These results suggest that effects of hypothermia on EAA concentrations during cerebral ischemia may be the result of both a delay until initial EAA release as well as a direct effect of temperature on the rate of amino acid release. The observed temperature effects are more consistent with carrier-mediated processes controlling EAA release.

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In this work, we propose a new invariant for 2D persistence modules called the compressed multiplicity and show that it generalizes the notions of the dimension vector and the rank invariant. In addition, we propose an "interval-decomposable approximation" δ * (M ) of a 2D persistence module M . In the case that M is interval-decomposable, we show that δ * (M ) = M . Furthermore, even for representations M not necessarily interval-decomposable, δ * (M ) preserves the dimension vector and the rank invariant of M .

In persistent homology [13] of filtrations, the indecomposable decompositions provide the persistence diagrams. In multidimensional persistence [9] it is known to be impossible to classify all indecomposable modules. One direction is to consider the subclass of intervaldecomposable persistence modules, which are direct sums of interval representations. We introduce the definition of pre-interval representations, a more algebraic definition, and study the relationships between pre-interval, interval, and indecomposable thin representations. We show that over the "equioriented" commutative 2D grid, these concepts are equivalent. Moreover, we provide an algorithm for determining whether or not an nD persistence module is interval/preinterval/thin-decomposable, under certain finiteness conditions and without explicitly computing decompositions.