Computer Science and Mathematics

Abstract: We present GLYBATOMAQ™, a rank-centric and quantum-geometric framework for GLIPR1-focused in silico screening. The framework treats docking as a fixed-protocol comparative oracle and places the main methodological emphasis on auditable rank movement, positive-semidefinite operator geometry, DFT-derived electronic descriptors, QMC-style uncertainty auditing, and MQWalk topology validation. To make the quantum-geometric contribution explicit for quantum-geometry reporting, we introduce Bures/Fubini-Study-style distance controls, local metric and curvature penalties, quantum Fisher information-inspired sensitivity diagnostics, Berry-type gauge-consistency checks, and a candidate-level assembly certificate. Quantum-geometry reporting elements define the reporting schema, connect each mathematical object to a computational decision, and show how DFT, QMC, MQWalk, curvature, and diagnostic penalties are fused without claiming experimental affinity, efficacy, or biomolecular quantum transport. The output is a reproducible leaderboard and audit bundle for GLIPR1-oriented computational hypotheses: rank shifts are accepted only when supported by electronic descriptors, uncertainty-aware energetic evidence, operator-overlap topology, and chemistry-safe HMC/HSX feasibility constraints.

Abstract: A graph G=(V,E) together with a positive real-valued weight-function w:V→R+ or w:E→R+ is called a weighted graph and is denoted by (G;w). In this paper, we introduce the concepts of connectivity, edge-connectivity, and restricted edge-connectivity for a weighted graph (G;w), and we prove general bounds analogous to those in the unweighted case. Furthermore, we study the connectivity and edge-connectivity of the line graph and the P2-path graph of a weighted graph, establishing upper and lower bounds for each of these parameters.

Abstract: Social service professionals operate in legally sensitive, administratively intensive, and context-dependent environments in which decision-making requires the simultaneous interpretation of regulatory norms, institutional procedures, and individual case circumstances. This paper proposes a conceptual model of a Personal Legal and Social Artificial Intelligence (AI) Assistant intended to support professional decision-making in social services, and demonstrates its functionality through a working prototype. The model is formulated as a domain-specific retrieval-augmented generation (RAG) framework in which a controlled legal and social document corpus is processed through text extraction, chunking, semantic indexing via SentenceTransformer embeddings, top-k retrieval through cosine similarity, and bounded large-language-model reasoning to produce grounded and explainable responses. The proposed framework is informed by three successive prototype versions and by observed sensitivity to corpus scope, document prioritization, and prompt constraints. The current prototype version operates on a prioritized corpus of sixteen Bulgarian normative acts complemented by three supplementary resources, comprising 883 indexed fragments, and uses DeepSeek as the reasoning model accessed through the OpenRouter API. The functionality of the model is validated through a representative use case concerning child protection, in which the prototype identifies the applicable legal provisions, exposes the retrieved documentary evidence, and generates a four-part structured analysis comprising legal qualification, applicable provisions, legal consequences, and recommendations for action. The main contribution lies in the formalization and prototype-level demonstration of a domain-specific AI assistant that combines legal grounding, social-context awareness, and bounded language-model reasoning for trustworthy decision support in regulated social-service practice.

Abstract: Probabilistic graphical models (PGMs) provide a powerful framework for modelling complex systems, but inference over loopy graphs requires approximate methods whose accuracy depends on how factors are clustered in the graphical representation. Existing factor clustering methods rely on the number of variables in a cluster as a proxy for memory cost and informational content---a loose upper bound that leads to suboptimal merging decisions. We address this limitation by proposing an efficient algorithm for estimating the joint entropy of a group of clusters without explicitly multiplying out the constituent factors, thereby avoiding the exponential computational cost that makes exact computation prohibitive. The algorithm integrates naturally with both static and dynamic graph restructuring methods, and reduces to the Kikuchi entropy approximation when applied to the complete graph. Experiments on models with up to 24 variables demonstrate that the algorithm produces accurate (when compared to ideal junction tree performance) entropy estimates across diverse model types, with errors remaining within tight bounds. Scalability is further validated on a substantially larger model defined over 2640 random variables. These results confirm that accurate entropy estimation is achievable wherever reliable probabilistic inference is possible, and that the proposed estimation algorithm yields objectively close approximations, thereby supporting improved clustering decisions in PGM structuring algorithms.

Abstract: Smartphone-based plant identification increasingly serves as the edge tier of agricultural Internet of Things (IoT) systems, where models must adapt to crowdsourced data under bandwidth, memory, and energy constraints. No prior work has systematically investigated continual learning at the scale of thousands of fine-grained medicinal plant species, nor how retraining frequency affects the cost–performance trade-off in an IoT model-lifecycle setting. We evaluate three continual learning strategies—naïve fine-tuning, experience replay, and Learning without Forgetting—under periodic retraining schedules (updating every K increments), tested on 2,719 species (≥25 images each) from the Viet Medi Species 2026 dataset (310,647 images; 4,799 species total). All three strategies exhibit negative forgetting (performance improvement rather than degradation) in the instance-incremental setting, with naïve fine-tuning and LwF showing the strongest gains. Periodic retraining with K=2 reduces retraining operations by approximately 50% while maintaining performance. A baseline MobileNetV2 model achieves 54.07% top-10 accuracy across 2,719 species and has been deployed via TensorFlow Lite (FP16, ∼11.5 MB) in the Med Herb Lens Android application. Naïve fine-tuning is recommended as the practical default for instance-incremental agricultural IoT deployments.

Abstract: The Traveling Salesman Problem (TSP) remains a pivotal NP-hard challenge in combinatorial optimization, with critical applications spanning logistics, manufacturing, and industrial scheduling. While Ant Colony Optimization (ACO) is renowned for its distributed search and positive feedback, conventional variants frequently encounter premature convergence and “combinatorial explosion” in computational costs as problem scales expand. To overcome these bottlenecks, this paper proposes the Globally Adaptive Ant Colony System (GACS), a robust metaheuristic incorporating stagnation recovery and candidate-list pruning. The GACS framework integrates three synergistic strategies: (1) A K-nearest neighbor candidate-list compression that significantly reduces the search tree’s branching factor, maintaining high-quality solutions while ensuring effective linear scalability under fixed parameter configurations; (2) A global-adaptive pheromone weighting scheme that dynamically calibrates reinforcement intensity, facilitating a seamless transition from broad exploration to localized refinement; and (3) A multi-level stagnation recovery mechanism utilizing pheromone smoothing to preserve population diversity and bypass sophisticated local optima. Comprehensive evaluations on synthetic datasets and 33 benchmark instances from TSPLIB demonstrate that GACS consistently outperforms several recently published metaheuristic algorithms (including ABCSS, DSMO, and DWHO). Notably, GACS achieves a 5.5-fold acceleration in computational efficiency over hybrid genetic-ACO models and secures a favorable Average Rank of 1.44 across standard benchmarks. These results confirm that GACS provides a competitive balance between optimization accuracy and computational economy, offering a scalable and resilient paradigm for large-scale combinatorial optimization.

Abstract: In this paper, we first introduce the notion of a Nijenhuis operator on Leibniz triple systems, which can generate a trivial deformation. Then we use Nijenhuis operators to define product structures on a Leibniz triple system. There exists a product structure on a Leibniz triple system if and only if the Leibniz triple system is the direct sum of two subalgebras. There are some special product structures, each of which corresponds to a special decomposition of a Leibniz triple system. Parallelly, we study a complex structure on a Leibniz triple system. Finally, we add a compatibility condition between a product structure and a complex structure to introduce the notion of a complex product structure on a Leibniz triple system.

Abstract: In this paper, we study when the core inverse of a ring element coincides with its (b,c)-inverse, i.e., core-(b,c)-inverse. To establish a broader framework for generalized inverses, we define core-EP-(b,c)-inverse that serves as a natural extension of the generalized core inverse and (b,c) inverse. We characterize this new generalized inverse by combining the core-(b,c)-inverses and quasinilpotents. This generalized inverse is thereby examined through a novel limit-based approach. The polar-like properties of the core inverse are presented. Finally, we investigate the connection between the core-EP-(b,c) inverse and core-(b,c)-inverse. In particular, we derive the reverse law for the core-EP inverse by means of core-EP-(b,b) inverse.

Abstract: Intrusion detection in microgrid systems is a cyber-physical task that requires correlating different data from networks, hosts, and endpoints to create actionable evidence. Existing approaches largely treat intrusion detection as a classification problem and provide explanations at the sample or feature level. However, these explanations lack physical interpretability and fail to reveal cross-modal interactions underlying system decisions. As a result, operators cannot reliably trace detected anomalies to the physical layer, limiting the ability to diagnose root causes. This leads to incorrect or delayed responses and potentially compromises the safety of microgrid operations. This work proposes a physical and data-link layer explainable intrusion detection framework via cross-modal evidence reasoning. This framework reformulates intrusion detection as an operation Q\&A task over structured multi-modal evidence, including network flows, Software-Defined Networking (SDN) states, system calls, and power measurements. By designing an evidence-based explanation mechanism, sample importance is aligned with structured evidence and aggregated into physical modalities to construct evidence representations. These representations are further transformed into structured features to build joint decision models, enabling the extraction of decision paths and their conversion into interpretable reasoning processes grounded in physical evidence. The proposed framework is evaluated on realistic cyber–physical microgrid datasets. It provides consistent and physically meaningful explanations, revealing distinct cross-modal evidence patterns across different cyber attacks. This work advances intrusion detection from samples to physical-layer reasoning, enabling trustworthy security analysis in microgrid systems.

Abstract: The rapid rise of Large Language Model (LLM) agents is driving a fundamental paradigm shift in Multi-Agent Systems (MAS) research, moving from manually orchestrated static architectures toward automated configuration and optimization. Despite its significant potential, this frontier lacks a systematic and rigorous survey with clearly defined operational boundaries. To address this gap, this paper provides a comprehensive review of Automated MAS Optimization, formally anchoring it as the P4 paradigm within a six-stage evolutionary framework spanning from Foundation LLMs (P0) to Agentic Swarms (P5). We introduce precise mathematical definitions for core concepts, establishing a unified MAS configuration space that encompasses agent-level, system-level, and underlying components, and formulate the optimization objective as a holistic system-utility maximization problem. Furthermore, we partition P4 into three operationally distinct sub-paradigms based on the orthogonal dimensions of optimization timing and effect persistence: Design-Time Adaptive MAS, Test-Time Adaptive MAS, and Self-Evolving MAS. Guided by this taxonomy, we systematically review over 200 state-of-the-art works, covering both general methodologies and domain-specific applications. Beyond algorithmic perspectives, we critically examine key supporting issues including benchmarking, evaluation, and safety, while analyzing the evolutionary trajectory toward decentralized, emergent P5 Agentic Swarms. Finally, we identify core open challenges and propose future research directions centered on holistic configuration co-optimization, life-cycle evaluation, endogenous safety mechanisms, and the controllable transition from P4 to P5. This survey aims to provide a rigorous theoretical foundation and strategic navigation for researchers and practitioners in this rapidly evolving field.

Abstract: This paper studies neural network layers that use learnable Lie-group actions as structured feature-space transformations. Instead of treating Lie groups only as input-domain symmetry constraints, the proposed approach embeds real-valued features into local vector banks, learns coordinates in a Lie algebra, maps these coordinates to group elements through the matrix exponential, and applies the resulting matrices to intermediate feature vectors. The framework supports groups such as SO(3), SU(2), and SU(3), and can be used either as a standalone structured backbone or as a component inside conventional neural architectures. The experimental evaluation covers several settings: tabular classification, tabular regression, synthetic signal denoising, generative adversarial learning, and recursive time-series forecasting. The classification and regression studies compare dense neural baselines, MLP–Lie hybrids, deeper Lie-group architectures, CatBoost, and ExtraTrees across repeated train-validation-test splits. The denoising experiment compares a classical autoencoder with an SU(3)-based autoencoder on synthetic oscillatory signals. The GAN experiment inserts an SU(3) layer into the discriminator and compares it with a standard convolutional GAN on MNIST digit generation. The time-series experiments compare a regular Transformer, a hybrid Transformer with one Lie-group layer, a Lie-group Transformer, and CatBoost under recursive holdout forecasting. The results show that Lie-group feature transformations are useful in selected settings, but they are not uniformly superior across all tasks. In classification, the structured models improve over the dense baseline on several datasets, while tree-based methods remain strongest on others. In regression, MLP–Lie models are competitive on some tasks, but CatBoost and ExtraTrees are often stronger. The clearest improvement is observed in signal denoising, where the Lie-group autoencoder reduces reconstruction error and improves signal-to-noise ratio. In the GAN experiment, the Lie-group discriminator gives moderate improvements in stability and discriminator metrics. In time-series forecasting, Lie-group Transformer variants improve over the regular Transformer on some series, while CatBoost remains a strong rolling-window baseline. Overall, the results support a dataset-dependent interpretation. Lie-group layers can act as useful structured feature mixers, especially when local vector structure or oscillatory behavior is relevant. At the same time, their benefit depends on the task, architecture, and computational cost. The framework therefore provides a practical basis for studying when algebraic feature-space transformations improve learning and when simpler baselines are sufficient.

Abstract: Precision medicine focuses on customizing diagnostic, prevention and treatment approaches by accounting for the individual characteristics of each patient. This personalization draws on diverse sources of information including clinical records, genomic data, medical imaging, lifestyle patterns and environmental factors. As the volume and complexity of such multimodal healthcare data continue to expand, machine learning (ML) and deep learning (DL) techniques have become crucial for identifying complex patterns, estimating disease risk, and supporting personalized treatment decisions. Despite their efficiency, many of these models function as opaque systems, generating forecasts without clearly indicating the reasoning behind them. This lack of transparency can undermine clinician confidence, hinder adoption in clinical practice, and raise ethical as well as regulatory concerns, particularly in healthcare contexts where decisions must be explainable and defensible. Explainable Artificial Intelligence (XAI) addresses these challenges by providing methods that make model behaviour more transparent and interpretable. Techniques such as SHAP, LIME, saliency and attention-based visualizations, counterfactual analysis, and rule-based explanations enable clinicians to inspect the rationale behind predictions, evaluate alignment with established medical knowledge, and identify potential sources of bias within data or algorithms. From a patient perspective, explain-ability improves communication, supports informed consent, and strengthens trust in AI-supported care. Regulatory authorities also depend on transparent and interpretable systems to ensure accountability, traceability and compliance with clinical safety requirements. This paper offers a comprehensive examination of explainable AI in the context of precision medicine. It introduces fundamental XAI concepts, organizes key methodological approaches, and reviews applications spanning genomics, medical imaging, and electronic health record (EHR) analytics. The chapter also discusses methods for assessing explanation quality, highlights the role of human-centred design, and addresses critical ethical and legal considerations. It concludes by outlining ongoing challenges and future research directions aimed at developing reliable, interpretable AI systems that can be effectively integrated into advanced personalized healthcare.

Abstract: As Large Language Models (LLMs) evolve into autonomous agents for long-horizon tasks, managing unbounded interaction trajectories under fixed context budgets becomes a core systems challenge. Unlike standard long-context documents, agent trajectories are heterogeneous and interleave observations, reasoning traces, and tool executions, so compression must preserve temporal dependencies, actionable state, and structural fidelity. Yet existing methods remain fragmented, making it difficult to compare design choices and reason about their reliability implications. This survey introduces a unified taxonomy of agent context compression along three dimensions: compression target (what is compressed), compression mechanism (how it is transformed and retained), and control policy (who decides when compression is triggered). We further organize recurring failures in compressed execution into F1: Pre-compression Decision Error, F2: In-compression Information Loss, and F3: Post-compression Access Failure, and examine domain-specific trade-offs in software engineering, web navigation, and deep research. By unifying the design space, failure taxonomy, and evaluation perspective, this survey provides a foundation for building scalable and recoverable LLM agents. A collection of papers available at https://github.com/YerbaPage/Awesome-Context-Compression.

Abstract: Model fusion integrates the capabilities from source models into a single target model. As the open-source AI ecosystem matures, Hugging Face has hosted more than 2M models. This growing pool provides a rich base for model reuse and capability integration. Yet existing surveys often cover only separate parts of this space, and they do not provide a unified definition or a systematic taxonomy. This survey defines model fusion and organizes prior work into three levels: parameter-level, representation-level, and behavior-level fusion. We also review related metrics, benchmarks, and applications, summarize current challenges, and identify future directions. Our goal is to provide a clear map of this area and support future work on model fusion.

Abstract: In the historical development of various fields of mathematics, significant advances have occurred in areas such as algebra, abstract algebra, group theory, and numerous other mathematical and scientific domains. Contributions from mathematicians such as Dio- phantus, Goldbach, Euler, Girolamo Cardano, Johannes Kepler, Poncelet, Henri Poincaré, George Cantor, Felix Klein, David Hilbert, and Hermann Weyl have been fundamental, particularly in the pursuit of increasingly complex and deeper structures within geometry and topology. In this work, the division operation in the Alpha group is defined by analogy with the Kronecker tensor product. The representation of quaternion theory, based on De Moivre’s theorem, is employed for the construction of the matrices. The Alpha Group di- vision operation is then applied to analyze the various tensor metrics resulting from plane rotations over the interval from 0 to 2π radians. Since the general transformation kernel of the 4 × 4 matrix is defined within the Alpha group, it is possible to observe the variabil- ity associated with the tangent and cotangent functions that constitute the transformation matrix. The Alpha group, defined through a generalized division operation, thus provides a geometric and topological representation of infinity via the kernel transformation of the 4 × 4 matrix. Ultimately, this work seeks to connect the ideas developed by Poncelet and Cantor regarding the formation of imaginary elements in infinite projections with the con- cept of different types of infinity, as interpreted through the application of group theory.

Abstract: Recent cyber incidents have become increasingly sophisticated through 'Living-off-the-Land (LotL)' techniques that exploit legitimate behavior and multi-stage attacks. This demands advanced reasoning capabilities to discern attack contexts within fragmented, large-scale logs. However, closed network environments with physical network separation (air-gapped), such as national critical infrastructure, restrict the use of high-performance cloud LLMs, limiting the adoption of cutting-edge AI-based analysis technologies. This research proposes a Local LLM-based intrusion analysis framework that can operate independently within closed networks to overcome these constraints. The proposed framework combines (i) an Offline Knowledge Distillation technique that transfers the analytical reasoning process of external high-performance models to the Local LLM after security review, and (ii) an AI agent orchestration structure that controls the analysis procedure step-by-step and suppresses hallucinations. Experiments and validation using the public dataset (Atomic Red Team) demonstrate that the proposed model achieves significantly higher detection accuracy (88.4%) and MITRE ATT&CK mapping performance (0.91 F1-Score) compared to existing general-purpose Local LLMs. Furthermore, it suppressed hallucination rates to 6.2% through an automated verification mechanism and significantly improved analysis efficiency by refining large-scale logs to focus on core events. This study quantitatively demonstrates that AI-based intrusion incident analysis automation is achievable using a single GPU server even under the resource constraints of closed networks, presenting a practical solution for intelligent security monitoring.

Abstract: Advanced artificial intelligence systems increasingly exhibit behaviors that are not adequately captured by component-local metrics, benchmark scores, or layer-specific monitoring. Such behaviors arise across coupling surfaces, control regimes, deployment boundaries, and emergent interaction patterns, indicating that the relevant analytical object is the composed system rather than the isolated component. This article introduces \emph{SORT-AI} as a \emph{Level-0 structural assessment architecture} for advanced AI systems and as the canonical domain reference within the SORT-AI research line. The framework organizes the AI domain along four main axes: \emph{Domain} as the problem space, \emph{Cluster} as the structural problem class, \emph{Application} as a recurrent structural problem form, and \emph{Structural Dimensions} V1 to V4 as the diagnostic grammar linking observed phenomena to structural causes, effect spaces, and decision surfaces. Below the application level, the architecture admits a further diagnostic decomposition into \emph{Scenario Classes}, \emph{Metric Sets}, and a \emph{Regime Classification} that distinguishes core, boundary, and overlap regimes. Applications are therefore treated not only as recurrent structural problem forms, but also as structured regime spaces. The current AI domain comprises 52 applications distributed across five clusters: Coupling, Learning, Control, Emergence, and Evidence. To make the domain paper self-contained at the level of AI-domain interpretation, a compact mathematical basis is provided using a closed set of 22 idempotent operators, a global consistency projector, a calibrated projection kernel, and a structured projection space in which AI systems are read as operator chains on structured execution states. Within this architecture, the Core-3 applications serve as three complementary structural coupling axes: \sortapp{AI.01} expresses physical/interconnect coupling, \sortapp{AI.04} logical/runtime-control coupling, and \sortapp{AI.13} semantic/agentic coupling. Runtime Control Coherence, represented by \sortapp{AI.04}, is used as the canonical example to illustrate how locally correct control mechanisms can generate globally incoherent behavior under scale. The paper further incorporates SORT-Sovereign as a meta-domain that projects technical structural findings into strategic, regulatory, and state decision spaces. In this form, SORT-AI is positioned as a reusable Level-0 structural assessment foundation for subsequent domain-specific analyses and application-level studies across the AI domain.

Abstract: Previous research has shown sector-conditional asymmetry in implied volatility levels and in option returns. However, no prior work has parameterized that asymmetry at the effective-theta layer in a form that fires a non-discretionary rule trigger. This study supplies that parameterization, its formulation, the first observation, and the corpus evidence. An effective theta is defined as Θe=αs,r⋅ΘBS, where ΘBS is the standard Black-Scholes (BS) theta and αs,r is a sector- and regime-conditional scaling factor. A SIMDEC decomposition is used to partition the input space and to determine the corner where α matters most. The use of SIMDEC renders all AI-created solutions free of hallucination and fully explainable. A “first observation” arising from a three-position long-call cohort traversing terminal decay is deployed using eleven intraday snapshots tracked on the trajectory at primary-source resolution. The cohort behaviour matches the α parameterisation to existing market conditions. To empirically evaluate the effectiveness of the approach, a SIMDEC L2 corpus from the same deployment supplies population-level support across 12 sectors and a three-tier quality stratification. The L2 corpus is the output of the THETA AI/ML pipeline – a multi-architecture deep-learning inference system that treats SIMDEC joint-state partitioning and Sobol variance decomposition as complementary interpretability inputs, with the regime classifier carrying the labels and the composite quality scorer carrying the stratification. The mathematical formulation and overall analysis of the asymmetry in the effective-theta provides a “next level” contribution to traditional option methodology.

Abstract: Large language models (LLMs) increasingly require robust evaluation under realistic instruction-following conditions, particularly for fine-tuned task-specific adapters operating in multilingual environments. This study proposes a scenario-adaptive evaluation framework for assessing the reliability of fine-tuned text models across two application regimes: misinformation detection (disinfo) and knowledge-grounded factual biography generation (heroes). The framework integrates automated generation of balanced risk-oriented scenarios, bilingual evaluation in English and Ukrainian, the LLM-as-a-Judge paradigm, and multidimensional robustness analysis through the Alignment Robustness Index (ARI). Six LoRA-adapted models based on Qwen2.5-3B-Instruct, SmolLM2-1.7B-Instruct, and TinyLlama-1.1B-Chat-v1.0 were evaluated. The implemented pipeline generated 2052 scenarios and 6156 model responses, producing a final bilingual analytical subset of 4104 judged records. Experimental results show that task-specific adaptation produces task-dependent robustness profiles. In the disinfo case, Qwen2.5-3B achieved the strongest overall performance, combining the highest safety and classification accuracy. In contrast, the heroes case revealed a more compressed and multidimensional vulnerability space without a single dominant model. The results further demonstrate the importance of multilingual evaluation, as weaker adapters exhibited substantially larger cross-lingual safety gaps. Overall, the proposed framework provides a reproducible and practically applicable methodology for auditing fine-tuned language models under imperfect instructions.

Abstract: Seismic attribute selection remains a critical yet often heuristic component in deep learning-based segmentation workflows. In this work, we propose a redundancy-aware framework to systematically analyse the contribution of seismic attributes by combining input-space statistics, representational similarity (CKA), and error-based evaluation. Our results show that statistical redundancy in the input space does not directly translate to functional redundancy within the network. In particular, attributes such as amplitude and instantaneous phase may exhibit high similarity at the input level while producing distinct error patterns and meaningful performance gains. We further demonstrate that complementary attributes do not necessarily yield additive improvements. While some combinations introduce conflicting interactions that limit global performance, others provide stable and consistent improvements across classes. Notably, the combination of amplitude, phase, and local variance forms a minimal informative subset that improves segmentation performance in a balanced manner, particularly in challenging facies. These findings highlight that attribute selection should be guided by functional complementarity and stability of interaction rather than by input diversity alone. The proposed framework provides a principled approach for identifying effective attribute subsets, contributing to more efficient and interpretable seismic segmentation workflows.