Minimizers are widely used to sample representative k -mers from biological sequences in many applications, such as read mapping and taxonomy prediction. In most scenarios, having the minimizer scheme select as few k -mer positions as possible (i.e., having a low density) is desirable to reduce computation and memory cost. Despite the growing interest in minimizers, learning an effective scheme with optimal density is still an open question, as it requires solving an apparently challenging discrete optimization problem on the permutation space of k -mer orderings. Most existing schemes are designed to work well in expectation over random sequences, which have limited applicability to many practical tools. On the other hand, several methods have been proposed to construct minimizer schemes for a specific target sequence. These methods, however, only approximate the original objective with likewise discrete surrogate tasks that are not able to significantly improve the density performance. This article introduces the first continuous relaxation of the density minimizing objective, DeepMinimizer , which employs a novel Deep Learning twin architecture to simultaneously ensure both validity and performance of the minimizer scheme. Our surrogate objective is fully differentiable and, therefore, amenable to efficient gradient-based optimization using GPU computing. Finally, we demonstrate that DeepMinimizer discovers minimizer schemes that significantly outperform state-of-the-art constructions on human genomic sequences.

A model‐based experimental design is formulated and solved as a large‐scale NLP problem. The key idea of the proposed approach is the extension of model equations with sensitivity equations forming an extended sensitivities‐state equation system. The resulting system is then totally discretized and simultaneously solved as constraints of the NLP problem. Thereby, higher derivatives of the parameter sensitivities with respect to the control variables are directly calculated and exact. This is an advantage in comparison with proposed sequential approaches to model‐based experimental design so far, where these derivatives have to be additionally integrated throughout the optimization steps. This can end up in a high‐computational load especially for systems with many control variables. Furthermore, an advanced sampling strategy is proposed which combines the strength of the optimal sampling design and the variation of the collocation element lengths while fully using the entire optimization space of the simultaneous formulation. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4169–4183, 2013

Minimizers are k-mer sampling schemes designed to generate sketches for large sequences that preserve sufficiently long matches between sequences. Despite their widespread application, learning an effective minimizer scheme with optimal sketch size is still an open question. Most work in this direction focuses on designing schemes that work well on expectation over random sequences, which have limited applicability to many practical tools. On the other hand, several methods have been proposed to construct minimizer schemes for a specific target sequence. These methods, however, require greedy approximations to solve an intractable discrete optimization problem on the permutation space of k-mer orderings. To address this challenge, we propose: (a) a reformulation of the combinatorial solution space using a deep neural network reparameterization; and (b) a fully differentiable approximation of the discrete objective. We demonstrate that our framework, DeepMinimizer, discovers minimizer schemes that significantly outperform state-of-the-art constructions on genomic sequences.

No abstract

No abstract