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Mathematics
Set Theory, Logic, Probability, Statistics
Similarity between -/+ weighted distributions
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[QUOTE="Jarvis323, post: 6025438, member: 475688"] I think it's quite complicated to explain all of the details (which I only partially understand myself). Maybe my previous explanation wasn't quite right. Also, I was trying to generalize enough that I might get some suggestions that I could evaluate more deeply on my own. There is a particle distribution function, ##f(x,y,z,v_x,v_y,v_z,t)##. [URL]https://en.wikipedia.org/wiki/Distribution_function[/URL] There are [B]marker[/B] particles moving around in ##(x,y,z,vx,vy,vz)## that carry time varying weights. Their weights represent a change in the number of [B]real[/B] particles near ##(x,y,z,v_x,v_y,v_z)## between time steps. In other words, they evolve the particle distribution function. The data I have is just a large sample of the particles with their positions, velocities and weights. First we are binning them spatially, then binning their weights in ##(v_x,v_y,v_z)##. So each spatial bin has a weighted velocity histogram (although we could also use a GMM or something like that). These "distributions" represent an approximation of how many particles are leaving or entering the respective regions of phase-space, normalized by phase-space volume (change in particles per unit phase-space volume, by position and velocity). We want to merge similar spatial bins (to represent the merged bins instead with one histogram). So by locally merging, I mean merging adjacent spatial bins. I'm not completely clear on all of the insights that people will try to extract from the result, except that the shape and features are meaningful for studying the turbulence, self-organization phenomena, and for understanding and diagnosing issues regarding the degradation of simulation accuracy and performance. [/QUOTE]
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Similarity between -/+ weighted distributions
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