ABSTRACT. Identifying critical nodes in a graph is important to understand the structural characteristics and the connectivity properties of the network. In this paper, we focus on detecting critical nodes, or nodes whose deletion results in the minimum pair-wise connectivity among the remaining nodes. This problem, known as the CRITICAL NODE PROBLEM has applications in several fields including biomedicine, telecommunications, and military strategic planning. We show that the recognition version of the problem is N P -complete and derive a mathematical formulation based on integer linear programming. In addition, we propose a heuristic for the problem which exploits the combinatorial structure of the graph. The heuristic is then enhanced by the application of a local improvement method. A computational study is presented in which we apply the integer programming formulation and the heuristic to real and randomly generated data sets. For all instances tested, the heuristic is able to efficiently provide optimal solutions in a fraction of the time required by a commercial software package.

A combined genome-wide association and linkage study was used to identify loci causing variation in CF lung disease severity. A significant association (P=3. 34 × 10-8) near EHF and APIP (chr11p13) was identified in F508del homozygotes (n=1,978). The association replicated in F508del homozygotes (P=0.006) from a separate family-based study (n=557), with P=1.49 × 10-9 for the three-study joint meta-analysis. Linkage analysis of 486 sibling pairs from the family-based study identified a significant QTL on chromosome 20q13.2 (LOD=5.03). Our findings provide insight into the causes of variation in lung disease severity in CF and suggest new therapeutic targets for this life-limiting disorder.

Diabetes is a common age-dependent complication of cystic fibrosis (CF) that is strongly influenced by modifier genes. We conducted a genome-wide association study in 3,059 individuals with CF (644 with CF-related diabetes [CFRD]) and identified single nucleotide polymorphisms (SNPs) within and 5′ to the SLC26A9 gene that associated with CFRD (hazard ratio [HR] 1.38; P = 3.6 × 10−8). Replication was demonstrated in 694 individuals (124 with CFRD) (HR, 1.47; P = 0.007), with combined analysis significant at P = 9.8 × 10−10. SLC26A9 is an epithelial chloride/bicarbonate channel that can interact with the CF transmembrane regulator (CFTR), the protein mutated in CF. We also hypothesized that common SNPs associated with type 2 diabetes also might affect risk for CFRD. A previous association of CFRD with SNPs in TCF7L2 was replicated in this study (P = 0.004; combined analysis P = 3.8 × 10−6), and type 2 diabetes SNPs at or near CDKAL1, CDKN2A/B, and IGF2BP2 were associated with CFRD (P < 0.004). These five loci accounted for 8.3% of the phenotypic variance in CFRD onset and had a combined population-attributable risk of 68%. Diabetes is a highly prevalent complication of CF, for which susceptibility is determined in part by variants at SLC26A9 (which mediates processes proximate to the CF disease-causing gene) and at four susceptibility loci for type 2 diabetes in the general population.

Genetic studies of lung disease in cystic fibrosis (CF) are hampered by the lack of a severity measure that accounts for chronic disease progression and mortality attrition. Further, combining analyses across studies requires common phenotypes that are robust to study design and patient ascertainment.Using data from the North American Cystic Fibrosis Modifier Consortium (Canadian Consortium for CF Genetic Studies, Johns Hopkins University CF Twin and Sibling Study, and University of North Carolina/Case Western Reserve University Gene Modifier Study), the authors calculated age‐specific CF percentile values of FEV1 which were adjusted for CF age‐specific mortality data.The phenotype was computed for 2,061 patients representing the Canadian CF population, 1,137 extreme phenotype patients in the UNC/Case Western study, and 1,323 patients from multiple CF sib families in the CF Twin and Sibling Study. Despite differences in ascertainment and median age, our phenotype score was distributed in all three samples in a manner consistent with ascertainment differences, reflecting the lung disease severity of each individual in the underlying population. The new phenotype score was highly correlated with the previously recommended complex phenotype, but the new phenotype is more robust for shorter follow‐up and for extreme ages.A disease progression and mortality‐adjusted phenotype reduces the need for stratification or additional covariates, increasing statistical power, and avoiding possible distortions. This approach will facilitate large‐scale genetic and environmental epidemiological studies which will provide targeted therapeutic pathways for the clinical benefit of patients with CF. Pediatr. Pulmonol. 2011; 46:857–869. © 2011 Wiley‐Liss, Inc.

Gadolinium toxicity may occur in subjects with normal renal function. Central torso and peripheral arm and leg distribution pain were common features. Distal arm and leg skin thickening and rubbery subcutaneous tissue were seen in late stages. Clouded mentation is also common. Vigilance to identify additional cases and investigate strategies for prevention and treatment is warranted to increase even further the safety of a very safe diagnostic procedure, GBCA-enhanced magnetic resonance imaging.