Although S ∞ (the group of all permutations of N ) is size continuum, both it and its closed subgroups can be presented as the set of paths through a countable tree. The subgroups of S ∞ that can be presented this way with finite branching trees are exactly the profinite ones. We use these tree presentations to find upper bounds on the complexity of the existential theories of profinite subgroups of S ∞ , as well as to prove sharpness for these bounds. These complexity results enable us to distinguish a simple subclass of profinite groups, those with orbit independence , for which we find an upper bound on the complexity of the entire first-order theory. Additionally, given a profinite subgroup G of S ∞ and a Turing ideal I , we define G I to be the set of elements in G whose Turing degree lies in I . We examine to what extent and under what conditions G I will be an elementary subgroup of G . In particular, we construct a profinite group whose subgroup of computable elements is not elementary even for existential formulas.
Following the approach of Gavryushkin, Khoussainov, and Stephan, we study countable linear orders realized by computably enumerable equivalence relations (ceers). A ceer E realizes a linear order L if there exists a computably enumerable binary relation ⊴ respecting E such that the induced quotient structure ( N / E ; ⊴ ) is isomorphic to L . The known results in this direction show that there is a highly nontrivial interplay between the computability-theoretic properties of a ceer E and the isomorphism types of orders L realizable by E . We obtain a complete characterization of well-orders L realizable by a given ceer E for the case when E realizes some ordinal α < ω ω . In particular, our characterization implies that for any ceer E with infinitely many equivalence classes, either the family of all well-orders realizable by E is contained inside the interval [ ω n ⋅ k ; ω n ⋅ ( k + 1 ) ) for some non-zero n , k < ω , or this family is cofinal in the computable ordinals. The proof of our result develops methods of fine-tuning the behavior of limit points of an E -realizable order L via the computability-theoretic properties of E .
In the first part of this paper, we will prove a new sufficient condition for a structure to have infinite punctual dimension and then apply it to show several new connections between the punctual dimension of a structure and its punctual degrees. In the second part of this paper, we contribute toward a classification of the density of punctual degrees for linear orders by proving that the punctual degrees of Z ⋅ n , for n > 1 , are dense.
In this study, we present a discrete switching host-parasitoid model that incorporates biological and chemical control interventions within the integrated pest management (IPM) measures. The coupling of multi-tactic control measures induces rich and complex dynamical behaviors in the proposed system. We begin by systematically characterizing the existence and stability of fixed points in the control subsystem. The analysis then proceeds to demonstrate how the system undergoes multiple bifurcation routes, including period-doubling, transcritical, and Neimark-Sacker bifurcations. Building on this theoretical foundation, extensive numerical simulations are conducted, not only corroborating our analytical predictions but also revealing emergent phenomena such as cascading period-doubling routes and chaotic regimes. Finally, high-resolution two-parameter stability diagrams are employed to identify the critical dynamical transition boundaries, and the corresponding ecological implications for practical pest management decision-making are elaborated in depth.
We analyze parameter identifiability in a Marchuk-type immune-response model using longitudinal whole-blood transcriptomic signatures from the influenza challenge. Latent states are extracted from curated gene signatures derived from nine symptomatic and eight asymptomatic subjects. The governing delay differential equations are cast in a linear-in-parameters form; derivatives are estimated by smoothing splines, coefficients are fit by ridge regression, and the delay tau is selected by grid search. We find that the parameters governing viral and innate dynamics are consistently identifiable, with low relative error, and are highly determined, whereas adaptive-immunity and tissue-damage parameters are poorly constrained by transcriptomics alone. Introducing a small additive background term and tissue dependence markedly reduces residual variance and stabilizes estimates. Symptomatic patients exhibit a characteristic regulatory delay near 21 h. These results show that aggregated transcriptomic time series can reliably identify some subsystems of classical immune models, but that adaptive immunity and damage dynamics require explicit structural extensions or additional data modalities. The study provides a practical identification pipeline and concrete guidance on model extensions needed for transcriptomic-driven mechanistic inference.
To address the core challenges in air-to-ground target re-identification (ReID), including network focus on invalid background information, poor adaptability to nonlinear feature distribution, and insufficient cross-domain generalization, this paper proposes a novel air-to-ground ReID framework based on Neighborhood Feature Centralization Attention (NFCA). On the basis of Coordinate Attention, the framework introduces a parameter-free Neighborhood Feature Centralization mechanism to build a lightweight attention module, which enhances cross-feature semantic interaction and suppresses background noise while retaining precise position encoding. It achieves end-to-end direct optimization of sample pair similarity through binary cross-entropy loss, eliminating the proxy task bias of traditional classification loss and adapting to the nonlinear structure of feature space. A multi-source data-driven training strategy is constructed by fusing ReID datasets and general classification datasets, which expands the coverage of feature space and narrows the distribution gap between training data and real air-to-ground scenarios without additional manual annotation. Experiments show that the proposed method achieves leading mAP values on the self-developed UAV air-to-ground dataset JC-1, the public person ReID dataset Market-1501, and the public vehicle ReID dataset VehicleID. Sufficient statistical validation, ablation experiments and cross-domain tests verify the advancement, reliability and generalization of the proposed method in complex air-to-ground scenarios.
Corporate tax avoidance has become a major governance and fiscal sustainability concern, particularly in developing economies where corporate tax revenues constitute a critical source of public financing. While prior research suggests that board gender diversity (BGD) enhances ethical oversight and monitoring, its effectiveness in constraining aggressive tax planning may depend on firms' informational and technological environments. This study examines whether artificial intelligence (AI) capability strengthens the governance role of BGD in reducing corporate tax avoidance. Using a balanced panel of 1586 non-financial firms from developing economies over the period 2009-2023, the analysis employs firm FE models and dynamic two-step System GMM estimations to address unobserved heterogeneity, endogeneity, and the persistence of corporate tax behavior. The results indicate that BGD is positively associated with effective tax rates, implying lower levels of corporate tax avoidance. Furthermore, AI capability-measured using a lagged specification-significantly strengthens this relationship, suggesting that firms with higher AI adoption exhibit a stronger governance effect of gender-diverse boards on tax compliance. Additional robustness tests-including alternative tax avoidance measures, alternative BGD specifications, heterogeneity analysis, and selection-bias corrections using Heckman, propensity score matching (PSM), and instrumental variable (2SLS) approaches-confirm the stability of the findings. Overall, the results highlight the complementary role of technological capability and board diversity in strengthening corporate governance (CG) and fiscal discipline in developing economies.
Aero-engine defects often exhibit micro-scale and high-frequency characteristics under complex metallic textures, which makes precise segmentation difficult. Most existing pixel-level methods rely on spatial-domain modeling and lack frequency-domain decoupling. As a result, high-frequency details are easily hidden by low-frequency background information. In addition, repeated downsampling weakens the representation of fine-grained structures, leading to inaccurate boundary localization and limited robustness. To address these issues, a spectrum-driven hierarchical learning network is proposed for aero-engine defect segmentation. First, a dual-band spectral module is constructed using the discrete cosine transform to separate high-frequency and low-frequency components, providing stable and physically meaningful frequency-domain priors for the network. Second, a detail-guided module is designed where high-frequency features adaptively guide skip connections, compensating information loss during encoding and improving boundary recovery. Furthermore, a low-frequency-driven region-aware modeling module is developed. The internal defect regions, boundary areas, and background regions are modeled hierarchically. A dynamic hyper-kernel generation mechanism performs region-sensitive convolutional modeling, improving adaptation to complex structural variations. Extensive experiments on the Turbo19 and NEU-Seg datasets demonstrate that the proposed method produces accurate defect boundaries and achieves mIoU scores of 89.82% and 91.44%, improving over the second-best method by 5.22% and 4.42%, respectively.
This work considers admissibility-enforcing reconstruction of reaction-channel subgroup levels on prescribed total-subgroup support and probabilities, a setting in which conventional exact reconstruction may produce negative reaction-channel levels. The proposed reconstruction relaxes conventional full matching by retaining selected low-order channel quantities associated with limiting dilution responses exactly, while fitting the remaining matching conditions in a constrained least-squares sense under nonnegativity. The exact-retention constraints are embedded through a null-space parametrization, which reduces the reconstruction to a convex optimization problem over the remaining degrees of freedom. Two variants are examined: a single-retention formulation, which is automatically feasible for nonnegative retained data, and a two-retention formulation, which is more restrictive and depends on compatibility with the fixed total-subgroup rule. Numerical tests for 238U capture data show that the proposed reconstruction removes the negative reaction-channel levels observed in the violating groups. Restoring admissibility entails deterioration in response accuracy relative to the unconstrained full-matching baseline, reflecting the trade-off between exact matching and nonnegativity on the fixed rule. Of the two variants considered, the single-retention formulation shows more stable overall behavior in the present comparison. In particular, for all violating cases at orders N >= 10, it restores nonnegativity, with the reported 95th-percentile relative errors in the folded effective cross section not exceeding 8.90 & times;10-7.
Accurate short-horizon downlink throughput prediction is essential for automation in high-density 5G deployments (e.g., stadiums and events), where user load, scheduling decisions, and interference conditions change rapidly and produce highly variable user-perceived rates. This paper benchmarks lightweight regression models for per-user throughput prediction from readily available radio access network (RAN) key performance indicators (KPIs) and studies a risk-aware extension that augments point forecasts with calibrated uncertainty and an abstention (deferral) rule. Experiments use a strictly time-ordered train/calibration/test protocol on the Liverpool 5G High-Density Demand (L5GHDD) dataset. The target is strongly zero-inflated (about 62% of samples at 0 Mbps) and heavy-tailed, creating regimes where average-error optimization can mask rare but operationally important bursts. In the point-prediction benchmark, the best model is a tuned two-stage support vector regressor with a mean absolute error (MAE) of 0.452 Mbps, while the strongest single-stage model attains a weighted mean absolute percentage error (WMAPE) of 56.200%. For uncertainty quantification, we compare standard split conformal prediction against two input-adaptive alternatives. Constant-width split conformal attains 88.900% marginal coverage for a nominal 90% target with an average interval width of 2.288 Mbps, but width-based deferral is degenerate because all intervals have the same size. Variable-length conformal intervals preserve near-nominal coverage (91.100%) while producing informative width variation: normalized conformal reduces the average width to 1.344 Mbps, and conformalized quantile regression reduces it to 0.641 Mbps. At a deferral threshold of 1.500 Mbps, constant-width conformal defers all samples, whereas normalized conformal still acts on 61.200% of samples with selective MAE 0.219 Mbps. These results show that input-adaptive uncertainty is necessary for meaningful selective prediction in heteroscedastic 5G throughput dynamics.
As social infrastructure intensively developed during the high economic growth period of the 1970s faces simultaneous aging, there is an urgent need to transition from conventional reactive maintenance to preventive maintenance utilizing various data (data-driven asset management. However, the greatest barrier in practice is that inspection data is unevenly distributed in analog formats such as paper and unstructured files, and heavily relies on the subjective visual evaluation of expert engineers (e.g., discrete graded evaluations from A to D). The intervention of this "Assessor Bias" makes it difficult to ensure the robustness required for direct statistical analysis. This paper serves as a bridge between this analog expert knowledge and quantitative data science. It formulates human cognitive conflicts (true state, peer pressure, avoidance of cognitive load) using the distance-decay model of the Analytic Hierarchy Process (AHP) and the Softmax function, constructing a micro-macro link model accompanied by stochastic variations. Through large-scale multi-agent simulations (N=107) validating the model's convergence, it was demonstrated that in long-tail distributions formed under peer pressure, macroscopic statistical distance metrics such as the Kullback-Leibler (KL) divergence ignore the fact that a small number of true signals are non-linearly suppressed, causing a statistical misinterpretation that "the error is within an acceptable range". This implies that as long as macroscopic statistical indicators are over-trusted, signs of critical deterioration (minorities) will be structurally marginalized. Returning to the debate on "Homogeneity (Homogenit & auml;t)" in German social statistics, this paper advocates that in order to realize objective "Micro-segmentation of Homogeneous Statistical Populations," a paradigm shift from qualitative methods relying on human intuition to quantitative methods incorporating multi-criteria decision making is essential, rather than simply expanding the sample size.
Tool-using AI agents couple a language model with controller logic, memory, and external tools such as browsers, email, calendars, file systems, and transaction APIs. This architecture expands capability, but it also enlarges the security boundary: agents routinely ingest untrusted content while holding privileges that can reveal private data and trigger external side effects. The resulting failures are not limited to poor text generation; they include prompt injection, indirect injection through tool outputs, confused-deputy behavior, unauthorized actions, and misleading claims about the tool state. Because large-scale testing on deployed products is difficult, vendor-specific, and ethically sensitive, we present a transparent, theoretical simulation-based framework for evaluating user-facing risk in tool-using agents. The methodological contribution is a formal threat model that separates compromise, harm, and severity, and a Monte Carlo evaluation pipeline that maps architectural choices (permissions, retrieval, memory exposure, and approvals) and defensive controls to comparable outcome metrics. We instantiate the framework for six representative threat scenarios and nine defense configurations, reporting attack success rate (ASR), benign task success, latency overhead, and severity-weighted harm. Across scenarios, the least-privilege tool design is the strongest single broad control, human-in-the-loop approvals sharply reduce high-impact actions and exports but degrade under user error and habituation, retrieval allowlisting nearly eliminates indirect injection while leaving other channels largely unaffected, and rate limiting reduces tail severity more than ASR. These results position agent safety as an architectural and operational problem and because they arise from an assumption-explicit simulator rather than field measurements, should be read as comparative design guidance rather than incident-rate estimates for any deployed product.
Class imbalance among arrhythmia types and electrocardiogram (ECG) signal complexity present significant challenges for automated ECG-based arrhythmia detection. This research proposes an innovative approach that combines Genetic Algorithm (GA) optimization of Convolutional Neural Network (CNN) hyperparameters with morphological skeletonization of ECG images. The MIT-BIH Arrhythmia Database served as the primary data source, with the ECG signal converted to skeletonized representations emphasizing QRS complex geometry. A GA-optimized model was compared against a heuristic (manual design) baseline to determine optimal kernel and filter configurations. Evaluation emphasized not only overall accuracy but also robust metrics for minority classes. The optimized model achieved 97.26% accuracy, with macro recall improving substantially from 77.36% to 83.10% (+5.74%). These results demonstrate that evolutionary optimization enhances detection sensitivity to subtle geometric patterns, effectively mitigating class imbalance without artificial oversampling techniques.
Modern user authentication systems increasingly need user and device-behavior-aware adaptive mechanisms to detect evolving threats beyond the traditional authentication framework of static credential verification. This paper proposes a hybrid multi-model framework for personalized user-level anomaly detection using a data-driven Hybrid Anomaly Score (HAS). The primary contribution lies in deriving the HAS using the joint integration of three adaptive attributes: dynamically computed per-user deviation thresholds conditioned on individual behavioral history, profile-age-aware baseline weights reflecting user cohort maturity, and criticality-scaled aggregation with the security impact of each detection methodology. The framework is evaluated on a large-scale real-world dataset and demonstrates strong detection performance, while achieving low inference latency suitable for real-time enterprise deployment. The ablation analysis of the framework confirms that dynamic weighting and personalized threshold substantially improve detection stability and convergence with an effective and deployable solution for large-scale authentication environments.
Deriving from the Latin “ovum” (egg), the oval is a commonly used term, but does not have the status of a standard geometric figure like a circle or ellipse. Consequently, the oval lacks both a mathematical descriptive basis to attribute a set of key geometric parameters and an elegant formula to describe its contours. Herein, we consider the basis for deriving the formula of an oval for typical egg profiles. Specifically, these are round, ellipsoid, classic oval, pyriform (conical) and biconical shapes. To do this, we adhered to four basic postulates: (i) the ability to describe all possible egg shapes; (ii) a minimum set of measurable geometric parameters; (iii) the application of some universal indices (ratios of key geometric dimensions) to describe mathematical models; (iv) conformity with the “Main Axiom of the Mathematical Formula of the Bird’s Egg.” Additionally, we sought to comply with the principles of mathematical elegance. Following these theoretical assumptions and practical verification, we obtained a mathematically supported, elegant formula for this well-known but non-standardized geometric figure. The derived oval geometry equation will find use in applied problems of biology, construction, engineering and school curricula, alongside the classical figures of the circle and ellipse.
Taking the Singularly Perturbed System (SPS) as a model of ODE system separation into fast and slow subsystems by an arbitrarily small parameter, we state and prove a theorem on the decomposition of an Ordinary Differential Equations (ODE) system without the aforementioned arbitrarily small parameter. In accordance with the proven theorem, we implemented an algorithm to decompose an ODE system into fast and slow subsystems by coordinate transformation. A similar algorithm is called the Singular Perturbed Vector Field (SPVF) algorithm; however, it is not justified by any stated theorem. Since we have not found any theorem to propose a similar ODE decomposition in the literature, we have tried to fill the gap with our theorem and algorithm explanations through examples. Finally, we propose our concept on Marchuk’s infectious diseases model, which allows a different analysis of the original Marchuk’s ODE system with delay.
This study examines whether digital attention can serve as an engagement-based digital attention signal for fintech market performance. Using a revised panel of 70 firm-year observations from seven publicly verifiable fintech and payments firms over 2016-2025, the analysis combines financial outcomes, sector investment indicators, and digital variables related to web traffic, SEO visibility, social media presence, and app popularity. A Digital Attention Index (DAI) was constructed through arithmetic averaging and principal component analysis, with the first component explaining 82.39% of the digital-indicator variance. Fixed Effects models show that the DAI is positively and significantly associated with revenue, market capitalization, and net income, while sector investment is generally weak or insignificant. Out-of-sample validation confirms that panel Fixed Effects specifications outperform pooled OLS, Ridge, and Random Forest models. App popularity is the strongest standalone predictor for revenue and net income, while social media performs best for market capitalization. However, first-difference models weaken most relationships, and Granger tests indicate bidirectional temporal ordering, with financial performance often preceding digital attention. Overall, the findings support the DAI as a useful computational signal of fintech performance, while emphasizing that predictive and causal claims require cautious interpretation.
This paper investigates the design and evaluation of compact convolutional neural networks (CNNs) for keyword spotting (KWS) and acoustic event detection under the stringent constraints of the TinyML paradigm. The research expands upon traditional binary classification approaches by addressing a multi-class acoustic scenario encompassing eight distinct categories: stop, no, go, yes, unknown, silence, noise_ambient, and noise_sudden. The primary objective is to evaluate the feasibility of deploying reliable acoustic detection systems on ultra-low-power microcontrollers for edge computing applications. To this end, five lightweight architectures were developed and benchmarked: AlexNet-Tiny, LeNet-Tiny, MobileNet-Tiny, VGG-Tiny, and CustomCNN-Tiny. The models were trained using Mel-spectrogram features and optimized through INT8 post-training quantization to facilitate embedded deployment. Hardware simulation was conducted targeting the XIAO nRF52840 Sense microcontroller (64 MHz, 256 KB RAM). Experimental results demonstrate that the Gold VGG-Tiny architecture achieves the highest classification accuracy (89.81%), while Silver MobileNet-Tiny provides the superior operational efficiency with the lowest inference latency (0.88 ms) and minimal energy consumption (14.4 & micro;J). Furthermore, the Bronze CustomCNN-Tiny model achieves the most reduced memory footprint (42.9 KB), highlighting its suitability for memory-constrained environments. Statistical validation using Cohen's Kappa, Matthews Correlation Coefficient (MCC), and Area Under the Curve (AUC) confirms the robustness and reliability of the proposed models. The potential application of this system is motivated by acoustic monitoring for the early detection of high-risk situations, such as gender-based violence. Future work will focus on on-device physical validation and real-world deployment in wearable safety electronics.
To ensure the reliable operation of speech systems across diverse environments, noise addition methods have emerged as the standard solution. However, existing methods offer limited coverage of real-world scenes and depend on pre-existing noise libraries and scene metadata. This paper presents prompt-based Dynamic Generative Scene-based Noise Addition (DGSNA), a novel approach driven by generative language models that integrates Dynamic Generation of Scene-based Information (DGSI) with Scene-based Noise Addition for Speech (SNAS). The DGSI module, with a BET (Background, Examples, Task) prompt framework, dynamically generates logic-compliant scene-based information, including scene dimensions, sound sources, and microphone positions, thereby addressing the challenges of scene enumeration and detailed description. Complementing this, the SNAS module employs a Time-Frequency Diffusion-based (TFD) Text-to-Audio model to synthesize scene-specific noise. By integrating this noise with clean speech via Room Impulse Response (RIR) filters, the module streamlines the traditionally labor-intensive process of replicating diverse acoustic environments. Experimental results show that DGSNA significantly enhances the robustness of speech recognition and keyword spotting models, achieving relative improvements of up to 11.32%. Furthermore, DGSNA is highly compatible with existing noise addition techniques.
Nature-inspired optimization algorithms (NIOAs) have attracted enormous attention thanks to their great capabilities in solving complex problems. This paper presents the novel Actiniaria optimization algorithm (ACTOA), inspired by the behavior and biological characteristics of Actiniaria (sea anemones). Actiniaria are known to have unique abilities to survive and interact with various marine environments. Therefore, they can provide an appropriate model for designing an optimization algorithm. This study aimed to balance the exploration and exploitation phases using Actiniaria’s two biological mechanisms: hunting and spawning. The exploration phase is developed with a hunting mechanism as a normal distribution of the searching particles with a reduced standard deviation (SD) around the best searching particle. Next, the dispersal of Actiniaria’s eggs in the exploitation phase under forces such as wind and ocean waves is simulated. The performance of ACTOA is assessed using a set of optimization parameters. The advantages of the algorithm’s performance were also examined by 59 test functions, and ACTOA outperformed modern algorithms. Ultimately, optimization of the three dams of Sariyar, Shafaroud, and Pine Flat was put on the agenda and the proposed algorithm showed that optimal solutions were found by the 700th, 840th, and 985th iterations, which resulted in savings of 28.2, 30, and 3.5 percent in concrete volume, respectively.
