Temperature relaxation in strongly-coupled binary ionic mixtures

A central problem in data science is to use potentially noisy samples of an unknown function to predict function values for unseen inputs. In classical statistics, the predictive error is understood as a trade-off between the bias and the variance that balances model simplicity with its ability to fit complex functions. However, overparametrized models exhibit counterintuitive behaviors, such as “double descent” in which models of increasing complexity exhibit decreasing generalization error. Other models may exhibit more complicated patterns of predictive error with multiple peaks and valleys. Neither double descent nor multiple descent phenomena are well explained by the bias-variance decomposition. We introduce a decomposition that we call the generalized aliasing decomposition (GAD) to explain the relationship between predictive performance and model complexity. The GAD decomposes the predictive error into three parts: (1) model insufficiency, which dominates when the number of parameters is much smaller than the number of data points, (2) data insufficiency, which dominates when the number of parameters is much greater than the number of data points, and (3) generalized aliasing, which dominates between these two extremes. We demonstrate the applicability of the GAD to diverse applications, including random feature models from machine learning, Fourier transforms from signal processing, solution methods for differential equations, and predictive formation enthalpy in materials discovery. Because key components of the generalized aliasing decomposition can be explicitly calculated from the relationship between model class and samples without seeing any data labels, it can answer questions related to experimental design and model selection before collecting data or performing experiments. We further demonstrate this approach on several examples and discuss implications for predictive modeling and data science.

We report on roughly 16 yr of photometric monitoring of the trans-Neptunian binary system (120347) Salacia–Actaea, which provides significant evidence that Salacia and Actaea are tidally locked to the mutual orbital period in a fully synchronous configuration. The orbit of Actaea is updated, followed by a Lomb–Scargle periodogram analysis of the ground-based photometry, which reveals a synodic period similar to the orbital period and a peak-to-peak lightcurve amplitude of Δm = 0.0900 ± 0.0036 mag (1σ uncertainty). Incorporating archival Hubble Space Telescope photometry that resolves each component, we argue that the periodicity in the unresolved data is driven by a longitudinally varying surface morphology on Salacia, and we derive a sidereal rotation period that is within 1σ of the mutual orbital period. A rudimentary tidal evolution model is invoked that suggests synchronization occurred within 1.1 Gyr after Actaea was captured/formed.

In response to the 2020 Update of the European Strategy for Particle Physics, the Future Circular Collider (FCC) Feasibility Study was launched as an international collaboration hosted by CERN. This report describes the FCC integrated programme, which consists of two stages: an electron-positron collider (FCC-ee) in the first phase, serving as a high-luminosity Higgs, top, and electroweak factory; followed by a proton-proton collider (FCC-hh) at the energy frontier in the second phase. The FCC-ee is designed to operate at four key centre-of-mass energies: the Z pole, the WW pair production threshold, the ZH production peak, and the top/anti-top production threshold—each delivering the highest possible luminosities to four experiments. Over 15 years of operation, FCC-ee will produce more than 6 trillion Z bosons, 200 million WW pairs, nearly 3 million Higgs bosons, and 2 million top anti-top pairs. Precise energy calibration at the Z pole and WW threshold will be achieved through frequent resonant depolarisation of pilot bunches. The sequence of operation modes between the Z, WW, and ZH substages remains flexible. The FCC-hh will operate at a centre-of-mass energy of approximately 85 TeV—nearly an order of magnitude higher than the LHC—and is designed to deliver 5 to 10 times the integrated luminosity of the upcoming High-Luminosity LHC. Its mass reach for direct discovery extends to several tens of TeV. In addition to proton-proton collisions, the FCC-hh is capable of supporting ion-ion, ion-proton, and lepton-hadron collision modes. This second volume of the Feasibility Study Report presents the complete design of the FCC-ee collider, its operation and staging strategy, the full-energy booster and injector complex, required accelerator technologies, safety concepts, and technical infrastructure. It also includes the design of the FCC-hh hadron collider, development of high-field magnets, hadron injector options, and key technical systems for FCC-hh.

Background: Understanding how different modeling strategies affect associations in nutritional epidemiology is critical, especially given the temporal complexity of dietary and health data.

Objective: To compare how different modeling frameworks—including isotemporal versus time-lagged designs and frequentist versus Bayesian inference—affect estimated associations between carbohydrate subtypes and adiposity.

Methods: Longitudinal data of 415 adults from the NoHoW Study were used to investigate associations between four carbohydrate predictors (free sugars, intrinsic sugars, starch, and dietary fiber) and three indices of adiposity (body fat percentage, BMI, and waist circumference) as outcomes. Four statistical approaches were used contrasting frequentist and Bayesian methods across both isotemporal (concurrent measurement) and time-lagged (6-month temporal shift) frameworks. To specifically evaluate change in adiposity outcomes over time, we implemented additional baseline-adjusted longitudinal models.

Results: Isotemporal and time-lagged models showed directional agreement for nearly all associations; in all but one case, the models either aligned in the direction of the association or differed only in relation to the null. However, time-lagged models identified statistically significant associations and produced larger effect sizes for body fat outcomes and for starch and fiber predictors. Other associations, including intrinsic and free sugars, were weaker and varied with model specification, losing statistical support under time-lagged models. Frequentist models exhibited greater variation across temporal frameworks, including one directional shift among significant associations. Effect estimates were substantially attenuated after adjustment for baseline adiposity.

Discussion: Time-lagged modeling shifted associations between carbohydrate intake and anthropometric outcomes, with increased effect sizes and additional significant associations for starch and fiber, and fewer statistically significant associations for intrinsic and extrinsic sugars. In contrast to frequentist models, Bayesian models yielded more stable and consistent estimates across time-lagged and isotemporal frameworks, showing no differences in the directions of associations across temporal frameworks. Models unadjusted for baseline adiposity overstate dietary impacts; including baseline adiposity is essential to isolate true diet-change effects from initial weight.

Conclusion: Our findings suggest that incorporating temporal structure, especially through Bayesian models, can uncover relevant relationships that concurrent models may overlook. This study demonstrates that model specification, both in temporal framework and statistical approach, meaningfully influences both the detection and interpretations of associations in nutritional epidemiology.

We present a detailed dynamical analysis of the Quaoar–Weywot system based on nearly 20 yr of high-precision astrometric data, including new Hubble Space Telescope observations and stellar occultations. Our study reveals that Weywot’s orbit deviates significantly from a purely Keplerian model, requiring the inclusion of Quaoar’s nonspherical gravitational field and center-of-body–center-of-light (COB-COL) offsets in our orbit models. We place a robust upper limit on Weywot’s orbital eccentricity (e < 0.02), substantially lower than previous estimates, which has important implications for the strength of mean-motion resonances acting on Quaoar’s ring system. Under the assumption that Quaoar’s rings lie in its equatorial plane, we detect Quaoar’s dynamical oblateness, J₂, at ∼2σ confidence. The low J₂ value found under that assumption implies that Quaoar is differentiated, with a total bulk density of 1751 ± 13 (stat.) kg m⁻³. Additionally, we detect significant COB-COL offsets likely arising from latitudinal albedo variations across Quaoar’s surface. These offsets are necessary to achieve a statistically robust orbit fit and highlight the importance of accounting for surface heterogeneity when modeling the orbits of dwarf planet moons. These findings improve our understanding of Quaoar’s interior and surface while providing key insights into the stability and confinement mechanisms of its rings.

Recent advances in Bragg coherent diffraction imaging (BCDI) experimental techniques permit routine measurement of multiple Bragg peaks from a single crystalline grain. The resulting images contain the full lattice distortion vector field which can be differentiated to provide lattice strain and rotation. With the advent of fourth-generation synchrotron light sources, such multi-peak datasets are produced at high rates, facilitating the need for rapid phase retrieval of the multiple peaks and subsequent image analysis. Here we describe and demonstrate a new implementation of a coupled phase retrieval technique for multi-peak BCDI which simultaneously treats each Bragg peak of the dataset and produces a three-dimensional image of the crystal's morphology and lattice distortion field. In addition, this method uses the redundant information contained in the various Bragg diffraction patterns to detect and suppress spurious signal appearing on the detector in a subset of the measurements. Compared with manual data editing, adaptive coupling produces a more consistent phase profile in reciprocal space and sharper surfaces in direct space, with no significant difference in computational cost. These improvements reduce the need for manual preprocessing and enable robust high-throughput analysis of multi-peak BCDI data, supporting near-real-time strain microscopy at modern synchrotron facilities.