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%

Boost-Invariant Running Couplings in Effective Hamiltonians

We apply a boost-invariant similarity renormalization group procedure to a light-front Hamiltonian of a scalar field phi of bare mass mu and interaction term g phi^3 in 6 dimensions using 3rd order perturbative expansion in powers of the coupling constant g. The initial Hamiltonian is regulated using momentum dependent factors that approach 1 when a cutoff parameter Delta tends to infinity. The similarity flow of corresponding effective Hamiltonians is integrated analytically and two counterterms depending on Delta are obtained in the initial Hamiltonian: a change in mu and a change of g. In addition, the interaction vertex requires a Delta-independent counterterm that contains a boost invariant function of momenta of particles participating in the interaction. The resulting effective Hamiltonians contain a running coupling constant that exhibits asymptotic freedom. The evolution of the coupling with changing width of effective Hamiltonians agrees with results obtained using Feynman diagrams and dimensional regularization when one identifies the renormalization scale with the width. The effective light-front Schroedinger equation is equally valid in a whole class of moving frames of reference including the infinite momentum frame. Therefore, the calculation described here provides an interesting pattern one can attempt to follow in the case of Hamiltonians applicable in particle physics.Comment: 24 pages, LaTeX, included discussion of finite x-dependent counterterm

Tectonic controls on post-subduction granite genesis and emplacement : the late Caledonian suite of Britain and Ireland

Rates of magma emplacement commonly vary as a function of tectonic setting. The late Caledonian granites of Britain and Ireland are associated with closure of the Iapetus Ocean and were emplaced into a varying regime of transpression and transtension throughout the Silurian and into the early Devonian. Here we evaluate a new approach for examining how magma volumes vary as a function of tectonic setting. Available radiometric ages from the late Caledonian granites are used to calculate probability density functions (age spectra), with each pluton weighted by outcrop area as a proxy for its volume. These spectra confirm an absence of magmatic activity during Iapetus subduction between c. 455 Ma and 425 Ma and a dominance of post-subduction magmas between c. 425 Ma and 380 Ma. We review possible reasons why, despite the widespread outcrop of the late Caledonian granites, magmatism appears absent during Iapetus subduction. These include shallow angle subduction or extensive erosion and tectonic removal of the arc. In contrast to previous work we find no strong difference in the age or major element chemistry of post-subduction granites across all terranes. We propose a common causal mechanism in which the down-going Iapetus oceanic slab peeled back and detached beneath the suture following final Iapetus closure. The lithospheric mantle was delaminated beneath the suture and for about 100 km back beneath the Avalonian margin. While magma generation is largely a function of gravitationally driven lithosphere delamination, strike-slip dominated kinematics in the overlying continental crust is what modulated granitic magma emplacement. Early Devonian (419–404 Ma) transtension permitted large volumes of granite emplacement, whereas the subsequent Acadian (late Early Devonian, 404–394 Ma) transpression reduced and eventually suppressed magma emplacement

Multimonopoles in gauge field theories

SIGLEAvailable from British Library Lending Division - LD:D53161/85 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

A combined evolutionary search and multilevel optimisation approach to graph-partitioning

The graph-partitioning problem is to divide a graph into several pieces so that the number of vertices in each piece is the same within some defined tolerance and the number of cut edges is minimised. Important applications of the problem arise, for example, in parallel processing where data sets need to be distributed across the memory of a parallel machine. Very effective heuristic algorithms have been developed for this problem which run in real-time, but it is not known how good the partitions are since the problem is, in general, NP-complete. This paper reports an evolutionary search algorithm for finding benchmark partitions. A distinctive feature is the use of a multilevel heuristic algorithm to provide an effective crossover. The technique is tested on several example graphs and it is demonstrated that our method can achieve extremely high quality partitions significantly better than those found by the state-of-the-art graph-partitioning packages

The FUELGEN alternative: an evolutionary approach. The architecture

This paper introduces a few architectural concepts from FUELGEN, that generates a "cloud" of reload patterns, like the generator in the FUELCON expert system, but unlike that generator, is based on a genetic algorithm. There are indications FUELGEN may outperform FUELCON and other tools as reported in the literature, in well-researched case studies, but careful comparisons have to be carried out. This paper complements the information in two other recent papers on FUELGEN. Moreover, a sequel project is outlined