406,547 research outputs found
Network-Configurations of Dynamic Friction Patterns
The complex configurations of dynamic friction patterns-regarding real time
contact areas- are transformed into appropriate networks. With this
transformation of a system to network space, many properties can be inferred
about the structure and dynamics of the system. Here, we analyze the dynamics
of static friction, i.e. nucleation processes, with respect to "friction
networks". We show that networks can successfully capture the crack-like shear
ruptures and possible corresponding acoustic features. We found that the
fraction of triangles remarkably scales with the detachment fronts. There is a
universal power law between nodes' degree and motifs frequency (for triangles,
it reads T(k)\proptok{\beta} ({\beta} \approx2\pm0.4)). We confirmed the
obtained universality in aperture-based friction networks. Based on the
achieved results, we extracted a possible friction law in terms of network
parameters and compared it with the rate and state friction laws. In
particular, the evolutions of loops are scaled with power law, indicating the
aggregation of cycles around hub nodes. Also, the transition to slow rupture is
scaled with the fast variation of local heterogeneity. Furthermore, the motif
distributions and modularity space of networks -in terms of withinmodule degree
and participation coefficient-show non-uniform general trends, indicating a
universal aspect of energy flow in shear ruptures
Asymptotic analysis for personalized Web search
Personalized PageRank is used in Web search as an importance measure for Web documents. The goal of this paper is to characterize the tail behavior of the PageRank distribution in the Web and other complex networks characterized by power laws. To this end, we model the PageRank as a solution of a stochastic equation , where 's are distributed as . This equation is inspired by the original definition of the PageRank. In particular, models the number of incoming links of a page, and stays for the user preference. Assuming that or are heavy-tailed, we employ the theory of regular variation to obtain the asymptotic behavior of under quite general assumptions on the involved random variables. Our theoretical predictions show a good agreement with experimental data
Zipf and Heaps laws from dependency structures in component systems
Complex natural and technological systems can be considered, on a
coarse-grained level, as assemblies of elementary components: for example,
genomes as sets of genes, or texts as sets of words. On one hand, the joint
occurrence of components emerges from architectural and specific constraints in
such systems. On the other hand, general regularities may unify different
systems, such as the broadly studied Zipf and Heaps laws, respectively
concerning the distribution of component frequencies and their number as a
function of system size. Dependency structures (i.e., directed networks
encoding the dependency relations between the components in a system) were
proposed recently as a possible organizing principles underlying some of the
regularities observed. However, the consequences of this assumption were
explored only in binary component systems, where solely the presence or absence
of components is considered, and multiple copies of the same component are not
allowed. Here, we consider a simple model that generates, from a given ensemble
of dependency structures, a statistical ensemble of sets of components,
allowing for components to appear with any multiplicity. Our model is a minimal
extension that is memoryless, and therefore accessible to analytical
calculations. A mean-field analytical approach (analogous to the "Zipfian
ensemble" in the linguistics literature) captures the relevant laws describing
the component statistics as we show by comparison with numerical computations.
In particular, we recover a power-law Zipf rank plot, with a set of core
components, and a Heaps law displaying three consecutive regimes (linear,
sub-linear and saturating) that we characterize quantitatively
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