Abstract: This study introduces a hybrid point cloud compression method that transfers from octree-nodes to voxel occupancy estimation to find its lower-bound bitrate by using a Binary Arithmetic Range Coder. In previous attempts, we've shown that our entropy compression model based on index convolution achieves promising performance while maintaining low complexity. However, our previous model lacks an autoregressive approach, which is apparently indispensable to compete with the current state-of-the-art of compression performance. Therefore, we adapt an autoregressive grouping method that iteratively populates, explores, and estimates the occupancy of 1-bit voxel candidates in a more discrete fashion. Furthermore, we refactored our backbone architecture by adding a distiller layer on each convolution, forcing every hidden feature to contribute to the final output. Our proposed model extracts local features using lightweight 1D convolution applied in varied ordering and analyzes causal relationships by optimizing the cross-entropy. This approach efficiently replaces the voxel convolution techniques and attention models used in previous works, providing significant improvements in both time and memory consumption. The effectiveness of our model is demonstrated on three datasets, where it outperforms recent deep learning-based compression models in this field.

Abstract: Modern information systems suffer from a fundamental architectural flaw: data coherence depends on external validation layers, creating systemic entropy and computational waste. We present the G Model, a mathematical framework that redefines information as points in a ge- ometric space where incoherence is mathematically impossible. Through a triaxial formalization (Meaning, Location, Connection) and an intrinsic coherence operator (Φ), the system guaran- tees that only valid data can exist within the managed universe (Ω). We formalize this with four fundamental axioms ensuring coherence, uniqueness, acyclicity, and deterministic propaga- tion. The model extends Codd’s normalization through five semantic normal forms addressing temporal and semantic coherence. We provide formal proofs of key theorems, including optimal propagation complexity and impossibility of inconsistency. This work represents a paradigm shift from “data storage systems” to “coherent information spaces,” providing a foundation for trustworthy AI training data and critical infrastructure where error is inadmissible.

Abstract: Cognitive bias introduces structural imbalance in exploration and exploitation within adaptive decision systems, yet existing approaches emphasize outcome accuracy or bias reduction while offering limited explanation of how internal decision structures regulate distortion during iterative search. This study develops a metaheuristic-based bias intervention module as a computational artifact for examining symmetry regulation at the process level of biased decision-making. Using controlled computational experiments, the study compares baseline, conventional metaheuristic, and intervention configurations through structural indicators that characterize decision accuracy, convergence stability, symmetry regulation, and bias reduction. The results show that adaptive decision coherence emerges through regulated structural adjustment rather than symmetry maximization. Across evaluated configurations, systems that maintain intermediate symmetry exhibit stable convergence and effective bias regulation, whereas configurations that preserve higher symmetry display structural rigidity and weaker regulation despite high outcome accuracy. These findings reposition cognitive bias as a structural force shaping adaptive rationality in algorithmic decision systems and advance design science research by expressing cognitive balance as measurable computational indicators for process-level analysis of regulated decision dynamics.

Abstract:

The Minimum Vertex Cover (MVC) problem is NP-hard even on unit disk graphs (UDGs), which model wireless sensor networks and other geometric systems. This paper presents an experimental comparison of three greedy algorithms for MVC on UDGs: degree-based greedy, edge-based greedy, and the classical 2-approximation based on maximal matching. Our evaluation on randomly generated UDGs with up to 500 vertices shows that the degree-based heuristic achieves approximation ratios between 1.636 and 1.968 relative to the maximal matching lower bound, often outperforming the theoretical 2-approximation bound in practice. However, it provides no worst-case guarantee. In contrast, the matching-based algorithm consistently achieves the proven 2-approximation ratio while offering superior running times (under 11 ms for graphs with 500 vertices). The edge-based heuristic demonstrates nearly identical performance to the degree-based approach. These findings highlight the practical trade-off between solution quality guarantees and empirical performance in geometric graph algorithms, with the matching-based algorithm emerging as the recommended choice for applications requiring reliable worst-case bounds.

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: Shannon entropy and Kolmogorov complexity describe complementary facets of information. We revisit Q2 from 27 Open Problems in Kolmogorov Complexity: whether all linear information inequalities including non‑Shannon‑type ones admit $$\mathcal{O}(1)$$-precision analogues for prefix‑free Kolmogorov complexity. We answer in the affirmative via two independent arguments. First, a contradiction proof leverages the uncomputability of $$K$$ to show that genuine algorithmic dependencies underlying non‑Shannon‑type constraints cannot incur length‑dependent overheads. Second, a coding‑theoretic construction treats the copy lemma as a bounded‑overhead coding mechanism and couples prefix‑free coding (Kraft's inequality) with typicality (Shannon-McMillan-Breiman) to establish $$\mathcal{O}(1)$$ precision; we illustrate the method on the Zhang-Yeung (ZY98) inequality and extend to all known non‑Shannon‑type inequalities derived through a finite number of copy operations. These results clarify the structural bridge between Shannon‑type linear inequalities and their Kolmogorov counterparts, and formalize artificial independence as the algorithmic analogue of copying in entropy proofs. Collectively, they indicate that the apparent discrepancy between statistical and algorithmic information manifests only as constant‑order effects under prefix complexity, thereby resolving a fundamental question about the relationship between statistical and algorithmic information structure.

Abstract: Reliable data availability and transparent governance are fundamental requirements for distributed edge-to-cloud systems that must operate across multiple administrative domains. Conventional cloud-centric architectures centralize control and storage, creating bottlenecks and limiting autonomous collaboration at the network edge. This paper introduces a decentralized governance and service-management framework that leverages Decentralized Autonomous Organizations (DAOs) and Decentralized Applications (DApps) to ensure verifiable, tamper-resistant, and continuously accessible data exchange among heterogeneous edge and cloud components. By embedding blockchain-based smart contracts into swarm-enabled edge infrastructures, the approach supports automated decision-making, auditable coordination, and fault-tolerant data sharing without reliance on trusted intermediaries. The proposed OASEES framework demonstrates how DAO-driven orchestration can improve data availability and accountability in real-world scenarios such as energy-grid balancing, structural-safety monitoring, and predictive maintenance of wind turbines. Results highlight that decentralized governance mechanisms enhance transparency, resilience, and trust, offering a scalable foundation for next-generation edge-to-cloud data ecosystems.

Abstract: Skyline Query, one of the profound tools that holds up tremendously when it comes to extracting valuable insights has witnessed multiple significant evolutions both in application domain and problem complexity over the years. In this SLR (Structural Literature Review), this study has tried to investigate the trends, evolutions of the application domain, and problem complexity from as early as 2008 until now. The authors divided the timespan into three major periods and analyzed 28 Scopus-indexed papers which this study chose using the PRISMA methodology. When looking at insights on application domain evolution, in the early years fundamental algorithmic research was taking place and it gradually shifted towards more specialized applications such as smart cities, IoT, and distributed computing. As the domains evolved, the complexity of the problems also spiked as a need to handle higher dimensionality in data, larger volume, and increased uncertainty became apparent. This paper provides impactful insights into how skyline query research domains have changed and tries to highlight future directions for addressing newer and more complex data management challenges.

Abstract: This project focuses on detecting anomalies in the shipment performance of a Business-to-Business supply chain using machine learning. Two models were used for the analysis: Isolation Forest and One-Class SVM. The model training was conducted using the 2024 data to minimize the impact of COVID-19. The data was cleaned and standardized. The key delivery-performance variables were also created to support more accurate anomaly detection. The Isolation Forest achieved an accuracy of approximately 87% with a 5% contamination factor, while the One-Class SVM achieved an accuracy of approximately 82%. Both models identified the Shipping Point as the primary contributor to delays. When the trained models were tested on the 2025 dataset, Isolation Forest returned more consistent results and captured a wider range of anomalies, including Delivery Delay and quantity shortages (partial deliveries), while the One-Class SVM focused more on timing issues. Overall, the study demonstrated that machine learning–based anomaly detection can help organizations identify delivery issues early and enhance shipment performance in B2B operations.

Abstract: People create facts rather than describe them; they formulate mathematical concepts rather than discover them. However, why can people design different mathematical concepts and use different tools to change reality?

Abstract: The Finite Ring Continuum (FRC) models physical structure as emerging from a sequence of finite arithmetic shells of order \(q = 4t+1\). While Euclidean shells \(\mathbb{F}_{p}\) support reversible Schr\"odinger dynamics, causal structure arises only in the quadratic extension \(\mathbb{F}_{p^2}\), where the finite-field Dirac equation is defined. This paper resolves the conceptual tension between the quadratic expansion \(\mathbb{F}_{p} \to \mathbb{F}_{p^2}\) and the linear progression of symmetry shells by introducing an algebraic innovation-consolidation cycle. Innovation corresponds to the temporary access to Lorentzian structure in the quadratic extension; consolidation extracts a finite invariant family and encodes it into the arithmetic of the next shell via a uniform G\"odel recoding procedure. We prove that any finite invariant set admits such a recoding, and we demonstrate the full mechanism through an explicit worked example for \(p = 13\). The results provide a coherent algebraic explanation for how finite representational systems---biological, computational, and physical---can acquire, assimilate and preserve structure.

Abstract: The P versus NP problem is a cornerstone of theoretical computer science, asking whether problems that are easy to check are also easy to solve. "Easy" here means solvable in polynomial time, where the computation time grows proportionally to the input size. While this problem's origins can be traced to John Nash's 1955 letter, its formalization is credited to Stephen Cook and Leonid Levin. Despite decades of research, a definitive answer remains elusive. Central to this question is the concept of NP-completeness. If even one NP-complete problem could be solved efficiently, it would imply that all NP problems could be solved efficiently, proving P=NP. This research proposes a groundbreaking claim: MONOTONE-MIN-3SAT can be solved in polynomial time and belongs to NP-complete, establishing the equivalence of P and NP.

Abstract: In the era of ever-greater data produced and collected, public health research is often limited by the scarcity of data. To improve this, we propose a data sharing in the form of Data Spaces, which provide technical, business, and legal conditions for an easier and trustworthy data exchange for all the participants. The data must be described in a commonly understandable way, which can be assured by machine-readable ontologies. We compared the semantic interoperability technologies used in the European Data Spaces initiatives and adopted them in our use case of physical development in children and youth. We propose an ontology describing data from the Analysis of Children’s Development in Slovenia (ACDSi) study in the Resource Description Framework (RDF) format and a corresponding Next Generation Systems Interface-Linked Data (NGSI-LD) data model. For this purpose, we developed a tool to generate a NGSI-LD data model using information from an ontology in RDF format. The tool builds on the declaration from the standard that the NGSI-LD information model follows the graph structure of RDF, so that such translation is feasible. The source RDF ontology is analyzed using standardized SPARQL Protocol and RDF Query Language (SPARQL), specifically using Property Path queries. The NGSI-LD data model is generated from the definitions collected in the analysis. Multiple ancestries of classes are also supported, even over multiple or common ontologies. These features may equip the tool to be used more broadly in similar contexts.

Abstract: Sequential data prediction presents a fundamental challenge across domains such as genomics and clinical monitoring, demanding approaches that balance predictive accuracy with computational efficiency. This paper introduces Ze, a novel hybrid system that integrates frequency-based counting with hierarchical Bayesian modeling to address the complex demands of sequential pattern recognition. The system employs a dual-processor architecture with complementary forward and inverse processing strategies, enabling comprehensive pattern discovery. At its core, Ze implements a three-layer hierarchical Bayesian framework operating at individual, group, and context levels, facilitating multi-scale pattern recognition while naturally quantifying prediction uncertainty. Implementation results demonstrate that the hierarchical Bayesian approach achieves an 8.3% accuracy improvement over standard Bayesian methods and 2.3× faster convergence through efficient knowledge sharing. The system maintains practical computational efficiency via sophisticated memory management, including automatic counter reset mechanisms that reduce storage requirements by 45%. Ze's modular, open-source design ensures broad applicability across diverse domains, including genomic sequence annotation, clinical time series forecasting, and real-time anomaly detection, representing a significant advancement in sequential data prediction methodology.

Abstract: The triangle finding problem is a cornerstone of complex network analysis, serving as the primitive for computing clustering coefficients and transitivity. This paper presents \texttt{Aegypti}, a practical algorithm for triangle detection and enumeration in undirected graphs. By combining a descending degree-ordered vertex-iterator with a hybrid strategy that adapts to graph density, \texttt{Aegypti} ensures a worst-case runtime of $\mathcal{O}(m^{3/2})$ for full enumeration, matching the theoretical limit for listing algorithms. Furthermore, we analyze the detection variant ($\texttt{first\_triangle}=\text{True}$), proving that sorting by non-increasing degree enables immediate termination in dense instances and sub-millisecond detection in scale-free networks. Extensive experiments confirm speedups of $10\times$ to $400\times$ over NetworkX, establishing \texttt{Aegypti} as the fastest pure-Python approach currently available.

Abstract: The Minimum Vertex Cover (MVC) problem is a fundamental NP-complete problem in graph theory that seeks the smallest set of vertices covering all edges in an undirected graph G = (V, E). This paper presents the find_vertex_cover algorithm, an innovative approximation method that transforms the problem to maximum degree-1 instances via auxiliary vertices. The algorithm computes solutions using weighted dominating sets and vertex covers on reduced graphs, enhanced by ensemble heuristics including maximum-degree greedy and minimum-to-minimum strategies. Our approach guarantees an approximation ratio strictly less than √2 ≈ 1.414, which would contradict known hardness results unless P = NP. This theoretical implication represents a significant advancement beyond classical approximation bounds. The algorithm operates in O(m log n) time for n vertices and m edges, employing component-wise processing and linear-space reductions for efficiency. Implemented in Python as the Hvala package, it demonstrates excellent performance on sparse and scale-free networks, with profound implications for complexity theory. The achievement of a sub-√2 approximation ratio, if validated, would resolve the P versus NP problem in the affirmative. This work enables near-optimal solutions for applications in network design, scheduling, and bioinformatics while challenging fundamental assumptions in computational complexity.

Abstract: Noise can substantially distort both chaotic and physiological dynamics, obscuring deterministic patterns and altering the apparent complexity of signals. Accurately identifying and characterizing such perturbations is essential for reliable analysis of dynamical and biomedical systems. This study combines complexity-based features with supervised learning to characterize and predict noise perturbations in time series data. Using two chaotic systems (Rössler and Lorenz) and synthetic electrocardiogram (ECG) signals, we generated controlled Gaussian, pink, and low-frequency noise of varying intensities and extracted a diverse set of 18 complexity metrics derived from both raw signals and phase-space embeddings. The analysis systematically evaluates how these metrics behave under different noise regimes and intensities and identifies the most discriminative features for noise classification tasks. Approximate Entropy, Mean Absolute Deviation, and Condition Number emerged as the strongest predictors for noise intensity, while Condition Number, Sample Entropy, and Permutation Entropy most effectively differentiated noise categories. Across all systems, the proposed framework reached an average accuracy of 99.9% for noise presence and type classification and 96.2% for noise intensity, significantly surpassing previously reported benchmarks for noise characterization in chaotic and physiological time series. These results demonstrate that complexity metrics encode both structural and statistical signatures of stochastic contamination.

Abstract: We propose a new hypothetical framework to explore the relationship between the Birch--Swinnerton-Dyer conjecture (BSD) and computational complexity theory. This paper introduces two central conjectures: a Reduction Conjecture, which posits the existence of a polynomial-time parsimonious reduction from \#P-complete problems to the counting of integer solutions for Tunnell's equations, and a Solution Density Conjecture, which posits that these solution counts are sufficiently well-distributed. We then formally prove that if these two conjectures are true, a surprising conditional result follows: the assumptions of P = NP and the truth of the BSD conjecture would imply the collapse of the counting complexity class \#P to FP. Our main conditional result is that if BSD is true, our conjectures hold, and the widely believed separation \#P $\neq$ FP holds, then P $\neq$ NP. This work reframes the P versus NP problem as a question about two deep, open problems in number theory: the existence of a "complexity-to-arithmetic" reduction and the statistical distribution of solution counts to Tunnell's specific quadratic forms.

Abstract: This paper introduces a computational framework called the Periodic Pairing Matrix model, which provides a foundation for modeling periodic interactions between cyclic sequences. The model formalizes pairing between two sequences using configurable step sizes, creating a deterministic pattern that repeats over a fixed cycle. We present a comprehensive analysis of its properties, including periodic behavior, coverage conditions, and vacancy patterns. The framework offers a unified approach to resource scheduling, sparse neural network design, and other domains that benefit from structured periodic interactions. Through case studies in distributed computing and deep learning, we show improvements in resource utilization, reaching full utilization under optimal settings, and faster neural network training with gains of about forty percent, while maintaining performance. The Periodic Pairing Matrix model enables principled design of systems with predictable and analyzable periodic behavior.

Abstract: Many data processing applications involve binary matrices for storing digital contents, and employ the methods of linear algebra. One of the frequent tasks is to invert large binary matrices. At present, there seem to be no documented algorithms for inverting such matrices. This paper fills the gap by reporting these three results. First, an efficient and provably correct recursive blockwise algorithm based on pivoted PLU factorization is reported to invert the binary matrices of sizes as large as several thousands of bits. Second, assuming the Bruhat matrix decomposition, a fast method is developed for effectively enumerating all elements of the general linear groups. Third, the minimum number of bit-flips is determined to make any singular binary matrix non-singular, and thus, invertible. The proposed algorithms are implemented in C++, and they are publicly available on Github. These results can be readily generalized to other finite fields, for example, to enable linear algebraic methods for matrices containing quantized values.