Search Results (1,911)

Self-organized criticality (SOC) describes a class of dynamical systems that may evolve toward statistically critical states characterized by scale-free avalanche-like events. In this work, we study an SOC-inspired discrete toy model and examine the avalanche-size statistics generated by local stochastic interactions. The aim is to explore whether a minimal avalanche model can reproduce statistical features that are formally reminiscent of multiscale turbulent phenomenology. We present a mathematical formulation of the toy model, analyze its numerical avalanche-size distribution, and discuss its relation to concepts of scaling, intermittency, and energy cascades in turbulence. The comparison with Navier–Stokes turbulence is therefore interpreted as a qualitative and statistical analogy, not as a physically complete correspondence. The results suggest that SOC-inspired toy models can provide a useful exploratory framework for understanding heavy-tailed activity and multiscale organization. Full article

We present a novel framework for modeling reaction time distributions in the context of video games aimed at providing a performance tool to support the design of new levels. Modern games generate rich behavioral telemetry (including reaction times, success rates, and interaction patterns) that can be leveraged to understand player behavior and inform adaptive game design. Given a set of general parameters describing a newly designed level, the framework predicts the corresponding reaction time distribution, offering actionable insight during the design process. To address this problem, we employ a combination of statistical fitting via maximum likelihood estimation, weighted approximations, and Lipschitz-based estimators in Wasserstein space. This mathematical framework establishes the groundwork for future AI-based extensions, using metric-space learning to predict distributions for unseen level configurations. The methodology provides theoretical guarantees under mild mathematical assumptions, ensuring bounded estimation errors through the assumption of Lipschitz continuity. Three approaches are proposed, all grounded in a Lipschitz characterization of the metric model parameters, which embeds the vector representation of levels into the 1-Wasserstein space of reaction time distributions. The practical applicability of the framework is demonstrated on a dataset of 480 gameplay observations across 24 participants and 20 distinct trials, testing all three fitting procedures on a set of representative examples. Full article

This paper introduces a random activation framework for cure rate modeling that provides a novel latent mechanistic interpretation of the standard mixture cure model, utilizing a Waring-distributed number of latent causes. The proposed approach represents unobserved heterogeneity through a discrete latent variable interpreted as the number of potential risk factors, providing a flexible and biologically interpretable characterization of individual susceptibility. In contrast to classical competing risks models based on extremal operators or deterministic activation schemes, the event time is assumed to arise from a stochastic selection among latent causes. This random activation mechanism defines a unified probabilistic framework in which the cure fraction emerges naturally as the probability of having zero latent causes. The Waring distribution is adopted to model the latent count structure due to its hierarchical formulation, which accommodates overdispersion and heavy-tailed behavior strictly within the latent parametrization of individual risk factors. Under this framework, while the population survival function mathematically reduces to the classical mixture cure representation, the model provides an alternative structure where covariates directly impact the expected latent burden. Parameter estimation for the identifiable regression structure is performed via maximum likelihood, and the finite-sample performance of the estimators is assessed through Monte Carlo simulations, showing accurate parameter recovery and stable inferential properties. An application to real survival data illustrates the practical relevance and epidemiological interpretability of the proposed framework. Overall, this work extends the understanding of existing cure rate models by integrating latent count structures and stochastic activation within a coherent setting, providing a powerful interpretation tool for heterogeneous survival data with long-term survivors. Full article

Soil is the principal physical space for water conservation (WC), so analyzing the driving forces of soil on WC is significant for studying WC services and integrated environmental management. Guangdong Province, a major economic province in China, was taken as a research case to deeply analyze the spatiotemporal pattern of WC function from 2000 to 2020 with InVEST, and to reveal its soil driving forces using a classical mathematical statistics method. We found that, from 2000 to 2020, the WC functions in Guangdong Province exhibited significant spatiotemporal differences. High-value regions were mainly concentrated in the northern and western mountainous regions, while low-value areas were primarily in the Pearl River Delta. The total WC in Guangdong showed a fluctuating upward trend, with 10.71% of its area experiencing extremely significant improvement in the Pearl River Delta, followed by Northern Guangdong. Moreover, WC is influenced by the types and distribution areas of different soils. Red soil has the highest WC depth and volume, followed by paddy soil, while lateritic red soil has the lowest WC depth. Furthermore, soil components exhibited complex stratified relationships with precipitation-normalized WC (PNWC). Components characterized by cation exchange capacity (CEC), pH, and total exchangeable bases (TEB) were positively associated with PNWC, whereas aluminum saturation (ALSA) showed a negative association within the corresponding soil components. The findings provide an important scientific basis for the ecological governance of ecosystem WC functions and water resource management. Full article

The problem of bilevel decision-making under multi-expert uncertain information is addressed in this paper. Traditional fuzzy bilevel models are unable to accurately quantify expert consensus and capture evaluation hesitation. To overcome these limitations, a fully hesitant fuzzy bilevel linear programming model is proposed, in which all coefficients and decision variables are characterized by hesitant fuzzy numbers. By virtue of $(\alpha ,k)$-cuts, the original model is equivalently transformed into an interval-valued bilevel programming problem and further decomposed into best–best and worst–worst sub-models to derive the upper and lower bounds of optimal solutions. Under the Slater constraint qualification, Karush–Kuhn–Tucker (KKT) conditions are adopted to convert the two sub-models into single-level mathematical programs with complementarity constraints (MPCCs), thereby enabling efficient model solving. The proposed method is applied to the resource allocation problem in quantum communication networks. The numerical results demonstrate that the optimal solution interval converges to a unique core value as the membership-level $\alpha$ increases, while a larger consensus parameter k reduces the fuzzy support set without altering the core solution. Full article

The control of micro energy grids (MEGs) is characterized by volatility, uncertainty, and decentralization. Traditional power distribution algorithms, designed for centralized, dispatchable generators, are inadequate for MEG environments. Controllable load management provides peak shaving, load balancing, frequency regulation, and voltage stability, as well as fast balancing services for renewable energy grids in distributed power systems. A non-grid-tied inverter costs a fraction of its grid-tied counterpart for the same capacity. In the initial setting, one or more inverters are used. As the demand grows, more non-grid-tied inverters are added to the mix. Non-grid-tied inverters cannot be connected in parallel. There is no practical solution available in the market for the optimum utilization of this type of setting. Unlike a grid-tied microgrid, in non-grid-tied mode, a microgrid uses grid power only when needed, prioritizing renewable sources. This paper explores autonomous strategies for controlling and coordinating multiple renewable energy sources in MEG settings. It reviews and develops an algorithmic framework for optimal load distribution among multiple renewable sources, including solar photovoltaic (PV), wind turbines, and battery energy storage systems (BESSs). The proposed framework integrates resource forecasting, multi-objective optimization, and adaptive supervisory control to ensure stability, maximize renewable penetration, and minimize operational costs. Performance considerations, mathematical modelling, and potential implementation architectures are discussed. A hybrid approach, combining multiple algorithms, is therefore proposed. In this paper a real-life solution is proposed to a real-life problem. Full article

Microplastics, MPs, plastic particles with dimensions between 0.1 and 5 mm, represent an important environmental pollutant. The removal of microplastics from natural and wastewater is a challenging research topic. In this regard, high-performance technical solutions must be identified, which can be based on existing treatment and purification technologies, to ensure their removal at concentration values in accordance with the legislation in force. In this study, the efficiency of removing some fractions of polyurethane microplastics, with dimensions smaller than 500 µm, from aqueous synthetic solutions with a concentration of 0.2 g L⁻¹, i.e., around 175 NTU, was evaluated. In the first stage of the study, the doses of coagulants and flocculants effective for the removal of microplastics were identified through the Jar Test. The variation in turbidity and their removal efficiencies were evaluated in the presence of classic coagulants, such as aluminum sulfate, Al₂(SO₄)₃·18H₂O, SA; iron sulfate (ferrous sulfate), FeSO₄, IS; polyaluminum chloride, [Al₂(OH)_nCl_6−n], PAC; Aloe Vera, AV, a flocculant; and activated carbon, AC, of the Norit GAC 830 W type. Classic coagulants, such as aluminum sulfate, have a good efficiency in removing microplastics, being able to provide a residual turbidity in the range of 6–10 NTU after a retention time of 50–60 min. In the second stage of the study, the removal efficiency of microplastics was tested using a laboratory pilot plant—called in the study the Smart Decantation-Filtration System, SDFS. The efficiency of the decanter was studied using Response Surface Methodology (RSM) to identify mathematical models that characterize the influence of key process variables: flow rate (A), microplastic size (B) and aluminum sulfate concentration (C) on microplastic removal efficiency. Sedimentation in the specially constructed decanter can raise the optimal value of the removal efficiency of polyurethane microplastics to 98.98%, and filtration can ensure an efficiency that reaches over 99.5%. Through this research, we aimed to identify viable solutions that can be applied to remove microplastics, MPs, from natural and wastewater. A novel element is the fact that we chose to study the removal of polyurethane, which is studied little in the literature. We identified the optimal doses of coagulants and flocculants that help sedimentation of MPs. The efficiency of an installation called Smart Decantation-Filtration System, specially designed to ensure increased efficiency in the removal of microplastics, was determined. The results obtained were encouraging. Full article

Even before the discovery of DNA, Claude Shannon developed a mathematical model of Mendelian inheritance. Unlike the widely recognized Hardy–Weinberg equilibrium, Shannon’s genetic algebra has received little scholarly attention. Here, we revisit Shannon’s algebra and develop two complementary extensions for modern population genetics. First, we formulate a finite population version of Shannon’s framework, moving beyond the idealized infinite population setting to propagate allelic and genotypic frequencies under realistic sampling conditions. Second, we combine Shannon’s algebra with an analytical genotype–phenotype mapping framework to characterize genotypic configurations compatible with observed phenotypic frequencies, using auxiliary variables to express the inherent degeneracy of the genotype–phenotype relationship. Together, these extensions provide a unified framework in which phenotypic observations constrain the underlying genetic structure, and these constraints are propagated through inheritance via Shannon’s algebra. The resulting analytical expressions for offspring phenotypic distributions apply to both complete and incomplete penetrance and extend naturally to multilocus systems. This work highlights Shannon’s algebra as a flexible analytical tool for two complementary problems: (i) forward propagation of genetic information in finite populations, and (ii) analytical description of phenotypic inheritance from inferred genotypic information. Full article

The main objective of this study is to investigate smoking dynamics, identify the most influential factors governing smoking behavior, and develop effective intervention strategies through the integration of fractional-order modeling, sensitivity analysis, optimal control theory, and artificial neural networks (ANNs). A nonlinear fractional-order compartmental model is formulated by dividing the population into potential smokers, light smokers, heavy smokers, and quit smokers. The smoking reproduction number is derived to characterize the transmission and persistence of smoking behavior within the population. To determine the impact of model parameters on smoking dynamics, both normalized forward sensitivity analysis and global sensitivity analysis based on Latin Hypercube Sampling (LHS) with Partial Rank Correlation Coefficient (PRCC) are performed. The obtained results identify the most sensitive transmission and progression parameters and demonstrate their important role in shaping smoking prevalence within the community. Furthermore, the classical integer-order model is compared with the fractional-order formulation, where the fractional model provides a more realistic description due to its ability to incorporate memory and hereditary effects associated with smoking behavior. An optimal control framework involving awareness and treatment strategies is further introduced to investigate effective smoking reduction policies. The numerical results demonstrate that awareness campaigns reduce smoking initiation, while treatment interventions increase smoking cessation, and the combined implementation of both strategies produces the most significant reduction in smoking prevalence. The consistency between the sensitivity analysis and optimal control results further supports the reliability of the proposed framework. Numerical simulations are carried out to analyze the qualitative and quantitative behavior of the system under different epidemiological scenarios. In addition, an ANN-based computational framework is employed as an efficient numerical tool to accurately approximate the complex dynamics of the proposed fractional-order smoking model with very low prediction error. Overall, the present study provides a comprehensive mathematical and computational framework for understanding, analyzing, and controlling smoking behavior within a population. Full article

This study investigates non-isothermal laminar flow of waxy crude oil in a pipe. Due to heat exchange with the surroundings, the flow cools along the pipe length, resulting in a gradual transformation of the oil rheology from Newtonian to viscoplastic behavior. The mathematical model is based on the generalized Navier–Stokes equations coupled with the Shvedov–Bingham rheological model and the effective viscosity approach. The governing equations were solved numerically using the control volume method in the velocity–pressure formulation. The numerical simulations produced velocity, temperature, and effective viscosity fields, as well as pressure-drop data characterizing the rheological state of the waxy crude oil throughout the pipe flow domain. It was established that, in the central region of the inlet flow, the oil retains Newtonian behavior, whereas viscoplastic behavior begins to develop near the pipe wall. Further downstream, the flow progressively transforms into a viscoplastic state over the entire pipe cross-section, accompanied by the formation of stagnant near-wall regions and a plug-flow core. Full article

Studying Bingham flows in permeable media under a periodic magnetic field enhances the understanding of yield-stress fluids for applications like oil recovery and filtration. This study combines non-Newtonian behavior with porous-medium resistance and magnetic variations, facilitating the analysis of complex flow phenomena, including oscillatory yielding and improved flow control in porous structures. The viscous potential theory is employed to streamline the mathematical processes. The utilization of linear governing partial differential equations of motion, along with appropriate nonlinear boundary conditions, yields additional simplifications. The investigation yields a nonlinear Mathieu oscillator that governs the interfacial displacement. A non-perturbative method is used to convert this nonlinear ordinary differential equation into a linear equation. A non-dimensional formulation minimizes the fundamental variables required to characterize the system by establishing a collection of dimensionless physical characteristics. The study analyzes a nonlinear Mathieu oscillator with complex coefficients to explore system dynamics related to elevation. By simplifying the variable coefficients, it enhances the examination of stability and resonance behavior. Despite inherent complexities, the work effectively clarifies fundamental concepts, contributing to a more coherent understanding of the subject. The Hartman number, magnetic field, and magnetic permeability ratio exert a destabilizing effect. Conversely, the Bingham parameter, Weber number, and periodic frequency exert a stabilizing influence. Full article

This paper develops an optimal control framework for a mechanical–structural model of bone remodeling that couples osteocytes, osteoblasts, and osteoclasts with bone density, incorporating porosity-dependent feedback mechanisms. To represent clinically relevant interventions, three bounded control functions are introduced: anabolic stimulation of osteoblast activity, anti-resorptive suppression of osteoclast-mediated resorption, and structural modulation of porosity feedback. The controlled system is shown to be mathematically well-posed, and the necessary optimality conditions are derived via Pontryagin’s Maximum Principle, leading to explicit characterizations of the optimal controls. The resulting state–adjoint system is solved numerically using a forward–backward sweep method. Numerical results demonstrate that the optimal intervention effectively suppresses osteoclast activity and drives the system toward higher, more stable bone density levels than the uncontrolled dynamics. In particular, the anti-resorptive control consistently plays the dominant role in shaping the optimal strategy. A cost-effectiveness analysis based on ACER, ICER, and the efficient frontier shows that strategies involving anti-resorptive inhibition achieve the greatest therapeutic gains at moderate cost, while additional controls yield only marginal improvements. Sensitivity analysis further indicates that parameters associated with osteoclast dynamics and bone formation have the strongest influence on density-related outcomes. Full article

This research explores the existence of solutions for a class of random fractional differential equations characterized by bounded delay, specifically within the context of Fréchet spaces. Random fractional differential equations serve as powerful mathematical tools for modeling complex phenomena subjected to stochastic perturbations and hereditary effects. Despite their significance, establishing solution existence in infinite-dimensional spaces remains a challenging task. By integrating the properties of the noncompactness measures with a generalized Darbo fixed point approach, we establish new existence results for the associated Darboux-type problem under milder compactness conditions. To illustrate the practical utility of these analytical results and demonstrate the validity of our theoretical framework, a representative example is provided. Full article

Background/Objectives: Lipid-based nanocarriers have emerged as promising systems for improving the delivery of poorly soluble drugs by enhancing stability, bioavailability, and controlled release. This work aimed to formulate solid lipid nanoparticles (SLN) and nanostructured lipid carriers (NLC) containing ciprofloxacin (CIP) using solvent-free procedures. Methods: The systems were extensively characterized using dynamic light scattering (DLS), transmission electron microscopy (TEM), and atomic force microscopy (AFM) to study the nanoparticles in the solid state. Furthermore, in vitro drug release was evaluated, and mathematical modeling was applied to analyze the resulting release kinetics. Additionally, storage stability was assessed at 4 °C and 25 °C over a period of 8 months. Results: The results indicated that SLN with an average size of ~50 nm (SLN 50) and NLC with mean diameters of ~25, 50, and 100 nm (NLC 25, NLC 50 and NLC 100 respectively) were successfully prepared. DLS measurements showed narrow particle size distributions (PdI ≤ 0.2) and negative zeta potentials ranging from −3.7 to −7.7 mV. Encapsulation efficiencies were remarkably high for most systems, reaching ~98% for SLN 50, NLC 50, and NLC 100, while the smallest formulation (NLC 25) showed a lower efficiency (~80%). Both TEM and AFM confirmed the formation of spherical nanoscale structures consistent with the sizes determined by DLS. Release studies revealed a strong influence of particle size on kinetics: NLC 25 exhibited rapid release (~95% within 30 min), whereas NLC 100 showed a sustained profile (<20% after 6 h). Dissolution profiles were accurately described by the Lumped-Gonzo kinetic model (R² > 0.98), enabling estimation of dissolution efficiency. Conclusions: These findings confirm that lipid-based nanocarriers can be engineered to precisely control CIP release. Full article

This study develops a game-theoretic framework to analyze collaborative advertising decisions between manufacturers and retailers in seasonal product supply chains characterized by competitive–cooperative channel relationships. We formulate a mathematical programming model to jointly optimize advertising efforts, the manufacturer’s advertising cost-sharing rate, order quantities, and inventory decisions across distinct channel configurations—including a single manufacturer–retailer dyad and a competitive multi-channel market. Numerical experiments and sensitivity analyses are conducted to investigate how key structural parameters—particularly demand elasticity and channel power asymmetry—influence overall system performance and equilibrium decision outcomes. Results indicate that well-designed collaborative advertising mechanisms enhance total channel profitability and, under specific conditions, yield Pareto-improving outcomes for both parties. This study makes three primary contributions: (i) it integrates inter-firm competition with intra-channel cooperation within a unified strategic framework; (ii) it jointly coordinates advertising and inventory decisions—two critical operational levers—rather than treating them in isolation; and (iii) it embeds financial arrangements (e.g., cost sharing) endogenously into the analytical model, thereby offering a novel, theoretically grounded, and practically implementable decision-support framework for distribution systems operating in complex, dynamic market environments. Full article