1,500 reputation
322
bio website dustingmixon.wordpress.com
location Air Force Institute of Technology
age 30
visits member for 1 year, 7 months
seen 5 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

8h
revised Not-lonely runners
added 6 characters in body
16h
answered Not-lonely runners
1d
awarded  Popular Question
1d
revised Weil's Riemann Hypothesis for dummies?
added 166 characters in body
2d
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 $d$?
2d
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