Here, we test if time series clustering can identify emergent temporal patterns across multiple sites. For our study we examine patterns of carbon cycling in rivers because the lack of high frequency data has previously precluded examination of temporal patterns in these systems. While other systems have been described to exhibit a seasonal rhythm of carbon cycling in relation to their primary environmental forcings, rivers are unique in that they are subject to more stochastic processes. We attempt to identify discrete temporal regimes of carbon cycling in rivers and compare these to other systems.
Catanese observed that complex tori are characterized among compact Kähler manifolds X by the fact that their integral cohomology rings are exterior algebras on H1(X,Z) and asked whether this remains true under the weaker assumption that the rational cohomology ring is an exterior algebra on H1(X,Q). (We call the corresponding compact Kähler manifolds ``rational cohomology tori".) We give a negative answer to Catanese's question by producing explicit examples. We also prove some structure theorems for rational cohomology tori. This is work in collaboration with Z. Jiang, M. Lahoz, and W. F. Sawin.