Zobrazeno 1 - 10
of 54
pro vyhledávání: '"Lutz, Neil"'
We prove three results on the dimension structure of complexity classes. 1. The Point-to-Set Principle, which has recently been used to prove several new theorems in fractal geometry, has resource-bounded instances. These instances characterize the r
Externí odkaz:
http://arxiv.org/abs/2109.05956
Autor:
Lutz, Jack H., Lutz, Neil
We investigate the relationship between algorithmic fractal dimensions and the classical local fractal dimensions of outer measures in Euclidean spaces. We introduce global and local optimality conditions for lower semicomputable outer measures. We p
Externí odkaz:
http://arxiv.org/abs/2006.08468
The point-to-set principle of J. Lutz and N. Lutz (2018) has recently enabled the theory of computing to be used to answer open questions about fractal geometry in Euclidean spaces $\mathbb{R}^n$. These are classical questions, meaning that their sta
Externí odkaz:
http://arxiv.org/abs/2004.07798
Autor:
Lutz, Jack H., Lutz, Neil
Algorithmic fractal dimensions -- constructs of computability theory -- have recently been used to answer open questions in classical geometric measure theory, questions of mathematical analysis whose statements do not involve computability theory or
Externí odkaz:
http://arxiv.org/abs/1912.00284
Publikováno v:
In Information and Computation October 2023 294
When selecting locations for a set of facilities, standard clustering algorithms may place unfair burden on some individuals and neighborhoods. We formulate a fairness concept that takes local population densities into account. In particular, given $
Externí odkaz:
http://arxiv.org/abs/1908.09041
Matter, especially DNA, is now programmed to carry out useful processes at the nanoscale. As these programs and processes become more complex and their envisioned safety-critical applications approach deployment, it is essential to develop methods fo
Externí odkaz:
http://arxiv.org/abs/1902.06171
We consider the multi-armed bandit setting with a twist. Rather than having just one decision maker deciding which arm to pull in each round, we have $n$ different decision makers (agents). In the simple stochastic setting, we show that a "free-ridin
Externí odkaz:
http://arxiv.org/abs/1810.08743
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:
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