Uncertainty Computation at Finite Distance in Nonlinear Mixed Effects Models-a New Method Based on Metropolis-Hastings Algorithm.

The standard errors (SE) of the maximum likelihood estimates (MLE) of the population parameter vector in nonlinear mixed effect models (NLMEM) are usually estimated using the inverse of the Fisher information matrix (FIM). However, at a finite distance, i.e. far from the asymptotic, the FIM can underestimate the SE of NLMEM parameters. Alternatively, the standard deviation of the posterior distribution, obtained in Stan via the Hamiltonian Monte Carlo algorithm, has been shown to be a proxy for the SE, since, under some regularity conditions on the prior, the limiting distributions of the MLE and of the maximum a posterior estimator in a Bayesian framework are equivalent. In this work, we develop a similar method using the Metropolis-Hastings (MH) algorithm in parallel to the stochastic approximation expectation maximisation (SAEM) algorithm, implemented in the saemix R package. We assess this method on different simulation scenarios and data from a real case study, comparing it to other SE computation methods. The simulation study shows that our method improves the results obtained with frequentist methods at finite distance. However, it performed poorly in a scenario with the high variability and correlations observed in the real case study, stressing the need for calibration.

Analysing the performance of a health innovation ecosystem in the COVID-19 crisis: complexity and chaos theory perspective.

BACKGROUND: This research delves into the complexity management of collaborative networks and interorganizational systems in the health innovation ecosystem on the basis of a best practice in the coronavirus disease 2019 (COVID-19) crisis. The objective is to offer specific solutions and guidelines to stakeholders in the health innovation ecosystem to control the chaos resulting from unexpected events along the ecosystem development and evolution path. METHODS: For this purpose, the performance of the Health Innovation Ecosystem in Iran (the Every Home is a Health Base plan) has been examined through a detailed and in-depth analysis of events and actions taken using documents, reports and interviews with experts. The practical application of chaos and complex adaptive system features (adaptation, time horizons, edge of chaos, sensitivity to initial conditions, state space and strange attractors) is introduced to identify and manage the transition from a state where the health innovation ecosystem is on the edge of chaos and prone to failure. Data were collected through studying documents, reports and interviews with experts, and then analysed using qualitative content analysis techniques, open and axial coding and metaphors derived from complexity and chaos theories. RESULTS: The findings indicate that to understand and embrace the complexity of the health innovation ecosystem throughout its development and evolution and manage and lead it through the edge of chaos towards successful interorganizational systems performance, it is necessary to use gap analysis to achieve consensus, establish a highly interactive governance structure with key stakeholders of the ecosystem, maintain flexibility to control bifurcations (butterfly effect), prevent transforming emergency solutions into standard routines and ensure the sustainability of the ecosystem against future threats by long-term financial security. CONCLUSIONS: This research provides insights into the dynamics of complex health systems and offers strategies for promoting successful innovation through collaborative networks and interorganizational systems in the development and evolution of the health innovation ecosystem. By embracing complexity and chaos, healthcare professionals, policy-makers and researchers can collaboratively address complex challenges and improve outcomes in health network activities. The conclusion section provides guidelines for successfully managing the complexity of the ecosystem and offers suggestions for further research.

Asymmetric impact of patents on green technologies on Algeria's Ecological Future.

This study examines how patents on green technologies impact Algeria's ecological footprint from 1990 to 2022 while controlling for economic growth and energy consumption. The objectives are to analyze the asymmetric effects of positive and negative shocks in these drivers on ecological footprint and provide policy insights on leveraging innovations and growth while minimizing environmental harm. Given recent major structural shifts in Algeria's economy, time series data exhibits nonlinear dynamics. To accommodate this nonlinearity, the study employs an innovative nonlinear autoregressive distributed lag approach. The findings indicate that an upsurge in green technologies (termed as a positive shock) significantly reduces the ecological footprint, thereby enhancing ecological sustainability. Interestingly, a decline in green technologies (termed as a negative shock) also contributes to reducing the ecological footprint. This highlights the crucial role of clean technologies in mitigating ecological damage in both scenarios. Conversely, a positive shock in economic growth increases ecological footprint, underscoring the imperative for environmentally friendly policies in tandem with economic expansion. Negative shocks, however, have minimal impact. In a similar vein, positive shock in energy consumption increases ecological footprint, underlining the importance of transitioning towards cleaner energy sources. Negative shock has a smaller but still noticeable effect. The results confirm asymmetric impacts, with positive and negative changes in the drivers affecting Algeria's ecological footprint differently. To ensure long-term economic and ecological stability, Algeria should prioritize eco-innovation and green technology development. This will reduce dependence on fossil fuels and create new, sustainable industries.

A study on the dynamic impact of carbon emission trading on green and high-quality development.

As a pivotal element in market mechanisms, carbon trading is increasingly recognized as crucial for achieving China's Carbon Peaking and Carbon Neutrality Goals. This study introduces a comprehensive dynamic model, integrating carbon trading, emissions, economic growth, and green technology innovation, to offer a holistic understanding of the interplay between these domains. Utilizing principles from nonlinear dynamics and chaos theory, the model is adept at simulating various scenarios and assessing the effectiveness of government policies in stabilizing these complex systems. In-depth analysis provided by this research sheds light on the nuanced impact of carbon trading policies on sustainable development. Key findings highlight (1) Carbon trading's essential role as a catalyst in propelling sustainable and high-quality growth. (2) A strong positive relationship is observed between the sophistication of the carbon trading mechanism and its effectiveness in stimulating green technology innovation and fostering high-quality green development. Notably, carbon trading's influence on green technology innovation markedly enhances the efficacy of carbon emission reduction strategies. (3) Government regulations are instrumental in augmenting carbon prices, thus incentivizing increased corporate participation in emission reduction and enhancing the overall impact of carbon emission reduction. Nevertheless, the study identifies a critical threshold in regulatory intensity, beyond which there is a risk of system destabilization ( a 3 ≥ 0.032 ). These findings underscore the imperative for developing an integrated national carbon emission trading market, prioritizing sustainable growth strategies and diligently pursuing China's environmental objectives.

Exploring asymmetric influence of R&D expenditures on CO2 emissions in China: evidence from nonlinear ARDL model.

R&D spending upsurges technological advancement and innovation which results in lowering energy consumption and environmental degradation. The current study investigates the asymmetrical impact of R&D spending on CO2 emissions in China via employing annual data from 1980 to 2021 and the NARDL model for empirical analysis. The estimated results of the NARDL model confirmed that there are asymmetries in positive and negative coefficients of R&D spending in China. The results depict that the positive shock in R&D spending exerts a negative and statistically significant impact on CO2 emissions in both runs implying that an increase in R&D spending lowers CO2 emissions. However, the negative coefficient of R&D spending yields a positive and statistically significant impact on CO2 emissions revealing the fact that a negative shock in R&D spending results in the upsurge of CO2 emissions in China. According to these findings, the impact of positive and negative shocks in R&D spending on CO2 emissions is asymmetric. The findings also show that the impact of a negative shock in R&D spending is greater than the impact of a positive shock on CO2 emissions. In addition to the negative shock in R&D spending, increases in energy consumption, economic growth, and FDI inflows also contribute to an upsurge in CO2 emissions in China. The robustness of the estimated results is assessed using standard fully modified ordinary least square (FMOLS) and dynamic ordinary least square (DOLS) models. The FMOLS and DOLS results have been confirmed to be sound and consistent with the results of the NARDL model. The study suggests that the economic strategies should aim at investing in R&D spending to foster environment-friendly technological innovations and to lower environmental degradation in China.

Assessment of nonlinear dose-response relationships via nonparametric regression.

We propose a simple approach to assess whether a nonlinear parametric model is appropriate to depict the dose-response relationships and whether two parametric models can be applied to fit a dataset via nonparametric regression. The proposed approach can compensate for the ANOVA, which is sometimes conservative, and is very easy to implement. We illustrate the performance by analyzing experimental examples and a small simulation study.

Forecast of clean energy generation in China based on new information priority nonlinear grey Bernoulli model.

The forecast of clean energy power generation is of major prominence to energy structure adjustment and the realization of sustainable economic development in China. In order to scientifically predict clean energy power generation data, a structure-adaptive nonlinear grey Bernoulli model submitted to the new information priority criterion (abbreviated as IANGBM) is established. Firstly, an improved conformable fractional accumulation operator that conforms to the priority of new information is proposed, which can effectively extract the information from small samples. Then, IANGBM is derived from the Bernoulli differential equation, and the perturbation bound theory proves that this model is suitable for the analysis of small sample data. In addition, the grey wolf optimization algorithm is utilized to optimize the model parameters to make the model more adaptable and generalized. To verify the superiority of the model, two cases consisting of wind and nuclear power generation prediction are implemented by comparing eight benchmark models involving IANGBM, GM, FGM, FANGBM, LR, SVM, BPNN, and LSTM. The experiment results demonstrate that the proposed model achieves higher prediction accuracy compared to the other seven competing models. Finally, the future nuclear and wind power generation from 2023 to 2030 are predicted by adopting the IANGBM(1,1) model. For the next 8 years, nuclear power generation will maintain stable development, while wind energy power generation will grow rapidly.

[Application of brain functional connectivity and nonlinear dynamic analysis in brain function assessment for infants with controlled infantile spasm]. / 脑功能连接及非线性动力学分析在发作控制的婴儿痉挛症患儿脑功能评估中的应用.

OBJECTIVES: To investigate the role of brain functional connectivity and nonlinear dynamic analysis in brain function assessment for infants with controlled infantile spasm (IS). METHODS: A retrospective analysis was performed on 14 children with controlled IS (IS group) who were admitted to the Department of Neurology, Anhui Provincial Children's Hospital, from January 2019 to January 2023. Twelve healthy children, matched for sex and age, were enrolled as the control group. Electroencephalogram (EEG) data were analyzed for both groups to compare the features of brain network, and nonlinear dynamic indicators were calculated, including approximate entropy, sample entropy, permutation entropy, and permutation Lempel-Ziv complexity. RESULTS: Brain functional connectivity showed that compared with the control group, the IS group had an increase in the strength of functional connectivity, and there was a significant difference between the two groups in the connection strength between the Fp2 and F8 channels (P<0.05). The network stability analysis showed that the IS group had a significantly higher network stability than the control group at different time windows (P<0.05). The nonlinear dynamic analysis showed that compared with the control group, the IS group had a significantly lower sample entropy of Fz electrode (P<0.05). CONCLUSIONS: Abnormalities in brain network and sample entropy may be observed in some children with controlled IS, and it is suggested that quantitative EEG analysis parameters can serve as neurological biomarkers for evaluating brain function in children with IS.

Estimation of nonlinear mixed-effects continuous-time models using the continuous-discrete extended Kalman filter.

Many intensive longitudinal measurements are collected at irregularly spaced time intervals, and involve complex, possibly nonlinear and heterogeneous patterns of change. Effective modelling of such change processes requires continuous-time differential equation models that may be nonlinear and include mixed effects in the parameters. One approach of fitting such models is to define random effect variables as additional latent variables in a stochastic differential equation (SDE) model of choice, and use estimation algorithms designed for fitting SDE models, such as the continuous-discrete extended Kalman filter (CDEKF) approach implemented in the dynr R package, to estimate the random effect variables as latent variables. However, this approach's efficacy and identification constraints in handling mixed-effects SDE models have not been investigated. In the current study, we analytically inspect the identification constraints of using the CDEKF approach to fit nonlinear mixed-effects SDE models; extend a published model of emotions to a nonlinear mixed-effects SDE model as an example, and fit it to a set of irregularly spaced ecological momentary assessment data; and evaluate the feasibility of the proposed approach to fit the model through a Monte Carlo simulation study. Results show that the proposed approach produces reasonable parameter and standard error estimates when some identification constraint is met. We address the effects of sample size, process noise variance, and data spacing conditions on estimation results.

Uncertainty quantification in the assessment of human exposure to pulsed or multi-frequency fields.

Objective:pulsed fields or waveforms with multi-frequency content have to be assessed with suitable methods. This paper deals with the uncertainty quantification associated to these methods.Approach:among all possible approaches, the weighted peak method (WPM) is widely employed in standards and guidelines, therefore, in this paper, we consider its implementation both in time domain and frequency domain. For the uncertainty quantification the polynomial chaos expansion theory is used. By means of a sensitivity analysis, for several standard waveforms, the parameters with more influence on the exposure index are identified and their sensitivity indices are quantified. The output of the sensitivity analysis is used to set up a parametric analysis with the aim of evaluating the uncertainty propagation of the analyzed methods and, finally, also several measured waveforms generated by a welding gun are tested.Main results:it is shown that the time domain implementation of the weighted peak method provides results in agreement with the basilar mechanisms of electromagnetic induction and electrostimulation. On the opposite, the WPM in frequency domain is found to be too sensitive to parameters that should not influence the exposure index because its weight function includes sharp variations of the phase centered on real zeros and poles. To overcome this issue, a new definition for the phase of the weight function in frequency domain is proposed.Significance:it is shown that the time domain implementation of the WPM is the more accurate and precise. The standard WPM in frequency domain has some issues that can be avoided with the proposed modification of the phase definition of the weight function. Finally, all the codes used in this paper are hosted on a GitHub and can be freely accessed athttps://github.com/giaccone/wpm_uncertainty.

Multiple objective immune wolf colony algorithm for solving time-cost-quality trade-off problem.

The importance of the time-cost-quality trade-off problem in construction projects has been widely recognized. Its goal is to minimize time and cost and maximize quality. In this paper, the bonus-penalty mechanism is introduced to improve the traditional time-cost model, and considering the nonlinear relationship between quality and time, a nonlinear time-cost quality model is established. Meanwhile, in order to better solve the time-cost-quality trade-off problem, a multi-objective immune wolf colony optimization algorithm has been proposed. The hybrid method combines the fast convergence of the wolf colony algorithm and the excellent diversity of the immune algorithm to improve the accuracy of the wolf colony search process. Finally, a railway construction project is taken as an example to prove the effectiveness of the method.

A biosensing system employing nonlinear dynamic analysis-assisted neural network for drug-induced cardiotoxicity assessment.

Preclinical investigation of drug-induced cardiotoxicity is of importance for drug development. To evaluate such cardiotoxicity, in vitro high-throughput interdigitated electrode-based recording of cardiomyocytes mechanical beating is widely used. To automatically analyze the features from the beating signals for drug-induced cardiotoxicity assessment, artificial neural network analysis is conventionally employed and signals are segmented into cycles and feature points are located in the cycles. However, signal segmentation and location of feature points for different signal shapes require design of specific algorithms. Consequently, this may lower the efficiency of research and the applications of such algorithms in signals with different morphologies are limited. Here, we present a biosensing system that employs nonlinear dynamic analysis-assisted neural network (NDANN) to avoid the signal segmentation process and directly extract features from beating signal time series. By processing beating time series with fixed time duration to avoid the signal segmentation process, this NDANN-based biosensing system can identify drug-induced cardiotoxicity with accuracy over 0.99. The individual drugs were classified with high accuracies over 0.94 and drug-induced cardiotoxicity levels were accurately predicted. We also evaluated the generalization performance of the NDANN-based biosensing system in assessing drug-induced cardiotoxicity through an independent dataset. This system achieved accuracy of 0.85-0.95 for different drug concentrations in identification of drug-induced cardiotoxicity. This result demonstrates that our NDANN-based biosensing system has the capacity of screening newly developed drugs, which is crucial in practical applications. This NDANN-based biosensing system can work as a new screening platform for drug-induced cardiotoxicity and improve the efficiency of bio-signal processing.

The Water Budget Myth and Its Recharge Controversy: Linear vs. Nonlinear Models.

The water budget myth, which is the idea that safe pumping must not exceed the initial recharge, gave rise to a controversy about the role of recharge in assessing the sustainability of groundwater development. To refute the concept of safe yield, a simplified water budget equation is used, which equals the total pumping rate to the sum of capture and storage change. Since initial recharge and discharge are canceled out from this equation, it is concluded that sustainable pumping has nothing to do with recharge. Investigating the assumptions underlying this equation, it is seen that it expresses the superposition principle, which implicitly assumes the groundwater reservoir can be depleted indefinitely and boundary conditions are an infinite source of water. To evaluate sustainability, however, the limits of the aquifer system must be examined accurately. Theoretically, this can only be accomplished applying nonlinear models, in which case setting up the simplified water budget equation is impossible without knowing the initial conditions. Hence, excluding recharge when assessing sustainable pumping may not be done inconsiderately, which is illustrated by two examples. An analytical solution, developed by Ernst in 1971 to simulate flow to a well in a polder area with a nonlinear function for drainage, even shows that it is not necessarily a misconception to assume the cone of depression stops expanding when the pumping rate is balanced by the infiltration rate.

A hybrid optimization method to design a sustainable resilient supply chain in a perishable food industry.

To integrate the location, inventory, and routing (LIR) problems arising in designing a resilient sustainable perishable food supply network (RSPFSN), a bi-objective optimization model is developed. To improve the resiliency and sustainability of the RSPFSN, a dynamic pricing strategy is used to cope with the disrupting events, along with minimizing the total cost and CO2 emission of the whole network. One of the important features of the proposed model is taking into account the effects of route disruptions and traffic conditions on the deterioration of products. To solve the mixed-integer nonlinear bi-objective optimization model, a novel hybrid method is developed using the Heuristic Multi-Choice Goal Programming and Utility Function Genetics Algorithm (HMCGP-UFGA). To improve resiliency, the dynamic pricing strategy, considering the traffic condition, can lead to around a 20% improvement in both cost and CO2 emission, based on the results of our case study in a dairy supply chain. Besides, the results of sensitivity analysis display the high flexibility of the proposed approach for various problems.

Asymmetric impacts of renewable energy consumption and economic complexity on economic growth in Saudi Arabia: evidence from the NARDL model.

This paper examines the asymmetric impacts of both renewable energy consumption and economic complexity on Saudi Arabia's economic growth in nonlinear autoregressive distributed lag (NARDL) frameworks. We firstly adopt the methodology of both standard NARDL and multiple threshold NARDL (MT-NARDL) models using quarterly data over the period 2000Q1-2015Q4. Then, we test the direction of the causal relationships between the underlying variables using both symmetric and asymmetric Granger causality tests. Our results from the standard NARDL model indicate that the long-term impact of a negative shock in renewable energy consumption on economic growth is significantly negative, while the short-term impact of either positive or negative shocks has a significant positive effect. Moreover, both positive and negative shocks in economic complexity have significant negative effects on economic growth in the long term, while economic growth is only affected by the negative change in economic complexity in the short term. Our estimates based on the best MT-NARDL model indicate that, in the long run, the effect of extremely large changes in renewable energy consumption is significantly different from the effect of small changes in renewable energy consumption on Saudi Arabia's economic growth. However, the effect of extremely large changes in economic complexity does not significantly differ from the effect of small changes in economic complexity on economic growth in the long run. Alternatively, in the short run, the effects of extremely large changes in both renewable energy consumption and economic complexity are not significantly different from the effects of small changes in those variables on economic growth. Finally, the symmetric/asymmetric causality nexus between positive/negative shocks to either renewable energy consumption or economic complexity and positive/negative shocks to economic growth is found to be neutral. The findings of this study provide deeper insights into the relationship between renewable energy consumption, economic complexity, and economic growth in Saudi Arabia and can be used for recommending different policies in the long run and short run.

Nonfragile Output Feedback Tracking Control for Markov Jump Fuzzy Systems Based on Integral Reinforcement Learning Scheme.

In this article, a novel integral reinforcement learning (RL)-based nonfragile output feedback tracking control algorithm is proposed for uncertain Markov jump nonlinear systems presented by the Takagi-Sugeno fuzzy model. The problem of nonfragile control is converted into solving the zero-sum games, where the control input and uncertain disturbance input can be regarded as two rival players. Based on the RL architecture, an offline parallel output feedback tracking learning algorithm is first designed to solve fuzzy stochastic coupled algebraic Riccati equations for Markov jump fuzzy systems. Furthermore, to overcome the requirement of a precise system information and transition probability, an online parallel integral RL-based algorithm is designed. Besides, the tracking object is achieved and the stochastically asymptotic stability, and expected H∞ performance for considered systems is ensured via the Lyapunov stability theory and stochastic analysis method. Furthermore, the effectiveness of the proposed control algorithm is verified by a robot arm system.

Bartlett and Bartlett-type corrections in heteroscedastic symmetric nonlinear regression models.

This paper provides general expressions for Bartlett and Bartlett-type correction factors for the likelihood ratio and gradient statistics to test the dispersion parameter vector in heteroscedastic symmetric nonlinear models. This class of regression models is potentially useful to model data containing outlying observations. Furthermore, we develop Monte Carlo simulations to compare size and power of the proposed corrected tests to the original likelihood ratio, score, gradient tests, corrected score test, and bootstrap tests. Our simulation results favor the score and gradient corrected tests as well as the bootstrap tests. We also present an empirical application.

Hill-type, bioinspired actuation delivers energy economy in DC motors.

Electromagnetic motors convert stored energy to mechanical work through a linear force-velocity (FV) relationship. In biological systems, however, muscle actuation is characterized by the hyperbolic FV mechanisms of the Hill muscle-in which a parameterαcharacterizes the degree of nonlinearity. Previous work has shown that bioinspiration in human-engineered systems can contribute favorable mechanical attributes-such as energy efficiency, self-stability, and flexibility, among others. In this study, we first construct an easily amendable, bioinspired electromagnetic motor which produces FV curves that mimic the Hill model of muscle with a high degree of accuracy. A proportional-integral-differential (PID) controller converges the characteristically linear FV relationship of a DC motor to nonlinear Hill-type force outputs. The bioinspired electric motor does a fixed amount of work by lifting a 147.5 g mass, and we record the translational velocity of the mass and the nonlinear applied force of the motor. Under optimized gain coefficients in the PID, the bioinspired motor achieves agreement ofR2>0.99with the Hill muscle model. Studies have shown that designing biologically inspired actuators produce comparatively energy efficient systems. We investigate the energy economy of actuating our motor with nonlinear, Hill-type forces in direct comparison with conventional linear FV actuation techniques. We find that the bioinspired motor delivers energy economy with respect to energy consumption and conversion: the nonlinear, Hill-type DC motor reduces the energetic cost of actuation when delivering a fixed amount of mechanical work.

An Optimized Damping Grey Population Prediction Model and Its Application on China's Population Structure Analysis.

Population, resources and environment constitute an interacting and interdependent whole. Only by scientifically forecasting and accurately grasping future population trends can we use limited resources to promote the sustainable development of society. Because the population system is affected by many complex factors and the structural relations among these factors are complex, it can be regarded as a typical dynamic grey system. This paper introduces the damping accumulated operator to construct the grey population prediction model based on the nonlinear grey Bernoulli model in order to describe the evolution law of the population system more accurately. The new operator can give full play to the principle of new information first and further enhance the ability of the model to capture the dynamic changes of the original data. A whale optimization algorithm was used to optimize the model parameters and build a smooth prediction curve. Through three practical cases related to the size and structure of the Chinese population, the comparison with other grey prediction models shows that the fitting and prediction accuracy of the damping accumulated-nonlinear grey Bernoulli model is higher than that of the traditional grey prediction model. At the same time, the damping accumulated operator can weaken the randomness of the original data sequence, reduce the influence of external interference factors, and enhance the robustness of the model. This paper proves that the new method is simple and effective for population prediction, which can not only grasp the future population change trend more accurately but also further expand the application range of the grey prediction model.

Non-linear effects of heterogeneous environmental regulations on industrial relocation: Do compliance costs work?

Reasonably designing environmental regulations for compliance-driven industrial relocation can avoid new pollution havens. The Cournot duopoly model simulates that the necessary condition for industrial relocation is differentiated market costs. Then, based on the province-industrial data of six Chinese pollution-intensive industries during 2005-2019, this study applies spatial Durbin model to explore the non-linear effects of heterogeneous environmental regulations on industrial relocation. Results shown that command-and-control environmental regulation manifests a U-shaped curve with local industrial relocation, with inverted U-shaped spillover effect radiating a road distance of 650 km, and both internal and external costs play the mediating roles; Market incentive environmental regulation has inverted U-shaped curves with industrial relocation in local and neighboring regions, it creates dual costs and works well in both short and long terms, which is the most potential regulatory tool to avoid pollution relocation accompanying industrial relocation; Voluntary environmental regulation exhibits inverted U-shaped relationships with industrial relocation in direct and spillover effects, and works through increased external cost rather than internal cost. Its spatial spillover radiates the longest 1250 km due to rapid spread of public opinions, but this effect takes more than 3 years to be effective.