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The accurate ab-initio simulation of molecules and periodic solids with diagrammatic perturbation theory is an important task in quantum chemistry, condensed matter physics, and materials science. In this article, we present the WeakCoupling module of the open-source software package Green, which implements fully self-consistent diagrammatic weak coupling simulations, capable of dealing with real materials in the finite-temperature formalism. The code is licensed under the permissive MIT license. We provide self-consistent GW (scGW) and self-consistent second-order Green's function perturbation theory (GF2) solvers, analysis tools, and post-processing methods. This paper summarizes the theoretical methods implemented and provides background, tutorials and practical instructions for running simulations. 

Adjacency polytopes appear naturally in the study of nonlinear emergent phenomena in complex networks. The ``"PQ-type" adjacency polytope, denoted $$\nabla^{\mathrm{PQ}}_G$$ and which is the focus of this work, encodes rich combinatorial information about power-flow solutions in sparse power networks that are studied in electric engineering. Of particular importance is the normalized volume of such an adjacency polytope, which provides an upper bound on the number of distinct power-flow solutions. In this article we show that the problem of computing normalized volumes for $$\nabla^{\mathrm{PQ}}_G$$ can be rephrased as counting $D(G)$-draconian sequences where $D(G)$ is a certain bipartite graph associated to the network. We prove recurrences for all networks with connectivity at most $$1$$ and, for $$2$$-connected graphs under certain restrictions, we give recurrences for subdividing an edge and taking the join of an edge with a new vertex. Together, these recurrences imply a simple, non-recursive formula for the normalized volume of $$\nabla^{\mathrm{PQ}}_G$$ when $$G$$ is part of a large class of outerplanar graphs; we conjecture that the formula holds for all outerplanar graphs. Explicit formulas for several other (non-outerplanar) classes are given. Further, we identify several important classes of graphs $$G$$ which are planar but not outerplanar that are worth additional study. 

Abstract Coral oxygen isotopes (δ¹⁸O) from the central equatorial Pacific provide monthly resolved records of El Niño‐Southern Oscillation activity over past centuries to millennia. However, calibration studies usingin situdata to assess the relative contributions of warming and freshening to coral δ¹⁸O records are exceedingly rare. Furthermore, the fidelity of coral δ¹⁸O records under the most severe thermal stress events is difficult to assess. Here, we present six coral δ¹⁸O records andin situtemperature, salinity, and seawater δ¹⁸O data from Kiritimati Island (2°N, 157°W) spanning the very strong 2015/16 El Niño event. Local sea surface temperature (SST) anomalies of +2.4 ± 0.4°C and seawater δ¹⁸O anomalies of −0.19 ± 0.02‰ contribute to the observed coral δ¹⁸O anomalies of −0.58 ± 0.05‰, consistent with a ∼70% contribution from SST and ∼30% from seawater δ¹⁸O. Our results demonstrate that Kiritimati coral δ¹⁸O records can provide reliable reconstructions even during the largest class of El Niño events. 

Abstract The El Niño–Southern Oscillation (ENSO) represents the largest source of year‐to‐year global climate variability. While Earth system models suggest a range of possible shifts in ENSO properties under continued greenhouse gas forcing, many centuries of preindustrial climate data are required to detect a potential shift in the properties of recent ENSO extremes. Here we reconstruct the strength of ENSO variations over the last 7,000 years with a new ensemble of fossil coral oxygen isotope records from the Line Islands, located in the central equatorial Pacific. The corals document a significant decrease in ENSO variance of ~20% from 3,000 to 5,000 years ago, coinciding with changes in spring/fall precessional insolation. We find that ENSO variability over the last five decades is ~25% stronger than during the preindustrial. Our results provide empirical support for recent climate model projections showing an intensification of ENSO extremes under greenhouse forcing.