Abstract: As artificial intelligence systems scale in depth, dimensionality, and internal coupling, their behavior becomes increasingly governed by deep compositional transformation chains rather than isolated functional components. Iterative projection, normalization, and aggregation mechanisms induce complex operator dynamics that can generate structural failure modes, including representation drift, non-local amplification, instability across transformation depth, loss of aligned fixed points, and the emergence of deceptive or mesa-optimizing substructures. Existing safety, interpretability, and evaluation approaches predominantly operate at local or empirical levels and therefore provide limited access to the underlying structural geometry that governs these phenomena. This work introduces \emph{SORT-AI}, a projection-based structural safety module that instantiates the Supra-Omega Resonance Theory (SORT) backbone for advanced AI systems. The framework is built on a closed algebra of 22 idempotent operators satisfying Jacobi consistency and invariant preservation, coupled to a non-local projection kernel that formalizes how information and influence propagate across representational scales during iterative updates. Within this geometry, SORT-AI provides diagnostics for drift accumulation, operator collapse, invariant violation, amplification modes, reward-signal divergence, and the destabilization of alignment-relevant fixed points. SORT-AI is intentionally architecture-agnostic and does not model specific neural network designs. Instead, it supplies a domain-independent mathematical substrate for analysing structural risk in systems governed by deep compositional transformations. By mapping AI failure modes to operator geometry and kernel-induced non-locality, the framework enables principled analysis of emergent behavior, hidden coupling structures, mesa-optimization conditions, and misalignment trajectories. The result is a unified, formal toolset for assessing structural safety limits and stability properties of advanced AI systems within a coherent operator–projection framework.

Abstract: Fourier Decomposition (FD) and Koopman Mode Decomposition (KMD) are important tools for time series data analysis, applied across a broad spectrum of applications. Both aim to decompose time series functions into superpositions of countably many wave functions, with strikingly similar mathematical foundations. These methodologies derive from the linear decomposition of functions within specific function spaces: FD uses a fixed basis of sine and cosine functions, while KMD employs eigenfunctions of the Koopman linear operator. A notable distinction lies in their scope: FD is confined to periodic functions, while KMD can decompose functions into exponentially amplifying or damping waveforms, making it potentially better suited for describing phenomena beyond FD’s capabilities. However, practical applications of KMD often show that despite accurate approximation of training data, its prediction accuracy is limited. This paper clarifies that this issue is closely related to the number of wave components used in decomposition, referred to as the degree of a KMD. Existing methods use predetermined, arbitrary, or ad hoc values for this degree. We demonstrate that using a degree different from a uniquely determined value for the data allows infinite KMDs to accurately approximate training data, explaining why current methods, which select a single KMD from these candidates, struggle with prediction accuracy. Furthermore, we introduce mathematically supported algorithms to determine the correct degree. Simulations verify that our algorithms can identify the right degrees and generate KMDs that can make accurate predictions, even with noisy data.

Abstract: Accurate classification of thyroid nodules in ultrasound remains challenging due to limited labeled data and the weak ability of conventional feature representations to capture complex, multi-directional textures. To address these issues, we propose a geometry-aware framework that integrates the adaptive Bandelet Transform (BT) with transfer learning (TL) for benign–malignant thyroid nodule classification. The method first applies BT to enhance directional and structural encoding of ultrasound images through quadtree-driven geometric adaptation, then mitigates class imbalance using SMOTE and expands data diversity via targeted augmentation. The resulting images are classified using several ImageNet-pretrained architectures, with VGG19 providing the most consistent performance. Experiments on the publicly available DDTI dataset show that BT-based preprocessing improves performance over classical wavelet representations across multiple quadtree thresholds, with the best results achieved at T=30. Under this setting, the proposed BT+TL(VGG19) model attains 98.91% accuracy, 98.11% sensitivity, 97.31% specificity, and a 98.89% F1-score, outperforming comparable approaches reported in the literature. These findings suggest that coupling geometry-adaptive transforms with modern TL backbones can provide robust, data-efficient ultrasound classification. Future work will focus on validating generalizability across larger multi-centre datasets and exploring transformer-based classifiers.

Abstract: Subject-driven text-to-image (T2I) generation presents a significant challenge in balancing subject fidelity and text alignment, with traditional fine-tuning approaches proving inefficient. We introduce ContextualGraftor, a novel training-free framework for robust subject-driven T2I generation, leveraging the powerful FLUX.1-dev multimodal diffusion-transformer. It integrates two core innovations: Adaptive Contextual Feature Grafting (ACFG) and Hierarchical Structure-Aware Initialization (HSAI). ACFG enhances feature matching in attention layers through a lightweight contextual attention module that dynamically modulates reference feature contributions based on local semantic consistency, ensuring natural integration and reduced semantic mismatches. HSAI provides a structurally rich starting point by employing multi-scale structural alignment during latent inversion and an adaptive dropout strategy, preserving both global geometry and fine-grained subject details. Comprehensive experiments demonstrate that ContextualGraftor achieves superior performance across key metrics, outperforming state-of-the-art training-free methods like FreeGraftor. Furthermore, our method maintains competitive inference efficiency, offering an efficient and high-performance solution for seamless subject integration into diverse, text-prompted environments.

Abstract: The merging of the Internet of Things (IoT) and Artificial Intelligence (AI) advances has intensified challenges related to data authenticity and security. These advancements necessitate a multi-layered security approach in ensuring security, reliability and integrity of critical infrastructure and intelligent surveillance systems. This paper proposes a two-layered security approach combining a discrete cosine transform least significant bit 2 (DCT-LSB-2) – with artificial neural networks (ANN) for data forensic validation and mitigating deepfakes. The proposed model encodes validation codes within the LSBs of cover images captured by an IoT camera on the sender side, leveraging the DCT approach to enhance the resilience against steganalysis. On the receiver side, a reverse DCT-LSB-2 process decodes the embedded validation code, which is subjected to authenticity verification by a pre-trained ANN model. The ANN validates the integrity of the decoded code, and ensures that only device-originated, untampered images are accepted. The proposed framework achieved an average SSIM of 0.9927 across the entirely investigated embedding capacity of between 0 to 1.988 bpp. DCT-LSB-2 showed a stable Peak Signal-to-Noise Ratio (average 42.44 dB) under different evaluated payloads of between 0 to 100 kB. The proposed model achieved a resilient and robust multi-layered data forensic validation system.

Abstract: In this study, we establish novel hypergeometric representations for the two classical sequences that are the Pell and Jacobsthal sequences. Building on Dilcher’s hypergeometric formulation of the Fibonacci sequence, we extend similar results and derive analogous structures for these two classical sequences. The results unify several known identities, provide new explicit representations, and offer a broader perspective on hypergeometric interpretations of linear second order recurrence sequences.

Abstract: Digital product passports outline information about a product’s lifecycle, circularity, and sustainability related data. Sustainability data contains claims about carbon footprint, recycled material composition, ethical sourcing of production materials, etc. Also, upcoming regulatory directives require companies to disclose this type of information. However, current sustainability reporting practices face challenges, such as greenwashing, where companies make incorrect claims that are difficult to verify. There is also a challenge of disclosing sensitive production information when other stakeholders, such as consumers or other economic operators, wish to independently verify sustainability claims. Zero-knowledge proofs (ZKPs) provide a cryptographic system for verifying statements without revealing sensitive information. The goal of this research paper is to explore ZKP cryptography, trust models, and implementation concepts for extending DPP capability in privacy-aware reporting and verification of sustainability claims in products. To achieve this goal, first, formal representations of sustainability claims are provided. Then, a data matrix and trust model for the proof generation are developed. An interaction sequence is provided to show different components for various proof generation and verification scenarios for sustainability claims. Lastly, the paper provides a circuit template for the proof generation of an example claim and a credential structure for their input data validation.

Abstract:

Marine scientific research missions often face challenges such as heterogeneous multi-source data, unstable links, and high packet loss rates. Traditional approaches decouple integrity verification from encryption, rely on full-packet processing, and depend on synchronous sessions, making them inefficient and insecure under fragmented and out-of-order transmissions. The HMR+EMR mechanism proposed in this study integrates “block-level verification” with “hybrid encryption collaboration” into a unified workflow: HMR employs entropy-aware adaptive partitioning and chain-based indexing to enable incremental verification and breakpoint recovery, while EMR decouples key distribution from parallelized encryption, allowing encryption and verification to proceed concurrently under unstable links and reducing redundant retransmissions or session blocking. Experimental results show that the scheme not only reduces hashing latency by 45%–55% but also maintains a 94.1% successful transmission rate under 20% packet loss, demonstrating strong adaptability in high-loss, asynchronous, and heterogeneous network environments. Overall, HMR+EMR provides a transferable design concept for addressing integrity and security issues in marine data transmission, achieving a practical balance between performance and robustness.

Abstract: This paper presents a general algorithm for rapidly generating all N×N Latin squares, along with its precise counting framework and isomorphic (quasi-group) polynomial algorithms. It also introduces efficient algorithms for solving Latin square-filling problems. Numerous combinatorial isomorphism problems, including Steiner triple systems, Mendelsohn triple systems, 1-factorization, networks, affine planes, and projective planes, can be reduced to Latin square isomorphism. Since groups are true subsets of quasigroups and group isomorphism is a subproblem of quasi-group isomorphism, this makes group isomorphism an automatically P-problem. A Latin square of order N is an N×N matrix where each row and column contain exactly N distinct symbols, with each symbol appearing only once. A matrix derived from such a multiplication table forms an N-order Latin square. In contrast, a binary operation derived from an N-order Latin square as a multiplication table constitutes a pseudogroup over the Q set. I discovered four new algebraic structures that remain invariant under permutation of rows and columns, known as quadrilateral squares. All N×N Latin squares can be constructed using three or all four of these quadrilateral squares. Leveraging the algebraic properties of quadrilateral squares that remain unchanged by permutation, we designed an algorithm to generate all N×N Latin squares without repetition when permuted, resulting in the first universal and nonrepetitive algorithm for Latin square generation. Building on this, we established a precise counting framework for Latin squares. The generation algorithm further reveals deeper structural aspects of Latin squares (pseudogroups). Through studying these structures, we derived a crucial theorem: two Latin squares are isomorphic if their subline modularity structures are identical. Based on this important and key theorem, and combined with other structural connections discussed in this paper, a polynomial-time algorithm for Latin square isomorphism has been successfully designed. This algorithm can also be directly applied to solving quasigroup isomorphism, with a time complexity of 5/16(n⁵−2n⁴−n³+2n²)+2n³ Furthermore, more symmetrical properties of Latin squares (pseudogroups) were uncovered. The problem of filling a Latin grid is a classic NP-complete problem. Solving a fillable Latin grid can be viewed as generating grids that satisfy constraints. By leveraging the connections between parametric group algebra structures revealed in this paper, we have designed a fast and accurate algorithm for solving fillable Latin grids. I believe the ultimate solution to NP- complete problems lies within these connections between parametric group algebra structures, as they directly affect both the speed of solving fillable Latin grids and the derivation of precise counting formulas for Latin grids.

Abstract: This work presents a hybrid chaotic–cryptographic image encryption method that integrates a physical two-dimensional delta-kicked oscillator with a PBKDF2-HMAC-SHA256 key derivation function. The key consists in a 12-symbol human key and four user-defined salt words into 256-bit high-entropy material, later converted for the KDF into 96 balanced decimal digits that seed the chaotic functions. The encryption occurs on the real domain, using a partition–permutation mechanism followed by modular diffusion, both governed by chaos. Experimental results confirm the perfect reversibility of the process, high randomness (entropy = 7.9981), and zero adjacent-pixel correlation. Known and chosen plaintext attacks revealed no statistical dependence between cipher and plain images, while NPCR≈99.6% and UACI≈33.9% demonstrate complete diffusion. The PBKDF2-based key derivation expands the key space to 2256 combinations, effectively eliminating weak-key conditions and enhancing reproducibility. The proposed approach bridges deterministic chaos and modern cryptography, offering a secure and verifiable method for protecting sensitive images.

Abstract: We will prove the generalized stability of an additive-quadratic-cubic functional equation in the sprit of Găvruţa.

Abstract: Artificial intelligence systems increasingly score, sort, and advise people in welfare, policing, education, and employment. Many of these systems are trusted on the basis of thin evidence such as benchmark scores, internal tests on historical data, or polished demonstrations rather than robust evaluation in the real world. This paper argues that such deployments invert the burden of proof, because people must show that they were harmed while vendors rarely have to show that their tools work fairly and reliably for the communities they affect. Drawing on documented cases in child welfare, online proctoring, and facial recognition, I propose a simple evidence ladder for AI that ranges from basic lab tests to independent audits, monitored field trials, and formal certification with ongoing review. The novelty is a cross domain, five level scaffold that any team can use to state its current proof and to plan concrete steps toward stronger evidence. I link these levels to familiar engineering practices and to current policy frameworks including the OECD AI Principles, the NIST AI Risk Management Framework, and the European Union AI Act. The central claim is that demanding evidence scaled to the stakes of the decision is a basic form of respect for the people whose lives AI systems judge.

Abstract: Modern multi-cloud and edge-cloud systems replicate both data and access control policies across geographically distributed nodes under weak consistency models. In asynchronous environments with possible network partitions, policy updates (additions and revocations of rules, delegation and revocation of privileges) may occur concurrently, causing conflicts and potential privilege escalation when naïve conflict resolution schemes such as last-writer-wins (LWW) or add-wins are used. This paper proposes a formal model of Policy-CRDT, a conflict-free replicated data type (CRDT) for sets of access control policies with a remove-wins strategy, based on the two-phase set (2P-Set) and a join-semilattice structure on replica states. At the CRDT abstraction level, each replica state is represented by a pair of monotonically growing sets of added and revoked policy identifiers, and state merging is defined as a commutative, associative, and idempotent union operator. We show that the proposed data type satisfies the standard Strong Eventual Consistency (SEC) conditions for state-based CRDTs: replica states form a join-semilattice, local updates are monotone, and the merge function computes least upper bounds, which ensures convergence of replicas once they have received the same set of updates. We formally prove that the remove-wins strategy guarantees inevitable suppression of any policy for which at least one revocation exists in the global history, in contrast to LWW and add-wins schemes that can admit dangerous states with excessive permissions. We further propose an architecture for deploying Policy-CRDT in a distributed PDP/PEP infrastructure in the spirit of Zero Trust and NIST SP 800-207/800-207A, and we present an analytical evaluation of convergence latency and the probability of potentially dangerous states compared to alternative strategies. The results demonstrate that Policy-CRDT provides formally grounded convergence of access control policies at reasonable overhead and is semantically safe in multi-cloud and edge deployment scenarios.

Abstract: In the contemporary cybersecurity landscape, the detection of code-mixed malicious scripts embedded within high-trust domains (e.g., governmental and academic websites) constitutes a critical defensive challenge. Traditional Transformer-based models, while effective in natural language processing, often exhibit "Structural Bias," where they erroneously interpret the benign complexity of legacy HTML structures as malicious obfuscation, resulting in elevated false positive rates. To address this limitation, this study proposes an XAI-Driven Hybrid Architecture that synergizes context-aware semantic embeddings from WangChanBERTa with outlier-robust structural features. Validated on a rigorously curated high-fidelity corpus of 5,000 samples, our model achieves a state-of-the-art F1-Score of 0.9908. Beyond standard metrics, Explainable AI (XAI) diagnosis reveals a critical "Dual-Validation" mechanism: structural features effectively veto semantic hallucinations triggered by benign complexity, acting as a crucial safety net. Crucially, the proposed architecture functions as a 'Dual-Validation' mechanism, where structural features effectively veto semantic hallucinations triggered by benign complexity. The integration of these components leads to a 50% reduction in the False Positive Rate (FPR), decreasing from 0.024 in baseline scenarios to 0.012, thereby confirming the operational significance of Selective Integration. This method effectively reduces 'alert fatigue,' providing a scalable solution for SOC analysts tasked with protecting critical infrastructure from advanced code-mixed threats.

Abstract:

We derive an operationally defined lower bound on the physical time \( \Delta t \)required to execute any information-processing task, based on the total entropy produced \( \Delta\Sigma \). The central result, \( \Delta t \geq \tau_{\Sigma} \Delta\Sigma \), introduces the Process-Dependent Dissipation Timescale \( \tau_{\Sigma} \equiv 1/\langle \dot{\Sigma} \rangle_{\text{max}} \), which quantifies the maximum achievable entropy production rate for a given physical platform. We derive \( \tau_{\Sigma} \) from microscopic system-bath models and validate our framework against experimental data from superconducting qubit platforms. Crucially, we obtain a Measurement Entropic Time Bound:\( \Delta t_{\text{meas}} \geq \tau_{\Sigma} k_{\text{B}}[H(P) - S(\rho)] \), relating measurement time to information gained. Comparison with IBM and Google quantum processors shows agreement within experimental uncertainties. This framework provides a thermodynamic interpretation of quantum advantage as reduced entropy production per logical inference and suggests concrete optimization strategies for quantum hardware design.

Abstract: Traditional mean–variance portfolio optimization is ill-suited to cryptocurrency markets, where extreme volatility, fat-tailed distributions, and unstable correlations undermine variance as a risk measure. To overcome these limitations, this paper develops a unified entropy-based framework for portfolio diversification grounded in the Maximum Entropy Principle (MaxEnt). Within this formulation, Shannon entropy, Tsallis entropy, and Weighted Shannon Entropy (WSE) emerge as complementary specifications derived analytically via the method of Lagrange multipliers, ensuring mathematical tractability and interpretability. Empirical validation is conducted on a portfolio of four leading cryptocurrencies—Bitcoin (BTC), Ethereum (ETH), Solana (SOL), and Binance Coin (BNB)—using weekly return data from January to March 2025. Results reveal that Shannon entropy converges to near-uniform diversification, Tsallis entropy (q = 2) penalizes concentration more strongly and enhances robustness against tail risk, while WSE integrates asset-specific informational priorities, aligning allocations with investor preferences or market characteristics. Comparative analysis confirms that all three models yield allocations more resilient and structurally balanced than variance-driven portfolios, mitigating estimation risk and concentration effects. This study provides a coherent mathematical formulation of entropy-based portfolio optimization by embedding Shannon, Tsallis, and Weighted Shannon entropies within a common Maximum Entropy (MaxEnt) optimization framework. Beyond its immediate empirical scope, this work also opens several avenues for future research. First, entropy-based portfolio construction can be extended to dynamic multi-period settings with transaction costs and liquidity frictions, which are particularly relevant in cryptocurrency markets. Second, the framework may be generalized to incorporate alternative entropy measures such as Rényi or Kaniadakis entropy, enabling more refined sensitivity to tail risks and nonlinear dependencies. The proposed framework provides a flexible foundation for future extensions toward dynamic, multi-period portfolio optimization under uncertainty.

Abstract: We present a supervised method to estimate two local descriptors of time-series dynamics, the mean-reversion rate θ and a heavy tail estimate α, from short windows of data. These parameters summarize recovery behavior and tail heaviness and are useful for interpreting stochastic signals in sensing applications. The method is trained on synthetic, dimensionless Ornstein–Uhlenbeck processes with α-stable noise, ensuring robustness for non-Gaussian and heavy-tailed inputs. Gradient-boosted tree models (CatBoost) map window-level statistical features to discrete (α, θ) categories with high accuracy and predominantly adjacent-class confusion. Using the same trained models, we analyze daily financial returns, daily sunspot numbers, and NASA POWER climate fields for Austria. The method detects changes in local dynamics, including shifts in financial tail structure after 2010, weaker and more irregular solar cycles after 2005, and a redistribution in clear-sky shortwave irradiance around 2000. Because it relies only on short windows and requires no domain-specific tuning, the framework provides a compact diagnostic tool for signal processing, supporting characterization of local variability, detection of regime changes, and decision making in settings where long-term stationarity is not guaranteed.

Abstract: Following Livadiotis G. and McComas D. J. (2023) [1], we propose a new type of DNA frameshift mutations that occur spontaneously due to information exchange between the DNA sequence of length bases (n) and the mutation sequence of length bases (m), and respect the kappa-addition symbol ⊕κ. We call these proposed mutations Kappa-Frameshift Background (KFB) mutations. We find entropy defects originate in the interdependence of the information length systems (or their interconnectedness, that is, the state in which systems with a significant number of constituents (information length bases) depend on, or are connected with each) by the proposed KFB-mutation). We also quantify the correlation among DNA information length bases (n) and (m) due to information exchange. In the presence of entropy defects, the Landauer’s bound and minimal metabolic rate for a biological system are modified. We observe that the different n and κ scales are manifested in the double evolutionary emergence of the proposed biological system through subsystems correlations. For specific values of the kappa parameter we can expect deterministic laws associated with a single biological polymer in the short term before the polymer explores over time all the possible ways it can exist.

Abstract: This paper addresses the challenge of efficiently identifying and classifying resource contention behaviors in cloud computing environments. It proposes a deep neural network method based on multi-scale temporal modeling and attention-based feature enhancement. The method takes time series resource monitoring data as input. It first applies a Multi-Scale Dilated Convolution (MSDC) module to extract features from resource usage patterns at different temporal resolutions. This allows the model to capture the multi-stage dynamic evolution of resource contention behaviors. An Attention-based Feature Weighting (AFW) module is then introduced. It learns attention weights along both the temporal and feature dimensions. This enables the model to emphasize key time segments and core resource metrics through saliency modeling and feature enhancement. The overall architecture supports end-to-end modeling. It can automatically learn temporal patterns of resource contention without relying on manual feature engineering. To evaluate the effectiveness of the proposed method, this study constructs a range of contention scenarios based on real-world cloud platform data. The model is assessed under different structural configurations and task conditions. The results show that the proposed model outperforms existing mainstream temporal classification models across multiple metrics, including accuracy, recall, F1-score, and AUC. It demonstrates strong feature representation and classification capabilities, especially in handling high-dimensional, multi-source, and dynamic data. The proposed approach offers practical support for resource contention detection, scheduling optimization, and operational management in cloud platforms.

Abstract: Federated Learning (FL) and Split Learning (SL) maintain client data privacy during collaborative training by keeping raw data on distributed clients and only sharing model updates (FL) or intermediate results (SL) with the centralized server. However, this level of privacy is insufficient, as both FL and SL remain vulnerable to security risks like poisoning and various inference attacks. To address these flaws, we introduce SplitML, a secure and privacy-preserving framework for Federated Split Learning (FSL). SplitML generalizes and formalizes FSL using IND−CPAD secure Fully Homomorphic Encryption (FHE) combined with Differential Privacy (DP) to actively reduce data leakage and inference attacks. This framework allows clients to use different overall model architectures, collaboratively training only the top (common) layers while keeping their bottom layers private. For training, clients use multi-key CKKS FHE to aggregate weights. For collaborative inference, clients can share gradients encrypted with single-key CKKS FHE to reach a consensus based on Total Labels (TL) or Total Predictions (TP). Empirical results show that SplitML significantly improves protection against Membership Inference (MI) attacks, reduces training time, enhances inference accuracy through consensus, and incurs minimal federation overhead.