Faster Min-Plus Product for Monotone Instances

In this paper, we show that the time complexity of monotone min-plus product of two $n\times n$ matrices is $\tilde{O}(n^{(3+\omega)/2})=\tilde{O}(n^{2.687})$, where $\omega < 2.373$ is the fast matrix multiplication exponent [Alman and Vassilevska Williams 2021]. That is, when $A$ is an arbitrary integer matrix and $B$ is either row-monotone or column-monotone with integer elements bounded by $O(n)$, computing the min-plus product $C$ where $C_{i,j}=\min_k\{A_{i,k}+B_{k,j}\}$ takes $\tilde{O}(n^{(3+\omega)/2})$ time, which greatly improves the previous time bound of $\tilde{O}(n^{(12+\omega)/5})=\tilde{O}(n^{2.875})$ [Gu, Polak, Vassilevska Williams and Xu 2021]. Then by simple reductions, this means the following problems also have $\tilde{O}(n^{(3+\omega)/2})$ time algorithms: (1) $A$ and $B$ are both bounded-difference, that is, the difference between any two adjacent entries is a constant. The previous results give time complexities of $\tilde{O}(n^{2.824})$ [Bringmann, Grandoni, Saha and Vassilevska Williams 2016] and $\tilde{O}(n^{2.779})$ [Chi, Duan and Xie 2022]. (2) $A$ is arbitrary and the columns or rows of $B$ are bounded-difference. Previous result gives time complexity of $\tilde{O}(n^{2.922})$ [Bringmann, Grandoni, Saha and Vassilevska Williams 2016]. (3) The problems reducible to these problems, such as language edit distance, RNA-folding, scored parsing problem on BD grammars. [Bringmann, Grandoni, Saha and Vassilevska Williams 2016]. Finally, we also consider the problem of min-plus convolution between two integral sequences which are monotone and bounded by $O(n)$, and achieve a running time upper bound of $\tilde{O}(n^{1.5})$. Previously, this task requires running time $\tilde{O}(n^{(9+\sqrt{177})/12}) = O(n^{1.859})$ [Chan and Lewenstein 2015].Comment: 26 page

Rapid oxygenation of Earths atmosphere 2.33 billion years ago

Molecular oxygen (O[subscript 2]) is, and has been, a primary driver of biological evolution and shapes the contemporary landscape of Earth’s biogeochemical cycles. Although “whiffs” of oxygen have been documented in the Archean atmosphere, substantial O2 did not accumulate irreversibly until the Early Paleoproterozoic, during what has been termed the Great Oxygenation Event (GOE). The timing of the GOE and the rate at which this oxygenation took place have been poorly constrained until now. We report the transition (that is, from being mass-independent to becoming mass-dependent) in multiple sulfur isotope signals of diagenetic pyrite in a continuous sedimentary sequence in three coeval drill cores in the Transvaal Supergroup, South Africa. These data precisely constrain the GOE to 2.33 billion years ago. The new data suggest that the oxygenation occurred rapidly—within 1 to 10 million years—and was followed by a slower rise in the ocean sulfate inventory. Our data indicate that a climate perturbation predated the GOE, whereas the relationships among GOE, “Snowball Earth” glaciation, and biogeochemical cycling will require further stratigraphic correlation supported with precise chronologies and paleolatitude reconstructions.National Science Foundation (U.S.) (EAR-1338810)National Natural Science Foundation (China) ((grant no. 41472170)Wellcome Trust Sanger Institute ( 111 Project grant no. B08030)National Basic Research Program of China (973 Program)United States. National Aeronautics and Space Administration (NASA Astrobiology Institute award NNA13AA90A

Response of carbon cycle to drier conditions in the mid-Holocene in central China

The effect of Asian summer monsoon hydrological changes on key biogeochemical processes remains poorly understood. Here, using a suite of biomarkers, the authors reconstruct palaeohydrological conditions during the Holocene and show that the peatland carbon cycle is strongly sensitive to paleohydrological changes

Nitrogen fixation sustained productivity in the wake of the Palaeoproterozoic Great Oxygenation Event

The marine nitrogen cycle is dominated by redox-controlled biogeochemical processes and, therefore, is likely to have been revolutionised in response to Earth-surface oxygenation. The details, timing, and trajectory of nitrogen cycle evolution, however, remain elusive. Here we couple nitrogen and carbon isotope records from multiple drillcores through the Rooihoogte–Timeball Hill Formations from across the Carletonville area of the Kaapvaal Craton where the Great Oxygenation Event (GOE) and its aftermath are recorded. Our data reveal that aerobic nitrogen cycling, featuring metabolisms involving nitrogen oxyanions, was well established prior to the GOE and that ammonium may have dominated the dissolved nitrogen inventory. Pronounced signals of diazotrophy imply a stepwise evolution, with a temporary intermediate stage where both ammonium and nitrate may have been scarce. We suggest that the emergence of the modern nitrogen cycle, with metabolic processes that approximate their contemporary balance, was retarded by low environmental oxygen availability

Nitrogen fixation sustained productivity in the wake of the Palaeoproterozoic Great Oxygenation Event

The marine nitrogen cycle is dominated by redox-controlled biogeochemical processes and, therefore, is likely to have been revolutionised in response to Earth-surface oxygenation. The details, timing, and trajectory of nitrogen cycle evolution, however, remain elusive. Here we couple nitrogen and carbon isotope records from multiple drillcores through the Rooihoogte-Timeball Hill Formations from across the Carletonville area of the Kaapvaal Craton where the Great Oxygenation Event (GOE) and its aftermath are recorded. Our data reveal that aerobic nitrogen cycling, featuring metabolisms involving nitrogen oxyanions, was well established prior to the GOE and that ammonium may have dominated the dissolved nitrogen inventory. Pronounced signals of diazotrophy imply a stepwise evolution, with a temporary intermediate stage where both ammonium and nitrate may have been scarce. We suggest that the emergence of the modern nitrogen cycle, with metabolic processes that approximate their contemporary balance, was retarded by low environmental oxygen availability.National Science Foundation (U.S.) (Grant EAR-1338810)National Science Foundation (U.S.) (Grant EAR-1455258