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

Minimising the expected commute time

Motivated in part by a problem in simulated tempering (a form of Markov chain Monte Carlo) we seek to minimise, in a suitable sense, the time it takes a (regular) diffusion with instantaneous reflection at 0 and 1 to travel from the origin to $1$ and then return (the so-called commute time from 0 to 1). We consider the static and dynamic versions of this problem where the control mechanism is related to the diffusion's drift via the corresponding scale function. In the static version the diffusion's drift can be chosen at each point in [0,1], whereas in the dynamic version we are only able to choose the drift at each point at the time of first visiting that point. The dynamic version leads to a novel type of stochastic control problem

The Chemical Composition of Cernis 52 (BD+31 640)

We present an abundance analysis of the star Cernis 52 in whose spectrum we recently reported the napthalene cation in absorption at 6707.4 {\AA}. This star is on a line of sight to the Perseus molecular complex. The analysis of high-resolution spectra using a chi^2-minimization procedure and a grid of synthetic spectra provides the stellar parameters and the abundances of O, Mg, Si, S, Ca, and Fe. The stellar parameters of this star are found to be T_{eff} = 8350 +- 200 K, logg= 4.2 +- 0.4 dex. We derived a metallicity of [Fe/H] = -0.01 +- 0.15. These stellar parameters are consistent with a star of $\sim 2$ \Msun in a pre-main-sequence evolutionary stage. The stellar spectrum is significantly veiled in the spectral range 5150-6730 {\AA} up to almost 55 per cent of the total flux at 5150 {\AA} and decreasing towards longer wavelengths. Using Johnson-Cousins and 2MASS photometric data, we determine a distance to Cernis 52 of 231$^{+135}_{-85}$ pc considering the error bars of the stellar parameters. This determination places the star at a similar distance to the young cluster IC 348. This together with its radial velocity, v_r=13.7+-1 km/s, its proper motion and probable young age support Cernis 52 as a likely member of IC 348. We determine a rotational velocity of v\sin i=65 +- 5 km/s for this star. We confirm that the stellar resonance line of \ion{Li}{1} at 6707.8 {\AA} is unable to fit the broad feature at 6707.4 {\AA}. This feature should have a interstellar origin and could possibly form in the dark cloud L1470 surrounding all the cluster IC 348 at about the same distance.Comment: Accepted for publication in The Astrophysical Journa