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We present a fast, differentially private algorithm for high-dimensional covariance-aware mean estimation with nearly optimal sample complexity. Only exponential-time estimators were previously known to achieve this guarantee. Given n samples from a (sub-)Gaussian distribution with unknown mean μ and covariance Σ, our (ϵ,δ)-differentially private estimator produces μ~ such that ∥μ−μ~∥Σ≤α as long as n≳dα2+dlog1/δ√αϵ+dlog1/δϵ. The Mahalanobis error metric ∥μ−μ^∥Σ measures the distance between μ^ and μ relative to Σ; it characterizes the error of the sample mean. Our algorithm runs in time O~(ndω−1+nd/\eps), where ω<2.38 is the matrix multiplication exponent.We adapt an exponential-time approach of Brown, Gaboardi, Smith, Ullman, and Zakynthinou (2021), giving efficient variants of stable mean and covariance estimation subroutines that also improve the sample complexity to the nearly optimal bound above.Our stable covariance estimator can be turned to private covariance estimation for unrestricted subgaussian distributions. With n≳d3/2 samples, our estimate is accurate in spectral norm. This is the first such algorithm using n=o(d2) samples, answering an open question posed by Alabi et al. (2022). With n≳d2 samples, our estimate is accurate in Frobenius norm. This leads to a fast, nearly optimal algorithm for private learning of unrestricted Gaussian distributions in TV distance.Duchi, Haque, and Kuditipudi (2023) obtained similar results independently and concurrently. 

Balance problems affect more than eight million adults, and the percentage of balance problems increases with age. Globally, the population is aging, making balance problems a relevant topic of investigation. Balance impairments are the primary cause of falls, which result in debilitating injuries, especially for the elderly population. There is a significant opportunity for students in engineering and other disciplines to explore and contribute to research and education in this area. In this work, a group of graduate students from electrical, industrial, and mechanical engineering present research that will be mapped into an educational module on this topic. This module is co-created with faculty and domain experts. Sensors of various types are being investigated for monitoring gait and identifying the propensity for losing balance. A survey of the state of the art of sensor technology pertaining to balance is conducted. Models of human balance during quiet standing are investigated. An interactive simulation tool is developed to allow students to vary the model parameters and gain an intuitive understanding of the engineering principles involved. For engineering students, this offers many opportunities to better understand how topics they study in engineering courses relate to a significant societal problem. For students in courses such as statics, dynamics, and control systems, the concepts of change in the center of mass, the center of pressure, the inverted pendulum, and stability can be reinforced in relation to the balance dynamics problem. This paper describes the framework that will be used in an educational module that will improve undergraduate engineering concepts through balance dynamics experiments and simulations, and present interdisciplinary research problems to graduate students. This study contributes to an Innovations in Graduate Education National Science Foundation research project. 

We present results of the detailed study of several hundred Hamamatsu H12700 Multianode Photomultiplier Tubes (MaPMTs), characterizing their response to the Cherenkov light photons in the second Ring Imaging Cherenkov detector, a part of the CLAS12 upgrade at Jefferson Lab. The total number of pixels studied was 25536. The single photoelectron spectra were measured for each pixel at different high voltages and light intensities of the laser test setup. Using the same dedicated front-end electronics as in the first RICH detector, the setup allowed us to characterize each pixel’s properties such as gain, quantum efficiency, signal crosstalk between neighboring pixels, and determine the signal threshold values to optimize their efficiency to detect Cherenkov photons. A recently published state-of-the-art mathematical model, describing photon detector response functions measured in low light conditions, was extended to include the description of the crosstalk contributions to the spectra. The database of extracted parameters will be used for the final selection of the MaPMTs, their arrangement in the new RICH detector, and the optimization of the operational settings of the front-end electronics. The results show that the characteristics of the H12700 MaPMTs satisfy our requirements for the position-sensitive single photoelectron detectors. 

Climate change and unsustainable land management practices have resulted in extensive soil degradation, including alteration of soil structure (i.e., aggregate and pore size distributions), loss of soil organic carbon, and reduction of water and nutrient holding capacities. Although soil structure, hydrologic processes, and biogeochemical fluxes are tightly linked, their interaction is often unaccounted for in current ecohydrological, hydrological and terrestrial biosphere models. For more holistic predictions of soil hydrological and biogeochemical cycles, models need to incorporate soil structure and macroporosity dynamics, whether in a natural or agricultural ecosystem. Here, we present a theoretical framework that couples soil hydrologic processes and soil microbial activity to soil organic carbon dynamics through the dynamics of soil structure. In particular, we link the Millennial model for soil carbon dynamics, which explicitly models the formation and breakdown of soil aggregates, to a recent parameterization of the soil water retention and hydraulic conductivity curves and to solute and O₂diffusivities to soil microsites based on soil macroporosity. To illustrate the significance of incorporating the dynamics of soil structure, we apply the framework to a case study in which soil and vegetation recover over time from agricultural practices. The new framework enables more holistic predictions of the effects of climate change and land management practices on coupled soil hydrological and biogeochemical cycles.

 

The late-time integrated Sachs-Wolfe (ISW) imprint of $R\gtrsim 100~h^{-1}\, \mathrm{Mpc}$ superstructures is sourced by evolving large-scale potentials due to a dominant dark energy component in the ΛCDM model. The aspect that makes the ISW effect distinctly interesting is the repeated observation of stronger-than-expected imprints from supervoids at z ≲ 0.9. Here we analyse the un-probed key redshift range 0.8 < z < 2.2 where the ISW signal is expected to fade in ΛCDM, due to a weakening dark energy component, and eventually become consistent with zero in the matter dominated epoch. On the contrary, alternative cosmological models, proposed to explain the excess low-z ISW signals, predicted a sign-change in the ISW effect at z ≈ 1.5 due to the possible growth of large-scale potentials that is absent in the standard model. To discriminate, we estimated the high-z ΛCDM ISW signal using the Millennium XXL mock catalogue, and compared it to our measurements from about 800 supervoids identified in the eBOSS DR16 quasar catalogue. At 0.8 < z < 1.2, we found an excess ISW signal with AISW ≈ 3.6 ± 2.1 amplitude. The signal is then consistent with the ΛCDM expectation (AISW = 1) at 1.2 < z < 1.5 where the standard and alternative models predict similar amplitudes. Most interestingly, we also observed an opposite-sign ISW signal at 1.5 < z < 2.2 that is in 2.7σ tension with the ΛCDM prediction. Taken at face value, these recurring hints for ISW anomalies suggest an alternative growth rate of structure in low-density environments at $\sim 100~h^{-1}\, \mathrm{Mpc}$ scales.

 

The visibility of high-redshift Lyman-alpha emitting galaxies (LAEs) provides important constraints on galaxy formation processes and the Epoch of Reionization (EoR). However, predicting realistic and representative statistics for comparison with observations represents a significant challenge in the context of large-volume cosmological simulations. The thesan project offers a unique framework for addressing such limitations by combining state-of-the-art galaxy formation (IllustrisTNG) and dust models with the arepo-rt radiation-magnetohydrodynamics solver. In this initial study, we present Lyman-alpha centric analysis for the flagship simulation that resolves atomic cooling haloes throughout a $(95.5\, \text{cMpc})^3$ region of the Universe. To avoid numerical artefacts, we devise a novel method for accurate frequency-dependent line radiative transfer in the presence of continuous Hubble flow, transferable to broader astrophysical applications as well. Our scalable approach highlights the utility of LAEs and red damping-wing transmission as probes of reionization, which reveal nontrivial trends across different galaxies, sightlines, and frequency bands that can be modelled in the framework of covering fractions. In fact, after accounting for environmental factors influencing large-scale ionized bubble formation such as redshift and UV magnitude, the variation across galaxies and sightlines mainly depends on random processes including peculiar velocities and self-shielded systems that strongly impact unfortunate rays more than others. Throughout the EoR local and cosmological optical depths are often greater than or less than unity such that the exp (− τ) behaviour leads to anisotropic and bimodal transmissivity. Future surveys will benefit by targeting both rare bright objects and Goldilocks zone LAEs to infer the presence of these (un)predictable (dis)advantages.

 

In this study we present AI Prediction of Equatorial Plasma Bubbles (APE), a machine learning model that can accurately predict the Ionospheric Bubble Index (IBI) on the Swarm spacecraft. IBI is a correlation (R²) between perturbations in plasma density and the magnetic field, whose source can be Equatorial Plasma Bubbles (EPBs). EPBs have been studied for a number of years, but their day‐to‐day variability has made predicting them a considerable challenge. We build an ensemble machine learning model to predict IBI. We use data from 2014 to 2022 at a resolution of 1s, and transform it from a time‐series into a 6‐dimensional space with a corresponding EPBR²(0–1) acting as the label. APE performs well across all metrics, exhibiting a skill, association and root mean squared error score of 0.96, 0.98 and 0.08 respectively. The model performs best post‐sunset, in the American/Atlantic sector, around the equinoxes, and when solar activity is high. This is promising because EPBs are most likely to occur during these periods. Shapley values reveal that F10.7 is the most important feature in driving the predictions, whereas latitude is the least. The analysis also examines the relationship between the features, which reveals new insights into EPB climatology. Finally, the selection of the features means that APE could be expanded to forecasting EPBs following additional investigations into their onset.