Joint Vertex Degrees in an Inhomogeneous Random Graph Model

In a random graph, counts for the number of vertices with given degrees will typically be dependent. We show via a multivariate normal and a Poisson process approximation that, for graphs which have independent edges, with a possibly inhomogeneous distribution, only when the degrees are large can we reasonably approximate the joint counts as independent. The proofs are based on Stein's method and the Stein-Chen method with a new size-biased coupling for such inhomogeneous random graphs, and hence bounds on distributional distance are obtained. Finally we illustrate that apparent (pseudo-) power-law type behaviour can arise in such inhomogeneous networks despite not actually following a power-law degree distribution.Comment: 30 pages, 9 figure

Asymptotic behaviour of gossip processes and small world networks

Both small world models of random networks with occasional long range connections and gossip processes with occasional long range transmission of information have similar characteristic behaviour. The long range elements appreciably reduce the effective distances, measured in space or in time, between pairs of typical points. In this paper, we show that their common behaviour can be interpreted as a product of the locally branching nature of the models. In particular, it is shown that both typical distances between points and the proportion of space that can be reached within a given distance or time can be approximated by formulae involving the limit random variable of the branching process.Comment: 30 page

The shortest distance in random multi-type intersection graphs

Using an associated branching process as the basis of our approximation, we show that typical inter-point distances in a multitype random intersection graph have a defective distribution, which is well described by a mixture of translated and scaled Gumbel distributions, the missing mass corresponding to the event that the vertices are not in the same component of the graph.Comment: 32 page

Adapting to Climate Change in Reindeer Herding: The Nation-State as Problem and Solution.

This paper discusses the role of nation-states and their systems of gover- nance as sources of barriers and solutions to adaptation to climate change from the point of view of Saami reindeer herders. The Saami, inhabiting the northernmost areas of Fennoscandia, is one of more than twenty ethnic groups in the circumpolar Arctic that base their traditional living on reindeer herding. Climate change is likely to affect the Saami regions severely, with winter temperatures predicted to increase by up to 7 centigrade. We argue that the pastoral practices of the Saami herders are inherently better suited to handle huge natural variation in climatic con- ditions than most other cultures. Indeed, the core of their pastoral practices and herding knowledge is skillful adaptation to unusually frequent and rapid change and variability. This paper argues that the key to handle permanent changes successfully is that herders themselves have sufficient degrees of freedom to act. Considering the similarities in herding practices in the fours nation-states between which Saami culture is now divided . Norway, Sweden, Finland, and Russia . the systems of governance are surprisingly different. Indeed, the very definition of what is required to be defined as an ethnic Saami is very different in the three Nordic countries. We argue that timely adjust- ments modifying the structures of governance will be key to the survival of the Saami reindeer herding culture. Since the differences in governance regimes . and the need to change national governance structures . are so central to our argument, we spend some time tracing the origins of these systems.

The upper-atmosphere extension of the ICON general circulation model (version: Ua-icon-1.0)

How the upper-atmosphere branch of the circulation contributes to and interacts with the circulation of the middle and lower atmosphere is a research area with many open questions. Inertia-gravity waves, for instance, have moved in the focus of research as they are suspected to be key features in driving and shaping the circulation. Numerical atmospheric models are an important pillar for this research. We use the ICOsahedral Non-hydrostatic (ICON) general circulation model, which is a joint development of the Max Planck Institute for Meteorology (MPI-M) and the German Weather Service (DWD), and provides, e.g., local mass conservation, a flexible grid nesting option, and a non-hydrostatic dynamical core formulated on an icosahedral-triangular grid. We extended ICON to the upper atmosphere and present here the two main components of this new configuration named UA-ICON: an extension of the dynamical core from shallow- to deep-atmosphere dynamics and the implementation of an upper-atmosphere physics package. A series of idealized test cases and climatological simulations is performed in order to evaluate the upper-atmosphere extension of ICON. © Author(s) 2019

Electron-phonon coupling and its evidence in the photoemission spectra of lead

We present a detailed study on the influence of strong electron-phonon coupling to the photoemission spectra of lead. Representing the strong-coupling regime of superconductivity, the spectra of lead show characteristic features that demonstrate the correspondence of physical properties in the normal and the superconducting state, as predicted by the Eliashberg theory. These features appear on an energy scale of a few meV and are accessible for photoemission only by using modern spectrometers with high resolution in energy and angle.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. Let