Nonlinear Model Research Articles

A dynamical systems model for the total fission rate in Drp1-dependent mitochondrial fission

Mitochondrial hyperfission in response to cellular insult is associated with reduced energy production and programmed cell death. Thus, there is a critical need to understand the molecular mechanisms coordinating and regulating the complex process of mitochondrial fission. We develop a nonlinear dynamical systems model of dynamin related protein one (Drp1)-dependent mitochondrial fission and use it to identify parameters which can regulate the total fission rate (TFR) as a function of time. The TFR defined from a nondimensionalization of the model undergoes a Hopf bifurcation with bifurcation parameter μ = k + M k - where M is the total concentration of mitochondrial fission factor (Mff) and k+ and k− are the association and dissociation rate constants between oligomers on the outer mitochondrial membrane. The variable μ can be thought of as the maximum build rate over the disassembling rate of oligomers. Though the nondimensionalization of the system results in four dimensionless parameters, we found the TFR and the cumulative total fission (TF) depend strongly on only one, μ. Interestingly, the cumulative TF does not monotonically increase as μ increases. Instead it increases with μ to a certain point and then begins to decrease as μ continues to increase. This non-monotone dependence on μ suggests interventions targeting k+, k−, or M may have a non-intuitive impact on the fission mechanism. Thus understanding the impact of regulatory parameters, such as μ, may assist future therapeutic target selection.

Joint optimization of overbooking and seat allocation for high-speed railways considering stochastic demand

To mitigate empty seat loss caused by random passenger no-show behavior, this study extends seat allocation to joint optimization of overbooking and seat allocation for high-speed railways (HSR). Assuming that stochastic passenger demand follows a specific distribution and considering various constraints, including train capacity, demand, and denied boarding rate constraints, a nonlinear stochastic programming model for joint optimization of overbooking and seat allocation for HSR is constructed with the aim of maximizing railway expected revenue. To solve this optimization model, a multi-level optimization algorithm is designed. Based on the sampling averaging approximation method, demand scenarios and passenger no-show scenarios are generated and the optimization problem is decomposed, including the joint optimization of overbooking and seat allocation under a single demand scenario, and the ticket adjustment under other demand scenarios. For the former, it is further divided into two sub-problems according to the stochastic nature of passenger no-show behavior, which is optimized iteratively. Finally, the effectiveness of the proposed model and algorithm is evaluated through numerical studies. The results demonstrate that the proposed joint optimization method effectively addresses the randomness of passenger demand and no-show behavior, thereby improving HSR expected revenue and making up for the empty seat loss resulting from passenger no-show behavior.

Optimal Control of Nonlinear, Nonautonomous, Energy Harvesting Systems Applied to Point Absorber Wave Energy Converters

Pursuing sustainable energy solutions has prompted researchers to focus on optimizing energy extraction from renewable sources. Control laws that optimize energy extraction require accurate modeling, often resulting in time-varying, nonlinear differential equations. An energy-maximizing optimal control law is derived for time-varying, nonlinear, second-order, energy harvesting systems. We demonstrate that sustaining periodic motion under this control law when subjected to periodic disturbances necessitates identifying appropriate initial conditions, inducing the system to follow a limit cycle. The general optimal solution is applied to two point absorber wave energy converter models: a linear model where the analytical derivation of initial conditions suffices and a nonlinear model demanding a numerical approach. A stable limit cycle is obtained for the latter when the initial conditions lie within an ellipse centered at the origin of the phase plane. This work advances energy-maximizing optimal control solutions for nonautonomous nonlinear systems with application to point absorbers. The results also shed light on the significance of initial conditions in achieving physically realizable periodic motion for periodic energy harvesting systems.

Flatness-based nonlinear internal model control with disturbances compensation via improved extended state observer for remotely operated vehicle

Flatness-based nonlinear internal model control with disturbances compensation via improved extended state observer for remotely operated vehicle

Harvest Harmony: Integrating Linear and Nonlinear Machine Learning Models for Precision Crop Recommendation

This research presents a comprehensive crop recommendation system that combines linear and nonlinear machine learning models to forecast suitable crops based on soil and environmental factors. The study evaluates the performance of Logistic Regression (linear) alongside Random Forest, Gradient Boosting, and XGBoost (nonlinear models) in delivering accurate crop suggestions. Precision, recall, and F1-score metrics are employed to assess the models' effectiveness. The dataset incorporates vital soil characteristics, such as nitrogen, phosphorus, and potassium levels, and environmental parameters like temperature, humidity, pH, and rainfall. The results demonstrate that while linear models like Logistic Regression offer simplicity, nonlinear models such as XGBoost excel in capturing complex data patterns, providing more precise recommendations. This dual-model strategy empowers farmers to make informed decisions tailored to specific farming conditions, boosting agricultural productivity. The study underscores the importance of integrating both linear and nonlinear machine learning techniques to achieve optimal crop recommendations, encouraging resource efficiency and sustainable agricultural practices.

AN INVESTIGATION ON NONLINEAR OPTION PRICING BEHAVIOURS THROUGH A NEW FRÉCHET DERIVATIVE-BASED QUADRATURE APPROACH

Abstract Complicated option pricing models attract much attention in financial industries, as they produce relatively better accurate values by taking into account more realistic assumptions such as market liquidity, uncertain volatility and so forth. We propose a new hybrid method to accurately explore the behaviour of the nonlinear pricing model in illiquid markets, which is important in financial risk management. Our method is based on the Newton iteration technique and the Fréchet derivative to linearize the model. The linearized equation is then discretized by a differential quadrature method in space and a quadratic trapezoid rule in time. It is observed through computations that the accurate solutions for the model emerge using very few grid points and time elements, compared with the finite difference method in the literature. Furthermore, this method also helps to avoid consideration of the convergence issues of the Newton approach applied to the nonlinear algebraic system containing many unknowns at each time step if an implicit method is used in time discretization. It is important to note that the Fréchet derivative supports to enhance the convergence order of the proposed iterative scheme.

Dual-Sliding-Surface Robust Control for the PEMFC Air-Feeding System Based on Terminal Sliding Mode Algorithm

The proton exchange membrane fuel cell (PEMFC) is the most widely used fuel cell, but it also has some limitations. One of the research pain points is controlling the oxygen content in PEMFCs. A moderate excess of oxygen boosts electrochemical reaction efficiency, while an appropriate oxygen content ensures system stability. In this paper, a fourth-order nonlinear mathematical model of a PEMFC stack air supply system is established to solve the problem of optimal oxygen excess ratio (OER) control under dynamic load conditions. Based on the model, a nonsingular terminal sliding mode controller (NTSMC) based on a sliding mode observer (SMO) is proposed. The NTSM exhibits superior robustness and performance compared to other sliding mode structures. Meanwhile, the SMO accurately predicts system states, facilitating precise control actions. Additionally, the dual sliding mode surfaces enhance system stability against parameter uncertainties and external disturbances. Our results demonstrate that the proposed controller outperforms traditional ones in terms of robustness and performance, which significantly enhances PEMFC system efficiency and stability.

Innovative Analytical and Semi-Analytical Approaches to the Nonlinear Fisher-KPP Model: Accurate Computational Solutions and Applications

Innovative Analytical and Semi-Analytical Approaches to the Nonlinear Fisher-KPP Model: Accurate Computational Solutions and Applications

Optimising bearing degradation prediction: a bayesian vector autoregressive-assisted DeepAR model approach

Abstract Accurate prediction of the remaining useful life of bearings is crucial for the maintenance of rotating machinery. Current research often involves extracting multidimensional features from vibration signals to construct health degradation indicator, and health indicator is directly used for degradation prediction. However, constructed health indicator exhibit complex nonlinearity and fail to utilize the correlations with the original multidimensional features. To address this limitation, we propose an integrated prediction framework, known as the bayesian vector autoregression-assisted DeepAR method. The proposed two step prediction framework combines the advantages of covariance prediction and temporal correlation prediction, and realizes the full utilization of multidimensional features correlation information. Additionally, the proposed approach utilizes the intrinsic properties of statistical models to constrain improve the prediction results of deep learning methods, achieving nonlinear modeling of the degradation indicator while maintaining the stability of the prediction results. This process of prediction, re-estimation and adaptive adjustment achieves a balance in model performance. Finally, experimental studies using the PRONOSTIA and XJTU-SY datasets validate the effectiveness of the proposed method in improving the prediction accuracy of bearing health degradation indicators and enhancing the stability of multistep prediction in deep model.

Asymmetric limit cycles within Lorenz chaos induce anomalous mobility for a memory-driven active particle

On applying a small bias force, nonequilibrium systems may respond in paradoxical ways such as with giant negative mobility (GNM)—a large net drift opposite to the applied bias, or giant positive mobility (GPM)—an anomalously large drift in the same direction as the applied bias. Such behaviors have been extensively studied in idealized models of externally driven passive inertial particles. Here, we consider a minimal model of a memory-driven active particle inspired from experiments with walking and superwalking droplets, whose equation of motion maps to the celebrated Lorenz system. By adding a small bias force to this Lorenz model for the active particle, we uncover a dynamical mechanism for simultaneous emergence of GNM and GPM in the parameter space. Within the chaotic sea of the parameter space, a symmetric pair of coexisting asymmetric limit cycles separate and migrate under applied bias force, resulting in anomalous transport behaviors that are sensitive to the active particle's memory. Our work highlights a general dynamical mechanism for the emergence of anomalous transport behaviors for active particles described by low-dimensional nonlinear models. Published by the American Physical Society 2024

Vibration characteristics of rolling bearing cage under speed variation conditions

Speed variation conditions will deteriorate the stress state of the rolling bearing internal components and aggravate the vibration of the cage, thereby affecting the service life and reliability of rolling bearings. In this paper, a nonlinear dynamic analysis model of the cylindrical roller bearing is established considering the rubbing effect and hydrodynamic contact between the cage and the guiding ring, as well as the sliding between the cage and other rolling elements. The vibration characteristics of the cage is discussed under the start-stop conditions and different fluctuations of rotation rate. The results show that the vibration of the cage mainly occurs at the middle and late stages of the acceleration process, and the impact mainly occurs at the middle stage of the deceleration process under the start-stop conditions. Moreover, the fluctuation of inner ring speed will enhance the unstable motion of the cage, among which the vibration and impact of the cage are most severe under the rectangular fluctuation of speed, followed by simple harmonic and triangular fluctuations. The findings can provide a theoretical guidance for improving the performance of rolling bearings and ensuring their safe and reliable operation.

Sugarcane, corn silage and concentrate levels in cattle diet

This study evaluated two roughage types (sugarcane and corn silage) and two concentrate feed levels (0 and 25% of the total dry matter) in the cattle diet, in a 2x2 factorial design, and compared passage rate measurements (indicator and rumen evacuation). Four Holstein-Zebu heifers cannulated in the rumen and ileum were evaluated, in a 4x4 Latin square design. Stool samples (8th - 10th day) and rumen fluid (8th day) were collected and the rumen was emptied (14th and 16th day). Treatments were compared by contrast, evaluating the effects of roughage, concentrate feed and interaction between these factors. Dry matter (DM) intake and neutral detergent fiber corrected for ash and protein (apNDF) were highest for animals fed corn silage, and DM and organic matter (OM) intake were highest when fed concentrate. There was no roughage effect on ruminal mass, but concentrate decreased ruminal NDF in the total digesta mass. The coefficients of total digestion of crude protein (CP), apNDF and non-fiber carbohydrates (NFC) were higher for sugarcane than corn silage. Concentrate feed improved the total digestibility of OM and NFC. Passage rates evaluated by the marker technique and rumen evacuation were similar. Corn silage or 25% concentrate in the cattle diet improved consumption, intake rate and nutrient digestibility. The particle passage rate can be estimated by rumen evacuation or by adjusting a nonlinear mathematical model.

How Sophisticated Are Neural Networks Needed to Predict Long-Term Nonadiabatic Dynamics?

Nonadiabatic dynamics is key for understanding solar energy conversion and photochemical processes in condensed phases. This often involves the non-Markovian dynamics of the reduced density matrix in open quantum systems, where knowledge of the system's prior states is necessary to predict its future behavior. In this study, we explore time-series machine learning methods for predicting long-time nonadiabatic dynamics based on short-time input data, comparing these methods with the physics-based transfer tensor method (TTM). To understand the impact of memory time on these approaches, we demonstrate that non-Markovian dynamics can be represented as a linear map within the Nakajima-Zwanzig generalized quantum master equation framework. We further propose a practical method to estimate the effective memory time, within a given tolerance, for reduced density matrix propagation. Our predictive models are applied to various physical systems, including spin-boson models, multistate harmonic (MSH) models with Ohmic spectral densities and for a realistic organic photovoltaic system composed of a carotenoid-porphyrin-fullerene triad dissolved in tetrahydrofuran. Results indicate that the simple linear-mapping fully connected neural network (FCN) outperforms the more complicated nonlinear-mapping networks including the gated recurrent unit (GRU) and the convolutional neural network/long short-term memory (CNN-LSTM) in systems with short memory times, such as spin-boson and MSH models. Conversely, the nonlinear CNN-LSTM and GRU models yield higher accuracy in the triad MSH systems characterized by long memory times. These findings offer valuable insights into the role of effective memory time in non-Markovian quantum dynamics, providing practical guidance for the application of time-series machine learning models to complex chemical systems.

Nonlinear association between lung needle path CT attenuation values and postprocedural immediate pneumothorax following computed tomography-guided lung biopsy: a retrospective cohort study.

Pneumothorax is a potential complication following computed tomography-guided lung biopsy (CT-LB). However, the relationship between the lung needle path CT attenuation values and risk of post-procedural immediate pneumothorax remains unclear. The study aims to investigate this relationship. The present single-center retrospective cohort study analyzed the data obtained from 453 patients who underwent CT-LB from 2019 to 2022. The relationship between the lung needle path CT attenuation values and post-procedural immediate pneumothorax was assessed using restricted cubic splines, which were adjusted for potential confounders, and validated using linear and nonlinear binomial logistic models. A total of 453 patients (mean age: 60.2 ± 12.0 years old, 217 male patients) were evaluated. The incidence of post-procedural immediate pneumothorax was 41.06% (186/453). The median needle path CT attenuation was - 831 Hounsfield units (Hu). The linear models indicated an unstable association between lung needle path CT attenuation and post-procedural immediate pneumothorax (odds ratio: 0.99, 95% confidence interval: 0.99-1.00). The nonlinear analysis identified an inflection point at a CT attenuation value of -805 Hu. A stronger negative link was identified for needle path CT attenuation values below - 805 Hu (odds ratio: 0.99, 95% confidence interval: 0.98-0.99) between the needle path CT attenuation value and pneumothorax, while no statistically significant association was identified between these when the CT attenuation value was above - 805 Hu. There is a nonlinear association between the lung needle path CT attenuation values and risk of post-procedural immediate pneumothorax. For CT attenuation values below - 805 Hu, increasing the needle path CT attenuation values might reduce the risk of pneumothorax.

DeepRSMA: a cross-fusion based deep learning method for RNA-small molecule binding affinity prediction.

RNA is implicated in numerous aberrant cellular functions and disease progressions, highlighting the crucial importance of RNA-targeted drugs. To accelerate the discovery of such drugs, it is essential to develop an effective computational method for predicting RNA-small molecule affinity (RSMA). Recently, deep learning based computational methods have been promising due to their powerful nonlinear modeling ability. However, the leveraging of advanced deep learning methods to mine the diverse information of RNAs, small molecules and their interaction still remains a great challenge. In this study, we present DeepRSMA, an innovative cross-attention-based deep learning method for RSMA prediction. To effectively capture fine-grained features from RNA and small molecules, we developed nucleotide-level and atomic-level feature extraction modules for RNA and small molecules, respectively. Additionally, we incorporated both sequence and graph views into these modules to capture features from multiple perspectives. Moreover, a Transformer-based cross-fusion module is introduced to learn the general patterns of interactions between RNAs and small molecules. To achieve effective RSMA prediction, we integrated the RNA and small molecule representations from the feature extraction and cross-fusion modules. Our results show that DeepRSMA outperforms baseline methods in multiple test settings. The interpretability analysis and the case study on spinal muscular atrophy (SMA) demonstrate that DeepRSMA has the potential to guide RNA-targeted drug design. The codes and data are publicly available at https://github.com/Hhhzj-7/DeepRSMA. Supplementary data are available at Bioinformatics online.

Threshold Modeling for Antibiotic Stewardship in Oman.

Antimicrobial stewardship supports rational antibiotic use. However, balancing access to antibiotic treatment while controlling resistance is challenging. This research used a threshold logistic modelling approach to identify targets for antibiotic usage associated with carbapenem-resistant Acinetobacter baumannii (CRAb), carbapenem-resistant Klebsiella pneumonia (CRKP), and extended-spectrum β-lactamases- producing Escherichia coli (ESBL-producing E. coli) incidence in hospitals. This study utilises an ecological population-level design. Monthly pathogen cases and antibiotic use were retrospectively determined for inpatients between January 2015 and December 2023. The hospital pharmacy and microbiology information systems were used to obtain this data. Thresholds were identified by applying nonlinear modelling and logistic regression. Incidence rates of 0.199, 0.175, and 0.146 cases/100 occupied bed-days (OBD) for CRAb, CRKP, and ESBL-producing E. coli, respectively, were determined as the cutoff values for high (critical) incidence rates. Thresholds for aminoglycosides (0.59 defined daily dose (DDD)/100 OBD), carbapenems (6.31 DDD/100 OBD), piperacillin-tazobactam (3.71 DDD/100 OBD), third-generation cephalosporins (3.71 DDD/100 OBD), and fluoroquinolones (1.91 DDD/100 OBD), were identified. Exceeding these thresholds would accelerate the gram-negative pathogens' incidence rate above the critical incidence levels. Employing the threshold logistic approach enabled near real-time performance monitoring feedback, risk scores and alert signals for when the incidence of the selected pathogens are entering critical levels. Threshold logistic models can help inform and implement effective antimicrobial stewardship interventions to manage resistance within hospital settings.

Research on cross regional green certificate bilateral distributed robust trading strategy based on Bayesian theory.

To ensure the effective implementation of the compulsory green certificate transaction in China, a multi-participant cross-regional green certificate bilateral transaction model considering the relevant technical characteristics of the unit is proposed to solve the problems such as the mismatch between the supply and demand of green certificates and the reduction of the transaction plan by the grid operation constraints in the current green certificate transaction. To mobilize the initiative of participants, the model adopts the bilateral transaction of free negotiation. To balance the interests of transaction participants, the paper analyzes the complex interaction of multi participants in cross-regional bilateral transactions by using cooperative game theory. Simultaneously, the model considers multiple uncertainties among participants and takes into account the correlation of photovoltaic power in multiple periods. Based on the distributed robust theory, the multivariate nonlinear model and mixed-effect model of Bayesian are proposed to construct the fuzzy sets of the probability distribution for wind and photovoltaic power. On this basis, the paper analyzes the strategic behaviors of multi participants affected by uncertainty factors in the cross-regional green certificate bilateral trade through a numerical example, and quantitatively analyzes the sensitivity of each participant's transaction plan affected by uncertainty factors. The results show that the degree of competition will affect the strategic behavior and income of the participants, and the full cooperation mode can not only avoid the risk of fluctuations in the transaction price and transaction power within the alliance but also stabilize the supply and demand of green certificate transactions.

Physics-informed two-tier neural network for non-linear model order reduction

AbstractIn recent years, machine learning (ML) has had a great impact in the area of non-intrusive, non-linear model order reduction (MOR). However, the offline training phase often still entails high computational costs since it requires numerous, expensive, full-order solutions as the training data. Furthermore, in state-of-the-art methods, neural networks trained by a small amount of training data cannot be expected to generalize sufficiently well, and the training phase often ignores the underlying physical information when it is applied with MOR. Moreover, state-of-the-art MOR techniques that ensure an efficient online stage, such as hyper reduction techniques, are either intrusive or entail high offline computational costs. To resolve these challenges, inspired by recent developments in physics-informed and physics-reinforced neural networks, we propose a non-intrusive, physics-informed, two-tier deep network (TTDN) method. The proposed network, in which the first tier achieves the regression of the unknown quantity of interest and the second tier rebuilds the physical constitutive law between the unknown quantities of interest and derived quantities, is trained using pretraining and semi-supervised learning strategies. To illustrate the efficiency of the proposed approach, we perform numerical experiments on challenging non-linear and non-affine problems, including multi-scale mechanics problems.

Development of an Optimized Non-Linear Model for Precise Dew Point Estimation in Variable Environmental Conditions

Accurate dew point estimation is crucial for measuring water condensation in various fields such as environmental studies, agronomy, or water harvesting, among others. Despite the numerous models and equations developed over time, including empirical and machine learning approaches, they often involve trade-offs between accuracy, simplicity, and computational cost. A major limitation of the current approaches is the lack of balance among these three factors, limiting their practical applications under diverse conditions. This research addresses these key challenges by developing a new, streamlined equation for dew point estimation. Using the Magnus–Tetens equation, deemed as the most reliable equation, as a benchmark, and by applying a process of non-linear regression fitting and parametric optimization, a new equation was derived. The results demonstrate high accuracy with a streamlined implementation, validated through extensive data and computational simulations. This study highlights the importance of accurate dew point modeling, especially under variable environmental conditions, provides a reliable solution to existing limitations, paving the way for enhanced efficiency in related processes and research endeavors, and offers researchers and practitioners a practical tool for more effective modeling of water condensation phenomena.

A class of stable nonlinear non-Hermitian skin modes

Abstract The non-Hermitian skin effect (NHSE) is a well-known phenomenon in open topological systems that causes a large number of eigenstates to become localized at the boundary. Although many aspects of its theory have been investigated in linear systems, this phenomenon remains novel in nonlinear models. In the first step of this paper, we look at the conditions for the presence of quasi-skin modes in a semi-infinite, one-dimensional, nonlinear, nonreciprocal lattice. In the following phase, we explore the survival time of the quasi-skin mode in a finite nonlinear lattice with open edges. We study the dependency of the survival time on the system's parameters and demonstrate how the nonreciprocity of the system affects the survival time. This study introduces a method for achieving a stable localized state in a nonlinear finite lattice.