Modeling dimethylsulphide production in the upper ocean

Dimethylsulphide (DMS) is produced by upper ocean ecosystems and emitted to the atmosphere, where it may have an important role in climate regulation. Several attempts to quantify the role of DMS in climate change have been undertaken in modeling studies. We examine a model of biogenic DMS production and describe its endogenous dynamics and sensitivities. We extend the model to develop a one-dimensional version that more accurately resolves the important processes of the mixed layer in determining the ecosystem dynamics. Comparisons of the results of the one-dimensional model with an empirical relationship that describes the global distribution of DMS, and also with vertical profiles of DMS in the upper ocean measured at the Bermuda Atlantic Time Series, suggest that the model represents the interaction between the biological and physical processes well on local and global scales. Our analysis of the model confirms its veracity and provides insights into the important processes determining DMS concentration in the oceans

The Simplest Binary Word with Only Three Squares

We re-examine previous constructions of infinite binary words containing few distinct squares with the goal of finding the "simplest", in a certain sense. We exhibit several new constructions. Rather than using tedious case-based arguments to prove that the constructions have the desired property, we rely instead on theorem-proving software for their correctness