1,373 reputation
320
bio website dustingmixon.wordpress.com
location Air Force Institute of Technology
age 30
visits member for 1 years, 4 months
seen Apr 4 at 17:45
I am an assistant professor at the Air Force Institute of Technology. My research tends to fall into (at least) one of three categories:

- Matrix design for various engineering applications
- Compressed sensing and sparse signal processing
- Phase retrieval in finite-dimensional vector spaces

Feb
4
comment Incoherence of the row/column span
The subspaces which are optimally incoherent in your sense are spanned by the rows of something called a unit norm tight frame. See the introduction of this paper and references therein: arxiv.org/abs/1106.0921
Jan
18
awarded  Nice Answer
Jan
16
answered Submitting a companion paper with detailed proofs ?
Dec
31
comment Examples of ubiquitous objects that are hard to find?
I feel like (b) comes up quite a bit in complexity theory. Take any "hard" instance of an NP-complete problem whose answer is "yes" and try to find a certificate. For example, find a clique of size $n^\epsilon$ that the devil hid in an ER graph with $p=1/2$.
Dec
31
comment What is this expander-mixing-type graph property?
Wow, you're right. I ignored a log factor in $n$ on the right-hand side, thinking I didn't need it, but I do. For the sake of documentation, I found a lot of useful information by googling "graph discrepancy".
Dec
30
asked What is this expander-mixing-type graph property?
Dec
30
asked Examples of ubiquitous objects that are hard to find?
Dec
28
answered Probabilistic Johnson-Lindenstrauss Lemma for arbitrary points
Dec
28
comment Probabilistic Johnson-Lindenstrauss Lemma for arbitrary points
Let $f$ be a random projection. Then it will be JL with high probability, regardless of $X$. If I make $X$ a little larger (by including $z$), $f$ will still be JL with high probability. Is this useful to you, or do you want to fix $f$ and only use the randomness in $z$?
Dec
28
comment Probabilistic Johnson-Lindenstrauss Lemma for arbitrary points
Don't get me wrong - I read what you already wrote, but it is not clear what you are asking. Consider rephrasing the question.
Dec
28
comment Is there such a thing
Given your reformulation, the existence of this rank-2 Hermitian is implied by the 4M-4 conjecture (specifically, taking M=4). The conjecture is already known to be true for M=2 and 3. I offer US$100 for a proof of the conjecture on my blog: dustingmixon.wordpress.com/2013/03/19/…
Dec
28
comment Probabilistic Johnson-Lindenstrauss Lemma for arbitrary points
What is your question exactly?
Dec
26
accepted Sets whose elements are mutually “weakly” coprime?
Dec
25
comment Sets whose elements are mutually “weakly” coprime?
Not sure how rigorous this can be made, but it seems like when $n$ is large, $\nu_p$ of a random member of $\{1,\ldots,n\}$ nearly behaves like a geometric random variable with success probability $1-1/p$. As such, I would think that each member of $S$ will tend to have a large (i.e., uncommon) prime divisor, and the size of $S$ would be dictated by the collision probability of these large primes.
Dec
25
comment Sets whose elements are mutually “weakly” coprime?
@panoramix - Yes, I'd like to see the proof. :)
Dec
25
comment Sets whose elements are mutually “weakly” coprime?
Thanks - Can you include a reference?
Dec
25
comment Sets whose elements are mutually “weakly” coprime?
Yes, S is A. Thanks.
Dec
25
revised Sets whose elements are mutually “weakly” coprime?
edited body
Dec
24
asked Sets whose elements are mutually “weakly” coprime?
Dec
12
awarded  Yearling