scholarly journals Survival probability of random walks leaping over traps

2021 ◽  
Vol 2021 (12) ◽  
pp. 123203
Author(s):  
Gaia Pozzoli ◽  
Benjamin De Bruyne
Keyword(s):  
Random Walks ◽  
Survival Probability ◽  
First Passage Time ◽  
Finite Size ◽  
Passage Time ◽  
Deterministic Systems ◽  
Diffusive Limit ◽  
Point Absorbers ◽  
The Mean ◽  
Special Case

Abstract We consider one-dimensional discrete-time random walks (RWs) in the presence of finite size traps of length ℓ over which the RWs can jump. We study the survival probability of such RWs when the traps are periodically distributed and separated by a distance L. We obtain exact results for the mean first-passage time and the survival probability in the special case of a double-sided exponential jump distribution. While such RWs typically survive longer than if they could not leap over traps, their survival probability still decreases exponentially with the number of steps. The decay rate of the survival probability depends in a non-trivial way on the trap length ℓ and exhibits an interesting regime when ℓ → 0 as it tends to the ratio ℓ/L, which is reminiscent of strongly chaotic deterministic systems. We generalize our model to continuous-time RWs, where we introduce a power-law distributed waiting time before each jump. In this case, we find that the survival probability decays algebraically with an exponent that is independent of the trap length. Finally, we derive the diffusive limit of our model and show that, depending on the chosen scaling, we obtain either diffusion with uniform absorption, or diffusion with periodically distributed point absorbers.

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.

scholarly journals Comparison of Multiple Random Walks Strategies for Searching Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Zhongtuan Zheng ◽  
Hanxing Wang ◽  
Shengguo Gao ◽  
Guoqiang Wang
Keyword(s):  
Random Walks ◽  
Random Network ◽  
Probability Distributions ◽  
First Passage Time ◽  
Shortest Paths ◽  
Passage Time ◽  
Practical Significance ◽  
First Passage ◽  
The Mean ◽  
High Degree

We investigate diverse random-walk strategies for searching networks, especially multiple random walks (MRW). We use random walks on weighted networks to establish various models of single random walks and take the order statistics approach to study corresponding MRW, which can be a general framework for understanding random walks on networks. Multiple preferential random walks (MPRW) and multiple simple random walks (MSRW) are two special types of MRW. As search strategies, MPRW prefers high-degree nodes while MSRW searches for low-degree nodes more efficiently. We analyze the first passage time (FPT) of wandering walkers of MRW and give the corresponding formulas of probability distributions and moments, and the mean first passage time (MFPT) is included. We show the convergence of the MFPT of the first arriving walker and find the MFPT of the last arriving walker closely related with the mean cover time. Simulations confirm analytical predictions and deepen discussions. We use a small random network to test the FPT properties from different aspects. We also explore some practical search-related issues by MRW, such as detecting unknown shortest paths and avoiding poor routings on networks. Our results are of practical significance for realizing optimal routing and performing efficient search on complex 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>

scholarly journals The Random Walks between Pseudo-Specific DNA Sites as Model of the Facilitated Diffusion of DNA-Binding Proteins

2015 ◽  
Vol 10 (2) ◽  
pp. 473-481
Author(s):  
Р.Т. Сибатов ◽  
R.T. Sibatov
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Regulatory Protein ◽  
Free Path Length ◽  
Mean Free Path ◽  
Passage Time ◽  
Facilitated Diffusion ◽  
One Dimensional ◽  
Ballistic Motion ◽  
The Mean

The facilitated diffusion of a regulatory protein in the process of searching for a specific target site on the DNA molecule is considered. On the basis of the hypothesis of ballistic motion of the protein between scatterings of pseudo-specific sites, we proposed a phenomenological model of one-dimensional translocation of the protein along DNA. Combining this approach with the model of discrete random walks we were able to get the relationships between the mean first passage time and such characteristics as the binding energy, the mean free path length between pseudo-specific sites, the speed of protein movement and the temperature. These dependencies allow revealing the thermal and energetic optima, at which minimum values of searching time are achieved.

scholarly journals Mean First Passage Time of Preferential Random Walks on Complex Networks with Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Zhongtuan Zheng ◽  
Gaoxi Xiao ◽  
Guoqiang Wang ◽  
Guanglin Zhang ◽  
Kaizhong Jiang
Keyword(s):  
Complex Networks ◽  
Random Walks ◽  
First Passage Time ◽  
Network Models ◽  
Passage Time ◽  
Main Role ◽  
Mean First Passage Time ◽  
Eigenvalues And Eigenvectors ◽  
First Passage ◽  
The Mean

This paper investigates, both theoretically and numerically, preferential random walks (PRW) on weighted complex networks. By using two different analytical methods, two exact expressions are derived for the mean first passage time (MFPT) between two nodes. On one hand, the MFPT is got explicitly in terms of the eigenvalues and eigenvectors of a matrix associated with the transition matrix of PRW. On the other hand, the center-product-degree (CPD) is introduced as one measure of node strength and it plays a main role in determining the scaling of the MFPT for the PRW. Comparative studies are also performed on PRW and simple random walks (SRW). Numerical simulations of random walks on paradigmatic network models confirm analytical predictions and deepen discussions in different aspects. The work may provide a comprehensive approach for exploring random walks on complex networks, especially biased random walks, which may also help to better understand and tackle some practical problems such as search and routing on networks.

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.

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