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The Topology of Interdependent Multi-Domain Behavioral Systems

DECUR Partnership

Year selected for award: 2019

The Topology of Interdependent Multi-Domain Behavioral Systems

Program: DECUR Partnership

Co-Principal Investigators: Nina Fefferman, University of Tennessee, and Nakeya Williams, United States Merchant Marine Academy

Years of Award: 2020-2022

Managing Service Agency: Air Force Office of Scientific Research

Project Description:
Many problems in communication and domain interoperability have been modeled using networks, however, standard network methods cannot capture multi-way communication beyond the union of all pair-wise interactions in a group. This fundamentally limits the types of questions that can be addressed by these networks methods. We will instead extend our initial results from earlier work using simplicial sets, a concept form algebraic topology that is capable of explicitly capturing multi-way communications, to consider the challenges faced by multi-domain systems. Our goal is to develop tools to predict how group composition and topological structure shape the efficiency, robustness, and resilience of systems and use them to understand organizational strategies across scales. 

This work will involve 1) building of explicit case studies of multi-domain organizational challenges faced by the military, 2) creating novel mathematical functions that operate on higher-order topologies to capture those case studies, 3) characterizing novel feature sets of the higher-order topologies that might drive dynamics of the proposed functions, 4) finding real-world, simple test cases for model validation, 5) using both simulation and analytic tools to discover the optimal topological structures for different functional goals (e.g. robustness to cascading failure, global information-sharing efficiency, etc.), and 6) extending consideration of desired features to include multi-objective criteria, 7) creating software to provide simulation-based predictions for function behavior on different topologies, and 8) laying the foundation for new mathematical theory, proposing classifications of topologies/functions that could enable prediction without the need for explicit simulation. Together, these outcomes will meaningfully advance the nature of questions that can be asked about multi-domain communications systems. 

Information sharing, collaborative/complementary decision making, and multi-domain interdependency are integral to accomplishing military goals and managing challenges in both military and civilian intelligence for national defense. By developing a tool that can characterize successful interaction structures that foster efficiency for important objectives, the military may be able to design more efficient interdependent structures for particular tasks, or at least better understand and isolate points of potential weakness.