Nuclear-size self-energy and vacuum-polarization corrections to the bound-electron g factor

The finite nuclear-size effect on the leading bound-electron g factor and the one-loop QED corrections to the bound-electron g factor is investigated for the ground state of hydrogen-like ions. The calculation is performed to all orders in the nuclear binding strength parameter Z\alpha\ (where Z is the nuclear charge and \alpha\ is the fine structure constant) and for the Fermi model of the nuclear charge distribution. In the result, theoretical predictions for the isotope shift of the 1s bound-electron g factor are obtained, which can be used for the determination of the difference of nuclear charge radii from experimental values of the bound-electron g factors for different isotopes

Graph Theory and Networks in Biology

In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape

High transport currents in mechanically reinforced MgB2 wires

We prepared and characterized monofilamentary MgB2 wires with a mechanically reinforced composite sheath of Ta(Nb)/Cu/steel, which leads to dense filaments and correspondingly high transport currents up to Jc = 10^5 A/cm^2 at 4.2 K, self field. The reproducibility of the measured transport currents was excellent and not depending on the wire diameter. Using different precursors, commercial reacted powder or an unreacted Mg/B powder mixture, a strong influence on the pinning behaviour and the irreversibility field was observed. The critical transport current density showed a nearly linear temperature dependency for all wires being still 52 kA/cm^2 at 20 K and 23 kA/cm^2 at 30 K. Detailed data for Jc(B,T) and Tc(B) were measured.Comment: 21 pages, 13 figures, revised version, to be published in Supercond. Sci. Techno

Characterizing the Initial Phase of Epidemic Growth on some Empirical Networks

A key parameter in models for the spread of infectious diseases is the basic reproduction number $R_0$, which is the expected number of secondary cases a typical infected primary case infects during its infectious period in a large mostly susceptible population. In order for this quantity to be meaningful, the initial expected growth of the number of infectious individuals in the large-population limit should be exponential. We investigate to what extent this assumption is valid by performing repeated simulations of epidemics on selected empirical networks, viewing each epidemic as a random process in discrete time. The initial phase of each epidemic is analyzed by fitting the number of infected people at each time step to a generalised growth model, allowing for estimating the shape of the growth. For reference, similar investigations are done on some elementary graphs such as integer lattices in different dimensions and configuration model graphs, for which the early epidemic behaviour is known. We find that for the empirical networks tested in this paper, exponential growth characterizes the early stages of the epidemic, except when the network is restricted by a strong low-dimensional spacial constraint, such as is the case for the two-dimensional square lattice. However, on finite integer lattices of sufficiently high dimension, the early development of epidemics shows exponential growth.Comment: To be included in the conference proceedings for SPAS 2017 (International Conference on Stochastic Processes and Algebraic Structures), October 4-6, 201