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Abstract Using our recently developed X‐ray diffraction basedforce constantsapproach, we have determined the equilibrium Si isotope fractionation between omphacite/garnet, quartz/kyanite, and quartz/zircon at temperatures relevant to the petrogenesis. We find that Na strongly affects the Si isotope fractionation between omphacite and garnet. Our results have suggested that the omphacite and garnet in eclogite collected in the Dabie Mountain, as well as the kyanite and its host quartz veins, are isotopically in equilibrium, which further suggests that the Dabie Mountain eclogites and its host veins underwent the same high pressure‐temperature condition during their formation. The Si isotope fractionation determined by our methods, together with published mass spectroscopy measurements, DFT‐CIPW calculations and sigmoid fitting on various felsic granites, have suggested that the Si isotope fraction between zircon and whole rock “saturates” at ∼0.45‰ at 1000 K when the SiO₂content in the granite is above ∼70 wt%. 

Abstract Nowadays, multidimensional data are often available from educational testing. One natural issue is to identify whether more dimensional data are useful in fitting the item response data. To address this important issue, we develop a new decomposition of Widely Applicable Information Criterion (WAIC) via the posterior predictive ordinate (PPO) under the joint model for the response, response time and two additional educational testing scores. Based on this decomposition, a new model assessment criterion is then proposed, which allows us to determine which of the response time and two additional scores are most useful in fitting the response data and whether other dimensional data are further needed given that one of these dimensional data is already included in the joint model with the response data. In addition, an efficient Monte Carlo method is developed to compute PPO. An extensive simulation study is conducted to examine the empirical performance of the proposed joint model and the model assessment criterion in the psychological setting. The proposed methodology is further applied to an analysis of a real dataset from a computerized educational assessment program. 

Wearable devices for continuous health monitoring in humans are constantly evolving, yet the signal quality may be improved by optimizing electrode placement. While the commonly used locations to measure electrodermal activity (EDA) are at the fingers or the wrist, alternative locations, such as the torso, need to be considered when applying an integrated multimodal approach of concurrently recording multiple bio-signals, such as the monitoring of visceral pain symptoms like those related to irritable bowel syndrome (IBS). This study aims to quantitatively determine the EDA signal quality at four torso locations (mid-chest, upper abdomen, lower back, and mid-back) in comparison to EDA signals recorded from the fingers. Concurrent EDA signals from five body locations were collected from twenty healthy participants as they completed a Stroop Task and a Cold Pressor task that elicited salient autonomic responses. Mean skin conductance (meanSCL), non-specific skin conductance responses (NS.SCRs), and sympathetic response (TVSymp) were derived from the torso EDA signals and compared with signals from the fingers. Notably, TVSymp recorded from the mid-chest location showed significant changes between baseline and Stroop phase, consistent with the TVSymp recorded from the fingers. A high correlation (0.77–0.83) was also identified between TVSymp recorded from the fingers and three torso locations: mid-chest, upper abdomen, and lower back locations. While the fingertips remain the optimal site for EDA measurement, the mid-chest exhibited the strongest potential as an alternative recording site, with the upper abdomen and lower back also demonstrating promising results. These findings suggest that torso-based EDA measurements have the potential to provide reliable measurement of sympathetic neural activities and may be incorporated into a wearable belt system for multimodal monitoring. 

The recent surge in computerized testing brings challenges in the analysis of testing data with classic item response theory (IRT) models. To handle individually varying and irregularly spaced longitudinal dichotomous responses, we adopt a dynamic IRT model framework and then extend the model to link with individual characteristics at a hierarchical level. Further, we have developed an algorithm to select important characteristics of individuals that can capture the growth changes of one’s ability under this multi-level dynamic IRT model, where we can compute the Bayes factor of the proposed model including different covariates using a single Markov chain Monte Carlo output from the full model. In addition, we have shown the model selection consistency under the modified Zellner–Siow prior, and we have conducted simulations to illustrate the properties of the model selection consistency in finite samples. Finally, we have applied our proposed model and computational algorithms to a real data application, called EdSphere dataset, in educational testing. 

Density Functional Theory (DFT) has become a cornerstone in the modeling of metals. However, accurately simulating metals, particularly under extreme conditions, presents two significant challenges. First, simulating complex metallic systems at low electron temperatures is difficult due to their highly delocalized density matrix. Second, modeling metallic warm-dense materials at very high electron temperatures is challenging because it requires the computation of a large number of partially occupied orbitals. This study demonstrates that both challenges can be effectively addressed using the latest advances in linear-scaling stochastic DFT methodologies. Despite the inherent introduction of noise into all computed properties by stochastic DFT, this research evaluates the efficacy of various noise reduction techniques under different thermal conditions. Our observations indicate that the effectiveness of noise reduction strategies varies significantly with the electron temperature. Furthermore, we provide evidence that the computational cost of stochastic DFT methods scales linearly with system size for metal systems, regardless of the electron temperature regime.