Influence Spread in the Heterogeneous Multiplex Linear Threshold Model

Abstract

The linear threshold model (LTM) has been used to study spread on single-layer networks defined by one inter-agent sensing modality and agents homogeneous in protocol. We define and analyze the heterogeneous multiplex LTM to study spread on multi-layer networks with each layer representing a different sensing modality and agents heterogeneous in protocol. Protocols are designed to distinguish signals from different layers: an agent becomes active if a sufficient number of its neighbors in each of any a of the m layers is active. We focus on Protocol OR, when a = 1, and Protocol AND, when a = m, which model agents that are most and least readily activated, respectively. We develop theory and algorithms to compute the size of the spread at steady state for any set of initially active agents and to analyze the role of distinguished sensing modalities, network structure, and heterogeneity. We show how heterogeneity manages the tension in spreading dynamics between sensitivity to inputs and robustness to disturbances.

Collective intelligence as a public good

“…Collective intelligence for managing this trade-off can be measured in various ways. Zhong et al (2021) study how a group of agents responds to an external stimulus, when agents share information over multiple network layers, each representing a different sensing modality, and when they differ in how readily they react. The trade-off is measured as the difference between the benefit of responding to true-positives and the cost of responding to false-positives.…”

“…The trade-off is measured as the difference between the benefit of responding to true-positives and the cost of responding to false-positives. The methodology determines where in the given multi-layer network to locate more readily responsive individuals and where to locate less readily responsive individuals so that at the level of the group the measure is optimized (Zhong et al, 2021).…”

Simulating Spreading of Multiple Interacting Processes in Complex Networks

“…A spreading model in the sense as in [12], with extension to multilayer networks similarly to [13] SIR-UA Suspected-Infected ∼ Unaware-Aware Two coexisting spreading models in the sense as in [8],…”

“…Therefore, one needs to define how to aggregate impulses from layers of the network influencing the actor. We adopted here the approach proposed originally for LTM extended for multiplex networks (described in [13]) called "protocol functions" (or strategies). In this study, we used two extreme ones: OR, i.e.…”

“…7. A spreading model in the sense as in [11], [12], with extension to multilayer networks as in [13]…”