Graded Differential Geometry of Graded Matrix Algebras

We study the graded derivation-based noncommutative differential geometry of the $Z_2$-graded algebra ${\bf M}(n| m)$ of complex $(n+m)\times(n+m)$-matrices with the ``usual block matrix grading'' (for $n\neq m$). Beside the (infinite-dimensional) algebra of graded forms the graded Cartan calculus, graded symplectic structure, graded vector bundles, graded connections and curvature are introduced and investigated. In particular we prove the universality of the graded derivation-based first-order differential calculus and show, that ${\bf M}(n|m)$ is a ``noncommutative graded manifold'' in a stricter sense: There is a natural body map and the cohomologies of ${\bf M}(n|m)$ and its body coincide (as in the case of ordinary graded manifolds).Comment: 21 pages, LATE

Environmental changes in a Mediterranean river: implications for the fish assemblage

This study examined the impacts of climate change on hydrology and fish population dynamics in a river in central Spain. The objectives were to: (i) contextualise long-term trends in the hydrology (1943–2012) and climate (1985–2011) of the study area, and (ii) identify the environmental factors driving fish population dynamics (1998–2012). Air and water temperatures progressively increased over the study period, whereas there were substantial reductions in mean spring river discharges but increases in peak-flow discharges during the spawning and early larval period of endemic cyprinids in recent decades. In particular, the changes in spring river discharges could have fundamental implications for the future status of the endemic cyprinids because this study revealed a positive influence of stable and low flow conditions during the spawning and early larval period (in late spring) on recruitment success (young-of-the-year densities). The density of young-of-the-year Salmo trutta appeared most influenced by flow conditions during fry emergence and the early larval period (in early spring), with the highest densities associated with low peak-flow hydrological pulses. Overall, fish abundances were significantly influenced by the frequency and duration of high and low hydrological pulses, but there were interspecific and ontogenetic differences in their influence. We conclude that although it is widely accepted that global warming should favour cyprinid over salmonid species, future shifts in hydrology due to climate change could negatively affect some cyprinids, including endemic species