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The Maximum Leaf Spanning Arborescence problem (MLSA) in directed acyclic graphs (dags) is defined as follows: Given a directed acyclic graph G and a vertex r∈ V(G) r∈V(G) from which every other vertex is reachable, find a spanning arborescence rooted at r maximizing the number of leaves (vertices with out-degree zero). The MLSA in dags is known to be APX-hard as reported by Nadine Schwartges, Spoerhase, and Wolff (Approximation and Online Algorithms, Springer, Berlin Heidelberg, 2012) and the best known approximation guarantee of (7/5) 75 is due to Fernandes and Lintzmayer (J. Comput. Syst. Sci. 135: 158–174,2023): They prove that any α α-approximation for the hereditary 3-set packing problem, a special case of weighted 3-set packing, yields a \\max {(4/3),α } max43,α-approximation for the MLSA in dags, and provide a (7/5) 75-approximation for the hereditary 3-set packing problem. In this paper, we improve upon this result by providing a (4/3) 43-approximation for the hereditary 3-set packing problem, and, thus, the MLSA in dags. The algorithm that we study is a simple local search procedure considering swaps of size up to 10 and can be analyzed via a two-stage charging argument. We further provide a clear picture of the general connection between the MLSA in dags and set packing by rephrasing the MLSA in dags as a hereditary set packing problem. With a much simpler proof, we extend the reduction by Fernandes and Lintzmayer and show that an α α-approximation for the hereditary k-set packing problem implies a \\max {((k+1)/k),α } maxk+1k,α-approximation for the MLSA dags. On the other hand, we provide lower bound examples proving that our approximation guarantee of (4/3) 43 is best possible for local search algorithms with constant improvement size.

There has been significant work recently on integer programs (IPs) \\min {c^(⊤) x :Ax≤ b, x∈ ℤⁿ} minc⊤x:Ax≤b,x∈Zn with a constraint marix A with bounded subdeterminants. This is motivated by a well-known conjecture claiming that, for any constant Δ ∈ ℤ_(>0) Δ∈Z>0, Δ Δ-modular IPs are efficiently solvable, which are IPs where the constraint matrix A∈ ℤ^(m× n) A∈Zm×n has full column rank and all n× n n×n minors of A are within {-Δ , … , Δ } -Δ,⋯,Δ. Previous progress on this question, in particular for Δ =2 Δ=2, relies on algorithms that solve an important special case, namely strictly Δ Δ-modular IPs, which further restrict the n× n n×n minors of A to be within {-Δ , 0, Δ } -Δ,0,Δ. Even for Δ =2 Δ=2, such problems include well-known combinatorial optimization problems like the minimum odd/even cut problem. The conjecture remains open even for strictly Δ Δ-modular IPs. Prior advances were restricted to prime Δ Δ, which allows for employing strong number-theoretic results. In this work, we make first progress beyond the prime case by presenting techniques not relying on such strong number-theoretic prime results. In particular, our approach implies that there is a randomized algorithm to check feasibility of strictly Δ Δ-modular IPs in strongly polynomial time if Δ ≤ 4 Δ≤4.

This meta-analysis evaluated the effectiveness of data-driven learning (DDL) among low-proficiency L2 English learners, addressing the mixed results found in previous meta-analyses. The study incorporated 38 studies involving 2085 participants, yielding 37 effect sizes from control-experimental (C/E) studies and 42 from pre- and post-test (P/P) studies. The findings demonstrated that DDL had a medium effect in C/E studies (g = 0.71) and a large effect in P/P studies (g = 1.43). The moderator analyses, based on the corpus-based language pedagogy (CBLP) framework by Ma et al. (2022), examined 7 pedagogical moderators. The results reaffirmed the efficacy of DDL in teaching lexicogrammatical items and suggested DDL’s curriculum flexibility; the duration of DDL did not significantly impact its effectiveness. Unique to this meta-analysis were findings that DDL was more effective for low-proficiency L2 learners of English when employing the following pedagogical strategies that cater to the cognitive-social nature of DDL: (1) utilizing paper-based concordancing to facilitate the pedagogical processing of corpus resources, (2) leveraging learners’ first language (L1) to improve comprehension of concordance meanings, (3) applying interactive communication with teacher verbal guidance or teacher verbal feedback attuned to learner responsiveness, and (4) providing teacher support in collaborative work to reduce the collaborative cognitive load on learners. Finally, this study proposed a holistic approach to CBLP design tailored to low-proficiency L2 learners, which presents an essential frontier for future research.

Blended learning (BL) is regarded as an effective strategy for combining traditional face-to-face classroom activities with various types of online learning tools (e.g., e-books). An effective feature of e-books is the ability to use digital notes. When e-books are used in BL, the strategic adoption of note-taking provides benefit that influence the learner' progress for self-regulated learning (SRL) and course achievements. However, learners tend to be unsure about how note-taking is performed using online learning materials and lack sequential patterns of e-book note-taking for SRL. Thus, in this paper, an exploratory study was conducted in an undergraduate course that implemented the BL design. The learning task for the blended learners in the present study was to study the learning material using BookRoll, an e-book system, during in-class and out-of-class learning sessions. Lag sequential analysis of the e-book learning behavior data was conducted to identify the blended learners' sequential behaviors of e-book note-taking for the cognitive strategy use of SRL. Moreover, the difference between higher- and lower-achievement blended learners in terms of their sequential behaviors of e-book note-taking for SRL was revealed. This study can help educators provide evidence-based educational feedback to learners regarding the identified sequential patterns of e-book note-taking that can be applied as effective strategies for promoting the cognitive strategy use of SRL and improvement of course achievement in BL.

Mobile technology is regarded as a helpful tool facilitating language learning. However, the success of mobile technology largely depends on learners’ acceptance. This study explored the factors that may affect students’ intention formation regarding mobile-assisted language learning (MALL) in the context of higher education through the lens of action control theory. The study adopted mixed methods: an online survey of 557 students and individual interviews with 70 students. The findings indicated factors in each of the three dimensions (preoccupation, hesitation, and volatility) of action control theory that positively or negatively influenced the students’ intention to use mobile technology for language learning. According to the findings, these influential factors may be related experiences in the preoccupation dimension, design and feature interference of MALL applications and teachers’ teaching style influence in the hesitation dimension, and overall appraisal and performance impact and other novelty interference in the volatility dimension. Students’ success in initiating and completing a MALL task depends on mainly depends on their acceptance of MALL, and this acceptance is affected by these factors in a positive or negative direction. The strengthening of the positive influence and the weakening of the negative influence caused by these factors should be paid attention to in the process of performing and engaging in a MALL task. Students’ concerns regarding the use of mobile technology in language education are addressed with suggestions for future research and practice in light of the findings.

This study employed drawing and co-word analysis techniques to explore students’ preferences for AI-assisted learning environments. A total of 64 teacher education students from a university in Taiwan participated in the study. The participants were asked to describe their perceptions of AI-assisted learning in the form of drawings and text descriptions. In order to analyze the content of the students’drawings, a coding scheme was developed based on the activity theory framework. Based on the results of the analysis, it was found that students placed more importance on personalized guidance and appropriate learning content provision. In addition, students acknowledged that AI technology can be used flexibly in different fields and situations. Interestingly, more than half of the students agreed that robots play important roles in AI-assisted learning. This indicates that the students expected a social AI learning companion. However, it was found that students’ expectations of an AI learning environment were less connected to the real environment and did not reveal learning activities with higher order thinking. In addition to the need for accurate and fast AI computing, this result indicated that professional instructional guidance is also an expectation that students have of AI education.