Search Results (7,540)

Sandflies spread the neglected vector-borne disease anthroponotic cutaneous leishmaniasis (ACL), which only affects humans. Despite decades of control, asymptomatic carriers, vector pesticide resistance, and low public awareness prevent eradication. This study proposes a fractional-order optimal control model that integrates biological and behavioral aspects of ACL transmission to better understand its complex dynamics and intervention responses. We model asymptomatic human illnesses, insecticide-resistant sandflies, and a dynamic awareness function under public health campaigns and collective behavioral memory. Four time-dependent control variables—symptomatic treatment, pesticide spraying, bed net use, and awareness promotion—are introduced under a shared budget constraint to reflect public health resource constraints. In addition, Caputo fractional derivatives incorporate memory-dependent processes and hereditary effects, allowing for epidemic and behavioral states to depend on prior infections and interventions; on the other hand, standard integer-order frameworks miss temporal smoothness, delayed responses, and persistence effects from this memory feature, which affect optimal control trajectories. Next, we determine the optimality conditions for fractional-order systems using a generalized Pontryagin’s maximum principle, then solve the state–adjoint equations numerically with an efficient forward–backward sweep approach. Simulations show that fractional (memory-based) dynamics capture behavioral inertia and cumulative public response, improving awareness and treatment efforts. Furthermore, sensitivity tests indicate that integer-order models do not predict the optimal allocation of limited resources, highlighting memory effects in epidemiological decision-making. Consequently, the proposed method provides a realistic and flexible mathematical basis for cost-effective and sustainable ACL control plans in endemic settings, revealing how memory-dependent dynamics may affect disease development and intervention efficiency. Full article

Most machine learning algorithms operate on vectorized data with Euclidean structures because of the significant mathematical advantages offered by Hilbert space, but improved representational efficiency may offset more involved learning on non-Euclidean structures. Recently, a method that integrates the marginalized graph kernel into the Gaussian process regression framework was used to learn directly on molecular graphs. Here, we describe an implementation of this method for crystalline materials based on effective crystal graph representations: the molecular graphs of 128-atom supercells of body-centered cubic (BCC) iron with periodic boundary conditions. Regressors trained on hundreds of time steps of a density functional theory molecular dynamics (DFT-MD) simulation achieved root mean square errors of less than 5 meV/atom. The mechanical stability of BCC iron was investigated at high pressure and elevated temperature using regressors trained on short DFT-MD runs, including at conditions found in the inner core of the earth. Phonon dispersions obtained from the short runs show that BCC iron is mechanically stable at 360 GPa when the temperature is above 2500 K. Atoms in the super cell were displaced in the direction of the first, second, and third nearest-neighbors from selected configurations that included thermal atomic displacements, and forces exerted on the displaced atoms were computed by numerical differentiation of the regressors. Full article

This paper presents research and theoretical development of a mathematical model that, first, allows us to understand how the positional exactitude of the output link of a four-bar mechanism depends on the manufacturing dimensional tolerances. To find this dependence, the total differentials of the kinematic constraint functions that govern the field of positions must be determined for each kinematic cycle of the mechanism under consideration. These total differentials lead to a system of equations whose solution gives the positional errors of the movable output links as a function of the manufacturing dimensional errors and an incidence matrix that varies with each one of the positions of the input element. On the other hand, the theoretical transmission ratio between the output velocities with respect to the input velocity of the articulated kinematic chain is defined, and for determining the total errors in each ratio, the total differential of each one of them is calculated, showing a clear dependence with respect to the positional errors of the output links (previously defined) of the mechanism. The sum of the theoretical transmission ratio and its respective error provides the real transmission ratio. Furthermore, the described methodology allows for determining the sensitivity (influence coefficients) in the transmission ratios due to errors inherent in the link lengths. Finally, the presented analytical approach is numerically implemented through an example of articulated parallelogram design, principally characterizing in graphic form the transmission ratios in their regions of permitted movements and blocking positions, for a specific IT degree of precision of the bilateral dimensional tolerances of their functional geometric parameters, with the objective of analyzing every aspect related to the performance of the mechanisms. This formalism is validated through three particular design cases using a CAD model in a simulation module of kinematic motion analysis; additionally, the evolution of the transmission angle is discussed. The methods and conclusions proposed in this document also leave open the way as future work to study separately the magnitudes and signs of the positional errors and the transmission ratio, or even the influence coefficients themselves, in order to assign the most convenient degree of IT precision for each link in the mechanism with the purpose of reducing errors in the designs and obtain better efficiency in the transmission ratio. Full article

Coordination algorithms are required to minimise congestion when every robot in a robotic swarm has a common target area to visit. Some of these algorithms use artificial potential fields to enable path planning to become distributed and local. An efficiency measure for comparing them is the time to complete a task in relation to the number of individuals in the swarm. To compare distinct solutions as the swarm grows, experiments with different numbers of robots must be simulated to form a plot of the function of the task completion time versus the number of robots or other parameters. Nevertheless, plotting it for many robots through simulation is time-consuming. Additionally, the inference of a global swarm behaviour as the task completion time from the local individual robot motion controller based on potential fields and other dynamical variables is intractable and requires experimental analysis. Based on that, equations are presented and compared with simulation data for estimating the expected task completion time of state-of-the-art algorithms, robots using only attractive and repulsive force fields and mixed teams for the common target area problem in robotic swarms with not only the number of robots as input but also environment- and algorithm-related global variables, such as the size of the common target area and the working area, average speed and average distance between the robots. This paper is a fundamental first step to start a discussion on how better approximations can be achieved and which mathematical theories about local-to-global analysis are better suited to this problem. Full article

(1) Background: This research examines the study of crude oil generation mechanisms in the Diapir Fold Area (exaggerated diapirism alignment) through two representative cases. The geology of the respective area, along with the tectonics and the formation conditions of the hydrocarbons, is presented. (2) Methods: Based on the research of the international study and local research study, the authors simulated two sediment burial models (from the previously mentioned area), suggesting the hydrocarbon generation conditions and tracing the sediment burial curves. (3) Results: Based on these, the depths, the geological ages of the formations generating hydrocarbons, and the time in millions of years were established. (4) Conclusions: A mathematical model based on Artificial Intelligence is presented to resolve an oil generation in a diapirism area. Full article

In response to the high energy consumption and carbon emission issues in the electrolytic aluminum industry, this paper proposes a multi-time-scale optimization and control method for electrolytic aluminum plants with high photovoltaic penetration. First, a plant architecture is established, which includes traditional power systems, renewable energy systems, and electrolytic aluminum loads. A mathematical model for flexible resources such as thermal power units, on-load tap-changing transformers, thyristor-controlled voltage regulators, saturable reactors, and electrolytic cells is developed. Based on this, a two-level optimization control strategy is designed, consisting of a day-ahead and real-time control layer: the day-ahead layer targets economic and low-carbon operation, while the real-time layer aims to stabilize the DC bus voltage. Using actual data from an electrolytic aluminum plant in Southwest China, simulations are conducted on the MATLAB 2021a platform, and the effectiveness of the strategy is verified through hardware-in-the-loop experiments. The results demonstrate that the proposed method can effectively increase the photovoltaic utilization rate, reduce thermal power output and operational costs, and decrease carbon emissions, providing a feasible solution for the green and low-carbon transformation of the electrolytic aluminum industry. Full article

This study presents a novel error model that distinguishes between constant and variable components of systematic error (bias) in measurement systems, particularly within clinical laboratory settings. Traditional approaches often conflict with these components, resulting in miscalculations of total error and measurement uncertainty. Through mathematical deduction and computer simulations, the authors demonstrate that the standard deviation derived from long-term quality control (QC) data includes both random error and the variable bias component, challenging its use as a sole estimator of random error. The proposed model defines the constant component of systematic error (CCSE) as a correctable term, while the variable component (VCSE(t)) behaves as a time-dependent function that cannot be efficiently corrected. The study further reveals that long-term QC data are not normally distributed, contradicting prevailing assumptions in metrology. It advocates for revised definitions in the International Vocabulary of Metrology (VIM3), emphasizing the need to distinguish between bias types determined under different measurement conditions. By applying this refined model, laboratories can enhance decision-making accuracy and more accurately estimate measurement error and uncertainty. The findings have implications beyond clinical laboratories, suggesting a paradigm shift in how systematic error is conceptualized and managed across all domains of metrology. Full article

Cavitation phenomenon in piston pumps not only causes vibration and noise but also leads to component damage. Conventional diagnostic methods suffer from low accuracy, while deep learning approaches lack interpretability. To address these limitations, this paper proposes an intelligent fault diagnosis method based on the rough set Attribute Weighted Convolutional Neural Network (RSAW-CNN). First, based on cavitation mechanisms and the mathematical model, the computational fluid dynamics model of the piston pump is established to simulate the failure condition. Subsequently, employing rough set theory, an original fault decision table is constructed, discretized, and subjected to attribute reduction. A weight matrix is generated according to the importance of each data channel in the classification decision and embedded into the input layer of the Convolutional Neural Network (CNN) to enhance the influence of key features. Decision rules are also extracted to provide interpretable decision support for fault diagnosis. Experimental results demonstrate that the proposed RSAW-CNN method achieves an average diagnostic accuracy of over 99.2%. Compared to the backpropagation neural network, residual neural network, CNN, and the CNN with squeeze-and-excitation networks, its average accuracy has improved by 15.87%, 10.83%, 7.48%, and 5.40%. The proposed method not only exhibits high diagnostic accuracy but also offers strong interpretability and reliability. Full article

To enhance the accuracy and efficiency of reliability analyses for an aero-engine vectoring exhaust nozzle (VEN), a dual-stochastic extreme response surface method based on the genetic algorithm (DSERSM-GA) is developed by integrating the genetic algorithm, the random extremum response surface method, and the dual response surface method in the paper. In the proposed method, a limited set of Monte Carlo samples is strategically utilized to construct and optimize a population-based response surface model, forming a robust mathematical framework for reliability prediction. The uncertainty sources considered include aerodynamic loads acting on the vector nozzle, material densities of the expansion plate and triangular link, as well as the elastic moduli of these components. Stress and deformation responses of both the expansion plate and triangular link are employed as the performance metrics. The proposed DSERSM-GA methodology is validated through dynamic reliability simulations applied to a vector nozzle system, yielding distributions and corresponding reliability indices of critical responses. Comparative analyses against traditional Monte Carlo Simulation (MCS) and conventional Extreme Response Surface Methods (ERSM) demonstrate that the DSERSM-GA significantly reduces computational costs while preserving high predictive accuracy. Full article

This review examines 80 research studies on electric vehicle (EV) range prediction published between 2013 and 2024. We categorized all studies into three methodological groups such as machine learning (ML), mathematical modeling (MM), and simulation modeling (SM). The analysis reveals a clear dominance of ML models (48.8% of studies), followed by simulation models (32.5%), mathematical models (12.5%), and hybrid models (6.2%). Among the ML techniques, Neural Networks (25%), Multiple Linear Regression (17.5%), and Decision Trees (16.25%) were the most frequently employed, highlighting the growing emphasis on data-driven and adaptive methods. While simulation techniques are most prevalent within MM studies. Hybrid models, which integrate multiple methods, are gaining popularity for improving prediction accuracy. We also reviewed performance metrics such as Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) which reflect the diversity of evaluation strategies across the field. We highlight unsolved challenges including robust feature selection, real-time data integration, and battery degradation modeling. Finally, We suggest future research should focus on combining different modeling approaches, using more advanced data-driven methods, and improving reliability through data sharing and collaboration. Full article

Fractional differential equations offer a natural framework for describing systems in which present states are influenced by the past. This work presents a nonlinear Caputo-type fractional differential equation (FDE) with a nonlocal initial condition and attempts to describe a model of memory-dependent behavioral adaptation. The proposed framework uses a fractional-order derivative $\eta \in (0,1)$ to discuss the long-term memory effects. The existence and uniqueness of solutions are demonstrated by Banach’s and Krasnoselskii’s fixed-point theorems. Stability is analyzed through Ulam–Hyers and Ulam–Hyers–Rassias benchmarks, supported by sensitivity results on the kernel structure and fractional order. The model is further employed for behavioral despair and learned helplessness, capturing the role of delayed stimulus feedback in shaping cognitive adaptation. Numerical simulations based on the convolution-based fractional linear multistep (FVI–CQ) and Adams–Bashforth–Moulton (ABM) schemes confirm convergence and accuracy. The proposed setup provides a compact computational and mathematical paradigm for analyzing systems characterized by nonlocal feedback and persistent memory. Full article

Wire rope joints are critical components requiring detailed mechanical analysis. This study investigates the stress/strain characteristics at the joint root under axial impact and combined tension-bending loads. A mathematical model was derived from the rope’s spatial structure, enabling the construction of 3D simulation and finite element models. Explicit dynamic analysis revealed distinct stress evolution patterns. Under axial impact, the joint root wires experience instantaneous peak stress causing core, inner, and outer wire yielding, though stress rapidly decreases and stabilizes. During stable loading, maximum stress (67% of impact peak) occurs on the joint root’s secondary outer wire. Under combined tension-bending, maximum stress dynamically shifts to the tension-side secondary outer wire at the joint root. Critically, both loading conditions identify the joint root’s secondary outer wire as the primary danger zone, with combined tension-bending producing a maximum local stress 1.04 times higher than axial impact. These findings highlight consistent failure locations and quantify relative stress magnitudes under complex loading. Full article

This study addresses developing systematic guidelines for the design of concentration control in the oxidation of benzene to maleic anhydride within a tubular reactor. The influence of step size selection and temperature sensor location on the tuning and performance of a PI/P cascade control system applied to the oxidation process was evaluated. The reactor’s dynamic behavior was analyzed using numerical simulations based on the solution of the Fortran mathematical model. Sensor positions and multiple step sizes (from +10% to −10%) were analyzed to characterize reactor dynamics and optimize control parameters. The results show that a controller design corresponding to a −9% step in the jacket temperature offered the best performance, ensuring process stability and selectivity. In contrast, step changes between +10% and −8% caused temperature deviations beyond safe limits. Since maleic anhydride is an essential precursor in the production of resins, plastics, lubricants, and pharmaceutical intermediates, optimizing the efficiency and safety of its production represents a significant benefit to the global chemical industry. Full article

The angular momentum flowmeter addresses critical challenges in aviation fuel flow measurement during commercial flight operations. This study designed a visualization platform to observe the dynamic responses of internal components under varying flow conditions. By employing the sliding mesh method coupled with an angular momentum algorithm, it enabled the dynamic rotation simulation of the upstream straight-bladed rotor and provided calculation of the deflection angle in the downstream straight-bladed rotor of an angular momentum flowmeter. Experimental results categorize the flow process into three distinct regimes based on flat and spiral spring response states: pre-spring, single-spring, and dual-spring regimes. Under a flow condition of 0.091 kg/s, the upstream straight-bladed rotor maintained stable rotation at a speed of 1.1 rad/s. At a flow rate of 0.20 kg/s, the flat spring initiated outward expansion, and with further increase in flow rate, the rotational speed of the upstream straight-bladed rotor remained within the range of 25.34–26.21 rad/s. Mathematical analysis demonstrates that the flat spring configuration extends the lower measurement limit and promotes dissipation of the secondary vortex through dominant kinetic energy of the primary vortex during dual-spring operation, thereby improving high-pressure zone stability. This work elucidates the operational mechanism of angular momentum flowmeters and provides a theoretical basis for structural optimization. Full article

Dimensionality reduction is fundamental for analyzing high-dimensional data, supporting visualization, denoising, and structure discovery. We present a systematic, large-scale benchmark of three widely used methods—Principal Component Analysis (PCA), Isometric Mapping (Isomap), and t-Distributed Stochastic Neighbor Embedding (t-SNE)—evaluated by average silhouette scores to quantify cluster preservation after embedding. Our full factorial simulation varies sample size $n\in \{100,200,300,400,500\}$, noise variance ${\sigma }^2\in \{0.25,0.5,0.75,1,1.5,2\}$, and feature count $p\in \{20,50,100,200,300,400\}$ under four generative regimes: (1) a linear Gaussian mixture, (2) a linear Student-t mixture with heavy tails, (3) a nonlinear Swiss-roll manifold, and (4) a nonlinear concentric-spheres manifold, each replicated 1000 times per condition. Beyond empirical comparisons, we provide mathematical results that explain the observed rankings: under standard separation and sampling assumptions, PCA maximizes silhouettes for linear, low-rank structure, whereas Isomap dominates on smooth curved manifolds; t-SNE prioritizes local neighborhoods, yielding strong local separation but less reliable global geometry. Empirically, PCA consistently achieves the highest silhouettes for linear structure (Isomap second, t-SNE third); on manifolds the ordering reverses (Isomap > t-SNE > PCA). Increasing ${\sigma }^2$ and adding uninformative dimensions (larger p) degrade all methods, while larger n improves levels and stability. To our knowledge, this is the first integrated study combining a comprehensive factorial simulation across linear and nonlinear regimes with distribution-based summaries (density and violin plots) and supporting theory that predicts method orderings. The results offer clear, practice-oriented guidance: prefer PCA when structure is approximately linear; favor manifold learning—especially Isomap—when curvature is present; and use t-SNE for the exploratory visualization of local neighborhoods. Complete tables and replication materials are provided to facilitate method selection and reproducibility. Full article