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Selective and site-specific boron-doping of polycyclic aromatic hydrocarbon frameworks often give rise to redox and/or photophysical properties that are not easily accessible with the analogous all-carbon systems. Herein, we report ligand-mediated control of boraphenanthrene closed- and open-shell electronic states, which has led to the first structurally characterized examples of neutral bis(9-boraphenanthrene) (2–3) and its corresponding biradical (4). Notably, compounds 2 and 3 show intramolecular charge transfer absorption from the 9-boraphenanthrene units to p-quinodimethane, exhibiting dual (red-shifted) emission in solution due to excited state conjugation enhancement (ESCE). Moreover, while boron-centered monoradicals are ubiquitous, biradical 4 represents a rare type of open-shell singlet compound with 95% biradical character, among the highest of any reported boron-based polycyclic species with two radical sites. 

This paper identifies a structural property of data distributions that enables deep neural networks to learn hierarchically. We define the ``staircase'' property for functions over the Boolean hypercube, which posits that high-order Fourier coefficients are reachable from lower-order Fourier coefficients along increasing chains. We prove that functions satisfying this property can be learned in polynomial time using layerwise stochastic coordinate descent on regular neural networks -- a class of network architectures and initializations that have homogeneity properties. Our analysis shows that for such staircase functions and neural networks, the gradient-based algorithm learns high-level features by greedily combining lower-level features along the depth of the network. We further back our theoretical results with experiments showing that staircase functions are learnable by more standard ResNet architectures with stochastic gradient descent. Both the theoretical and experimental results support the fact that the staircase property has a role to play in understanding the capabilities of gradient-based learning on regular networks, in contrast to general polynomial-size networks that can emulate any Statistical Query or PAC algorithm, as recently shown. 

Abstract Reconstructing past climates remains a difficult task because pre‐instrumental observational networks are composed of geographically sparse and noisy paleoclimate proxy records that require statistical techniques to inform complete climate fields. Traditionally, instrumental or climate model statistical relationships are used to spread information from proxy measurements to other locations and to other climate variables. Here ensembles drawn from single climate models and from combinations of multiple climate models are used to reconstruct temperature variability over the last millennium in idealized experiments. We find that reconstructions derived from multi‐model ensembles produce lower error than reconstructions from single‐model ensembles when reconstructing independent model and instrumental data. Specifically, we find the largest decreases in error over regions far from proxy locations that are often associated with large uncertainties in model physics, such as mid‐ and high‐latitude ocean and sea‐ice regions. Furthermore, we find that multi‐model ensemble reconstructions outperform single‐model reconstructions that use covariance localization. We propose that multi‐model ensembles could be used to improve paleoclimate reconstructions in time periods beyond the last millennium and for climate variables other than air temperature, such as drought metrics or sea ice variables. 

Abstract Attribution and prediction of global and regional warming requires a better understanding of the magnitude and spatial characteristics of internal global mean surface air temperature (GMST) variability. We examine interdecadal GMST variability in Coupled Modeling Intercomparison Projects, Phases 3, 5, and 6 (CMIP3, CMIP5, and CMIP6) preindustrial control (piControl), last millennium, and historical simulations and in observational data. We find that several CMIP6 simulations show more GMST interdecadal variability than the previous generations of model simulations. Nonetheless, we find that 100‐year trends in CMIP6 piControl simulations never exceed the maximum observed warming trend. Furthermore, interdecadal GMST variability in the unforced piControl simulations is associated with regional variability in the high latitudes and the east Pacific, whereas interdecadal GMST variability in instrumental data and in historical simulations with external forcing is more globally coherent and is associated with variability in tropical deep convective regions.