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 | |
stats | profile views | 947 |
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
- 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 |