Abstract: Nitric acid production is among the most significant industrial point sources of nitrous oxide, which is a greenhouse gas with a global warming potential approximately 298 times that of carbon dioxide, yet the large installed base of legacy dual-pressure plants continues to operate with non-selective catalytic tail gas treatment systems that offer limited greenhouse gas abatement and impose rigid thermal constraints on the gas turbine cycle. A steady-state digital twin of an industrial dual-pressure nitric acid plant producing 52 t per hour of 60 wt.% nitric acid is developed, validated against measured plant data, and used to evaluate two selective catalytic retrofit configurations. The first heats raw tail gas to catalyst ignition temperature using the existing process heater, then raises the purified gas to turbine inlet conditions by mixing with flue gas from a newly installed combustion chamber. The second achieves the required temperature rise internally through catalytic fuel gas oxidation within an additional catalyst shelf in a two-bed reactor, eliminating supplementary combustion equipment entirely. The first configuration reduces total greenhouse gas emissions by 37% in carbon dioxide equivalent terms, eliminates ammonia slip, and enables a 5% production capacity increase worth 5.75 million EUR per year, at a capital cost of 4.77 million EUR and a discounted payback period of 16 months. The second achieves a 43% emissions reduction at a capital cost of 1.34 million EUR, reduces annual utility costs by 1.75 million EUR, and recovers its investment within 2.6 months without increasing electricity demand. The results demonstrate that selective catalytic tail gas treatment retrofit is a value-generating investment rather than a compliance cost. Projected across the global fleet of unabated dual-pressure plants, equivalent adoption could reduce sectoral nitrous oxide emissions by more than 21 Mt of carbon dioxide equivalent per year, representing over half the identified global industry mitigation potential.

Abstract: The intensive development of transport infrastructure globally and in Poland has led to a rapid increase in the number of bridge structures. Prestressed concrete is currently the most widely utilized structural material, accounting for 43.4% of these structures. A primary advantage of prestressed concrete is its capability to achieve considerable span lengths; consequently, its percentage share in terms of total bridge surface area is even higher, reaching 58.2% by the end of 2017. Although visual inspections are feasible for exposed tendon components, evaluating the residual prestressing force and diagnosing internal cable degradation—such as corrosion, grout deterioration, and voids—in post-tensioned structures presents a significant technical and scientific challenge. This paper introduces a structural health monitoring (SHM) approach, utilizing either periodic inspections or continuous electronic monitoring, to evaluate anchorage condition. The proposed methodology employs a novel measurement system that identifies structural anomalies by utilizing pattern recognition algorithms applied to acoustic emission (AE) signals. Furthermore, the identified pattern classes have been correlated with crack opening widths. This correlation enables the tracking of crack propagation effects on structural stiffness, while simultaneously monitoring other degradative processes, including active corrosion and anchorage slippage.

Abstract: Artificial intelligence (AI) is increasingly used in construction to forecast duration, monitor progress, prioritise risk, support procurement and logistics, improve supply chain visibility, and compare environmental trade-offs. These applications are often judged by their technical performance, yet that does not show whether, or how, an analytical output changes a project decision. This paper addresses that gap through governed decision translation: the process by which an AI-enabled output is inter-preted, validated, challenged, authorized, assigned for implementation, documented, and reviewed. A structured integrative review with framework synthesis was con-ducted using a ScienceDirect seed stream and targeted Web of Science cross-checks. The 34-study corpus was classified by evidence relevance and appraised across study design, deployment maturity, outcome proximity, and methodological credibility. Most studies focus on forecasting, monitoring, optimization, and decision support. Only one provides clear evidence of implementation in a live project, while two others approach an identifiable project-control intervention pathway. The evidence therefore supports theory building rather than causal claims of performance improvement. The resulting Governed AI Project Controls Framework distinguishes the data and analytical foundations of AI-enabled control from the decision interface, governed translation, authorised intervention, value domains, and subsequent learning. It also separates structural, procedural, and interpretive governance. Productivity related performance is treated as relatively close to intervention, resilience as a dynamic capability, and net-zero-oriented delivery as a more cumulative environmental domain. The evidence supports carbon-, energy-, waste-, and material-aware decisions, but not claims of achieved net-zero delivery. The paper offers a conditional explanation of how AI-supported insights may acquire authority, operational consequence, and accountability in temporary, multi-organisational construction projects, together with propositions, boundary conditions, and observable indicators for empirical testing.

Abstract: We report the installation and first two years of operation of an EM27/SUN Fourier transform spectrometer at the CNR-ISAC facility in Bologna, Italy, the first instrument of its kind operating in the Po Valley, one of the European region mostly affected by anthropogenic pollution. The instrument is integrated into the COCCON network and it retrieves total columns and column-averaged dry air mole fractions of CO₂, CH₄, CO, and H₂O using the PROFFAST processing chain as per standardized COCCON protocols. The data is filtered with the fitted solar gas shift in the O₂ absorption band for quality controls, and here we study the seasonality of the retrieved products. To assess the relationship between column-integrated and near-surface measurements, we present a case-study comparison against a co-located Cavity Ring-Down Spectroscopy analyzer for CO₂ and CH₄ over a single day, using ceilometer-derived Mixed Aerosol Layer height to interpret the differing diurnal variability between the two techniques, with CRDS showing substantially larger amplitude swings driven by boundary-layer dynamics and surface emission/sink processes. We further validate the EM27/SUN against TROPOMI satellite retrievals of XCH₄ and total-column CO over the full observing period, finding low systematic biases (-0.13% and 0.60% respectively) consistent with satellite mission requirements and comparable to TCCON stations at similar latitudes. As a case-study, we show that both instruments jointly detected an anomalous CO enhancement in July-August 2024 attributable to long-range transport of Canadian wildfires smoke, illustrating the capability of ground-based FTIR observations to identify high-altitude pollution intrusions undetectable by in-situ instrumentation alone. These results establish the EM27/SUN in Bologna as a robust reference for satellite validation and a valuable tool for characterizing atmospheric transport events in the Po Valley.

Abstract: The integration of large language models and autonomous agents into data engineering is shifting data systems from human-specified pipelines to processes in which agents interpret requirements, select sources, generate transformations, invoke tools, and communicate analytical results. This shift introduces a governance gap: a dataset may satisfy established quality requirements and a generated query may execute successfully while the agent applies an incorrect metric, combines incompatible grains, uses unauthorized sources, or produces conclusions without evidential support. We develop a conceptual framework for Agentic Data Engineering, the engineering domain concerned with specifying, validating, governing, and auditing data processes in which AI agents operate under delegated authority. An evidence-informed analysis of six foundations—Data Contracts, Semantic Layers, Data Quality, Guardrails, AI Governance, and Data Provenance—shows that existing controls are essential but fragmented. The framework integrates them through four artifacts: Agentic Data Contracts, Agentic Expectations, Agentic Data Provenance, and Agentic Data Governance, and defines Quality of Agentic Data Use as the central evaluative construct. A lifecycle model, a reference architecture, a failure taxonomy, a multidimensional evaluation scheme, and an illustrative governed sales-analysis scenario operationalize the framework and provide a foundation for the empirical validation of trustworthy agentic data systems.

Abstract: To determine the reprocessing potential of mining liabilities, a comprehensive evaluation of the tailings deposit at the former Halcon mining unit in central Peru was conducted. Direct and indirect methods were employed, including geophysical surveys, sampling through six drill holes up to 9.62 meters deep, textural analysis, mineralogical characterization (optical microscopy, SEM, XRD, and reflectance spectroscopy), and ICP-MS chemical analysis, complemented by geostatistical modeling for resource estimation. Geochemical and mineralogical results reveal highly oxidizing, acidic conditions (pH 1.83–4.91) and significant concentrations of Zn (5.46%), Pb (1.58%), Cu (1.67%), Ag (244 ppm), and Au (3.6 ppm). These economic minerals predominate in fine-grained fractions with high degrees of liberation, favoring metallurgical recovery. Geostatistical modeling estimated a total tailings tonnage of 87,642 tons, highlighting zones of high localized economic potential, particularly for Zn and Ag. Considering specific recovery scenarios, penalties, operational costs, and metal prices, a net financial benefit of approximately US$11.35 million was projected. This pioneering study demonstrates the feasibility of converting environmental liabilities into economic assets through strategic reprocessing initiatives, contributing a robust model for mine tailings valorization within the South American circular economy framework.

Abstract: This study investigates upcycled high-density polyurethane (HD-PUR) as a substitute for conventional cement-based screed in multi-story reinforced concrete (RC) buildings. Conventional screed (≈2400 kg/m³) adds substantial seismic dead mass without con-tributing to lateral stiffness, amplifying base shear, inter-story drift, and overturning moments. HD-PUR, produced from industrial waste via mechanical re-pressing, has a density of ≈150 kg/m³ and thermal conductivity of 0.025 W/m·K, yielding a 16-fold mass reduction and near-negligible inter-story heat transfer. Three-dimensional finite element models of 5-, 10-, and 15-story moment-resisting RC frames were developed in SAP2000, with modal and response spectrum analyses per-formed per the Turkish Building Earthquake Code (TBEC, 2018). HD-PUR substitution reduced base shear by 11.2–16.8% and inter-story drift by 10–18% across all models. These trends were validated against an existing five-story RC building in Beyoğlu, Is-tanbul (site class ZC; PGA = 0.359 g; in-situ concrete class C14), modelled in SAP2000 and STA. The fundamental period shortened from 0.888 s to 0.793 s, global base shear (FX) decreased by 10.5%, vertical base reaction (FZ) decreased by 16.6%, and the non-linear pushover-based performance level improved from Collapse Prevention to Life Safety without any intervention on load-bearing members. Thermal calculations per TS 825 indicate an 18% reduction in the building envelope's heating degree-day load, while life-cycle assessment data reported in the literature point to appreciably lower embodied carbon, supporting circular economy objectives. In short, HD-PUR floor fillers offer a low-cost strategy that jointly improves seismic re-silience, energy efficiency, and environmental performance in multi-story RC buildings.

Abstract: Emotion recognition in children’s drawings is difficult because affect is carried by sparse strokes, symbolic objects, and overall composition rather than by the stable appearance statistics of photographs. Work in this area typically reports a single accuracy figure, which says little about which predictions can be trusted. We built a reproducible four-class benchmark (Angry, Fear, Happy, Sad) on an existing public corpus of 818 children’s drawings and compared three transfer-learning regimes under identical stratified five-fold splits with nested model selection: ResNet-50, ViT-B/16, and an end-to-end fine-tuned SigLIP image encoder (SigLIP-FT). Reliability was assessed using top-1–top-2 probability margins, expected calibration error (ECE), and margin-based selective prediction. Five annotators independently labeled all images under a pre-specified analysis plan, providing a human reference point on the same items. SigLIP-FT reached the highest macro-F1 (0.773±0.028) ahead of ViT-B/16 (0.700±0.040) and ResNet-50 (0.598±0.038), and was the best calibrated (ECE 0.119). Margin-based abstention raised its macro-F1 to 0.818 at 73.0% coverage and 0.867 at 55.0%. Fear was also the least reliably judged category for annotators (Krippendorff’s α=0.422), yet their majority vote recovered the corpus labels with macro-F1 0.960, well above the model. Coverage–performance behavior, rather than a single full-coverage score, is therefore the appropriate reporting standard for ambiguous visual domains of this kind.

Abstract: Vibrio parahaemolyticus is a halophilic, Gram-negative bacterium widely distributed in marine and estuarine environments and recognized as a leading cause of seafood-associated gastroenteritis worldwide. In recent decades, its global emergence has been driven by environmental changes, particularly ocean warming, as well as the intensification of aquaculture and the globalization of seafood trade. This narrative review provides a comprehensive overview of the epidemiology, virulence factors, antimicrobial resistance, and One Health dimensions of V. parahaemolyticus. The pathogen’s ability to cause disease in humans is largely determined by key virulence determinants, including thermostable direct hemolysin (TDH), TDH-related hemolysin (TRH), and secretion systems that facilitate host colonization and cytotoxicity. From a One Health perspective, V. parahaemolyticus represents a critical interface among environmental, animal, and human health, and also causes severe diseases in aquaculture, including acute hepatopancreatic necrosis disease (AHPND) and translucent postlarval disease (TPD) in shrimp, as well as vibriosis in bivalve mollusks such as oysters, where infection may result in tissue damage and substantial larval and juvenile mortality, with important economic consequences. The increasing emergence of antimicrobial-resistant strains further complicates clinical management and highlights the role of environmental reservoirs and aquaculture practices in the dissemination of resistance. Additionally, climate-driven changes in temperature, salinity, and marine ecosystems are expanding the geographic distribution and seasonal dynamics of this pathogen. Strengthening integrated surveillance systems, improving food safety practices, and promoting interdisciplinary research, including studies of the molecular mechanisms underlying interactions between the epigenome and V. parahaemolyticus, are essential to mitigate the growing risks associated with V. parahaemolyticus. A comprehensive One Health approach is critical to address its evolving impact on global public health and food security.

Abstract: Land subsidence is a widespread geological hazard in urban areas, yet accurate prediction remains challenging due to the complex, non-linear spatio-temporal dynamics governing subsurface deformation. In this work, the PEGNet (Peridynamics-Emergent-GAT-GRU Network) method integrates Graph Attention Networks (GAT) with Gated Recurrent Units (GRU) under a three-level embedding strategy to predict land subsidence at monitoring points. Peridynamics gradient and emergent velocity features are fused with multi-source data at the feature level; multi-head graph attention captures spatial dependencies among monitoring points at the structure level; and a Peridynamics-based loss regularizer penalizes unrealistic spatial gradients while an attention entropy regularizer encourages focused attention patterns at the constraint level. Evaluated in Tongzhou District, Beijing over 60 months, the model achieves an RMSE of 5.16 mm, outperforming the GAT-GRU baseline by 25.1% and reducing RMSE by 51.7% relative to GCN-LSTM. Comprehensive ablation studies and baseline comparisons validate each component, showing that the dual-constraint framework effectively suppresses large-magnitude outliers. This work demonstrates that coupling macro-micro priors with spatio-temporal deep learning provides an effective paradigm for integrating physical and geoscience principles into data-driven subsidence prediction.

Abstract: This study constructs a two-period model where a regulator determines the level of precautionary capital, information-generating reporting, and the design of supervisory information systems, while providers respond by participating. When reporting successfully produces a verified diagnostic, continuation capital is set afterward, but reporting incurs various costs, including variable, participation, and fixed setup costs, before its information is utilized. In a Bayesian context, the diagnostic's gross decision value is weakly nonnegative because it can be disregarded. Reporting is only activated if its discounted decision value and any screening benefits outweigh its net costs and setup expenses. Under recursive maxmin assumptions, an admissible prior that makes the adverse state certain introduces a certainty boundary: diagnosis cannot alter the continuation capital once the conditions are met, and precaution substitutes for learning. Priors that are uniformly interior allow for ongoing learning. Recursive smooth ambiguity models positive reporting at finite levels of ambiguity aversion and converges to the maxmin boundary under specified conditions, without implying overall monotonicity. A joint-selection theorem compares scenarios with no reporting, common, and specialized reporting architectures after optimizing intensity. An architecture that keeps the common experiment and adds an ignorable signal slightly improves gross information but may reduce net surplus. Kenya’s virtual-asset framework provides a dated institutional example but neither calibrates the model nor reveals its core mechanism. The results are supported by analytical proofs, independent recalculations, and reproducible code.

Abstract: Eggplant (Solanum melongena L.) is a major horticultural crop for which genetic transformation and genome editing could accelerate functional genomics and precision breeding, but their routine use remains constrained by regeneration recalcitrance, strong genotype dependence, and fragmented methodological reporting. This review critically assesses Agrobacterium-mediated transformation protocols, genome-editing studies, and emerging in planta virus-based approaches across the complete workflow, from explant preparation and nucleic-acid delivery to regeneration, selection, plant recovery, and outcome assessment. The major variables shaping transformation success are examined, including explant type and age, pre-culture, bacterial strain, infection and co-culture conditions, acetosyringone, regeneration medium, selection pressure, shoot recovery, rooting, and efficiency assessment. The evidence indicates that reported performance differences are difficult to interpret because studies often rely on genotype-specific optimization, incomplete methodological description, and non-equivalent efficiency metrics. Complementary strategies are also discussed, including virus-induced gene silencing, virus-induced gene editing, biolistics, protoplast delivery, floral dip-inspired approaches, highly regenerable model genotypes, and morphogenic regulators. Finally, the review outlines priorities to move eggplant biotechnology from proof-of-concept toward reproducible breeding pipelines: standardized reporting, direct protocol comparisons, genotype-aware optimization, mechanistic studies of recalcitrance, and transformation-competent reference lines. Although centered on eggplant, the methodological framework and reporting priorities identified here are relevant to other horticultural crops in which genotype-dependent regeneration limits genome engineering. Together, these priorities provide a roadmap from isolated proof-of-concept experiments to reproducible and breeding-relevant genome-editing pipelines.

Abstract: Why cancer develops remains one of the central unsolved problems of biology. The Eco-Evolutionary Ground-State Theory of Cancer proposes that malignant transformation results from the conditional reactivation of an ancient ecological survival system whose evolutionary origins extend deep into early eukaryotic evolution. The theory reconstructs approximately one billion years of cancer genome evolution. It proposes that the common ancestor of Amoebozoa, Metazoa, and Fungi (AMF) evolved adaptive regulatory programs enabling survival under fluctuating ecological conditions, particularly changing oxygen availability. Rather than disappearing during the evolution of multicellularity, these programs became integrated into the metazoan genome as an evolutionarily conserved ancestral genomic compartment that normally remains epigenetically suppressed. Malignant transformation is initiated when an irreversibly damaged self-renewing host cell escapes apoptosis, enters reparative senescence, and undergoes unicellularization through reactivation of this ancestral genomic compartment. This transition establishes the eco-evolutionary stemgermline, which functions as the primary regulatory system governing carcinogenesis, tumor progression, cellular plasticity, genome reconstruction, metastatic dissemination, and therapeutic resistance. The genomic instability and phenotypic heterogeneity of malignant tumors are interpreted as downstream consequences of this hierarchical organization rather than its primary cause. The theory further proposes that recurrent unicellularization originally evolved as an adaptive mechanism during the transition to multicellularity but subsequently became transformed through host co-evolution into a parasite-like cellular system. By integrating genome evolution, stemgermline biology, oxygen ecology, and host–parasite co-evolution, the Eco-Evolutionary Ground-State Theory provides a unified evolutionary explanation for both the origin of cancer and the remarkable biological properties that characterize malignant disease.

Abstract: Background and Objectives: Biological correlates of admission consciousness remain incompletely characterized in older adults with acute ischemic stroke treated with intravenous thrombolysis. We evaluated associations between admission Glasgow Coma Scale (GCS) and pre-thrombolysis hematologic, inflammatory, iron-status, and micronutrient parameters, while considering the oral-systemic relevance of the resulting biological pattern. Materials and Methods: This retrospective single-center cohort included 95 unique patients aged ≥65 years treated between 2020 and 2024. Spearman correlations used the original GCS scores (11–14). Proportional-odds models used ordered categories (11–12, 13, and 14), adjusted for age and sex, with additional National Institutes of Health Stroke Scale (NIHSS) adjustment; false discovery rate (FDR) correction was applied. Results: Admission GCS correlated most strongly with RDW-CV (rho = −0.843; 95% bootstrap CI, −0.892 to −0.774) and MCV (rho = 0.779; 95% CI, 0.668 to 0.866). In age- and sex-adjusted models, odds ratios per 1-SD increase were 5.15 for hemoglobin, 3.17 for log-transformed ferritin, 4.49 for serum iron, 4.90 for log-transformed vitamin B12, 0.18 for C-reactive protein, and 0.018 for RDW-CV (all FDR-adjusted p < 0.001). Directions remained consistent after NIHSS adjustment. MCV showed a nonlinear association, with a model-derived turning point at 86.6 fL. Biomarkers were associated with absolute GCS at 24 hours but not with the direction of 24-hour change after FDR correction. Conclusions: The pre-thrombolysis biological profile was associated with the restricted range of admission GCS observed in this cohort. The convergence of hematologic, micronutrient, and inflammatory associations provides an exploratory oral-systemic research perspective but does not establish oral disease or an oral source for the systemic findings.

Abstract: Chronic obstructive pulmonary disease (COPD) is one of the leading causes of morbidity and mortality worldwide. Finding patients with early COPD is already difficult, but even those have already an advanced disease in the biological point of view with irreversible lung damage. A lot of effort is done to find the parameters for detection of patients with early pathophysiological changes before they develop airflow limitation. The importance of this stage is recently recognized and has different labels as “pre-COPD” and “early COPD”. Exhaled breath temperature (EBT) is a non-invasive method to detect and monitor inflammation in the respiratory system. Most studies on EBT have been performed in asthma and showed the utility of this approach to assess changes in airway inflammation. In the COPD patients, the number of airways and their vasculature is reduced and EBT decreases proportionally to the level of destruction, but is still increased during the COPD exacerbation. In recent studies, change in EBT after smoking a cigarette in patients without a diagnosis of COPD was significantly predictive for disease progression after 2 years. Early interventions based on these results should be tested for efficacy in prevention of the development of overt COPD.

Abstract: Among low-lying sandy coasts, where erosion represents a major challenge, artificial beach nourishment is extensively used as mitigation strategy. This study investigates the long-term morphological evolution of Lido di Dante beach (Northern Emilia-Romagna, Italy), a highly subsiding and erosion-prone coastal sector characterized by different configurations of rigid defence structures. The analysis is based on 12 multi-temporal topo-bathymetric survey datasets acquired between 2007 and 2025, covering the complete monitoring sequences of three regional nourishment interventions (Progettone 2, 3, 4). An integrated methodological approach combining sediment budget calculations, shoreline evolution analysis, cross-shore profile assessment, and beach slope evaluation was applied to characterize the morphological response of the nourished system. Results show a consistent post-nourishment response among the three interventions, with effective beach recovery followed by sediment redistribution from the subaerial and intertidal zones towards the nearshore. However, the morphological evolution showed marked spatial variability, reflecting the influence of coastal defence structures on sediment redistribution pathways. The findings highlight the need for repeated nourishment interventions to maintain long-term beach stability at Lido di Dante. Furthermore, the study demonstrates the importance of accurate long-term topo-bathymetric monitoring for evaluating nourishment performance and supporting adaptive coastal management strategies in complex coastal environments.

Abstract: Artificial Intelligence (AI)-enabled systems are now increasingly deployed across safety-critical, mission-critical, and socio-technical domains. Existing engineering disciplines offer mature approaches to human, organisational safety and software assurance; however, AI-enabled systems can exhibit characteristics such as probabilistic behaviour, data dependency, limited explainability, and adaptation that challenge traditional assurance methods. Our research examines assurance principles across three domains that arguably dominated assurance reforms in capability development during different periods: 1) human-human organisational assurance, circa 1980 to 2000, 2) software assurance, circa 2000 to 2020, and 3) assurance of AI-enabled systems, emerging since 2020. We synthesise established literature and frameworks from each paradigm, including the NIST AI Risk Management Framework, while recognising that AI assurance remains an evolving discipline. We contribute a unified set of 20 assurance precepts for safety-critical AI-enabled capabilities. These precepts are mapped across four quadrants of assurance activities, responsibilities and critical questions, and organized within a novel Dual Assurance Spiral for AI-Enabled Capabilities (DAS4AIC). Through comparative analysis, we demonstrate how classical safety principles extend from human-dominant assurance through software-dominant assurance to the assurance of AI-enabled systems. Importantly, some human-dominant assurance precepts map more directly to AI-enabled system than through software assurance. This finding may help explain operational concerns about the erosion of accountabilities, ethical responsibility and effective human oversight when AI is introduced into safety-critical capabilities. The proposed mapping was evaluated through a face-validity workshop involving an experienced and diverse group of assurance practitioners. The workshop identified critical assurance gaps, particularly in data governance, explainability, and human-autonomy teaming. We discuss the implications for organizational governance and argue that effective governance provides the foundation for auditing, training, and validating and monitoring AI-enabled systems in safety critical operational environments. To our knowledge, this is the first study to systematically align merging AI-assurance principles with the earlier and still overlapping, human–dominant and software-dominant assurance paradigms.

Abstract: For an \( n\times n \) complex matrix \( A \), let \( W(A)=\{x^*Ax : x\in\mathbb{C}^n,\ \lVert x\rVert_2=1\} \) be its numerical range. Here \( x^* \) denotes the conjugate transpose, \( \lVert\,\cdot\,\rVert_2 \) the Euclidean norm, and \( \lVert\,\cdot\,\rVert \) the induced operator norm. For every complex polynomial \( p \), we prove that \( \lVert p(A)\rVert\leq2\max_{z\in W(A)}\lvert p(z)\rvert \) and consequently that \( W(A) \) is a 2-spectral set for \( A \). This proves Crouzeix's conjecture, and the constant is optimal. The central ingredient is a positive-real completion theorem relative to an auxiliary eigenbasis: an adjoint-algebra constraint on the resolvent defect of a normalized matrix-valued Carathéodory function forces the underlying matrix to have norm at most 2. The classical positive double-layer calculus supplies such completions for \( f(B) \) whenever the auxiliary matrix \( B \) has simple spectrum; the eigenvalues of \( f(B) \) may repeat. Sampling the associated Herglotz kernel at half the conjugate diagonal entries and at the origin cancels the completion term and leaves a comparison of two weighted Gramians; a Stein identity yields the sharp estimate. Simple-spectrum approximation and convex outer approximation by domains with continuously differentiable boundary yield the general theorem.

Abstract: In this paper, we introduce and study the positive-influence Roman dominating function (PIRDF), a novel graph-theoretic concept that unifies Roman domination with positive-influence domination. A labeling f : V(G) → {0,1,2} is a PIRDF if it satisfies the Roman domination condition and the set of positively labeled vertices forms a positive-influence dominating set, meaning every unlabeled vertex has at least half of its neighbors positively labeled. The positive-influence Roman domination number, \( \gamma_R^{PI}(G) \), is defined as the minimum weight of a PIRDF of G. We establish several tight bounds. We prove that the associated decision problem is NP-complete for general graphs, and show that it is solvable in linear time for graph classes of bounded clique-width via a LinEMSOL₁ formulation. Exact values of \( \gamma_R^{PI}(G) \) are computed for several standard graph families, including paths, cycles, complete graphs, complete bipartite graphs, star graphs, and friendship graphs. In addition, degree-based bounds are derived, and graphs attaining the lower bound \( \gamma_R^{PI}(G) = 1 + \lceil \delta/2 \rceil \) are fully characterized.

Abstract: Existing models of the circadian clock in Arabidopsis thaliana are conventionally formulated by integer-order ordinary differential equations (ODEs), which inherently lack the capacity to adequately capture non-local history-dependent regulatory dynamics that arise from sequential biochemical processes such as transcription, translation and protein degradation. Here we construct a Caputo fractional-order model of the Arabidopsis core circadian system and establish local existence and uniqueness, non-negativity, and boundedness of solutions under non-negative initial conditions. Model parameters are fitted to wild-type mRNA expression profiles collected under a standard 12 h light/12 h dark (12L12D) photoperiod. Without any subsequent refitting of parameters, the predictive performance of the fractional-order model is validated on two independent test datasets: wild-type expression time series under three additional photoperiod regimes, and publicly available expression data for major circadian clock loss-of-function mutants. Compared with the original ODE counterpart, the fractional-order formulation exhibits substantially improved performance in reproducing the post-peak decay kinetics and extended tough phase of the PRR5/TOC1 regulatory module. Quantitative error evaluation confirms that the fractional-order model achieves consistently lower mean squared errors across all four photoperiod conditions, and outperforms the integer-order counterpart in two of the four tested mutant backgrounds, indicating that performance gains are not uniformly distributed across all genetic perturbations. Through Matignon-type stability analysis and extensive numerical simulations, we identify a well-defined critical fractional-order threshold. When the fractional order exceeds this critical value, the system’s unique positive equilibrium loses its stability, giving rise to sustained oscillations. From a systems biology perspective, the introduction of fractional-order operators provides a compact phenomenological representation of aggregated historical memory effects and may influence the amplitude, phase, and long-term robustness of the core circadian-clock oscillations. This work offers a new mathematical framework for refining the dynamical characterization of eukaryotic circadian pacemakers.