Estimating the structures at high or low quantiles has become an important subject and attracted increasing attention across numerous fields. However, due to data sparsity at tails, it usually is a challenging task to obtain reliable estimation, especially for high-dimensional data. This paper suggests a flexible parametric structure to tails, and this enables us to conduct the estimation at quantile levels with rich observations and then to extrapolate the fitted structures to far tails. The proposed model depends on some quantile indices and hence is called the quantile index regression. Moreover, the composite quantile regression method is employed to obtain non-crossing quantile estimators, and this paper further establishes their theoretical properties, including asymptotic normality for the case with low-dimensional covariates and non-asymptotic error bounds for that with high-dimensional covariates. Simulation studies and an empirical example are presented to illustrate the usefulness of the new model.
In intelligent education, personalized mathematics question generation aims to produce mathematics questions that satisfy educational requirements while supporting adaptive assessment and learning. Existing LLM-based single-agent and multi-agent methods improve generation flexibility, but they still tend to rely on aggregated feedback or model randomness, making it difficult to jointly ensure dimension-wise objective alignment and controllable diversity. To address these challenges, we propose EduAgentQG, a multi-agent collaborative framework for personalized mathematics question generation with explicit diversity and objective-aware evaluation. EduAgentQG organizes question generation as a closed-loop process of planning, writing, evaluation, refinement, and checking: structured generation plans and multiple generation directions guide candidate generation, while fine-grained evaluation verifies logical correctness, solvability, and objective alignment in knowledge concepts, difficulty, grade level, and core competencies. We first construct a mathematics question generation benchmark containing 10,273 questions across Grades 1–9, covering 634 knowledge concepts, 16 core competencies, and three difficulty levels; for evaluation, it is organized into two subsets: MathChoice, with 489 educational objectives for multiple-choice question generation, and MathBlank, with 500 educational objectives for fill-in-the-blank question generation. Experiments using Gemini-2.5-Flash, GPT-4o-mini, and Qwen2.5-72B-Instruct show that EduAgentQG consistently outperforms COT, COTN, ReAct, and EQPR in diversity, Objective Consistency, and Win Rate. On Gemini-2.5-Flash, EduAgentQG improves Win Rate by 3.90 and 4.75 percentage points on MathChoice and MathBlank, respectively, over the strongest baseline, demonstrating its ability to generate diverse, solvable, and educationally aligned personalized mathematics questions with stronger controllability.
The growing demand for rare earth elements (REEs) creates the need to search for new sources of their extraction. This experimental study aimed to investigate behavior of selected REEs during a hydrothermal liquefaction (HTL) of sewage sludge (SS) focused on their partitioning in the HTL products. The HTL experiments were carried out at 350 degrees C and for 30 min. residence time in a batch reactor, without and with addition of different catalysts. Among the tested REEs, Dy, Er, Eu, Gd, Ho, La, Lu, Nd, Pr, Sm, Tb, Tm, Y and Yb showed high affinity for the HTL biochar (above 99 %). Sc and Ce migrated into the aqueous phase (AP), but only at the level from thousandths to tenths of mg/dm3. The highest Ce content (53.2---874 mg/kg) was found in HTL biochar, but it should also be emphasized that the Y content (11.0---19.8 mg/kg) and La content (5.6---43.2 mg/kg) were relatively high. The presence of CeO2 as a catalyst resulted in significant increase in the contents of Gd, Ce, Nd and Sm in biochar. The trend towards binding to the post-process biochar is promising in terms of recovering critical raw materials from sewage sludge.
A weakly diffusive predator-prey model with Michaelis-Menten type harvesting term is studied. If the diffusion rate of the prey and the predator is small enough and the natural growth rate of the prey is much larger than the natural growth rate of the predator, the model becomes a singular perturbation problem. First, using the traveling wave transformation, we transform the problem into a multi-scale fast-slow system with two small parameters. After that, the geometric singular perturbation theory is employed to show the existence of the heteroclinic orbit, canard explosion and relaxation oscillation period of the fast-slow system. We obtain the existence of traveling wave solutions and periodic solutions of the original reaction-diffusion model. Numerical examples illustrate our theoretical results.
The article starts with the social controversy over the Chinese actress Li Jinming, who gained brief but notable prominence through her leading role in iPartment (2009–2014), a Chinese urban sitcom widely regarded as the dometic adaptation of Friends. In September 2023, archival footage of her ostensibly ‘tragic’ entanglement in a rural, patriarchal household from the 2014 reality TV show Celebrities Come to My Home, which had aired nearly a decade prior, resurfaced and went viral on Chinese social media.Rather than focusing on the social controversy sparked by Li regarding the family pressures faced by urban women who marry below their social status, this article points out that the binary epistemology, educated women versus rural (single) men implicit in the controversy, represents a mode of cognitive warfare imbued with a teleological belief in progress, which the paper theorizes as ‘urban feminism’.To trace this volatile field, the study examines multiple texts illustrative of fictional television dramas, high-profile digital controversies, state-sanctioned broadcasting, and reality shows, along with participatory digital remixes and the cascading online disputes erupting across the cyber-sphere, in an attempt to probe into how gender antagonism is transformed into a digital spectacle rooted in the urban-rural divide. While reclaiming narrative power, urban feminism operates primarily on an epistemic approach that prioritizes visibility over structural critique or offline solidarity. Ultimately, by excluding rural women's struggles and avoiding systemic intervention, urban feminism risks reducing cognitive warfare to performance, leaving the broader gender revolution unfinished.
