Maximal entropy random walk improves efficiency of trapping in dendrimers

Abstract

We use maximal entropy random walk (MERW) to study the trapping problem in dendrimers modeled by Cayley trees with a deep trap fixed at the central node. We derive an explicit expression for the mean first passage time from any node to the trap, as well as an exact formula for the average trapping time (ATT), which is the average of the source-to-trap mean first passage time over all non-trap starting nodes. Based on the obtained closed-form solution for ATT, we further deduce an upper bound for the leading behavior of ATT, which is the fourth power of $\ln N$, where $N$ is the system size. This upper bound is much smaller than the ATT of trapping depicted by unbiased random walk in Cayley trees, the leading scaling of which is a linear function of $N$. These results show that MERW can substantially enhance the efficiency of trapping performed in dendrimers.

arXiv commentDefinitive version accepted for publication in The Journal of Chemical Physics

References in corpus (30)

• First-passage times in complex scale-invariant media
• Weighted evolving networks: coupling topology and weights dynamics
• Continuous-Time Quantum Walks: Models for Coherent Transport on Complex Networks
• Entropy Rate of Diffusion Processes on Complex Networks
• Localization of maximal entropy random walk
• Global mean first-passage times of random walks on complex networks
• First-passage times for random walks in bounded domains
• First passage time for random walks in heterogeneous networks
• The Shannon and the Von Neumann entropy of random networks with heterogeneous expected degree
• Exact mean first-passage time on the T-graph
• Maximal-entropy random walks in complex networks with limited information
• Random walks on weighted networks
• Exact solution for mean first-passage time on a pseudofractal scale-free web
• Occupation times of random walks in confined geometries: From random trap model to diffusion limited reactions
• Coherent exciton transport in dendrimers and continuous-time quantum walks
• Random Walks on deterministic Scale-Free networks: Exact results
• Flow graphs: interweaving dynamics and structure
• Exact calculations of first-passage quantities on recursive networks
• Determining mean first-passage time on a class of treelike regular fractals
• Random walks in weighted networks with a perfect trap: An application of Laplacian spectra
• Centrality measures and thermodynamic formalism for complex networks
• Eigenvalues of normalized Laplacian matrices of fractal trees and dendrimers: Analytical results and applications
• Trapping in dendrimers and regular hyperbranched polymers
• Laplacian spectra of recursive treelike small-world polymer networks: Analytical solutions and applications
• Effective target arrangement in a deterministic scale-free graph
• Influence of trap location on the efficiency of trapping in dendrimers and regular hyperbranched polymers
• Maximal entropy random walk in community finding
• Exact Solution for Statics and Dynamics of Maximal Entropy Random Walk on Cayley Trees
• Maximal-entropy random walk unifies centrality measures
• Optimal scale-free network with a minimum scaling of transport efficiency for random walks with a perfect trap

Cited by in corpus (4)

• Mixed random walks with a trap in scale-free networks including nearest-neighbor and next-nearest-neighbor jumps
• Mean trapping time for an arbitrary node on regular hyperbranched polymers
• Anomalous behavior of trapping in extended dendrimers with a perfect trap
• Non-Backtracking Centrality Based Random Walk on Networks