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Abstract Mount Elbrus, Europe's tallest and largely glaciated volcano, is made of silicic lavas and is known for Holocene eruptions, but the size and state of its magma chamber remain poorly constrained. We report high spatial resolution U–Th–Pb zircon ages, co-registered with oxygen and hafnium isotopic values, span ~ 0.6 Ma in each lava, documenting magmatic initiation that forms the current edifice. The best-fit thermochemical modeling constrains magmatic fluxes at 1.2 km 3 /1000 year by hot (900 °C), initially zircon-undersaturated dacite into a vertically extensive magma body since ~ 0.6 Ma, whereas a volcanic episode with eruptible magma only extends over the past 0.2 Ma, matching the age of oldest lavas. Simulations explain the total magma volume of ~ 180 km 3 , temporally oscillating δ 18 O and εHf values, and a wide range of zircon age distributions in each sample. These data provide insights into the current state (~ 200 km 3 of melt in a vertically extensive system) and the potential for future activity of Elbrus calling for much-needed seismic imaging. Similar zircon records worldwide require continuous intrusive activity by magmatic accretion of silicic magmas generated at depths, and that zircon ages do not reflect eruption ages but predate them by ~ 10 3 to 10 5  years reflecting protracted dissolution–crystallization histories. 

Why the Challenger Deep, the deepest point on Earth’s solid surface, is so deep is unclear, but part of the reason must be the age and density of the downgoing plate. Northwest Pacific oceanic crust subducting in the Izu-Bonin-Mariana Trench is Cretaceous and Jurassic, but the age and nature of Pacific oceanic crust subducting in the southernmost Mariana Trench remains unknown. Here we present the first study of seafloor basalts recovered by the full-ocean-depth crewed submersible Fendouzhe from the deepest seafloor around the Challenger Deep, from both the overriding and downgoing plates. 40Ar/39Ar ages indicate that downgo¬ing basalts are Early Cretaceous (ca. 125 Ma), indicating they are part of the Pacific plate rather than the nearby Oligocene Caroline microplate. Downgoing-plate basalts are slightly enriched in incompatible elements but have similar trace element and Hf isotope compositions to other northwest Pacific mid-ocean ridge basalts (MORBs). They also have slightly enriched Sr-Nd-Pb isotope compositions like those of the Indian mantle domain. These features may have formed with contributions from plume-derived components via plume-ridge interac¬tions. One sample from the overriding plate gives an 40Ar/39Ar age of ca. 55 Ma, about the same age as subduction initiation, to form the Izu-Bonin-Mariana convergent margin. Our results suggest that 50%–90% of the Pb budget of Mariana arc magmas is derived from the subducted MORBs with Indian-type isotope affinity. 

In a multi-agent path finding (MAPF) problem, the task is to move a set of agents to their goal locations without conflicts. In the real world, unexpected events may delay some of the agents. In this paper, we therefore study the problem of finding a p-robust solution to a given MAPF problem, which is a solution that succeeds with probability at least p, even though unexpected delays may occur. We propose two methods for verifying that given solutions are p-robust. We also introduce an optimal CBS-based algorithm, called pR-CBS, and a fast suboptimal algorithm, called pR-GCBS, for finding such solutions. Our experiments show that a p-robust solution reduces the number of conflicts compared to optimal, non-robust solutions. 

The MAPF problem is the fundamental problem of planning paths for multiple agents, where the key constraint is that the agents will be able to follow these paths concurrently without colliding with each other. Applications of MAPF include automated warehouses and autonomous vehicles. Research on MAPF has been flourishing in the past couple of years. Different MAPF research papers make different assumptions, e.g., whether agents can traverse the same road at the same time, and have different objective functions, e.g., minimize makespan or sum of agents' actions costs. These assumptions and objectives are sometimes implicitly assumed or described informally. This makes it difficult to establish appropriate baselines for comparison in research papers, as well as making it difficult for practitioners to find the papers relevant to their concrete application. This paper aims to fill this gap and support researchers and practitioners by providing a unifying terminology for describing common MAPF assumptions and objectives. In addition, we also provide pointers to two MAPF benchmarks. In particular, we introduce a new grid-based benchmark for MAPF, and demonstrate experimentally that it poses a challenge to contemporary MAPF algorithms.