We study the size of minimum feedback vertex sets in digraphs under degree constraints. Our focus is on oriented graphs and arbitrary digraphs of bounded maximum degree. A digraph D is an oriented graph if D does not have a pair of opposite arcs. The degree of a vertex v of D is the sum of the in-degree and out-degree of v. Let fvs(D) be the minimum number of vertices whose deletion from D makes it acyclic. Let D be a digraph with n vertices and maximum degree Δ. We prove the following bounds. If D is an oriented graph, then fvs(D)≤3n7 when Δ≤4 and fvs(D)≤n2 when Δ≤5. If D is a connected digraph, Δ≤4 and D is not obtained from an odd undirected cycle by replacing every edge with a pair of opposite arcs with the same endvertices, then fvs(D)≤n2. If D is an arbitrary digraph with Δ≤5 then fvs(D)≤2n3. The above bounds are all sharp. The obtained bounds refine and extend earlier results on feedback vertex sets in sparse digraphs, and contribute to a more detailed understanding of how local degree restrictions influence global acyclicity properties.
Background Think-aloud traditionally has been conceptualized as a means of accessing cognitive processes through verbal report. The nine studies in this special issue reveal a broader methodological transition in which verbal protocols increasingly are combined with eye tracking, retrospective cueing, classroom observation, qualitative and quantitative coding, process mining, and epistemic network analysis. Purpose This meta-commentary synthesizes the nine studies together with Hu and Gao's commentary on culturally aware think-aloud research and considers what they collectively imply for the future of process-tracing research in learning and instruction. Results The special issue demonstrates that contemporary process tracing is becoming multimodal, transformational, and implicitly mixed methodological. However, greater methodological sophistication also creates new inferential problems: different traces represent different aspects of cognition; transformations can alter what is represented; integration often remains implicit; ecological validity is relational rather than merely situational; and verbalization itself is culturally situated. Building on these observations, I propose a representational–recursive perspective in which process-tracing research is organized around the design, transformation, integration, and recursive interrogation of multiple representations. I extend this framework further to cultural legitimation, representational equity, and human–AI inquiry. Conclusions The future of think-aloud research lies not in replacing verbal protocols, but in repositioning them within theoretically coherent multimodal systems. Progress will depend on making representational choices explicit, integrating evidence recursively, evaluating meta-inferences across traces, embedding cultural and equity considerations throughout the research process, and using artificial intelligence transparently and accountably.
This study explores the physicochemical properties and microbiological community structure of oil-contaminated soils from Midrand and Roodepoort, South Africa. Due to sample pooling, the analysis provides a composite profile for investigating site-specific microbial adaptations rather than replicated ecological inference. The soils of Midrand exhibited acidity (pH around 5.5-5.9), elevated levels of heavy metals (e.g., Zn exceeding 1000 mg/kg), and the presence of 5-6 ring polycyclic aromatic hydrocarbons (PAHs). The soils in Roodepoort exhibited a near-neutral pH (about 6.2-7.2), characterized by specific metal concentrations (e.g., Cr exceeding 150 mg/kg) and an elevated presence of four-ring polycyclic aromatic hydrocarbons (PAHs). Metagenomic analysis indicated distinct microbial communities: Pseudomonas spp. were prevalent in Midrand, while Bacillus spp. were dominant in Roodepoort. Correlation analysis suggested connections between pollutants and microbial taxa; however, these findings are tentative. Recovered metagenome-assembled genomes (MAGs) indicated genetic potential for polycyclic aromatic hydrocarbon (PAH) degradation in Midrand and for metal resistance in Roodepoort. The findings suggest that localised pollution profiles are associated with unique microbial community structures and genetic potentials, providing a genomic basis for proposing site-specific bioremediation strategies. The research underscores the necessity for measures that take into account pollutant composition, soil pH, and microbial adaptation.
Anaerobic digestion (AD) of animal manures for biogas production faces challenges including nutritional imbalance, foaming, and process instability. This study evaluated bioaugmentation with surfactant-degrading microbial consortia and cell-free extracts derived from well-characterized oil-contaminated soils during cow and pig manure digestion. These previously analyzed soils contained distinct microbial communities dominated by Pseudomonas in acidic, high-PAH soils and Bacillus in neutral-pH soils with genetic potential for hydrocarbon degradation. Over 30 days, six treatments were assessed using the Automatic Methane Potential Test System (AMPTS II), with pH monitoring, foaming analysis, and 16S rRNA sequencing coupled with PICRUSt2 functional prediction. Supplementation with microbial consortia and extract markedly increased cumulative biogas outputs (cow manure: 407.76 to 603.28 mL/gVS and pig manure: 403.82 to 627.5 mL/gVS), biomethane by 30-50%, reduced digestion time by 5-6 days, and improved pH stability. Foaming reduction was substrate-specific: extracts reduced foam by up to 60% in pig manure, while consortia reduced it by up to 65% in cow manure. Microbial analysis revealed enrichment of fermentative and syntrophic taxa (Clostridium sensu stricto and Paludibacter) and upregulation of methanogenesis pathways (tetrahydromethanopterin S-methyltransferase). This study illustrates that tailored bioaugmentation utilizing consortia from hydrocarbon-contaminated soils provides an environmentally sustainable method to enhance methane yields, improve stability, and control foaming in manure AD, with outcomes significantly affected by the type of manure and amendment strategy employed.
This study addresses the perception of Sub-Saharan Africa (SSA) as a region with limited financial capabilities and technological advancement to enhance environmental sustainability. Conducted across 24 SSA countries from 2000 to 2021, the research employs instrumental IV and panel quantile regressions. It shows that financialization, when coupled with innovation-driven activities, positively impacts environmental sustainability. The findings reveal refined relationships, indicating that the impact of financialization on environmental sustainability varies based on contextual factors. Notably, positive effects are observed, particularly in terms of enhancing access to credit and promoting innovation initiatives. The study underscores the importance of addressing emissions and promoting environmental sustainability in SSA through strengthened financial systems and innovation promotion. By highlighting the potential for decoupling economic growth from environmental degradation, the research provides valuable insights for policymaking and sustainable development efforts in the region.
