123,459 research outputs found
Quantitative toxicity prediction using topology based multi-task deep neural networks
The understanding of toxicity is of paramount importance to human health and
environmental protection. Quantitative toxicity analysis has become a new
standard in the field. This work introduces element specific persistent
homology (ESPH), an algebraic topology approach, for quantitative toxicity
prediction. ESPH retains crucial chemical information during the topological
abstraction of geometric complexity and provides a representation of small
molecules that cannot be obtained by any other method. To investigate the
representability and predictive power of ESPH for small molecules, ancillary
descriptors have also been developed based on physical models. Topological and
physical descriptors are paired with advanced machine learning algorithms, such
as deep neural network (DNN), random forest (RF) and gradient boosting decision
tree (GBDT), to facilitate their applications to quantitative toxicity
predictions. A topology based multi-task strategy is proposed to take the
advantage of the availability of large data sets while dealing with small data
sets. Four benchmark toxicity data sets that involve quantitative measurements
are used to validate the proposed approaches. Extensive numerical studies
indicate that the proposed topological learning methods are able to outperform
the state-of-the-art methods in the literature for quantitative toxicity
analysis. Our online server for computing element-specific topological
descriptors (ESTDs) is available at http://weilab.math.msu.edu/TopTox/Comment: arXiv admin note: substantial text overlap with arXiv:1703.1095
Quantized Gromov-Hausdorff distance
A quantized metric space is a matrix order unit space equipped with an
operator space version of Rieffel's Lip-norm. We develop for quantized metric
spaces an operator space version of quantum Gromov-Hausdorff distance. We show
that two quantized metric spaces are completely isometric if and only if their
quantized Gromov-Hausdorff distance is zero. We establish a completeness
theorem. As applications, we show that a quantized metric space with 1-exact
underlying matrix order unit space is a limit of matrix algebras with respect
to quantized Gromov-Hausdorff distance, and that matrix algebras converge
naturally to the sphere for quantized Gromov-Hausdorff distance.Comment: 34 pages. An oversight appeared in Proposition 4.9 of Version 1. This
proposition has been deleted. Also some type errors have been correcte
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