Search Results (100)

We study a stochastic differential model for the dynamics of institutional corruption, extending a deterministic three-variable system—corruption perception, proportion of sanctioned acts, and policy laxity—by incorporating Gaussian perturbations into key parameters. We prove global existence and uniqueness of solutions in the physically relevant domain, and we analyze the linearization around the asymptotically stable equilibrium of the deterministic system. Explicit mean square bounds for the linearized process are derived in terms of the spectral properties of a symmetric matrix, providing insight into the temporal validity of the linear approximation. To investigate global behavior, we relate the first exit time from the domain of interest to backward Kolmogorov equations and numerically solve the associated elliptic and parabolic PDEs with FreeFEM, obtaining estimates of expectations and survival probabilities. An application to the case of Mexico highlights nontrivial effects: while the spectral structure governs local stability, institutional volatility can non-monotonically accelerate global exit, showing that highly reactive interventions without effective sanctions increase uncertainty. Policy implications and possible extensions are discussed. Full article

Wave-powered desalination systems integrate reverse osmosis (RO) with renewable ocean energy, providing a sustainable and environmentally responsible approach to freshwater production. This study aims to investigate wave-powered RO desalination using supervised and deep machine learning (ML) models to predict the effects of variable feed flow on permeate recovery and salt rejection under dynamic hydrodynamic conditions. Multiple ML models, including Gaussian process regression (GPR), support vector machines (SVMs), multi-layer perceptron (MLP), linear regression (LR), and decision trees (DTs) were systematically assessed for the prediction of permeate recovery and salt rejection (%) using three distinct input configurations: limited physicochemical features (M1), flow- and salinity-related parameters (M2), and a comprehensive variable set incorporating temperature (M3). GPR achieved near-perfect predictive accuracy R² values (~1.00) with minimal errors for permeate recovery and salt rejection, attributed to its flexible kernel and probabilistic design. MLP and SVM also performed well, though they showed greater sensitivity to feature complexity. In contrast, DT models exhibited limited generalization and higher error rates, particularly when key features were excluded. Sensitivity analyses revealed that feed pressure (FP) and brine salinity (BS) were dominant positive influencers of permeate recovery and salt rejection. In contrast, brine flow (BF) and permeate salinity (PS) had negative impacts. Full article

This theoretical work investigates the linear (absorption and emission) and nonlinear (first hyperpolarizability and TPA) optical properties of donor–$\pi$–acceptor (D–$\pi$–A) molecular architectures based on functionalized benzoxazoles, with potential applications in optoelectronic technologies such as OLEDs and solar cells. Four $\pi$-conjugated compounds were studied in the gas phase and in polar (methanol) and nonpolar (toluene) solvents, employing DFT with the B3LYP and CAM-B3LYP functionals and the 6-311++G(d,p) basis set, as implemented in Gaussian and Dalton. The results reveal that the chemical environment induces spectral shifts and modulates the intensity of electronic transitions. In particular, the compound 2-((4-((5-nitro-2-oxo-1,3-benzoxazol-3(2H)-yl)amino)phenyl)methyl)-1,3-benzoxazole exhibited outstanding behavior in methanol, with a significant increase in dipole moment, polarizability, and first hyperpolarizability (static and dynamic at 1064 nm), reaching a TPA cross-section close to 150 GM. These findings highlight the key role of ionic substituents in tuning the optical response of $\pi$-conjugated systems and underscore their potential as functional materials for high-performance light-emitting and energy-conversion devices. Full article

Microbial growth and inhibition are complex biological processes influenced by diverse environmental and chemical factors, posing challenges for accurate modelling and prediction. Traditional mechanistic models often struggle to capture the nonlinear and multidimensional interactions inherent in real-world food systems, especially when multiple environmental variables and inhibitors are involved. This study presents the development of a novel, dynamic software platform that integrates classical predictive microbiology models—including both one-step and two-step frameworks—with advanced machine learning (ML) methods such as Support Vector Regression, Random Forest Regression, and Gaussian Process Regression. Uniquely, this platform enables direct comparisons between two-step and one-step modelling approaches across four widely used growth models (modified Gompertz, Logistic, Baranyi, and Huang) and three inhibition models (Log-Linear, Log-Linear + Tail, and Weibull), offering unprecedented flexibility for model evaluation and selection. Furthermore, the platform incorporates ML-based modelling for both microbial growth and inhibition, expanding predictive capabilities beyond traditional parametric frameworks. Validation against experimental and literature datasets demonstrated the platform’s high predictive accuracy and robustness, with machine learning models, particularly Gaussian Process Regression and Random Forest Regression, outperforming classical models. This versatile platform provides a powerful, data-driven decision-support tool for researchers, industry professionals, and regulatory bodies in areas such as food safety management, shelf-life estimation, antimicrobial testing, and environmental monitoring. Future work will focus on further optimization, integration with large public microbial databases, and expanding applications in emerging fields of predictive microbiology. Full article

This article presents a preliminary study on the potential application of artificial intelligence methods for assessing the durability of HTS tapes in superconducting fault current limiters (SFCLs). Despite their importance for the selectivity and reliability of power networks, these devices remain at the prototype testing stage, and the phenomena occurring in HTS tapes during their operation—particularly the degradation of tapes due to cyclic transitions into the resistive state—are difficult to model owing to their highly non-linear and dynamic nature. A concept of an engineering decision support system (EDSS) has been proposed, which, based on macroscopically measurable parameters (dissipated energy and the number of transitions), aims to enable the prediction of tape parameter degradation. Within the scope of the study, five approaches were tested and compared: Gaussian process regression (GPR) with various kernel functions, k-nearest neighbours (k-NN) regression, the random forest (RF) algorithm, piecewise cubic hermite interpolating polynomial (PCHIP) interpolation, and polynomial approximation. All models were trained on a limited set of experimental data. Despite the quantitative limitations and simplicity of the adopted methods, the results indicate that even simple GPR models can support the detection of HTS tape degradation in scenarios where direct measurement of the critical current is not feasible. This work constitutes a first step towards the construction of a complete EDSS and outlines directions for further research, including the need to expand the dataset, improve validation, analyse uncertainty, and incorporate physical constraints into the models. Full article

We investigate the bridge problem for stochastic processes, that is, we analyze the statistical properties of trajectories constrained to begin and terminate at a fixed position within a time interval $\tau$. Our primary focus is the time-reversal symmetry of these trajectories: under which conditions do the statistical properties remain invariant under the transformation $t\to \tau -t$? To address this question, we compare the stochastic differential equation describing the bridge, derived equivalently via Doob’s transform or stochastic optimal control, with the corresponding equation for the time-reversed bridge. We aim to provide a concise overview of these well-established derivation techniques and subsequently obtain a local condition for the time-reversal asymmetry that is specifically valid for the bridge. We are specifically interested in cases in which detailed balance is not satisfied and aim to eventually quantify the bridge asymmetry and understand how to use it to derive useful information about the underlying out-of-equilibrium dynamics. To this end, we derived a necessary condition for time-reversal symmetry, expressed in terms of the current velocity of the original stochastic process and a quantity linked to detailed balance. As expected, this formulation demonstrates that the bridge is symmetric when detailed balance holds, a sufficient condition that was already known. However, it also suggests that a bridge can exhibit symmetry even when the underlying process violates detailed balance. While we did not identify a specific instance of complete symmetry under broken detailed balance, we present an example of partial symmetry. In this case, some, but not all, components of the bridge display time-reversal symmetry. This example is drawn from a minimal non-equilibrium model, namely Brownian Gyrators, that are linear stochastic processes. We examined non-equilibrium systems driven by a "mechanical” force, specifically those in which the linear drift cannot be expressed as the gradient of a potential. While Gaussian processes like Brownian Gyrators offer valuable insights, it is known that they can be overly simplistic, even in their time-reversal properties. Therefore, we transformed the model into polar coordinates, obtaining a non-Gaussian process representing the squared modulus of the original process. Despite this increased complexity and the violation of detailed balance in the full process, we demonstrate through exact calculations that the bridge of the squared modulus in the isotropic case, constrained to start and end at the origin, exhibits perfect time-reversal symmetry. Full article

Currently, one of the most important challenges facing autonomous vehicles’ development due to varying driving conditions is effective path tracking while considering lateral stability. To address this issue, this study proposes the optimization of the linear quadratic regulator (LQR) control system by using the genetic algorithm (GA) to support the vehicle in following the predefined path accurately, minimizing the sideslip, and stabilizing the vehicle’s yaw rate. The dynamic system model of the vehicle is represented based on yaw rate angle, lateral speed, and vehicle sideslip angle as the variables of the state space model, with the steering angle as an input parameter. Using the GA to optimize the LQR control by tuning the weighting of the Q and R matrices led to enhancing the system response and minimizing deviation errors via a proposed cost function of GA. The simulation results were obtained using MATLAB/Simulink 2024a, with a representation of a predefined path as a Gaussian path. Under external and internal disturbances, such as road conditions, lateral wind, and actuator delay, the model demonstrates improved tracking performance and reduced sideslip angle and lateral acceleration by adjusting the longitudinal vehicle speed. This work highlights the effectiveness of robust control in addressing path planning, driving stability, and safety in autonomous vehicle systems. Full article

Soft and flexible capacitive tactile sensors are vital in prosthetics, wearable health monitoring, and soft robotics applications. However, achieving accurate real-time force detection and spatial localization remains a significant challenge, especially in dynamic, non-rigid environments like prosthetic liners. This study presents a real-time force point detection and tracking system using a custom-fabricated soft elastomeric capacitive sensor array in conjunction with image processing and machine learning techniques. The system integrates Otsu’s thresholding, Connected Component Labeling, and a tailored cluster-tracking algorithm for anomaly detection, enabling real-time localization within 1 ms. A $6\times 6$ Dragon Skin-based sensor array was fabricated, embedded with copper yarn electrodes, and evaluated using a UR3e robotic arm and a Schunk force-torque sensor to generate controlled stimuli. The fabricated tactile sensor measures the applied force from 1 to 3 N. Sensor output was captured via a MUCA breakout board and Arduino Nano 33 IoT, transmitting the Ratio of Mutual Capacitance data for further analysis. A Python-based processing pipeline filters and visualizes the data with real-time clustering and adaptive thresholding. Machine learning models such as linear regression, Support Vector Machine, decision tree, and Gaussian Process Regression were evaluated to correlate force with capacitance values. Decision Tree Regression achieved the highest performance ($R^2=0.9996, RMSE=0.0446$), providing an effective correlation factor of $51.76$ for force estimation. The system offers robust performance in complex interactions and a scalable solution for soft robotics and prosthetic force mapping, supporting health monitoring, safe automation, and medical diagnostics. Full article

The construction industry faces a growing need for automation to reduce costs, improve accuracy and productivity, and address labor shortages. One area that stands to benefit significantly from automation is panelized prefabricated building envelope retrofits, which can improve a building’s energy efficiency in heating and cooling interior spaces. In this paper, we propose using cable-driven parallel robots (CDPRs), which can effectively lift and handle large objects, to install these panels. However, implementing CDPRs presents significant challenges because of their nonlinear dynamics, complex trajectory planning, and precise control requirements. To tackle these challenges, this work focuses on a new application of established control and trajectory optimization theories in a CDPR simulation of a building envelope retrofit under real-world conditions. We first model the dynamics of CDPRs, highlighting the critical role of damping in system behavior. Building on this dynamic model, we formulate a trajectory optimization problem to generate feasible and efficient motion plans for the robot under operational and environmental constraints. Given the high precision required in the construction industry, accurately tracking the optimized trajectory is essential. However, challenges such as partial observability and external vibrations complicate this task. To address these issues, a Linear Quadratic Gaussian control framework is applied, enabling the robot to track the optimized trajectories with precision. Simulation results show that the proposed controller enables precise end effector positioning with errors under 4 mm, even in the presence of external wind disturbances. Through comprehensive simulations, our approach allows for an in-depth exploration of the system’s nonlinear dynamics, trajectory optimization, and control strategies under controlled yet highly realistic conditions. The results demonstrate the feasibility of CDPRs for automating panel installation and provide insights into their practical deployment. Full article

In recent years, the field of multi-source navigation data fusion has witnessed substantial advancements, propelled by the rapid development of multi-sensor technologies, Artificial Intelligence (AI) algorithms and enhanced computational capabilities. On one hand, fusion methods based on filtering theory, such as Kalman Filtering (KF), Particle Filtering (PF), and Federated Filtering (FF), have been continuously optimized, enabling effective handling of non-linear and non-Gaussian noise issues. On the other hand, the introduction of AI technologies like deep learning and reinforcement learning has provided new solutions for multi-source data fusion, particularly enhancing adaptive capabilities in complex and dynamic environments. Additionally, methods based on Factor Graph Optimization (FGO) have also demonstrated advantages in multi-source data fusion, offering better handling of global consistency problems. In the future, with the widespread adoption of technologies such as 5G, the Internet of Things, and edge computing, multi-source navigation data fusion is expected to evolve towards real-time processing, intelligence, and distributed systems. So far, fusion methods mainly include optimal estimation methods, filtering methods, uncertain reasoning methods, Multiple Model Estimation (MME), AI, and so on. To analyze the performance of these methods and provide a reliable theoretical reference and basis for the design and development of a multi-source data fusion system, this paper summarizes the characteristics of these fusion methods and their corresponding application scenarios. These results can provide references for theoretical research, system development, and application in the fields of autonomous driving, unmanned vehicle navigation, and intelligent navigation. Full article

Background: The sense of agency (SoA)—the subjective experience of controlling one’s own actions and their consequences—is a fundamental aspect of human cognition, volition, and motor control. Understanding how the SoA arises and is disrupted in neuropsychiatric disorders has significant implications for human–machine interface (HMI) design for neurorehabilitation. Traditional cognitive models of agency often fail to capture its full complexity, especially in dynamic and uncertain environments. Objective: This review synthesizes computational models—particularly predictive coding, Bayesian inference, and optimal control theories—to provide a unified framework for understanding the SoA in both healthy and dysfunctional brains. It aims to demonstrate how these models can inform the design of adaptive HMIs and therapeutic tools by aligning with the brain’s own inference and control mechanisms. Methods: I reviewed the foundational and contemporary literature on predictive coding, Kalman filtering, the Linear–Quadratic–Gaussian (LQG) control framework, and active inference. I explored their integration with neurophysiological mechanisms, focusing on the somato-cognitive action network (SCAN) and its role in sensorimotor integration, intention encoding, and the judgment of agency. Case studies, simulations, and XR-based rehabilitation paradigms using robotic haptics were used to illustrate theoretical concepts. Results: The SoA emerges from hierarchical inference processes that combine top–down motor intentions with bottom–up sensory feedback. Predictive coding frameworks, especially when implemented via Kalman filters and LQG control, provide a mechanistic basis for modeling motor learning, error correction, and adaptive control. Disruptions in these inference processes underlie symptoms in disorders such as functional movement disorder. XR-based interventions using robotic interfaces can restore the SoA by modulating sensory precision and motor predictions through adaptive feedback and suggestion. Computer simulations demonstrate how internal models, and hypnotic suggestions influence state estimation, motor execution, and the recovery of agency. Conclusions: Predictive coding and active inference offer a powerful computational framework for understanding and enhancing the SoA in health and disease. The SCAN system serves as a neural hub for integrating motor plans with cognitive and affective processes. Future work should explore the real-time modulation of agency via biofeedback, simulation, and SCAN-targeted non-invasive brain stimulation. Full article

Many real-world multivariable systems need to be modeled to capture the interconnected behavior of their physical variables and to understand how uncertainty in actuators and sensors affects the system dynamics. In system identification, some estimation algorithms are formulated as multivariate data problems by assuming symmetric noise distributions, yielding deterministic system models. Nevertheless, modern multivariable systems must incorporate the uncertainty behavior as a part of the system model structure, taking advantage of asymmetric distributions to model the uncertainty. This paper addresses the uncertainty modeling and identification of a class of multivariable linear dynamic systems, adopting a Stochastic Embedding approach. We consider a nominal system model and a Gaussian mixture distributed error-model driven by an exogenous input signal. The error-model parameters are treated as latent variables and a Maximum Likelihood algorithm that functions by marginalizing the latent variables is obtained. An Expectation-Maximization algorithm that jointly uses the measurements from multiple independent experiments is developed, yielding closed-form expressions for the Gaussian mixture estimators and the noise variance. Numerical simulations demonstrate that our approach yields accurate estimates of both the multivariable nominal system model parameters and the noise variance, even when the error-model non-Gaussian distribution does not correspond to a Gaussian mixture model. Full article

Terrestrial and satellite communications, tactical data links, positioning, navigation, and timing (PNT), as well as distributed sensing will continue to require precise timing and the ability to synchronize and disseminate time effectively. However, the supply of space-qualified clocks that meet Global Navigation Satellite Systems (GNSS)-level performance standards is limited. As the awareness of potential disruptions to GNSS due to adversarial actions grows, the current reliance on GNSS-level timing appears costly and outdated. This is especially relevant given the benefits of developing robust and stable time scale references in orbit, especially as various alternatives to GNSS are being explored. The onboard realization of clock ensembles is particularly promising for applications such as those providing the on-demand dissemination of a reference time scale for navigation services via a proliferated Low-Earth Orbit (pLEO) constellation. This article investigates potential inter-satellite network architectures for coordinating time and frequency across pLEO platforms. These architectures dynamically allocate radio resources for clock data transport based on the requirements for pLEO time scale formations. Additionally, this work proposes a model-based control system for wireless networked timekeeping systems. It envisions the optimal placement of critical information concerning the implicit ensemble mean (IEM) estimation across a multi-platform clock ensemble, which can offer better stability than relying on any single ensemble member. This approach aims to reduce data traffic flexibly. By making the IEM estimation sensor more intelligent and running it on the anchor platform while also optimizing the steering of remote frequency standards on participating platforms, the networked control system can better predict the future behavior of local reference clocks paired with low-noise oscillators. This system would then send precise IEM estimation information at critical moments to ensure a common pLEO time scale is realized across all participating platforms. Clock steering is essential for establishing these time scales, and the effectiveness of the realization depends on the selected control intervals and steering techniques. To enhance performance reliability beyond what the existing Linear Quadratic Gaussian (LQG) control technique can provide, the minimal-cost-variance (MCV) control theory is proposed for clock steering operations. The steering process enabled by the MCV control technique significantly impacts the overall performance reliability of the time scale, which is generated by the onboard ensemble of compact, lightweight, and low-power clocks. This is achieved by minimizing the variance of the chi-squared random performance of LQG control while maintaining a constraint on its mean. Full article

Brownian motion has been studied since 1827, leading to numerous important advances in many branches of science and to it being studied primarily as a stochastic dynamical system. In this paper, we present a deterministic model for the Brownian motion for a particle in a constant force field based on the Ornstein–Uhlenbeck model. By adding one degree of freedom, the system evolves into three differential equations. This change in the model is based on the Jerk equation with commutation surfaces and is analyzed in three cases: overdamped, critically damped, and underdamped. The dynamics of the proposed model are compared with classical results using a random process with normal distribution, where despite the absence of a stochastic component, the model preserves key Brownian motion characteristics, which are lost in stochastic models, giving a new perspective to the study of particle dynamics under different force fields. This is validated by a linear average square displacement and a Gaussian distribution of particle displacement in all cases. Furthermore, the correlation properties are examined using detrended fluctuation analysis (DFA) for compared cases, which confirms that the model effectively replicates the essential behaviors of Brownian motion that the classic models lose. Full article

This paper investigates the dynamic modeling and robust control of a Mecanum-wheeled vehicle (MWV) under load disturbances and measurement noise. The system is modeled as a cascaded state-space representation, where the motor transfer function (PWM input → torque output) and the vehicle transfer function (torque input → vehicle speed output) are combined. The PWM-induced motor delay is linearized, and the complete dynamic model is derived using Lagrangian mechanics, addressing the limitations of conventional models that are incomplete and unable to decouple control signals from disturbance signals. For the developed model, a robust stability controller is designed by integrating Internal Model Control (IMC) with a Disturbance Observer (DOB), enhancing real-time disturbance rejection. Open-loop experiments validate the model’s accuracy, showing a Dynamic Time Warping (DTW) error of 0.2662 m, significantly lower than the 0.3198 m observed in traditional models. In closed-loop simulations, under load disturbances ($T_L=0.1$ to $T_L=-0.7$) and Gaussian noise (power: 0.0001–0.00005), the proposed IMC + DOB controller achieves 97.6% faster stabilization than IMC and 98.3% faster than PID, demonstrating superior convergence speed, robustness, and disturbance rejection. This study provides a novel control strategy that effectively handles non-square system dynamics while mitigating external disturbances in real time. The proposed framework enhances trajectory tracking accuracy and stability, with potential applications in autonomous robotics and vehicular systems. Full article