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We continue our investigation of viscoelasticity by extending the Holzapfel-Simo approach discussed in Part I to the fully nonlinear regime. By scrutinizing the relaxation property for the non-equilibrium stresses, it is revealed that a kinematic assumption akin to the Green-Naghdi type is necessary in the design of the potential. This insight underscores a link between the so-called additive plasticity and the viscoelasticity model under consideration, further inspiring our development of a nonlinear viscoelasticity theory. Our strategy is based on Hill's hyperelasticity framework and leverages the concept of generalized strains. Notably, the adopted kinematic assumption makes the proposed theory fundamentally different from the existing models rooted in the notion of the intermediate configuration. The computation aspects, including the consistent linearization, constitutive integration, and modular implementation, are addressed in detail. A suite of numerical examples is provided to demonstrate the capability of the proposed model in characterizing viscoelastic material behaviors at large strains.

Geometric deep learning has demonstrated a great potential in non-Euclidean data analysis. The incorporation of geometric insights into learning architecture is vital to its success. Here we propose a curvature-enhanced graph convolutional network (CGCN) for biomolecular interaction prediction, for the first time. Our CGCN employs Ollivier-Ricci curvature (ORC) to characterize network local structures and to enhance the learning capability of GCNs. More specifically, ORCs are evaluated based on the local topology from node neighborhoods, and further used as weights for the feature aggregation in message-passing procedure. Our CGCN model is extensively validated on fourteen real-world bimolecular interaction networks and a series of simulated data. It has been found that our CGCN can achieve the state-of-the-art results. It outperforms all existing models, as far as we know, in thirteen out of the fourteen real-world datasets and ranks as the second in the rest one. The results from the simulated data show that our CGCN model is superior to the traditional GCN models regardless of the positive-to-negativecurvature ratios, network densities, and network sizes (when larger than 500).

Geometric deep learning (GDL) models have demonstrated a great potential for the analysis of non-Euclidian data. They are developed to incorporate the geometric and topological information of non-Euclidian data into the end-to-end deep learning architectures. Motivated by the recent success of discrete Ricci curvature in graph neural network (GNNs), we propose TorGNN, an analytic Torsion enhanced Graph Neural Network model. The essential idea is to characterize graph local structures with an analytic torsion based weight formula. Mathematically, analytic torsion is a topological invariant that can distinguish spaces which are homotopy equivalent but not homeomorphic. In our TorGNN, for each edge, a corresponding local simplicial complex is identified, then the analytic torsion (for this local simplicial complex) is calculated, and further used as a weight (for this edge) in message-passing process. Our TorGNN model is validated on link prediction tasks from sixteen different types of networks and node classification tasks from three types of networks. It has been found that our TorGNN can achieve superior performance on both tasks, and outperform various state-of-the-art models. This demonstrates that analytic torsion is a highly efficient topological invariant in the characterization of graph structures and can significantly boost the performance of GNNs.

Geometric deep learning (GDL) has demonstrated huge power and enormous potential in molecular data analysis. However, a great challenge still remains for highly efficient molecular representations. Currently, covalent-bond-based molecular graphs are the de facto standard for representing molecular topology at the atomic level. Here we demonstrate, for the first time, that molecular graphs constructed only from non-covalent bonds can achieve similar or even better results than covalent-bond-based models in molecular property prediction. This demonstrates the great potential of novel molecular representations beyond the de facto standard of covalent-bond-based molecular graphs. Based on the finding, we propose molecular geometric deep learning (Mol-GDL). The essential idea is to incorporate a more general molecular representation into GDL models. In our Mol-GDL, molecular topology is modeled as a series of molecular graphs, each focusing on a different scale of atomic interactions. In this way, both covalent interactions and non-covalent interactions are incorporated into the molecular representation on an equal footing. We systematically test Mol-GDL on fourteen commonly-used benchmark datasets. The results show that our Mol-GDL can achieve a better performance than state-of-the-art (SOTA) methods. Source code and data are available at https://github.com/CS-BIO/Mol-GDL.

Motivation: Enhancers are important cis-regulatory elements that regulate a wide range of biological functions and enhance the transcription of target genes. Although many feature extraction methods have been proposed to improve the performance of enhancer identification, they cannot learn position-related multiscale contextual information from raw DNA sequences. Results: In this article, we propose a novel enhancer identification method (iEnhancer-ELM) based on BERT-like enhancer language models. iEnhancer-ELM tokenizes DNA sequences with multi-scale k-mers and extracts contextual information of different scale k-mers related with their positions via an multi-head attention mechanism. We first evaluate the performance of different scale k-mers, then ensemble them to improve the performance of enhancer identification. The experimental results on two popular benchmark datasets show that our model outperforms stateof-the-art methods. We further illustrate the interpretability of iEnhancer-ELM. For a case study, we discover 30 enhancer motifs via a 3-mer-based model, where 12 of motifs are verified by STREME and JASPAR, demonstrating our model has a potential ability to unveil the biological mechanism of enhancer. Availability and implementation: The models and associated code are available at https://github.com/chen-bioinfo/iEnhancer-ELM Contact: junjiechen@hit.edu.cn Supplementary information: Supplementary data are available at Bioinformatics Advances online., Comment: 8 pages, 5 figures. It is a new accepted version

Hard point-contact spectroscopy and scanning probe microscopy/spectroscopy are powerful techniques for investigating materials with strong expandability. To support these studies, tips with various physical and chemical properties are required. To ensure the reproducibility of experimental results, the fabrication of tips should be standardized, and a controllable and convenient system should be set up. Here a systematic methodology to fabricate various tips is proposed, involving electrochemical etching reactions. The reaction parameters fall into four categories: solution, power supply, immersion depth, and interruption. An etching system was designed and built so that these parameters could be accurately controlled. With this system, etching parameters for copper, silver, gold, platinum/iridium alloy, tungsten, lead, niobium, iron, nickel, cobalt, and permalloy were explored and standardized. Among these tips, silver and niobium's new recipes were explored and standardized. Optical and scanning electron microscopies were performed to characterize the sharp needles. Relevant point-contact experiments were carried out with an etched silver tip to confirm the suitability of the fabricated tips., Comment: The article has been accepted by Review of Scientific Instruments. After it is published, it will be found at https://aip.scitation.org/journal/rsi