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Journals and Conferences
DNA nanotechnology uses the information processing capabilities of nucleic acids to design self-assembling, programmable structures and devices at the nanoscale. Devices developed to date have been programmed to implement logic circuits and neural networks, capture or release specific molecules, and traverse molecular tracks and mazes. Here we investigate… (More)
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 (classical) Hausdorff dimension of generalized sets of Furstenberg type.
We study the interaction between polynomial space randomness and a fundamental result of analysis, the Lebesgue differentiation theorem. We generalize Ko’s framework for polynomial space computability in Rn to define weakly pspace-random points, a new variant of polynomial space randomness. We show that the Lebesgue differentiation theorem holds for every… (More)
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. We draw on Kolmogorov complexity and geometrical arguments to show that if the effective Hausdorff… (More)
We prove a downward separation for Σ2-time classes. Specifically, we prove that if Σ2E does not have polynomial size non-deterministic circuits, then Σ2SubEXP does not have fixed polynomial size nondeterministic circuits. To achieve this result, we use Santhanam’s technique  on augmented Arthur-Merlin protocols defined by Aydinlioğlu and van Melkebeek… (More)
Chemical reaction networks (CRNs) model the behavior of molecules in a well-mixed solution. The emerging field of molecular programming uses CRNs not only as a descriptive tool, but as a programming language for chemical computation. Recently, Chen, Doty and Soloveichik introduced rate-independent continuous CRNs (CCRNs) to study the chemical computation of… (More)
When p is a computable real so that p ≥ 1, the isometry degree of a computable copy B of l is defined to be the least powerful Turing degree that computes a linear isometry of l onto B. We show that this degree always exists and that when p 6= 2 these degrees are precisely the c.e. degrees.