How often do you invoke spectral gap theorems to choose dimensionality for your data, if ever?
I have never done so; in fact I'm not sure what it means. Could you expand a bit?
Given a graph, one can write down the adjacency matrix for the graph; its first eigenvalue must be positive; scale the matrix so that the first eigenvalue is one. Now there is a theorem, known as the spectral gap theorem (there are parallel theorems that I'm not totally familiar with) which says that the difference between the first and second eigenvalue must be at least some number (on the order of 5% if I recall; I don't have a good reference handy).
I went to a colloquium where someone was collecting data which could be made to essentially look like a g...
In response to falenas108's "Ask an X" thread. I have a PhD in experimental particle physics; I'm currently working as a postdoc at the University of Cincinnati. Ask me anything, as the saying goes.
This is an experiment. There's nothing I like better than talking about what I do; but I usually find that even quite well-informed people don't know enough to ask questions sufficiently specific that I can answer any better than the next guy. What goes through most people's heads when they hear "particle physics" is, judging by experience, string theory. Well, I dunno nuffin' about string theory - at least not any more than the average layman who has read Brian Greene's book. (Admittedly, neither do string theorists.) I'm equally ignorant about quantum gravity, dark energy, quantum computing, and the Higgs boson - in other words, the big theory stuff that shows up in popular-science articles. For that sort of thing you want a theorist, and not just any theorist at that, but one who works specifically on that problem. On the other hand I'm reasonably well informed about production, decay, and mixing of the charm quark and charmed mesons, but who has heard of that? (Well, now you have.) I know a little about CP violation, a bit about detectors, something about reconstructing and simulating events, a fair amount about how we extract signal from background, and quite a lot about fitting distributions in multiple dimensions.