Fixed-Parameter Tractability of Multicut in Directed Acyclic Graphs

The Multicut problem, given a graph G, a set of terminal pairs $\mathcal{T}=\{(s_i,t_i)\ |\ 1\leq i\leq r\}$, and an integer $p$, asks whether one can find a cutset consisting of at most $p$ nonterminal vertices that separates all the terminal pairs, i.e., after removing the cutset, $t_i$ is not reachable from $s_i$ for each $1\leq i\leq r$. The fixed-parameter tractability of Multicut in undirected graphs, parameterized by the size of the cutset only, has been recently proved by Marx and Razgon [SIAM J. Comput., 43 (2014), pp. 355--388] and, independently, by Bousquet, Daligault, and Thomassé [Proceedings of STOC, ACM, 2011, pp. 459--468], after resisting attacks as a long-standing open problem. In this paper we prove that Multicut is fixed-parameter tractable on directed acyclic graphs when parameterized both by the size of the cutset and the number of terminal pairs. We complement this result by showing that this is implausible for parameterization by the size of the cutset only, as this version of the problem remains $W[1]$-hard

Multi-budgeted Directed Cuts

In this paper, we study multi-budgeted variants of the classic minimum cut problem and graph separation problems that turned out to be important in parameterized complexity: SKEW MULTICUT and DIRECTED FEEDBACK ARC SET. In our generalization, we assign colors 1, 2,..., l to some edges and give separate budgets k(1), k(2),..., k(l) for colors 1, 2,..., l. For every color i is an element of {1,..., l}, let E-i be the set of edges of color i. The solution C for the multi-budgeted variant of a graph separation problem not only needs to satisfy the usual separation requirements (i.e., be a cut, a skew multicut, or a directed feedback arc set, respectively), but also needs to satisfy that vertical bar C boolean AND E-i vertical bar <= k(i) for every i is an element of {1,..., l}. Contrary to the classic minimum cut problem, the multi-budgeted variant turns out to be NP-hard even for l = 2. We propose FPT algorithms parameterized by k = k(1) + ... + k(l) for all three problems. To this end, we develop a branching procedure for the multi-budgeted minimum cut problem that measures the progress of the algorithm not by reducing k as usual, by but elevating the capacity of some edges and thus increasing the size of maximum source-to-sink flow. Using the fact that a similar strategy is used to enumerate all important separators of a given size, we merge this process with the flow-guided branching and show an FPT bound on the number of (appropriately defined) important multi-budgeted separators. This allows us to extend our algorithm to the Skew Multicut and Directed Feedback Arc Set problems. Furthermore, we show connections of the multi-budgeted variants with weighted variants of the directed cut problems and the Chain l-SATproblem, whose parameterized complexity remains an open problem. We show that these problems admit a bounded-in-parameter number of "maximally pushed" solutions (in a similar spirit as important separators are maximally pushed), giving somewhat weak evidence towards their tractability

Large-scale analysis of association between LRP5 and LRP6 variants and osteoporosis

CONTEXT: Mutations in the low-density lipoprotein receptor-related protein 5 (LRP5) gene cause rare syndromes characterized by altered bone mineral density (BMD). More common LRP5 variants may affect osteoporosis risk in the general population.OBJECTIVE: To generate large-scale evidence on whether 2 common variants of LRP5 (Val667Met, Ala1330Val) and 1 variant of LRP6 (Ile1062Val) are associated with BMD and fracture risk.DESIGN AND SETTING: Prospective, multicenter, collaborative study of individual-level data on 37,534 individuals from 18 participating teams in Europe and North America. Data were collected between September 2004 and January 2007; analysis of the collected data was performed between February and May 2007. Bone mineral density was assessed by dual-energy x-ray absorptiometry. Fractures were identified via questionnaire, medical records, or radiographic documentation; incident fracture data were available for some cohorts, ascertained via routine surveillance methods, including radiographic examination for vertebral fractures.MAIN OUTCOME MEASURES: Bone mineral density of the lumbar spine and femoral neck; prevalence of all fractures and vertebral fractures.RESULTS: The Met667 allele of LRP5 was associated with reduced lumbar spine BMD (n = 25,052 [number of participants with available data]; 20-mg/cm2 lower BMD per Met667 allele copy; P = 3.3 x 10(-8)), as was the Val1330 allele (n = 24,812; 14-mg/cm2 lower BMD per Val1330 copy; P = 2.6 x 10(-9)). Similar effects were observed for femoral neck BMD, with a decrease of 11 mg/cm2 (P = 3.8 x 10(-5)) and 8 mg/cm2 (P = 5.0 x 10(-6)) for the Met667 and Val1330 alleles, respectively (n = 25 193). Findings were consistent across studies for both LRP5 alleles. Both alleles were associated with vertebral fractures (odds ratio [OR], 1.26; 95% confidence interval [CI], 1.08-1.47 for Met667 [2001 fractures among 20 488 individuals] and OR, 1.12; 95% CI, 1.01-1.24 for Val1330 [1988 fractures among 20,096 individuals]). Risk of all fractures was also increased with Met667 (OR, 1.14; 95% CI, 1.05-1.24 per allele [7876 fractures among 31,435 individuals)]) and Val1330 (OR, 1.06; 95% CI, 1.01-1.12 per allele [7802 fractures among 31 199 individuals]). Effects were similar when adjustments were made for age, weight, height, menopausal status, and use of hormone therapy. Fracture risks were partly attenuated by adjustment for BMD. Haplotype analysis indicated that Met667 and Val1330 variants both independently affected BMD. The LRP6 Ile1062Val polymorphism was not associated with any osteoporosis phenotype. All aforementioned associations except that between Val1330 and all fractures and vertebral fractures remained significant after multiple-comparison adjustments.CONCLUSIONS: Common LRP5 variants are consistently associated with BMD and fracture risk across different white populations. The magnitude of the effect is modest. LRP5 may be the first gene to reach a genome-wide significance level (a conservative level of significance [herein, unadjusted P < 10(-7)] that accounts for the many possible comparisons in the human genome) for a phenotype related to osteoporosis

Genetic determinants of heel bone properties: genome-wide association meta-analysis and replication in the GEFOS/GENOMOS consortium

Quantitative ultrasound of the heel captures heel bone properties that independently predict fracture risk and, with bone mineral density (BMD) assessed by X-ray (DXA), may be convenient alternatives for evaluating osteoporosis and fracture risk. We performed a meta-analysis of genome-wide association (GWA) studies to assess the genetic determinants of heel broadband ultrasound attenuation (BUA; n = 14 260), velocity of sound (VOS; n = 15 514) and BMD (n = 4566) in 13 discovery cohorts. Independent replication involved seven cohorts with GWA data (in silico n = 11 452) and new genotyping in 15 cohorts (de novo n = 24 902). In combined random effects, meta-analysis of the discovery and replication cohorts, nine single nucleotide polymorphisms (SNPs) had genome-wide significant (P < 5 × 10(-8)) associations with heel bone properties. Alongside SNPs within or near previously identified osteoporosis susceptibility genes including ESR1 (6q25.1: rs4869739, rs3020331, rs2982552), SPTBN1 (2p16.2: rs11898505), RSPO3 (6q22.33: rs7741021), WNT16 (7q31.31: rs2908007), DKK1 (10q21.1: rs7902708) and GPATCH1 (19q13.11: rs10416265), we identified a new locus on chromosome 11q14.2 (rs597319 close to TMEM135, a gene recently linked to osteoblastogenesis and longevity) significantly associated with both BUA and VOS (P < 8.23 × 10(-14)). In meta-analyses involving 25 cohorts with up to 14 985 fracture cases, six of 10 SNPs associated with heel bone properties at P < 5 × 10(-6) also had the expected direction of association with any fracture (P < 0.05), including three SNPs with P < 0.005: 6q22.33 (rs7741021), 7q31.31 (rs2908007) and 10q21.1 (rs7902708). In conclusion, this GWA study reveals the effect of several genes common to central DXA-derived BMD and heel ultrasound/DXA measures and points to a new genetic locus with potential implications for better understanding of osteoporosis pathophysiology

Genetic Sharing with Cardiovascular Disease Risk Factors and Diabetes Reveals Novel Bone Mineral Density Loci.

Bone Mineral Density (BMD) is a highly heritable trait, but genome-wide association studies have identified few genetic risk factors. Epidemiological studies suggest associations between BMD and several traits and diseases, but the nature of the suggestive comorbidity is still unknown. We used a novel genetic pleiotropy-informed conditional False Discovery Rate (FDR) method to identify single nucleotide polymorphisms (SNPs) associated with BMD by leveraging cardiovascular disease (CVD) associated disorders and metabolic traits. By conditioning on SNPs associated with the CVD-related phenotypes, type 1 diabetes, type 2 diabetes, systolic blood pressure, diastolic blood pressure, high density lipoprotein, low density lipoprotein, triglycerides and waist hip ratio, we identified 65 novel independent BMD loci (26 with femoral neck BMD and 47 with lumbar spine BMD) at conditional FDR < 0.01. Many of the loci were confirmed in genetic expression studies. Genes validated at the mRNA levels were characteristic for the osteoblast/osteocyte lineage, Wnt signaling pathway and bone metabolism. The results provide new insight into genetic mechanisms of variability in BMD, and a better understanding of the genetic underpinnings of clinical comorbidity

New genetic loci link adipose and insulin biology to body fat distribution.

Body fat distribution is a heritable trait and a well-established predictor of adverse metabolic outcomes, independent of overall adiposity. To increase our understanding of the genetic basis of body fat distribution and its molecular links to cardiometabolic traits, here we conduct genome-wide association meta-analyses of traits related to waist and hip circumferences in up to 224,459 individuals. We identify 49 loci (33 new) associated with waist-to-hip ratio adjusted for body mass index (BMI), and an additional 19 loci newly associated with related waist and hip circumference measures (P < 5 × 10(-8)). In total, 20 of the 49 waist-to-hip ratio adjusted for BMI loci show significant sexual dimorphism, 19 of which display a stronger effect in women. The identified loci were enriched for genes expressed in adipose tissue and for putative regulatory elements in adipocytes. Pathway analyses implicated adipogenesis, angiogenesis, transcriptional regulation and insulin resistance as processes affecting fat distribution, providing insight into potential pathophysiological mechanisms

Rhinitis associated with asthma is distinct from rhinitis alone: TARIA‐MeDALL hypothesis

Asthma, rhinitis, and atopic dermatitis (AD) are interrelated clinical phenotypes that partly overlap in the human interactome. The concept of “one-airway-one-disease,” coined over 20 years ago, is a simplistic approach of the links between upper- and lower-airway allergic diseases. With new data, it is time to reassess the concept. This article reviews (i) the clinical observations that led to Allergic Rhinitis and its Impact on Asthma (ARIA), (ii) new insights into polysensitization and multimorbidity, (iii) advances in mHealth for novel phenotype definitions, (iv) confirmation in canonical epidemiologic studies, (v) genomic findings, (vi) treatment approaches, and (vii) novel concepts on the onset of rhinitis and multimorbidity. One recent concept, bringing together upper- and lower-airway allergic diseases with skin, gut, and neuropsychiatric multimorbidities, is the “Epithelial Barrier Hypothesis.” This review determined that the “one-airway-one-disease” concept does not always hold true and that several phenotypes of disease can be defined. These phenotypes include an extreme “allergic” (asthma) phenotype combining asthma, rhinitis, and conjunctivitis.info:eu-repo/semantics/publishedVersio

Non-Standard Errors

In statistics, samples are drawn from a population in a data-generating process (DGP). Standard errors measure the uncertainty in estimates of population parameters. In science, evidence is generated to test hypotheses in an evidence-generating process (EGP). We claim that EGP variation across researchers adds uncertainty: Non-standard errors (NSEs). We study NSEs by letting 164 teams test the same hypotheses on the same data. NSEs turn out to be sizable, but smaller for better reproducible or higher rated research. Adding peer-review stages reduces NSEs. We further find that this type of uncertainty is underestimated by participants