Direct, physically-motivated derivation of the contagion condition for spreading processes on generalized random networks

For a broad range single-seed contagion processes acting on generalized random networks, we derive a unifying analytic expression for the possibility of global spreading events in a straightforward, physically intuitive fashion. Our reasoning lays bare a direct mechanical understanding of an archetypal spreading phenomena that is not evident in circuitous extant mathematical approaches.Comment: 4 pages, 1 figure, 1 tabl

Stability analysis of financial contagion due to overlapping portfolios

Common asset holdings are widely believed to have been the primary vector of contagion in the recent financial crisis. We develop a network approach to the amplification of financial contagion due to the combination of overlapping portfolios and leverage, and we show how it can be understood in terms of a generalized branching process. By studying a stylized model we estimate the circumstances under which systemic instabilities are likely to occur as a function of parameters such as leverage, market crowding, diversification, and market impact. Although diversification may be good for individual institutions, it can create dangerous systemic effects, and as a result financial contagion gets worse with too much diversification. Under our model there is a critical threshold for leverage; below it financial networks are always stable, and above it the unstable region grows as leverage increases. The financial system exhibits "robust yet fragile" behavior, with regions of the parameter space where contagion is rare but catastrophic whenever it occurs. Our model and methods of analysis can be calibrated to real data and provide simple yet powerful tools for macroprudential stress testing.Comment: 25 pages, 8 figure

Spin Network States in Gauge Theory

Given a real-analytic manifold M, a compact connected Lie group G and a principal G-bundle P -> M, there is a canonical `generalized measure' on the space A/G of smooth connections on P modulo gauge transformations. This allows one to define a Hilbert space L^2(A/G). Here we construct a set of vectors spanning L^2(A/G). These vectors are described in terms of `spin networks': graphs phi embedded in M, with oriented edges labelled by irreducible unitary representations of G, and with vertices labelled by intertwining operators from the tensor product of representations labelling the incoming edges to the tensor product of representations labelling the outgoing edges. We also describe an orthonormal basis of spin networks associated to any fixed graph phi. We conclude with a discussion of spin networks in the loop representation of quantum gravity, and give a category-theoretic interpretation of the spin network states.Comment: 19 pages, LaTe

Pair Formation within Multi-Agent Populations

We present a simple model for the formation of pairs in multi-agent populations of type A and B which move freely on a spatial network. Each agent of population A (and B) is labeled as Ai (and Bj) with i=1,.. NA (and j=1,..NB) and carries its own individual list of characteristics or 'phenotype'. When agents from opposite populations encounter one another on the network, they can form a relationship if not already engaged in one. The length of time for which any given pair stays together depends on the compatibility of the two constituent agents. Possible applications include the human dating scenario, and the commercial domain where two types of businesses A and B have members of each type looking for a business partner, i.e. Ai+Bj-->Rij. The pair Rij then survives for some finite time before dissociating Rij-->Ai+Bj. There are many possible generalizations of this basic setup. Here we content ourselves with some initial numerical results for the simplest of network topologies, together with some accompanying analytic analysis.Comment: Special Issue on Complex Networks, edited by Dirk Helbin

Improved Methods for Network Screening and Countermeasure Selection for Highway Improvements

Network screening and countermeasure selection are two crucial steps in the highway improvement process. In network screening, potential improvement locations are ranked and prioritized based on a specific method with a set of criteria. The most common practice by transportation agencies has been to use a simple scoring method, which, in general, weighs and scores each criterion and then ranks the locations based on their relative overall scoring. The method does not deal well with criteria that are qualitative in nature, nor does it account for the impacts of correlation among the criteria. The introduction of Analytic Hierarchy Process (AHP) provides agencies with a method to include both quantitative and qualitative criteria. However, it does not address the issue on correlation. This dissertation explores the use of both Analytic Network Process (ANP) and Fuzzy Analytic Network Process (FANP) for their potential capabilities to address both issues. Using urban four-lane divided highways in Florida for bicycle safety improvements, both ANP and FANP were shown to provide more reasonable rankings than AHP, with FANP providing the best results among the methods. After the locations are ranked and prioritized for improvements, the next step is to evaluate the potential countermeasures for improvements at the selected top-ranked locations. In this step, the standard practice has been to use Crash Modification Factors (CMFs) to quantify the potential impacts from implementing specific countermeasures. In this research, CMFs for bicycle crashes on urban facilities in Florida were developed using the Generalized Linear Model approach with a Zero-Inflated Negative Binomial (ZINB) distribution. The CMFs were tested for their spatial and temporal transferability and the results show only limited transferability both spatially and temporally. The CMFs show that, in general, wider lanes, lower speed limits, and presence of vegetation in the median reduce bicycle crashes, while presence of sidewalk and sidewalk barrier increase bicycle crashes. The research further considered bicycle exposure using the bicycle activity data from the Strava smartphone application. It was found that increased bicycle activity reduces bicycle crash probabilities on segments but increases bicycle crash probabilities at signalized intersections. Also, presence of bus stops and use of permissive signal phasing at intersections were found to increase bicycle crash probabilities