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In this study, we propose iDNA-ABF, a multi-scale deep biological language learning model that enables the interpretable prediction of DNA methylations based on genomic sequences only. Benchmarking comparisons show that our iDNA-ABF outperforms state-of-the-art methods for different methylation predictions. Importantly, we show the power of deep language learning in capturing both sequential and functional semantics information from background genomes. Moreover, by integrating the interpretable analysis mechanism, we well explain what the model learns, helping us build the mapping from the discovery of important sequential determinants to the in-depth analysis of their biological functions.

The first-passage failure of single-degree-of-freedom nonlinear oscillators with fractional derivative under Gaussian white noise excitations is studied. First, the term associated with fractional derivative is approximately equivalent to amplitude-dependent quasi-linear damping and stiffness forces by using the generalized harmonic balance technique and the given system is replaced by an equivalent nonlinear stochastic system without fractional derivative. Then, the equivalent nonlinear stochastic system state is approximately represented by a one-dimensional diffusive process through stochastic averaging. The backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the conditional mean of first-passage time are established from the averaged Itô equation of the total energy and solved numerically, respectively. Finally, two examples are worked out in detail and the analytical results are validated by those from the Monte Carlo simulation of original systems.

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Recently, machine learning methods have been developed to identify various peptide bio-activities. However, due to the lack of experimentally validated peptides, machine learning methods cannot provide a sufficiently trained model, easily resulting in poor generalizability. Furthermore, there is no generic computational framework to predict the bioactivities of different peptides. Thus, a natural question is whether we can use limited samples to build an effective predictive model for different kinds of peptides. To address this question, we propose Mutual Information Maximization Meta-Learning (MIMML), a novel meta-learning-based predictive model for bioactive peptide discovery. Using few samples from various functional peptides, MIMML can sufficiently learn the discriminative information amongst various functions and characterize functional differences. Experimental results show excellent performance of MIMML though using far fewer training samples as compared to the state-of-the-art methods. We also decipher the latent relationships among different kinds of functions to understand what meta-model learned to improve a specific task. In summary, this study is a pioneering work in the field of functional peptide mining and provides the first-of-its-kind solution for few-sample learning problems in biological sequence analysis, accelerating the new functional peptide discovery. The source codes and datasets are available on https://github.com/TearsWaiting/MIMML.