Maximal entropy random walk improves efficiency of trapping in dendrimers

Peng, Xin; Zhang, Zhongzhi

doi:10.1063/1.4883335

Cited by 16 publications

(10 citation statements)

References 70 publications

(90 reference statements)

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“…These works uncovered the effects of the topology on the transport efficiency. There are also many works devoted to improving the transport efficiency by designing appropriate biased random walk strategies [28][29][30]. By introducing the proper weight to each edge of the network and designing a proper biased random walk strategy, one can shorten the MFPT to obtain higher transport efficiency on the underling networks [31][32][33][34][35].…”

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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Section: Introductionmentioning

confidence: 99%

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

2021

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“…The mean of FPTs to a given target over all starting nodes is known as mean firstpassage time (MFPT), which plays an essential role in various realistic situations, such as trapping problem 19 , target search 5,20 , and lighting harvesting [21][22][23] . MFPT has been deeply studied in different networks [24][25][26][27][28] , including the Sierpinski fractal [29][30][31] , the T -fractal [32][33][34][35][36] , dendrimers [37][38][39] and hyperbrached polymers 37,38 squarea) Electronic mail: zhangzz@fudan.edu.cn; http://www.researcherid.com/rid/G-5522-2011 planar lattices 40 , scale-free networks [41][42][43][44][45] , as well as weighted networks 46,47 .…”

Section: Introductionmentioning

confidence: 99%

Mixed random walks with a trap in scale-free networks including nearest-neighbor and next-nearest-neighbor jumps

Zhang

Dong

Sheng

2015

The Journal of Chemical Physics

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Random walks including non-nearest-neighbor jumps appear in many real situations such as the diffusion of adatoms and have found numerous applications including PageRank search algorithm; however, related theoretical results are much less for this dynamical process. In this paper, we present a study of mixed random walks in a family of fractal scale-free networks, where both nearest-neighbor and next-nearest-neighbor jumps are included. We focus on trapping problem in the network family, which is a particular case of random walks with a perfect trap fixed at the central high-degree node. We derive analytical expressions for the average trapping time (ATT), a quantitative indicator measuring the efficiency of the trapping process, by using two different methods, the results of which are consistent with each other. Furthermore, we analytically determine all the eigenvalues and their multiplicities for the fundamental matrix characterizing the dynamical process. Our results show that although next-nearest-neighbor jumps have no effect on the leading scaling of the trapping efficiency, they can strongly affect the prefactor of ATT, providing insight into better understanding of random-walk process in complex systems.

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“…Light harvesting by dendrimers can be described by trapping process [7][8][9][10][11] , which is a kind of random walks with a deep trap positioned at a given site, absorbing all particles visiting it. The highly desirable quantity for this paradigmatic dynamical process is trapping time (TT), also known as mean first-passage time (MFPT) [12][13][14][15][16][17][18] , which is the expected time for a particle starting off from a source point to first reach the trap.…”

Section: Introductionmentioning

confidence: 99%

“…The trapping problem in compact dendrimers was first addressed in Refs. [7][8][9][10][11] , where the MFPT from the peripheral node to the central node was computed both in the presence and in the absence of a fixed energy bias. Partly inspired by these works, applying the theory of finite Markov chain, the ex-act expression for MFPT from an arbitrary node to the central node was derived in Refs.…”

Section: Introductionmentioning

confidence: 99%

Anomalous behavior of trapping in extended dendrimers with a perfect trap

Zhang

2015

The Journal of Chemical Physics

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Compact and extended dendrimers are two important classes of dendritic polymers. The impact of the underlying structure of compact dendrimers on dynamical processes has been much studied, yet the relation between the dynamical and structural properties of extended dendrimers remains not well understood. In this paper, we study the trapping problem in extended dendrimers with generation-dependent segment lengths, which is different from that of compact dendrimers where the length of the linear segments is fixed. We first consider a particular case that the deep trap is located at the central node, and derive an exact formula for the average trapping time (ATT) defined as the average of the source-to-trap mean first passage time over all starting points. Then, using the obtained result we deduce a closed-form expression for the ATT to an arbitrary trap node, based on which we further obtain an explicit solution to the ATT corresponding to the trapping issue with the trap uniformly distributed in the polymer systems. We show that the trap location has a substantial influence on the trapping efficiency measured by the ATT, which increases with the shortest distance from the trap to the central node, a phenomenon similar to that for compact dendrimers. In contrast to this resemblance, the leading terms of ATTs for the three trapping problems differ drastically between extended and compact dendrimers, with the trapping processes in the extended dendrimers being less efficient than in compact dendrimers.

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Maximal entropy random walk improves efficiency of trapping in dendrimers

Cited by 16 publications

References 70 publications

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

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

Mixed random walks with a trap in scale-free networks including nearest-neighbor and next-nearest-neighbor jumps

Anomalous behavior of trapping in extended dendrimers with a perfect trap

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