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Time dependent observations of point-to-point correlations of the velocity vector field (structure functions) are necessary to model and understand fluid flow around complex objects. Using thermal gradients, we observed fluid flow by recording fluorescence of$${\text{He}}_{2}^{*}$$${\text{He}}_2^{\ast }$excimers produced by neutron capture throughout a ~ cm³volume. Because the photon emitted by an excited excimer is unlikely to be recorded by the camera, the techniques of particle tracking (PTV) and particle imaging (PIV) velocimetry cannot be applied to extract information from the fluorescence of individual excimers. Therefore, we applied an unsupervised machine learning algorithm to identify light from ensembles of excimers (clusters) and then tracked the centroids of the clusters using a particle displacement determination algorithm developed for PTV.

 

Motivated by robust dynamic resource allocation in operations research, we study the Online Learning to Transport (OLT) problem where the decision variable is a probability measure, an infinite-dimensional object. We draw connections between online learning, optimal transport, and partial differential equations through an insight called the minimal selection principle, originally studied in the Wasserstein gradient flow setting by Ambrosio et al. (2005). This allows us to extend the standard online learning framework to the infinite-dimensional setting seamlessly. Based on our framework, we derive a novel method called the minimal selection or exploration (MSoE) algorithm to solve OLT problems using mean-field approximation and discretization techniques. In the displacement convex setting, the main theoretical message underpinning our approach is that minimizing transport cost over time (via the minimal selection principle) ensures optimal cumulative regret upper bounds. On the algorithmic side, our MSoE algorithm applies beyond the displacement convex setting, making the mathematical theory of optimal transport practically relevant to non-convex settings common in dynamic resource allocation. 

Variations in the Atlantic Meridional Overturning Circulation (AMOC) redistribute heat and nutrients, causing pronounced anomalies of temperature and nutrient concentrations in the subsurface ocean. However, exactly how millennial‐scale deglacial AMOC variability influenced the subsurface is debated, and the role of other deglacial forcings of subsurface temperature change is unclear. Here, we present a new deglacial temperature reconstruction, which, with published records, helps assess competing hypotheses for deglacial warming in the upper tropical North Atlantic. Our record provides new evidence of regional subsurface warming in the western tropical North Atlantic within the core of modern Antarctic Intermediate Water (AAIW) during Heinrich Stadial 1 (HS1), an early deglacial interval of iceberg discharge into the North Atlantic. Our results are consistent with model simulations that suggest subsurface heat accumulates in the northern high‐latitude convection regions and along the upper AMOC return path when the AMOC weakens, and with warming due to rising greenhouse gases. Warming of AAIW may have also contributed to warming in the tropics at modern AAIW depths during late HS1. Nutrient andreconstructions from the same site suggest a link between AMOC intensity and the northward extent of AAIW in the northern tropics across the deglaciation and on millennial time scales. However, the timing of the initial deglacial increase in AAIW to the northern tropics is ambiguous. Deglacial trends and variability ofin the upper North Atlantic have likely biased temperature reconstructions based on the elemental composition of calcitic benthic foraminifera.