31 research outputs found
Multilinear Time Invariant System Theory
In biological and engineering systems, structure, function and dynamics are
highly coupled. Such interactions can be naturally and compactly captured via
tensor based state space dynamic representations. However, such representations
are not amenable to the standard system and controls framework which requires
the state to be in the form of a vector. In order to address this limitation,
recently a new class of multiway dynamical systems has been introduced in which
the states, inputs and outputs are tensors. We propose a new form of
multilinear time invariant (MLTI) systems based on the Einstein product and
even-order paired tensors. We extend classical linear time invariant (LTI)
system notions including stability, reachability and observability for the new
MLTI system representation by leveraging recent advances in tensor algebra.Comment: 8 pages, SIAM Conference on Control and its Applications 2019,
accepted to appea
Observability of Hypergraphs
In this paper we develop a framework to study observability for uniform
hypergraphs. Hypergraphs are generalizations of graphs in which edges may
connect any number of nodes, thereby representing multi-way relationships which
are ubiquitous in many real-world networks including neuroscience, social
networks, and bioinformatics. We define a canonical multilinear dynamical
system with linear outputs on uniform hypergraphs which captures such multi-way
interactions and results in a homogeneous polynomial system. We derive a
Kalman-rank-like condition for assessing the local weak observability of this
resulting system and propose techniques for its efficient computation. We also
propose a greedy heuristic to determine the minimum set of observable nodes,
and demonstrate our approach numerically on different hypergraph topologies,
and hypergraphs derived from an experimental biological dataset.Comment: 7 pages, 3 figures, 2 algorithms, lots of math