han
Reputation
Top tag
Next privilege 100 Rep.
Edit community wikis
Badges
5
Newest
Impact
~1k people reached

• 0 posts edited
• 0 helpful flags
• 2 votes cast

# 21 Actions

 Jul13 awarded Commentator Jul13 comment Integration problem in matrix calculus thx, this looks reasonable to me. Jul13 accepted Integration problem in matrix calculus Jul13 asked Integration problem in matrix calculus Nov6 comment Efficient method for detecting a convex body in $\mathbb{R}^n$ Thanks @NielsDiepeveen for the remark. It is true that this algorithm can make a correct decision with high probability after testing enough pairs. I'm trying to figure out how high is that. Nov5 awarded Scholar Nov5 accepted Samples in the convex body vs. samples on the convex surface Nov5 comment Samples in the convex body vs. samples on the convex surface Thanks @MikeSpivey for this nice and clear answer. The example is really convincing. Nov5 awarded Supporter Nov5 comment Efficient method for detecting a convex body in $\mathbb{R}^n$ Thanks @ChristianBlatter for the remark. It's true that a trivial sampler will take a long time to mix on such $K_1$. Fortunately, there is an algorithm for bringing a convex body into near-isotropic position. Nov5 asked Samples in the convex body vs. samples on the convex surface Nov5 revised Efficient method for detecting a convex body in $\mathbb{R}^n$ added 77 characters in body Nov5 revised Efficient method for detecting a convex body in $\mathbb{R}^n$ deleted 8 characters in body Nov5 comment Efficient method for detecting a convex body in $\mathbb{R}^n$ Thanks Christian Blatter, point taken. Nov5 awarded Editor Nov5 revised Efficient method for detecting a convex body in $\mathbb{R}^n$ added 358 characters in body Nov5 comment Efficient method for detecting a convex body in $\mathbb{R}^n$ Thanks, but suppose one of these two bodies is a convex polytope, which means the boundary between $K_1$ and $K_2$ is a set of hyperplanes $\mathcal{H}=\{H_1,H_2,\ldots,H_n\}$. I think this approach will fail when two points are on the same hyperplane $H\in \mathcal{H}$. Nov4 comment Efficient method for detecting a convex body in $\mathbb{R}^n$ Assume $K_0$ is a hypercube in $\mathbf{R}^n$. $K_1$ is a hypersphere in this cube and $K_2=K_1^c$. It satisfies the first assumption and $K_0$ is convex. Nov4 comment Efficient method for detecting a convex body in $\mathbb{R}^n$ Besides three assumptions listed above, I don't know any other information about $K_1$ and $K_2$. The only information can be used is the membership oracle, which reports whether a query point $x$ is in $K_1$ or in $K_2$, but provides no other information. Nov4 awarded Student