Zobrazeno 1 - 10
of 241
pro vyhledávání: '"Stull D"'
Autor:
Fiedler, Jacob B., Stull, D. M.
In this paper, we give improved bounds on the Hausdorff dimension of pinned distance sets of planar sets with dimension strictly less than one. As the planar set becomes more regular (i.e., the Hausdorff and packing dimension become closer), our lowe
Externí odkaz:
http://arxiv.org/abs/2408.00889
Autor:
Fiedler, Jacob B., Stull, D. M.
We prove that if $E\subseteq \R^2$ is analytic and $1
Externí odkaz:
http://arxiv.org/abs/2309.11701
Autor:
Stull, D. M.
In this paper, we use algorithmic tools, effective dimension and Kolmogorov complexity, to study the fractal dimension of distance sets. We show that, for any analytic set $E\subseteq\R^2$ of Hausdorff dimension strictly greater than one, the \textit
Externí odkaz:
http://arxiv.org/abs/2207.12501
Autor:
Stull, D. M.
Let $L_{a,b}$ be a line in the Euclidean plane with slope $a$ and intercept $b$. The dimension spectrum $\spec(L_{a,b})$ is the set of all effective dimensions of individual points on $L_{a,b}$. The dimension spectrum conjecture states that, for ever
Externí odkaz:
http://arxiv.org/abs/2102.00134
Autor:
Stull, D. M.
The point-to-set principle \cite{LutLut17} characterizes the Hausdorff dimension of a subset $E\subseteq\R^n$ by the \textit{effective} (or algorithmic) dimension of its individual points. This characterization has been used to prove several results
Externí odkaz:
http://arxiv.org/abs/2101.11152
Autor:
Stull, D. M.
The behavior of the Hausdorff dimension of a set when projected onto a subspace is a fundamental question in fractal geometry. In this paper, we settle a question of Fassler and Orponen concerning the dimension of a set when projected onto a family o
Externí odkaz:
http://arxiv.org/abs/1912.08060
Autor:
Lutz, Neil, Stull, D. M.
In this paper we use the theory of computing to study fractal dimensions of projections in Euclidean spaces. A fundamental result in fractal geometry is Marstrand's projection theorem, which shows that for every analytic set E, for almost every line
Externí odkaz:
http://arxiv.org/abs/1711.02124
Autor:
Stull, D. M.
We prove a downward separation for $\mathsf{\Sigma}_2$-time classes. Specifically, we prove that if $\Sigma_2$E does not have polynomial size non-deterministic circuits, then $\Sigma_2$SubEXP does not have \textit{fixed} polynomial size non-determini
Externí odkaz:
http://arxiv.org/abs/1701.04428
Autor:
Lutz, Neil, Stull, D. M.
This paper investigates the algorithmic dimension spectra of lines in the Euclidean plane. Given any line L with slope a and vertical intercept b, the dimension spectrum sp(L) is the set of all effective Hausdorff dimensions of individual points on L
Externí odkaz:
http://arxiv.org/abs/1701.04108
Autor:
Lutz, Neil, Stull, D. M.
We use Kolmogorov complexity methods to give a lower bound on the effective Hausdorff dimension of the point (x, ax+b), given real numbers a, b, and x. We apply our main theorem to a problem in fractal geometry, giving an improved lower bound on the
Externí odkaz:
http://arxiv.org/abs/1612.00143