Search Results (4,004)

Uncertainty-aware decision-making increasingly relies on multimodal sensing pipelines that must fuse correlated measurements, propagate uncertainty, and trigger reliable control actions. This study develops a unified mathematical framework for multimodal data fusion and Bayesian decision-making under uncertainty. The approach integrates adaptive Covariance Intersection (aCI) for correlation-robust sensor fusion, a Gaussian state–space backbone with Kalman filtering, heteroskedastic Bayesian regression with full posterior sampling via an affine-invariant MCMC sampler, and a Bayesian likelihood-ratio test (LRT) coupled to a risk-sensitive proportional–derivative (PD) control law. Theoretical guarantees are provided by bounding the state covariance under stability conditions, establishing convexity of the aCI weight optimization on the simplex, and deriving a Bayes-risk-optimal decision threshold for the LRT under symmetric Gaussian likelihoods. A proof-of-concept agro-environmental decision-support application is considered, where heterogeneous data streams (IoT soil sensors, meteorological stations, and drone-derived vegetation indices) are fused to generate early-warning alarms for crop stress and to adapt irrigation and fertilization inputs. The proposed pipeline reduces predictive variance and sharpens posterior credible intervals (up to 34% narrower 95% intervals and 44% lower NLL/Brier score under heteroskedastic modeling), while a Bayesian uncertainty-aware controller achieves 14.2% lower water usage and 35.5% fewer false stress alarms compared to a rule-based strategy. The framework is mathematically grounded yet domain-independent, providing a probabilistic pipeline that propagates uncertainty from raw multimodal data to operational control actions, and can be transferred beyond agriculture to robotics, signal processing, and environmental monitoring applications. Full article

To meet stringent efficiency and environmental targets, future gas turbines require increased turbine inlet temperatures while maintaining low NO${}_x$ emissions and accommodating hydrogen-blended fuels. Axially staged combustion has emerged as a key technology to address these challenges. This paper presents a mathematical model for the rapid prediction of NO emissions in axially staged combustors fueled with hydrogen-blended methane. The model integrates a simplified thermal NO mechanism with a set of dimensionless staging variables, providing a unified description of flow, mixing, and reaction processes. Its accuracy was validated against a detailed chemical reaction network (CRN). The model was applied to identify feasible low-emission staging windows across different hydrogen-blending ratios and to systematically analyze the effects of secondary-stage mixing quality, operating parameters, and fuel composition on optimal staging and emissions. Results demonstrate that coordinating the combustion strategies of the primary and secondary stages enables effective NO control across a wide fuel range. This work provides a theoretical foundation for the design of low-emission, fuel-flexible axially staged combustors. Full article

Addressing the difficulty of intuitively identifying and effectively correcting induced heave error in multibeam measurements, this paper proposes a two-stage methodology comprising error identification and correction. This scheme includes an error discrimination method based on regression diagnostics and an error correction method based on Partial Least Squares Regression (PLSR). By establishing a mathematical model between bathymetric discrepancies and attitude parameters, statistical diagnosis and effective identification of the error are achieved. To further mitigate the impact of induced heave error on bathymetric data, an elimination model based on PLSR is developed, enabling high-precision prediction and compensation of the induced heave error. Validation using field survey data demonstrates that this method can effectively estimate the installation offset parameters of the attitude sensor. After correction, the root mean square of bathymetric discrepancies between adjacent survey lines is reduced by approximately 78.8%, periodic stripe-shaped distortions along the track direction are essentially eliminated, and the quality of terrain mosaicking is significantly improved. This provides an effective solution for controlling induced heave error under complex topographic conditions. Full article

This paper develops a mathematically grounded neuro-fuzzy control framework for IoT-enabled irrigation systems in precision agriculture. A discrete-time, physically motivated model of soil moisture is formulated to capture the nonlinear water dynamics driven by evapotranspiration, irrigation, and drainage in the crop root zone. A Mamdani-type fuzzy controller is designed to approximate the optimal irrigation strategy, and an equivalent Takagi–Sugeno (TS) representation is derived, enabling a rigorous stability analysis based on Input-to-State Stability (ISS) theory and Linear Matrix Inequalities (LMIs). Online parameter estimation is performed using a Recursive Least Squares (RLS) algorithm applied to real IoT field data collected from a drip-irrigated orchard. To enhance prediction accuracy and long-term adaptability, the fuzzy controller is augmented with lightweight artificial neural network (ANN) modules for evapotranspiration estimation and slow adaptation of membership-function parameters. This work provides one of the first mathematically certified neuro-fuzzy irrigation controllers integrating ANN-based estimation with Input-to-State Stability (ISS) and LMI-based stability guarantees. Under mild Lipschitz continuity and boundedness assumptions, the resulting neuro-fuzzy closed-loop system is proven to be uniformly ultimately bounded. Experimental validation in an operational IoT setup demonstrates accurate soil-moisture regulation, with a tracking error below 2%, and approximately 28% reduction in water consumption compared to fixed-schedule irrigation. The proposed framework is validated on a real IoT deployment and positioned relative to existing intelligent irrigation approaches. Full article

With the rapid development of industries, hard sealing ball valves are increasingly adopted in extreme working conditions, especially for the advantage of high sealing performance. However, current research works on ball valves are lack of leakage rate prediction, which is an important issue. In this paper, a typical hard sealing ball valve is selected as the research object. Mathematical equations for sealing pressure are derived on both fixed and floating ball valves. The sealing pressure on the hard sealing side of the ball valve is analyzed, and the accuracy of the theoretical equation is verified. Meanwhile, the relationship between sealing performance factor and sealing pressure is fitted, and a prediction method of hard sealing ball valve is proposed, and also is validated experimentally. Results indicate that the sealing pressure obtained from the theoretical equation is conservative, as the actual pressure on the sealing surface exhibits a U-shaped distribution. The sealing performance factor varies with sealing pressure according to a piecewise function. It increases in the form of a power function when the pressure is less than 110 MPa and decreases in the form of a quadratic function when the pressure is higher than 110 MPa. The R² of the fitting equation is greater than 0.98%. Furthermore, the theoretical predictions are consistent with the experimental results in magnitude, confirming the reliability of the proposed prediction method. When the roughness is below 0.2, further reduction in the roughness has little effect on the sealing performance. Both roughness and sealing pressure should be considered comprehensively to enhance sealing performance. This work can benefit the leakage rate prediction and further study for the sealing performance improvement of hard sealing ball valves. Full article

This study establishes a comprehensive structural isomorphism between Conway’s Game of Life and the entrepreneurial process, analysing the latter as a complex adaptive system governed by non-linear dynamics rather than linear predictability. Through a rigorous qualitative approach based on a systematic literature review and abductive inference, the research identifies and correlates four fundamental dimensions: uncertainty, adaptability, growth, and sustainability. Transcending traditional metaphorical comparisons, this paper introduces a novel mathematical model that modifies Conway’s deterministic logic by incorporating an «Agency» variable (A). This critical addition quantifies how an entrepreneur’s internal capabilities can counterbalance environmental pressures (neighbourhood density) to determine survival thresholds, effectively transforming the simulation into a «Game of Life with Agency» where participants actively influence their viability potential (Ψ). The analysis explicitly correlates specific algorithmic configurations with real-world business phenomena: high-entropy initial states («The Soup») mirror early-stage market uncertainty where outcomes are probabilistic; «gliders» represent the necessity of strategic pivoting and continuous displacement for survival; and «oscillators» symbolise dynamic sustainability through rhythmic equilibrium rather than static permanence. Furthermore, the study validates the «Gosper Glider Gun» pattern as a model for scalable, generative growth. By bridging abstract systems theory with managerial practice, the research positions these simulations as «mental laboratories» for decision-making. The findings theoretically validate iterative methodologies like the Lean Startup and conclude that successful entrepreneurship operates on the «Edge of Chaos», providing a rigorous framework for navigating high stochastic uncertainty. Full article

Financial crises increasingly exhibit complex, interconnected patterns that traditional risk models fail to capture. The 2008 global financial crisis, 2020 pandemic shock, and recent banking sector stress events demonstrate how systemic risks propagate through multiple channels simultaneously—e.g., network contagion, extreme co-movements, and information cascades—creating a multidimensional phenomenon that exceeds the capabilities of conventional actuarial or econometric approaches alone. This paper addresses the fundamental challenge of modeling this multidimensional systemic risk phenomenon by proposing a mathematically formalized three-tier integration framework that achieves 19.2% accuracy improvement over traditional models through the following: (1) dynamic network-copula coupling that captures 35% more tail dependencies than static approaches, (2) semantic-temporal alignment of textual signals with network evolution, and (3) economically optimized threshold calibration reducing false positives by 35% while maintaining 85% crisis detection sensitivity. Empirical validation on historical data (2000–2023) demonstrates significant improvements over traditional models: 19.2% increase in predictive accuracy (R² from 0.68 to 0.87), 2.7 months earlier crisis detection compared to Basel III credit-to-GDP indicators, and 35% reduction in false positive rates while maintaining 85% crisis detection sensitivity. Case studies of the 2008 crisis and 2020 market turbulence illustrate the model’s ability to identify subtle precursor signals through integrated analysis of network structure evolution and semantic changes in regulatory communications. These advances provide financial regulators and institutions with enhanced tools for macroprudential supervision and countercyclical capital buffer calibration, strengthening financial system resilience against multifaceted systemic risks. Full article

Landslide dams, typically composed of newly deposited, loose, and heterogeneous materials, are highly susceptible to failure induced by overtopping and seepage, particularly under extreme hydrological conditions. Accurate prediction of such breaching processes is essential for flood risk management and emergency response, yet existing models generally consider only a single failure mechanism. This study develops a mathematical model to simulate landslide dam breaching under the coupled action of overtopping and seepage erosion. The model integrates surface erosion and internal erosion processes within a unified framework and employs a stable time-stepping numerical scheme. Application to three real-world landslide dam cases demonstrates that the model successfully reproduces key breaching characteristics across overtopping-only, seepage-only, and coupled erosion scenarios. The simulated breach hydrographs, reservoir water levels, and breach geometries show good agreement with field observations, with peak outflow and breach timing predicted with errors generally within approximately 5%. Sensitivity analysis further indicates that the model is robust to geometric uncertainties, as variations in breach outcomes remain smaller than the imposed parameter perturbations. These results confirm that explicitly accounting for the coupled interaction between overtopping and seepage significantly improves the representation of complex breaching processes. The proposed model therefore provides a reliable computational tool for analyzing landslide dam failures and supports more accurate hazard assessment under multi-mechanism erosion conditions. Full article

The Spanish conquest of the Inca empire in the early 16th century stands as one of the most striking examples of asymmetric historical collapse. In this paper, a simplified mathematical formulation is developed being inspired by Lotka–Volterra dynamics to describe, in a stylized quantitative manner, the interactions between the Inca state and the invading Spanish forces. The model is not intended to explain the historical events in a causal or predictive sense, but rather to capture and represent key mechanisms commonly identified in historical analyses. These include the demographic and political weakening caused by smallpox epidemics prior to direct contact, the internal fragmentation produced by the civil war and the introduction of external shocks such as the capture of Atahualpa and the fall of Cusco. Although intentionally minimalistic, the framework provides a dynamical illustration of how combined internal and external pressures can destabilize a complex society. This descriptive perspective situates the Inca collapse within the broader conceptual language of complex systems, emphasizing how nonlinear interactions, feedback and structural asymmetry shape trajectories of resilience and failure. Full article

Radial piston motors are expected to expand their applications in hydraulic drive systems due to their high torque density and mechanical robustness. However, its volumetric efficiency can be significantly affected by the multi-stroke operating characteristics and leakage occurring in the micro-clearances of the valve plate. In this study, a detailed modeling procedure for a multi-stroke radial piston motor is proposed using the 1D system simulation software Amesim. In particular, the dynamic interaction between the ports and pistons inside the motor is formulated using mathematical function-based expressions, enabling a more precise representation of the driving behavior and torque generation process. Furthermore, to characterize the leakage flow occurring in the micro-clearance between the fluid distributor and cylinder housing, the commercial CFD software Simerics MP+ was employed to analyze the three-dimensional flow characteristics within the leakage gap. Based on these CFD results, a leakage-path function was constructed and implemented in the Amesim model. As a result, the developed model exhibited strong agreement with reference data from an actual motor in terms of overall operating performance, including volumetric and mechanical efficiencies while consistently reproducing the leakage behavior observed in the CFD analysis. The simulation approach presented in this study demonstrates the capability to reliably capture complex fluid–mechanical interactions at the system level, and it can serve as an effective tool for performance prediction and optimal design of hydraulic motors. Full article

This investigation focuses on optimising the milling processes of white quinoa (Chenopodium quinoa Willd.) to enhance its industrial applications. Three milling technologies—knife, disc, and ball milling—were employed to produce flours characterised by various physicochemical analyses. The granulometric analysis indicated that ball milling achieved the finest particle size distribution, significantly improving water absorption capacity and dispersion. Mathematical modelling confirmed that the Rosin–Rammler–Bennett model provided superior predictive capability for rheological behaviour (R² > 0.9624). X-ray diffraction revealed a reduction in crystallinity as milling progressed, while differential scanning calorimetry indicated a decrease in gelatinisation enthalpy and temperature range, suggesting enhanced thermal processing efficiency. Ball milling of the quinoa flour resulted in marked structural changes, as observed by electron microscopy, which are associated in the literature with potential benefits for technological applications in gluten-free and health-oriented foods. Furthermore, fractionation of the flours yielded nutrient-rich bran, containing high levels of protein and fibre. These findings establish critical processing–structure–function relationships, promoting the scalable production of high-value quinoa ingredients that cater to the increasing demand for sustainable and health-oriented food solutions. Full article

Background/Objectives: Mathematical modelling provides a quantitative way to describe the fate and action of drugs in the oral cavity, where transport processes are shaped by salivary flow, pellicle formation, biofilm structure and the wash-out effect of gingival crevicular fluid (GCF). Local pharmacokinetics in the mouth differ substantially from systemic models, and therefore a dedicated framework is required. The aim of this work was to present a structured, physiologically based concept that links in vitro release testing with local pharmacokinetics and pharmacodynamics. Methods: A narrative review with elements of systematic search was conducted in PubMed, Scopus and Web of Science (1980–2025) for publications describing drug release, local PBPK, and PK/PD modelling in the oral cavity. Mathematical formulations were grouped into release kinetics, mini-PBPK transport and local PK/PD relations. Classical models (Higuchi, Korsmeyer–Peppas, Peppas–Sahlin) were integrated with a mini-PBPK structure describing saliva–mucosa–biofilm–pocket interactions. Results: The combined model captures adsorption to pellicle, diffusion within biofilm and wash-out by GCF. It allows simulation of variable clinical conditions, such as inflammation-related changes in Q_GCF, and links local exposure to pharmacodynamic outcomes. Case studies with PerioChip^®, Arestin^®, and Atridox^® demonstrate how mechanistic models explain observed therapeutic duration and low-systemic exposure. Conclusions: The proposed mini-PBPK framework bridges empirical release data and physiological transport in the oral cavity. It supports rational formulation design, optimisation of local dosage, and personalised prediction of drug retention in gingival pockets. This modelling approach can become a practical tool for the development of dental biomaterials and subgingival therapies. Full article

To enhance desalination efficiency and reduce experimental costs, the development of advanced mathematical models for EMS is essential. In this study, we propose a novel hybrid approach that integrates neural networks with high-accuracy numerical simulations of electroconvection. Based on dimensionless similarity criteria (Reynolds, Péclet numbers, etc.), we establish functional relationships between critical parameters, such as the dimensionless electroconvective vortex diameter and the plateau length of current–voltage curves. Training datasets were generated through extensive numerical experiments using our in-house developed mathematical model, while multilayer feedforward neural networks with backpropagation optimization were employed for regression tasks. The resulting AI (artificial intelligence)-driven hybrid models enable rapid prediction and optimization of EMS design and operating parameters, reducing computational and experimental costs. This research is situated at the intersection of membrane science, artificial intelligence, and computational modeling, forming part of a broader foresight agenda aimed at developing next-generation intelligent membranes and adaptive control strategies for sustainable water treatment. The methodology provides a scalable framework for integrating physically based modeling and machine learning into the design of high-performance electromembrane systems. Full article

In fixed orthodontic treatment, brackets are orthodontic attachments bonded to the tooth enamel, and their placement and removal may affect the underlying enamel surface. Enamel degradation is a critical factor for oral health, as it reduces the mechanical strength of teeth and increases susceptibility to caries and erosion. Accurate diagnosis of enamel changes is therefore essential for the evaluation of preventive and restorative treatments. In this study, enamel degradation was investigated via two integrated methods: energy-dispersive X-ray spectroscopy (EDS) and surface roughness measurement. The experimental protocol was performed in three stages: before bracket bonding, after bracket removal, and after applying a remineralization treatment. The experimental design included a repeated-measures structure, with stage (baseline, post-debonding, post-remineralization) as the within-tooth factor and bracket type (sapphire vs. metallic) as the between-tooth factor. Given the violation of the variance homogeneity assumption, group comparisons were ultimately performed using Welch ANOVA followed by Games–Howell post hoc tests, with Bonferroni-adjusted values used for pairwise comparisons. The presence of orthodontic brackets can influence enamel mineralization because the bonding and debonding procedures modify the enamel surface microtopography. These procedures can generate microcracks and surface irregularities, which may affect mineral exchange between enamel and the surrounding environment. In our study, bracket removal led to a significant decrease in the mean atomic percentages of Ca (from 32.65% to 16.37% for sapphire) and P (from 16.35% to 8.60% for sapphire), accompanied by a sharp increase in surface roughness. After remineralization, Ca and P levels increased, while roughness decreased. However, neither the mineral content nor the surface topography fully returned to the initial values, indicating that remineralization achieved only a partial recovery of enamel integrity. These findings highlight that the integrated EDS approach and roughness analysis offer a promising descriptive framework for assessing enamel degradation and monitoring the effectiveness of remineralization therapies. The generated mathematical model provides a powerful descriptive framework for the in vitro data obtained, correlating roughness with mineral composition and treatment stage. However, such a high goodness-of-fit (R² > 0.98) should be interpreted cautiously due to the risk of overfitting. Therefore, rigorous external validation is mandatory before this model can be considered a reliable predictive tool. It also highlights the importance of enamel remineralization therapies after orthodontic treatment, but also the importance of choosing personalized treatment strategies adapted to the enamel type. Full article

This work presents an advanced electro-physical model for hydrogenated amorphous silicon (a-Si:H) Junction Field Effect Transistors (JFETs) to enable the design of devices with energy-efficient analog interface building blocks for Lab-on-Chip (LoC) systems. The presence of this device can support monolithic integration with thin-film sensors and circuit-level design through a validated compact formulation. The model accurately describes the behavior of a-Si:H JFETs addressing key physical phenomena, such as the channel thickness dependence on the gate-source voltage when the channel approaches full depletion. A comprehensive framework was developed, integrating experimental data and mathematical refinements to ensure robust predictions of JFET performance across operating regimes, including the transition toward full depletion and the associated current-limiting behavior. The model was validated through a broad set of fabricated devices, demonstrating excellent agreement with experimental data in both the linear and saturation regions. Specifically, the validation was carried out at 25 °C on 15 fabricated JFET configurations (12 nominally identical devices per configuration), using the mean characteristics of 9 devices with standard-deviation error bars. In the investigated bias range, the devices operate in a sub-µA regime (up to several hundred nA), which naturally supports µW-level dissipation for low-power interfaces. This work provides a compact, experimentally validated modeling basis for the design and optimization of a-Si:H JFET-based LoC front-end/readout circuits within technology-constrained and energy-efficient operating conditions. Full article