One of the main reasons why computations-in particular, engineering computations-take long is that, to be on the safe side, models take into account all possible affecting features, most of which turn out to be not really relevant for the corresponding physical problem. From this viewpoint, it is desirable to find out which inputs are relevant. In general, the problem of checking the input's relevancy is itself NP-hard, which means, crudely speaking, that no feasible algorithm can always solve it. Thus, it is desirable to speed up this checking as much as possible. One possible way to speed up such a checking is to use quantum computing, namely, to use the Deutsch-Josza algorithm. However, this algorithm is just a way to solve this problem, it is not clear whether a more efficient (or even different) quantum algorithm is possible for solving this problem. In this paper, we show that the Deutsch-Josza algorithm is, in effect, the only possible way to use quantum computing for checking which inputs are relevant.
Deoxyribonucleic acid (DNA) origami is a method for the bottom-up self-assembly of complex nanostructures for applications, such as biosensing, drug delivery, nanopore technologies, and nanomechanical devices. Effective design of such nanostructures requires a good understanding of their mechanical behavior. While a number of studies have focused on the mechanical properties of DNA origami structures, considering defects arising from molecular self-assembly is largely unexplored. In this paper, we present an automated computational framework to analyze the impact of such defects on the structural integrity of a model DNA origami nanoplate. The proposed computational approach relies on a noniterative conforming to interface-structured adaptive mesh refinement (CISAMR) algorithm, which enables the automated transformation of a binary image of the nanoplate into a high fidelity finite element model. We implement this technique to quantify the impact of defects on the mechanical behavior of the nanoplate by performing multiple simulations taking into account varying numbers and spatial arrangements of missing DNA strands. The analyses are carried out for two types of loading: uniform tensile displacement applied on all the DNA strands and asymmetric tensile displacement applied to strands at diagonal corners of the nanoplate.
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