I'm excited to share our new paper w/ @mungowitz and @m_zavlanos introducing a decentralized mechanism for pricing and exchanging alternatives constrained by transaction costs: a thread 🧵 1/n Our decentralized model is based on max-plus (linear) algebra, a branch of tropical 🌴 geometry. The recipe is simple: times <- plus, plus <- max. Max-plus algebra reinvents linear algebra with varying degrees of success, e.g. eigenvalues, linear systems, regression... 2/n

what is a Laplacian? in the discrete domain where data is assigned to nodes of a network, maybe it's best defined as an operator that drives harmonic flow. in this video, nodes pass messages to neighbors, update their priors, and eventually reach consensus on their color. the graph Laplacian is an example of a network Laplacian that drives consensus dynamics. in fact, nodes come to agree on a color that is the average of all the initial colors.

fake news? i probably wouldn't be a mathematician (in training) if it wasn't for my extremely flexible public school system. i moved catholic school to a public elem. so that i could take advanced math. my high school @BHSNCougars even allowed me to take courses at @IndianaUniv

https://twitter.com/SteveMillerOC/status/1389456546753437699

even before i had a drivers liscence or a car, i would take a circuitous bus route to indiana u's campus from the high school. call me selfish/privileged. maybe i don't really fully understand or appreciate equity,

new preprint out with yiannis kantaros, @pappasg69 & @robertghrist that could be a game-changer when it come to information propagation over networks subject to semantic (read: logical) constraints arxiv.org/pdf/2009.00669… the problem the paper solves is a connectivity scheduling one, but this is only the beginning. consider a network (as pictured) of static sensors (w/ communication capabilities) that are continuously collecting information about their environment.

in honor of april showers, i give you a proximity radius filtration of a *sensor* network of @NEXRADROC weather radar stations (data provided by @NWS) tracking births and deaths of connected components of the corresponding clique complex of the filtration above does not tell much besides that the network is connected ~300km proximity radius which is somewhat higher than the typical NEXRAD range ~230km.