Computer Science and Mathematics

Abstract: We propose a framework that isolates a precise complexity-theoretic bottleneck between counting complexity and the Birch–Swinnerton-Dyer conjecture (BSD) via Tunnell’s theorem. The framework rests on two number-theoretic conjectures: a Reduction Conjecture asserting the existence of a polynomial-time reduction from any #P-complete problem to the counting of integer representations D_n = #{(x, y, z) : n = 8x² + 2y² + 16z²} (with counts preserved up to a polynomial factor), and a Solution Density Conjecture asserting that the values {D_n : n even square-free congruent} are sufficiently densely distributed (within the Eichler–Deligne ceiling D_n = O(n^1/2+ε)) to support iterated polynomial descent. We do not claim that P = NP implies #P = FP (the natural binary-search route fails because the threshold predicate [#I ≥ k] is PP-complete, not in NP, and PP is not known to collapse under P = NP). Instead, we prove a structural equivalence: under the two conjectures, BSD, and P = NP, #P ⊆ FP if and only if the specific family TunnellCount := {n 7→ D_n} is in FP. The framework thus does not resolve the #P ?= FP question; it converts it into a concrete, falsifiable arithmetic question about the polynomial-time tractability of representation counts on one specific ternary quadratic form. We identify three concrete open problems—parsimony in Matiyasevich representations, the distribution of weight-3/2 Fourier coefficients viaWaldspurger’s formula, and the FP-tractability of D_n itself—whose resolution would substantiate or refute the framework.

Abstract: Despite millennia of successful biological reproduction, the daily execution of child-rearing remains notoriously fraught and highly resistant to optimization. Societyfrequently attributes parental burnout and daily perceived failures in parenting tasks topsychological shortcomings, a lack of patience, or organizational failure. In this paper,we propose a mathematically rigorous defense of the exhausted parent by modelingroutine domestic tasks as formal decision problems. We demonstrate that the pursuit of“Optimal Parenting” (OP) is fundamentally intractable (assuming P ≠ NP). Byperforming polynomial-time reductions from classic NP-complete problems—specifically 0-1 Integer Linear Programming, Maximum Independent Set, and MAX-3-SAT—to simplified models of moral development, contradictory behavioral curricula,and developmental milestones, we prove that OP is strictly NP-hard. Consequently, weestablish that finding a perfect, conflict-free parenting strategy requires non-deterministic polynomial time, vastly exceeding the processing capabilities of anybiological parent. Our results mathematically absolve caregivers of domestic guilt andformally validate constraint relaxation (colloquially known as “lowering expectations”,or simply “doing one’s best”) as a necessary and optimal heuristic for surviving acomputationally hostile environment.

Abstract: The calibrated model reproduced the overall trend of specimen-to-specimen mechanical variation observed experimentally. Predicted stiffness values were in reasonable agreement with measured data. Fracture force predictions showed moderate agreement for dynamically tested specimens (R² = 0.60), which improved to R² = 0.88 after exclusion of one statistically identified outlier. Compared with a purely linear elastic formulation, the proposed viscoelastic model demonstrated modest improvement in stiffness prediction and more substantial improvement in fracture force prediction. These findings indicate that incorporating density-dependent viscoelastic effects improves representation of vertebral mechanical behavior, particularly at higher loading rates. Owing to its simplicity and computational efficiency, the proposed model requires only limited imaging input and may be useful for future biomechanical investigations, rapid screening, and injury risk prediction.

Abstract: Fragmentation of data is common in the U.S. healthcare system, which leads to substandard patient safety, excess administration waste, and impediments to public health monitoring. This paper proposes a relational database design, the Centralized-Decentralized Health Management System (CDHMS) that achieves a balance between conflicting requirements of local autonomy and federated access to data. The system is based on 15 normalized relations that are organized in 6 functional layers: core clinical infrastructure, Master Patient Index, Interoperability Mapping layer, Audit and Break-Glass logging subsystem, Patient consent and access-control framework, and a Role Based plus Attribute Based Access Control (RBAC+ABAC) model with 6 different user roles. The schema is deployed in MySQL Workbench 8.0 CE, with some sample mock data, and tested using 12 test queries. Results show the architecture enables no duplicate patient identities, reconciliation of incompatible coding vocabularies, granular patient consent management, and a tamper evident audit trail of all patient data access, including emergency overrides.

Abstract: To address the problems of strong noise, high asynchrony, pronounced subjectivity in risk labels, and insufficient model stability under extreme market conditions in multi-source risk signals within trading environments, a low-noise investment risk prediction method based on multimodal sensing signals and self-supervised representation learning is proposed. Market quotations, order books, terminal interactions, network transmission, device status, and news sentiment are uniformly modeled as risk perception signals. A temporal masking-based risk structure modeling module, a risk-oriented contrastive learning representation constraint mechanism, and a risk representation and downstream prediction task alignment strategy are designed to learn stable, transferable, and interpretable risk features. Experimental results show that the proposed method achieves the best performance in investment risk prediction, with mean squared error (MSE), mean absolute error (MAE), and root mean square error (RMSE) reaching 0.0164, 0.0851, and 0.1281, respectively, outperforming baseline models including generalized autoregressive conditional heteroskedast (GARCH), multi-layer perceptron (MLP), long short term memory (LSTM), temporal convolutional networks (TCN), and Transformer. The IC, RankIC, and AUC reach 0.496, 0.462, and 0.817, respectively, indicating stronger risk ranking capability and improved discrimination between high-risk and low-risk states. At the classification recognition level, the proposed method also demonstrates superior accuracy, precision, recall, and F1-score, indicating that potential high-risk assets can be identified more accurately. Ablation experiments verify the effectiveness of multimodal fusion, temporal masking, self-supervised contrastive constraints, and task alignment modules. Robustness experiments further show that lower prediction errors and higher AUC can still be maintained in high-volatility and extreme-shock markets, demonstrating strong noise resistance, stability, and practical application potential in complex sensing scenarios.

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: We derive a penalty strength criterion for ridge regression using stochastic complexity, which is a refined variant of the minimum description length principle. Since stochastic complexity doesn’t typically account for the effect of regularisation on complexity, despite its ability to simplify models, we are required to make a slight modification to the un- derlying coding scheme. Our scheme makes use of a weighted ensemble of regularised model fits rather than a mixture of maximum likelihood estimates. Under this modification, regularisation is interpreted as reducing model complexity by constraining flexibility. In the case of ridge regression, the complexity penalty term that we derive can be expressed analytically as the log determinant of the residual operator. We demonstrate the effect of this complexity penalty by fitting a linear readout to a reservoir computer.

Abstract: The Minimum Dominating Set problem is NP-hard, and the best known polynomial-time approximation factor is O(ln n), which is provably tight unless P = NP. We present a polynomial-time algorithm that reduces an arbitrary input graph to a planar kernel through forced-vertex extraction, pendant elimination, and greedy planarisation, and then applies Baker’s PTAS to that kernel. The algorithm runs in O(mn + m log m) time — in particular O(n log n) on sparse graphs — and is provably within twice the optimum whenever the reduction is tight. We give a structural witness mapping that injects the post-pruning forced-boundary set into the rest of the planar kernel, narrowing the unresolved gap in the analysis to a single inequality, |F| ≥ 2|F_R^pruned|. Should that inequality hold universally, a 2-approximation would follow and would imply P = NP. We complement the theory with an experimental study on thirteen DIMACS benchmark graphs: in every case the algorithm finishes in well under five minutes and returns a dominating set whose size is at most 1.80× the ILP optimum, with an average ratio of 1.42. An open-source implementation is provided as the Furones package (v0.2.6).

Abstract: Artificial Intelligence (AI) systems are increasingly embedded in development contexts across the Global South, yet limited evidence explains how individuals within marginalized communities behaviorally adapt to these technologies beyond structural access and governance conditions. Building on prior framework-based analysis, this study examines the micro-level processes through which users internalize and operationalize AI-enabled systems in everyday livelihood and learning activities. A mixed-method sequential explanatory design was employed using the same population across urban, peri-urban, and rural settings, integrating structured surveys with ethnographic observations, digital usage tracing, and behavioral mapping. The findings identify three dominant adaptation pathways: instrumental adoption driven by efficiency gains, socially negotiated use shaped by contextual constraints, and reflexive adaptation linked to learning and trust formation. Quantitative analysis indicates that user agency significantly mediates the relationship between access and effective utilization, while qualitative insights reveal that learning styles and socio-cultural conditions influence the depth and sustainability of engagement. The study concludes that inclusive AI outcomes depend not only on infrastructure and governance but also on dynamic human–technology interactions, where cognitive engagement and iterative feedback mechanisms play a central role. These findings extend existing models by introducing a behavioral adaptation dimension critical for designing context-sensitive and sustainable AI interventions.

Abstract: This paper presents a two-phase adaptive algorithm to solve the 2-Dimensional Maximum Sum Sub-array Problem. By reframing the search order to establish a single-column baseline first, the algorithm generates mathematical pruning bounds in O(NM) time. These bounds are utilized in a second phase to skip unpromising multi-column scans in O(1) time. This “Two-Phase” approach achieves a quadratic best-case floor of O(M² + NM), while significantly improving the expected performance across typical data distributions and maintaining the cubic worst-case. This adaptive strategy effectively bridges the gap between theoretical sub-cubic complexity and practical implementation.

Abstract: Feature selection is crucial for high-dimensional sensor and biomedical data because it reduces redundancy, improves generalization, and supports interpretable biomarker discovery. In this study, we propose a Binary Chaos-Enhanced Newton-Raphson-Based Optimizer (BCNRBO) for wrapper-based feature selection. The method integrates chaotic search dynamics, a Hamming-distance-based dynamic potential mechanism, and a new binary transfer function to enhance exploration and prevent premature convergence. BCNRBO was evaluated on 26 benchmark datasets using K-nearest neighbor (KNN), decision tree (DT), and Naive Bayes (NB) classifiers. The proposed method consistently achieved competitive or superior classification performance while selecting fewer features than competing binary metaheuristic methods. In particular, BCNRBO obtained the best feature reduction in 15 datasets with DT and 14 datasets with NB, and it achieved top Friedman ranks in 8 DT datasets and 9 NB datasets. Statistical tests confirmed significant improvements over competing methods in most pairwise comparisons. These results suggest that BCNRBO is a promising feature- selection strategy for sensor-derived biomedical and neurorehabilitation data, where compact and reliable digital biomarkers are needed.

Abstract: We present the Hvala algorithm, a linear-time ensemble approximation method for the Minimum Vertex Cover problem. Hvala combines three complementary heuristics — a maximal-matching 2-approximation, a linear-time maximum-degree greedy implemented via a bucket-queue, and the degree-1 weighted-reduction “Hallelujah heuristic” studied in a companion work — with a redundant-vertex pruning post-processing step, and returns the smallest of the four resulting covers. Theoretical guarantees. We prove rigorously that Hvala achieves worst-case approximation ratio ρ ≤ 2 for every finite, simple, undirected graph: the classical maximal-matching component alone already yields this bound, and the pruning step is shown to preserve cover validity while never increasing cover size. The companion work moreover establishes the strict pointwise inequality |C3| < 2 · OPT(G) on every finite simple graph — the Hallelujah heuristic’s approximation ratio is asymptotic to 2 (strictly less than 2 on each graph, with supremum equal to 2 over all graphs) — and we show that this strict pointwise inequality is inherited by Hvala. Hvala runs in O(n + m) time and O(n + m) space. Empirical performance. We validate Hvala on two independent experimental studies totalling 239 instances. The first uses 109 vertex-cover instances of the public NPBench collection (41 FRB hard instances and 68 DIMACS clique-complement graphs, both with known optima), completed in 126.97 seconds: Hvala attains mean approximation ratio 1.021, with maximum 1.192 on a single Sanchis adversarial instance. The second evaluates Hvala on 130 real-world large graphs from the Network Data Repository (Cai’s undirected simple graph collection), reaching up to 3 million vertices and 15 million edges, completed in approximately 95.5 minutes of cumulative solve time; on the 51 instances with published best-known cover sizes, mean ratio is 1.006 and maximum 1.036. Prospects for a √2 − ϵ bound. Across the combined 160 instances with known optima, every approximation ratio lies below 1.414; 93.8% lie below 1.05 and 96.9% below 1.10. The natural open problem we propose as the continuation of this work is whether there exists a fixed constant ϵ > 0 such that Hvala achieves uniform ratio √2 − ϵ — either on all graphs (which, by SETH-based hardness, would imply P = NP) or, more realistically, on broad but restricted graph classes (bounded degree, bounded clique number, bounded treewidth, or structural families such as power-law and expander-like graphs). We do not prove such a bound here and do not claim one holds on all graphs; what we claim is that the combination of rigorous ≤ 2 guarantee, pointwise strict < 2 inequality, linear time, and observed ratios uniformly below 1.414 makes Hvala a plausible vehicle for such a refined analysis. The algorithm is publicly available via PyPI as the hvala package.

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: The relevance of this study stems from the need for a scientifically sound assessment of the environmental risks associated with launch vehicle launches and for ensuring the environmental safety of areas potentially impacted by space activities. Comprehensive environmental monitoring in the impact areas of rocket parts and adjacent populated areas is particularly important, taking into account natural and climatic factors and the spatial heterogeneity of pollution. This study assessed the environmental impacts of the “Soyuz-2.1a” launch with the ““Progress MS-29”” cargo spacecraft in Kazakhstan based on integrated field research and geoinformation analysis. The study covered the launch area, adjacent populated areas, and the impact zone. A before-after control impact (BACI) design with distance stratification and wind pattern considerations was used to identify post-launch changes. Data containing values below the detection and quantification limits were processed using censored observation analysis methods (ROS Regression on Order Statistics and Kaplan-Meier). A spatial analysis of pollutant distribution was conducted, with thermal field and contour maps generated, revealing the anisotropy of the risk field and localized areas of increased environmental stress. An integrated environmental risk (HQ) metric was used to compare the state of atmospheric air, water, and soil, providing a unified approach to interpreting the results. It was established that the post-launch impact is localized and time-limited, with the greatest sensitivity observed in the soil component in the first period after launch. Measures are recommended to temporarily restrict access to areas of increased stress, conduct primary reclamation, and organize staged environmental monitoring using WebGIS technologies to support management decisions. The scientific novelty of the work lies in the development of an anisotropic model for assessing environmental risk taking into account wind rose and in the integration of methods for analyzing censored data into a unified system for monitoring environmental components.

Abstract:

We present \textsc{Aegypti}, a hybrid algorithm for detecting a single triangle in an undirected graph \( G = (V, E) \) with \( n = |V| \) vertices and \( m = |E| \) edges. The algorithm operates in two phases. In the \emph{fast path}, a clique-constrained Union-Find structure (\textsc{FastCliqueUF}) streams over the edges and merges components only when the union remains a clique; the moment any component reaches size~\( \geq 3 \), a triangle witness is returned. Because components remain of size at most \( 2 \) until the detecting merge, each \textsc{Union} costs only \( \Oh(1) \) (bitset operations touch \( \Oh(k/\wordlen) \) blocks with \( k=O(1) \)). The fast path therefore runs in \( \Oh(n^2/\wordlen + m) \) time (dominated by initialisation), using packed \texttt{uint64} SIMD bitset operations; on triangle-rich graphs this reduces to \( \Oh(n^2/\wordlen) \) in practice and is \( \Oh(n^2) \) in the RAM model. If the fast path finds no triangle, a \emph{fallback} using adjacency-set intersections solves the problem in \( \Oh(m^{3/2}) \) time. The overall running time is therefore \( T(G) \;=\; \Oh\!\left( \frac{n^2}{\wordlen} + m^{3/2} \right) \) in the worst case. On triangle-rich graphs the fast path typically terminates after processing only a small fraction of the edges, achieving \( \Oh(n^2/\wordlen) \) time in practice; on triangle-free graphs the fallback dominates. For triangle-containing graphs, \( \Oh(n^2/\wordlen) \)is at most as large as \( \Oh(m^{3/2}) \) whenever \( m = \Omega(n^{4/3}) \) (the dense regime), and the constant-factor savings from SIMD make it substantially faster in practice. We prove correctness, analyse the complexity of each phase, and validate the algorithm on the full Second DIMACS Implementation Challenge benchmark suite, where \textsc{Aegypti} detects triangles in all tested instances in under \( 12 \)s.

Abstract: Equality saturation explores equivalent program expressions via e-graphs, and its final step—extraction—selects one representative per equivalence class to form an output tree. Standard extraction minimizes a decomposable, single-node cost function that cannot capture multi-node structural patterns exploited by downstream systems such as SMT preprocessors and compiler backends. We formalize pattern-aware extraction as a weighted pattern cover problem on AND-OR directed acyclic graphs and establish its correspondence to tree covering in compiler instruction selection. Three challenges arise: annotation ambiguity from multiple candidates per class, context-dependent selection from depth-2 templates, and DAG sharing conflict. We show that the coupled selection-tiling problem reduces to a tree DP with three mutually exclusive tile-role states—independent, tile-root, and tile-leaf—generalizing BURS tree covering from fixed trees to AND-OR DAGs. A bottom-up pass computes optimal DP values; a top-down pass traces back decisions to produce the output tree. For template depth at most two, the algorithm computes an exact optimum in \( O(N \cdot K \cdot |\mathcal{P}| \cdot C_{\max}) \) time. Experiments on SMT-COMP hardware verification benchmarks show up 31× higher weighted pattern coverage than standard extraction, with depth-2 tiling contributing 45–51% additional improvement and overhead remaining within 2–3×, demonstrating exact, context-sensitive extraction at practical cost.

Abstract: Modified Anderson-Björck’s method [1] is a new robust and efficient bracketing root finding algorithm. It combines bisection with Anderson-Björk’s method to achieve both fast performance and worst-case optimality. It relies on linearity check criteria for switching methods and uses Anderson-Björk corrections to overcome the fixed endpoint issue of false-position. Initial benchmarks of this method have shown certain performance advantages compared to other methods like Ridders, Brent and ITP. In this paper, we propose further improvements of the method and perform some additional analysis and benchmarks of its behavior and performance.

Abstract: This study examines the interrelationships among AI Competency (AIC), Soft-Skill Competency (SSC), Strategic Intelligence (SI), and Innovative University Competency (IUC) within the context of Thailand’s higher education transformation. Grounded in Dynamic Capability Theory (DCT), Human Capital Theory (HCT), and the Strategic Intelligence Framework (SIF), the study explores how technological and human-centered capabilities collectively enhance institutional innovation. A quantitative explanatory research design was employed, and data were collected from 475 academic and administrative staff across six faculties at Mahasarakham University. Structural Equation Modeling (SEM) was used to test the hypothesized causal relationships and mediating effects among the constructs. The findings reveal that all proposed hypotheses were supported. AI Competency exerted the strongest total effect on IUC, indicating its pivotal role in driving innovation both directly and indirectly through Strategic Intelligence and Soft-Skill Competency. SSC also demonstrated a significant total effect, underscoring the importance of collaboration, communication, adaptability, and problem-solving in fostering innovative ecosystems. Strategic Intelligence emerged as a key mediating mechanism, transforming technological and human capabilities into innovative outcomes through analytical foresight, evidence-based judgment, and organizational agility. The model demonstrated excellent goodness-of-fit indices, confirming both theoretical rigor and empirical robustness. The study contributes to the literature by integrating digital capability, human adaptability, and strategic cognition into a unified framework for university innovation. In practice, the results emphasize that sustainable innovation in higher education requires the synergistic development of AI literacy, soft skills, and strategic foresight.

Abstract: To address the issues of insufficient convergence performance and high sensitivity to local optima in the traditional Whale Optimization Algorithm (WOA) when handling 3D path planning tasks for unmanned aerial vehicles (UAVs), this paper proposes an improved UAV path planning algorithm based on the Whale Optimization Algorithm (R*WOA). Firstly, the global search capability and path optimisation mechanism of the Rapidly Expanding Random Tree Star (RRT*) algorithm are utilised to generate a high-quality initial population, thereby enhancing population diversity and the algorithm’s global exploration capability; Secondly, the linear convergence factor of the traditional WOA is adjusted to a non-linear dynamic adjustment strategy based on the cosine function, enhancing global search capability in the early stages of iteration and local search capability in the later stages; simultaneously, a non-linear inertial weight is employed to modulate the position update mechanism of individuals, further enhancing the algorithm’s local optimisation accuracy and convergence stability in the later stages of iteration. Finally, comparative experimental results on a basic test function set and in scenarios constructed using Digital Elevation Models (DEMs) demonstrate that R*WOA exhibits stable optimisation performance, capable of planning safer paths that are shorter in length and smoother in trajectory.

Abstract: This paper introduces the formal framework of Symbolic Structures of Differences (SSD) as a novel approach to the analysis of seismic time series, aiming to provide early warning prior to the occurrence of a main shock. Unlike classical early warning systems based on P-wave detection, the SSD methodology identifies changes in the local geometry of geological deformation through the symbolic encoding of three-point differential structures. Each sample triplet (xk,xk+1,xk+2) is assigned a symbolic structure based on the signs of the first and second differences, generating a space of 27 possible local geometries. From the distribution of these structures, the following metrics are derived: SSD entropy (Esds), symbolic space activity (κ), transition entropy (ε), and the Relational SSD Coefficient (RSC). Preliminary retrospective analysis of data for five significant seismic events — Parkfield 2004 (M6.0), L'Aquila 2009 (M6.3), Tohoku 2011 (M9.0), and the Ridgecrest 2019 sequence (M6.4/M7.1) — shows statistically significant changes in SSD parameters within a time window of 47 to 89 seconds before the arrival of the P-wave. Hybrid systems combining SSD detection with classical P-wave analysis potentially offer superior warning time and accuracy compared to traditional approaches. We caution that the presented numerical results are based on a preliminary analysis of a small sample and require validation on an expanded dataset before any potential operational application.