Scaling of average receiving time on weighted polymer networks with some topological properties

Scientific Reports
Dandan YeYingze Zhang

Abstract

In this paper, a family of the weighted polymer networks is introduced depending on the number of copies f and a weight factor r. The topological properties of weighted polymer networks can be completely analytically characterized in terms of the involved parameters and/or of the fractal dimension. Moreover, assuming that the walker, at each step, starting from its current node, moves to any of its neighbors with probability proportional to the weight of edge linking them, namely weight-dependent walk. Then, we calculate the average receiving time (ART) with weighted-dependent walks, which is the sum of mean first-passage times (MFPTs) for all nodes absorpt at the trap located at the central node as a recursive relation. The obtained remarkable results display that when [Formula: see text], the ART grows sublinearly with the network size; when [Formula: see text], ART grows with increasing size N g as [Formula: see text]; when [Formula: see text], ART grows with increasing size N g as ln N g . In the treelike polymer networks, ART grows with linearly with the network size N g when r = 1. Thus, the weighted polymer networks are more efficient than treelike polymer networks in receiving information.

References

Nov 25, 2003·Nature·Ann E KrauseWilliam W Taylor
Mar 10, 2004·Proceedings of the National Academy of Sciences of the United States of America·A BarratA Vespignani
Oct 26, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A BlumenCh von Ferber
Oct 9, 2007·The Journal of Chemical Physics·Mircea Galiceanu, Alexander Blumen
Aug 8, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Zhongzhi ZhangJihong Guan
Sep 28, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Andrea Baronchelli, Romualdo Pastor-Satorras
Dec 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M Galiceanu
Mar 29, 2013·The Journal of Chemical Physics·Hongxiao Liu, Zhongzhi Zhang
Sep 13, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Zhongzhi ZhangYuan Lin
Dec 20, 2014·Scientific Reports·Yi QiZhongzhi Zhang

❮ Previous
Next ❯

Citations

Feb 21, 2019·Scientific Reports·Verena SchamboeckIvan Kryven

❮ Previous
Next ❯

Software Mentioned

ART
simeq

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.