On a Bounded Budget Network Creation Game

We consider a network creation game in which each player (vertex) has a fixed budget to establish links to other players. In our model, each link has unit price and each agent tries to minimize its cost, which is either its local diameter or its total distance to other players in the (undirected) underlying graph of the created network. Two versions of the game are studied: in the MAX version, the cost incurred to a vertex is the maximum distance between the vertex and other vertices, and in the SUM version, the cost incurred to a vertex is the sum of distances between the vertex and other vertices. We prove that in both versions pure Nash equilibria exist, but the problem of finding the best response of a vertex is NP-hard. We take the social cost of the created network to be its diameter, and next we study the maximum possible diameter of an equilibrium graph with n vertices in various cases. When the sum of players' budgets is n-1, the equilibrium graphs are always trees, and we prove that their maximum diameter is Theta(n) and Theta(log n) in MAX and SUM versions, respectively. When each vertex has unit budget (i.e. can establish link to just one vertex), the diameter of any equilibrium graph in either version is Theta(1). We give examples of equilibrium graphs in the MAX version, such that all vertices have positive budgets and yet the diameter is Omega(sqrt(log n)). This interesting (and perhaps counter-intuitive) result shows that increasing the budgets may increase the diameter of equilibrium graphs and hence deteriorate the network structure. Then we prove that every equilibrium graph in the SUM version has diameter 2^O(sqrt(log n)). Finally, we show that if the budget of each player is at least k, then every equilibrium graph in the SUM version is k-connected or has diameter smaller than 4.Comment: 28 pages, 3 figures, preliminary version appeared in SPAA'1

Comparison of Common Monogenic Defects in a Large Predominantly Antibody Deficiency Cohort

Background: Predominantly antibody deficiencies (PADs) are the most common primary immunodeficiencies, characterized by hypogammaglobulinemia and inability to generate effective antibody responses. Objective: We intended to report most common monogenic PADs and to investigate how patients with PAD who were primarily diagnosed as suffering from agammaglobulinemia, hyper-IgM (HIgM) syndrome, and common variable immunodeficiency (CVID) have different clinical and immunological findings. Methods: Stepwise next-generation sequencing and Sanger sequencing were performed for confirmation of the mutations in the patients clinically diagnosed as suffering from agammaglobulinemia, HIgM syndrome, and CVID. Results: Among 550 registered patients, the predominant genetic defects associated with agammaglobulinemia (48 Bruton's tyrosine kinase [BTK] and 6 μ heavy chain deficiencies), HIgM syndrome (21 CD40 ligand and 7 activation-induced cytidine deaminase deficiencies), and CVID (17 lipopolysaccharides-responsive beige-like anchor deficiency and 12 atypical Immunodeficiency, Centromeric instability, and Facial dysmorphism syndromes) were identified. Clinical disease severity was significantly higher in patients with μ heavy chain and CD40 ligand mutations compared with patients with BTK (P = .003) and activation-induced cytidine deaminase (P = .009) mutations. Paralysis following live polio vaccination was considerably higher in patients with μ heavy chain deficiency compared with BTK deficiency (P < .001). We found a genotype-phenotype correlation among patients with BTK mutations regarding clinical manifestation of meningitis and chronic diarrhea. Surprisingly, we noticed that first presentations in most patients with Immunodeficiency, Centromeric instability, and Facial dysmorphism were respiratory complications (P = .008), whereas first presentations in patients with lipopolysaccharides-responsive beige-like anchor deficiency were nonrespiratory complications (P = .008). Conclusions: This study highlights similarities and differences in the clinical and genetic spectrum of the most common PAD-associated gene defects. This comprehensive comparison will facilitate clinical decision making, and improve prognosis and targeted treatment

Comparison of Common Monogenic Defects in a Large Predominantly Antibody Deficiency Cohort

Predominantly antibody deficiencies (PADs) are the most common primary immunodeficiencies, characterized by hypogammaglobulinemia and inability to generate effective antibody responses