Nanocrystalline domains can be used to create robust anti-fatigue-fracture hydrogels for artificial cartilages and soft robots.

Slippery and hydrophilic surfaces find critical applications in areas as diverse as biomedical devices, microfluidics, antifouling, and underwater robots. Existing methods to achieve such surfaces rely mostly on grafting hydrophilic polymer brushes or coating hydrogel layers, but these methods suffer from several limitations. Grafted polymer brushes are prone to damage and do not provide sufficient mechanical compliance due to their nanometer‐scale thickness. Hydrogel coatings are applicable only for relatively simple geometries, precluding their use for the surfaces with complex geometries and features. Here, a new method is proposed to interpenetrate hydrophilic polymers into the surface of diverse polymers with arbitrary shapes to form naturally integrated “hydrogel skins.” The hydrogel skins exhibit tissue‐like softness (Young's modulus ≈ 30 kPa), have uniform and tunable thickness in the range of 5–25 µm, and can withstand prolonged shearing forces with no measurable damage. The hydrogel skins also provide superior low‐friction, antifouling, and ionically conductive surfaces to the polymer substrates without compromising their original mechanical properties and geometry. Applications of the hydrogel skins on inner and outer surfaces of various practical polymer devices including medical tubing, Foley catheters, cardiac pacemaker leads, and soft robots on massive scales are further demonstrated.

The adhesion of soft connective tissues (tendons, ligaments, and cartilages) on bones in many animals can maintain high toughness (∽800 J m−2) over millions of cycles of mechanical loads. Such fatigue-resistant adhesion has not been achieved between synthetic hydrogels and engineering materials, but is highly desirable for diverse applications such as artificial cartilages and tendons, robust antifouling coatings, and hydrogel robots. Inspired by the nanostructured interfaces between tendons/ligaments/cartilages and bones, we report that bonding ordered nanocrystalline domains of synthetic hydrogels on engineering materials can give a fatigue-resistant adhesion with an interfacial fatigue threshold of 800 J m−2, because the fatigue-crack propagation at the interface requires a higher energy to fracture the ordered nanostructures than amorphous polymer chains. Our method enables fatigue-resistant hydrogel coatings on diverse engineering materials with complex geometries. We further demonstrate that the fatigue-resistant hydrogel coatings exhibit low friction and low wear against natural cartilages.

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Nonnegative matrix factorization (NMF) and symmetric NMF (SymNMF) have been shown to be effective for clustering linearly separable data and nonlinearly separable data, respectively. Nevertheless, many practical applications demand constrained algorithms in which a small number of constraints in the form of must-link and cannot-link are available. In this paper, we propose an NMF-based constrained clustering framework in which the similarity between two points on a must-link is enforced to approximate 1 and the similarity between two points on a cannot-link is enforced to approximate 0. We then formulate the framework using NMF and SymNMF to deal with clustering of linearly separable data and nonlinearly separable data, respectively. Furthermore, we present multiplicative update rules to solve them and show the correctness and convergence. Experimental results on various text data sets, University of California, Irvine (UCI) data sets, and gene expression data sets demonstrate the superiority of our algorithms over existing constrained clustering algorithms.