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Geophysical detection of subducted mid–ocean ridge basalt (MORB) in the lower mantle is hindered by uncertainties in the elasticity of Fe,Al,Mg,Ti–bearing davemaoite, a key MORB component. Using Brillouin spectroscopy and x-ray diffraction, we determined the elasticity of a Ca_0.906(1)Fe²⁺_0.027(1)Fe³⁺_0.042(1)Mg_0.033(1)Al_0.072(1)Ti_0.020(1)Si_0.912(1)O₃davemaoite up to 113 gigapascals and 2294 K. We found that it exhibited a shear wave velocity 10 to 20% slower than end-member davemaoite, making it the slowest phase among major lower-mantle minerals. Our models show that MORB, containing 20 to 25 volume percent davemaoite, potentially contributes to large low-shear-velocity provinces (LLSVPs), whereas a cumulate layer enriched in davemaoite crystallized from basal magma ocean may comprise ultralow-velocity zones (ULVZs). Davemaoite’s ability to host incompatible and heat-producing elements possibly links LLSVPs and ULVZs to mantle plume initiation and geochemical signatures of ocean island basalts. 

Abstract Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the errors. We depart from existing literature by showing that with random regressors, linear regression inference is robust to correlated errors with unknown correlation structure. The existing theoretical analyses for linear regression are no longer valid because even the asymptotic normality of the least squares coefficients breaks down in this regime. We first prove the asymptotic normality of the t statistics by establishing their Berry–Esseen bounds based on a novel probabilistic analysis of self-normalized statistics. We then study the local power of the corresponding t tests and show that, perhaps surprisingly, error correlation can even enhance power in the regime of weak signals. Overall, our results show that linear regression is applicable more broadly than the conventional theory suggests, and they further demonstrate the value of randomization for ensuring robustness of inference. 

In this paper, we propose differentially private algorithms for robust (multivariate) mean estimation and inference under heavy-tailed distributions, with a focus on Gaussian differential privacy. First, we provide a comprehensive analysis of the Huber mean estimator with increasing dimensions, including non-asymptotic deviation bound, Bahadur representation, and (uniform) Gaussian approximations. Secondly, we privatize the Huber mean estimator via noisy gradient descent, which is proven to achieve near-optimal statistical guarantees. The key is to characterize quantitatively the trade-off between statistical accuracy, degree of robustness and privacy level, governed by a carefully chosen robustification parameter. Finally, we construct private confidence intervals for the proposed estimator by incorporating a private and robust covariance estimator. Our findings are demonstrated by simulation studies. 

The data-driven newsvendor problem with features has recently emerged as a significant area of research, driven by the proliferation of data across various sectors such as retail, supply chains, e-commerce, and healthcare. Given the sensitive nature of customer or organizational data often used in feature-based analysis, it is crucial to ensure individual privacy to uphold trust and confidence. Despite its importance, privacy preservation in the context of inventory planning remains unexplored. A key challenge is the nonsmoothness of the newsvendor loss function, which sets it apart from existing work on privacy-preserving algorithms in other settings. This paper introduces a novel approach to estimating a privacy-preserving optimal inventory policy within the f-differential privacy framework, an extension of the classical [Formula: see text]-differential privacy with several appealing properties. We develop a clipped noisy gradient descent algorithm based on convolution smoothing for optimal inventory estimation to simultaneously address three main challenges: (i) unknown demand distribution and nonsmooth loss function, (ii) provable privacy guarantees for individual-level data, and (iii) desirable statistical precision. We derive finite-sample high-probability bounds for optimal policy parameter estimation and regret analysis. By leveraging the structure of the newsvendor problem, we attain a faster excess population risk bound compared with that obtained from an indiscriminate application of existing results for general nonsmooth convex loss. Our bound aligns with that for strongly convex and smooth loss function. Our numerical experiments demonstrate that the proposed new method can achieve desirable privacy protection with a marginal increase in cost. This paper was accepted by J. George Shanthikumar, data science. Funding: This work was supported by the National Science Foundation [Grants DMS-2113409 and DMS 2401268 to W.-X. Zhou, and FRGMS-1952373 to L. Wang]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.01268 . 

Abstract Herein, we report the first systematic study of the oxidative addition of aryl bromides to a Pd^Icenter to generate organometallic Pd^IIIcomplexes. These isolable Pd^IIIcomplexes stabilized by tetradentate macrocyclic pyridinophane ligands exhibit distinct UV–vis and EPR spectroscopic signatures that allowed for the monitoring of their generation in situ. These ligand scaffolds were sterically and electronically tuned using a modular synthetic approach to probe the kinetic properties and activation parameters of the oxidative addition reaction, and a combination of UV–vis and cryo stopped‐flow spectroscopic studies reveal a rapid oxidative addition step occurring at a Pd^Icenter. In addition, these results are in strong agreement with our recent reactivity studies, which demonstrated that mononuclear Pd^Isystems are competent catalysts in Kumada cross‐coupling reactions, and thus set the stage for an improved understanding of potential catalytic applications for odd‐electron Pd systems.