The functional and computational power of a network emerges as a property of the system operating as a coherent whole at a global scale, not at the scale of individual nodes. A natural question to ask is what are the physical principles that allow a collection of nodes to interact in such a way that they produce emergent global network dynamics? There is in general a lack of sufficient theory capable of providing insights into universal physical principles that bridge individual node dynamics to the behavior of the network as a whole in a deterministic way. Here, we show that in any physically constructible geometric network, the geometry of the network  constrains and bounds signaling and the flow of information through the network , and develop a theory derived from foundational principles of neural signaling that can both describe and predict the dynamics of geometric networks from considerations of node dynamics. We provide empirical evidence that at least some important examples of widely different naturally occurring and engineered networks , specifically, the prevalence of the small world network topology, axonal branching of pyramidal neurons in the visual cortex, and the internet router network, are capable of approaching a state of optimal dynamical efficiency, a concept that is derived from the theory. The framework we develop has a wide range of (non-biological) engineering and neurophysiological applications .
The functional and computational power of a network emerges as a prop- erty of the system operating as a coherent whole at a global scale, not at the scale of individual nodes. A natural question to ask is what are the physical principles that allow a collection of nodes to interact in such away that they produce emergent global network dynamics? Here, we address this question by developing a generalized theoretical framework that formally describes how in any physically constructible geometric network, the geome- try of the network i.e. its physical structure, constrains and bounds signaling and the flow of information through the network . This then in turn predicts the emergent dynamics of the network. Our results illustrate how the in- terplay between strictly local geometric and temporal process at the scale of individual node pairs directly affects the behavior of the whole network. We also provide empirical evidence that at least some important examples of widely different naturally occurring and engineered networks follow these theoretical principles .
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property
prop- erty
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a way
away
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There is in general a lack of sufficient theory capable of providing insights into universal physical principles that bridge individual node dynamics to the behavior of the network as a whole in a deterministic way.
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show that
address this question by developing a generalized theoretical framework that formally describes how
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geometry
geome- try
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i.e. its physical structure,
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, and develop a theory derived from foundational principles of neural signaling that can both describe and predict the dynamics of geometric networks from considerations of node dynamics. We
. This then in turn predicts the emergent dynamics of the network. Our results illustrate how the in- terplay between strictly local geometric and temporal process at the scale of individual node pairs directly affects the behavior of the whole network. We also
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, specifically, the prevalence of the small world network topology, axonal branching of pyramidal neurons in the visual cortex, and the internet router network, are capable of approaching a state of optimal dynamical efficiency, a concept that is derived from the theory. The framework we develop has a wide range of (non-biological) engineering and neurophysiological applications
follow these theoretical principles