Dynamics on Complex Networks and Applications

At the eight-year anniversary of Watts & Strogatz's work on the collective dynamics of small-world networks and seven years after Barabasi & Albert's discovery of scale-free networks, the area of dynamical processes on complex networks is at the forefront of the current research on nonlinear dynamics and complex systems. This volume brings together a selection of original contributions in complementary topics of statistical physics, nonlinear dynamics and biological sciences, and is expected to provide the reader with a comprehensive up-to-date representation of this rapidly developing area.Comment: Preface article of the Physica D Special Issue "Dynamics on Complex Networks and Applications" (4 pages). Full issue available at http://www.sciencedirect.com/science/journal/0167278

Epidemics on Networks: Reducing Disease Transmission Using Health Emergency Declarations and Peer Communication

Understanding individual decisions in a world where communications and information move instantly via cell phones and the internet, contributes to the development and implementation of policies aimed at stopping or ameliorating the spread of diseases. In this manuscript, the role of official social network perturbations generated by public health officials to slow down or stop a disease outbreak are studied over distinct classes of static social networks. The dynamics are stochastic in nature with individuals (nodes) being assigned fixed levels of education or wealth. Nodes may change their epidemiological status from susceptible, to infected and to recovered. Most importantly, it is assumed that when the prevalence reaches a pre-determined threshold level, P*, information, called awareness in our framework, starts to spread, a process triggered by public health authorities. Information is assumed to spread over the same static network and whether or not one becomes a temporary informer, is a function of his/her level of education or wealth and epidemiological status. Stochastic simulations show that threshold selection P* and the value of the average basic reproduction number impact the final epidemic size differentially. For the Erdos-Renyi and Small-world networks, an optimal choice for P* that minimize the final epidemic size can be identified under some conditions while for Scale-free networks this is not case

Properties of kinetic transition networks for atomic clusters and glassy solids

A database of minima and transition states corresponds to a network where the minima represent nodes and the transition states correspond to edges between the pairs of minima they connect via steepest-descent paths. Here we construct networks for small clusters bound by the Morse potential for a selection of physically relevant parameters, in two and three dimensions. The properties of these unweighted and undirected networks are analysed to examine two features: whether they are small-world, where the shortest path between nodes involves only a small number or edges; and whether they are scale-free, having a degree distribution that follows a power law. Small-world character is present, but statistical tests show that a power law is not a good fit, so the networks are not scale-free. These results for clusters are compared with the corresponding properties for the molecular and atomic structural glass formers ortho-terphenyl and binary Lennard-Jones. These glassy systems do not show small-world properties, suggesting that such behaviour is linked to the structure-seeking landscapes of the Morse clusters.JM acknowledges the support of a Sackler Studentship from the University of Cambridge. Part of this work was performed while DM was a member of the Department of Chemistry at the University of Cambridge, financially supported by the Engineering and Physical Sciences Research Council and the European Research Council

Discriminating different classes of biological networks by analyzing the graphs spectra distribution

The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world topology. Recent studies indicate that some pathologies present topological network alterations relative to norms seen in the general population. Therefore, methods to discriminate the processes that generate the different classes of networks (e.g., normal and disease) might be crucial for the diagnosis, prognosis, and treatment of the disease. It is known that several topological properties of a network (graph) can be described by the distribution of the spectrum of its adjacency matrix. Moreover, large networks generated by the same random process have the same spectrum distribution, allowing us to use it as a "fingerprint". Based on this relationship, we introduce and propose the entropy of a graph spectrum to measure the "uncertainty" of a random graph and the Kullback-Leibler and Jensen-Shannon divergences between graph spectra to compare networks. We also introduce general methods for model selection and network model parameter estimation, as well as a statistical procedure to test the nullity of divergence between two classes of complex networks. Finally, we demonstrate the usefulness of the proposed methods by applying them on (1) protein-protein interaction networks of different species and (2) on networks derived from children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) and typically developing children. We conclude that scale-free networks best describe all the protein-protein interactions. Also, we show that our proposed measures succeeded in the identification of topological changes in the network while other commonly used measures (number of edges, clustering coefficient, average path length) failed

Development Options for Local Seed Systems in Mozambique. Working Paper Series no. 5

Large quantities of free or subsidized seed have been distributed to small-scale farmers in Mozambique under postwar resettlement and drought/flood relief programs. A joint study by ICRISAT and World Vision assessed the impact of relief seed distribution, the adoption of new varieties distributed through relief programs, and the performance of local seed systems. While there was undoubtedly a need for well-targeted emergency assistance, seed losses associated with war, drought, and floods appear to have been overestimated. Village seed systems are remarkably efficient in meeting seed requirements and maintaining varietal diversity, even under drought or flood conditions. However, there remains scope for improving household seed selection and storage practices. In addition, sustainable seed supply systems (both community-level and commercial) are needed to improve the access of small-scale farmers to new varieties. Despite the massive demand for seed for public distribution efforts, domestic production capabilities remain small, and most seed is still imported. The problems include shortages of breeder seed, poor market infrastructure, high marketing costs, uncertainty about levels of commercial seed demand, and farmer dependence on free seed. Specific recommendations are offered for strengthening both local and commercial seed supply systems in Mozambique