Clayton W. Commander

Detecting critical nodes in sparse graphs

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 NP-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.

Genome-wide association and linkage identify modifier loci of lung disease severity in cystic fibrosis at 11p13 and 20q13.2

A combined genome-wide association and linkage study was used to identify loci causing variation in cystic fibrosis lung disease severity. We identified a significant association (P = 3.34 × 10−8) near EHF and APIP (chr11p13) in p.Phe508del homozygotes (n = 1,978). The association replicated in p.Phe508del 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 quantitative trait locus on chromosome 20q13.2 (log10 odds = 5.03). Our findings provide insight into the causes of variation in lung disease severity in cystic fibrosis and suggest new therapeutic targets for this life-limiting disorder.

Genetic Modifiers of Cystic Fibrosis–Related Diabetes

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.

The wireless network jamming problem

Abstract In adversarial environments, disabling the communication capabilities of the enemy is a high priority. We introduce the problem of determining the optimal number and locations for a set of jamming devices in order to neutralize a wireless communication network. This problem is known as the wireless network jamming problem. We develop several mathematical programming formulations based on covering the communication nodes and limiting the connectivity index of the nodes. Two case studies are presented comparing the formulations with the addition of various percentile constraints. Finally, directions of further research are addressed.

Identifying Critical Nodes in Protein-Protein Interaction Networks

In recent years, the study of biological networks has incre ased dramatically. These problems have piqued the interest of researchers in ma ny disciplines from biology to mathematics. In particular, many problems of interest to biological scientists can be modeled as combinatorial optimization problems and studie d by operations researchers. In this chapter, we consider the problem of identifying the c ritical nodes of a network and its potential applications to protein-protein interac tion networks. More specifically, we are interested in determining the smallest set of nodes wh ose removal from the graph maximally disconnects the network. Recent techniques for i dent fying critical nodes in telecommunication networks are applied to the study of prot ein-protein interaction graphs and the results are analyzed.

A novel lung disease phenotype adjusted for mortality attrition for cystic fibrosis Genetic modifier studies

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.

Mucin Variable Number Tandem Repeat Polymorphisms and Severity of Cystic Fibrosis Lung Disease: Significant Association with MUC5AC

Variability in cystic fibrosis (CF) lung disease is partially due to non-CFTR genetic modifiers. Mucin genes are very polymorphic, and mucins play a key role in the pathogenesis of CF lung disease; therefore, mucin genes are strong candidates as genetic modifiers. DNA from CF patients recruited for extremes of lung phenotype was analyzed by Southern blot or PCR to define variable number tandem repeat (VNTR) length polymorphisms for MUC1, MUC2, MUC5AC, and MUC7. VNTR length polymorphisms were tested for association with lung disease severity and for linkage disequilibrium (LD) with flanking single nucleotide polymorphisms (SNPs). No strong associations were found for MUC1, MUC2, or MUC7. A significant association was found between the overall distribution of MUC5AC VNTR length and CF lung disease severity (p = 0.025; n = 468 patients); plus, there was robust association of the specific 6.4 kb HinfI VNTR fragment with severity of lung disease (p = 6.2×10−4 after Bonferroni correction). There was strong LD between MUC5AC VNTR length modes and flanking SNPs. The severity-associated 6.4 kb VNTR allele of MUC5AC was confirmed to be genetically distinct from the 6.3 kb allele, as it showed significantly stronger association with nearby SNPs. These data provide detailed respiratory mucin gene VNTR allele distributions in CF patients. Our data also show a novel link between the MUC5AC 6.4 kb VNTR allele and severity of CF lung disease. The LD pattern with surrounding SNPs suggests that the 6.4 kb allele contains, or is linked to, important functional genetic variation.

Cardinality-Constrained Critical Node Detection Problem

We consider methodologies for managing risk in a telecommunication network based on identification of the critical nodes. The objective is to minimize the number of vertices whose deletion results in disconnected components which are constrained by a given cardinality. This is referred to as the CARDINALITY CONSTRAINED CRITICAL NODE PROBLEM (CC-CNP), and finds application in epidemic control, telecommunications, and military tactical planning, among others. From a telecommunication perspective, the set of critical nodes helps determine which players should be removed from the network in the event of a virus outbreak. Conversely, in order to maintain maximum global connectivity, it should be ensured that the critical nodes remain intact and as secure as possible. The presence of these nodes make a network vulnerable to attacks as they are crucial for the overall connectivity. This is a variation of the CRITICAL NODE DETECTION PROBLEM which has a known complexity and heuristic procedure. In this chapter, we review the recent work in this area, provide formulations based on integer linear programming and develop heuristic procedures for CC-CNP. We also examine the relations of CC-CNP with the well known NODE DELETION PROBLEM and discuss complexity results as a result of this relation.

Sensors: Theory, Algorithms, and Applications

The objective of this book is to advance the current knowledge of sensor research particularly highlighting recent advances, current work, and future needs. The goal is to share current technologies and steer future efforts in directions that will benefit the majority of researchers and practitioners working in this broad field of study.

Polynomial-time identification of robust network flows under uncertain arc failures

We propose Linear Programming (LP)-based solution methods for network flow problems subject to multiple uncertain arc failures, which allow finding robust optimal solutions in polynomial time under certain conditions. We justify this fact by proving that for the considered class of problems under uncertainty with linear loss functions, the number of entities in the corresponding LP formulations is polynomial with respect to the number of arcs in the network. The proposed formulation is efficient for sparse networks, as well as for time-critical networked systems, where quick and robust decisions play a crucial role.