Computer Science and Mathematics

Abstract: We give a certified finite verification of the literal vertex formulation currently displayed as Erd\H{o}s Problem \#580. Namely, for every $1\le n\le 19$, an $n$-vertex graph having at least $\lceil n/2\rceil$ vertices of degree at least $\lceil n/2\rceil$ contains every tree on at most $\lfloor n/2\rfloor$ vertices. The only order requiring new computer-assisted analysis is $n=18$. An edge-minimal counterexample is reduced to a host partition $V(G)=L\sqcup S$ with $|L|=|S|=9$, degree exactly $9$ on $L$, and $S$ independent. Exact embedding theorems cover $42$ of the $47$ non-isomorphic trees on nine vertices. The five remaining trees reduce, by deleting their leaves, to four rooted cores. For each core we construct a Boolean formula whose models are precisely the reduced hosts avoiding that rooted core. All four formulas are unsatisfiable. The deposited data include complete CNF instances and DRUP refutations. The archived traces were validated by reverse unit propagation, all four formulas are independently solved as unsatisfiable by a second SAT solver, a standalone semantic audit reconstructs the complete formulas---including all $3735$ base clauses and every avoidance clause---without importing the production generator, the complete $47$-tree witness table is generated from the classifier, and regeneration from the published encoder reproduces all four CNFs byte for byte. This is a finite partial result concerning trees on at most $n/2$ vertices; it does not settle the stronger classical formulation asking for trees with at most $n/2$ edges.

Abstract: Over a finite prime shell \(\mathbb F_p\), \(p=4\kappa+1\), the roles of \(\pi\) and \(e\) are exact residues: the half-period \(\pi=2\kappa\), and the exponential marker \(e=g^{\lambda(i)}\). We determine the exact relation between these carriers and the classical values. Each classical value is the horizon readout of a chain of framed rationals \(n!/!n\) for \(e\); the Wallis, arcsin and Machin chains for \(\pi\); at IEEE-754 double precision the constants are the readouts of \(18!/!18\) and the Machin partial \(M_{10}\). Inside the shell the same chains carry exact residue lines that the readout deletes: the line of \(e\) is antiperiodic and terminates on Kurepa's left factorial, universal existence being equivalent to Kurepa's hypothesis; the line of $\pi$ is legible exactly up to the angular address of -1 and terminates on the calibration face \(\pi^{-1}\equiv-2\). Angularly the constants are dual: \(\chi(-1)=e^{i\pi}\) holds exactly in every shell, while radian calibration of \(e\) is impossible in every shell and abundant across shells. \(\pi\) is structural, \(e\) statistical; transcendence belongs to the external completion, never to the shell element. All exact claims are machine-verified in integer and rational arithmetic.

Abstract: Cloud service continuous delivery involves computing, storage, permission, scheduling, and monitoring modules. Because complex service dependencies may hide cross-service anomalies under insufficient test coverage, this study proposes a quality assessment method combining test coverage mapping and release risk prediction. A directed dependency graph is built for interfaces, resource creation, volume mounting, permission verification, read/write performance, exception recovery, cross-version compatibility, and rollback paths. GraphSAGE learns associations among service nodes, test cases, and historical failures, while CatBoost predicts release failure probability. The dataset contains 31 pipelines, 126 modules, 460 integration cases, 9 release-change types, 2,800 release records, and 72 million execution data points. The coverage graph identifies 37 high-risk uncovered nodes, with storage mounting, permission propagation, resource initialization, and cross-version compatibility accounting for 72.9%. CatBoost achieves 90.8% accuracy and 0.934 AUC. Fault injection shows that dependency timeouts, permission anomalies, and storage latency raise failure probability by 31.5%, 24.7%, and 19.2%. After adding critical-path tests, core coverage increases from 68.4% to 91.2%, and monthly rollbacks fall from 26 to 14. This method supports risk control for banking, insurance, medical, education, and SaaS cloud services.

Abstract: Scientific AI systems can generate hypotheses and explanations, but many opti-mize plausibility more than refutability. This paper presents a falsification-drivenmulti-agent framework in which specialized agents propose hypotheses, build causalmodels, design adversarial tests, and verify formal claims. The architecture com-bines hypothesis generation, causal reasoning, falsification, formal verification, andpersistent orchestration through a shared memory state that records assumptions,counterexamples, interventions, and proof obligations. By treating failed predictionsand invalid proof attempts as useful learning signals, the framework shifts discoveryfrom fluent claim production toward disciplined claim survival. On simulated dis-covery tasks, the full system improves verified discovery rate from 0.42 to 0.76 andreduces false-positive hypothesis retention from 0.31 to 0.08. Scaling experimentsshow a peak discovery quality factor of 0.83 with eight agents, supporting the prin-ciple that scientific AI should prioritize systematic refutation, causal identifiability,and machine-checkable proof.

Abstract: Tabular anomaly detection (TAD) assigns anomaly scores to unusual samples in tables and supports applications in finance, healthcare, cybersecurity, industrial monitoring, and data-quality assurance. Its central challenge stems from the heterogeneous and weakly structured nature of tabular data: unlike images, sequences, and graphs, tables lack native spatial, temporal, or relational structure while mixing heterogeneous feature types without a common metric, so the notions of distance, density, and dependency that detectors rely on must be induced through representation and encoding choices. Part of what defines an anomaly may also reside outside processed values, in column semantics, domain rules, or schema information that standard pipelines discard. Recent TAD research spans non-deep detectors, deep task-specific models, large language model-based methods, and foundation model-based methods. These directions differ in supervision, information access, evaluation protocols, and downstream use, yet existing surveys examine neighboring areas largely in isolation. This survey provides a unified account of TAD by organizing existing detectors according to how they form anomaly scores. Beyond method taxonomy, it reviews enhancement and adaptation for deployment, benchmarks and evaluation protocols, and downstream tasks built on TAD outputs. It aims to clarify method assumptions and provide a more comparable basis for future TAD research.

Abstract: Simultaneous localization and mapping (SLAM) is a foundational capability for autonomous navigation in unknown environments. Its performance is strongly coupled to the type, quality, and reliability of available sensor data, limiting the portability of navigation systems across heterogeneous mobile robot platforms. This paper presents a cross-platform adaptive navigation framework that decouples localization providers from platform-specific sensing configurations. A sensor abstraction layer normalizes heterogeneous and low-fidelity sensor inputs into a unified representation, enabling structured operational modes constructed according to available sensing modalities, computational constraints, and environmental characteristics. A learning-based performance prediction module is further designed to estimate impending SLAM degradation and support proactive mode switching. Due to middleware constraints within the Pepper NAOqi stack, this predictive component was not deployed during experimental evaluation and remains part of the proposed architecture for future validation. Experimental results on real indoor navigation tasks demonstrate improved robustness and portability compared to fixed SLAM configurations without manual retuning.

Abstract: Trusted Data Spaces (TDS) have emerged as the core infrastructure for secure, privacy-preserving data circulation across industries and jurisdictions. However, state-of-the-art TDS implementations suffer from centralized platform monopoly, rigid cross-border governance failure, unfair value distribution, and poor scalability for global-scale collaboration. This paper proposes DAO-TDS, a novel decentralized autonomous trusted data space paradigm that enables centerless, cryptography-governed, and value-closed-loop data circulation. We make three core contributions: (1) We formalize the first anti-monopoly, incentive-compatible game-theoretic model for distributed TDS governance, with rigorous provable security guarantees; (2) We design an original Proof of Data Contribution (PoDC) consensus mechanism and a post-quantum secure Crypto-DAO governance protocol, with formal security proofs under the Universal Composability (UC) framework; (3) We implement a full prototype of DAO-TDS and conduct comprehensive, reproducible evaluations, showing that it supports 10,000+ distributed nodes with >12,000 TPS and <2s 99th-percentile confirmation latency, while delivering >80% of generated value to data contributors (vs. <50% in centralized platforms). While the proposed paradigm demonstrates strong performance and security guarantees, it still faces challenges in adaptive cross-jurisdictional compliance and lightweight edge node deployment, which require further investigation.

Abstract: Continual Learning (CL) rose to prominence with the rise of deep architectures, and then entered a winter as large language models (LLMs) gave the impression that learning over time was no longer needed. We argue that this winter was not a failure but, in fact, a necessary transition. Intelligence cannot be separated from the time in which an agent lives and acts, and the arrival of agentic systems built on large models returns CL to its proper place: not the narrow question of how representations are formed, but the principle by which agents organise their knowledge as its environment changes. We call these systems Continual Learning Agents, designed from the start for adaptation and consolidating what they learn. We follow this path from the early ideas about machines that learn over time, through the era of deep CL, towards an holistic view in which learning continuously and the design of the agent can no longer be held apart, and in which the hard problems of Artificial Intelligence (AI) and those of CL are seen to converge.

Abstract: This paper aims to formulate well-defined Rota-Baxter operators on Hopf π-algebras. To this end, we construct convolution algebras over π-graded structures, and further investigate the properties of antipodes and homomorphisms of Hopf π-algebras. Finally, we present the definition of Rota-Baxter Hopf π-algebras and construct valid examples.

Abstract: This paper proposes a switching mode beamforming (SMVB) technique for a two-microphone array setup in a multi-source acoustic environment with one dominant target and two interferers. The proposed method adaptively switches between a robust minimum variance beamformer (RMVB) and a linearly constrained minimum variance (LCMV) beamformer based on the eigenvalue characteristics of the spatial covariance matrix. The eigenvalue distribution is used to infer the signal environment and select the appropriate beamforming strategy. Simulation results show that the proposed SMVB method outperforms conventional MVDR, RMVB, and LCMV beamformers in terms of interference suppression and target signal preservation, achieving improved output signal-to-interference-plus-noise ratio (SINR) and overall signal quality.

Abstract: This study analyzes patterns of stress and exhaustion among student pilots throughout flight training using a combination of physiological and self-reported measurements. The Perceived Stress Scale (PSS-10) was used to measure perceived stress and exhaustion before and after each flight, while physiological data, including heart rate (HR), electrodermal activity (EDA), skin temperature, and acceleration, were continuously recorded during flight sessions. To identify recurring patterns in arousal and workload, physiological signals were preprocessed and analyzed across the flight stages. The findings indicate a buildup of workload-related weariness over time, as evidenced by steady increases in EDA and skin temperature across flights, as well as post-flight increases in self-reported exhaustion. Heart rate responses were more event-specific, with brief spikes during high-demand phases of flight. Overall, the findings demonstrate the value of combining physiological signals with subjective reports to identify patterns of stress and fatigue during real-world flight training and highlight the potential of data-driven approaches for monitoring pilot well-being.

Abstract: Organizations in the Arab world run employee and stakeholder surveys on tools that were built for English first. Arabic support in those tools is usually a translated interface on top of an English analytical pipeline, and the analysis itself tends to stop at raw response counts. This paper describes OrgPulse AI, a web platform I built to measure organizational health in Arabic and English through surveys structured around weighted thematic axes. The platform computes a deterministic set of metrics without any AI involvement: axis scores normalized to a 0-100 scale, top-box favorability, a consensus index derived from response dispersion, a worst-case margin of error, and an improvement priority ranking defined as axis weight multiplied by its performance gap. A second, optional layer adds inferential statistics on top of these descriptives: Welch's t-test for segment comparisons, normal-approximation confidence intervals, and Cronbach's alpha for axis-level internal consistency, all implemented from first principles and verified against reference values. Large language models sit outside this statistical core as a design and narration layer: GPT-4o drafts survey structures, questions, and weights during creation, and Claude Sonnet 4 writes executive narratives over the computed results. The paper also describes a portal mechanism that lets a parent organization share reports with subsidiary or client entities through PIN-gated pages, a pattern that matches how Saudi government bodies distribute assessment results to affiliated units. I state the platform's limitations plainly: the instrument is user-defined rather than psychometrically validated, scores aggregate at the question level rather than the respondent level, and the exploratory dialect-signal layer described in Section 5.2 has not been validated against human-coded ground truth. The contribution is an architectural and measurement pattern, documented from the actual implementation, for teams building survey analytics in languages that mainstream tools treat as an afterthought.

Abstract: We prove that finitary strongly taut paracompact locally small spaces are mild (all their subspaces are strict). We apply this result to show that all paracompact locally definable spaces over o-minimal structures are mild.

Abstract: The current paper suggests a new image encrypting method, which combines an original and designed Block Cellular Connection (BCC) algebra with the Advanced Encryption Standard (AES) in Cipher Block Chaining (CBC) mode. The strong validity of the suggested approach is proved by experimental assessment of conventional grayscale images with high NPCR (99.78%), UACI (33.85%), and entropy (7.99), and low correlation coefficients in horizontal, vertical, and diagonal scan directions. These findings demonstrate the possibilities of the BCC-AES-CBC hybrid to be used in secure and efficient image encryption applications.

Abstract: This paper investigates the precise upper bound of the third-order Hankel determinant for the inverse functions within the function classes $\mathcal S^{*}_{e}$, $\mathcal C_{e}$, $\mathcal S^{*}_{\mathcal L}$, and $\mathcal C_{\mathcal L}$. Additionally, it establishes the upper bound for the second-order Hankel determinant of the logarithmic coefficient in function class $\mathcal S^{*}_{\mathcal L}$, as well as the third-order Hankel determinant for function class $\mathcal C_{car}$.

Abstract: Evaluation of artificial intelligence concentrates on local performance — accuracy, calibration, robustness — while the upstream normative and volitional architecture that fixes what a system is for remains largely unexamined by those metrics. Existing scholarship has established that bias, proxy variables, problem formulation, measurement, alignment, and governance are value-laden; what remains insufficiently integrated is a single propagation account connecting moral grounding, authorized volition, teleological translation, representation, AI execution, and feedback. This article develops such an account: the Normative–Volitional Architecture of AI-Mediated Action, M → W → T → R → E → I_AI → D → A → C. Moral grounding (M) constrains what may legitimately be pursued; human or institutional volition (W) commits to a direction; teleological specification (T) translates that commitment into objectives and proxies; representation (R) determines which reality is available to the system; and AI performs inference and execution within that structure. The central argument is that AI executes an operational representation of authorized will; it does not independently legitimize ultimate ends. Systemic error therefore arises not only from malformed will but from the normative translation gap between defensible purposes and their operational encodings, and it persists under normative closure — the absence of an institutionalized feedback path through which consequences can reopen objectives, representations, and authority, rather than merely retraining models. Documented cases in healthcare allocation, risk assessment, hiring, engagement optimization, and welfare administration illustrate how locally correct outputs can constitute globally misleading trajectories, and a reflexive governance framework specifies remedies at each architectural layer.

Abstract: This study aims to construct a lightweight action recognition pipeline for work environments that does not rely on detailed manual labeling to achieve both the reduction of manual labeling load in the offline stage and the lightweight recognition of user actions in the online stage. The proposed method generates pseudo-labels from accelerometer data using time-series clustering. Extending the labeling scheme to other subjects, it integrates data from multiple subjects into a common set of action classes. Furthermore, it trains a lightweight action recognition model using the obtained pseudo-labels, which enables us to evaluate the trade-off between model complexity and recognition performance when the method is deployed on edge devices. The process verifies not only the transferability of action structures using pseudo-labels, but also the applicability of lightweight models to sequential action recognition.

Abstract: Object detection has evolved from classical feature-based methods to deep-learning frameworks, with the YOLO (You Only Look Once) family becoming one of the most widely adopted paradigms for real-time detection. Despite rapid architectural change from YOLOv1 to YOLO26, the literature remains fragmented, lacking a unified synthesis that integrates structural innovations, quantitative benchmarking, and domain-specific deployment. This review provides a longitudinal analysis of the YOLO lineage—from Darknet backbones to hypergraph-enhanced correlation modeling (YOLOv13) and end-to-end, NMS-free architectures (YOLO26), and from anchor-based to anchor-free, decoupled, and end-to-end heads. We compile and harmonize source-reported metrics (mAP, FPS, FLOPs, parameters) across canonical datasets (PASCAL VOC, MS COCO, KITTI) and domain benchmarks, treating the result as a cross-source synthesis rather than hardware-normalized re-benchmarking. Recent 2025–2026 advances are highlighted: YOLOv13 reports a +3.0% mAP@[0.5:0.95] gain over YOLO11-N (38.6%→41.6%) through high-order correlation modeling, while YOLO26 reports up to 43% faster CPU inference relative to YOLO11. Through a multi-sector analysis across seven application domains, we map design choices to operational constraints, identify persistent challenges (domain generalization, small-object localization, open-set detection), and outline a research agenda emphasizing hybrid correlation-enhancement architectures, deployment-centric training, data-efficient learning, and sustainability-aware benchmarking.

Abstract: We provide two separate and important results. First, we formalize a provable separation betweensyntactic and semantic computation for AI learning systems by virtue of the existence of hallucinations.We define run-level “hallucination” under a contract κ= (Lκ,Evalκ,winκ), where truth of an assertedproposition is graded by an external evaluator Evalκ within a fixed decision window. This separationallows us to prove the Transparency Impossibility Theorem: there is no total computable procedurethat, from a single run’s activation log, produces a finite, tape-transparent provenance deciding whetherthe run’s assertion is a hallucination without invoking Evalκ or a Halting/Oracle equivalent. The proofis a halting-encoded diagonal reduction. Rice’s theorem (Rice, 1953) and Tarski’s undefinabilitytheorem (Tarski, 1956) provide independent, complementary impossibility results — Rice rulesout global deciders for nontrivial extensional properties of programs; Tarski rules out an internaltruth predicate for sufficiently expressive Lκ — which we treat as background and supportingmotivation rather than as part of the activation-based reduction itself. Second, in this work we presenta layered account of computation and meaning. The base layer captures effective methods by Turingmachines (Turing, 1937; Church, 1936a). The next layers treat definability, truth, and semantic fixedpoints (Gödel, 1962; Tarski, 1956; Kripke, 1975). Then, we then connect these layers to compression,and description length, which act as practical limits on representation and inference (Li & Vitányi,2008). The aim is clarity about limits. However, we do not enlarge the class of computable sets.Instead, we separate internal effective acceptance from externally grounded acceptance with finitetranscripts. This separation lets us ask when explanation should work, and when it must fail. Rice’stheorem marks undecidable semantic properties that matter for explanation (Rice, 1953). Buildingon this, five corollaries organize the space: completeness, incompleteness, undefinability, groundedacceptance under budgets, and compression ceilings. Each yields a concrete probe or prediction. Theresult is a theoretical framework Church-Turing-Kripke-Meyer (CTKM) to explain how systems canproduce correct but non-derivable behavior without implying hypercomputation. The frameworkalso provides a falsification route insofar as we propose a Diophantine test to refute claims that crossthe classical boundary. Additionally, we offer a conditional description-length lens to mark whenfinite grounding changes acceptance without changing computability. In short, the framework keepscomputability classical while making the role of semantics and resources explicit and testable.

Abstract: This article develops duality principles and numerical results for a large class of non-convex variational models. The main results are based on fundamental tools of convex analysis, duality theory and calculus of variations. More specifically the approach is established for a class of non-convex functionals similar as those found in some models in phase transition. Moreover, we develop a general duality principle for quasi-convex relaxed formulations for some models in the vectorial calculus of variations. Concerning applications of such results are presented for a non-linear model of plates and for nonlinear elasticity. Finally, in some sections we present concerning numerical examples and the respective softwares.