Wave propagation for reaction-diffusion equations on infinite random trees

The asymptotic wave speed for FKPP type reaction-diffusion equations on a class of infinite random metric trees are considered. We show that a travelling wavefront emerges, provided that the reaction rate is large enough. The wavefront travels at a speed that can be quantified via a variational formula involving the random branching degrees $\vec{d}$ and the random branch lengths $\vec{\ell}$ of the tree. This speed is slower than that of the same equation on the real line $\mathbb{R}$, and we estimate this slow down in terms of $\vec{d}$ and $\vec{\ell}$. Our key idea is to project the Brownian motion on the tree onto a one-dimensional axis along the direction of the wave propagation. The projected process is a multi-skewed Brownian motion, introduced by Ramirez [Multi-skewed Brownian motion and diffusion in layered media, Proc. Am. Math. Soc., Vol. 139, No. 10, pp.3739-3752, 2011], with skewness and interface sets that encode the metric structure $(\vec{d}, \vec{\ell})$ of the tree. Combined with analytic arguments based on the Feynman-Kac formula, this idea connects our analysis of the wavefront propagation to the large deviations principle (LDP) of the multi-skewed Brownian motion with random skewness and random interface set. Our LDP analysis involves delicate estimates for an infinite product of $2\times 2$ random matrices parametrized by $\vec{d}$ and $\vec{\ell}$ and for hitting times of a random walk in random environment. By exhausting all possible shapes of the LDP rate function (action functional), the analytic arguments that bridge the LDP and the wave propagation overcome the random drift effect due to multi-skewness.Comment: 63 pages, 4 Figure

Chain-of-Thought Tuning: Masked Language Models can also Think Step By Step in Natural Language Understanding

Chain-of-Thought (CoT) is a technique that guides Large Language Models (LLMs) to decompose complex tasks into multi-step reasoning through intermediate steps in natural language form. Briefly, CoT enables LLMs to think step by step. However, although many Natural Language Understanding (NLU) tasks also require thinking step by step, LLMs perform less well than small-scale Masked Language Models (MLMs). To migrate CoT from LLMs to MLMs, we propose Chain-of-Thought Tuning (CoTT), a two-step reasoning framework based on prompt tuning, to implement step-by-step thinking for MLMs on NLU tasks. From the perspective of CoT, CoTT's two-step framework enables MLMs to implement task decomposition; CoTT's prompt tuning allows intermediate steps to be used in natural language form. Thereby, the success of CoT can be extended to NLU tasks through MLMs. To verify the effectiveness of CoTT, we conduct experiments on two NLU tasks: hierarchical classification and relation extraction, and the results show that CoTT outperforms baselines and achieves state-of-the-art performance.Comment: EMNLP2023 Main Conferenc

Unlock the Potential of Counterfactually-Augmented Data in Out-Of-Distribution Generalization

Counterfactually-Augmented Data (CAD) -- minimal editing of sentences to flip the corresponding labels -- has the potential to improve the Out-Of-Distribution (OOD) generalization capability of language models, as CAD induces language models to exploit domain-independent causal features and exclude spurious correlations. However, the empirical results of CAD's OOD generalization are not as efficient as anticipated. In this study, we attribute the inefficiency to the myopia phenomenon caused by CAD: language models only focus on causal features that are edited in the augmentation operation and exclude other non-edited causal features. Therefore, the potential of CAD is not fully exploited. To address this issue, we analyze the myopia phenomenon in feature space from the perspective of Fisher's Linear Discriminant, then we introduce two additional constraints based on CAD's structural properties (dataset-level and sentence-level) to help language models extract more complete causal features in CAD, thereby mitigating the myopia phenomenon and improving OOD generalization capability. We evaluate our method on two tasks: Sentiment Analysis and Natural Language Inference, and the experimental results demonstrate that our method could unlock the potential of CAD and improve the OOD generalization performance of language models by 1.0% to 5.9%.Comment: Expert Systems With Applications 2023. arXiv admin note: text overlap with arXiv:2302.0934

Can Teaching Enthusiasm Partially Predict the Reading Attainment of Low-income Students in Secondary Schools in England?

The poverty achievement gap in early reading is a persistent issue in England and around the world, potentially disadvantaging poor students and their further study. This new study employs student-perceived teaching enthusiasm and reading attitudes to help explain the poverty attainment gap. The sample was 5,242 15-year-old participants in PISA 2018 from 175 secondary schools in England. Path analysis is used to investigate the potential effect of teaching enthusiasm on the reading attainment of low-income students. The findings indicate that family socioeconomic status remains an important predictor of students' reading achievement. Students from economically privileged families tend to rate teaching enthusiasm more highly and express a positive reading attitude, which can partially explain the poverty attainment gap in reading. Therefore, teachers might be able to enhance low-income students’ reading outcomes and close the poverty attainment gap a little through enhanced teaching enthusiasm to cultivate students’ positive reading attitudes

Semiconductor-based nanocomposites for photocatalytic H-2 production and CO2 conversion

Semiconductor-based photocatalysis has attracted much attention in recent years because of its potential for solving energy and environmental problems that we are now facing. Among many photocatalytic reactions, the splitting of H2O into H-2 and O-2 and the reduction of CO2 with H2O into organic compounds such as CH4 and CH3OH are two of the most important and challenging reactions. Many studies have been devoted to designing and preparing novel photocatalytic materials for these two reactions. This article highlights recent advances in developing semiconductor-based nanocomposite photocatalysts for the production of H-2 and the reduction of CO2. The systems of semiconductor-cocatalyst, semiconductor-carbon (carbon nanotube or graphene) and semiconductor-semiconductor nanocomposites have mainly been described. It has been demonstrated that the design and preparation of nanocomposites with proper structures can facilitate charge separation/migration and decrease the charge recombination probability, thus promoting the photocatalytic activity. Keeping the reduction and oxidation processes in different regions in the nanocomposite may also enhance the photocatalytic efficiency and stability. The location and size of cocatalysts, the interfacial contact between semiconductor and carbon materials, and the heterojunctions between different semiconductors together with the suitable alignment of band edges of semiconductors are key factors determining the photocatalytic behaviours of the nanocomposite catalysts

Developing the Symptoms and Functional Impairment Rating Scale:A Multi-Dimensional ADHD Scale

Objective: This research developed a practical, multi-dimensional attention deficit hyperactivity disorder (ADHD) rating scale (i.e., the Symptoms and Functional Impairment Rating Scale, SFIRS) for Chinese children, aged 6-12 years, with ADHD. Methods: The structural validity, criterion validity, internal consistency, and test-retest reliability of the scale were evaluated. Item screening was conducted with 412 ADHD patients and 322 developmentally typical controls. Results: The scale includes 44 items, divided among Hyperactivity-Impulsivity, Self-Control, Inattention, Self-Management, Academic Performance, and Social Interaction. The six-factor model showed good data fit, with each factor significantly correlated with its corresponding criterion (r=0.690-0.841). The Cronbach's α of the full scale was 0.976. Total score test-retest reliability was r=0.816 (p<0.01). Conclusion: The SFIRS thus demonstrated good reliability and validity and may be used to assess ADHD among children aged 6-12 years in China