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[1811.01491] Discrepancy in random hypergraph models
We study hypergraph discrepancy in two closely related random models of hypergraphs on n vertices and m hyperedges. The first model, 1, is when every vertex is present in exactly t randomly chosen hyperedges. The premise of this is closely tied to, and motivated by the Beck-Fiala conjecture. The second, perhaps more natural model, 2, is when the entries of the m×n incidence matrix is sampled in an i.i.d. fashion, each with probability p. We prove the following:
1. In 1, when log10n≪t≪n‾√, and m=n, we show that the discrepancy of the hypergraph is almost surely at most O(t√). This improves upon a result of Ezra and Lovett for this range of parameters.
2. In 2, when p=12, and n=Ω(mlogm), we show that the discrepancy is almost surely at most 1. This answers an open problem of Hoberg and Rothvoss.
hypergraphs  graph-theory  random-graphs  rather-interesting  sampling  generative-models  algorithms  looking-to-see  to-write-about  to-simulate  consider:performance-measures 
12 days ago by Vaguery
A web application to sequence, play and slice YouTube video’s live in the browser. You need a MIDI controller of some sort and a browser with MIDI support (I think that’s Chrome or Opera?), connect them to the web app, set cue points (or auto-chop the video) and play them from your controller.
strumenti  video  musica  sampling  youtube  online  fordjbatman 
28 days ago by nicoladagostino
python - Stratified Sampling in Pandas - Stack Overflow
df = pd.DataFrame(dict(
A=[1, 1, 1, 2, 2, 2, 2, 3, 4, 4],

df.groupby('A', group_keys=False).apply(lambda x: x.sample(min(len(x), 2)))
pandas  sample  sampling  stratified-sampling  deep-learning  skew 
6 weeks ago by nharbour

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