1,520 reputation
322
bio website dustingmixon.wordpress.com
location Air Force Institute of Technology
age 30
visits member for 1 year, 7 months
seen 18 hours ago
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

Jul
23
revised Not-lonely runners
added 6 characters in body
Jul
23
answered Not-lonely runners
Jul
22
awarded  Popular Question
Jul
22
revised Weil's Riemann Hypothesis for dummies?
added 166 characters in body
Jul
21
comment Weil's Riemann Hypothesis for dummies?
Thanks! Do we know what $c_1(d)$ is, or do we have a bound in terms of $d$?
Jul
21
asked Weil's Riemann Hypothesis for dummies?
Jul
2
awarded  Curious
Jun
5
comment Is this statement which relates the Fourier transform of a function to its singularities correct?
Note that $\cos(at)$ and $\sin(at)$ also sound the same (and yet are orthogonal). This is because your ear encodes the sound wave by having different parts of the basilar membrane resonate with different frequencies; as such, you effectively hear the spectrogram, i.e., your ear is "blind" to global phase, as Noah Stein suggested. This is a crucial idea in speech processing, see for example "On signal reconstruction without phase" by Balan, Casazza and Edidin.
May
30
comment Is it easy to produce hard-to-color graphs?
Joel - Regarding your final comment "in which nearly every instance is hard", are there any well-known problems which are known to have this property?
May
24
accepted Can the Legendre symbol be calculated in polynomial time?
May
24
answered $\|T\|_2 \le \sqrt{\|T\|_1\|T\|_\infty}$
May
24
asked Can the Legendre symbol be calculated in polynomial time?
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