Scaling of the first-passage time and the survival probability on exact and quasi-exact self-similar structures

1989 ◽  
Vol 22 (7) ◽  
pp. 887-902 ◽  
Author(s):  
B Kahng ◽  
S Redner
Keyword(s):  
Survival Probability ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Self Similar

scholarly journals Probing Protein Shelf Lives from Inverse Mean First Passage Times

2019 ◽  
Author(s):  
Vishal Singh ◽  
Parbati Biswas
Keyword(s):  
Protein Aggregation ◽  
Rate Constants ◽  
Survival Probability ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
First Order Kinetics ◽  
The Mean ◽  
Passage Times ◽  
Good Agreement

Protein aggregation is investigated theoretically via protein turnover, misfolding, aggregation and degradation. The Mean First Passage Time (MFPT) of aggregation is evaluated within the framework of Chemical Master Equation (CME) and pseudo first order kinetics with appropriate boundary conditions. The rate constants of aggregation of different proteins are calculated from the inverse MFPT, which show an excellent match with the experimentally reported rate constants and those extracted from the ThT/ThS fluorescence data. Protein aggregation is found to be practically independent of the number of contacts and the critical number of misfolded contacts. The age of appearance of aggregation-related diseases is obtained from the survival probability and the MFPT results, which matches with those reported in the literature. The calculated survival probability is in good agreement with the only available clinical data for Parkinson’s disease.<br>

Calculations of first passage time of delayed tree-like networks

2015 ◽  
Vol 29 (28) ◽  
pp. 1550200
Author(s):  
Shuai Wang ◽  
Weigang Sun ◽  
Song Zheng
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
The Novel ◽  
Mean First Passage Time ◽  
First Passage ◽  
Initial Node ◽  
Network Parameters ◽  
Self Similar ◽  
The Mean

In this paper, we study random walks in a family of delayed tree-like networks controlled by two network parameters, where an immobile trap is located at the initial node. The novel feature of this family of networks is that the existing nodes have a time delay to give birth to new nodes. By the self-similar network structure, we obtain exact solutions of three types of first passage time (FPT) measuring the efficiency of random walks, which includes the mean receiving time (MRT), mean sending time (MST) and mean first passage time (MFPT). The obtained results show that the MRT, MST and MFPT increase with the network parameters. We further show that the values of MRT, MST and MFPT are much shorter than the nondelayed counterpart, implying that the efficiency of random walks in delayed trees is much higher.

Determining entire mean first-passage time for Cayley networks

2018 ◽  
Vol 29 (01) ◽  
pp. 1850009 ◽  
Author(s):  
Xiaoqian Wang ◽  
Meifeng Dai ◽  
Yufei Chen ◽  
Yue Zong ◽  
Yu Sun ◽  
...  
Keyword(s):  
First Passage Time ◽  
Polymer Networks ◽  
Laplacian Matrix ◽  
Constant Term ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Laplacian Spectra ◽  
Self Similar ◽  
The Relationship

In this paper, we consider the entire mean first-passage time (EMFPT) with random walks for Cayley networks. We use Laplacian spectra to calculate the EMFPT. Firstly, we calculate the constant term and monomial coefficient of characteristic polynomial. By using the Vieta theorem, we then obtain the sum of reciprocals of all nonzero eigenvalues of Laplacian matrix. Finally, we obtain the scaling of the EMFPT for Cayley networks by using the relationship between the sum of reciprocals of all nonzero eigenvalues of Laplacian matrix and the EMFPT. We expect that our method can be adapted to other types of self-similar networks, such as vicsek networks, polymer networks.

scholarly journals Probing Protein Shelf Lives from Inverse Mean First Passage Times

2019 ◽  
Author(s):  
Vishal Singh ◽  
Parbati Biswas
Keyword(s):  
Protein Aggregation ◽  
Rate Constants ◽  
Survival Probability ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
First Order Kinetics ◽  
The Mean ◽  
Passage Times ◽  
Good Agreement

Protein aggregation is investigated theoretically via protein turnover, misfolding, aggregation and degradation. The Mean First Passage Time (MFPT) of aggregation is evaluated within the framework of Chemical Master Equation (CME) and pseudo first order kinetics with appropriate boundary conditions. The rate constants of aggregation of different proteins are calculated from the inverse MFPT, which show an excellent match with the experimentally reported rate constants and those extracted from the ThT/ThS fluorescence data. Protein aggregation is found to be practically independent of the number of contacts and the critical number of misfolded contacts. The age of appearance of aggregation-related diseases is obtained from the survival probability and the MFPT results, which matches with those reported in the literature. The calculated survival probability is in good agreement with the only available clinical data for Parkinson’s disease.<br>

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

scholarly journals Credit Gap Risk in a First Passage Time Model with Jumps

2009 ◽  
Author(s):  
Natalie Packham ◽  
Lutz Schloegl ◽  
Wolfgang M. Schmidt
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Model ◽  
Gap Risk ◽  
Credit Gap
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