The present paper is concerned with the optimal weight of vibrating string equations with the first two eigenvalues $\lambda_1$ and $\lambda_2$ being given. Applying the method of critical equations in $L^p[0,1]$ for $p \gt 1$ and the inverse spectral theory of Sturm–Liouville problems with measure coefficients, we find that the optimal weight can be uniquely determined if and only if $\lambda_2 \ge 2\lambda_1$ provided that the weight is non-negative and symmetrical. As an application, we provide an estimation of the extremum for partial trace of the first two eigenvalues on a sphere in $L^1[0,1]$.

Traditional large-scale educational data are typically static and updated periodically, making it difficult to capture the dynamic changes in real time. However, recent technological advancements allow online exam platforms to collect students’ response data in real time. While item response theory (IRT) estimation methods are widely recognized for their accuracy, they are primarily designed for offline environments. When real-time data continuously arrives and online parameter estimation is required, these methods become computationally impractical. To address this challenge, we propose a recursive stochastic algorithm, i.e., truncated average stochastic Newton algorithm (TASNA), for the efficient online parameter estimation within the IRT framework. This algorithm significantly improves computational efficiency compared to the expectation–maximization (EM) algorithm implemented in the mirt package in R. The algorithm offers a powerful alternative to the traditional offline EM method. Furthermore, we investigate the asymptotic properties of the algorithm, proving its almost sure convergence and asymptotic normality. Numerical experiments using both simulated and real data demonstrate the practicality of the proposed method.

Language AI has become a popular tool across the humanities and social sciences, but it has yet to gain traction in socio-cultural anthropology. Fieldnotes, the core data for anthropologists, present a unique opportunity and challenge for applying language AI to understand diverse human behavior and experience. Anthropological fieldnotes are communicative products in cultural contexts through immersive, extensive and idiosyncratic fieldwork. To read fieldnotes, anthropologists typically engage in qualitative, reflexive interpretations, attuned to local meaning systems and intersubjective encounters. This paper demonstrates a novel synergy, combining anthropological expertise and various AI technologies to analyze natural observation texts about children’s peer-interactions, especially their moral dramas, in the historical context of rural Taiwan during the Cold War. These fieldnotes were collected by the late anthropologists Arthur Wolf and Margery Wolf in the world’s first anthropological study focused on Han Chinese children. Engagement with AI in this project began as methodological cross-fertilization, transforming raw fieldnotes into a text-as-data pipeline and discovering how ethnographic close-reading, machine-learning techniques (e.g., unsupervised topic modeling), transformer models (e.g., S-BERT) and generative models (e.g., GPT) can complement and augment each other’s value. Capitalizing on the systematic nature of Arthur Wolf’s fieldnotes, as well as the special protagonists of these fieldnotes – playful children, the most voracious learners – this paper compares how children, the anthropologist and AI make sense of pretend-fight moral dramas. Such a human–AI hybrid experiment embodies layered-interdisciplinarity at methodological, epistemological and, to some extent, ontological levels, anchored at children’s social cognition. Situated at the intersection of anthropology, digital humanities, developmental science and data science, this work sheds light on the similarities and differences in how machines and humans learn and make sense of morality, and by doing so, critically reflect on the nature of socio-moral intelligence.

To investigate the characteristics of a turbulent boundary layer (TBL) over the curved edge of the bow of submarine technology program office (SUBOFF) model, wall-resolved large-eddy simulation is conducted at a Reynolds number of $\mathop {\textit{Re}}\nolimits _L = 1.1 \times {10^6}$ based on the model length and free-stream velocity. Instead of using a trip wire at the bow surface, turbulent inflow is added to the simulation to induce boundary layer transition. The effects of geometric curvature and inflow turbulence intensity (ITI) are examined. With a low ITI level, natural transition takes place at the rear end of the straight section. With higher ITI levels, turbulence emerges immediately and evolves gradually, following a strong favourable-pressure-gradient (FPG) region near the forehead, which is significantly influenced by the large streamwise curvature. Within the FPG region, the root mean square of the wall pressure fluctuation (WPF) decreases rapidly, with the frequency spectra of WPF exhibiting good scalability with outer variables. Moreover, higher turbulence intensity levels lead to larger skin friction, which is related to the development of the TBL. To elucidate the generation mechanism of skin friction, the dynamic decomposition is derived in the curvilinear coordinate system. The mean convection and streamwise pressure gradient make the largest contributions to the local skin friction. Furthermore, an analysis of the energy transfer process based on the Reynolds stress transport equations in the curvilinear coordinate system is presented, highlighting the significant impact of geometric effects, particularly on the production term.

We investigate how the government, as a customer, affects a supplier’s environmental policies. We find that government contractors have significantly lower levels of toxic pollution. Exploring the mechanisms, we show that government contractors reduce pollution by strengthening internal environmental governance and increasing investments in pollution abatement. Further analysis rules out alternative explanations related to reduced economic activities and financial constraints. Overall, our results highlight the government’s important role in disciplining corporate environmental misbehavior.

Germplasm resources are the foundation for improving crop varieties and a strategic asset for global food security. They also advance plant breeding, agricultural biotechnology and the production of essential agricultural goods. To assess the distribution, diversity and conservation status of food crop germplasm in the Hainan Province, China, we conducted a detailed survey of the Hainan Island. Between 2017 and 2022, we collected 330 food crop germplasm resources, encompassing 16 cereal crops, including rice, maize, sweet potato. The collected germplasm resources exhibited traits of high resistance to both biotic and abiotic stresses, including common diseases and drought stress, as well as superior quality and adaptability to poor soil conditions such as sandy land. However, challenges such as low productivity and hybrid degradation were identified. These resources were primarily found in Haikou City, Baisha County, Danzhou City, Wuzhishan City and Sanya City. Additionally, we collected several ancient local varieties and endangered germplasm resources such as ‘Jiezi rice’ and ‘Wuzhishan maize’. This study serves as a reference for the conservation, development and utilization of local food crop germplasm resources in Hainan Province and lays the foundation for breeding and developing new varieties.

This paper examines the impact of financially constrained intermediate inputs on within-industry total factor productivity loss. Utilizing exogenous tax reforms in China as a natural experiment, our difference-in-difference analysis reveals that reduced tax burdens lead to increased firm-level intermediate inputs, particularly among financially constrained firms. We incorporate financially constrained intermediate inputs into a partial equilibrium model of firm dynamics. Our calibration suggests that financially constrained intermediate inputs play a quantitatively more important role in accounting for misallocation than financially constrained capital. The presence of financially constrained intermediate inputs introduces a downward bias in the measurement of value-added productivity, especially for firms in the top decile of gross-output productivity. As a result, the average “efficient” levels of capital and labor for the top decile firms in the standard Hsieh and Klenow (2009) exercise are lower than what is truly efficient.

The recent expansion of cross-cultural research in the social sciences has led to increased discourse on methodological issues involved when studying culturally diverse populations. However, discussions have largely overlooked the challenges of construct validity – ensuring instruments are measuring what they are intended to – in diverse cultural contexts, particularly in developmental research. We contend that cross-cultural developmental research poses distinct problems for ensuring high construct validity owing to the nuances of working with children, and that the standard approach of transporting protocols designed and validated in one population to another risks low construct validity. Drawing upon our own and others’ work, we highlight several challenges to construct validity in the field of cross-cultural developmental research, including (1) lack of cultural and contextual knowledge, (2) dissociating developmental and cultural theory and methods, (3) lack of causal frameworks, (4) superficial and short-term partnerships and collaborations, and (5) culturally inappropriate tools and tests. We provide guidelines for addressing these challenges, including (1) using ethnographic and observational approaches, (2) developing evidence-based causal frameworks, (3) conducting community-engaged and collaborative research, and (4) the application of culture-specific refinements and training. We discuss the need to balance methodological consistency with culture-specific refinements to improve construct validity in cross-cultural developmental research.

Survey instruments and assessments are frequently used in many domains of social science. When the constructs that these assessments try to measure become multifaceted, multidimensional item response theory (MIRT) provides a unified framework and convenient statistical tool for item analysis, calibration, and scoring. However, the computational challenge of estimating MIRT models prohibits its wide use because many of the extant methods can hardly provide results in a realistic time frame when the number of dimensions, sample size, and test length are large. Instead, variational estimation methods, such as Gaussian variational expectation–maximization (GVEM) algorithm, have been recently proposed to solve the estimation challenge by providing a fast and accurate solution. However, results have shown that variational estimation methods may produce some bias on discrimination parameters during confirmatory model estimation, and this note proposes an importance-weighted version of GVEM (i.e., IW-GVEM) to correct for such bias under MIRT models. We also use the adaptive moment estimation method to update the learning rate for gradient descent automatically. Our simulations show that IW-GVEM can effectively correct bias with modest increase of computation time, compared with GVEM. The proposed method may also shed light on improving the variational estimation for other psychometrics models.

Latent class models with covariates are widely used for psychological, social, and educational research. Yet the fundamental identifiability issue of these models has not been fully addressed. Among the previous research on the identifiability of latent class models with covariates, Huang and Bandeen-Roche (Psychometrika 69:5–32, 2004) studied the local identifiability conditions. However, motivated by recent advances in the identifiability of the restricted latent class models, particularly cognitive diagnosis models (CDMs), we show in this work that the conditions in Huang and Bandeen-Roche (Psychometrika 69:5–32, 2004) are only necessary but not sufficient to determine the local identifiability of the model parameters. To address the open identifiability issue for latent class models with covariates, this work establishes conditions to ensure the global identifiability of the model parameters in both strict and generic sense. Moreover, our results extend to the polytomous-response CDMs with covariates, which generalizes the existing identifiability results for CDMs.

Establishing the invariance property of an instrument (e.g., a questionnaire or test) is a key step for establishing its measurement validity. Measurement invariance is typically assessed by differential item functioning (DIF) analysis, i.e., detecting DIF items whose response distribution depends not only on the latent trait measured by the instrument but also on the group membership. DIF analysis is confounded by the group difference in the latent trait distributions. Many DIF analyses require knowing several anchor items that are DIF-free in order to draw inferences on whether each of the rest is a DIF item, where the anchor items are used to identify the latent trait distributions. When no prior information on anchor items is available, or some anchor items are misspecified, item purification methods and regularized estimation methods can be used. The former iteratively purifies the anchor set by a stepwise model selection procedure, and the latter selects the DIF-free items by a LASSO-type regularization approach. Unfortunately, unlike the methods based on a correctly specified anchor set, these methods are not guaranteed to provide valid statistical inference (e.g., confidence intervals and p-values). In this paper, we propose a new method for DIF analysis under a multiple indicators and multiple causes (MIMIC) model for DIF. This method adopts a minimal $L_1$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L_1$$\end{document} norm condition for identifying the latent trait distributions. Without requiring prior knowledge about an anchor set, it can accurately estimate the DIF effects of individual items and further draw valid statistical inferences for quantifying the uncertainty. Specifically, the inference results allow us to control the type-I error for DIF detection, which may not be possible with item purification and regularized estimation methods. We conduct simulation studies to evaluate the performance of the proposed method and compare it with the anchor-set-based likelihood ratio test approach and the LASSO approach. The proposed method is applied to analysing the three personality scales of the Eysenck personality questionnaire-revised (EPQ-R).

With the growing attention on large-scale educational testing and assessment, the ability to process substantial volumes of response data becomes crucial. Current estimation methods within item response theory (IRT), despite their high precision, often pose considerable computational burdens with large-scale data, leading to reduced computational speed. This study introduces a novel “divide- and-conquer” parallel algorithm built on the Wasserstein posterior approximation concept, aiming to enhance computational speed while maintaining accurate parameter estimation. This algorithm enables drawing parameters from segmented data subsets in parallel, followed by an amalgamation of these parameters via Wasserstein posterior approximation. Theoretical support for the algorithm is established through asymptotic optimality under certain regularity assumptions. Practical validation is demonstrated using real-world data from the Programme for International Student Assessment. Ultimately, this research proposes a transformative approach to managing educational big data, offering a scalable, efficient, and precise alternative that promises to redefine traditional practices in educational assessments.

Vessel collision risk estimation is crucial in navigation manoeuvres, route planning, risk control, safety management and forewarning issues. The interaction possibility is a good method to quantify the near-miss collision risks of multi-ships. Current models, however, are mostly concerned about the movements in an unrestricted isotropic travel environment or network environment. This article simultaneously addresses these issues by developing a novel environment–kinetic compound space–time prism to capture potential spatial–temporal interactions of multi-ships in constrained dynamic environments. The approach could significantly reduce the overestimation of the individual vessel’s potential travel area and the interaction possibility of encountering vessels in restricted water. The proposed environmental–kinetical compound space–time prism (EKC-STP)-based method enables identifying where and when multi-ships possibly interacted in the constraint water area, as well as how the interaction possibility pattern changed from day to day. The collision risk evaluation results were validated through comparison with other methods. The full picture of hierarchical collision risk distribution in port areas is determined and could be employed to provide quantifiable references for efficient and practical anti-collision measures establishment.