Abstract: A systematic evaluation of salt tolerance at the seedling stage was conducted using 143 maize inbred lines in this study. The results showed that salt stress significantly inhibited seedling growth and enabled the identification of several elite salt-tolerant inbred lines, including B114. Salt tolerance was significantly positively correlated with anti-oxidant capacity. Under salt stress, the highly salt-tolerant line B114 exhibited lower membrane damage, stronger reactive oxygen species scavenging capacity, and a significantly higher survival rate than the salt-sensitive line PHT55. Using random for-est-based machine learning, 50 core salt tolerance-related genes were unbiasedly identified from high-dimensional transcriptomic data. Functional enrichment analysis revealed that these genes were primarily involved in redox regulation, ion homeostasis maintenance, and stress signal transduction pathways. This study established a maize salt tolerance evaluation system closely aligned with field conditions and demonstrated that coordi-nated temporal transcriptional regulation represents a core molecular mechanism under-lying high salt tolerance in maize. The elite salt-tolerant germplasm and key candidate genes identified in this study provide valuable genetic resources and a theoretical founda-tion for molecular breeding of salt-tolerant maize adapted to saline-alkaline soils.

Abstract: Pinus radiata is a commercially valuable forest species whose productivity is increasingly threatened by climate change-related biotic and abiotic stresses such as diseases, soil salinization and rising temperatures. Taking as a starting point a sufficiently optimized somatic embryogenesis propagation protocol for radiata pine, this study aimed to evaluate the morphological and biochemical responses embryogenic cell lines subjected to different elicitors such as methyl jasmonate and tagatose during proliferation or sodium butyrate at maturation stage. The effect of various stresses such as salinity and high temperatures was evaluated at proliferation and germination stages. Then, biochemical analyses (total protein, hydrogene peroxide and malondialdehide contents) were carried out in embryogenic tissues and plants and the growth was also assessed in these tissues and in somatic plants. This latter growth assessment led to a classification of plants depending on their suitability to be planted ex vitro. Several embryogenic cell lines were tested and the response to elicitation or stress was found highly genotype-dependent however some trends could be observed particularly when assessing growth. These results suggest that somatic embryogenesis combined with stress priming or elicitor application may be a viable strategy to enhance biotic and abiotic stress tolerance in radiata pine.

Abstract: Traditional Digital Twins (DTs) in energy sectors lack cyber-threat awareness, while cybersecurity DTs overlook downstream physical impacts. Loosely coupled co-simulations attempt to bridge this gap but introduce computational lags that mask critical cross-domain vulnerabilities. To address these limitations, this paper proposes a unified, tightly coupled DT framework that integrates energy systems and cybersecurity domains into a single environment. The methodology models the precise mathematical, thermal, and electrical constraints of key assets to capture cross-domain feedback loops. Specifically, a power transformer and a microgrid-connected inverter serve as case studies to map cyberattack vectors directly onto physical definitions. Numerical validation evaluates multiple threat scenarios, including supervisory, measurement, and physical-level (harmonic) attacks on the transformer, alongside short-circuit and hybrid phase-harmonic attacks on the inverter. Results demonstrate how subtle digital disruptions propagate past communication layers to induce physical degradation and operational stress. By explicitly detailing the governing equations and providing sensitivity analyses, this work delivers a transparent, high-fidelity methodology for protecting critical cyber-physical infrastructures from asset-destructive manipulations.

Abstract: Background. Lower limb exoprostheses often lead to stump dermatological pathologies. The mechanisms by which mechanical microtraumas progress to non-healing ulcerative defects due to dysbiosis remain poorly understood. Study Objective. To analyze mechanical, inflammatory, and infectious stump skin complications and justify the role of bacterial and mycological dysbiosis in blocking tissue regeneration. Materials and Methods. Scale for the Assessment of Narrative Review Articles principles were used to quality control the narrative review. A targeted search was conducted in PubMed and Scopus databases. Search dates ranged date in January 1980 to May 2026. Results. Skin damage dynamics were categorized into three stages: adaptation (up to 12 months), chronic reactive changes (12–24 months), and late proliferative-infectious destruction (>24 months). The sealed sleeve space creates 100% humidity and alkalization (pH >6.5). This causes a "fungal shift," where resident Malassezia spp. lose dominance to invasive Candida albicans and non-dermatophyte molds (Aspergillus spp., Fusarium spp.). These pathogens form polymicrobial biofilms with Staphylococcus aureus. At the molecular level, delayed regeneration is driven by “frustrated phagocytosis”: macrophages, unable to engulf large fungal hyphae, continuously release reactive oxygen species and enzymes, trapping the wound in the inflammatory phase. Excessive matrix degradation and suppressed angiogenic factors further block epithelialization. Conclusion. The skin under a prosthesis socket forms a unique pathological biotope. Successful regeneration requires preventive mycobiota correction and targeted management of biophysical parameters (pH, humidity) within the “skin-liner” interface.

Abstract: Exposing foams stabilized by photoswitchable surfactants to UV light induces changes in surface surfactant concentration, leading to significant alterations in foam behaviour such as the generation of Marangoni flow and change in foam drainage patterns. The occurrence of Marangoni flow can be observed when either all elements of the foam or only their films are exposed to UV light. Conversely, changes in foam drainage occur when a macroscale portion of a foam column is exposed to UV light. To explore these phenomena, numerical models are developed and validated using experimental data. These models simulate the scale and profile of Marangoni flow from foam networks to films as well as the drainage flow within the foam network. Microscale findings demonstrate that Marangoni flow can be controlled by adjusting the intensity and duration of UV light exposure. Macroscopically, the drainage profile in exposed foam regions undergoes significant changes with varying UV intensity. Furthermore, beyond a certain threshold, the foam drainage reverses direction, contrary to gravity. The effect of foam interfacial mobility on the reversed drainage of both interior and exterior foams is analyzed. The findings provide a potential tool to control foam drainage behaviour without the need to modify other variables.

Abstract: Multimodal misinformation detection has advanced from text-only classification toward joint processing of language, imagery, and social metadata. Yet much of the literature still treats adaptation as an internal fusion problem rather than a systems-level routing problem, leaving open the question of when multimodal escalation is warranted and how expert usage can be reduced without materially weakening predictive quality. This paper introduces MemANS, an event-driven, in-memory Agentic Name Search architecture for multimodal misinformation detection. MemANS treats inference as a resolution process over named experts: a default text–metadata resolver handles ordinary cases, while a specialist is invoked only when cross-modal disagreement and confidence conditions jointly indicate that additional reasoning is justified. The empirical study is conducted on a balanced, fully image-available Fakeddit benchmark comprising 5400 training instances, 840 validation instances, and 840 test instances across six misinformation classes. On the final test set, MemANS achieves 0.6182 macro-F1, 0.6167 accuracy, 0.5405 MCC, and 0.8726 weighted one-vs-rest AUC, clearly surpassing the always-on fusion baseline (0.5732 macro-F1) with a statistically supported gain of 0.0454 (p < 0.001) while using only 1.7202 average experts versus 2.0000. The results indicate that Agentic Name Search is a viable and practically meaningful multimedia-systems abstraction for adaptive multimodal reasoning.

Abstract: This research paper examines the critical intersection of traditional ecological knowledge (TEK) protection, dam development, and glacial lake outburst flood (GLOF) mitigation in mountain regions, particularly the Hindu Kush-Karakoram-Himalaya (HKKH) region. Drawing from 77 peer-reviewed studies, this review synthesizes evidence on how indigenous and local knowledge systems can be protected and integrated into large-scale infrastructure projects and disaster risk reduction strategies. Key findings reveal that while TEK offers invaluable insights for GLOF early warning systems and community-based adaptation, significant gaps persist in formal protection mechanisms, particularly in dam planning contexts. The paper identifies successful participatory frameworks, documents persistent challenges in knowledge integration, and proposes policy recommendations for safeguarding TEK while enhancing climate resilience in vulnerable mountain communities. This synthesis is particularly timely given the accelerating impacts of climate change on glacial systems and the expansion of hydropower infrastructure in high-mountain Asia.

Abstract: The reliability of unrelated-donor searches depends on high-resolution HLA typing, yet a large fraction of records in national stem-cell donor registries were generated at low or intermediate resolution and are therefore under-used in modern matching. Here we develop an Extreme Learning Machine (ELM) approach that upgrades low/mid- to high-resolution HLA data by learning the haplotype and diplotype structure of a national donor population and assigning the most probable high-resolution genotypes together with posterior probabilities. The model was trained on the Greek national registry (Hellenic Transplant Organization, established 2002; 117,345 donors, ~20% low-resolution) and validated on two independent Greek cohorts (ORAM, n = 20,100; GRPT, n = 4,353) using accuracy and call-rate metrics. The population-specific ELM achieved a per-locus accuracy of 70–94% (depending on the confidence threshold) with an overall call rate of 98.1%, recovering usable high-resolution information and increasing the proportion of registry donors usable in high-resolution matching. The method is fast, lightweight and population-tailored, complementing established expectation-maximisation imputation tools.

Abstract: Relevance. The solvent accessible surface area (SASA) of amino acid residues is a key characteristic for protein structure analysis, but precise methods for calculating it (e.g., FreeSASA) are computationally expensive. Empirical approximations based on the res-idue interaction network (RIN) graph can provide high speed while maintaining ac-ceptable accuracy. Proposed approach. Three empirical functions for estimating relative SASA are pro-posed: approx_sasa, surface_score, and exp_sasa using the degree of the node in RIN as an argument. We present a comparative study of two approaches to graph construction: the classical Cα-graph (threshold 8 Å) and the graph of heavy atoms (Heavy-Atom Graph, HAG, threshold 5.0 Å). The parameters were calibrated on a sample of 509 protein structures (128,794 residues) from various origins using the true relative SASA calculated by the FreeSASA library. Main results. An extended set of 11 RIN topological features was developed and vali-dated, including basic node characteristics, centrality measures (betweenness, eigen-vector, closeness) and hydrophobic subgraph features. Training ensemble models (Random Forest, XGBoost) with these features made it possible to achieve: Random Forest on HAG: MAE = 0.057 ± 0.033, Pearson r = 0.915 ± 0.080 (best result), Random Forest on Cα graph: MAE = 0.066 ± 0.041, Pearson r = 0.890 ± 0.100. Comparison with GNN. We compared our approach with graph neural networks (GCN, GAT, GraphSAGE). GraphSAGE on HAG showed a result close to Random Forest: MAE = 0.0715, Pearson r = 0.8917, indicating the potential applicability of graph neural net-works when using HAG. GCN and GAT performed significantly worse (MAE = 0.14–0.15, Pearson r = 0.51–0.61). Computational efficiency. Empirical formulas are calculated in 0.008 ms per structure (~26,000× faster than FreeSASA), Random Forest in prediction mode is calculated in 36.5 ms (~6× faster than FreeSASA). HAG construction takes 21 times longer than a Cα graph (279.5 ms vs. 13.3 ms). Practical significance. The proposed empirical features are recommended for large-scale pipelines critical to speed and interpretability. Random Forest on HAG is the optimal choice for tasks that require maximum accuracy (MAE = 0.057, Pearson r = 0.915). GraphSAGE on HAG can be considered as an alternative when using deep learning.

Abstract: Background: Anti-doping education in most national systems remains anchored to knowledge-transmission models that catalogue banned substances and sanctions but rarely address the organizational, social, and motivational architecture surrounding a young athlete's decision to dope. Whether a management-oriented curriculum — grounded in the resource-based view (RBV) and stakeholder theory — outperforms conventional, rule-based instruction is untested in a developing-nation setting with acute resource constraints. Methods: We conducted a two-arm, parallel-group randomized controlled trial with 321 elite athletes aged 13–19 (intervention n = 161; control n = 160) recruited across athletics, football, and swimming federations in Ethiopia. The intervention arm received a six-session, management-oriented curriculum built on RBV and stakeholder-theory principles; the control arm received a duration- and format-matched conventional WADA/NADA-style knowledge curriculum. Anti-doping knowledge, attitudinal alignment, and ethical/moral reasoning were assessed pre- and post-intervention. Analyses used repeated-measures ANOVA, a 2×2 (modality × gender) factorial ANOVA, and bootstrapped mediation modeling with Sobel tests. Results: The intervention group improved on knowledge by 45% (18.5→26.9, η² = .05), on attitudinal alignment by 30% (22.4→29.1, η² = .04), and on ethical reasoning by 35% (23.0→31.0, η² = .06), each significantly larger than control-group gains (all p < .001). Gains were present in both sexes but numerically larger for male athletes (+38% vs. +29% in ethical reasoning). Mediation analysis showed that anti-doping knowledge significantly channeled the intervention's effect onto both attitudes (indirect effect = 6.57, Sobel z = 9.50, p < .001) and ethical reasoning (indirect effect = 6.20, Sobel z = 8.95, p < .001), while a substantial direct effect persisted after accounting for the mediator. Conclusions: A management-based curriculum that builds athlete capability and engages the surrounding stakeholder network produces markedly larger and more durable gains in knowledge, attitudes, and ethical reasoning than conventional rule-recitation education, with cognitive mastery acting as a partial mediator rather than the sole mechanism of change. These findings support a shift in anti-doping education policy — particularly in resource-constrained federations — toward capability-building, stakeholder-engaged pedagogy.

Abstract: Quantum mechanics elevates non-commutativity from a mathematical curiosity to a physical axiom: observables are promoted to operators, and Poisson brackets are replaced by commutators. This ``quantization procedure'' has remained a postulate for a century, with no explanation of \textit{why} nature demands non-commuting observables. We argue that the answer has been hiding in plain sight since 1843: the quaternion algebra $\HH$, whose defining relation $\mathbf{i}\mathbf{j} = -\mathbf{j}\mathbf{i} = \mathbf{k}$ makes it the unique non-commutative normed division algebra over $\R$.We develop this argument in three tiers of increasing rigor. First, we prove that the 44-vector $\mathbb{Z}_3$-triality vacuum lattice---a zero-parameter discrete structure established in prior work---is \textit{exactly} the orbit closure of the quaternion basis under $\mathbb{Z}_3 \subset \SU(2)$. The three closure operations are unified as conjugations by a single $q_T \in \SU(2)$ (Proposition~3.1), and a group-theoretic proof via the $A_2$ root lattice decomposition of $\R^3 = V_0 \oplus V_1$ yields $|L_{44}| = 44$ (Theorem~3.1). Second, we derive the canonical commutation relation $[\hat{x},\hat{p}] = i\hbar$ from quaternion algebra through the constructive chain $\HH \to \HH_\C \cong M(2,\C) \to \mathcal{F}_B(\C^2) \to$ Heisenberg algebra, with $\hbar = \sqrt{3}\,S_0$ where $\sqrt{3}$ is the geometric quantum number of the $\mathbb{Z}_3$ rotation angle and $S_0$ the fundamental action scale of the lattice. Third, we construct the full Hilbert space framework via the GNS representation of $\HH$ as a C$^*$-algebra (Appendix~A).The Pauli algebra, Dirac algebra, and spin-statistics connection admit progressively weaker claims: the Pauli algebra is identically the quaternion algebra (theorem); the Dirac algebra inherits quaternion structure through $\mathrm{Cl}(3,0) \cong \HH \oplus \HH$ (structural); the spin-statistics connection is a geometric interpretation suggested by the framework. What was discovered as a mathematical structure in 1843, applied as a computational technique in 1925, and axiomatized as a postulate ever since, is revealed as the geometric foundation of quantum non-commutativity: \textit{quaternion multiplication is the mathematical origin of why observables fail to commute.

Abstract:

The COVID-19 pandemic led to a dramatic increase in healthcare‑associated infections (HAIs) and antimicrobial resistance (AMR), particularly in intensive care units (ICUs). This study aimed to provide a comprehensive genetic characterisation of opportunistic pathogens (OPs) circulating in the ICUs of two infectious diseases hospitals repurposed for treating severe COVID‑19 patients. Whole‑genome sequencing (WGS) was performed on 175 isolates recovered from patients and the hospital environment (including personal protective equipment, PPE) between 2021 and 2023. The species composition included Klebsiella pneumoniae (n=53), Acinetobacter baumannii (n=60), Staphylococcus aureus (n=20), Enterococcus faecalis (n=20), Escherichia coli (n=10), Proteus mirabilis (n=5), Pseudomonas aeruginosa (n=4), Enterococcus faecium (n=2), and Klebsiella variicola (n=1). Bioinformatic analysis included multilocus sequence typing (MLST), core genome single‑nucleotide polymorphism (SNP) analysis, phylogenetic reconstruction, and in silico detection of resistance and virulence genes and plasmid replicons. Among K. pneumoniae isolates, the high‑risk clone ST512 (47.2%) carrying bla_KPC‑3, pmrB(R256G), gyrA(S83I), oqxAB, qacEdelta1 and fosA dominated and showed intra‑hospital spread (9 patients, 7 PPE, 9 surfaces). A. baumannii was represented by ST2 (40.0%, all bla_OXA‑23‑positive), ST78 (28.3%, bla_OXA‑72/90) and ST19 (3.3%). For E. coli, clonal complex CC14 (including ST1193) carried bla_CTX‑M‑15, marR(S3N) and fluoroquinolone resistance mutations. S. aureus isolates were assigned to CC15, CC8, CC22 (MRSA) and CC97. Resistance genes against up to nine antimicrobial classes were identified. Core genome SNP analysis confirmed direct transmission of K. pneumoniae (1–6 SNP differences) between patients and healthcare worker gloves. PPE was a major reservoir (68.4% of environmental isolates). High frequencies of IncF, rep5a/rep16, rep9 and IncC plasmids were detected in E. coli, S. aureus, E. faecalis and P. mirabilis, respectively. The study demonstrates the power of WGS for high‑resolution epidemiological surveillance, confirms the critical role of contaminated PPE in nosocomial transmission, and highlights the dominance of internationally spreading MDR clones in COVID‑19 ICUs.

Abstract: In this paper, we introduce the weighted generalized Moore-Penrose inverse within the framework of a Banach *-algebra. We characterize this new generalized inverse by employing the weighted MP-inverse and the generalized core-EP inverse. The connections with specific outer inverses are elucidated. Consequently, the attributes of the associated generalized inverses for complex matrices and bounded linear operators on Hilbert spaces are extended to the broader context of Banach algebras.

Abstract: Stem blight, caused by Phomopsis asparagi, is the most serious disease of asparagus (Asparagus officinalis L.) cultivation in warm regions of east and southeast Asia including Japan. Although Asparagus kiusianus, a wild species endemic to Japan, shows strong resistance and is cross-compatible with cultivated asparagus, the genetic basis of this resistance remains unclear. In this study, we used BC₁ populations from interspecific crosses between A. officinalis and A. kiusianus to dissect the inheritance of stem blight resistance and identify markers suitable for marker-assisted selection. Disease severity was evaluated by P. asparagi inoculation, and RAD sequencing was used to construct a linkage map and perform QTL analysis. Segregation patterns suggested that resistance was controlled by major genes and polygenic factors depending on the cross combination. A major QTL was detected on chromosome 1, and SNP_PRK showed significant association (LOD > 3). A dCAPS marker derived from SNP_PRK identified resistant individuals, with about 80% of heterozygotes showing resistance. CAPS marker PR1 discriminated susceptible, resistant, and heterozygous genotypes, and its genotyping results for all three genotypes were identical to those obtained with PRK. This marker may therefore provide a useful basis for selecting resistant lines in breeding programs.

Abstract: Background/Objectives: Cardiovascular disease is the leading cause of death in adults aged 65 years and over, yet older adults have long had the weakest claim on cardiology’s evidence base, even though international and constitutional law affirms their full right to health, free from age-based discrimination. We mapped the empirical and normative evidence on the gap between older adults’ legal entitlement to cardiovascular care and its clinical implementation, and identified thematic domains for future intervention research. Methods: Following the Arksey and O’Malley framework, refined by Levac and colleagues and by the Joanna Briggs Institute guidance and reported in line with PRISMA-ScR, we searched PubMed and Scopus for English-language sources published between 1980 and 2025 and retrieved institutional reports of the WHO, the UN and the Council of Europe from official repositories. Categories were derived inductively, and every source was checked against the Crossref record. Results: Twenty-nine sources met the inclusion criteria across six categories: history of legal protection, contemporary legal frameworks, ageism in cardiology, cardiac rehabilitation, bioethics, and institutional reports. Older patients were consistently under-represented in trials, referred less often to cardiac rehabilitation, and offered less guideline-concordant acute care; no source documented full closure of the gap. Conclusions: The entitlement is firmly established but is not matched by the evidence base, the guidelines or the rehabilitation infrastructure. Closing the gap calls for age-inclusive trials, geriatric outcomes in cardiovascular guidelines, and rehabilitation adapted to multimorbidity and frailty.

Abstract: Drug overdose contributes to a significant portion of adolescent deaths. Studies have established the relationship between drug overdose rates and drug type and adolescent population cohort size, but there has been little research investigating a correlation between geographic region (Northeast, Midwest, South, and West) and adolescent drug overdose mortality rates. We hypothesized regional differences exist, and that the South would have the highest adolescent drug overdose rates, as relates to lowest socioeconomic status (SES). We determined the correlation between adolescent drug overdose rates and United States census region to determine whether regional differences exist. In this study, publicly-available CDC Wonder adolescent (18-24) drug overdose data (2018-2024) was filtered by census region and analyzed. A chi-squared test contingency test was done to determine the significance in correlation between adolescent drug overdose mortality rates and census region. We found the West census region had the highest drug overdose rates per 100,000 adolescents (14.8%), while the Northeast had the lowest rate (12.1%). A chi-squared contingency test was performed to determine the correlation between adolescent drug overdose mortality rate and census region. A statistically-significant difference among the census regions was found (χ² = 175.2, p <0.00001). Despite having the highest median income, the West had the highest mortality rate; in contrast, despite having the lowest median income, the South had only the third-highest mortality rate. We conclude adolescent drug overdose mortality rates differed between census region, though the results contradicted the hypothesis that there would be a consistently-inverse relationship between such mortality rate and census region SES (median income).

Abstract: 3D scene reconstruction and novel view synthesis have undergone a paradigm shift with the advent of 3D Gaussian Splatting (3DGS). Unlike computationally intensive volumetric rendering, 3DGS leverages a point-based representation with a differentiable tile-based rasterizer. This elegant synthesis achieves state-of-the-art visual fidelity at real-time rendering frame rates. As the 3DGS literature grows rapidly, existing surveys have primarily organized the field around downstream applications. In contrast, this survey provides a rasterization-centric analysis, treating the differentiable rasterization pipeline as the core computational engine of 3DGS. We begin by delineating the mathematical foundations of Gaussian splatting and tracing its lineage from classical volume rendering. Subsequently, we propose a fine-grained taxonomy that categorizes the literature across three hierarchical dimensions: (1) representation and optimization, (2) rasterization pipeline innovations, and (3) scenario-driven rasterization extensions. By deconstructing these algorithmic advances in rasterization, we offer quantitative insights into hardware-algorithm co-design and outline critical trajectories for future research. To support the community, we maintain a continually updated repository of relevant literature and open-source implementations at https://github.com/3DAgentWorld/Advanced3DGS.

Abstract: Mobi spaces provide an algebraic abstraction of interpolation between points. In this paper we investigate their relation with geodesic structures. We present a construction of mobi spaces from a parametrized map, formulate conditions under which the mobi axioms follow from a given parametrization, and show that a broad class of second-order differential equations naturally gives rise to mobi spaces. This establishes a general framework linking geodesic motion and mobi structures. As an illustration, we obtain an explicit mobi space associated with a metric of non-constant negative curvature. Taken together, these results suggest that mobi spaces may provide a useful axiomatic framework for the study of geodesic interpolation.

Abstract: Contact-rich manufacturing processes such as surface cleaning, deburring, and polishing require precise force regulation and complex trajectory tracking that are challenging to automate using conventional robot programming methods. Learning from Demonstration (LfD) offers a powerful alternative to transfer these expert skills from human operators to robotic systems. The objective of this study is to systematically map academic publications addressing LfD applications in robotic deburring and polishing between 2016 and 2026, classify the algorithmic structures, sensory modalities, and control configurations employed, and identify key industrial integration challenges. In accordance with the PRISMA 2020 guidelines, a systematic search was conducted across Scopus, Web of Science, IEEE Xplore, and Google Scholar databases. Out of 288 initially retrieved records, duplicate removal and a two-stage screening process (title/abstract followed by full-text review) resulted in a final corpus of 24 primary studies included for qualitative synthesis. The included studies were classified into five algorithmic clusters: Dynamic Movement Primitives (DMPs) and variants (37.5%), probabilistic and statistical models (33.3%), deep learning and generative AI architectures (16.7%), autonomous dynamical systems (8.3%), and direct impedance control (4.2%). Force/torque sensing remains the dominant modality (70.8%), though recent years document a trend toward multimodal perception and generative action policies (e.g., Diffusion Policies). The findings confirm that while LfD offers substantial cost-reduction and flexibility benefits for small and medium-sized enterprises (SMEs), technical barriers such as the sim-to-real transfer gap, high-frequency impact dynamics in deburring, and the autonomous identification of local non-polishing areas (LNP-areas) continue to limit widespread industrial deployment.

Abstract: (1) Background: Hom-type algebras, proposed by Yau, generalize classical algebras via twisting maps. Dendriform and tridendriform algebras, introduced by Loday and Vallette, decompose associative multiplications and play significant roles in algebraic K-theory and operad theory. Rota-Baxter operators, originating from analysis and probability, have become a vital bridge connecting multiple disciplines. The π-graded structure, a classical tool in algebra, decomposes algebraic objects into direct sums indexed by a group π. (2) Methods: We systematically investigate the properties and construction methods of Rota-Baxter operators on π-graded Hom-algebras, and establish the derivation relations among π-graded Hom-tridendriform algebras, π-graded Hom-dendriform algebras and π-graded Hom-algebras. (3) Results: We prove that the generalized form, namely the π-graded Rota-Baxter system, is equivalent to π-graded Hom-dendriform algebras. Several iterative construction methods for π-graded Rota-Baxter Hom-algebras are also provided. (4) Conclusions: The structural equivalence between π-graded Rota-Baxter Hom-systems and π-graded Hom-dendriform algebras is established, providing a unified framework for these algebraic structures.