Exact calculations of first-passage properties on the pseudofractal scale-free web

Peng, Junhao; Agliari, Elena; Zhang, Zhongzhi

doi:10.1063/1.4927085

Cited by 37 publications

(18 citation statements)

References 39 publications

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“…The first-passage problem on a (1, 2)-flower has been extensively investigated in the past few years [14,[42][43][44][45]; the mean of the FPT to a given hub is also obtained for some special cases, such as (u = 2, v = 2) and (u = 1, v = 3) [13,17]. However, for generic u and v, the exact expressions for FPT, FRT, and GFPT at finite size N t are still unknown and will be obtained in this paper.…”

Section: Network Modelmentioning

confidence: 99%

Scaling laws for diffusion on (trans)fractal scale-free networks

Peng,

Agliari

2019

Preprint

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Fractal (or transfractal) features are common in real-life networks and are known to influence the dynamic processes taking place in the network itself. Here we consider a class of scale-free deterministic networks, called (u, v)-flowers, whose topological properties can be controlled by tuning the parameters u and v; in particular, for u > 1, they are fractals endowed with a fractal dimension d f , while for u = 1, they are transfractal endowed with a transfractal dimension df . In this work we investigate dynamic processes (i.e., random walks) and topological properties (i.e., the Laplacian spectrum) and we show that, under proper conditions, the same scalings (ruled by the related dimensions), emerge for both fractal and transfractal.

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Section: Network Modelmentioning

confidence: 99%

Scaling laws for diffusion on (trans)fractal scale-free networks

Peng,

Agliari

2019

Preprint

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“…In contrast to other networks, the R(FRT) of Cayley trees differs when the network size N → ∞. We find that R(FRT) → ∞ on many networks, including Sierpinski gaskets [44][45][46] , Vicsek fractals 43,47,48 , T-graphs [49][50][51] , pseudofractal scale-free webs 52,53 , (u, v) flowers [54][55][56][57] , and fractal and non-fractal scale-free trees [58][59][60][61][62] . Thus the fluctuation of FRT in these networks is huge and the F RT is not a reliable FRT estimate.…”

Section: Introductionmentioning

confidence: 98%

Analysis of fluctuations in the first return times of random walks on regular branched networks

Peng

Shao

et al. 2018

The Journal of Chemical Physics

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The first return time (FRT) is the time it takes a random walker to first return to its original site, and the global first passage time (GFPT) is the first passage time for a random walker to move from a randomly selected site to a given site. We find that in finite networks, the variance of FRT, Var(FRT), can be expressed as Var(FRT) = 2⟨FRT⟩⟨GFPT⟩ - ⟨FRT⟩ - ⟨FRT⟩, where ⟨·⟩ is the mean of the random variable. Therefore a method of calculating the variance of FRT on general finite networks is presented. We then calculate Var(FRT) and analyze the fluctuation of FRT on regular branched networks (i.e., Cayley tree) by using Var(FRT) and its variant as the metric. We find that the results differ from those in such other networks as Sierpinski gaskets, Vicsek fractals, T-graphs, pseudofractal scale-free webs, (u, v) flowers, and fractal and non-fractal scale-free trees.

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“…In the past several decades, the first-passage properties have attracted lots of attention [15][16][17][18], and the mean first-passage time has been extensively studied. Some of them focus on disclosing the effects of the topology on the MFPT (or GMFPT), and lots of results have been obtained for unbiased random walks on different networks, such as Sierpinski gaskets [19,20], pseudofractal scale-free web [21,22], scale-free Koch networks [9,23], (u, v) flowers [24], and many fractal scale-free trees [9,21,[25][26][27]. The MFPT and GMFPT are useful indicators for the transport efficiency of the network.…”

Section: Introductionmentioning

confidence: 99%

Optimizing the First-Passage Process on a Class of Fractal Scale-Free Trees

2021

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First-passage processes on fractals are of particular importance since fractals are ubiquitous in nature, and first-passage processes are fundamental dynamic processes that have wide applications. The global mean first-passage time (GMFPT), which is the expected time for a walker (or a particle) to first reach the given target site while the probability distribution for the position of target site is uniform, is a useful indicator for the transport efficiency of the whole network. The smaller the GMFPT, the faster the mass is transported on the network. In this work, we consider the first-passage process on a class of fractal scale-free trees (FSTs), aiming at speeding up the first-passage process on the FSTs. Firstly, we analyze the global mean first-passage time (GMFPT) for unbiased random walks on the FSTs. Then we introduce proper weight, dominated by a parameter w(w>0), to each edge of the FSTs and construct a biased random walks strategy based on these weights. Next, we analytically evaluated the GMFPT for biased random walks on the FSTs. The exact results of the GMFPT for unbiased and biased random walks on the FSTs are both obtained. Finally, we view the GMFPT as a function of parameter w and find the point where the GMFPT achieves its minimum. The exact result is obtained and a way to optimize and speed up the first-passage process on the FSTs is presented.

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Exact calculations of first-passage properties on the pseudofractal scale-free web

Cited by 37 publications

References 39 publications

Scaling laws for diffusion on (trans)fractal scale-free networks

Scaling laws for diffusion on (trans)fractal scale-free networks

Analysis of fluctuations in the first return times of random walks on regular branched networks

Optimizing the First-Passage Process on a Class of Fractal Scale-Free Trees

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