Abstract: The Nicolas criterion gives an equivalent formulation of the Riemann Hypothesis as an inequality involving the Euler totient function evaluated at primorial numbers. A natural strategy for establishing this inequality is to prove that a suitable subsequence of the associated ratio sequence is eventually strictly decreasing under the assumption that the Riemann Hypothesis is false. The present work shows that such a subsequence exists. When this monotonicity property is combined with the known limiting behavior of the ratio sequence and the Nicolas equivalence, a contradiction emerges: assuming the Riemann Hypothesis is false forces the subsequence to converge to a limit that is simultaneously equal to $e^{\gamma}$ (by a subsequence argument) and strictly less than $e^{\gamma}$ (by strict monotonicity). The Riemann Hypothesis therefore follows as a direct consequence.

Abstract: Let $ \xi(z) $ be the Riemann xi function. In a previous paper we prove the boundedness of coefficients of the power series expansion of $ \xi'(1/z)/\xi(1/z) $ and thus give a proof of the Riemann hypothesis. In this paper we generalize the method there to the study of the extended Riemann hypothesis for general number fields.

Abstract: Network access control and identity legitimacy verification have been implemented by establishing a secure foundation for the trusted establishment of communication entities. However, successful identity authentication alone does not guarantee secure communication. In open-network environments, it remains essential to establish a secure session key via a robust key agreement mechanism—one that prevents explicit disclosure of identity information while ensuring post-quantum security. To address these requirements, we propose a lattice-based key agreement protocol. The protocol integrates identity binding, implicit authentication, and session key establishment into a single ciphertext exchange. Furthermore, it supports secure key evolution and revocation verification through a version-control mechanism and a blockchain-maintained revocation list—thus realizing a comprehensive, post-quantum-secure key agreement scheme under reasonable computational and communication overhead.

Abstract: The classical binary heap sink operation based on swap has a significant write overhead. We examine two intuitive improvements: swapping siblings (verified via bounded SMT search) and adding a local hint called pref (the hint-assisted variant). In our bounded SMT checks and implementation comparisons, we did not find evidence that these variants provide consistent benefits; PerfView measurements show the hint-assisted variant was slower in most configurations. Our results suggest that reverting to the straightforward hole-based sink is the practical choice for write-efficient implementations

Abstract: This study addresses the problem of zero-shot generalization (ZSG) in deep reinforcement learning by proposing an MNK game strategy learning method based on a Fully Convolutional Deep Q-Network (FCN-DQN). Research in deep reinforcement learning aims to develop algorithms that can generalize well to unseen environments at deployment time, thereby avoiding overfitting to the training environment. Solving this problem is crucial for real-world applications, where environments are diverse, dynamic, and inherently unpredictable. By constructing a fully convolutional reinforcement learning policy network composed entirely of convolutional layers with padding to preserve feature map dimensions, the proposed model is able to handle input boards of varying spatial sizes. The model effectively learns local pattern-based strategies and approximations of the k-in-a-row evaluation function rather than performing global search. Furthermore, due to parameter sharing, the network has a relatively small number of parameters and is able to share policy representations across different board scales, thereby improving both sample efficiency and inference efficiency. Experimental results demonstrate that, after being trained on a 3×3 board, the proposed model is able to achieve a certain degree of zero-shot generalization performance in larger, unseen board environments.

Abstract: Today, data are no longer confined to numerical values arranged in row-by-column matrices or stored neatly within relational databases. One of the defining characteristics of big data is its high variety, encompassing unstructured and multimodal forms such as text, audio, images, and video. These data types dominate contemporary domains including social media, digital humanities, biomedical research, education, and surveillance systems, yet they remain difficult to manage and analyze using traditional data management architectures. To cope with this shift, modern data management systems must move beyond schema-driven designs and incorporate multimodal artificial intelligence capable of understanding, integrating, and reasoning across heterogeneous data modalities. This article examines how multimodal AI—particularly large multimodal foundation models—can be leveraged to support the ingestion, representation, organization, and analysis of unstructured data. It discusses emerging multimodal data management frameworks, outlines a conceptual pipeline for multimodal data analysis, and highlights key challenges related to scalability, interpretability, and governance. By situating multimodal AI at the core of data management, this work argues that effective data analysis in the era of big data requires systems that treat meaning, context, and cross-modal relationships as first-class computational objects rather than afterthoughts.

Abstract: Citizen-reporting platforms generate high-volume, multilingual streams of service requests, yet operational triage often relies on coarse category labels and manual inspection. This study develops an explainable, calibration-aware analytics pipeline for FixMyStreet Brussels reports, combining text-based urgency modeling, topic discovery, and spatio-temporal hotspot scoring to support municipal decision-making. From 522,132 raw reports, we build an English-normalized text field for modeling, derive resolution-time outcomes from closed cases, and curate a 1,000-item gold standard with an explicit high-urgency class. A TF–IDF logistic regression baseline achieves strong classification performance and, after probability calibration, yields well-behaved confidence estimates suitable for risk-aware prioritization. Topic-level analyses reveal dominant themes related to sidewalks, road damage, and bulky waste, and hotspot scores highlight persistent, high-impact issue clusters. Event detection on aggregated signals did not identify statistically significant shocks during the analysis window, suggesting that the observed dynamics are driven by chronic, recurring problems rather than abrupt anomalies. Explainability audits via SHAP expose linguistically intuitive drivers for urgent cases (e.g., dangerous, risk, accident) and complaint-oriented terms (e.g., abandoned, illegal, dirty), providing transparent hooks for governance review.

Abstract: Decentralized federated learning (DFL) eliminates the single point of failure inherent in server-based architectures, enabling peer-to-peer collaborative model training. However, the absence of a central authority makes DFL particularly vulnerable to Byzantine attacks from malicious participants. Existing Byzantine-robust methods often fail to exploit the network topology structure of DFL. We propose TrustGraph-DFL, a novel defense mechanism that leverages graph-based trust modeling for Byzantine resilience. Our key insight is that consistency between a neighbor's model update direction and a node's local validation gradient can serve as an effective trust indicator. Each node computes consistency scores by comparing received updates against locally computed validation gradients, then maps these scores to dynamic edge weights for robust weighted aggregation. Experiments on CIFAR-10 demonstrate that TrustGraph-DFL achieves 3--5% higher accuracy than existing methods under 30% Byzantine nodes while maintaining a low false positive rate (approximately 9% at 50% Byzantine fraction, compared to 35% for Krum).

Abstract: This study examines the multifaceted application of machine learning and artificial intelligence (AI) in two key, dynamically developing sectors: cryptocurrency market capitalisation forecasting and customer service optimisation. An analysis of the effectiveness of various regression models (Linear, Lasso, and Decision Tree Regression) in predicting the market capitalisation of 3 leading cryptocurrencies shows that a model's success is highly dependent on the specific characteristics of the asset. While linear models achieve exceptional accuracy (R2>0.99) for most major and liquid cryptocurrencies, nonlinear approaches like Decision Tree Regression prove superior for assets with more complex and nonlinear market dynamics, highlighting the need for a flexible approach to model selection. In parallel, the study analyses the implementation of AI in customer service, reviewing chat communication data with the AI assistant "Naomi" (January 26–February 8, 2025). The AI "Naomi" demonstrated high overall effectiveness in chat communication, resolving over 60% of inquiries. However, a significant number of unresolved chats due to customer inactivity or AI limitations indicate areas for further optimisation. In conclusion, the effective application of AI and machine learning requires a strategic approach tailored to the specific field. The key to success lies in careful model selection, prioritising technical reliability, and continuous adaptation and optimisation based on empirical data and a deep understanding of AI's limitations.

Abstract: This work constructs, analyzes and simulates a modified SIR epidemiological model for the spread of a generic long-time disease, in which the coefficients of infectivity and death rate are system variables. Diseases, such as COVID-19, have demonstrated very clearly that infectivity and death rates can change over time, even for the same variant of the virus, due to vaccination, improved treatments, better analysis, better medications, etc. This motivates us to model a generic disease where the infectivity and death rates are state variables as a part of the systems's evolving in time. The model consists of a coupled system of five differential equations. The analysis shows the existence, positivity and boundedness of the solutions. A short discussion of the Endemic (EE) and Disease-Free (DFE) equilibria and their stability is provided. Then, computer simulations depict two typical cases of dynamic behaviors, one when the DFE is stable and attracting, and one in which the EE is stable and attracting. These also show how the system approaches these steady states.

Abstract: Early identification of Autism Spectrum Disorder (ASD) traits in infants is crucial for early intervention, which can greatly improve the child’s quality of life. Solutions that use voice analysis offer a promising non-invasive way to detect ASD. However, most current studies depend on extracting specific voice markers from certain datasets and do not include validation across different groups. In this paper, we propose a supervised contrastive learning method for identifying ASD based on infant vocalizations. We extend the Time-Frequency Consistency (TF-C) framework from self-supervised learning to a contrastive approach that uses labels. Our method takes advantage of both time-related and frequency-related data through a dual-branch encoder. It applies supervised contrastive constraints during pre-training to reduce variation within classes while boosting separation between different classes in the embedding space. We pre-train the model using diagnostic labels on a dataset that includes typically developing (TD), Attention-Deficit Hyperactivity Disorder (ADHD), and ASD infants from an open-access dataset, and then fine-tune it with a simple classification head. Evaluation on a cross-cohort group of participants shows the model generalizes well and can distinguish ASD from non-ASD infants, achieving up to 100.00 % accuracy on non-verbal vocalizations.

Abstract: We investigate discrete-time deterministic systems on finite state spaces equipped with symmetry groups, extending the analysis to actions of arbitrary countable linearly ordered groups. Under the assumption of strong recurrence, characterized by the absence of weakly wandering sets of positive measure, we establish the structural constraints governing dynamical invariants. For systems associated with amenable groups, we employ Følner sequences to rigorously define asymptotic frequencies and demonstrate that maximal Shannon entropy emerges naturally from the system's architecture rather than stochastic assumptions. We show that the interplay of strong recurrence and symmetry enforces specific distribution patterns; while transitive symmetry leads to a uniform stationary distribution and maximal entropy, we provide a generalized formula for non-transitive cases based on orbit decomposition. These results bridge classical recurrence theory and ergodic decomposition with modern measure-theoretic entropy, illustrated through concrete examples for both finite and infinite countable settings.

Abstract: We develop a geometric and combinatorial framework for the distinct-prime Goldbach conjecture—the assertion that every even integer 2N ≥ 8 is the sum of two distinct primes. The framework rests on three components: (1) a novel geometric equivalence reformulating the problem in terms of nested squares with semiprime areas, (2) a rigorous combinatorial reduction to a density condition on a set of straddling prime pair half-differences, and (3) extensive computational verification. The geometric construction reveals that the conjecture is equivalent to finding, for each N ≥ 4, an integer M ∈ [1,N −3] such that the L-shaped region N² − M² between nested squares has area P · Q where P = N − M and Q = N + M are both prime. We define D_N = {(Q − P)/2 | 2 < P < N < Q < 2N, both prime}∩{1,...,N − 3} to be the set of achievable half-differences from straddling prime pairs that lie inside the admissible range. Our gap function G(N) = log²(2N) − ((N −3) − |D_N|) measures the margin by which the required density condition holds. Using explicit results from Dusart’s doctoral thesis, we rigorously establish Steps 1–3 of the density argument, including the bound |D_N| ≥ ln²N for N ≥ 3275. We formulate the remaining step—that the number of missing M-values is at most ln²(2N)—as the Density Hypothesis (G(N) > 0), supported by computational evidence: for all N ∈ [4,2¹⁴], G(N) > 0 holds universally, with minima strictly increasing across dyadic intervals. We prove that the Density Hypothesis, combined with finite verification for small N, implies the distinct-prime Goldbach conjecture via the pigeonhole principle.

Abstract: We define the function $Col: \mathbb{N} \to \mathbb{N}$ as the Collatz function, given by $3n + 1$ if $n$ is odd and $\displaystyle\frac{n}{2}$ if $n$ is even. The conjecture postulates that for any positive integer, at some point, its iteration will reach 1, or equivalently, every orbit will fall into the periodic cycle $\{4, 2, 1\}$. Two conditions would invalidate the conjecture: The existence of a divergent orbit or the presence of another cycle. We can study the dynamics of the orbits through the density of even terms in their orbit. If all points' accumulation density exceeds the value of $\displaystyle\frac{\ln(3)}{\ln(2)}$ then the orbit is bounded. The main result of this work is to show that there are no natural numbers such that the accumulation points of the pair density are less than $\displaystyle\frac{\ln(3)}{\ln(2)}$. In other words, there are no divergent orbits.

Abstract: The increasing demand for sustainable and affordable smart-city infrastructure has intensified the need for low-cost, near-real-time water-quality monitoring systems. In this study, we propose Water-QI, a low-cost Internet of Things (IoT)-based environmental monitoring platform that combines budget-friendly sensors with deep learning for Water Quality Index (WQI) assessment and forecasting. The sensing platform measures five key physicochemical parameters, namely temperature, total dissolved solids (TDS), pH, turbidity, and electrical conductivity, enabling continuous multi-parameter monitoring in urban water environments. To model temporal variations in water quality under both cloud-based and edge-oriented deployment scenarios, we evaluate multiple Gated Recurrent Unit (GRU) architectures with different widths and depths. Experiments are conducted at two temporal resolutions, hourly and minute-level, in order to examine the trade-off between predictive accuracy and computational cost. In the hourly scenario, the single-layer GRU with 64 units achieved the best overall balance, reaching a validation RMSE of 0.0281 and a test R² of 0.9820, while deeper stacked GRU models degraded performance substantially. In the minute-resolution scenario, shallow wider GRU models produced the best results, with the single-layer GRU with 512 units attaining the lowest validation RMSE (0.025548) and the 256-unit variant achieving nearly identical accuracy with much lower inference cost. The results show that increasing model width can yield marginal improvements at high temporal granularity, whereas excessive recurrent depth consistently harms convergence and generalization. Overall, the findings indicate that shallow GRU architectures provide the most practical solution for accurate, low-cost, and scalable near-real-time water-quality forecasting. In particular, the 64-unit GRU is the most suitable choice for hourly low-complexity operation, while the 256-unit GRU offers the best speed--accuracy trade-off for minute-level edge inference on resource-constrained devices.

Abstract: Long-term Holter analysis requires software tools capable of automating signal preprocessing, temporal segmentation, probabilistic computation, and result visualization in a reproducible and interpretable manner. In this research, a modular software system for automated analysis of cardiac dynamics was developed following a software engineering perspective and an iterative lifecycle based on Scrum, including requirements definition, sprint planning, development, integration, testing, review with a medical specialist, and refinement. The platform was designed to analyze standardized temporal windows of 12, 14, and 18 h extracted from original 24 h Holter-ECG recordings and integrates a frontend, a backend, and a Python® analytical engine within a unified client–server framework. It processes Excel or CSV files containing hourly average heart-rate values, performs structural validation, discretizes the data into 10 beats-per-minute intervals, constructs empirical probability distributions, identifies recurrent dynamic patterns, and generates structured JSON outputs for web-based visualization. A complementary preprocessing module was also implemented for raw PhysioNet ECG signal records, enabling the loading of .hea and .dat files, automated R-peak detection, and extraction of hourly average heart-rate values. The system was evaluated on 113 Holter records from three open-access databases: 85 from SHDB-AF, 19 from the Long-Term ST Database, and 9 from the MIT-BIH Normal Sinus Rhythm Database. Overall structural agreement at the record level was 58.4% (66/113). To conclude, this system provides a reproducible web application pipeline for Holter signal data processing and probabilistic cardiac dynamics analysis, integrating software development, preprocessing, classification, and interpretable visualization within a modular framework.

Abstract: This study develops a mobile-supported system that local governments can use in their irregular waste collection services within the scope of smart cities. Irregular waste refers to waste that individuals or organizations produce non-periodically, which arises unexpectedly or in an unusual manner. This waste can accumulate within the city and cause environmental pollution if it is not notified to the municipality or local government for collection. Unlike small-volume household waste collected at routine times, irregular waste is generally large-volume waste such as construction rubble, vegetable oil, mineral oil, and garden waste. Municipalities have different collection vehicles with varying capacities to suit different waste types and quantities. To increase efficiency in the waste collection process, waste locations should be sequenced and vehicles appropriate to the waste type should be allocated in planning. In the irregular waste collection system developed in this study, waste locations are marked on the map applications running on mobile devices, and notifications are sent to the municipality. This provides a faster, more traceable, and effortless service compared to traditional telephone or petition-based notification methods. The Google Maps API was used for processing and visualizing the notification locations on the map. Notification data is recorded in a database by municipality, and daily or 4-hour planning is done using this data. In this study, genetic algorithm and differential evolution algorithm were used for vehicle routing and vehicle type optimization. To compare the efficiency of both methods, 4 different scenarios were designed with different numbers of waste locations and different types and quantities of waste, and the successes of the methods were compared. Route optimization is calculated not statically, however, using real-time traffic data with Google Distance Matrix API integration, generating the shortest and most economical travel route between waste locations. In this way, efficiency is increased for densely populated city centers while providing citizens with an innovative irregular waste collection infrastructure using more up-to-date technologies.

Abstract: Sign language translation (SLT) aims to convert sign language videos into spoken language text, serving as a critical bridge for communication between the Deaf and hearing communities. While recent advances in Multimodal Large Language Models (MLLMs) have shown promising results in gloss-free SLT, existing methods typically rely on single-modality visual features, failing to fully exploit the complementary nature of appearance and structural cues inherent in sign language. In this architectural proposition paper, we introduce SignFuse, a novel dual-stream cross-modal fusion framework that synergistically combines CNN-based visual features with Graph Convolutional Network (GCN)-based skeletal features for gloss-free sign language translation. Our framework introduces three key innovations: (1) a Cross-Modal Fusion Attention (CMFA) module that performs bidirectional cross-attention between visual and skeletal modalities to produce enriched multimodal representations; (2) a Hierarchical Temporal Aggregation (HTA) mechanism that captures sign language dynamics at multiple temporal scales—frame-level, segment-level, and sequence-level; and (3) a Progressive Multi-Stage Training blueprint that systematically aligns visual-skeletal features with the LLM’s linguistic space through contrastive pre-training, feature alignment, and LoRA-based fine-tuning. We provide the complete mathematical formulation, detailed architectural specifications, and a fully implemented PyTorch codebase. As the computational barriers to training MLLMs remain high, we formalize the experimental methodology required to validate this framework on standard benchmarks (PHOENIX-14T, CSL-Daily, How2Sign) and extend an open invitation to the broader research community to conduct empirical validation and advance this architectural paradigm through collaboration. This work is presented as a concept and architectural framework paper, aiming to establish a theoretical foundation and encourage future empirical validation by the research community.

Abstract: Intensive salmon farming is associated with high mortality rates, highlighting the need for new welfare indicators that can detect adverse conditions earlier and less invasively than many current approaches. Existing animal-based indicators used in the industry typically depend on subjective scoring and provide information mostly after welfare problems have already developed, such as emaciation, wounds, or scale loss. Preliminary data and ongoing investigation suggest that melanin-based skin pigmentation may change dynamically with stress and condition in salmonid fishes. In this study, we present a semi-automated methodology for assessing changes in the grayscale intensity of melanin-based skin spots within the operculum region of adult Atlantic salmon (Salmo salar) kept in sea water. The pipeline combines computer vision models to detect the operculum, segment individual spots, and extract grayscale-based features for spot-level analysis over time. The method was applied to out-of-water images collected before and after exposure to a confinement episode. The results showed an overall shift in grayscale intensity from black to pigmentation fading after the challenge, although responses varied among individuals. These findings indicate that the proposed methodology can detect temporal changes in opercular melanin-based spots under applied experimental conditions. We therefore present this work as proof of principle for using computer vision to quantify changes in melanin-based skin spots as a potentially useful, non-invasive indicator of stress and welfare in Atlantic Salmon.

Abstract: This paper is a comparative analysis of classical and fractional derivatives models using Mittag-Leffler function. The Caputo fractional derivative is used to generalize the classical exponential decay model in order to include memory effects. Transform methods are used to obtain solutions of the forms of the Mittag-Leffler function. Numerical simulations are performed to analyze the behavior of the system for different fractional orders. The findings reveal that the fractional model generalizes the classical solution and it features slower decay because of memory effects. The analysis is further generalized to second order system, in which the system results in a damped oscillatory behavior due to the presence of a fractional dynamics. The results indicate the significance of the fractional calculus in the modeling of complicated physical systems.