We develop a new methodology for forecasting matrix-valued time series with historical matrix data and auxiliary vector time series data. We focus on a time series of matrices defined on a static 2-D spatial grid and an auxiliary time series of non-spatial vectors. The proposed model, Matrix AutoRegression with Auxiliary Covariates (MARAC), contains an autoregressive component for the historical matrix predictors and an additive component that maps the auxiliary vector predictors to a matrix response via tensor-vector product. The autoregressive component adopts a bi-linear transformation framework following Chen et al. (2021), significantly reducing the number of parameters. The auxiliary component posits that the tensor coefficient, which maps non-spatial predictors to a spatial response, contains slices of spatially smooth matrix coefficients that are discrete evaluations of smooth functions on a spatial grid from a Reproducing Kernel Hilbert Space (RKHS). We propose to estimate the model parameters under a penalized maximum likelihood estimation framework coupled with an alternating minimization algorithm. We establish the joint asymptotics of the autoregressive and tensor parameters under fixed and high-dimensional regimes. Extensive simulations and a geophysical application for forecasting the global Total Electron Content (TEC) are conducted to validate the performance of MARAC.
The optimal power flow (OPF) is a multi-valued, non-convex mapping from loads to dispatch setpoints. The variability of system parameters (e.g., admittances, topology) further contributes to the multiplicity of dispatch setpoints for a given load. Existing deep learning OPF solvers are single-valued and thus fail to capture the variability of system parameters unless fully represented in the feature space, which is prohibitive. To solve this problem, we introduce a diffusion-based OPF solver, termed DiffOPF, that treats OPF as a conditional sampling problem. The solver learns the joint distribution of loads and dispatch setpoints from operational history, and returns the marginal dispatch distributions conditioned on loads. Unlike single-valued solvers, DiffOPF enables sampling statistically credible warm starts with favorable cost and constraint satisfaction trade-offs. We explore the sample complexity of DiffOPF to ensure the OPF solution within a prescribed distance from the optimization-based solution, and verify this experimentally on power system benchmarks.
In sub-Saharan Africa, population growth coupled with weak or missing markets for clean energy means that the absolute number of people relying on woodfuels for cooking is growing. Charcoal, which has distinctly different environmental and economic implications from firewood, has become one of the most consumed fuels in the region. However, among rural populations, the drivers and consequences of charcoal use remain under-studied. We examine rural woodfuel dynamics in Malawi, a majority rural country with high poverty, rapid population growth, lagging economic development, and abundant but rapidly declining forest resources. We examine how household energy transitions are influenced by concurrent demographic, economic, and land use changes. Using four waves of national household surveys and satellite-derived forest cover datasets, we investigate trends in household energy consumption, identify factors driving rural household fuel choices, and characterize geographic patterns of forest cover loss during 2004–2020. During this time, the share of rural households using charcoal grew from 3.9% to 13.4%. Rural households that are smaller, headed by younger individuals, and are asset-rich but land-poor had greater odds of using charcoal compared to firewood, indicating that rural livelihood dynamics have important consequences for household energy transitions. Several protected areas have experienced > 20% forest cover loss since 2001, characterized by geographic patterns consistent with unsanctioned woodfuel extraction. These findings emphasize a renewed need for integrated natural resources, energy, and livelihoods management strategies. Our insights provide information for policy makers to better predict and understand the continued growth of charcoal’s popularity in Malawi and similar contexts.
AI agents may soon become capable of autonomously completing valuable, long-horizon tasks in diverse domains. Current benchmarks either do not measure real-world tasks, or are not sufficiently difficult to meaningfully measure frontier models. To this end, we present Terminal-Bench 2.0: a carefully curated hard benchmark composed of 89 tasks in computer terminal environments inspired by problems from real workflows. Each task features a unique environment, human-written solution, and comprehensive tests for verification. We show that frontier models and agents score less than 65% on the benchmark and conduct an error analysis to identify areas for model and agent improvement. We publish the dataset and evaluation harness to assist developers and researchers in future work at tbench.ai.
Luminous quasars at the redshift frontier z > 7 serve as stringent probes of super-massive black hole (SMBH) formation and they are thought to undergo much of their growth obscured by dense gas and dust in their host galaxies. Fully characterizing the symbiotic evolution of SMBHs and hosts requires rest-frame optical observations that span spatial scales from the broad-line region (BLR) to the interstellar and circumgalactic medium (ISM and CGM). The James Webb Space Telescope (JWST) now provides the necessary spatially resolved spectroscopy to do so. However, the physical conditions that regulate the interplay between SMBHs and their hosts at the highest redshifts, especially the nature of early feedback phases, remain unclear. We present JWST/NIRSpec integral field unit (IFU) observations of J0313-1806 at z = 7.64, the most distant luminous quasar known. From the rest-frame optical spectrum of the unresolved quasar, we derived a black hole mass of M-BH = (1.63 +/- 0.10)& times;10(9) M-circle dot based on H beta lambda 4861 (H beta) and an Eddington rate of lambda = L/L-Edd = 0.80 +/- 0.05, consistent with previous Mg II lambda 2800-based estimates. J0313-1806 exhibits no detectable [O III] lambda lambda 4959, 5007 emission on nuclear scales (3 sigma upper limit equivalent width of [O III] lambda 5007 < 1.42 & Aring;). Most remarkably, we did detect an ionized gas shell extending out to similar to 1.8 kpc traced by H beta emission that also lacks any significant [O III] lambda lambda 4959, 5007, with a 3 sigma upper limit on the [O III] lambda 5007 to H beta flux ratio of log(10)(F([O III])/F(H beta)) = -1.15. Through photoionization modeling, we demonstrate that the extended emission is consistent with a thin, clumpy outflowing shell where [O III] is collisionally de-excited by dense gas. We interpret this structure as a fossil remnant of a recent blowout phase, providing evidence for episodic feedback cycles in one of the earliest quasars. These findings suggest that dense ISM phases may play a crucial role in shaping the spectral properties of quasars across cosmic time.
