that one could take a different approach to prove circuit lower bounds for P^{NP} that does not require proving any Karp-Lipton-style theorems along the way. We show this intuition is wrong: (weak) Karp-Lipton-style theorems for P^{NP} are equivalent to fixed-polynomial size circuit lower bounds for P^{NP}. That is, P^{NP} is not in SIZE[n^k] for all k if and only if (NP subset P_{/poly} implies PH subset i.o.- P^{NP}_{/n}). Next, we present new consequences of the assumption NP subset P_{/poly}, towards proving similar results for NP circuit lower bounds. We show that under the assumption, fixed-polynomial circuit lower bounds for NP, nondeterministic polynomial-time derandomizations, and various fixed-polynomial time simulations of NP are all equivalent. Applying this equivalence, we show that circuit lower bounds for NP imply better Karp-Lipton collapses. That is, if NP is not in SIZE[n^k] for all k, then for all C in {Parity-P, PP, PSPACE, EXP}, C subset P_{/poly} implies C subset i.o.-NP_{/n^epsilon} for all epsilon > 0. Note that unconditionally, the collapses are only to MA and not NP. We also explore consequences of circuit lower bounds for a sparse language in NP. Among other results, we show if a polynomially-sparse NP language does not have n^{1+epsilon}-size circuits, then MA subset i.o.-NP_{/O(log n)}, MA subset i.o.-P^{NP[O(log n)]}, and NEXP is not in SIZE[2^{o(m)}]. Finally, we observe connections between these results and the "hardness magnification" phenomena described in recent works

Sustainable management of groundwater extraction: An Australian perspective on current challenges

Study focus: Our incomplete knowledge of groundwater systems and processes imposes barriers in attempting to manage groundwater sustainably. Challenges also arise through complex institutional arrangements and decision-making processes, and the difficulty in involving stakeholders. In some areas, these difficulties have led to water table decline and impacts on groundwater users and groundwater-dependent ecosystems. However, there is potential to improve the sustainable use of groundwater resources through improvements in management practices. We discuss some of the challenges, and present survey results of research, government, and industry professionals across the groundwater sector in Australia. New hydrological insights for the region: The highest-ranked challenge identified in the survey was the difficulty in determining regional-scale volumetric water extraction limits. This is surprising given the criticism in the international literature of volumetric based approaches for groundwater management, and the decreased reliance on this approach in Australia and elsewhere in recent years. Other major challenges are the difficulty in determining and implementing maximum drawdown criteria for groundwater levels, determining water needs of ecosystems, and managing groundwater impacts on surface water. Notwithstanding these gaps in technical understanding and tools and a lack of resources for groundwater studies, improvements in stakeholder communication should enable more effective decision-making and improve compliance with regulations designed to protect groundwater and dependent ecosystems

A many-analysts approach to the relation between religiosity and well-being

The relation between religiosity and well-being is one of the most researched topics in the psychology of religion, yet the directionality and robustness of the effect remains debated. Here, we adopted a many-analysts approach to assess the robustness of this relation based on a new cross-cultural dataset (N=10,535 participants from 24 countries). We recruited 120 analysis teams to investigate (1) whether religious people self-report higher well-being, and (2) whether the relation between religiosity and self-reported well-being depends on perceived cultural norms of religion (i.e., whether it is considered normal and desirable to be religious in a given country). In a two-stage procedure, the teams first created an analysis plan and then executed their planned analysis on the data. For the first research question, all but 3 teams reported positive effect sizes with credible/confidence intervals excluding zero (median reported β=0.120). For the second research question, this was the case for 65% of the teams (median reported β=0.039). While most teams applied (multilevel) linear regression models, there was considerable variability in the choice of items used to construct the independent variables, the dependent variable, and the included covariates

A Many-analysts Approach to the Relation Between Religiosity and Well-being

The relation between religiosity and well-being is one of the most researched topics in the psychology of religion, yet the directionality and robustness of the effect remains debated. Here, we adopted a many-analysts approach to assess the robustness of this relation based on a new cross-cultural dataset (N = 10, 535 participants from 24 countries). We recruited 120 analysis teams to investigate (1) whether religious people self-report higher well-being, and (2) whether the relation between religiosity and self-reported well-being depends on perceived cultural norms of religion (i.e., whether it is considered normal and desirable to be religious in a given country). In a two-stage procedure, the teams first created an analysis plan and then executed their planned analysis on the data. For the first research question, all but 3 teams reported positive effect sizes with credible/confidence intervals excluding zero (median reported β = 0.120). For the second research question, this was the case for 65% of the teams (median reported β = 0.039). While most teams applied (multilevel) linear regression models, there was considerable variability in the choice of items used to construct the independent variables, the dependent variable, and the included covariates

Evidence that breast cancer risk at the 2q35 locus is mediated through IGFBP5 regulation.

GWAS have identified a breast cancer susceptibility locus on 2q35. Here we report the fine mapping of this locus using data from 101,943 subjects from 50 case-control studies. We genotype 276 SNPs using the 'iCOGS' genotyping array and impute genotypes for a further 1,284 using 1000 Genomes Project data. All but two, strongly correlated SNPs (rs4442975 G/T and rs6721996 G/A) are excluded as candidate causal variants at odds against >100:1. The best functional candidate, rs4442975, is associated with oestrogen receptor positive (ER+) disease with an odds ratio (OR) in Europeans of 0.85 (95% confidence interval=0.84-0.87; P=1.7 × 10(-43)) per t-allele. This SNP flanks a transcriptional enhancer that physically interacts with the promoter of IGFBP5 (encoding insulin-like growth factor-binding protein 5) and displays allele-specific gene expression, FOXA1 binding and chromatin looping. Evidence suggests that the g-allele confers increased breast cancer susceptibility through relative downregulation of IGFBP5, a gene with known roles in breast cell biology

Prevalence and architecture of de novo mutations in developmental disorders.

The genomes of individuals with severe, undiagnosed developmental disorders are enriched in damaging de novo mutations (DNMs) in developmentally important genes. Here we have sequenced the exomes of 4,293 families containing individuals with developmental disorders, and meta-analysed these data with data from another 3,287 individuals with similar disorders. We show that the most important factors influencing the diagnostic yield of DNMs are the sex of the affected individual, the relatedness of their parents, whether close relatives are affected and the parental ages. We identified 94 genes enriched in damaging DNMs, including 14 that previously lacked compelling evidence of involvement in developmental disorders. We have also characterized the phenotypic diversity among these disorders. We estimate that 42% of our cohort carry pathogenic DNMs in coding sequences; approximately half of these DNMs disrupt gene function and the remainder result in altered protein function. We estimate that developmental disorders caused by DNMs have an average prevalence of 1 in 213 to 1 in 448 births, depending on parental age. Given current global demographics, this equates to almost 400,000 children born per year

Factors Associated with Revision Surgery after Internal Fixation of Hip Fractures

Background: Femoral neck fractures are associated with high rates of revision surgery after management with internal fixation. Using data from the Fixation using Alternative Implants for the Treatment of Hip fractures (FAITH) trial evaluating methods of internal fixation in patients with femoral neck fractures, we investigated associations between baseline and surgical factors and the need for revision surgery to promote healing, relieve pain, treat infection or improve function over 24 months postsurgery. Additionally, we investigated factors associated with (1) hardware removal and (2) implant exchange from cancellous screws (CS) or sliding hip screw (SHS) to total hip arthroplasty, hemiarthroplasty, or another internal fixation device. Methods: We identified 15 potential factors a priori that may be associated with revision surgery, 7 with hardware removal, and 14 with implant exchange. We used multivariable Cox proportional hazards analyses in our investigation. Results: Factors associated with increased risk of revision surgery included: female sex, [hazard ratio (HR) 1.79, 95% confidence interval (CI) 1.25-2.50; P = 0.001], higher body mass index (fo

Publisher Correction: Evidence that breast cancer risk at the 2q35 locus is mediated through IGFBP5 regulation.

This corrects the article DOI: 10.1038/ncomms5999