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@PHDTHESIS{Merger:976873,
author = {Merger, Claudia},
othercontributors = {Helias, Moritz and Honerkamp, Carsten},
title = {{I}nteractions on structured networks},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2024-00402},
pages = {1 Online-Ressource : Illustrationen},
year = {2024},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, RWTH Aachen University, 2024},
abstract = {Structured systems appear ubiquitously in nature.
Indubitably, the structure of a system determines its
characteristic behavior. However, predicting the behavior of
a system given its structure, or vice versa, is not
straightforward. We here demonstrate that the mapping from
structure to behavior can be tackled using a systematic
fluctuation expansion, and develop a new method to infer
structure given observations of the system. Often, structure
can be represented as a network of nodes, where the nodes
represent the agents, the elementary degrees of freedom of
the system, and the connections define their interactions.
One common feature of structured systems are hubs: nodes
with significantly more connections than average, which are
expected to be key to the observed overall system behavior.
To understand the influence of hubs, we investigate to which
extent the hubs of a scale-free network can drive a system
of binary agents into an ordered or disordered state. We
find that a typical mean-field approach to these systems
introduces a nonphysical process: the signal sent by a node
to its neighbors may travel back and influence the same
node, leading to a self-feedback loop. The phenomenon is
most prominent in the presence of hubs; their accumulated
self-feedback grows with the number of connections. We show
that a second-order fluctuation correction eliminates this
spurious self-feedback. These insights are then translated
to a model of disease spreading: We investigate the SIR
model, where each agent can be in one of three states
(susceptible, infected, or recovered), and transitions
between these states follow a stochastic process. A typical
approach in literature to predict average infection curves
is to assume that all agents are statistically independent,
introducing self-feedback artificially into the system,
which yields inflated infection curves. We use a dynamical
Plefka expansion to calculate a fluctuation correction,
which eliminates the self-feedback effect, leading to more
accurate predictions on the spread of disease. We then
approach the reverse direction: inferring pairwise and
higher-order interactions from data, these interactions
constitute the structure of the underlying system. In
principle, inference problems require an optimization over
the space of all possible interactions, whose number
increases exponentially with the system size. Nevertheless,
machine learning models can infer structures efficiently
from data. Typically, however, the inferred structure is
hidden in the parameters of the trained mdoel. We here show
how to extract the learned structure, formulated in terms of
interactions up to the fourth order. This process uncovers
how the model hierarchically constructs interactions via
nonlinear transformations of pairwise relations. This yields
a fully understandable AI-powered tool for inference. Thus,
we close the loop, demonstrating how collective behavior can
emerge from structure and vice versa.},
cin = {136930 / 130000},
ddc = {570},
cid = {$I:(DE-82)136930_20160614$ / $I:(DE-82)130000_20140620$},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2024-00402},
url = {https://publications.rwth-aachen.de/record/976873},
}
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