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Recent measurements of the ionizing photon mean free path (MFP) based on composite quasar spectra may point to reionization ending at z < 6. These measurements are challenging because they rely on assumptions about the proximity zones of the quasars. For example, some quasars might have been close to neutral patches where reionization was still ongoing (‘neutral islands’), and it is unclear how they would affect the measurements. We address this question with mock MFP measurements from radiative transfer simulations. We find that, even in the presence of neutral islands, our mock MFP measurements agree to within $30~{{\ \rm per\ cent}}$ with the true spatially averaged MFP in our simulations, which includes opacity from both the ionized medium and the islands. The inferred MFP is sensitive at the $\lt ~50~{{\ \rm per\ cent}}$ level to assumptions about quasar environments and lifetimes for realistic models. We demonstrate that future analyses with improved data may require explicitly modelling the effects of neutral islands on the composite spectra, and we outline a method for doing this. Lastly, we quantify the effects of neutral islands on Lyman-series transmission, which has been modelled with optically thin simulations in previous MFP analyses. Neutral islands can suppress transmission at λrest < 912 Å significantly, up to a factor of 2 for zqso = 6 in a plausible reionization scenario, owing to absorption by many closely spaced lines as quasar light redshifts into resonance. However, the suppression is almost entirely degenerate with the spectrum normalization and thus does not significantly bias the inferred MFP.

 

Rare earth elements (REE) are critical elements found in monazite, xenotime, and hydrated REE phosphates which typically form in hydrothermal mineral deposits. Accurate predictions of the solubility of these REE phosphates and the speciation of REE in aqueous fluids are both key to understanding the controls on the transport, fractionation, and deposition of REE in natural systems. Previous monazite and xenotime solubility experiments indicate the presence of large discrepancies between experimentally derived solubility constants versus calculated solubilities by combining different data sources for the thermodynamic properties of minerals and aqueous species at hydrothermal conditions. In this study, these discrepancies were resolved by using the program GEMSFITS to optimize the standard partial molal Gibbs energy of formation (ΔfG°298) of REE aqueous species (REE3+ and REE hydroxyl complexes) at 298.15 K and 1 bar while keeping the thermodynamic properties fixed for the REE phosphates. A comprehensive experimental database was compiled using solubility data available between 25 and 300 °C. The latter permits conducting thermodynamic parameter optimization of ΔfG°298 for REE aqueous species. Optimal matching of the rhabdophane solubility data between 25 and 100 °C requires modifying the ΔfG°298 values of REE3+ by 1–6 kJ/mol, whereas matching of the monazite solubility data between 100 and 300 °C requires modifying the ΔfG°298 values of both REE3+ and REEOH2+ by ∼ 2–10 kJ/mol and ∼ 15–31 kJ/mol, respectively. For xenotime, adjustments of ΔfG°298 values by 1–26 kJ/mol are only necessary for the REE3+ species. The optimizations indicate that the solubility of monazite in acidic solutions is controlled by the light (L)REE3+ species at <150 °C and the LREEOH2+ species at >150 °C, whereas the solubility of xenotime is controlled by the heavy (H)REE3+ species between 25 and 300 °C. Based on the optimization results, we conclude that the revised Helgeson-Kirkham-Flowers equation of state does not reliably predict the thermodynamic properties of REE3+, REEOH2+, and likely other REE hydroxyl species at hydrothermal conditions. We therefore provide an experimental database (ThermoExp_REE) as a basic framework for future updates, extensions with other ligands, and optimizations as new experimental REE data become available. The optimized thermodynamic properties of aqueous species and minerals are available open access to accurately predict the solubility of REE phosphates in fluid-rock systems. 

Amidst the challenges posed by the high penetration of distributed energy resources (DERs), particularly a number of distributed photovoltaic plants (DPVs), in modern electric power distribution systems (MEPDS), the integration of new technologies and frameworks become crucial for addressing operation, management, and planning challenges. Situational awareness (SA) and situational intelligence (SI) over multi-time scales is essential for enhanced and reliable PV power generation in MEPDS. In this paper, data-driven digital twins (DTs) are developed using AI paradigms to develop actual and/or virtual models of DPVs, These DTs are then applied for estimating and forecasting the power outputs of physical and virtual PV plants. Virtual weather stations are used to estimate solar irradiance and temperature at user-selected locations in a localized region, using inferences from physical weather stations. Three case studies are examined based on data availability: physical PV plant, hybrid PV plants, and virtual PV plants, generating realtime estimations and short-term forecasts of PV power production that can support distribution system studies and decision-making. 

With the rapid growth of large language models, big data, and malicious online attacks, it has become increasingly important to have tools for anomaly detection that can distinguish machine from human, fair from unfair, and dangerous from safe. Prior work has shown that two-distribution (specified complexity) hypothesis tests are useful tools for such tasks, aiding in detecting bias in datasets and providing artificial agents with the ability to recognize artifacts that are likely to have been designed by humans and pose a threat. However, existing work on two-distribution hypothesis tests requires exact values for the specification function, which can often be costly or impossible to compute. In this work, we prove novel finite-sample bounds that allow for two-distribution hypothesis tests with only estimates of required quantities, such as specification function values. Significantly, the resulting bounds do not require knowledge of the true distribution, distinguishing them from traditional p-values. We apply our bounds to detect student cheating on multiple-choice tests, as an example where the exact specification function is unknown. We additionally apply our results to detect representational bias in machine-learning datasets and provide artificial agents with intention perception, showing that our results are consistent with prior work despite only requiring a finite sample of the space. Finally, we discuss additional applications and provide guidance for those applying these bounds to their own work. 

The variations in Lyαforest opacity observed atz> 5.3 between lines of sight to different background quasars are too strong to be caused by fluctuations in the density field alone. The leading hypothesis for the cause of this excess variance is a late, ongoing reionization process at redshifts below six. Another model proposes strong ionizing background fluctuations coupled to a short, spatially varying mean free path of ionizing photons, without explicitly invoking incomplete reionization. With recent observations suggesting a short mean free path atz∼ 6, and a dramatic improvement inz> 5 Lyαforest data quality, we revisit this latter possibility. Here, we apply the likelihood-free inference technique of approximate Bayesian computation (ABC) to jointly constrain the hydrogen photoionization rate Γ_HIand the mean free path of ionizing photonsλ_mfpfrom the effective optical depth distributions atz= 5.0–6.1 from XQR-30. We find that the observations are well-described by fluctuating mean free path models with average mean free paths that are consistent with the steep trend implied by independent measurements atz∼ 5–6, with a concomitant rapid evolution of the photoionization rate.

 

We show that the base polytopeP_Mof any paving matroidMcan be systematically obtained from a hypersimplex by slicing off certain subpolytopes, namely base polytopes of lattice path matroids corresponding to panhandle-shaped Ferrers diagrams. We calculate the Ehrhart polynomials of these matroids and consequently write down the Ehrhart polynomial ofP_M, starting with Katzman’s formula for the Ehrhart polynomial of a hypersimplex. The method builds on and generalizes Ferroni’s work on sparse paving matroids. Combinatorially, our construction corresponds to constructing a uniform matroid from a paving matroid by iterating the operation ofstressed-hyperplane relaxationintroduced by Ferroni, Nasr and Vecchi, which generalizes the standard matroid-theoretic notion of circuit-hyperplane relaxation. We present evidence that panhandle matroids are Ehrhart positive and describe a conjectured combinatorial formula involving chain forests and Eulerian numbers from which Ehrhart positivity of panhandle matroids will follow. As an application of the main result, we calculate the Ehrhart polynomials of matroids associated with Steiner systems and finite projective planes, and show that they depend only on their design-theoretic parameters: for example, while projective planes of the same order need not have isomorphic matroids, their base polytopes must be Ehrhart equivalent.