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In this paper, we use resource-bounded dimension theory to investigate polynomial size circuits. We show that for every i ≥ 0, P/poly has ith order scaled p 3-strong dimension 0. We also show that P/poly i.o. has p 3-dimension 1/2, p 3-strong dimension 1. Our results improve previous measure results of Lutz (1992) and dimension results of Hitchcock and… (More)

We exhibit a polynomial time computable plane curve Γ that has finite length, does not intersect itself, and is smooth except at one endpoint, but has the following property. For every computable parametrization f of Γ and every positive integer n, there is some positive-length subcurve of Γ that f retraces at least n times. In contrast, every computable… (More)

We use derandomization to show that sequences of positive pspace-dimension – in fact, even positive ∆ p k-dimension for suitable k – have, for many purposes, the full power of random oracles. For example, we show that, if S is any binary sequence whose ∆ p 3-dimension is positive, then BPP ⊆ P S and, moreover, every BPP promise problem is P S-separable. We… (More)

The " analyst's traveling salesman theorem " of geometric measure theory characterizes those subsets of Euclidean space that are contained in curves of finite length. This result, proven for the plane by Jones (1990) and extended to higher-dimensional Euclidean spaces by Okikiolu (1991), says that a bounded set K is contained in some curve of finite length… (More)

The base-k Copeland-Erdös sequence given by an infinite set A of positive integers is the infinite sequence CE k (A) formed by concatenating the base-k representations of the elements of A in numerical order. This paper concerns the following four quantities. • The finite-state dimension dim FS (CE k (A)), a finite-state version of classical Hausdorff… (More)

Consider the problem of calculating the fractal dimension of a set X consisting of all infinite sequences S over a finite alphabet Σ that satisfy some given condition P on the asymptotic frequencies with which various symbols from Σ appear in S. Solutions to this problem are known in cases where (i) the fractal dimension is classical (Hausdorff or packing… (More)

The dimension of a point x in Euclidean space (meaning the constructive Hausdorff dimension of the singleton set {x}) is the algorithmic information density of x. Roughly speaking, this is the least real number dim(x) such that r × dim(x) bits suffice to specify x on a general-purpose computer with arbitrarily high precision 2 −r. The dimension spectrum of… (More)

Resource-bounded measure is a generalization of classical Lebesgue measure that is useful in computational complexity. The central parameter of resource-bounded measure is the resource bound ∆, which is a class of functions. When ∆ is unrestricted, i.e., contains all functions with the specified domains and codomains, resource-bounded measure coincides with… (More)

- Guangjian Fan, Lianhui Sun, Peipei Shan, Xianying Zhang, Jinliang Huan, Xiaohong Zhang +13 others
- Nature communications
- 2015

Centrosome amplification is frequent in cancer, but the underlying mechanisms remain unclear. Here we report that disruption of the Kruppel-like factor 14 (KLF14) gene in mice causes centrosome amplification, aneuploidy and spontaneous tumorigenesis. Molecularly, KLF14 functions as a transcriptional repressor of Plk4, a polo-like kinase whose overexpression… (More)

- Lianhui Sun, Guangjian Fan, Peipei Shan, Xiaoying Qiu, Shuxian Dong, Lujian Liao +10 others
- Nature communications
- 2016

Maintenance of energy homeostasis is essential for cell survival. Here, we report that the ATP- and ubiquitin-independent REGγ-proteasome system plays a role in maintaining energy homeostasis and cell survival during energy starvation via repressing rDNA transcription, a major intracellular energy-consuming process. Mechanistically, REGγ-proteasome limits… (More)