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causal relationships between evolution and oxygenation of the ocean are
vigorously debated. At the heart of these uncertainties are inconsistencies
among reconstructed timelines for the rise of O2 in marine habitats. Attempts to
reconstruct the timing of marine oxygenation are often based on redox-sensitive
geochemical proxies that are prone to post-depositional alteration. Thus,
developing new proxies, more resistant to such alteration, is an important
direction forward for constraining major changes in atmospheric and marine
oxygen levels. Here, we utilize U–Pb dating in dolomite to reconstruct their
(re)crystallization ages and initial 207Pb/206Pb ratios; we find that they are
systematically younger and lower than expected, respectively. These
observations are explained by the resetting of the U–Pb system long after
deposition, followed by further evolution in a closed system. Initial 207Pb/206Pb
ratios have decreased from expected terrestrial values in the interval between
deposition and (re)crystallization, consistent with U decay, and can therefore be
used to reconstruct the initial 238U/206Pb ratios during deposition. Within our
dataset initial 238U/206Pb ratios remained low in Proterozoic to mid-Paleozoic
samples and increased dramatically in samples from the late-Paleozoic–early-
Mesozoic Eras. This rise is attributed to a higher ratio of U to Pb in seawater that
in turn influenced the fluid composition of carbonate crystallization sites.
Accordingly, we interpret the temporal shift in initial 238U/206Pb ratios to reflect
a late-Paleozoic increase in oxygenation of marine environments, corroborating
previously documented shifts in some redox-sensitive proxies. This timeline is
consistent with evolution-driven mechanisms for the oxygenation of late
Paleozoic marine environments and with suggestions that Neoproterozoic and
early Paleozoic animals thrived in oceans that overall and on long time scales
were oxygen-limited compared to the modern ocean.

I will discuss some well-known and less-known papers of Turing, exemplify the scope of deep, prescient ideas he put forth, and mention follow-up work on these by the Theoretical CS community.

No special background will be assumed.

Sparse principal component analysis (PCA) is a powerful method for low-rank and sparse signal recovery, applicable to covariance estimation, dimension reduction, and feature selection. In this work, we study a generalization of the covariance-thresholding approach to sparse PCA, improving results of R. Krauthgamer, B. Nadler, D. Vilenchik (2015), and Y. Deshpande, A. Montanari (2016). Through random matrix theory, we identify novel phase transition phenomena in high dimensions, providing insight into the limits of signal and support recovery. Our results rely on new concentration bounds for quadratic forms of kernel matrices, which are of independent interest. This research is a collaboration with Theodor Misiakiewicz (Yale) and Elad Romanov (Stanford).