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Updated: Sep 16, 2025

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

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Published on: September 8, 2023

A Categorical Framework for Quantifying Emergent Effects in Network Topology.

Johnny Jingze Li¹, Sebastian Pardo Guerra², Kalyan Basu³

¹Center for Engineered Natural Intelligence and Department of Mathematics, University of California San Diego, La Jolla, CA 92093, U.S.A. jil164@ucsd.edu.

Neural Computation

|July 8, 2025

Summary

We introduce a new framework using homological algebra to measure emergent effects in complex systems. This approach links system properties to network structure, enabling prediction and understanding of emergence.

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Area of Science:

Complex Systems Science
Network Theory
Computational Mathematics

Background:

Emergent effects are key to complex systems but lack theoretical measurement frameworks.
Understanding emergence requires quantifying properties not present in individual components.

Purpose of the Study:

To develop a computational measure for quantifying emergent effects in complex systems.
To establish a theoretical framework linking emergence to network topology and structure.

Main Methods:

Utilizing homological algebra to model emergence as structural nonlinearity.
Encoding emergence within the mathematical structure of cohomologies.
Applying the framework to network models for computational measurement.

Main Results:

Developed a novel computational measure of emergence based on network topology.
Demonstrated that the measure correlates with existing information-theoretic measures.
Showcased the framework's ability to predict and explain emergent effects.

Conclusions:

The proposed framework provides a robust method for measuring and understanding emergence.
Network topology and local structures are critical determinants of emergent potential.
This work offers a pathway to predict and analyze emergent phenomena in diverse complex systems.