This paper applies the updated fuzzy model proposed by Belhadj and Bounani in 2023 to microdata from the National Household Survey (ENAHO) for the province of Trujillo, La Libertad, Peru, to measure monetary poverty. The study demonstrates that this framework offers a more detailed, continuous assessment of poverty levels than traditional binary classifications. By assigning degrees of deprivation to various poverty indicators, the fuzzy approach captures the full intensity of deprivation, uncovering intermediate socioeconomic states that conventional methods systematically overlook. While the official binary classification by INEI categorizes 94.62% of Trujillo’s population as “non-poor,” the fuzzy methodology reveals that only 22.18% experience complete non-deprivation. Crucially, it exposes that 49.94% of the population resides in a state of “mild poverty”—a highly vulnerable segment rendered invisible by standard metrics. District-level disaggregation highlights sharp territorial disparities, ranging from severe structural vulnerability in Florencia de Mora (Fuzzy Poverty Index = 0.428) to consolidated stability in Víctor Larco Herrera (0.288). Ultimately, the fuzzy approach provides a more nuanced and realistic representation of poverty dynamics. This offers crucial insights for policymakers designing targeted poverty-reduction interventions.
Mastitis remains one of the most important infectious diseases affecting dairy cows, with substantial consequences for animal health, milk production, and farm profitability. In this study, we extend a nonlinear SIRS–P compartmental model for mastitis transmission in dairy cows by incorporating sensitivity analysis, optimal control, and cost-effectiveness analysis. The model consists of susceptible, infected, and recovered cow populations together with an environmental pathogen compartment, and accounts for direct cow-to-cow transmission, indirect transmission through environmental contamination, recovery, recurrence of infection, recruitment, and culling. A sensitivity analysis of the basic reproduction number R0 is performed to identify the parameters that most strongly influence mastitis transmission. An optimal control problem is then formulated using time-dependent controls that reduce direct transmission, reduce environmental contamination, and enhance recovery. Pontryagin’s Maximum Principle is applied to derive the optimality system, which is solved numerically using the forward–backward sweep method. Seven intervention strategies are compared through numerical simulations and cost-effectiveness analysis using ACER and ICER. The results indicate that the fully integrated strategy S7, which combines prevention and screening, environmental sanitation, and treatment, provides the largest overall disease reduction. However, Strategy S1, based on direct transmission reduction, offers the most cost-effective allocation of resources for reducing the mastitis infection burden.
In this work, we prove the strong convergence of an inertial iterative scheme to approximate solutions of the equilibrium fixed point problem associated with nonexpansive mappings in Hilbert spaces. Numerical simulations are carried out to examine the performance of the proposed approach. The results indicate that the proposed inertial approach achieves faster convergence when compared with existing comparable iterative schemes. We also investigate how different choices of initial values influence the convergence behavior of our algorithms and we compare these effects with those observed in classical iterative schemes through graphical illustrations. In applications, we used our approach to solve the signal processing problem. We also apply it to a mathematical model describing the spread of an infectious disease, which illustrates its relevance to real-world dynamical systems. Finally, we show that the proposed method can be applied in solving constrained optimization, variational inequality and split feasibility problems which highlight its flexibility and wide applicability.
Electron–positron pair production is one of the fundamental quantum electrodynamical (QED) processes and provides an important framework for investigating photon–matter interactions. In this work, the influence of linear photon polarization on electron–positron pair production in the electromagnetic field of the Be49 nucleus is investigated using both the conventional Bethe–Heitler formalism and its polarization-dependent extension. The differential cross sections are evaluated deterministically in Wolfram Mathematica 13.3 over the intermediate photon-energy range of 400–600 MeV and emission angles between 30° and 90°. The numerical results show that the largest differential cross sections are obtained at an incident photon energy of 400 MeV and an emission angle of 30°. A detailed examination of the angular distributions reveals a local change in the vicinity of 60°, which is interpreted because of the kinematic structure of the Bethe–Heitler formalism rather than a distinct production mechanism. A direct comparison with the conventional Bethe–Heitler model demonstrates that linear photon polarization consistently enhances the differential cross section throughout the investigated kinematic range. These leading-order theoretical results provide a systematic analysis of the combined energy and angular dependence of polarized pair production in the Be49 nucleus and contribute to a deeper understanding of polarization effects in intermediate-energy QED processes.
We study a delayed semilinear evolution equation with a Caputo time derivative and the spectral fractional Dirichlet Laplacian on a bounded connected domain. The model separates two forms of memory: the Caputo operator retains the distributed Volterra history, whereas the nonlinear production samples the single past state u(t−τ). Working in the strongly continuous phase space C0(Ω), we prove local well-posedness, positivity, a sup-norm continuation criterion, and a compatible weak formulation. In the delayed-source case with μ=0, the solution exists globally and remains bounded on every finite time interval, while the first Dirichlet mode admits an explicit recursive sequence of positive lower bounds across successive delay windows. In the dissipative case μ>0, p>q>1, histories satisfying the explicit smallness conditions remain in an invariant order interval and the L2-energy decays at a Mittag–Leffler rate. The scalar computations are presented only as heuristic first-mode surrogate experiments. In addition, an independent spatially resolved sine spectral-Galerkin/L1 computation of the PDE, with temporal and spectral refinement studies, is included as a numerical illustration.
Missing data remain a major challenge in breast cancer research because they can introduce bias, reduce statistical efficiency, and compromise the performance of predictive models. Although numerous imputation techniques have been proposed, their comparative performance under different missing-data mechanisms and their impact on downstream classification remain inadequately understood. This study systematically compared statistical and machine learning-based imputation methods using two publicly available breast cancer datasets representing complementary clinical settings. The methods were evaluated under simulated Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR) mechanisms using both reconstruction accuracy and downstream classification performance. The results showed that no single imputation method consistently achieved the best performance across both datasets. Regularized regression and machine learning-based methods generally outperformed conventional statistical approaches, although the optimal method depended on the characteristics of the dataset. Furthermore, the best-performing imputation methods preserved downstream classification performance despite the introduction of missing data, demonstrating that reconstruction accuracy alone is insufficient for selecting imputation strategies intended for predictive modelling. Overall, the findings highlight the importance of considering dataset characteristics, missing-data mechanisms, and the intended analytical objective when selecting imputation methods. The proposed evaluation framework provides a robust approach for assessing missing-data handling strategies in breast cancer prediction studies and other biomedical machine learning applications.
Suppose that T is a normal spanning tree (depth-first search tree) of a graph G. If e=xy and e′=uv are edges of G, satisfying x≺Tu≺Ty≺Tv, then they are called secant edges of G with respect to T. Suppose that G has no secant edges with respect to T. If T is a path, Ghazal and Al-Mniny proved that the chromatic number is at most 3. We conjecture that there is a positive constant γ such that, for any graph G that has no secant edges with respect to a normal spanning tree T, then χ(G)≤γ. We pose the problem of whether γ=4 suffices. We establish a positive answer in the case where T has at most one node.
Task-evoked EEG can reveal individual differences in cognitive processing, but it also creates a machine-learning challenge: many epochs are recorded from relatively few participants, and evaluation can be misleading if within-subject dependence is ignored. This study compared handcrafted, ROCKET, and EEGNet representations under subject-wise validation for classifying questionnaire-derived Dark Triad profiles from task-onset EEG. Dark Triad traits were assessed with the Dirty Dozen and clustered into four exploratory multivariate profiles using k-means. EEG was recorded during a visual speeded decision task, and epochs were extracted from −200 to 1000 ms around task onset. The final dataset included 1780 retained task-onset epochs from 30 participants. Three representations were evaluated under identical five-fold subject-wise cross-validation: XGBoost with handcrafted EEG features, XGBoost with ROCKET-derived time-series features, and compact EEGNet. All performance estimates were based only on predictions from held-out participants. The handcrafted model achieved balanced accuracy of 60.9%, whereas ROCKET and EEGNet improved performance to 74.3% and 76.2%, respectively, with only a modest difference between the waveform-based representations. A participant-level label-shuffling analysis of the out-of-fold predictions indicated that prediction–label alignment exceeded chance for all models. Across models, the mean probability assigned to the true cluster increased with psychometric cluster centrality, suggesting that borderline profiles were harder to classify. Signed channel-wise ablation of EEGNet suggested distributed model sensitivity, with the largest positive effects over posterior/parietal electrodes. The findings highlight the importance of participant-level validation, EEG signal representation, and psychometric label structure, while emphasizing the need for external validation in larger independent cohorts.
The Rayleigh–Logarithmic distribution provides a useful framework for modelling lifetime data by combining continuous lifetime variability with a logarithmic compounding mechanism. This study introduces a three-parameter Alpha Power Rayleigh–Logarithmic (APRL) distribution by applying the Alpha Power transformation to the classical Rayleigh–Logarithmic model. The additional transformation parameter allows the distributional shape, skewness, tail behaviour, and rate of increase in the hazard function to be adjusted while retaining the underlying structure of the baseline model. Several mathematical and reliability properties of the APRL distribution are derived, including the probability density and cumulative distribution functions, survival and hazard rate functions, quantile function, moments, order statistics, and mean residual life function. Model parameters are estimated by maximum likelihood using a multiple-start numerical optimization procedure, and the finite-sample performance of the estimators is investigated through Monte Carlo simulations under different parameter configurations and sample sizes. The simulation results show that estimation accuracy generally improves with increasing sample size, as reflected by decreasing bias, MSE, and RMSE, although estimation of the transformation parameter may exhibit greater variability for more extreme parameter settings. The practical performance of the APRL distribution is examined using the Aircraft Windshield Failure Times and Breaking Stress of Carbon Fibres datasets. Model comparisons based on information criteria, bootstrap-based goodness-of-fit assessment, and graphical diagnostics show that the APRL distribution provides competitive fits relative to several established lifetime distributions. In addition, mean time to failure and mean residual life analyses illustrate the practical interpretation of the reliability measures derived for the proposed model. Overall, the results support the APRL distribution as a useful alternative for the statistical analysis of lifetime and reliability data.
We study a Camassa–Holm-type equation with a prescribed, time-independent bottom profile, mt+(u+h(x))mx+2uxm+12hx(x)m=0,m=(1−∂x2)u. The model is considered here as a mathematically motivated bottom-modified Camassa–Holm equation. The bottom modifies the transport velocity and the lower-order term is chosen so that the basic momentum balance keeps the same cancellation structure as in the flat-bottom case. We clarify the meaning of a gentle bottom in terms of bounded multiplier norms of the prescribed profile and do not claim a complete asymptotic derivation from the Euler equations. Under suitable regularity assumptions on h, we prove local well-posedness in Sobolev spaces by verifying the hypotheses of Kato’s quasilinear semigroup theorem. We also derive an L2 momentum identity and a continuation criterion based on the integrability of ∥ux∥L∞. The proof of the continuation criterion is strengthened by combining the momentum bound with a high-order Hs energy estimate.
Fractional Brownian motion (fBm) provides a powerful stochastic framework for modeling long-range temporal dependence that cannot be represented by classical Brownian motion. This study presents a numerical and theoretical investigation of constrained fractional Brownian motion with applications to stochastic financial systems. An efficient simulation framework combining Fast Fourier Transform (FFT)-based circulant embedding and Markov Chain Monte Carlo (MCMC) sampling is developed to generate long correlated trajectories under absorbing boundary conditions. The proposed algorithm enables simulations with trajectory lengths up to L = 107 while reducing the computational complexity from O (L3) for direct covariance decomposition to approximately O(L log L). Numerical results accurately reproduce the theoretical autocorrelation function of fBm and confirm the expected persistence behavior governed by the Hurst exponent. Super-diffusive regimes (H > 0.5) exhibit persistent long-range correlations and enhanced survival probabilities, whereas sub-diffusive regimes (H < 0.5) display anti-persistent dynamics and increased boundary absorption. The fractional stochastic volatility formulation captures important characteristics associated with long-memory financial systems, including persistent volatility dynamics and implied-volatility structures. The proposed biophysical-based FFT–MCMC methodology provides an accurate, scalable, and computationally efficient framework for studying constrained fractional stochastic processes and offers a foundation for future investigations of fractional volatility models and related financial applications. A conceptual Adaptive Hurst Momentum framework is briefly discussed as a possible direction for future research.
Acetaldehyde is routinely monitored in neutral alcohol, but pooled precision summaries can obscure changes in performance across the working range. This study evaluated 446 valid GC–FID verification results obtained by three anonymized analysts on two gas chromatographic systems (GC 8890 and GC 7890B) at 0.6, 2.5, and 9.0 mg L−1. The analysis included measured concentration, recovery, relative bias, relative standard deviation (RSD), confidence intervals, and fixed-effect factorial analysis of variance (ANOVA). Mean recoveries for the GC 8890 and GC 7890B systems were 48.7% and 157.2% at 0.6 mg L−1, 92.1% and 124.8% at 2.5 mg L−1, and 92.0% and 103.1% at 9.0 mg L−1, respectively. Recovery RSD decreased from 47.8% and 18.4% at the lowest level to 4.2% and 3.0% at the highest level. Type III ANOVA identified significant verification-level, analyst, GC-system, and interaction effects. A contextual comparison with concentration-matched AOAC Appendix F targets classified both systems as outside the recovery and RSD benchmarks at the lowest level, showed system-specific partial conformity at the middle level, and placed both systems within the screening benchmarks at the highest level. The contribution of the study is an integrated decision framework in which predefined recovery and RSD targets are interpreted together with factorial interactions to determine when results may be pooled and when level- or system-specific control is required.
This paper establishes new Fejér and Hermite–Hadamard-type inequalities for functions of two variables whose mixed second-order partial derivatives satisfy coordinated GA-convexity or coordinated GA-quasi-convexity on a rectangle in the positive quadrant. Our main results are formulated for non-negative continuous weight functions that are not necessarily symmetric with respect to the geometric means of the interval endpoints, thereby extending the classical framework to genuinely asymmetric weights. However, to obtain explicit and sharp integral bounds in certain cases, we also employ a technical lemma that assumes a special symmetric setting where the weight function is symmetric on each coordinate with respect to h1h2 and k1k2. We clearly distinguish which theorems hold for general asymmetric weights and which depend on this symmetry condition. Our findings unify and extend numerous previously known results for both symmetric and non-symmetric weight functions.
The classical Regiomontanus problem asks for the position that maximizes the angle subtended by a fixed line segment, a problem originating in Euclidean geometry and observational astronomy. This work extends the problem to observers constrained to move along a circular path. The solution uses the geometric fact that the optimal viewpoint occurs precisely where the trajectory is tangent to an isoangle circle. This framework unifies configurations both exterior and interior to the circular path. The analytical solution is validated against direct numerical optimization, with agreement exceeding ten decimal places, and the subtended angle is shown to attain a unique maximum along each half of the circular trajectory. In the limit as the radius becomes large, the analytical result reduces to the classical linear case. Beyond its historical interest, a potential extension illustrates how this simple geometric condition can govern optimal viewing and highlights connections to modern imaging and vision systems.
Thehitting time index HT(G) is a recently introduced topological descriptor based on expected hitting times of a random walk on a graph. In this paper, we derive a closed-form formula for HT(G) for broom graphs Bn,d that holds for all parameters 2 <= d <= n-1, HT(Bn,d)=S1+S2+S3+(n-d)& sum;i=1d-1max{A(i),B(i)}, where S1,S2,S3,A(i),B(i) are explicitly defined. For d >= 2 and n >= 4d-8 we derive a simpler cubic polynomial formula in n, HT(Bn,d)=n3+adn2+bdn+cd, with explicitly given coefficients ad,bd,cd depending only on d. We also consider quartic polynomial formulas for special cases.
This technical note aims to present a theoretical analysis for cybertronics engineering (CE) for a class of dynamic supply chains for artificial intelligence (AI)-based products, services or hybrid solutions. The cybertronics-based analysis encompasses three classes of supply chains: (1) energy-based dynamic supply chains (DSC); (2) semiconductor manufacturing and quantum supply chains; and (3) retailing of the AI-based DSC solutions generated. Considering the nonlinear nature of DSC, to provide solutions for products and services based on AI-chained supply chains, novel robust control is addressed via sliding mode control (SMC) with proper stability analysis for the DSC.
Multi-objective optimization plays a fundamental role in solving complex engineering design problems characterized by conflicting objectives and nonlinear constraints. In this study, a novel hybrid optimization algorithm, named Multi-objective Lemurs Optimizer-Backtracking Search Algorithm (MOLOBSA), is proposed to improve the exploration and exploitation capabilities of existing metaheuristic methods. The proposed approach integrates the global exploration ability of the Lemurs Optimizer (LO) with the efficient mutation and crossover mechanisms of the Backtracking Search Algorithm (BSA) within a multi-objective optimization framework. The effectiveness of the proposed algorithm is evaluated using the CEC2020 multimodal multi-objective benchmark suite, where its performance is assessed using the PSP and IGDX performance indicators. In addition, the proposed method was successfully applied to the multi-objective design optimization of an I-beam structure, where the objectives were to minimize the structural weight and the maximum displacement under mechanical constraints. The obtained Pareto solutions exhibit better diversity and improved trade-off characteristics compared with those produced by the baseline algorithm.
This paper investigates recursion operators and nonlocal symmetry structures for the modified Veronese web equation. The novelty of the work lies in the explicit construction of a direct recursion operator and its inverse in the tangent-covering framework. Starting from a compatible linear covering with a spectral parameter, we derive both operators and interpret them as auto-B & auml;cklund transformations for the corresponding linearized equation. We also determine the contact symmetry algebra and compute the action of the two recursion operators on its infinitesimal generators. In particular, the inverse recursion operator produces shadows of nonlocal symmetries associated with conservation-law coverings. These results provide a concrete recursive mechanism for the symmetry space of the modified Veronese web equation and clarify its covering-based nonlocal geometric structure.
Graphical methods of correlation analysis, such as correlation n-ptychs or hotspots, focus on the identification of the strength and direction of functional relationships between sets of attributes in multidimensional datasets. Since these correlation structures only take into account values of the attributes, situations arise when the relationship is coincidental, meaning that there is no real-world causality between the values of the observed attributes but these values still exhibit significant correlation. This problem of correlation analysis as a whole motivates the need for semantic evaluation of significant relationships identified using its methods-a task that could potentially be time- and resource-intensive when conducted manually. However, modern results in the large language model area provide tools for the automatization of such tasks. Hence, this work focuses on the design and implementation of a novel large language model-based method for semantic evaluation of correlation structures embedded in a correlation graph, specifically correlation n-ptychs for n is an element of{3, 4, 5} and correlation hotspots. In the method, the large language model is automatically prompted to assess the semantic nature of relationships in the set of correlation substructures of the dataset, identify their real-world relevance, and visualize the result in the form of a Semantic evaluation card. The proposed approach is evaluated using two benchmarking datasets focusing on the visualization method used in the model, large language model interaction with the correlation substructures, and comparative analysis with previously used tools in the area.
