Random walks: trajectories analysis
Analysis of trajectories
Many processes in life we can try to understand deeper through analysis of trajectories.
It can be either my path in life, or my walk on a beach, or it can be time-series of tempreture T(t).
In the notebooks I tried to explain how generally to analyze trajectory of a general type.
Watching "Stalker" made me to come up with the mathematical problem.
There is a network where people can move. This network is a map of Zona, where Stalker eventually brings people
who would like to reach the Room, absorbing node on a network (after reaching this node a person turns to another state). The question is, starting from different place, how much the path each person takes is influencing time it takes to reach the Room? How much the shortest path is affected by the changes of Zona?
References:
L.Tupikina, D.Grebenkov “Temporal and structural heterogeneities in networks” arxiv, accept.Applied network Journ. (2019)
Github repository https://github.com/Liyubov/mobility_analysis
This framework allows to understand influence of structural and temporal heterogeneities on dynamics on networks: from random abstract to real-world transportation networks.
A heterogeneous continuous time random walk is an analytical formalism for studying and modeling diffusion processes in heterogeneous structures on microscopic and macroscopic scales. In this paper we study both analytically and numerically the effects of spatio-temporal heterogeneities onto the diffusive dynamics on different types of networks. We investigate how the distribution of the first passage time is affected by the global topological network properties and heterogeneities in the distributions of the travel times. In particular, we analyze transport properties of random networks and define network measures based on the first-passage characteristics. The heterogeneous continuous time random walk framework has potential applications in biology, social and urban science, search of optimal transport properties, analysis of the effects of heterogeneities or bursts in transportation networks.
References:
L.Tupikina, D.Grebenkov “Temporal and structural heterogeneities in networks” arxiv, accept.Applied network Journ. (2019)
D.Grebenkov, L. Tupikina “Heterogeneous continuous time random walk”, link to Physical Rev. E Journal E 97, 012148 (2018)
Dynamical characteristics for each type of network
This framework allows to understand influence of structural and temporal heterogeneities on dynamics on networks: from random abstract to real-world transportation networks.
The first passage time as a dynamical characteristics of the process.
References:
L.Tupikina, D.Grebenkov “Temporal and structural heterogeneities in networks” arxiv, accept.Applied network Journ. (2019)
D.Grebenkov, L. Tupikina “Heterogeneous continuous time random walk”, link to Physical Rev. E Journal E 97, 012148 (2018)