Abstract: The Collatz Conjecture, a deceptively simple problem in number theory, has remained unsolved for decades. This paper presents a rigorous proof of the Collatz Conjecture by demonstrating that all positive integer sequences generated by the Collatz function eventually reach the trivial 4-2-1 cycle. Our proof employs a novel, structurally driven approach based on a complete classification of positive integers into five mutually exclusive sets—namely, the Cycle, ROM3, Precursor, Immediate Successor, and Reachable sets—thus defining a complete state space for Collatz dynamics. We show that, when viewed as trajectories within this structured state space, all sequences are bounded and converge to the unique attractor, the 4-2-1 cycle. This state-space based methodology provides a definitive resolution to one of mathematics' most enduring open problems.

Abstract: The complete proof of the Collatz Conjecture is presented by constructing the Collatz infinite tree through inverse transformations of the Collatz equation. The inclusion of all natural numbers in the tree and the nonexistence of cycles other than the trivial 1-2-4-1 cycle are shown. For any given natural number N, specific branches of the tree are shown to contain all natural numbers up to N. This result is generalized for all N using mathematical induction, confirming the completeness of the tree. Analysis of the tree's structure demonstrates that the only cycle present is the trivial 1-2-4-1 cycle in the backbone. All conditions necessary for the existence of nontrivial cycles are shown to be unsatisfiable, affirming the conjecture's validity. An algorithm is also designed to construct the subtree containing all natural numbers up to any specified N, offering a practical complement to the theoretical proof.

Abstract: The theory states that numbers interact with spaces based on mathematical meaning, thus enabling numerical knowledge. The theory shows the possibility of using interrelated spaces to efficiently discover whether outcomes and origins are even or odd. The study uses a new form of computational thinking to reduce all the complexity of laborious information to simpler and more obtainable information. All this is possible due to the equivalent representations of even and odd numbers, but always applying rules to make it work. Thus, it is possible to discover the possibilities of origins and their outcomes.

Abstract: A pipeline burst or rupture causing a leak may significantly impact the environment and the reputation of the company operating the pipeline. In recent years, oil and gas pipelines have been expected to be equipped with leak detection systems for monitoring operations and detecting leaks. Although the leak detection methods used today may not prevent leaks from happening, they play a crucial role in limiting the impact of leaks. There is a wide variety of leak detection methods developed and tested. This research work reviews these methods and analyzes their advantages and limitations. It ends by highlighting the opportunities for future work to improve the reliability and adaptability of leak detection methods in subsea regions. Pipeline leakages pose significant environmental and economic risks to the oil and gas industry. Real-time monitoring systems employing deep learning models have shown promising results in detecting and identifying leakages. This systematic review synthesizes existing literature on deep learning-based real-time monitoring systems for oil and gas pipeline leakages. The work evaluates deep learning models' effectiveness in detecting pipeline leakages, analyzes the types of sensors and data used in real-time monitoring systems, and investigates the performance metrics and comparison of different deep learning architectures. The review included 20 studies employing Deep Learning Approaches to identify oil and gas pipeline leakages. Deep learning-based real-time monitoring systems demonstrate the potential for efficient and accurate detection of oil and gas pipeline leakage.

Abstract:

This study presents an official Software Requirement Specification (SRS) of a campus carpooling system to enhance transport efficiency, reduce traffic congestion, and ensure user safety. The report outlines functional and non-functional requirements, quality requirements, and acceptance conditions for system deployment. Some of the key features include real-time ride updates, user registration, security features, multi-platform compatibility, and an incentive-based reward scheme to promote user engagement. Through mapping requirements to stakeholders' goals, including syntactic requirement patterns, and defining acceptance criteria, the study ensures that there is a stable and convenient carpooling experience. The findings are favorable to green transportation solutions, upholding environmental awareness and operational effectiveness in universities.

Abstract: Nutrient analysis through mobile health applications can improve dietary choices, particularly among vulnerable populations. However, deploying sophisticated deep learning models on resource-constrained devices presents challenges in computational efficiency, model interpretability, and user trust. We propose a lightweight interpretable deep learning model for real-time nutrient analysis on mobile devices. Our approach uses depthwise separable convolutions, bottleneck units, and Shuffle Attention to reduce computational complexity while maintaining accuracy. For interpretability, we integrate Grad-CAM visualisations, LIME explanations, and Concept Activation Vectors. Our model achieves 92.3% accuracy in food recognition and 7.2% mean absolute error in nutrient estimation, with a model size of 11MB. Testing on resource-constrained devices shows inference times of 150ms on mid-range smartphones with minimal battery impact. User studies demonstrate high comprehension scores for interpretability features, with Grad-CAM visualisations achieving an 8.2/10 understanding score. These results show our model can effectively deliver nutrient analysis on budget mobile devices and in environments with limited infrastructure, making it particularly valuable for vulnerable populations facing both technical and infrastructural constraints.

Abstract: This retrospective study introduces a guided diffusion deep learning method to mitigate streaking artifacts in chest CT scans caused by scanner issues, physical effects, patient factors, and helical and multisection techniques. Data from 763 non-contrast CT series (110–140 kVp, 165 mAs average, 0.5–10 mm slices) across four centers included 47,032 artifact-affected and 49,609 artifact-free slices. The model was trained by concatenating artifact-free CT images with segmentation masks and anatomical ROIs to preserve structures during the diffusion process. Artifact-laden images were processed through the trained model to generate artifact-free outputs. Comparing samples with artifacts and those without from four centers, a statistically significant difference in SNR and CNR of anatomical ROIs (p<0.05) was observed. The generated images demonstrated high consistency with actual artifact-free samples, with lung field SNR values of 26.67±2.01 and 26.11±1.89, and CNR between lung fields and trachea of 3.76±0.77 and 3.78±0.56.  Results showed enhanced performance over CycleGAN and other diffusion models with SSIM 0.863±0.01 and PSNR 36.952±0.67(p<0.05), achieving high DSC for anatomical consistency. Findings demonstrate effective artifact reduction while maintaining structural integrity, offering potential clinical value in diagnostic accuracy and image quality enhancement.

Abstract: The market risk measurement of a trading portfolio in banks, specifically the practical implementation of the value-at-risk (VaR) and expected shortfall (ES) models, involves intensive recalls of the pricing engine. Machine learning algorithms may offer a solution to this challenge. In this study, we investigate the application of the Gaussian process (GP) regression and multi-fidelity modeling technique as approximation for the pricing engine. More precisely, multi-fidelity modeling combines models of different fidelity levels, defined as the degree of detail and precision offered by a predictive model or simulation, to achieve rapid yet precise prediction. We use the regression models to predict the prices of mono- and multi-asset equity option portfolios. In our numerical experiments, conducted with data limitation, we observe that both the standard GP model and multi-fidelity GP model outperform both the traditional approaches used in banks and the well-known neural network model in term of pricing accuracy as well as risk calculation efficiency.

Abstract: We introduce a groundbreaking framework that addresses the challenges inherent in multimodal emotion recognition when some data channels are absent. Unlike previous approaches, our method harnesses invariant feature learning coupled with missing modality synthesis to construct robust joint representations from incomplete inputs. By employing an advanced invariant feature constraint based on central moment discrepancy (CMD) measures and a novel cross-modality synthesis mechanism, our Universal Invariant Imagination Network (UIIN) significantly narrows the modality gap and enhances recognition accuracy. Extensive evaluations on benchmark datasets demonstrate that our approach consistently outperforms state-of-the-art methods under diverse missing-modality conditions. In addition to these key innovations, our framework also integrates a series of auxiliary regularization techniques and novel loss functions that further optimize the learning process. These enhancements enable the network to more effectively reconcile disparities between modalities and to maintain stable performance even when confronted with severe data degradation. Through rigorous quantitative and qualitative assessments, we validate the capability of our approach to adapt to dynamic and unpredictable environments, thereby offering a robust solution for practical implementations in affective computing.

Abstract:

The Question Generation System (QGS) for Information Technology (IT) education, designed to create, evaluate, and improve Multiple-Choice Questions (MCQs) using Knowledge graphs (KGs) and Large Language Models (LLMs), encounters three major needs: ensuring the generation of contextually relevant and accurate distractors, enhancing the diversity of generated questions, and balancing the higher-order thinking of questions to match various learning levels. To address these needs, we proposed a multi-agent system named Multi-Examiner, which integrates knowledge graphs, domain-specific search tools, and local knowledge bases, categorized according to Bloom’s taxonomy, to enhance the contextual relevance, diversity, and higher-order thinking of automatically generated information technology multiple-choice questions. We designed a multidimensional evaluation rubric to assess the semantic coherence, answer correctness, question validity, distractor relevance, question diversity, and higher-order thinking, and applied it to questions generated for six knowledge points from the second chapter of the "Information Systems and Society" textbook using both the Multi-Examiner system and GPT-4, alongside real exam questions, evaluated by 30 high school IT teachers. The results demonstrated that: (i) overall, questions generated by the Multi-Examiner system outperformed those generated by GPT-4 across all dimensions and closely matched the quality of human-crafted questions in several dimensions; (ii) domain-specific search tools significantly enhanced the diversity of questions generated by Multi-Examiner; (iii) GPT-4 generated better questions for knowledge points at the "remembering" and "understanding" levels, while Multi-Examiner significantly improved the higher-order thinking of questions for "evaluating" and "creating" levels. This study highlights the potential of multi-agent systems in advancing question generation.

Abstract:

In this paper, we demonstrate that the Maxwell eigenvalue problem can be solved by a nonconforming finite element and multigrid method. By using an appropriate operator, the eigenvalue problem can be viewed as a curl-curl problem. We obtain the approximate optimal error estimates on graded mesh. We also prove the convergence of the W-cycle and full multigrid algorithms for the corresponding discrete problem. The performance of these algorithms is illustrated by numerical experiments.

Abstract:

Recent advances in DevOps have dramatically reshaped software development and operations by emphasizing automation, continuous integration/delivery, and rapid feedback. However, organizations still struggle to achieve predictable improvements despite widespread adoption. In this study, we propose an “IDEAL-Enhanced DevOps” framework that integrates the five-phase IDEAL model—Initiate, Diagnose, Establish, Act, and Learn—into a DevOps transformation process. The proposed method lays out a structured approach to applying incremental improvements throughout the software delivery process. By a review of literature, in-depth analysis of case studies, and dis-semination of a questionnaire to practitioners in the field, this research explains how the IDEAL stages can be mapped to key processes in DevOps, address automation and scalability challenges, and facilitate a learning-centered, cooperative culture. The results show that a well-defined process-improvement approach can effectively reduce error incidence, enhance usability of tools, and significantly shorten time to get products to market. Our analysis shows that coupling IDEAL with DevOps not only clarifies responsibilities and organizational roles, but also lays a foundation for more resilient, high-quality, and adaptable software engineering methods.

Abstract: Digitalization is transforming the maritime sector, and the amount and variety of data generated is increasing rapidly. The true potential of data lies in its meaningful use to enable data-driven applications such as for highly-automated maritime systems or an efficient and secure traffic coordination. Data-driven applications usually rely on a heterogeneous data basis. The more context-related information is available, the better results the services can achieve. In practice, this poses an enormous challenge, as the heterogeneous data is not managed centrally by one single party, but is distributed across various actors. Therefore, a solution must be found for how distributed data can be used jointly and securely for the operation of maritime services without violating the sovereignty of the data providers. In this paper, a fully decentralized architecture is proposed to facilitate sovereign and secure data exchange between maritime actors, considering domain-specific challenges such as volatile connectivity, low bandwidth and the consideration of maritime standards. The approach is based on a data space architecture and demonstrates its functionality using a use case from maritime traffic management. It could be shown how the proposed architecture enables the acquisition of heterogeneous data from multiple providers and supports a safer and more efficient coordination of maritime traffic through the operation of a data-driven service.

Abstract: This paper deals with biometric identification based on unique patterns and characteristics of an individual’s handwriting, focusing on the dynamic writing process on a touchscreen device. Related work in this domain indicates the dominance of specific research approaches. Namely, in most cases, only the signature is analyzed, verification methods are more prevalent than recognition methods, and the provided solutions are mainly based on using a particular device or specific sensor for collecting biometric data. In this context, our work aims to fill the identified research gap by introducing a new handwriting-based user recognition technique. The proposed approach implements the concept of sensor fusion and does not rely exclusively on signatures for recognition but also includes other forms of handwriting, such as short sentences, words, or individual letters. Additionally, two different ways of handwriting input, using a stylus and a finger, are introduced into the analysis. In order to collect data on the dynamics of handwriting and signing, a specially designed apparatus was used with various sensors integrated into common smart devices, along with additional external sensors and accessories. A total of 60 participants took part in a controlled experiment to form a handwriting biometrics dataset for further analysis. To classify participants’ handwriting, custom architecture CNN models were utilized for feature extraction and classification tasks. The obtained results showed that the proposed handwriting recognition system achieves accuracies of 0.982, 0.927, 0.884, and 0.661 for signatures, words, short sentences, and individual letters, respectively. We further investigated the main effects of the input modality and the train set’s size on the system’s accuracy. Finally, an ablation study was carried out to analyze the impact of individual sensors within the fusion-based setup.

Abstract:

Green hydrogen, produced via renewable-powered electrolysis, has the potential to revolutionize energy systems, but its widespread adoption hinges on achieving competitive production costs. A critical challenge lies in optimising the hydrogen production process to address solar and wind energy's high variability and intermittency. This paper explores the role of artificial intelligence (AI) in reducing and streamlining hydrogen production costs by enabling advanced process optimisation, focusing on electricity cost management and system-wide efficiency improvements.

Abstract: Sequential recommendation is an advanced recommendation technique that utilizes the sequence of user behaviors to generate personalized suggestions by modeling the temporal dependencies and patterns in user preferences. However, it requires a server to centrally collect users' data, which poses a threat to the data privacy of different users. In recent years, federated learning has emerged as a distributed architecture that allows participants to train a global model while keeping their private data locally. This survey pioneers Federated Sequential Recommendation (FedSR), where each user joins as a participant in federated training to achieve a recommendation service that balances data privacy and model performance. We begin with an introduction to the background and unique challenges of FedSR. Then, we review existing solutions from two levels, each of which includes two specific techniques. Additionally, we discuss the critical challenges and future research directions in FedSR.

Abstract: In this work, we introduce a novel framework that augments language understanding systems with external multimodal graph structures. Instead of increasing the internal capacity of language models by scaling parameters, our approach leverages a dedicated external repository—an enriched knowledge graph—to provide additional visual and textual cues during inference. Specifically, given multilingual inputs (for example, German sentences), our method retrieves corresponding entities from the graph and incorporates their multimodal embeddings to boost performance on various downstream tasks. Our framework, herein referred to as \textbf{AlphaKG}, integrates state-of-the-art tuple-based and graph-based learning strategies to generate representations for entities and their inter-relations. By fusing data from diverse modalities such as textual descriptions available in 14 languages and multiple visual samples per entity, we design a robust representation learning scheme that is predictive of the underlying graph structure. Experiments on multilingual named entity recognition (NER) and crosslingual visual verb sense disambiguation (VSD) show promising results, with improvements reaching up to $0.7\%$ in F1 score for NER and up to $2.5\%$ in accuracy for VSD. Additionally, we derive new equations to refine the integration process between the retrieved external features and the language model inputs, thereby offering a comprehensive solution to enhance parameter efficiency while maintaining competitive performance.

Abstract: Scoliosis is a disorder characterised by an abnormal spinal curvature, which can lead to negative effects on patients, affecting their quality of life. Given its progressive nature, the classification of severity requires an accurate diagnosis and effective monitoring. The Cobb angle measurement method has been widely considered as the gold standard for a scoliosis assessment. Commonly, an expert assesses scoliosis severity manually by identifying the most tilted vertebrae of the spine. However, this method is tedious, time-consuming, and presents limitations in measurement accuracy due to the intraobserver and interobserver variability. This highlights the need for a more objective tool less sensitive to manual intervention. Nowadays, advancements in artificial intelligence are transforming the diagnosis of scoliosis. In this study, we propose a fully automated approach to measure the Cobb angle. A small dataset of 98 anterior-posterior full spine X-ray images was labelled and included for evaluation. We assessed the accuracy and performance of the Mask R-CNN architecture for spine detection and segmentation. Beyond the neural network´s performance, a workflow was developed to enable midline identification, detection of the most significantly tilted vertebrae, direct visualization of Cobb angles, and scoliosis severity assessment. The model achieved high segmentation accuracy, with mIoU of 0.8012 and mDSC of 0.8878, while maintaining a mean precision of 0.9145. The mean Cobb angle was 25.43° ± 10.85° (range: 11.50-54.00°) for manual measurements by observer A, 25.89° ± 10.00° (range: 10.00-53.00°) by observer B, and 26.69° ± 12.50° (range: 10.29-59.34°) for automated measurements. We achieved a Mean Absolute Difference of 3.31º ± 2.69º, a Mean Absolute Error of 2.96° ± 2.60°, and an Intraclass Correlation Coefficient (95% CI) of 0.928 between manual and automated measurements. The automated method required an average of 3.3 seconds per radiograph. Although further improvements are needed, these results demonstrate the high potential of the proposed model, which provides experts with improved interpretability and precision in Cobb angle calculation and severity classification by overlaying them onto the original X-ray images.

Abstract: The increasing requirement for efficient, cost-effective, and green transport has led to the implementation of a campus carpool scheme. In this paper, we discuss the process of engineering requirements for developing a carpool system to match university staff and students for daily commute on a shared basis. With the application of formal elicitation techniques, i.e., surveys and interviews, we elicited key user requirements and system constraints. The outcomes enumerate the principal issues of transport inefficiencies, costly commuting, and environmental concerns. Based on data collected, we determine system requirements functional and non-functional to achieve a secure, user-friendly, and efficient carpooling process. The research aids the growth of intelligent campus programs through presenting a scientific framework for deploying intelligent mobility solutions.

Abstract: Forest fires pose a major threat to ecosystems and human life; Therefore, early detec-tion is essential for effective prevention. Traditional detection methods often fall short of the need due to their large coverage and limitations in providing timely alerts. Alt-hough advances in drone technology and deep learning have opened up new possibili-ties for efficient and accurate forest fire detection, implementation rates remain low due to the complexity of deep learning algorithms. This study explores the application of small UAVs equipped with lightweight deep learning models for early forest fire detection. A high-quality dataset was constructed through aerial image analysis, which provided strong support for model training. Based on YOLOv5s, a YOLO-UFS (YOLO-UAVs for Fire and Smoke Detection) network is proposed, which combines enhancements such as C3-MNV4 module, BiFPN, new AF-lou loss function, anchorless detector and NAM attention mechanism. These modifications resulted in the model achieving 91.3% mAP under the same experimental conditions and using a self-built early forest fire dataset. Compared to the original model, the YOLO-UFS model im-proved accuracy, recall, and average accuracy by 3.8%, 4.1%, and 3.2%, respectively, while reducing floating-point arithmetic and parameter counting by 74.7% and 78.3%. Compared with other mainstream YOLO series algorithms, its performance on the UAV platform is superior, effectively balancing accuracy and real-time. In the later stages of the forest fire, using a public dataset, mAP0.5 increased from 85.2% to 86.3%, and mAP0.5:0.95 increased from 56.7% to 57.9%, resulting in an overall mAP increase of 3.3 percentage points. The optimized model demonstrates significant detection ad-vantages in the complex environment captured by small UAVs. This study uses air-borne visible images to provide effective data and methodological support for the early extinguishing of forest fires, which is helpful to achieve the "three early" goals of forest fire prevention (early detection, early mobilization, and early extinguishment). Future work will focus on exploring multi-sensor data capabilities to further improve the ac-curacy and reliability of detection.