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We introduce three new nonlinear continuous data assimilation algorithms. These models are compared with the linear continuous data assimilation algorithm introduced by Azouani, Olson, and Titi (AOT). As a proof-of-concept for these models, we computationally investigate these algorithms in the context of the 1D Kuramoto-Sivashinsky equations. We observe that the nonlinear models experience super-exponential convergence in time, and converge to machine precision significantly faster than the linear AOT algorithm in our tests. For both simplicity and completeness, we provide the key analysis of the exponential-in-time convergence in the linear case. 

Beneficial relationships between animals and microbial organisms (symbionts) are ubiquitous in nature. In the ocean, microbial symbionts are typically acquired from the environment and their composition across geographic locations is often shaped by adaptation to local habitat conditions. However, it is currently unknown how generalizable these patterns are across symbiotic systems that have contrasting ecological characteristics. To address this question, we compared symbiont population structure between deep-sea hydrothermal vent mussels and co-occurring but ecologically distinct snail species. Our analyses show that mussel symbiont populations are less partitioned by geography and do not demonstrate evidence for environmental adaptation. We posit that the mussel's mixotrophic feeding mode may lower its need to affiliate with locally adapted symbiont strains, while microhabitat stability and symbiont genomic mixing likely favors persistence of symbiont strains across geographic locations. Altogether, these findings further our understanding of the mechanisms shaping symbiont population structure in marine environmentally transmitted symbioses. 

Abstract The current United Nations Decade of Ocean Science for Sustainable Development (2021–2030; hereafter, the Decade) offers a unique opportunity and framework to globally advance ocean science and policy. Achieving meaningful progress within the Decade requires collaboration and coordination across Decade Actions (Programs, Projects, and Centres). This coordination is particularly important for the deep ocean, which remains critically under‐sampled compared to other ecosystems. Despite the limited sampling, the deep ocean accounts for over 95% of Earth's habitable space, plays a crucial role in regulating the carbon cycle and global temperatures, and supports diverse ecosystems. To collectively advance deep‐ocean science, we gathered representatives from 20 Decade Actions that focus at least partially on the deep ocean. We identified five broad themes that aim to advance deep‐ocean science in alignment with the Decade's overarching 10 Challenges: natural capital and the blue economy, biodiversity, deep‐ocean observing, best practices in data sharing, and capacity building. Within each theme, we propose concrete objectives (termed Cohesive Asks) and milestones (Targets) for the deep‐ocean community. Developing these Cohesive Asks and Targets reflects a commitment to better coordination across deep‐ocean Decade Actions. We aim to build bridges across deep‐ocean disciplines, which encompass natural science, ocean observing, policy, and capacity development.