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Data driven individualized decision making problems have received a lot of attentions in recent years. In particular, decision makers aim to determine the optimal Individualized Treatment Rule (ITR) so that the expected speci ed outcome averaging over heterogeneous patient-speci c characteristics is maximized. Many existing methods deal with binary or a moderate number of treatment arms and may not take potential treatment e ect structure into account. However, the e ectiveness of these methods may deteriorate when the number of treatment arms becomes large. In this article, we propose GRoup Outcome Weighted Learning (GROWL) to estimate the latent structure in the treatment space and the op- timal group-structured ITRs through a single optimization. In particular, for estimating group-structured ITRs, we utilize the Reinforced Angle based Multicategory Support Vec- tor Machines (RAMSVM) to learn group-based decision rules under the weighted angle based multi-class classi cation framework. Fisher consistency, the excess risk bound, and the convergence rate of the value function are established to provide a theoretical guaran- tee for GROWL. Extensive empirical results in simulation studies and real data analysis demonstrate that GROWL enjoys better performance than several other existing methods. 

Forest dynamics in arid and semiarid regions are sensitive to water availability, which is becoming increasingly scarce as global climate changes. The timing and magnitude of precipitation in the semiarid southwestern U.S. (“Southwest”) has changed since the 21st century began. The region is projected to become hotter and drier as the century proceeds, with implications for carbon storage, pest outbreaks, and wildfire resilience. Our goal was to quantify the importance of summer monsoon precipitation for forested ecosystems across this region. We developed an isotope mixing model in a Bayesian framework to characterize summer (monsoon) precipitation soil water recharge and water use by three foundation tree species (Populus tremuloides [aspen], Pinus edulis [piñon], and Juniperus osteosperma [Utah juniper]). In 2016, soil depths recharged by monsoon precipitation and tree reliance on monsoon moisture varied across the Southwest with clear differences between species. Monsoon precipitation recharged soil at piñon-juniper (PJ) and aspen sites to depths of at least 60 cm. All trees in the study relied primarily on intermediate to deep (10- 60 cm) moisture both before and after the onset of the monsoon. Though trees continued to primarily rely on intermediate to deep moisture after the monsoon, all species increased reliance on shallow soil moisture to varying degrees. Aspens increased reliance on shallow soil moisture by 13% to 20%. Utah junipers and co-dominant ñons increased their reliance on shallow soil moisture by about 6% to 12%. Nonetheless, approximately half of the post-monsoon moisture in sampled piñon (38-58%) and juniper (47- 53%) stems could be attributed to the monsoon. The monsoon contributed lower amounts to aspen stem water (24-45%) across the study area with the largest impacts at sites with recent precipitation. Therefore, monsoon precipitation is a key driver of growing season moisture that semiarid forests rely on across the Southwest. This monsoon reliance is of critical importance now more than ever as higher global temperatures lead to an increasingly unpredictable and weaker North American Monsoon. 

Organic trisradicals featuring three-fold symmetry have attracted significant interest because of their unique magnetic properties associated with spin frustration. Herein, we describe the synthesis and characterization of a triangular prism-shaped organic cage for which we have coined the name PrismCage6+ and its trisradical trication—TR3(•+). PrismCage6+ is composed of three 4,4'-bipyridinium dications and two 1,3,5-phenylene units bridged by six methylene groups. In the solid state, PrismCage6+ adopts a highly twisted conformation with close to C3 symmetry as a result of encapsulating one PF6− anion as a guest. PrismCage6+ undergoes stepwise reduction to its mono-, di- and trisradical cations in MeCN on account of strong electronic communication between its 4,4'-bipyridinium units. TR3(•+), which is obtained by reduction of PrismCage6+ employing CoCp2, adopts a triangular prism-shaped conformation with close to C2v symmetry in the solid state. Temperature-dependent continuous-wave and nutation frequency-selective EPR spectra of TR3(•+) in frozen N,N-dimethylformamide indicate its doublet ground state. The doublet-quartet energy gap of TR3(•+) is estimated to be −0.06 kcal mol−1 and the critical temperature of spin-state conversion is found to be ca. 50 K, suggesting that it displays pronounced spin-frustration at the molecular level. To the best of our knowledge, this example is the first organic radical cage to exhibit spin frustration. The trisradical trication of PrismCage6+ opens up new possibilities for fundamental investigations and potential applications in the fields of both organic cages and spin chemistry.