Nonlinear Nature Research Articles

Deep plug-and-play HIO approach for phase retrieval

In the phase retrieval problem, the aim is the recovery of an unknown image from intensity-only measurements such as Fourier intensity. Although there are several solution approaches, solving this problem is challenging due to its nonlinear and ill-posed nature. Recently, learning-based approaches have emerged as powerful alternatives to the analytical methods for several inverse problems. In the context of phase retrieval, a novel plug-and-play approach, to our knowledge, that exploits learning-based prior and efficient update steps has been presented at the Computational Optical Sensing and Imaging topical meeting, with demonstrated state-of-the-art performance. The key idea was to incorporate learning-based prior to the Gerchberg-Saxton type algorithms through plug-and-play regularization. In this paper, we present the mathematical development of the method including the derivation of its analytical update steps based on half-quadratic splitting and comparatively evaluate its performance through extensive simulations on a large test dataset. The results show the effectiveness of the method in terms of image quality, computational efficiency, and robustness to initialization and noise.

A critical review of medicolegal research and information asymmetries in investigating cases of extrajudicial executions and forced disappearances.

Medicolegal systems investigate the cause and manner of death, particularly differentiating between unintentional and intentional deaths. The examination of remains from unlawfully killed individuals is critical in exposing human rights violations. However, forensic medical investigations of these human remains can face multiple challenges, especially in contexts marked by limited resources, political influence, and sub-optimal investigative procedures. When killings are state-sanctioned or facilitated by well-resourced non-state actors, the clandestine disposal of remains can create a culture of impunity, leaving affected families and communities without recourse or resolution. This study aggregates articles in English and Spanish, examining the current state of how forensic medical research on extrajudicial executions and forced disappearances informs practice. It highlights critical gaps in the empirical literature, particularly in the reporting of the scientific findings that impact the investigation of victims of these unlawful killings. These cases' inherently non-linear and unpredictable nature, often influenced by chaotic and unstable conditions, can create disproportionate challenges for forensics practitioners. To address these gaps, this review suggests leveraging epidemiological frameworks to track data trends in these unlawful killings, supporting public health initiatives in prevention and policy. It emphasises the need for comprehensive documentation, robust databases, and adaptive forensic methodologies to navigate uncertainties and systemic limitations inherent in this complex and unpredictable domain of medicolegal death investigation.

Environmental technology’s diminishing marginal returns: a study of green patents and emission reductions in China

IntroductionDo environmental technologies always yield desirable returns? This study addresses this question through the lens of command-and-control environmental regulation. It explores the theoretical and empirical mechanisms influencing the efficacy of technology in reducing emissions, focusing on the non-linear characteristics of technological returns under equilibrium conditions.MethodsA socio-economic model integrating pollution discharge issues was developed to examine the marginal effects of emission reduction technology. Empirical validation was conducted using green patent data from Chinese listed companies (2005–2020) and pollution emissions data from various cities. Fixed effects models and generalized random forest models were employed to analyze the relationships.ResultsThe analysis revealed that technological innovation exhibits diminishing marginal returns in reducing emissions due to existing technological constraints. The results were further dissected by categorizing patents and city characteristics, shedding light on the factors influencing emission reduction effectiveness.DiscussionThe findings emphasize the importance of addressing the non-linear nature of technological innovation in environmental regulation. Policy recommendations include fostering tailored innovation strategies and supporting cities with unique characteristics to maximize technological impact on emission reduction.

Optimizing high-strength concrete compressive strength with explainable machine learning

This study leverages machine learning to enhance the prediction of high-strength concrete (HSC) compressive strength, addressing the limitations of conventional methods, which are often tedious, less reliable, and time-consuming. Extreme Gradient Boosting (XGB) serves as the primary model, with hyperparameter optimization via metaheuristic algorithms such as Cuckoo Search (CSA), Water Strider (WS), Leopard Seal (LS), Harris Hawk (HH), Invasive Weed (IW), and Forest Optimization (FO). A total of 681 data sets were collected from existing literature. The models underwent tenfold cross-validation, with the LS-XGB model achieving an almost ideal performance in testing sets. Other models, including CSA-XGB, WS-XGB, HH-XGB, IW-XGB, and FO-XGB, also demonstrated strong performance, each with R2 > 0.96. For model explainability, Shapley's Additive Explanation (SHAP) analysis has been applied to the best-performing LS-XGB model. The analysis revealed that cement and superplasticizer (SP) are the most crucial features contributing to HSC development, with optimal ranges identified at 600–900 kg/m3 for cement and 8–10 kg/m3 for SP. The study demonstrates on how feature interactions contribute to concrete materials compressive strength, providing better and above all sustainable constructions. Furthermore, the LS-XGB model's optimal performance depicts the strongly nonlinear nature of HSC materials, validated through a set of derived graphs. Additionally, 30 concrete cubes were prepared for experimental validation, and the datasets demonstrated an accuracy of 92% showcasing the ability of models to make well informed decision.

Modeling and adaptive NN control for SMA flexible actuating systems with modified GPI hysteresis model

In this study, a shape memory alloy (SMA) actuating system is constructed to achieve flexible actuation ability. To improve the actuating performance, an effective control scheme needs to be developed to address the negative effects caused by the nonlinear nature of the internal SMA material and accommodate complex operating conditions. A modified generalised Prandtl-Ishlinskii (MGPI) hysteresis model is proposed to accurately characterise the strong saturated asymmetric hysteresis nonlinearity in the SMA wires. The modification of the input shape function allows for greater flexibility in controller design. Using this hysteresis modelling approach, an adaptive neural network (NN) control with a command filter is designed to achieve superior control performance. Experimental results validate the effectiveness of the proposed controller strategy.

Enhancing transmission reach: performance analysis of WDM RoF PON OFDM system design with varied QAM schemes

Abstract Radio over fiber is upcoming and maturing technology in terms of security, reliability, and coverage for long-distance optical-wireless communication systems. The nonlinear behavior and dispersive nature of optical channels are performance restrictive factors limiting the long reach in such systems. Along with enhancing channel capacity and bandwidth for radio signals over a long distance, the use of OFDM-based such systems can overcome various performance degrading effects like phase modulation, electrical power attenuation, chromatic dispersion, and multipath fading. Here, we propose our design of an 8 channels WDM RoF PON system using the OFDM scheme. Performance analysis is carried out in terms of performance comparison for various modulation schemes like 8, 16, 128, 256, and 512 QAM levels applied on information for long transmission reach of a system up to 500Kms. 8 channels WDM system model is developed to analyze the performance at a higher data rate. System performance is evaluated with Q factor and EVM level parameters of recovered signals at various transmission distances.

Data-driven machine learning approach based on physics-informed neural network for population balance model

Population balance models (PBM) are a fundamental tool in the field of process engineering and materials science for understanding and forecasting particulate system dynamics. These models are essential for the design and optimization of a wide range of industrial processes because they capture the evolution of particle size distribution in response to different phenomena such as nucleation, growth, aggregation, and breakage. The complex and non-linear nature of these models makes it difficult to find the analytical solution and even sometimes the approximate solution. This paper introduces a novel machine learning approach based on physics-informed neural network (PINN) for the approximate solution of PBM. Our strategy utilizes the use of a customized neural network framework that has been developed and trained on data generated from simulated PBM by using a finite difference method for the differential operators to identify the underlying dynamics and patterns controlling the evolution of particle distribution. In general, PINN uses automatic differentiation for the computation of differential operators, which is based on the chain rule and needs several matrix operations for computing, which reduces the processing efficiency during the training. The PINN approach provides a flexible, effective and highly adaptable solution framework by utilizing neural networks to approximate the solution and defining the loss function as the sum of the differential equation’s residuals at specific random or regular points inside the domain, as well as the residuals of the initial and boundary conditions. It is shown numerically that this approach does not need a diffusion term for a stable solution, which is often needed in most numerical methods for solving these models. For further validation, we compare the results with the exact solution and find them with a very good agreement with each other.

Transfer Learning for Thickener Control

Thickener control is a key area of focus in the minerals processing industry, particularly due to its crucial role in water recovery, which is essential for sustainable resource management. The highly nonlinear nature of thickener dynamics presents significant challenges in modeling and optimization, making it a strong candidate for advanced surrogate modeling techniques. However, traditional data-driven approaches often require extensive datasets, which are frequently unavailable, especially in new plants or unexplored operational domains. Developing data-driven models without enough data representative of the dynamics of the system could result in incorrect predictions and consequently, unstable response of the controller. This paper proposes the application of a methodology that leverages transfer learning to address these data limitations to enhance surrogate modeling and model predictive control (MPC) of thickeners. The performance of three approaches—a base model, a transfer learning model, and a physics-informed neural network (PINN)—are compared to demonstrate the effectiveness of transfer learning in improving control strategies under limited data conditions.

The Discrete Ueda System and Its Fractional Order Version: Chaos, Stabilization and Synchronization

The Ueda oscillator is one of the most popular and studied nonlinear oscillators. Whenever subjected to external periodic excitation, it exhibits a fascinating array of nonlinear behaviors, including chaos. This research introduces a novel fractional discrete Ueda system based on Y-th Caputo fractional difference and thoroughly investigates its chaotic dynamics via commensurate and incommensurate orders. Applying numerical methods like maximum Lyapunov exponent spectra, bifurcation plots, and phase plane. We demonstrate the emergence of chaotic attractors influenced by fractional orders and system parameters. Advanced complexity measures, including approximation entropy (ApEn) and C0 complexity, are applied to validate and measure the nonlinear and chaotic nature of the system; the results indicate a high level of complexity. Furthermore, we propose a control scheme to stabilize and synchronize the introduced Ueda map, ensuring the convergence of trajectories to desired states. MATLAB R2024a simulations are employed to confirm the theoretical findings, highlighting the robustness of our results and paving the way for future works.

Solving Nonlinear Energy Supply and Demand System Using Physics-Informed Neural Networks

Nonlinear differential equations and systems play a crucial role in modeling systems where time-dependent factors exhibit nonlinear characteristics. Due to their nonlinear nature, solving such systems often presents significant difficulties and challenges. In this study, we propose a method utilizing Physics-Informed Neural Networks (PINNs) to solve the nonlinear energy supply–demand (ESD) system. We design a neural network with four outputs, where each output approximates a function that corresponds to one of the unknown functions in the nonlinear system of differential equations describing the four-dimensional ESD problem. The neural network model is then trained, and the parameters are identified and optimized to achieve a more accurate solution. The solutions obtained from the neural network for this problem are equivalent when we compare and evaluate them against the Runge–Kutta numerical method of order 5(4) (RK45). However, the method utilizing neural networks is considered a modern and promising approach, as it effectively exploits the superior computational power of advanced computer systems, especially in solving complex problems. Another advantage is that the neural network model, after being trained, can solve the nonlinear system of differential equations across a continuous domain. In other words, neural networks are not only trained to approximate the solution functions for the nonlinear ESD system but can also represent the complex dynamic relationships between the system’s components. However, this approach requires significant time and computational power due to the need for model training. Furthermore, as this method is evaluated based on experimental results, ensuring the stability and convergence speed of the model poses a significant challenge. The key factors influencing this include the manner in which the neural network architecture is designed, such as the selection of hyperparameters and appropriate optimization functions. This is a critical and highly complex task, requiring experimentation and fine-tuning, which demand substantial expertise and time.

EARTHQUAKE PREDICTION USING MACHINE LEARNING

Earthquakes are among the most devastating natural disasters, causing widespread destruction and loss of life. Accurate prediction of earthquakes remains a significant scientific challenge due to the complex and nonlinear nature of seismic activity. This project explores the potential of machine learning techniques to improve earthquake prediction by analyzing large-scale seismic data. By leveraging historical earthquake records, geophysical parameters, and real-time data, we aim to identify patterns and correlations that can provide early warnings. Our approach employs advanced machine learning models, such as deep neural networks, decision trees, and ensemble learning techniques, to process and analyze high-dimensional data. Feature engineering techniques are used to extract meaningful insights from seismic signals, and the models are trained and validated using comprehensive datasets. Performance metrics such as accuracy, precision, recall, and F1-score are used to evaluate the predictive capability of the models. The results demonstrate the feasibility of using machine learning to enhance earthquake prediction, offering the potential for earlier alerts and improved disaster preparedness

Stock Market Price Forecasting Using Metaheuristic Search Algorithms: A Comparative Analysis

Stock market forecasting is an essential factor in the daily operations of many companies and individuals. However, the complex and nonlinear nature of the stock market and the unpredictable variations in factors affecting stock prices present significant challenges in accurate forecasting. To address this, we employ four model-based metaheuristic search algorithms (MHs), namely the Crow Search Algorithm (CSA), Particle Swarm Optimizer (PSO), Gray Wolf Optimizer (GWO), and Dandelion Optimizer (DO), to estimate the parameters of stock market prices models. The data utilized in our experiments are extracted from the widely recognized stock index of Standard & Poor’s 500 (S&P 500), that serves as a representative benchmark for the United States stock market. Our findings demonstrate that the CSA outperforms other MHs by providing the best combination of parameters for modeling stock market prices. The optimized parameters for the CSA model yielded Variance-Account-For (VAF) values of 97.846% in the training set and 93.483% in the testing set. This suggests that CSA offers promising capabilities for enhancing the accuracy and effectiveness of stock market forecasting models.

Assessing disease progression in ALS: prognostic subgroups and outliers

Background The rate of disease progression, measured by the decline of ALS Functional Rating Scale-Revised (ALSFRS-R) from symptom onset to diagnosis (ΔFS) is a well-established prognostic biomarker for predicting survival. Objectives: This study aims to categorize a large patient cohort based on the initial ΔFS and subsequently investigate survival deviations from the expected prognosis defined by ΔFS. Methods 1056 ALS patients were stratified into three progression categories based on their ΔFS: slow progressors (below 25th percentile), intermediate progressors (between 25th and 75th percentiles), and fast progressors (above 75th percentile). Survival outcomes were classified as short survivors (<2 years), average survivors (2–5 years), and long survivors (>5 years). Clinical and demographic characteristics within each subgroup were then analyzed. Results ΔFS stratification yielded cutoff values of <0.29, 0.29–1.03, and >1.03 points/month. Long survivors comprised 26% and 21% were short survivors. Six percent of the fast progressors had a life expectancy of more than 5 years, and none of the clinical and demographic characteristics analyzed could fully explain this discrepancy. Conversely, 13% of intermediate progressors lived less than 2 years, according to a short-diagnostic delay in these patients. Discussion Our study reaffirms ΔFS as a prognostic biomarker for ALS. We disclosed outliers defying anticipated patterns. The observed shift in progression categories underscores the non-linear nature of disease progression. Genetic and unknown biological reasons may explain these deviations. Further research is needed to fully understand modulation of ALS survival.

Harmful algal bloom prediction using empirical dynamic modeling.

Harmful Algal Blooms (HABs) can originate from a variety of reasons, including water pollution coming from agriculture, effluent from treatment plants, sewage system leaks, pH and light levels, and the consequences of climate change. In recent years, HAB events have become a serious environmental problem, paralleling population growth, agricultural development, increasing air temperatures, and declining precipitation. Hence, it is crucial to identify the mechanisms responsible for the formation of HABs, accurately assess their short- and long-term impacts, and quantify their variations based on climate projections for developing accurate action plans and effectively managing resources. From this point of view, this present study utilizes empirical dynamic modeling (EDM) to predict chlorophyll-a concentration of Lake Erie. This method is characterized by its nonlinearity and nonparametric nature. EDM has a key advantage in that it overcomes the limitations of traditional statistical modeling by utilizing data-driven attractor reconstruction. Chlorophyll-a is a critical parameter in the prediction of HAB events. Lake Erie is an inland water body that experiences frequent HAB phenomena due to its location. The EDM demonstrated exceptional performance, and these findings imply that the EDM model can effectively capture the underlying dynamics of chlorophyll-a changes.

Active nonlinear vibration control of a buckled beam based on deep reinforcement learning

Vibration control in civil engineering is often challenging due to the nonlinear nature of structures. Traditional control strategies have limitations in terms of modeling accuracy and scalability, especially when analyzing complex nonlinear systems. To solve this problem, this study proposes a model-free active vibration control technique specifically for nonlinear systems, which employs deep reinforcement learning (DRL) to train a neural network controller. The effectiveness and practicality of the proposed method have been validated on a shallow, simply supported buckled beam. The results prove that DRL can significantly increase the safety margin and effectively mitigate buckling under high load levels without requiring extra energy. Compared with conventional model-based linear and polynomial controllers, the proposed control strategy demonstrates excellent adaptability and ease of implementation. This research aims to supplement and expand the existing understanding of DRL applications in structural control, pointing towards a promising direction for future technological advancements and real-world applications.

THE IMPACT OF FRACTIONAL COMPOSITION OF GAS OIL ON THE YIELD AND QUALITY OF CATALYTIC CRACKING PRODUCTS

The impact of the depth of selection of narrow gas oil fractions of Azeri-Chirag-Guneshli oils on the yield and quality of catalytic cracking products was studied. The impact of fractional and group hydrocarbon composition on the main directions of cracking is analyzed. 5 types of gas oil fractions selected in the range of 200-360, 200-410, 200-440, 200-460, and 200-500°C were used as feedstock for catalytic cracking. The results of catalytic cracking of narrow gas oil fractions of Azeri-Chirag-Guneshli oils indicate a nonlinear nature of the dependences on the boiling point limits. The highest total yield of light oil products was obtained by cracking gas oil fractions boiling in the range of 200-410 and 200-440°C, reaching 60.5 and 60.8%, respectively. At the same time, the main contribution to this indicator was made by the gasoline fraction (31.5-33.2%). It was based on paraffin-naphthenic hydrocarbons. The yield of the diesel fraction changed symbiotically with the increasing weight of the fractional composition of the raw material, reaching maximum values of 9.9% during the cracking of the gas oil fraction, boiling in the range of 200-500°C. Based on a comparison of the ratio of iso-butane to iso-butylene, it was concluded that the cracking of gas oil at 200-440°C was accompanied by a significant contribution of bimolecular hydrogen transfer reactions.

Robust MPPT Control of PMSG Wind Turbines Using Sliding Mode Control

Wind energy is becoming an increasingly promising technology and a more significant player in energy production. However, due to the nonlinear nature of the system and the impact of external conditions, an effective control strategy is crucial. In this paper, we employ Sliding Mode Control as a Maximum Power Point Tracker (MPPT) on a Buck-Boost converter to connect the DC load to the wind turbine generator. All system components are modeled and simulated using MATLAB/Simulink, and the results demonstrate the promising potential of the SMC method.

Could Sports Coaching Contexts Learn From Planning Models in Physical Education Contexts? Exploring the Parallels and Divergences Regarding Planning Between Both Contexts

Planning is essential for organising learning content in sports coaching and physical education (PE) contexts but depends on multiple and mutable circumstances in each context. Although learning and performance are present in both contexts, planning in PE is typically more centred on learning, while coaching tends to focus more on performance. Nonetheless, sports coaching planning also requires ongoing learning to support performance, with coaches outlining pedagogical strategies in their daily training plans to achieve both short- and long-term goals. From this perspective, planning models used in PE contexts may offer valuable insights for sports coaching contexts, helping coaches develop various pedagogical approaches to plan their learning tasks effectively. Therefore, this article explored the parallels and divergences between planning in sports coaching and PE contexts, encompassing the pedagogical goals and planning structures, alongside opportunities, barriers, remediation strategies, and practical implications potentially transferable to sports coaching. The article highlighted the importance of flexible planning structures to accommodate the nonlinear nature of learning. Specifically, coaching contexts can learn from PE how to plan sessions for athletes with diverse motivations and skill levels, as well as how to design learning tasks that develop psychosocial and psychological skills.

Frequency control of a multi-microgrid system using a muti-stage controller in an isolated mode

The interconnection of numerous standalone MGs leads towards the establishment of an isolated MMG system. The MMG system is a complex nonlinear system that creates functioning decline as a result of inadequate dampening under the unanticipated variability in the load demand and the generated power from sources of renewable energy catalogue. Nonlinear nature also comes in the system due to the variations in the system parameter and dynamically altering loading conditions. So, in the present work, a standalone MMG system with two areas system through renewable penetration, the operation of QOHSA aimed at the gain optimisation of MS-PID controller is exploited for limiting variation in power and frequency due to generation and load demand perturbation. The practicality of the considered controller (i.e. MS-PID) is unearthed by comparing the dynamic characteristics of isolated MMG systems along with other controllers like I, PI and PID controllers (i.e. classical controllers). The MS-PID controller configuration sustains the deviation of frequency under ±0.00249 Hz and ±0.0583 Hz for step and random change in load demand, respectively. The sensitivity analysis is executed to present the suitability for the extensive adaptations in the magnitude of MG parameters along with the circumstances of step/random load perturbation.

Forecasting A Major Banking Corporation Stock Prices Using LSTM Neural Networks

The increasing complexity of stock market predictions necessitates advanced computational techniques to address the unique challenges posed by financial data's non-linear and volatile nature. This study aims to leverage Long Short-Term Memory (LSTM) neural networks to accurately forecast stock prices, using historical data collected from a major banking corporation as a primary source. The LSTM model excels at processing sequential time-series data, allowing it to predict monthly stock closing prices over a one-year horizon with a high degree of precision. Our findings indicate a Root Mean Squared Error (RMSE) of 3.2, underscoring the model's efficiency and reliability in financial forecasting tasks. The novelty of this research lies in the systematic incorporation of preprocessing techniques and fine-tuned hyperparameters to optimize model performance. Furthermore, this study explores the practical implications of implementing LSTM models in real-world trading scenarios, analyzing their adaptability to dynamic market conditions and their potential integration into automated trading systems. These findings contribute to the growing body of knowledge in financial analytics and demonstrate the viability of machine learning-based solutions for accurate and robust market predictions.