The Gorenstein defect category

We consider the homotopy category of complexes of projective modules over a Noetherian ring. Truncation at degree zero induces a fully faithful triangle functor from the totally acyclic complexes to the stable derived category. We show that if the ring is either Artin or commutative Noetherian local, then the functor is dense if and only if the ring is Gorenstein. Motivated by this, we define the Gorenstein defect category of the ring, a category which in some sense measures how far the ring is from being Gorenstein.Comment: 11 pages, updated versio

Geography, population density, and per-capita income gaps across US states and Canadian provinces

We explain per-capita income gaps across US states and Canadian provinces by the following chain of causation. Geography determined where Europeans originally settled: in Northeastern USA, along those segments of the Atlantic coast where the climate was neither too hot (the US South), nor too cold (Canada). Higher population densities in this early settled region have prevailed to this day. This has in turn affected per-capita incomes because densely populated areas are conducive to skill accumulation; indicatively, many of the world’s top universities lie in this region. Our ordinary least-squares regressions show university education having a robust positive and significant effect on per-capita incomes. To control for endogeneity we run various instrumental-variable regressions: some where education today is instrumented with e.g. population density in 1900; and some where different sets of geography variables (e.g. temperature) are used as instruments. Our findings are consistent with the type of causal chain described.Geography; population density; income gaps; Canada; USA

Comment on "Regularizing capacity of metabolic networks"

In a recent paper, Marr, Muller-Linow and Hutt [Phys. Rev. E 75, 041917 (2007)] investigate an artificial dynamic system on metabolic networks. They find a less complex time evolution of this dynamic system in real networks, compared to networks of reference models. The authors argue that this suggests that metabolic network structure is a major factor behind the stability of biochemical steady states. We reanalyze the same kind of data using a dynamic system modeling actual reaction kinetics. The conclusions about stability, from our analysis, are inconsistent with those of Marr et al. We argue that this issue calls for a more detailed type of modeling