Computer Science and Mathematics

Abstract: This paper presents new optimal eighth-order families with weight functions for solving nonlinear systems, obtained as a generalization of the first optimal eighth-order CTT8 method introduced by Cordero, Torregrosa and Triguero-Navarro. The proposed schemes are constructed by combining a Newton-type predictor with high-order correction steps whose weight functions are suitably chosen to preserve optimal convergence while keeping a low computational cost. To the best of our knowledge, this work introduces the first family of optimal eighth-order methods for nonlinear systems, in the sense of the Cordero Torregrosa conjecture, developed through a weight-function technique. A complete local convergence analysis is carried out under standard smoothness assumptions, proving eighth-order convergence for nondegenerate solutions. The computational efficiency of the proposed methods is also studied and compared with several existing high-order iterative schemes. Numerical experiments on nonlinear systems of different dimensions confirm the theoretical order of convergence and show the robustness of the new families. In addition, a Fredholm integral equation is solved, followed by a semilinear elliptic Dirichlet problem, further illustrating the reliability and computational performance of the proposed weight-function-based methods.

Abstract: We establish unconditional almost-all ternary results for the restricted weighted Goldbach sum W_(a,q) \( W_{a,q}(n) := \sum_{\substack{p_1+p_2+p_3=n \\ p_1 \equiv a \pmod{q}}} (\log p_1)(\log p_2)(\log p_3), \quad q \geq 1,\ \gcd(a,q)=1 \), together with conditional extensions under the Density Hypothesis and the Generalized Riemann Hypothesis. Main results. (A) Almost-all via prime anchoring [Proved]. For every \( A > 0,\#\{n \leq X,\ n \text{ odd} : W_{a,q}(n) = 0\} \ll_{A,q} X(\log X)^{-A}. \) (B) Almost-all with full asymptotic [Proved]. For all odd \( n \leq X \) outside an exceptional set of size \( O_{A,q}(X(\log X)^{-A}),W_{a,q}(n) = \frac{J_{3,a,q}(n)}{\varphi(q)}\, n^2 + O_{A,q}\!\left(\frac{n^2}{(\log n)^A}\right), \) where the ternary singular series \( J_{3,a,q}(n) > 0 \) is positive and effectively computable. For \( (a,q) = (3,4) \) the main term equals \( (C_2 S(n)/4)\,n^2 \) with \( C_2 \in [0.6601618157,\, 0.6601618160] \). The minor-arc bound \( K_{\min}(q, A) \leq 2.10/\sqrt{\varphi(q)} \) is proved in full, self-containedly, via the exact \( L^2 \)-orthogonality identity \( \|S_{a,q}\|_{L^2}^2 = \|S\|_{L^2}^2/\varphi(q) \) and a Hölder \( (L^2, L^\infty, L^2) \) factorization. The exceptional-set constant is \( C_{\text{ternary}}(A,q) \leq 4.41/\varphi(q) \cdot 2^A \) [Proved]. Articles 1, 2, and 3 by the same author of this work provide all the black box input data. No GRH, no density hypothesis, and no ternary sieve are used in Parts (A) and (B).

Abstract: Spatial intelligence requires agents to form and utilize internal representations of the physical world for perception, reasoning, and generation. While recent advances in foundation models, embodied systems, and three-dimensional representation learning have substantially expanded spatial capabilities, existing research remains fragmented across heterogeneous tasks and model paradigms. This survey revisits spatial intelligence from a cognitive map perspective and positions cognitive maps as its representational blueprint. In this view, diverse lines of research can be understood through a shared question: how an internal spatial representation is constructed, maintained, reasoned over, and realized. To make this perspective operational, we define cognitive maps as internal spatial representations characterized by abstraction, globality, and persistency. Based on this definition, we organize the literature into three cognitive-map-centric processes that correspond to the core dimensions of spatial intelligence: perception for cognitive map construction, reasoning for internal inference with the map, and generation for external realization of the map. By adopting a mechanism-centric viewpoint, this survey connects previously isolated research directions into a coherent framework and identifies emerging challenges toward unified spatial intelligence systems. The related resources of this study are accessible at https://github.com/Klingsor-tyx/Awesome-Spatial-Cognitive-Map.

Abstract: Phishing is the most common cybersecurity threat. With phishing, attackers create a website or manipulate a URL in order to obtain a user’s sensitive information. Sensitive information can include a user’s credentials, payment details, or personal information. Phishing attacks target online users by baiting them to click on a fraudulent link. Phishing is a growing concern for users across the world. I propose a phishing detection framework that is lightweight, fast, and able to detect URLs with phishing content. The lightweight comparative phishing framework focuses on the extraction of a reduced number of URL features. These features include characteristics, structures, and patterns that are seen in URLs. These features prepare and place input to the three supervised machine learning methods: Logistic Regression, Decision Tree, and Random Forest. The frameworks were then evaluated based on four main classification metrics: accuracy, precision, recall, and F1-score. The Random Forest Classifier, within the lightweight comparative machine learning framework, was the most accurate in phishing detection with minimal computational requirements. The purpose of this lightweight framework was to offer real time cyber security solutions on browsers. The framework was scalable and efficient.

Abstract: Mythos-class frontier AI systems, defined operationally in prior work [1] by five indicators (capability, scaffold, access pattern, autonomy depth, persistence), exhibit discontinuous cyber-operational behavior that classical kill-chain models and artifact-centric taxonomies such as MITRE ATT&CK and ATLAS do not accommodate. The prior reference architecture specifies a four-layer defense and the Mythos-Class Posture Rubric (MCPR), whose runtime tier detects supervisability-evasion signatures empirically. This manuscript develops four contributions providing the theoretical scaffolding under which those empirical signatures cohere and the cross-operation extensions the scaffolding motivates. First, a relational systems-theoretic model treating the enterprise as three coupled frames (identity, trust, telemetry), with frame-shifts defined by three constitutive properties (non-locality, non-sequentiality, observability collapse). Second, a four-class taxonomy partitioning the relational space: presence, privilege, domain, and observability discontinuity. Third, a cross-operation detection matrix with four primary detection mechanisms operating on telemetry the prior architecture already produces. Fourth, integration extensions routing the new signals through the prior architecture’s mitigation stack without parallel architectural primitives. The framework is illustrated through a synthetic case study and grounded in systems-theoretic precedents (Ashby, Luhmann). The contribution is theoretical scaffolding and cross-operation extension to the prior reference architecture rather than a competing framework.

Abstract: In this work, we present a new geometric framework that integrates quaternion-based rotation and translation operators with a generalized inner product and vector product framework defined on Gielis-type superquadrics. By incorporating the multiplicative shape factor ρ(ϕ), we construct a family of rotation matrices and quaternion mappings adapted to the elastic and non-Euclidean behavior of biological growth surfaces. This framework enables smooth, direction-dependent deformations and provides a unified representation for curvature-induced growth, differential thickening, and torsional motions observed in plants. The proposed model provides a mathematically tractable and biologically interpretable tool in many applications in plants, animals and biomolecules. Potential applications include computational botany, growth-based animation, and the design of biologically inspired structures.

Abstract: For starlike, convex and bounded turning functions linked with nephroid function, the sharp upper bounds of the third-order Hankel determinant, the third-order Hankel determinant of inverse functions and the second-order Hankel determinant of logarithmic coefficients are computed.

Abstract: Coastal water quality monitoring is critical for ecosystem health and regulatory compliance under Vietnam’s QCVN 10:2023/BTMT standards. Thus, this study addressed the limitations of traditional predicting models by proposing a hybrid framework that integrate Hidden Markov Models (HMM, dual-branch Long Short-Term Memory (LSTM) networks, and attention mechanisms for multi class water quality classification. The model was developed using 1,305 daily observations from 2020-2023 of five water parameters – TSS, pH, TPH, Total Coliform, and DO – at the Sao Den-Ben Dinh station positioned in the east coast of Ho Chi Minh City. The hybrid architecture achieved a moderate accuracy of 74.87% and F1-score of 64.11%, representing a statistically significant improvement over a standalone HMM (44%), LSTM (68.2%), and ARIMA (70,77%). Attention weights identified a one-to-three-day lead time critical for predicting pollutions events. However, a significant limitation remains in a minority class detection, where the “Poor” category reached only 14% recall due to a severe 7:5:1 data imbalance. Generally, this framework provides an interpretable, regulatory-aligned decision-support tool for early-warning systems, offering a theoretically principled approach to capturing multi-scale temporal dynamics in coastal environments.

Abstract: Modeling a user's evolving goals, values, and affect over time is central to perspective-aware AI, yet progress is bottlenecked by the lack of longitudinal data with ground-truth labels for latent identity state. We introduce PAiNT (Perspective-Aware AI Identity and Narrative Toolkit), a generative framework that simulates long-horizon persona trajectories and emits corresponding multimodal artifacts with ontology-aligned labels of the latent identity state that produced them. PAiNT decouples identity dynamics from artifact generation via a typed Persona Matrix and Situation Graph, coordinated through a multi-agent loop with validation-gated transitions and bounded-window history conditioning. Across four personality archetypes, four backbone LLMs, and three architectural ablations, evaluated with a nine-metric suite calibrated on published longitudinal data, we find that (i) persona initialization produces a durable identity signal that persists above stochastic event noise; (ii) multi-agent orchestration and history conditioning govern distinct quality dimensions, with removal of either causing different failure modes; and (iii) a coherence frontier constrains the trade-off between temporal resolution and horizon, with substantial penalties at daily granularity. We release PAiNT and PAi-Bench, a human-validated benchmark of 1,200 labeled multimodal artifacts, at: https://anonymous.4open.science/r/paint-0411/.

Abstract: Assessment feedback on complex written reports remains one of higher education's most persistent and resource-intensive challenges, yet no principled framework exists for deciding which feedback tasks might appropriately involve artificial intelligence and which must remain human responsibilities. This paper addresses that gap by proposing a tripartite feedback framework that distinguishes three analytically distinct levels: low-level structural and presentational feedback, intermediate-level factual content validation, and high-level critical evaluation and synthesis. Grounded in established feedback theory, including Hattie and Timperley's feedback model and Boud and Molloy's sustainable feedback design principles, the framework provides pedagogically justified criteria for allocating tasks between AI systems and human assessors, rather than automating whatever technology can technically perform. Five non-negotiable boundary principles govern any AI involvement at the intermediate level, preserving human oversight, academic accountability, and assessment integrity. The paper examines current technological capabilities and limitations at each level, proposes a phased implementation pathway with explicit human-in-the-loop requirements, and addresses implications for feedback literacy, student agency, equity, and security. A comprehensive mixed-methods evaluation design specifying the evidence required for empirical validation is also presented. The framework's contribution lies not in prescriptive solutions but in providing structured categories, explicit boundary conditions, and validation criteria to guide context-sensitive institutional decision-making about AI integration in assessment.

Abstract: The growing integration of artificial intelligence into mineral exploration has created new opportunities for improving target selection and decision-making in geologically complex regions. This study presents an integrated multiple machine learning frame-work designed to address the assessment of exploration data quality. The analysis was conducted using an extensive geophysical and geochemical dataset comprising 221 ex-ploration sites distributed across the Brazilian Shield. Six widely adopted algorithms were comparatively evaluated, including Random Forest, XGBoost, AdaBoost, Decision Trees, K-Nearest Neighbors, and Logistic Regression. The results demonstrate that Random Forest achieved the highest accuracy in data quality classification (accuracy = 0.82, AUC = 0.85). Cross-validation confirmed model robustness (5-fold CV R² = 0.80 ± 0.02; accuracy = 0.82 ± 0.02). Feature importance and explainability analyses revealed that magnetic anomaly intensity, copper concentration, and alteration-related indices are the most influential predictors, reinforcing both the geological plausibility and the com-putational reliability of the models. This proposed methodology offers practical support for mineral exploration strategies across the Brazilian Shield and provides a scalable framework for future applications involving critical mineral systems.

Abstract: This paper presents an integrated framework for decentralized invoice-backed loan underwriting combining interpretable machine learning, dynamic pricing algorithms, and on-chain trust infrastructure. We develop and validate SHAP-explainable ML models for real-time default probability assessment, design a Reverse Kelly AMM smart contract for optimal risk-adjusted loan pricing, integrate ERC-725 identity and on-chain reputation scoring with an automated insurance reserve, and deploy the system on Ethereum testnet with end-to-end functional and security testing. Stress testing across simulated default and fraud scenarios demonstrates the model achieves AUC-ROC of 0.89 on validation data, maintains LP yields of 12–18% under normal conditions while containing non-performing loan ratios below 3% under adverse scenarios, and sustains reserve solvency across 95th percentile stress events. The framework addresses critical gaps in DeFi lending by bridging regulatory interpretability requirements with decentralized credit assessment, demonstrating both technical feasibility and economic viability for permissionless SME financing at scale.

Abstract: Software delivery is moving from deterministic pipelines toward autonomous environments where AI agents make runtime deployment decisions. Current DevOps governance assumes predictable execution and offers no mechanisms for constraining agents that generate plans on the fly. This leaves critical gaps in trust, accountability, policy enforcement, and failure containment. We present a conceptual architecture for bounded autonomous delivery, in which agents operate within externally enforced operational, security, reliability, and compliance constraints. The architecture separates planning, execution, policy enforcement, runtime verification, and human oversight into composable layers. We propose a taxonomy of autonomy levels and define operational invariants that limit what agents can do at runtime. A recurring scenario (deploying a payment microservice on an e-commerce platform during peak traffic) grounds the concepts in operational practice. The perspective positions governed autonomous delivery as an emerging discipline that demands new assurance models before organizations can trust agents with production systems.

Abstract: Software as a Service (SaaS) has become a key enabler of digital transformation and e-government modernization through scalable, flexible, and cost-effective service delivery. However, evidence of SaaS adoption in Southern African Development Community (SADC) public sectors remains limited and uneven. This study systematically reviews literature published between 2015 and 2025 on SaaS adoption, digital readiness, infrastructure, policy environments, and institutional capacity across SADC member states. Using PRISMA-guided screening, 31 studies were synthesized through narrative thematic analysis informed by the Technology–Organisation–Environment (TOE) framework and Institutional Theory. The findings reveal significant disparities in SaaS readiness across the region. South Africa is the only country with substantial empirical evidence of public-sector SaaS adoption, while most member states demonstrate only indirect indicators of readiness, including ICT maturity and e-government development. Four major barriers were identified: infrastructure deficits, policy and regulatory fragmentation, institutional capacity constraints, and uneven regional readiness. The study also identifies a “readiness paradox,” whereby stricter data sovereignty regulations co-exist with inadequate infrastructure for compliant SaaS deployment. The study contributes a contextualized framework for sustainable SaaS adoption in SADC public sectors.

Abstract: Many geometrical models have been created and applied in different subjects of sciences, such as physics, astronomy, biology,\ldots This paper presents a generalization of the recently defined $(\bar m,m)$-conformal mappings of Riemannian spaces. In this article, the affine connections of Riemannian spaces and symmetric affine connection spaces are combined. In this way, the characteristics of structures without external effects (Riemannian spaces) and with external effects (symmetric affine connection spaces) are geometrized. The main contributions of this research are: 1. Invariants of $(\bar m,m)$-conformal mappings of Riemannian spaces (review) and of geodesic mappings of symmetric affine connection spaces (review); 2. Actions and variational calculi with respect to some invariants obtained in 1; 3. Generalized Einstein's equations with respect to the analyzed transformations with clear reductions to standard ones.

Abstract:

The most challenging aspect of a pattern recognition problem is to identify a pattern with the help of its positive and negative features. The bipolar fuzzy sets (BFSs) are the mathematical tools that can express a pattern with the help of positive and negative membership functions, hereby making it possible to be expressed more conveniently than others. In this article, a real-valued function on the set of BFSs over a universe of discourse is proposed that fulfills the axioms of being a metric measure on the set of BFSs. The proposed metric can be formulated for both the discrete and the continuous universes of discourse. The efficacy of the proposed metric is validated through several important mathematical properties. Further, a bipolar fuzzy clustering algorithm for sentiment analysis is discussed in detail to demonstrate the usefulness of the proposed metric.

Abstract: Accurate R-peak detection in electrocardiogram (ECG) signals is fundamental for cardiovascular analysis. However, most existing methods address differences in sampling frequency (fs) through signal resampling or transfer learning, which may alter the temporal definition of annotated events. In this study, we propose a fs consistent framework for ECG R-peak detection that avoids both resampling and retraining. The proposed method is based on low-sampling morphological learning combined with physiological temporal constraints (PTC). A lightweight classifier (Extreme Gradient Boosting) is trained on 128 Hz ECG data (MIT-BIH Normal Sinus Rhythm Database, XGB) to learn local morphological structures, and feature extraction is defined in milliseconds with time-normalized derivatives to ensure consistency across fs. The trained model is directly applied to higher- fs datasets (360 Hz, 500 Hz, and 1000 Hz) without modification. Final peak locations are determined through deterministic processing, including PTC and local snap processing. Experimental results demonstrated that the proposed method achieved stable detection performance across multiple sampling frequencies. When evaluated in a sample-wise manner, the proposed method achieved mean F1-scores of 0.885 on MIT-BIH Arrhythmia Database (360 Hz), 0.848 on Lobachevsky University Electrocardiography Database (LUDB, 500 Hz, sinus rhythm), 0.837 on LUDB (500 Hz, arrhythmia), and 0.953 on PTB Diagnostic ECG Database (1000 Hz), without any resampling or retraining. The integration of probabilistic candidate detection and deterministic temporal alignment enables consistent peak localization under cross-frequency conditions. These findings demonstrate that augmenting machine learning with deterministic decision mechanisms provides a principled framework for fs -consistent ECG peak detection.

Abstract: This paper examines whether incremental prompt engineering can enable reliable LLM based pre-annotation of corpus texts in a low resource language setting. Using Lithuanian as a case study, we systematically evaluate multiple LLM prompt designs and assess their suitability for generating emotional manipulation annotations for corpus development. We find that performance varies with task complexity, and systematic prompt refinement measurably reduces output instability. Cross-model evaluation of the best-performing prompting strategy shows consistent and similar trends over several modern LLMs. Our results demonstrate that while structured prompts substantially improve output consistency and LLM assisted annotation can roughly approximate human produced labels for well-defined categories, the quality of results produced by contemporary LLMs is unsatisfactory for automatic pre-annotation of emotional manipulation techniques in a low resource language.

Abstract: Predicting patent examination outcomes under 35 U.S.C. §103 is inherently difficult because obviousness determinations require context-sensitive legal reasoning over prior art combinations that cannot be captured by surface-level text patterns alone. Existing automated approaches optimize for aggregate accuracy but offer no principled criterion for when their predictions should be trusted and when practitioner review remains necessary. We present TriageRAG (T-RAG), a two-stage decision-support framework that addresses this gap by treating classifier confidence as an explicit routing signal. A fine-tuned ModernBERT-large model first produces a prediction together with a calibrated confidence score; high-confidence predictions are delivered directly, while uncertain cases are escalated to a Large Language Model (LLM) that reasons over balanced retrieval from a knowledge base of 50,000 granted patents and 50,000 §103-rejected applications with full examiner Office Action text. This balanced retrieval ensures that escalated predictions are grounded in auditable, bidirectional evidence rather than opaque model parameters. Empirical evaluation on USPTO patent applications confirms that the confidence threshold provides a reliable escalation criterion: LLM verification yields the largest accuracy gains precisely on the cases the classifier is least certain about, and confidence-based routing is statistically superior to random routing at equivalent LLM utilization rates. Ablation studies further characterize the accuracy–cost trade-off across threshold values and reveal domain-specific reliability profiles that practitioners can use to calibrate their trust in system outputs by technology area. T-RAG thus serves as a transparent decision-support tool that not only predicts examination outcomes but provides structured guidance on where additional scrutiny is warranted.

Abstract: The Minimum Dominating Set problem is NP-hard, and the best known polynomial-time approxima-tion 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 elim-ination, and a linear-time forest projection, and then applies Baker’s PTAS to that kernel. The reduction outside the planar PTAS runs in O(n + m) worst-case time; with a linear-time fixed-ε implementation of Baker’s planar subroutine, the full algorithm is linear. The algorithm is provably within twice the optimum whenever the reduction is tight, and the implementation provides a linear-time sufficient--consistency certificate based on the proved forced-boundary inequality. We give a structural witness mapping that injects the post-pruning forced-boundary set into the rest of the planar kernel, explaining why pruning often improves the observed bound without turning the remaining gap into an estab-lished universal guarantee. We complement the theory with two experiments using Furones v0.2.8 with the --consistency flag: a certified run on 68 NPBench DIMACS clique-complement instances, and a comparison against NetworkX’s logarithmic approximation on a 64-graph compendium from VC-Bench. The NetworkX comparison certifies 63 of 64 instances; the lone uncertified instance still has logged upper-bound ratio 1.603 < 2, illustrating incompleteness of the current sufficient certificate rather than a poor empirical outcome.