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1d
comment “Most Similar Vector Problem” on an Integer Lattice?
Should there be an exponent on $[-M,\hspace{-0.02 in}M\hspace{.03 in}]$? $\;$
Jul
21
awarded  Popular Question
Jul
12
revised What is the following (matrix) operator called?
fixed title's grammar
Jul
11
revised Natural transformations induce homotopies - Is this true in the “fat” world?
fixed title's grammar
May
4
awarded  Yearling
Apr
28
comment What defines a “short proof”?
In fact, if "there are no short proofs of tautology" then coNP != NP. $\;$
Apr
27
awarded  Good Question
Apr
27
comment Random Diophantine polynomials: Percent solvable?
Presumably $\: \log C/C \:$ should be replaced with $\: (\log C)/C \;$. $\;\;\;\;$
Apr
19
comment is there a global obstruction for a diffeomorphism to be an isometry?
$x\mapsto x^3 \;$ is not a diffeomorphism from $\mathbf{R}$ to itself, since the inverse of that map is not differentiable at zero. $\;\;\;\;$
Apr
16
comment Rate of convergence in the Law of Large Numbers
You'll also need $\: |\mathbb{E}X_1\hspace{-0.02 in}| < \infty \:$ in order to reach the conclusions you claim from the laws of large numbers. $\;\;\;$
Apr
4
revised Why is differential Galois theory not widely used?
fixed title's grammar
Apr
1
comment How large do algebraic representations need to be for packing circles in squares?
I mean "at most $\:r-1\:$ from the origin" instead of $\:r+1\;$. $\;\;\;$ I believe the rest of my two previous comments are correct.) $\;\;\;\;\;\;\;$
Apr
1
comment How large do algebraic representations need to be for packing circles in squares?
If there is a bound on the bit-lengths of the coefficients that is better than $n^{O(n)}$, then that would yield a better bound for my problem (in particular, enough for the bounty), since it would provide an explicit constant for the main factor of the runtime. $\:$ (i.e., $n^{\hspace{.02 in}O(n)}$ becomes $\: n^{\hspace{.02 in}c\cdot n} \cdot \text{something_asymptotically_smaller_than_that} \;$.) $\;\;\;\;\;\;\;$
Apr
1
comment How large do algebraic representations need to be for packing circles in squares?
Essentially, "there are $\:2\cdot n\:$ reals such that the $n$ points described by those reals are each at most $\:r+1\:$ from the origin and at least $2$ from each other". $\;\;\;$ Thus, $s$ would be quadratic in $n$. $\:$ Do you know where they address the sizes of the coefficients produced by their global optimization algorithm? $\;\;\;\;\;\;\;$
Apr
1
comment How large do algebraic representations need to be for packing circles in squares?
I'm looking at Exercise 11.9 from the "For downloading the .pdf file of the book" link on the page you linked to, and as far as I can see, that will only improve on the result I cited when $\ell$ is $(\Omega(1))^k$ (using the notation of Algorithm 11.16). $\;$
Mar
31
comment Proof that no differentiable space-filling curve exists
@PabloShmerkin : $\:$ How can one show that? $\;\;\;\;$
Mar
30
comment Proof that no differentiable space-filling curve exists
However, a differentiable map (even on a compact interval) is not necessarily Lipschitz. $\hspace{1.27 in}$
Mar
27
comment Is $\sum_{k=1}^{n} \sin(k^2)$ bounded by a constant $M$?
@npbool : $\;\;\; \sin\hspace{-0.04 in}\Big(\hspace{-0.03 in}\frac{\pi}2\hspace{-0.03 in}\Big) = 1 \not< 1 \;\;\;\;\;\;\;\;\;$
Mar
23
asked How large do algebraic representations need to be for packing circles in squares?
Mar
13
comment Does Langton's ant cover every n by 6 gridded torus?
I'm not sure how much this would help, but one could try splitting the grid into congruent pieces and computing a lookup table with [after_colors,exit_edge] for each possible [entry_edge,before_colors]. $\:$ (Such a table could presumably be compressed, and might reveal that some a-priori-possible color configurations of the pieces are not actually possible.) $\;\;\;\;$