Tree-based Coarsening and Partitioning of Complex Networks

Many applications produce massive complex networks whose analysis would benefit from parallel processing. Parallel algorithms, in turn, often require a suitable network partition. For solving optimization tasks such as graph partitioning on large networks, multilevel methods are preferred in practice. Yet, complex networks pose challenges to established multilevel algorithms, in particular to their coarsening phase. One way to specify a (recursive) coarsening of a graph is to rate its edges and then contract the edges as prioritized by the rating. In this paper we (i) define weights for the edges of a network that express the edges' importance for connectivity, (ii) compute a minimum weight spanning tree $T^m$ with respect to these weights, and (iii) rate the network edges based on the conductance values of $T^m$'s fundamental cuts. To this end, we also (iv) develop the first optimal linear-time algorithm to compute the conductance values of \emph{all} fundamental cuts of a given spanning tree. We integrate the new edge rating into a leading multilevel graph partitioner and equip the latter with a new greedy postprocessing for optimizing the maximum communication volume (MCV). Experiments on bipartitioning frequently used benchmark networks show that the postprocessing already reduces MCV by 11.3%. Our new edge rating further reduces MCV by 10.3% compared to the previously best rating with the postprocessing in place for both ratings. In total, with a modest increase in running time, our new approach reduces the MCV of complex network partitions by 20.4%

Exceptionally Slow Rise in Differential Reflectivity Spectra of Excitons in GaN: Effect of Excitation-induced Dephasing

Femtosecond pump-probe (PP) differential reflectivity spectroscopy (DRS) and four-wave mixing (FWM) experiments were performed simultaneously to study the initial temporal dynamics of the exciton line-shapes in GaN epilayers. Beats between the A-B excitons were found \textit{only for positive time delay} in both PP and FWM experiments. The rise time at negative time delay for the differential reflection spectra was much slower than the FWM signal or PP differential transmission spectroscopy (DTS) at the exciton resonance. A numerical solution of a six band semiconductor Bloch equation model including nonlinearities at the Hartree-Fock level shows that this slow rise in the DRS results from excitation induced dephasing (EID), that is, the strong density dependence of the dephasing time which changes with the laser excitation energy.Comment: 8 figure

Spatial model of foot-and-mouth disease outbreak in an endemic area of Thailand

Foot-and-mouth disease (FDM) is a disease of cloven-hoofed animals with high costs in animal welfare and animal production. Up to now, transmission between farms in FMD-endemic areas has been given little attention. Between farm transmission can be quantified by distance independent transmission parameters and a spatial transmission kernel indicating the rate of transmission of an infected farm to susceptible farms depending on the distance. The spatial transmission kernel and distance-independent transmission parameters were estimated from data of an FMD outbreak in Lamphaya Klang subdistrict in Thailand between 2016 and 2017. The spatial between-farm transmission rate in Lamphaya Klang subdistrict was higher compared with the spatial between-farm transmission rate from FMDV in epidemic areas. The result can be explained by the larger size of the within-farm outbreak in the endemic area due to no culling. The inclusion of distance-independent transmission parameters improved the model fit, which suggests the presence of transmission sources from outside the area and spread within the area independent of the distance between farms. The remaining distance-dependent transmission was mainly local and could be due to over-the-fence transmission or other forms of contact between nearby farms. Farm size on the kernel positively affects the transmission rate, by increasing both infectivity and susceptibility with increasing farm size. The results showed that both distance-dependent transmission and distance-independent transmission were contributed to FMDV transmission in Lamphaya Klang outbreak. These transmission parameters help to gain knowledge about FMD transmission dynamic in the endemic area