Optimal redundancy against disjoint vulnerabilities in networks

Redundancy is commonly used to guarantee continued functionality in networked systems. However, often many nodes are vulnerable to the same failure or adversary. A "backup" path is not sufficient if both paths depend on nodes which share a vulnerability.For example, if two nodes of the Internet cannot be connected without using routers belonging to a given untrusted entity, then all of their communication-regardless of the specific paths utilized-will be intercepted by the controlling entity.In this and many other cases, the vulnerabilities affecting the network are disjoint: each node has exactly one vulnerability but the same vulnerability can affect many nodes. To discover optimal redundancy in this scenario, we describe each vulnerability as a color and develop a "color-avoiding percolation" which uncovers a hidden color-avoiding connectivity. We present algorithms for color-avoiding percolation of general networks and an analytic theory for random graphs with uniformly distributed colors including critical phenomena. We demonstrate our theory by uncovering the hidden color-avoiding connectivity of the Internet. We find that less well-connected countries are more likely able to communicate securely through optimally redundant paths than highly connected countries like the US. Our results reveal a new layer of hidden structure in complex systems and can enhance security and robustness through optimal redundancy in a wide range of systems including biological, economic and communications networks.Comment: 15 page

Assortativity and leadership emergence from anti-preferential attachment in heterogeneous networks

Many real-world networks exhibit degree-assortativity, with nodes of similar degree more likely to link to one another. Particularly in social networks, the contribution to the total assortativity varies with degree, featuring a distinctive peak slightly past the average degree. The way traditional models imprint assortativity on top of pre-defined topologies is via degree-preserving link permutations, which however destroy the particular graph's hierarchical traits of clustering. Here, we propose the first generative model which creates heterogeneous networks with scale-free-like properties and tunable realistic assortativity. In our approach, two distinct populations of nodes are added to an initial network seed: one (the followers) that abides by usual preferential rules, and one (the potential leaders) connecting via anti-preferential attachments, i.e. selecting lower degree nodes for their initial links. The latter nodes come to develop a higher average degree, and convert eventually into the final hubs. Examining the evolution of links in Facebook, we present empirical validation for the connection between the initial anti-preferential attachment and long term high degree. Thus, our work sheds new light on the structure and evolution of social networks

Barriers to the Employment of Welfare Recipients

Dramatic reductions in welfare caseloads since passage of the Personal Responsibility and WorkOpportunity Reconciliation Act of 1996 have not allayed policy concerns about the employability of recipients remaining on the rolls. Analysis of potential barriers to employment can address whether current recipients have problems that either singly or in combination make it difficult for them to comply with the new requirements for getting and keeping jobs. In this paper, we explore the prevalence and work effects of 14 potential barriers in a new survey of a representative sample of 753 urban single-mother recipients. We report the prevalence of the barriers and how their number predicts employment rates, controlling for demographic characteristics. We also analyze which individual barriers are associated with employment and how a model inclusive of a comprehensive array of barriers improves upon a traditional human capital model of the work effects of education and work and welfare history. Single mothers who received welfare in 1997 had higher rates of personal health and mental health problems, domestic violence, and children’s health problems than do women in national samples, but they were no more likely than the general population to be drug or alcohol dependent. Only 15 percent of respondents had none of the barriers and almost two-thirds had two or more barriers. The numbers of multiple barriers were strongly and negatively associated with working, and among the individual barriers, low education, lack of access to transportation, poor health, having drug dependence or a major depressive disorder, and several experiences of workplace discrimination reduced employment. Welfare-to-work programs need to be more finely targeted with respect to exemptions and service provision, and states should consider providing longer-term and enhanced supports for those who face low prospects of leaving welfare for employment.