Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Equivalence Between High-Order Network-Influence Frameworks:
  General-Threshold, Hypergraph-Triggering, and Logic-Triggering Models   In this paper, we study several high-order network-influence-propagation
frameworks and their connection to the classical network diffusion frameworks
such as the triggering model and the general threshold model. In one framework,
we use hyperedges to represent many-to-one influence -- the collective
influence of a group of nodes on another node -- and define the hypergraph
triggering model as a natural extension to the classical triggering model. In
another framework, we use monotone Boolean functions to capture the diverse
logic underlying many-to-one influence behaviors, and extend the triggering
model to the Boolean-function triggering model. We prove that the
Boolean-function triggering model, even with refined details of influence
logic, is equivalent to the hypergraph triggering model, and both are
equivalent to the general threshold model. Moreover, the general threshold
model is optimal in the number of parameters, among all models with the same
expressive power. We further extend these three equivalent models by
introducing correlations among influence propagations on different nodes.
Surprisingly, we discover that while the correlated hypergraph-based model is
still equivalent to the correlated Boolean-function-based model, the correlated
general threshold model is more restrictive than the two high-order models. Our
study sheds light on high-order network-influence propagations by providing new
insight into the group influence behaviors in existing models, as well as
diverse modeling tools for understanding influence propagations in networks.

15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
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The categories of this paper are: econ
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th