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visits member for 1 year, 4 months
seen Apr 10 at 11:18

Feb
16
answered Pigeonhole Principle -
Feb
9
comment Using “we have” in maths papers
@MarcvanLeeuwen "We have 'one has'"
Feb
8
awarded  Benefactor
Jan
14
comment Splitting a sandwich and not feeling deceived
Nice! You used the invisible hand of the market to cut the sandwich.
Jan
10
comment Why are mathematical proofs that rely on computers controversial?
I also enjoy how democratized math is. I think it's difficult to draw the line between ourselves and tools we use. ME + PEN + NOTEBOOK feels close to ME, but ME + PEN + PAPER + GENIUS MATHEMATICIAN feels less. What about a calculator to avoid careless arithmetic errors? Maple / Mathematica? Perhaps sometimes it's elegant to use tools: perhaps the quote that "the best mathematician is a lazy one" is somehow akin to "the deadliest weapon in the world is a Marine and his rifle." But even as I write this, I'm reminded that flying un-manned death robots are actually the deadliest weapons...
Jan
10
comment Why are mathematical proofs that rely on computers controversial?
@Shayne +1 I really agree that the most elegant part is often the narrowing of the solution space, but there are those of us who take great joy in the "last mile". The jump from the statement "It is possible to do this" to "I can do this in the 1 month with a normal computer" can also be a source of grand elegance. Methods like the FFT are beautiful in themselves, and are sometimes part of the engine that allows brute force to be practical for the last mile of a proof. In a way, it's narrowing the solution as well (in # steps rather than space). There is one mathematics, and it's everywhere!
Jan
9
awarded  Critic
Dec
15
awarded  Popular Question
Sep
26
comment In What order should I Learn math in?
+1 for Combinatorics. It's the gateway to statistics!
Sep
26
comment Surprising identities / equations
From your description, I thought you'd somehow made $0.99 = 1$, which would be, I agree, bragable.
Sep
4
revised How the dual LP solves the primal LP
edited title
Sep
2
revised How the dual LP solves the primal LP
added 157 characters in body
Aug
29
awarded  Promoter
Aug
23
comment Is there an expansion for element-wise scaled convolution?
@AnonSubmitter85 But the numerator must be 0 if the denominator is 0 (see post above-- since all vectors are nonnegative, a zero value $(b*d)_i$ requires all values in the product-sum must equal zero, meaning the same must be true in the numerator). The only question is whether l'Hopital's rule is valid here.
Aug
23
comment Is there an expansion for element-wise scaled convolution?
@AnonSubmitter85 I agree about the indeteriminate form you describe. Will $(a\cdot b)*(c\cdot d)_i$ approach $(a*c)_i$ when $(b*d)_i \approx 0$? I've seen this in practice (and it is certainly true when the convolution comes from an inner product of length 1), but just wanted to have a cleaner proof.
Aug
23
comment Is there an expansion for element-wise scaled convolution?
Then do you have any thoughts as to what the $n$th term would be in the case when the denominator approaches zero? I should note that all vectors are nonnegative, so if $(b*d)_n = 0$, then at least one of all $b_i$ or $d_i$ multiplied to compute $(b*d)_n$ must be zero, meaning the numerator is also going to zero for that term. My intuition says to replace with $(a*c)_n$ when $(b*d)_n\approx 0$ (rationalizing using l'Hopital's rule). Any thoughts?
Aug
22
revised Is there an expansion for element-wise scaled convolution?
edited body
Aug
22
asked Is there an expansion for element-wise scaled convolution?
Aug
20
revised Is there a way to do this with fast convolution?
Used explicit reversal of N instead of a clever (but not reproducible) math trick.
Aug
20
accepted Is there a way to do this with fast convolution?