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We demonstrate that a convex combination of the Nagumo and Perron growth conditions guarantees the existence of a unique solution to an ordinary differential equation, which can be obtained as the uniform limit of a sequence of successive approximations. Furthermore, we give a sufficient condition for the pathwise uniqueness of solutions to stochastic differential equations driven by Brownian motions. [ABSTRACT FROM AUTHOR]

Implantable biomedical patch used in treating abdominal wall defects requires antibacterial, anti‐adhesion, and pro‐healing activities to ensure surgical success and prevent postsurgical complications. However, it often encounters challenges in fulfilling these three critical properties simultaneously, as these processes can always be contradictory during treatment. Herein, to break the barriers between bactericidal activity and cytocompatibility, cell adhesion and anti‐adhesion, a bio‐inspired patch with an asymmetric Janus structure is developed. This bio‐inspired Janus patch features cicada wing‐inspired nanostructures on its top surface, enabling both mechano–bactericidal effects and promotion of fibroblast adhesion and proliferation, which stems from its inherent “selective biocidal activity” toward bacteria and mammalian cells. Subsequently, a poly‐zwitterion layer with robust nonfouling properties is grafted on the bottom surface, realizing cell adhesion and anti‐adhesion on two sides of the same patch. Compared to the commercially available polypropylene (PP) meshes, the top surface of the Janus patch, which faces the abdominal wall, demonstrates superior capabilities in preventing postoperative infection and promoting tissue repair. Simultaneously, the other side facing the viscera efficiently prevents any visceral tissue adhesion. With these prominent performances, the bio‐inspired Janus patch presents a pioneering strategy for designing next‐generation patches to treat abdominal wall defects. [ABSTRACT FROM AUTHOR]

Hyaluronic acid (HA) hydrogels have arisen as candidate materials to simulate the extracellular matrix and restore the functions of both cartilage and hard bones. However, integration of bone tissue adhesion and long-term osteogenic properties in one hydrogel is often ignored. Herein, a strategy to construct nanocomposite hydrogel with host tissue adhesive properties, enhanced mechanical strength, improved stability and osteogenic effects was developed. Simvastatin (SIM) was firstly incorporated into zeolitic imidazolate framework-8 (ZIF-8) and surface decoration with hydroxyapatite was realized to obtain SIM loaded and hydroxyapatite modified ZIF-8 particles (SP). As the inorganic strengthening component, SP could further cross-link the mixture of dopamine-hyaluronic acid (dHA) and tannic (TA) via coordination interaction to fabricate the hybrid adhesive hydrogel (dHA/TA/SP). Sufficient phenolic groups endowed dHA/TA/SP with excellent tissue adhesion and antibacterial properties, while incorporation of SP significantly improved the mechanical strength and stability of hydrogel. Further, due to the multiple protective effects of ZIF-8 and hydrogel, SIM was sustainably released from dHA/TA/SP. Together with the active Zn2+ and Ca2+, the expressions of ALP, OCN and RUNX2 were upregulated, and the mineralization was also promoted. With significant osteogenic effect in vitro and in vivo, this nanocomposite adhesive hydrogel holds great potential for bone defects repair. [Display omitted] [ABSTRACT FROM AUTHOR]

Hyaluronic acid (HA) hydrogels have arisen as candidate materials to simulate the extracellular matrix and restore the functions of both cartilage and hard bones. However, integration of bone tissue adhesion and long-term osteogenic properties in one hydrogel is often ignored. Herein, a strategy to construct nanocomposite hydrogel with host tissue adhesive properties, enhanced mechanical strength, improved stability and osteogenic effects was developed. Simvastatin (SIM) was firstly incorporated into zeolitic imidazolate framework-8 (ZIF-8) and surface decoration with hydroxyapatite was realized to obtain SIM loaded and hydroxyapatite modified ZIF-8 particles (SP). As the inorganic strengthening component, SP could further cross-link the mixture of dopamine-hyaluronic acid (dHA) and tannic (TA) via coordination interaction to fabricate the hybrid adhesive hydrogel (dHA/TA/SP). Sufficient phenolic groups endowed dHA/TA/SP with excellent tissue adhesion and antibacterial properties, while incorporation of SP significantly improved the mechanical strength and stability of hydrogel. Further, due to the multiple protective effects of ZIF-8 and hydrogel, SIM was sustainably released from dHA/TA/SP. Together with the active Zn2+ and Ca2+, the expressions of ALP, OCN and RUNX2 were upregulated, and the mineralization was also promoted. With significant osteogenic effect in vitro and in vivo, this nanocomposite adhesive hydrogel holds great potential for bone defects repair. [Display omitted] [ABSTRACT FROM AUTHOR]

Owing to the limited natural distributions and special medicine-industrial values of Viola philippica , it's urgently needed to explore its population-level differences for promoting the resource utilization efficiencies of this plant. The hypothesis of this study was that different populations of V. philippica plants would have broad-scale differences and interactions of leaf-accumulated metabolites and leaf-colonized bacteria. Hence, two populations (vi-p and vi-j) of this plant were typically collected in China for analyzing multiomics. At first, vi-p and vi-j leaf metabolomes (LMs) were presented with 1,003 metabolites; in contrast of vi-p-LMs, 445 differently accumulated metabolites (DAMs) were identified in vi-j-LMs, with the only up-regulated lipids, vitamin and ketone compounds, the only down-regulated aldehyde compounds, the most up-regulated flavonoids, and the most down-regulated phenylpropanoid compounds. In comparative of vi-p leaf transcriptomes (LTs), 4,645 differently expressed genes (DEGs) were identified in vi-j-LTs, which were typically involved in a series of extracellular defenses and secondary metabolic pathways; the DEGs were frequently co-enriched with DAMs in three biosynthesis pathways of phenylpropanoid, flavonoid, and α-linolenic acid. Furthermore, these DAMs were also found to have the significant correlations with some different types or/and abundances of leaf-assembled bacteria (DTAB) between vi-p and vi-j leaf-assembled bacterial communities (LABCs). Taken together, this study reveals the broad-scale patterns of regulating vi-p and vi-j leaf DAMs with DEGs and DTAB, suggesting that it's essential of keeping plant-population and -habitat diversities for harvesting population-level DAMs in V. philippica. • The plant-level functional metabolites were integrally uncovered in V. philippica. • Two plant populations were identified with differently accumulated metabolites (DAMs). • The typical DAMs were co-enriched with differently expressed genes (DEGs). • These DAMs were also correlated with different types or/and abundances bacteria (DTAB). [ABSTRACT FROM AUTHOR]