Time walkers and spatial dynamics of ageing information

TL;DR

This paper introduces time walkers, a model for the spatial dynamics of aging information that interacts with traces of varying age, creating a navigable landscape that improves search efficiency over random methods.

Contribution

The study presents a novel model of information spread called time walkers, capturing aging effects and interactions, and analyzes their properties on a two-dimensional lattice.

Findings

Time walkers generate a self-similar, river network-like information landscape.

Searching in the landscape outperforms random search, scaling with loop-erased random walks.

The model quantifies how information relevance decay affects spatial information distribution.

Abstract

The distribution of information is essential for living system's ability to coordinate and adapt. Random walkers are often used to model this distribution process and, in doing so, one effectively assumes that information maintains its relevance over time. But the value of information in social and biological systems often decay and must continuously be updated. To capture the spatial dynamics of ageing information, we introduce time walkers. A time walker moves like a random walker, but interacts with traces left by other walkers, some representing older information, some newer. The traces forms a navigable information landscape. We quantify the dynamical properties of time walkers moving on a two-dimensional lattice and the quality of the information landscape generated by their movements. We visualise the self-similar landscape as a river network, and show that searching in this landscape is superior to random searching and scales as the length of loop-erased random walks.