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Strictly Monotone Weight Functions on Directed Graphs
OUTLINE Introduction General Definitions When can any weight function be turned into a strictly monotone weight function? Weighted Directed Graphs in Applications Autonomous Driving Quantum Walks Artificial Neural Networks SUMMARY: We define a directed graph as a space with any binary relation, and we define a strictly monotone weight function on any directed graph. We prove when no weight function on a directed graph can be turned into a strictly monotone weight function, and we give a characterization of any strictly monotone weight function. Finally, we mention the use of weighted directed graphs in autonomous driving research, quantum information, and deep learning. Introduction Here is an example…
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