Global integrability for solutions to boundary value problems of anisotropic functionals

This paper deals with solutions to boundary value problems of anisotropic integral functionals I(u) = ∫Ω f(x,Du(x))dx, with the energy f(x,z) has growth pi with respect to zi, like in ∫Ω ((1+∑j=1n |Dju|pj )(p1-2)/p1 |D1u|2 + ⋯ + (1+∑j=1n |Dju|pj )(pn-2)/pn |Dnu|2) dx. We show that higher integrability of the boundary datum u* forces minimizers u to be more integrable. A similar result is obtained for obstacle problems

A comprehensive review of the recent advances on predicting drug-target affinity based on deep learning

Accurate calculation of drug-target affinity (DTA) is crucial for various applications in the pharmaceutical industry, including drug screening, design, and repurposing. However, traditional machine learning methods for calculating DTA often lack accuracy, posing a significant challenge in accurately predicting DTA. Fortunately, deep learning has emerged as a promising approach in computational biology, leading to the development of various deep learning-based methods for DTA prediction. To support researchers in developing novel and highly precision methods, we have provided a comprehensive review of recent advances in predicting DTA using deep learning. We firstly conducted a statistical analysis of commonly used public datasets, providing essential information and introducing the used fields of these datasets. We further explored the common representations of sequences and structures of drugs and targets. These analyses served as the foundation for constructing DTA prediction methods based on deep learning. Next, we focused on explaining how deep learning models, such as Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), Transformer, and Graph Neural Networks (GNNs), were effectively employed in specific DTA prediction methods. We highlighted the unique advantages and applications of these models in the context of DTA prediction. Finally, we conducted a performance analysis of multiple state-of-the-art methods for predicting DTA based on deep learning. The comprehensive review aimed to help researchers understand the shortcomings and advantages of existing methods, and further develop high-precision DTA prediction tool to promote the development of drug discovery

Cardioid oscillator-based pattern generator for imitating the time-ratio-asymmetrical behavior of the lower limb exoskeleton

IntroductionPeriodicity, self-excitation, and time ratio asymmetry are the fundamental characteristics of the human gait. In order to imitate these mentioned characteristics, a pattern generator with four degrees of freedom is proposed based on cardioid oscillators developed by the authors.MethodThe proposed pattern generator is composed of four coupled cardioid oscillators, which are self-excited and have asymmetric time ratios. These oscillators are connected with other oscillators through coupled factors. The dynamic behaviors of the proposed oscillators, such as phase locking, time ratio, and self-excitation, are analyzed via simulations by employing the harmonic balance method. Moreover, for comparison, the simulated trajectories are compared with the natural joint trajectories measured in experiments.Results and discussionSimulation and experimental results show that the behaviors of the proposed pattern generator are similar to those of the natural lower limb. It means the simulated trajectories from the generator are self-excited without any additional inputs and have asymmetric time ratios. Their phases are locked with others. Moreover, the proposed pattern generator can be applied as the reference model for the lower limb exoskeleton controlling algorithm to produce self-adjusted reference trajectories