The map equation

Many real-world networks are so large that we must simplify their structure before we can extract useful information about the systems they represent. As the tools for doing these simplifications proliferate within the network literature, researchers would benefit from some guidelines about which of the so-called community detection algorithms are most appropriate for the structures they are studying and the questions they are asking. Here we show that different methods highlight different aspects of a network's structure and that the the sort of information that we seek to extract about the system must guide us in our decision. For example, many community detection algorithms, including the popular modularity maximization approach, infer module assignments from an underlying model of the network formation process. However, we are not always as interested in how a system's network structure was formed, as we are in how a network's extant structure influences the system's behavior. To see how structure influences current behavior, we will recognize that links in a network induce movement across the network and result in system-wide interdependence. In doing so, we explicitly acknowledge that most networks carry flow. To highlight and simplify the network structure with respect to this flow, we use the map equation. We present an intuitive derivation of this flow-based and information-theoretic method and provide an interactive on-line application that anyone can use to explore the mechanics of the map equation. We also describe an algorithm and provide source code to efficiently decompose large weighted and directed networks based on the map equation.Comment: 9 pages and 3 figures, corrected typos. For associated Flash application, see http://www.tp.umu.se/~rosvall/livemod/mapequation

The Kato square root problem on vector bundles with generalised bounded geometry

We consider smooth, complete Riemannian manifolds which are exponentially locally doubling. Under a uniform Ricci curvature bound and a uniform lower bound on injectivity radius, we prove a Kato square root estimate for certain coercive operators over the bundle of finite rank tensors. These results are obtained as a special case of similar estimates on smooth vector bundles satisfying a criterion which we call generalised bounded geometry. We prove this by establishing quadratic estimates for perturbations of Dirac type operators on such bundles under an appropriate set of assumptions.Comment: Slight technical modification of the notion of "GBG constant section" on page 7, and a few technical modifications to Proposition 8.4, 8.6, 8.

On stoichiometry and intermixing at the spinel/perovskite interface in CoFe2O4/BaTiO3 thin films

The performance of complex oxide heterostructures depends primarily on the interfacial coupling of the two component structures. This interface character inherently varies with the synthesis method and conditions used since even small composition variations can alter the electronic, ferroelectric, or magnetic functional properties of the system. The focus of this article is placed on the interface character of a pulsed laser deposited CoFe2O4/BaTiO3 thin film. Using a range of state-of-the-art transmission electron microscopy methodologies, the roles of substrate morphology, interface stoichiometry, and cation intermixing are determined on the atomic level. The results reveal a surprisingly uneven BaTiO3 substrate surface formed after the film deposition and Fe atom incorporation in the top few monolayers inside the unit cell of the BaTiO3 crystal. Towards the CoFe2O4 side, a disordered region extending several nanometers from the interface was revealed and both Ba and Ti from the substrate were found to diffuse into the spinel layer. The analysis also shows that within this somehow incompatible composite interface, a different phase is formed corresponding to the compound Ba2Fe3Ti5O15, which belongs to the ilmenite crystal structure of FeTiO3 type. The results suggest a chemical activity between these two oxides, which could lead to the synthesis of complex engineered interfaces

The Effect of a Needs-Related Caries Preventive Program in Children and Young Adults – Results after 20 Years

The risk for caries development in children varies significantly for different age groups, individuals, teeth, and surfaces. Thus from a cost-effectiveness point of view, caries preventive measures must be integrated and based on predicted risk from age group down to individual tooth surfaces. Based on this philosophy and experiences from continuously ongoing research on evaluating and reevaluating separate and integrated caries preventive measures, as well as methods for prediction of caries risk, a needs-related caries preventive program was introduced for all 0–19-year-olds in the county of Värmland, Sweden, in 1979. The goals for the subjects following the program from birth to the age of 19 years were

Hyper-accreting black holes

Hyper-accretion disks are short-lived, powerful sources of neutrinos and magnetized jets. Such disks are plausible sources of gamma-ray bursts. This review describes the disk structure, the neutrino conversion to electron-positron plasma around the disk, and the post-burst evolution.Comment: 20 pages, to appear in the proceedings of "Cool discs, hot flows: The Varying Faces of Accreting Compact Objects", Funasdalen, Sweden, March 200

Extremely narrow spectrum of GRB110920A: further evidence for localised, subphotospheric dissipation

Much evidence points towards that the photosphere in the relativistic outflow in GRBs plays an important role in shaping the observed MeV spectrum. However, it is unclear whether the spectrum is fully produced by the photosphere or whether a substantial part of the spectrum is added by processes far above the photosphere. Here we make a detailed study of the $\gamma-$ray emission from single pulse GRB110920A which has a spectrum that becomes extremely narrow towards the end of the burst. We show that the emission can be interpreted as Comptonisation of thermal photons by cold electrons in an unmagnetised outflow at an optical depth of $\tau \sim 20$. The electrons receive their energy by a local dissipation occurring close to the saturation radius. The main spectral component of GRB110920A and its evolution is thus, in this interpretation, fully explained by the emission from the photosphere including localised dissipation at high optical depths.Comment: 14 pages, 11 figures, accepted to MNRA