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DNA carries more than the list of biochemical ingredients that drive the basic functions of living systems. The sequence of base pairs includes a multitude of structural and energetic signals, which determine the degree to which the long, threadlike molecule moves and how it responds to proteins and other molecules that control its processing and govern its packaging. The chemical composition of base pairs directs the spatial disposition and fluctuations of successive residues. The observed arrangements of these moieties in high-resolution protein–DNA crystal structures provide one of the best available estimates of the natural, sequence-dependent structure and deformability of the double-helical molecule. Here, we update the set of knowledge-based elastic potentials designed to describe the observed equilibrium structures and configurational fluctuations of the ten unique base-pair steps. The large number of currently available structures makes it possible to characterize the configurational preferences of the DNA base-pair steps within the context of their immediate neighbors, i.e., tetrameric context. Use of these knowledge-based potentials shows promise in accounting for known effects of sequence in long chain molecules, e.g., the degree of curvature reported in classic gel mobility studies and the recently reported sequence-dependent responses of supercoiled minicircles to nuclease cleavage. 

Physics-informed machine learning is emerging through vast methodologies and in various applications. This paper discovers physics-based custom loss functions as an implementable solution to additive manufacturing (AM). Specifically, laser metal deposition (LMD) is an AM process where a laser beam melts deposited powder, and the dissolved particles fuse to produce metal components. Porosity, or small cavities that form in this printed structure, is generally considered one of the most destructive defects in metal AM. Traditionally, computer tomography scans measure porosity. While this is useful for understanding the nature of pore formation and its characteristics, purely physics-driven models lack real-time prediction ability. Meanwhile, a purely deep learning approach to porosity prediction leaves valuable physics knowledge behind. In this paper, a hybrid model that uses both empirical and simulated LMD data is created to show how various physics-informed loss functions impact the accuracy, precision, and recall of a baseline deep learning model for porosity prediction. In particular, some versions of the physics-informed model can improve the precision of the baseline deep learning-only model (albeit at the expense of overall accuracy). 

A version of time-bounded Kolmogorov complexity, denoted KT, has received attention in the past several years, due to its close connection to circuit complexity and to the Minimum Circuit Size Problem MCSP. Essentially all results about the complexity of MCSP hold also for MKTP (the problem of computing the KT complexity of a string). Both MKTP and MCSP are hard for SZK (Statistical Zero Knowledge) under BPP-Turing reductions; neither is known to be NP-complete. Recently, some hardness results for MKTP were proved that are not (yet) known to hold for MCSP. In particular, MKTP is hard for DET (a subclass of P) under nonuniform ≤^{NC^0}_m reductions. In this paper, we improve this, to show that the complement of MKTP is hard for the (apparently larger) class NISZK_L under not only ≤^{NC^0}_m reductions but even under projections. Also, the complement of MKTP is hard for NISZK under ≤^{P/poly}_m reductions. Here, NISZK is the class of problems with non-interactive zero-knowledge proofs, and NISZK_L is the non-interactive version of the class SZK_L that was studied by Dvir et al. As an application, we provide several improved worst-case to average-case reductions to problems in NP, and we obtain a new lower bound on MKTP (which is currently not known to hold for MCSP).