  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.
