Multiple Palaeoproterozoic carbon burial episodes and excursions

Organic-rich rocks (averaging 2–5% total organic carbon) and positive carbonate-carbon isotope excursions (View the MathML source and locally much higher, i.e. the Lomagundi-Jatuli Event) are hallmark features of Palaeoproterozoic successions and are assumed to archive a global event of unique environmental conditions following the c. 2.3 Ga Great Oxidation Event. Here we combine new and published geochronology that shows that the main Palaeoproterozoic carbon burial episodes (CBEs) preserved in Russia, Gabon and Australia were temporally discrete depositional events between c. 2.10 and 1.85 Ga. In northwest Russia we can also show that timing of the termination of the Lomagundi-Jatuli Event may have differed by up to 50 Ma between localities, and that Ni mineralisation occurred at c. 1920 Ma. Further, CBEs have traits in common with Mesozoic Oceanic Anoxic Events (OAEs); both are exceptionally organic-rich relative to encasing strata, associated with contemporaneous igneous activity and marked by organic carbon isotope profiles that exhibit a stepped decrease followed by a stabilisation period and recovery. Although CBE strata are thicker and of greater duration than OAEs (100 s of metres versus metres, ∼106 years versus ∼105 years), their shared characteristics hint at a commonality of cause(s) and feedbacks. This suggests that CBEs represent processes that can be either basin-specific or global in nature and a combination of circumstances that are not unique to the Palaeoproterozoic. Our findings urge circumspection and re-consideration of models that assume CBEs are a Deep Time singularity

Distributed Community Detection in Dynamic Graphs

Inspired by the increasing interest in self-organizing social opportunistic networks, we investigate the problem of distributed detection of unknown communities in dynamic random graphs. As a formal framework, we consider the dynamic version of the well-studied \emph{Planted Bisection Model} \sdG(n,p,q) where the node set $[n]$ of the network is partitioned into two unknown communities and, at every time step, each possible edge $(u,v)$ is active with probability $p$ if both nodes belong to the same community, while it is active with probability $q$ (with $q<<p$) otherwise. We also consider a time-Markovian generalization of this model. We propose a distributed protocol based on the popular \emph{Label Propagation Algorithm} and prove that, when the ratio $p/q$ is larger than $n^{b}$ (for an arbitrarily small constant $b>0$), the protocol finds the right "planted" partition in $O(\log n)$ time even when the snapshots of the dynamic graph are sparse and disconnected (i.e. in the case $p=\Theta(1/n)$).Comment: Version I

Application of time-dependent density functional theory to optical activity

As part of a general study of the time-dependent local density approximation (TDLDA), we here report calculations of optical activity of chiral molecules. The theory automatically satisfies sum rules and the Kramers-Kronig relation between circular dichroism and optical rotatory power. We find that the theory describes the measured circular dichroism of the lowest states in methyloxirane with an accuracy of about a factor of two. In the chiral fullerene C_76 the TDLDA provides a consistent description of the optical absorption spectrum, the circular dichroism spectrum, and the optical rotatory power, except for an overall shift of the theoretical spectrum.Comment: 17 pages and 13 PostScript figure