luna VS CoinBLAS

Check out https://github.com/greatscottgadgets/luna and https://github.com/tinyfpga/TinyFPGA-Bootloader

What the hell, here are a bunch of half-baked ideas that I haven't made time for because I'm lazy and stressed out and exhausted:

1. Designing a protocol and air interface for an amateur radio cellular network. This started out with some spread spectrum experiments and an interest in low-probability-of-intercept (below the noise floor) communication. The idea I have now is sort of a cross between APRS and DMR using modern modulation techniques. The network would consist of amateur rooftop "cells" with internet connections, and mobile transponders that communicate with those cells. There'd be some sort of callsign or key based addressing scheme and IP-like network topology discovery. Everything will be authenticated. I'd love to have an encrypted mode, but unless the laws change, it probably isn't going to happen.

2. Open-source firmware or gateware implementation of a USB PD controller that supports entering/exiting alternate modes properly. Inspired by Kate Temkin's Luna project [1]. I got the impression that PD was out of scope for LUNA, at least for the time being, but it would be really nice to have both a USB and PD stack that could be integrated onto a small, inexpensive chip without the proprietary mess.

[1] https://github.com/greatscottgadgets/luna

When you consider that a graph and a matrix are isomorphic, doing vector matrix multiplication takes a vector with a set value, say row 4, and multiplies it by a matrix where row 4 has values present that represent edges to the nodes that are adjacent to it (ie "adjacency" matrix). The result is a vector with the next "step" in a BFS across the graph, do that in a loop and you step across the whole graph.

A cool result of this is, for example, taking an adjacency matrix and squaring it is the "Friend of a Friend" graph. It takes every node/row and multiplies it by itself, returning a matrix that are adjacent to the adjacencies of each node, ie, the friends (adjacencies of the adjacencies) of friends (adjacencies) of the nodes.

Deeper traversal are just higher nodes, a matrix cubed are the friends of the friends of the friends.

A picture is worth a thousand words, see figure 7 of this paper:

https://arxiv.org/pdf/1606.05790.pdf

Also check out figure 8, this shows how incidence matrices can work to represent hyper and multi graphs. An pair of incidence matrices reprsent two graphs, one from nodes to edges and the other from edges to nodes, these are n by m and m by n. When you multiply them, you get a square adjacency matrix that "projects" the incidence into an adjacency. This can be used to collapse hypergraphs into simple graphs that use different semirings to combine the multiple edges.

For some pretty pictures of this kind of stuff, check out CoinBLAS (note I am not a crypto-bro, it was just a very handy extremely large multi-graph that I could easily download in chunks to play with):

https://github.com/Graphegon/CoinBLAS/

Python wrapper around The GraphBLAS API:

https://github.com/michelp/pygraphblas

For an upcoming paper we've open sourced using pygraphblas to analyse the bitcoin graph using the GAP benchmarks on a server with 1TB of RAM:

https://github.com/Graphegon/CoinBLAS