Computer Science and Mathematics

Abstract: In this paper, we are concerned with the existence of crossing periodic solutions for a class of second order discontinuous undamped Duffing equations. By applying the Poincaré-Bohl theorem, we obtain several existence results of 2π crossing periodic solutions.

Abstract: Recent research in cancer detection and monitoring is based on the development of multi-agent systems. They are used for multidimensional multimodal health data integration, medical data augmentation, knowledge representation, predictive diagnosis, and personalized treatment schemes. This paper addresses the last two challenges by introducing intelligent agents to build clustering, classification, and treatment-recommendation models, while also improving overall process time through feature selection and the identification of critical malignant cases. In the first stage, the Wrapper Selection Agent based on Random Forests generated an optimized model with a 98.68% accuracy. Then, the Outlier-based Clustering and Critical Malignant Cases Agents detected the critical malignant cases with a 0.84 Silhouette Score. In the next step, Treatment Clustering and Decision Rules Agents built a perfect model that proposes a personalized treatment for the patients identified by the previous agents. The entire process is automated and provides treatment recommendations in 32.85 seconds.

Abstract: The Minimum Dominating Set problem is NP-hard, and the best known polynomial-time approximation factor is O(ln n), which is provably tight unless P = NP. We present a polynomial-time algorithm that reduces an arbitrary input graph to a planar kernel through forced-vertex extraction, pendant elimination, and greedy planarisation, and then applies Baker’s PTAS to that kernel. The algorithm runs in O(mn + m log m) time — in particular O(n log n) on sparse graphs — and is provably within twice the optimum whenever the reduction is tight. We give a structural witness mapping that injects the post-pruning forced-boundary set into the rest of the planar kernel, narrowing the unresolved gap in the analysis to a single inequality, |F| ≥ 2|F_R^pruned|. Should that inequality hold universally, a 2-approximation would follow and would imply P = NP. We complement the theory with an experimental study on thirteen DIMACS benchmark graphs: in every case the algorithm finishes in well under five minutes and returns a dominating set whose size is at most 1.80× the ILP optimum, with an average ratio of 1.42. An open-source implementation is provided as the Furones package (v0.2.6).

Abstract: This paper introduces the dual process machine learning paradigm, which builds upon the unified machine learning and physics field framework. By integrating machine learning architectures and physics models into a single field-theoretical entity and constructing hidden layers and learning weights based on physical systems, complex machine learning is interpreted as a set of physical interactions. The super dual process machine learning leverages duality relations inherent in physical systems, enabling a simplified "dual" process to replicate the statistical behavior of the original complex "primary" process. We demonstrate that the super dual process opens a new pathway for AI engineering, wherein algebraic structures from underlying physical principles guide model design and computation. We present both the theoretical foundations and practical implementations of super dual machine learning, achieving improved scalability and efficiency compared to traditional methods.

Abstract: The classification of banana ripeness remains an important task in the food industry, as it directly affects the quality of the product and its shelf life. This paper presents an automated ripeness assessment system implemented using a comparative analysis of machine learning and deep learning algorithms. We tested the effectiveness of Random Forest, a custom CNN model, as well as the pre-trained ResNet50, EfficientNetB0, and VGG16 models, based on a dataset of 9960 images categorized into 3 ripeness stages (overripe, ripe, unripe). The results show the superiority of deep neural networks over classical methods: the ResNet50 architecture demonstrated 98% accuracy with a macro-averaged F1-score of 96%. The implementation of the proposed solution in the retail sector can automate ripeness monitoring and significantly reduce food waste.

Abstract: The European crafts ecosystem faces critical structural threats, declining practitioner numbers, weakening intergenerational transmission, limited digital literacy, and competition from industrial imitation. Existing online craft communities are narrowly material-specific and structurally illsuited to the cross-disciplinary dialogue required for systemic sector transformation. This paper presents the design, iterative development, and pilot evaluation of the Craeft Community, a multi-stakeholder Virtual Community of Prac-tice (VCoP) developed within the Horizon Europe CRAEFT project. Three research questions guided the study: how a multi-stakeholder VCoP should be structured to overcome disciplinary fragmentation; to what extent a stewarded digital forum can operationalize Situated Learning and Communities of Practice theory and what factors facilitate or inhib-it engagement and post-funding sustainability. Using design-based research, the platform evolved through four iterative phases, culminating in restructuring from a material-based architecture into five transversal thematic pillars, driven by survey evidence from 151 European craft professionals and systematic stakeholder feedback. The pilot phase yielded 86 registered members, 31 posts, and 27 interactions, with Transmission & Training as the most engaged pillar. Qualitative analysis reveals substantive cross-disciplinary discourse alongside a structural Effort-Engagement Gap, a persistent tension between forum partic-ipation demands and the gravitational pull of mainstream social media. The study demonstrates that a thematically organized, stewarded VCoP can meaningfully opera-tionalize apprenticeship-based learning in digital settings, advancing craft heritage preservation, economic resilience, and hybrid professional identity formation at the inter-section of craft and technology.

Abstract: Recent medical world-model rubrics have mainly described a linear progression from representation and forecasting to action-conditioned simulation, counterfactual evaluation, and planning/control. This Perspective starts from a different goal: biomedical world models should not merely predict likely trajectories, but help make biological trajectories steerable. Steerability requires five linked functions: defining state, measuring state, specifying intervention-induced state movement, simulating alternative transitions, and inspecting deviations. We therefore propose the Deductively Constrained Capomics World Model, a closed-loop architecture organized around five corresponding constraint checkpoints: CP1 state representation, CP2 intrinsic-capability quantification, CP3 intervention-response semantics, CP4 counterfactual transition, and CP5 quality-control feedback. The framework shifts biomedical world modeling from a “what-if” simulator toward a quality-controlled “why-not” steering system, in which failed or unexpected transitions can be traced to state measurement, intervention specification, module response, state transition, or downstream phenotypic propagation. Within this architecture, module-level intrinsic capability (mIC) provides the proposed state variable, and Capomics provides its measurement framework. In the current prototype, DNA methylation is used to estimate module-level mIC values and assemble them into an mIC vector, while other omics and physiological readouts may be incorporated in future implementations. The accompanying depression case study illustrates how the cycle can be instantiated as a thought experiment for state-matched intervention reasoning and deviation inspection. The framework does not claim validated treatment planning or guaranteed efficacy; it is intended as a hypothesis-generating scaffold for biomedical world models, longitudinal intervention studies, and future biomedical applications.

Abstract: The rapid growth of organic waste volumes in urban areas and increasing environmental pressures necessitate the transition toward sustainable and risk-informed municipal waste management systems. This study aims to develop a data-driven decision support framework for the risk-informed management of municipal organic waste within the context of sustainable urban development. The proposed approach integrates multi-source municipal data, advanced preprocessing techniques, entropy-based feature weighting, and an ensemble of machine learning models, including Random Forest, Gradient Boosting, and XGBoost. An integrated environmental risk index is formulated to quantify the state of the waste management system and to support predictive analytics. The results demonstrate high predictive performance and reveal that key risk drivers include demographic pressure, transport accessibility, infrastructure characteristics, and seasonal variability of waste generation. The developed framework enables the integration of predictive risk analytics into municipal decision support systems, facilitating optimized waste collection logistics, infrastructure planning, and early identification of critical conditions. The findings confirm that data-driven approaches can significantly enhance the efficiency and adaptability of urban waste management systems. The proposed framework contributes to sustainable urban development by supporting circular economy principles and enabling proactive, risk-aware governance of municipal organic waste systems.

Abstract: We present the first application of the Multifractal Model of Asset Returns (MMAR; Mandelbrot, Fisher & Calvet, 1997) to an implied volatility index. Using 9,118 daily observations of the CBOE VIX spanning January 1990 to March 2026—a period encompassing four economic cycles—we implement the complete MMAR estimation pipeline: partition functions, OLS-fitted scaling exponents, Legendre-transformed multifractal spectrum, lognormal cascade calibration, fractional Brownian motion generation, and Monte Carlo validation. VIX log-returns strongly reject Gaussianity (KS p<10⁻¹⁰, excess kurtosis 6.73). The scaling function τ^(q)=−0.022q²+0.230q−1.031 is strictly concave, confirming genuine multiscaling. The Hurst exponent H^=0.189 places VIX in the strongly subdiffusive regime (fractal dimension dH=1.811), consistent with its mean-reverting character and in sharp contrast with the persistent scaling of equity price indices. The most probable Hölder exponent α^₀=0.230 exceeds H^, rendering the lognormal cascade admissible: λ^=1.219 and σ^²=0.633. Formal validation via 10,000 Monte Carlo MMAR simulations and 1,000 Gaussian benchmarks reveals a partial but insufficient fit. MMAR produces mean excess kurtosis of 4.10 against the empirical 6.73—capturing 61% of tail mass but falling significantly short. Kolmogorov–Smirnov tests reject both models at all conventional significance levels. We interpret the residual kurtosis gap as evidence that the lognormal cascade underestimates the most extreme VIX spikes, with implications for volatility derivatives pricing.

Abstract: The audit of Information Security Management Systems (ISMS) under ISO/IEC 27001:2022 has traditionally relied on human auditors whose competence, experience, and judgment shape audit outcomes. While effective, this human-centric approach suffers from inter-auditor variability, high cost, scheduling constraints, and limited scalability — challenges magnified by the post-pandemic shift toward remote audits and the growing volume of organisations seeking certification. Recent advances in Natural Language Processing (NLP), Computer Vision (CV), and Large Language Models (LLMs) suggest that significant portions of the audit workflow could be augmented by machine learning. However, prior research has examined these technologies in isolation; no integrated conceptual framework yet exists that unifies document review, field observation, and interviewing under a single multi-modal pipeline tailored to ISO/IEC 27001 audits and explicitly grounded in the audit methodology of ISO 19011:2018. This paper proposes such a framework — the Multi-Modal ML-Augmented ISO 27001 Audit Framework (M³A-Framework). We synthesise insights from ISO 19011:2018 audit guidelines, recent advances in AI-driven assurance, and the design science research paradigm to develop a five-stage conceptual model that augments the seven-step evidence-collection process specified in ISO 19011 Clause 6.4.7 and that extends the audit-methods matrix of ISO 19011 Annex A (Table A.1). The framework comprises: (1) audit planning and scoping; (2) multi-modal evidence collection through NLP for document analysis, CV for physical control verification (supported by inspection robots and drones), and LLM-based conversational AI for interview; (3) ML-based evidence processing and triangulation; (4) confidence-weighted finding classification using Explainable AI; and (5) human-in-the-loop validation. The framework explicitly maps each module to the 93 controls of Annex A of ISO/IEC 27001:2022 and to the audit phases mandated by ISO 19011. We further propose a set of testable propositions, evaluation metrics, and ethical considerations that ground the framework in both academic rigour and practical deployability.

Abstract: This paper focuses on the optimization of engineering decision-making under uncertain environments. Engineering decision-making requires optimizing the input of production materials and the selection of equipment and processes under the constraints of cost and expected return to minimize costs and maximize production benefits. As an efficient formal verification technique, model checking provides a new approach to solve this problem. Traditional model checking mainly focuses on qualitative verification, while quantitative model checking techniques (such as probabilistic and possibilistic model checking) have been developed gradually, among which possibilistic model checking is more suitable for systems with fuzzy uncertainty. However, existing possibilistic model checking techniques have obvious defects: first, they only target closed systems and do not consider the interaction between the system and the external environment; second, the simple information aggregation method leads to information desynchronization and information loss; third, they cannot model and verify systems with incomplete information. Model checking technology based on possibilistic decision processes considers uncertain action selection and initially solves the problem of modeling and verification of open systems. The author has introduced the idea of quality constraints into possibilistic temporal logic to solve the problems of information desynchronization and information loss in possibilistic model checking; moreover, the author has established the theories of Intuitionistic Fuzzy Kripke Structure (IFKS) and Intuitionistic Fuzzy Computation Tree Logic (IFCTL), which can model and verify systems with incomplete information. To improve the usability and accuracy of engineering decisions, this paper will draw on the ideas and methods of uncertain selection of decision behaviors, quality constraints, and incompleteness modeling, extend IFKS to Weighted Intuitionistic Fuzzy Kripke Structure (WIFKS), induce IFCTL to Intuitionistic Fuzzy Decision Tree Logic (IFDTL), propose an algorithm for solving IFDTL model checking problems, and present a solution algorithm for multi-attribute engineering decision-making based on IFDTL model checking, along with its correctness proof and complexity analysis. Finally, a case study of Qinling health-preserving tourism planning is given to verify the rationality and efficiency of the proposed method, providing a new formal solution for uncertain engineering decision-making.

Abstract: Real-time system monitoring without human intervention is an important issue nowadays. The challenge is to find the learning model that best suits each system. In hydropower systems, critical situations occur when the water reaches the spill level or the minimum exploitation level. The actual learning models use past data to detect such instances. Our approach is to build models on future data, which is more appropriate for learning from real data. Given that the current forecasting methods are well developed and have proven their performance (the RBF Regressor achieved an RMSE of 0.291 in the current work), we propose forecasting data stored within the next month and using it to build clustering and classification models. The results show that our proposed approach achieves higher classification accuracy (99.51%) and higher or comparable Precision, Recall, F-Measure, and MCC than those of other models trained on similar datasets.

Abstract: Complex adaptive systems (CAS) have two defining characteristics. First, they are complex, i.e., composed of several interacting parts. Second, they are adaptive, i.e., their behavior can be changed in response to external stimuli and changes in the external environment. Due to this, managing such systems is quite challenging. Traditional approaches have involved defining policies that determine the behavior of any CAS under particular circumstances. However, such approaches are rigid and inflexible, since they are dependent on pre-specified policies. To that end, in this position paper, we describe an intent-driven approach to modeling and managing CAS. This would be a more flexible approach, not dependent on any specific policies, but which can be customized based on the context in which the CAS is functioning. We describe the various components of our approach, which include compositional reasoning to decompose the intent into sub-intents as per the context; mapping the sub-intents onto the execution model which will satisfy the intent; and feeding back the results of the execution to facilitate continual learning and continuous improvement in managing the CAS. In particular, one aspect that we highlight is the application of neurochaos learning, which uses chaos theory to facilitate rapid continual learning that would help improve the overall efficiency of our approach. For each component of our approach, we also present several research questions that need to be addressed before intent-driven management of CAS can become a reality.

Abstract: Quantumgateestimationandtomographypipelinesroutinelycombineintrinsicallydefined likelihoods with priors or regularization terms specified in local Euclidean coordinates. This practice implicitly replaces the Haar reference measure on SU(2) with Lebesgue measure, specifying a different statistical model rather than a reparametrization of the intended one. Weshowthat omitting the associated chart-volume factor alters the optimization objective itself, modifying its gradient field and stationary-point structure. The mismatch persists arbitrarily close to the identity, so that flat-coordinate surrogate objectives can converge to points that are non-stationary for the corresponding Haar-consistent objective even in regimes where local Gaussian approximations are assumed valid. We prove a formal non-equivalence proposition and validate a leading-order Fisher-information correction analytically and numerically. Large-scale multi-start optimization experiments (N = 11,900 runs) demonstrate that the discrepancy is regime-dependent and most pronounced under moderate-to-strong regularization or limited data. The fix requires a single-line modification to any gradient-based optimizer. These results identify reference-measure selection as an explicit modeling decision with direct consequences for optimization and inference in gate-set tomography, randomized benchmarking, and Bayesian gate estimation on curved parameter manifolds.

Abstract: Product recognition in e-commerce live streaming is hindered by rapid viewpoint changes, occlusions, motion blur, and inconsistencies between visual and spoken information. Existing approaches typically focus on individual components such as detection, OCR, or speech recognition, which limits their effectiveness in end-to-end scenarios.To address this problem, we propose an integrated framework that combines task-oriented keyframe selection with multimodal semantic fusion. The framework first uses D-FINE to localize product regions, and then selects informative frames through two complementary strategies. Strategy A considers both detection confidence and Laplacian-based sharpness, while Strategy B combines detection confidence with a learned image-quality score estimated by an EfficientNetV2-based model. OCR, visual recognition, and ASR are then applied to the selected data, and a Qwen-Plus large language model is used to integrate multimodal evidence into structured product outputs. Experiments on an in-house dataset demonstrate significant gains over a last-frame baseline. Strategy A increases Perfect Match Rate from 58.00% to 80.00% and Product Name Recognition Accuracy from 78.00% to 98.00%. Strategy B achieves 77.00% and 98.00%, respectively. Ablation studies further show that the full multimodal framework consistently outperforms unimodal and dual-modality variants. In addition, Top-K analysis indicates that single-frame inference provides a good balance between performance and efficiency.Overall, the proposed framework offers an effective and practical solution for product recognition in complex live-streaming scenarios.

Abstract: The coming era of autonomous AI agents demands a discovery mechanism capable of navigating millions of tools, yet existing solutions buckle under \( \mathcal{O}(N) \) complexity and centralized governance. Instead of building another fragile overlay, we propose ToolDNS, a radical framework that retrofits semantic tool discovery onto the Internet's most resilient substrate: the Domain Name System (DNS). By embedding functional intent and organizational trust into a hierarchical namespace, ToolDNS transforms an expensive semantic search into a series of lightweight, \( \mathcal{O}(\log N) \) name resolutions. We introduce three protocol-compliant enhancements to enable decentralized governance and semantic pruning: partially unfolded names, EDNS0 intent payloads, and logical subdomains. To rigorously evaluate this approach across the fragmented tooling landscape, we construct and release a large-scale heterogeneous benchmark comprising \( 33,688 \) real-world tools spanning MCP, A2A, RESTful, and Skill protocols. On this dataset, ToolDNS slashes the per-query search space by \( 95.26\% \) while matching state-of-the-art retrieval accuracy. Furthermore, its UDP-native design reduces discovery latency by orders of magnitude compared to HTTP-based registries. Our work demonstrates that scalable AI interoperability requires not more middleware, but a smarter utilization of the infrastructure already beneath our feet.

Abstract: Maritime ports—now deeply digitalized andinterdependent—face escalating cyber risk amid hybridgeopolitical pressures, complex vendor ecosystems, andwidening social dependence on uninterrupted trade flows.Situated at the intersection of the Belt and Road Initiative andthe Trans-Caspian International Transport Route, the CaspianBasin exemplifies both the promise of data-driven logistics andthe vulnerability of fragmented cybersecurity governance. Thisstudy extends the Strategic Data Alignment Framework(SDAF), originally designed to align corporate strategy withdata governance, into a cybersecurity governance model forcritical maritime infrastructure under hybrid threat conditions.Using comparative policy analysis and benchmarking againstcontemporary global standards (e.g., NIS2-style obligations,maritime cyber guidelines, and digital trade principles), thestudy identifies systemic weaknesses in harmonization,institutional capacity, supply-chain assurance, and resilienceplanning. It reconceptualizes cyber-resilience as a strategicresource and proposes a five-step roadmap combining regionalthreat-intelligence sharing, vendor risk controls, standardsalignment, AI-enabled detection, and stress-tested recovery.The findings underscore urgent needs for coordinated action tosafeguard digital corridors and the societies they serve.

Abstract: This paper presents a comprehensive cross-era analysis of the algorithmic evolution of Large Language Models (LLMs) through four developmental epochs: Before Transformer (pre-2017), Transformer (post-2017), Instruction-tuned \& Open-source LLMs, and Multimodal Agents (2024-2025). A novel innovation pathway framework is introduced that traces causal relationships between architectural breakthroughs and emergent capabilities, addressing critical research gaps in three dimensions: (1) Cross-paradigm synthesis connecting statistical foundations to modern multimodal systems, (2) Causal innovation mapping demonstrating how architectural choices propagate through model generations, and (3) Cross-domain capability analysis quantifying transfer between representation learning, knowledge acquisition, behavioral alignment, and multimodal integration. This analysis reveals that LLM progression represents fundamental paradigm shifts rather than incremental improvements, with transformer architectures, human feedback mechanisms, and open-source ecosystems collectively enabling the transition from specialized NLP tools to general reasoning systems. We provide empirical evidence through case studies of capability emergence, quantify innovation impacts using performance metrics, and examine safety implications through recent jailbreak analysis and refusal mechanism studies. The contributions include: (a) a unified lifecycle synthesis with original analytical framework, (b) innovation trajectory mapping with causal pathway analysis, and (c) validated evolutionary principles for forecasting next-generation AI capabilities.

Abstract: Self-regulated transportation networks belong to the class of continuous network models and are widely used not only in biological applications, such as vascular systems, neural networks or tissues regeneration but also in urban infrastructure and in communication technologies. Their well-established tree structure prevents the formation of loops, which limits their ability to capture an important feature observed in real systems: when a disruption or damage occurs, the network should be able to reorganize to restore transport pathways. In this work, we propose alternative modeling strategies to incorporate this capability. These approaches allow the network to adapt to perturbations by modifying its structure and, in some cases, by creating alternative routes that compensate for damaged regions. Numerical results illustrate how the modified models can reproduce self-repair mechanisms that are not captured by standard formulations.

Abstract: ZPIF (Zero Pair Interaction Functional) is introduced as a quadratic spectral operator framework extending the classical explicit formula of the Riemann zeta function. Unlike the standard linear spectral decomposition, ZPIF incorporates second-order interactions between spectral modes within a Hilbert space formulation. The framework includes a rigorous operator definition, spectral expansion, trace-class regularization, and conditional convergence under truncation. A computational scheme based on numerical zeta zeros is also proposed. The novelty of ZPIF lies in introducing a quadratic spectral energy functional consistent with classical spectral heuristics without assuming unresolved conjectures. Numerical experiments demonstrate nonlinear growth behavior and quadratic interaction effects that are absent in classical linear formulations.