Local Structural Properties and Attribute Characteristics in 2-mode Networks: p∗ Models to Map Choices of Theater Events 1

Choices of plays made by theatergoers can be considered as a 2-mode or affiliation network. In this article we illustrate how p? models (an exponential family of distributions for random graphs) can be used to uncover patterns of choices. Based on audience research in three theater institutions in Ghent (Belgium), we analyze the loyalty for an institution, the diversity in audience composition as well as more complex local structural patterns. The results seem to indicate that theater audiences are generally loyal to an institution. However, when controlling for more complex structural patterns, such as the co-attendance of identical plays, the tendency toward mobility across institutions becomes more pronounced. By integrating both attribute-specific patterns and more complex structural patterns in the same model social network analysis offers the possibility to investigate differences in co-attendance, loyalty and audience diversity.     

Application of the Floquet theory to multiple quantum NMR of dipolar-coupled multi-spin systems under magic angle spinning

A new analytical Liouville-space representation of the time-propagator under magic angle spinning (MAS) is introduced using the formalized quantum Floquet theory. This approach has the advantage that it is applicable to the analysis of any type of NMR experiment where MAS is combined with multiple-pulse excitation. General relationships describing the spectral parameters in multiple-quantum (MQ) MAS spectra are derived in this representation. Their use is illustrated with an application to double-quantum (DQ) NMR spectra of dipolar-coupled multi-spin systems. Corresponding to the separation of the MAS time-propagator into a rotor modulated and a dephasing component, two distinct mechanisms for DQ excitation are identified. One of them exploits the rotor-modulated component to excite DQ coherences through dipolar-recoupling techniques, which are familiar for spin pairs. Analytical expressions of the integral intensities and linewidths in the resulting DQ sideband pattern are derived in the form of power series expansions of the inverse rotor frequency, of which coefficients depend on structural parameters. In a multi-spin system they can most reliably be extracted in the fast spinning regime. The other mechanism exploits the dephasing component, which is characteristic to multi-spin systems only. This is shown to give rise to DQ coherences by free evolution at full rotor periods. The possibility to exploit it for selective excitation of higher order MQ coherences is discussed. In either case, the dephasing component also leads to residual broadening. The main results of the theoretical developments are demonstrated experimentally on adamantane.