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My mathematically-oriented work generally explores discrete geometric and probabilistic themes in physics, computation, and communication. Jack of most trades, master of none.

I can be reached at s.huntsman.1#alumni#nyu#edu (make the obvious substitutions for #).


Jun
22
comment Stationary distribution for time-inhomogeneous Markov process
You might also find the multiplicative ergodic theorem helpful.
Jun
22
comment Stationary distribution for time-inhomogeneous Markov process
Consider a time-inhomogeneous Markov process $X_t$ on a finite state space. Let $Q(t)$ denote the generator, and let $P(s,t)$ denote the corresponding transition kernel, i.e. $P(s,t) = U^{-1}(s)U(t)$, where the Markov propagator is \begin{equation} U(t) := \mathcal{TO}^* \exp \int_0^t Q(s) \ ds, \end{equation} and $\mathcal{TO}^*$ indicates the formal adjoint or reverse time-ordering operator. Now an initial distribution $\pi(0)$ is propagated as $\pi(t) = \pi(0)U(t)$. (See, e.g., Kleinrock, L. Queueing Systems, vol. 1. Wiley (1975).)
Jun
18
comment Determinant Evaluation
Have you looked at Krattenthaler's papers on determinants?
Jun
9
answered A $d$-form on ${\mathbb R}^n$ that vanishes on $\binom{d+n-1}{n-1}$ general points, vanishes identically
May
27
awarded  pr.probability
May
19
comment Smooth bivariate functions identifiable under permutations
For $f$ symmetric and otherwise nice you may want to consider it as a graphon, cf. people.math.osu.edu/glasscock.4/graphons.pdf
May
12
comment Regular epimorphisms in the category of simple undirected graphs
@DominicvanderZypen -- It doesn't answer the question: it merely reinforces Todd's comment and gives context along those lines.
May
12
comment Regular epimorphisms in the category of simple undirected graphs
combinatorics.org/ojs/index.php/eljc/article/view/v15i1a1
May
6
awarded  Nice Answer
May
3
comment Avoiding mean-curvature flow dumbbell neck-pinch by inflating a surface
en.wikipedia.org/wiki/Dilation_(morphology)
Apr
28
comment Group theory in machine learning
first-mm.eu/files/kersting2012ecai_faia.pdf
Apr
28
comment Finite-space dynamical systems
pub.uni-bielefeld.de/publication/2508475
Apr
26
comment Decidability of $x^3+y^3+z^3 = c$
The latest relevant reference seems to be Elsenhans, A.-S. and Jahnel, J. "New sums of three cubes". Math. Comp. 78, 1227 (2009).
Apr
26
comment Decidability of $x^3+y^3+z^3 = c$
Poonen's article "Undecidability in number theory" begins: "Does the equation $x^3+y^3+z^3 = 29$ have a solution in integers? Yes: $(3, 1, 1)$, for instance. How about $x^3+y^3+z^3 = 30$? Again yes, although this was not known until 1999: the smallest solution is $(−283059965, −2218888517, 2220422932)$. And how about $x^3+y^3+z^3 = 33$? This is an unsolved problem."
Apr
23
comment Ordered lattice point enumeration
math.ucdavis.edu/~latte
Apr
22
comment A digraph related to permutations
mathoverflow.net/questions/49555
Apr
22
answered Volume of a region given by a Constraint Satisfaction Problem
Apr
9
comment Deep Learning / Deep neural nets for mathematician
This is more for physicists but nevertheless looks like it should be pretty insightful: arxiv.org/abs/1410.3831
Apr
9
comment When few simple conditions yield a unique intricate structure
It is worth pointing out that two of your examples (j-invariant and sporadic simple groups) are related through moonshine, as is the intricate structure of the Golay code.
Apr
8
answered Differential form equation in Bowen's lecture notes