A Robust Amorphous Hierarchy from Persistent Nodes

For a very large network deployed in space with only nearby nodes able to talk to each other, we want to do tasks like robust routing and data storage. One way to organize the network is via a hierarchy, but hierarchies often have a few critical nodes whose death can disrupt organization over long distances. I address this with a system of distributed aggregates called Persistent Nodes, such that spatially local failures disrupt the hierarchy in an area proportional to the diameter of the failure. I describe and analyze this system, which has been implemented in simulation.

The Structure of Mathematical Knowledge

This report develops a conceptual framework in which to talk about mathematical knowledge. There are several broad categories of mathematical knowledge: results which contain the traditional logical aspects of mathematics; examples which contain illustrative material; and concepts which include formal and informal ideas, that is, definitions and heuristics.