Tuning the average path length of complex networks and its influence to the emergent dynamics of the majority-rule model

We show how appropriate rewiring with the aid of Metropolis Monte Carlo computational experiments can be exploited to create network topologies possessing prescribed values of the average path length (APL) while keeping the same connectivity degree and clustering coefficient distributions. Using the proposed rewiring rules we illustrate how the emergent dynamics of the celebrated majority-rule model are shaped by the distinct impact of the APL attesting the need for developing efficient algorithms for tuning such network characteristics.Comment: 10 figure

Efficient Distributed Online Prediction and Stochastic Optimization with Approximate Distributed Averaging

We study distributed methods for online prediction and stochastic optimization. Our approach is iterative: in each round nodes first perform local computations and then communicate in order to aggregate information and synchronize their decision variables. Synchronization is accomplished through the use of a distributed averaging protocol. When an exact distributed averaging protocol is used, it is known that the optimal regret bound of $\mathcal{O}(\sqrt{m})$ can be achieved using the distributed mini-batch algorithm of Dekel et al. (2012), where $m$ is the total number of samples processed across the network. We focus on methods using approximate distributed averaging protocols and show that the optimal regret bound can also be achieved in this setting. In particular, we propose a gossip-based optimization method which achieves the optimal regret bound. The amount of communication required depends on the network topology through the second largest eigenvalue of the transition matrix of a random walk on the network. In the setting of stochastic optimization, the proposed gossip-based approach achieves nearly-linear scaling: the optimization error is guaranteed to be no more than $\epsilon$ after $\mathcal{O}(\frac{1}{n \epsilon^2})$ rounds, each of which involves $\mathcal{O}(\log n)$ gossip iterations, when nodes communicate over a well-connected graph. This scaling law is also observed in numerical experiments on a cluster.Comment: 30 pages, 2 figure

Higher Spin Superfield interactions with the Chiral Supermultiplet: Conserved Supercurrents and Cubic Vertices

We investigate cubic interactions between a chiral superfield and higher spin superfield corresponding to irreducible representations of the $4D,\, \mathcal{N}=1$ super-Poincar\'{e} algebra. We do this by demanding an invariance under the most general transformation, linear in the chiral superfield. Following Noether's method we construct an infinite tower of higher spin supercurrent multiplets which are quadratic in the chiral superfield and include higher derivatives. The results are that a single, massless, chiral superfield can couple only to the half-integer spin supermultiplets $(s+1,s+1/2)$ and for every value of spin there is an appropriate improvement term that reduces the supercurrent multiplet to a minimal multiplet which matches that of superconformal higher spins. On the other hand a single, massive, chiral superfield can couple only to higher spin supermultiplets of type $(2l+2\hspace{0.3ex},\hspace{0.1ex}2l+3/2)$ and there is no minimal multiplet. Furthermore, for the massless case we discuss the component level higher spin currents and provide explicit expressions for the integer and half-integer spin conserved currents together with a R-symmetry current

Seismolosical studies of magma injection processes: volcano monitoring and imaging of magma chambers

The processes associated with magma injection at shallow depths within the crust have been the topic of many geophysical studies, some investigating the seismicity that accompanies volcanic activity and others attempting to map the subsurface extent and geometry of the resulting magma bodies. The aim of this study is to obtain a better understanding of these processes by investigating the nature of seismic signals that accompany volcanic eruptions and by seismically imaging a magma body beneath a mid-ocean ridge, both located on, or adjacent to Iceland. The seismic phenomena associated with the 1996 Vatnajӧkull subglacial eruption in central Iceland, have been studied using data recorded by both temporary (HOTSPOT) and permanent (SIL) seismic networks. These networks comprise 60 broadband and short-period three-component seismographs and cover most parts of the country. Two very active volcanic systems, Bárdarbunga and Grimsvӧtn, are situated underneath the Vatnajokull ice cap. The volcanoseismic signals recorded there were categorised according to their waveform shape and frequency content, into three groups: (a) low-frequency events (1-2 Hz); (b) mixed-frequency events (1-4 Hz); and (c) volcanic tremor. The eruption was preceded by intense seismic activity which began with a = 5.6 earthquake located at the Bárdarbunga volcanic system. The epicentres of the earthquake swarm that followed the M(_w), = 5.6 event initially delineated the Bárdarbunga caldera rim and then migrated towards Grimsvӧtn, to a place where a fissure was later observed. Pre-eruptive tremor started at least two days before the eruption as a harmonic signal around five narrow frequency bands (0.5-0.7, 1.6, 2.2, 2.8 and 3.2 Hz). Co-eruptive tremor started as a broadband, continuous signal which evolved into low-amplitude background tremor interrupted by high-amplitude, cigar-shaped bursts. Further analysis revealed that continuous tremor and the cigar-shaped bursts had all the characteristics of low- dimensional chaotic signals. Geophysical and geochemical evidence suggest that a lateral migration of magma from Bárdarbunga facilitated the rupture of the roof of a magma chamber, situated at the fissure area, which subsequently erupted as tephra on the glacier. The second phase of the RAMESSES (Reykjanes Ridge Axial Melt Experiment: Structural Synthesis from Electromagnetic and Seismics) experiment involved the acquisition of multichannel seismic reflection data from 39 along- and across-axis lines shot over the magmatically active 57º 45'N axial volcanic ridge. The data from one along-axis line were processed using a variety of techniques that mainly aimed at reducing the large amount of coherent noise present, a result of scattered energy at the rough seabed. The final processed section revealed a number of reflection events that could be interpreted as intra-crustal reflections, originating from the interface between pillow lavas and sheeted dykes, and from the top part of a thin melt lens

Marine Protected Areas as a central element of ecosystem-based management: defining their location, size and number

Journal homepage: http://www.int-res.com/journals/meps