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A mathematical model is designed to investigate Tuberculosis (TB) disease under the vaccination, treatment, and environmental impact with real cases. First, we introduce the model formulation in non-integer order derivative and then, extend the model into fractional order derivative. The fractional system's existence, uniqueness, and other relevant properties are shown. Then, we study the stability analysis of the equilibrium points. The disease-free equilibrium (DFE) 0 is locally asymptotically stable (LAS) when ℛ v < 1. Further, we show the global asymptotical stability (GAS) of the endemic equilibrium (EE) ∗ for ℛ v > 1 and 0 for ℛ v ≤ 1. The existence of bifurcation analysis in the model is investigated, and it is shown the system possesses the forward bifurcation phenomenon. Sensitivity analysis has been performed to determine the sensitive parameters that impact ℛ v. We consider the real TB statistics from Khyber Pakhtunkhwa in Pakistan and parameterized the model. The computed basic reproduction number obtained using the real cases is ℛ 0 ≈ 3.6615. Various numerical results regarding disease elimination of the sensitive parameters are shown graphically. [ABSTRACT FROM AUTHOR]

Physics informed neural network (PINN) demonstrates powerful capabilities in solving forward and inverse problems of nonlinear partial differential equations (NLPDEs) through combining data-driven and physical constraints. In this paper, two PINN methods that adopt tanh and sine as activation functions, respectively, are used to study data-driven solutions and parameter estimations of a family of high order KdV equations. Compared to the standard PINN with the tanh activation function, the PINN framework using the sine activation function can effectively learn the single soliton solution, double soliton solution, periodic traveling wave solution, and kink solution of the proposed equations with higher precision. The PINN framework using the sine activation function shows better performance in parameter estimation. In addition, the experiments show that the complexity of the equation influences the accuracy and efficiency of the PINN method. The outcomes of this study are poised to enhance the application of deep learning techniques in solving solutions and modeling of higher-order NLPDEs. [ABSTRACT FROM AUTHOR]

Abstract Physics informed neural network (PINN) demonstrates powerful capabilities in solving forward and inverse problems of nonlinear partial differential equations (NLPDEs) through combining data-driven and physical constraints. In this paper, two PINN methods that adopt tanh and sine as activation functions, respectively, are used to study data-driven solutions and parameter estimations of a family of high order KdV equations. Compared to the standard PINN with the tanh activation function, the PINN framework using the sine activation function can effectively learn the single soliton solution, double soliton solution, periodic traveling wave solution, and kink solution of the proposed equations with higher precision. The PINN framework using the sine activation function shows better performance in parameter estimation. In addition, the experiments show that the complexity of the equation influences the accuracy and efficiency of the PINN method. The outcomes of this study are poised to enhance the application of deep learning techniques in solving solutions and modeling of higher-order NLPDEs.

In this paper, the effectiveness of recently proposed Hunger Games Search (HGS) optimization tool, which simulates behavioural choices of the predators in the animal kingdom, in estimating model parameters of idealized causative sources from Self-Potential (SP) anomalies is presented. Before the parameter estimations, the modal analyses of the model parameter pairs and parameter tuning processes were performed to characterize the optimization problem and to decide the optimal value of the control parameter of HGS algorithm, respectively. Subsequently, the proposed optimizer was applied on some synthetic SP data sets and four anomalies obtained from India, Türkiye, Canada, and Indonesia. Multiple and intercalating causative sources were considered in the synthetic and real data cases, and HGS algorithm produced satisfactory solutions. In the composite anomaly cases a second moving average procedure successfully removed the undesired background effects. Uncertainty appraisal analyses showed the validity of the model parameter estimations. The outputs of HGS optimizer were also compared with those of the well-established and popular standard particle swarm optimization regarding convergence rate, robustness, stability, and accuracy. Applications presented here clearly showed that SP anomalies can be inverted more effectively via HGS since the procedure has the ability to search the predefined model space extensively without being trapped into numerous local minima and approximate the global minimum more precisely. Thus, it is recommended to use the HGS algorithm in model parameter estimation studies using SP anomalies. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the mean exit time and the scale function for the geometric Brownian motion with Markovian switching, in which the drift coefficients and the diffusion coefficients are associated with regime changes. The explicit expressions of mean exit time and scale function are obtained by solving the corresponding Poisson problem. Furthermore, we estimate parameters for the geometric Brownian motion with Markovian switching by composite likelihood and explore some properties of the estimates. Computer simulations are performed to illustrate our proposed algorithm, showing high accuracy of the estimators. [ABSTRACT FROM AUTHOR]

To develop standard optical biosensors, the simulation procedure takes a lot of time. For reducing that enormous amount of time and effort, machine learning might be a better solution. Effective indices, core power, total power, and effective area are the most crucial parameters for evaluating optical sensors. In this study, several machine learning (ML) approaches have been applied to predict those parameters while considering the core radius, cladding radius, pitch, analyte, and wavelength as the input vectors. We have utilized least squares (LS), LASSO, Elastic-Net (ENet), and Bayesian ridge regression (BRR) to make a comparative discussion using a balanced dataset obtained with the COMSOL Multiphysics simulation tool. Furthermore, a more extensive analysis of sensitivity, power fraction, and confinement loss is also demonstrated using the predicted and simulated data. The suggested models were also examined in terms of R 2 -score, mean average error (MAE), and mean squared error (MSE), with all of the models having an R 2 -score of more than 0.99, and it was also shown that optical biosensors had a design error rate of less than 3%. This research might pave the way for machine learning-based optimization approaches to be used to improve optical biosensors. [ABSTRACT FROM AUTHOR]

High order statistics are useful for automatic modulation recognition and parameter estimations. In this paper, we cast the problem of recovering high order statistics of PSK signals taken from nonuniform compressive samples as a one of recovering a low-rank matrix from missing or corrupted observations. This is a new model to describe the high order statistics of PSK signals. Unlike traditional uniformly Nyquist samples, our method uses the advanced optimization technique, which is guaranteed to find the low-rank matrix by simultaneously fixing the missing entries. Simulation results demonstrate that our method achieves accurate estimates of the major portion of the high order statistics. The new technique can be used to fulfil automatic modulation recognition (AMR) and rough estimations of parameters. More specifically, low-rank structure of PSK signals is studied. In contrast to the existing $l_{1}$ optimization criteria, our method proposed here is computationally more efficient and provides high accuracy.

A pattern net assisted mapping artificial neural network (PAMANN) model for estimation of parameters in problem with large data (1300 × 121 matrix size) is reported. A pattern net‐based multilayer perceptron neural network (MLPNN) model for clustering the data, followed by mapping MLPNN model for mapping the target with the input, is developed as PAMANN model. A heat transfer problem with combined mode conduction and radiation in porous medium is solved numerically, and is called direct model. In the inverse model, a PAMANN model is developed by using data generated through the direct model. The PAMANN model is able to estimate two parameters (extinction coefficient β and convective coupling P2) after taking temperature profile as input. The model is tested for different number of neurons in hidden layer, and different levels of noise in input data. Twelve different algorithms are explored in training of mapping MLPNN, and compared for performance. Levenberg–Marquardt algorithm is found to estimate the parameters with high accuracy, but took high CPU time. Bayesian regularization is found to consume very high CPU time with moderate accuracy in estimation of parameters. Variations in hidden layer neuron number and noise in input data, were done to analyze the performance of mapping MLPNN with different training algorithms. Algorithms O‐Step Secant, conjugate gradient with Polak‐Ribiére updates, and conjugate gradient with Fletcher‐Reeves updates are able to handle all variations of noise and number of neurons in hidden layer, with good accuracy of estimation and low CPU time consumption. Under high computational resource LM algorithm can be used for all cases. Up to 0.99132 value of regression coefficient is obtained in mapping MLPNN model with 15 hidden neurons, indicating the high accuracy of the model. With the help of PAMANN model, highly accurate (absolute error 1.78%) estimation of parameters is obtained. The model can handle upto 1% noise in input data, while giving accurate results. [ABSTRACT FROM AUTHOR]

The resurgence of monkeypox causes considerable healthcare risks needing efficient immunization programs. This work investigates the monkeypox disease dynamics in the UK, focusing on the impact of vaccination under real data. The key difficulty is to correctly predict the spread of the disease and evaluate the success of immunization efforts. We construct a mathematical model for monkeypox infection and extend it to the fractional case considering the Caputo derivative. The analysis ensures the positivity, boundedness, and uniqueness of the solution for the non-integer system. We conduct a local asymptotical stability analysis (LAS) at the disease-free equilibrium (DFE) D 0 , showing the result for R 0 <1. Additionally, we demonstrate the existence of multiple endemic equilibria and provide conditions for backward bifurcation, which are illustrated graphically. Using real case data from the UK, we estimate model parameters via the nonlinear least square method. Our results show that, without vaccination, R 2 ≈0.8, whereas vaccination reduces it to R 2 v =0.48. We perform sensitivity analysis to identify key parameters influencing disease elimination, presenting the outcomes through graphs. To solve numerically the fractional model, we outline a numerical scheme and provide detailed results under various parameter assumptions. Our findings suggest that high vaccine efficacy, a low waning rate of the vaccines, and increased vaccination of the infected people can significantly reduce the future cases of monkeypox in the UK. The present study offers a comprehensive framework for monkeypox dynamics and informs public health strategies for effective disease control and prevention., Competing Interests: Declaration of competing interest The authors are declared that they no potential conflict of interest regarding the publication of this work., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

This work presents an accurate, scalable, and efficient hybrid machine learning (ML) and neural network (NN) model based, cross‐platform application to analyze and estimate crucial device parameters like scattering (S‐) parameter, gain, power, device‐width and traps of GaN high electron mobility devices. A hybrid multilayer perceptron random forest (RF) model with 13 input parameters was trained on Technology Computer‐Aided Design generated data. An inclusive view of device physics using various device parameters has been presented, which helps to develop insights into structural architecture, DC, and RF performance of the device, and its trade‐off as a function of frequency and biases, all in one go. Moreover, a cross‐platform graphical user interface application is developed to ease the complete process, which further makes the platform scalable to other devices as well. The extremely fast prediction time of 3–7 s and 35–40 ms in regression and classification, respectively, depict the excellent time efficiency of the proposed approach. The results show superior performance with the global mean absolute error (MAE) ranging from 8e−5 to 0.010 and mean squared error (MSE) ranging from 5e−7 to 0.072 accounts for the overall accuracy of 99% and above for the S‐parameter and current gain predictions. A maximum 0.06% variation in the prediction of device width over 140 iterations depicts the excellent generalization capability of the model. The evaluated results thus direct the usefulness of the cross‐platform applications in accelerating accurate device parameter estimations and efficient optimization in device design. [ABSTRACT FROM AUTHOR]

Abstract In this work, we develop and analyze a nonautonomous mathematical model for the spread of the new corona-virus disease (COVID-19) in Saudi Arabia. The model includes eight time-dependent compartments: the dynamics of low-risk S L $S_{L}$ and high-risk S M $S_{M}$ susceptible individuals; the compartment of exposed individuals E; the compartment of infected individuals (divided into two compartments, namely those of infected undiagnosed individuals I U $I_{U}$ and the one consisting of infected diagnosed individuals I D $I_{D}$ ); the compartment of recovered undiagnosed individuals R U $R_{U}$ , that of recovered diagnosed R D $R_{D}$ individuals, and the compartment of extinct Ex individuals. We investigate the persistence and the local stability including the reproduction number of the model, taking into account the control measures imposed by the authorities. We perform a parameter estimation over a short period of the total duration of the pandemic based on the COVID-19 epidemiological data, including the number of infected, recovered, and extinct individuals, in different time episodes of the COVID-19 spread.

To develop standard optical biosensors, the simulation procedure takes a lot of time. For reducing that enormous amount of time and effort, machine learning might be a better solution. Effective indices, core power, total power, and effective area are the most crucial parameters for evaluating optical sensors. In this study, several machine learning (ML) approaches have been applied to predict those parameters while considering the core radius, cladding radius, pitch, analyte, and wavelength as the input vectors. We have utilized least squares (LS), LASSO, Elastic-Net (ENet), and Bayesian ridge regression (BRR) to make a comparative discussion using a balanced dataset obtained with the COMSOL Multiphysics simulation tool. Furthermore, a more extensive analysis of sensitivity, power fraction, and confinement loss is also demonstrated using the predicted and simulated data. The suggested models were also examined in terms of R2-score, mean average error (MAE), and mean squared error (MSE), with all of the models having an R2-score of more than 0.99, and it was also shown that optical biosensors had a design error rate of less than 3%. This research might pave the way for machine learning-based optimization approaches to be used to improve optical biosensors.

A dynamic two‐level artificial neural network (DTLANN) approach is used for the estimation of parameters in combined mode conduction–radiation heat transfer in a porous medium. Four commonly used neural networks: feed forward, cascade forward, fitnet, and radial basis are used in mapping artificial neural network (ANN), and their performance is compared under noisy big data (10,302 × 1300 matrix size). Governing equations for heat transfer in the porous medium through conduction and radiation modes are solved by finite volume method and discrete transfer method. This numerical model is called a direct model. A large amount of data is generated by using the direct model for different values of extinction coefficient β and convective coupling P2. These data were divided into different groups (class) based on the temperature difference between the gas and solid phase. In the inverse analysis, a new pair of temperature profiles for the solid and gas phase is taken as input and classified with the help of a pattern net artificial neural network model. On the basis of classification, data from that particular class and its neighbor class are used for training the mapping ANN model. After the training of the mapping ANN model, corresponding values of β and P2 are obtained as output for any new input. This DTLANN model has a high regression coefficient (R) of.99131 and can predict highly accurate values of parameters under a huge dataset with noise, within much less CPU time. [ABSTRACT FROM AUTHOR]

The purpose of this work is to analyze the dynamics of dengue fever in newly introduced operator known as fractal-fractional Atangana-Baleanu. Initially, we formulate a new dengue model with hospitalization class of notified infected cases and present the model basic results. Stability results for the model are shown when R0

We study the h-discrete and h-discrete fractional representation of a pharmacokinetics-pharmacodynamics (PK-PD) model describing tumor growth and anticancer effects in continuous time considering a time scale h𝕅0, where h > 0. Since the measurements of the drug concentration in plasma were taken hourly, we consider h = 1/24 and obtain the model in discrete time (i.e. hourly). We then continue with fractionalizing the h-discrete nabla operator in the h-discrete model to obtain the model as a system of nabla h-fractional difference equations. In order to solve the fractional h-discrete system analytically we state and prove some theorems in the theory of discrete fractional calculus. After estimating and getting confidence intervals of the model parameters, we compare residual squared sum values of the models in one table. Our study shows that the new introduced models provide fitting as good as the existing models in continuous time.

A method to detect solitary internal waves passing through the sensors area in shallow water and estimate their parameters is proposed in this paper using distributed acoustic sensors. The proposed detection method is based on cross correlation of the (envelop of) channel impulse responses estimated from broadband signals transmitted between the sensor nodes with the reference impulse responses in the absence of solitary internal waves. An iterative sequential parameter estimation method is proposed based on time domain matching of the measured channel impulse responses with modeled impulse responses. Simultaneous parameter estimation can be obtained using a global search method such as the matched field inversion. Simulation studies are carried out using environmental acoustic data collected in the northern South China Sea. The results show that the proposed method can effectively detect the existence of passing SIWs, and their parameters can be estimated with reasonable accuracy even under low signal-to-noise ratio conditions.

We formulate a simple susceptible‐infectious‐recovery (SIR) model to describe the spread of the coronavirus under strict social restrictions. The transmission rate in this model is exponentially decreasing with time. We find a formula for basic reproduction function and estimate the maximum number of daily infected individuals. We fit the model to induced death data in Italy, United States, Germany, France, India, Spain, and China over the period from the first reported death to August 7, 2020. We notice that the model has excellent fit to the disease death data in these countries. We estimate the model's parameters in each of these countries with 95% confidence intervals. We order the strength of social restrictions in these countries using the exponential rate. We estimate the time needed to reduce the basic reproduction function to one unit and use it to order the quality of social restrictions in these countries. The social restriction in China was the strictest and the most effective and in India was the weakest and the least effective. Policy‐makers may apply the Chinese successful social restriction experiment and avoid the Indian unsuccessful one. [ABSTRACT FROM AUTHOR]

We study the discrete and discrete fractional representation of a pharmacokinetics - pharmacodynamics (PK-PD) model describing tumor growth and anti-cancer effects in continuous time considering a time scale hℕ0h$h\mathbb{N}_0^h$, where h > 0. Since the measurements of the tumor volume in mice were taken daily, we consider h = 1 and obtain the model in discrete time (i.e. daily). We then continue with fractionalizing the discrete nabla operator to obtain the model as a system of nabla fractional difference equations. The nabla fractional difference operator is considered in the sense of Riemann-Liouville definition of the fractional derivative. In order to solve the fractional discrete system analytically we state and prove some theorems in the theory of discrete fractional calculus. For the data fitting purpose, we use a new developed method which is known as an improved version of the partial sum method to estimate the parameters for discrete and discrete fractional models. Sensitivity analysis is conducted to incorporate uncertainty/noise into the model. We employ both frequentist approach and Bayesian method to construct 90 percent confidence intervals for the parameters. Lastly, for the purpose of practicality, we test the discrete models for their efficiency and illustrate their current limitations for application.

In this work, we develop and analyze a nonautonomous mathematical model for the spread of the new corona-virus disease (COVID-19) in Saudi Arabia. The model includes eight time-dependent compartments: the dynamics of low-risk S L and high-risk S M susceptible individuals; the compartment of exposed individuals E; the compartment of infected individuals (divided into two compartments, namely those of infected undiagnosed individuals I U and the one consisting of infected diagnosed individuals I D ); the compartment of recovered undiagnosed individuals R U , that of recovered diagnosed R D individuals, and the compartment of extinct Ex individuals. We investigate the persistence and the local stability including the reproduction number of the model, taking into account the control measures imposed by the authorities. We perform a parameter estimation over a short period of the total duration of the pandemic based on the COVID-19 epidemiological data, including the number of infected, recovered, and extinct individuals, in different time episodes of the COVID-19 spread. [ABSTRACT FROM AUTHOR]

The aim of this study was to compare the covariance structures by using Maximum Likelihood (ML), Restricted Maximum Likelihood (REML) and Minimum Variance Quadratic Unbiased Estimator (MIVQUE) in the estimation methods in repeated measures design with mixed model approach. In the study, live weight (birth, 30th, 60th, 90th, 120th day) values of 60 head Kilis goats from birth to 120 days old were used as research data. For the purpose of evaluate of the relationship among the data, Compound symmetry (CS), Variance components (VC), (First-order autoregressive (AR(1)), Unstructured (UN), Toeplitz (TOEP), Heterogenous compound symetry (CSH), Heterogenous first-order autoregressive (ARH(1)), Heterogenous toeplitz (TOEPH), First-Order Autoregressive Moving-Avarege (ARMA(1,1)), Toeplitz With Two Bands (TOEP(2)), First-order factor analytic (FA(1)), Equal Diagonal Factor Analytic (FA1(1)), Unstructured correlations (UNR), Banded Unstructured (UN(1)), Ante-Depence (ANTE(1)) covariance structures were used. The most appropriate covariance structure was selected according to 2Ln(L), AIC, AICC and BIC information criteria in modeling the relationship between data in all three estimation methods (ML, REML and MIVQUE0), UN and UNR covariance structures were determined as the most appropriate covariance structures, although they gave the same results. [ABSTRACT FROM AUTHOR]

COVID-19 or coronavirus is a newly emerged infectious disease that started in Wuhan, China, in December 2019 and spread worldwide very quickly. Although the recovery rate is greater than the death rate, the COVID-19 infection is becoming very harmful for the human community and causing financial loses to their economy. No proper vaccine for this infection has been introduced in the market in order to treat the infected people. Various approaches have been implemented recently to study the dynamics of this novel infection. Mathematical models are one of the effective tools in this regard to understand the transmission patterns of COVID-19. In the present paper, we formulate a fractional epidemic model in the Caputo sense with the consideration of quarantine, isolation, and environmental impacts to examine the dynamics of the COVID-19 outbreak. The fractional models are quite useful for understanding better the disease epidemics as well as capture the memory and nonlocality effects. First, we construct the model in ordinary differential equations and further consider the Caputo operator to formulate its fractional derivative. We present some of the necessary mathematical analysis for the fractional model. Furthermore, the model is fitted to the reported cases in Pakistan, one of the epicenters of COVID-19 in Asia. The estimated value of the important threshold parameter of the model, known as the basic reproduction number, is evaluated theoretically and numerically. Based on the real fitted parameters, we obtained R 0 ≈ 1.50 . Finally, an efficient numerical scheme of Adams–Moulton type is used in order to simulate the fractional model. The impact of some of the key model parameters on the disease dynamics and its elimination are shown graphically for various values of noninteger order of the Caputo derivative. We conclude that the use of fractional epidemic model provides a better understanding and biologically more insights about the disease dynamics. [ABSTRACT FROM AUTHOR]

New developments for parameter and time-delay identification are presented for discrete nonlinear systems with delayed input. The proposed approach is based on overparametrization approach which involves subsuming the delay term into an extended numerator polynomial of the linear block of Wiener time-delay system. On this basis, the parameter identification problem can be then solved using recursive least squares-based optimization techniques and then, the delay is calculated directly based on the extended numerator polynomial identified: For a noise-free system, all extended numerator parameters are equal to zero. However in the noisy-output case, it is necessary to introduce an upper bound and the extended parameters whose values are smaller than a threshold level should be identified as zero. Then, the delay is determined as the first number of null extended parameter values. In addition, the convergence of the identified parameter vector is studied. The performances of the proposed identification algorithms are illustrated through simulation examples. [ABSTRACT FROM AUTHOR]

To study the parameter estimating effects of a free-floating tumbling space target, the extended Kalman filter (EKF) scheme is utilized with different high-nonlinear translational and rotational coupled kinematic & dynamic models on the LIDAR measurements. Applying the aforementioned models and measurements results in the situation where one single state can be estimated differently with varying accuracies since the EKFs based on different models have different observabilities. In the proposed EKFs, the traditional quaternions based kinematics and dynamics and the dual vector quaternions (DVQ) based kinematics and dynamics are used for the modeling of the relative motions between a chaser satellite and an uncooperative target. In the non-contact estimating scenarios, only highly nonlinear relative attitude and range measurements: the grapple fixture on the target measured from the chaser satellite via vision-based sensors, can be used. By evaluating the results of the EKFs, the observability properties of each EKF are studied analytically and numerically with the the Observability Gramian matrices (OG) and the standard deviations for every estimated parameters. The analysis of observability perform intensive studies and reveal the intrinsic factors that affect the accuracy and stability of the parameters estimation of an uncooperative space target. Finally, the analytical and numerical results show the optimal composition of the kinematic & dynamic models and measurements. [ABSTRACT FROM AUTHOR]

The urgency of the work is caused by the fact that the power spectrum as well as the correlation function, is one of the most important characteristics of the second order of stochastic process. The spectrum shows what kind of harmonics prevails in the process, its structure; allows estimating spectral composition of the studied useful signals and noises. It is possible to synthesize (recover) signal, as well as to construct linear, including optimal filters, to obtain error estimates of linear filtering by the spectra. The main aim of the study is to evaluate the power spectrum of a stationary random process as a first-order spline under the following measurement schemes: one measurement is made every moment, a random number of measurements is made every moment. Study of statistical characteristics of the estimates. The methods used in the study: the methods of probability theory and mathematical statistics are used for calculation. The results: The authors obtained an unbiased estimate of the power spectrum as a first-order spline in two schemes of measurement: one measurement is made every moment, a random number of measurements is made every moment. It is shown that the variance of estimates behaves asymptotically like 1 / T, where Т is the time of observation.

Accurate and reliable estimation of kinetic parameters of pollutant biodegradation processes is essential for environmental and health risk assessment. Common biodegradation models proposed in the literature, such as the nonlinear Monod equation and its simplified versions (e.g. Michaelis-Menten-like and first-order equations), are problematic in terms of accuracy of kinetic parameters due to the parameter correlation. However, a comparison between these models in terms of accuracy and reliability, related to data imprecision, has not been performed in the literature. This task is necessary, mainly because the model selection cannot be straightforward, as shown in this work. To facilitate the comparison, novel statistics summarising the accuracy and reliability of estimations are introduced. The main objective is to establish relationships between these statistics (trough new diagnostic indicators) to limit the probability of pitfalls or to avoid the negative impact of an improper model selection. Such anticipation is an imperative need in the biodegradation modelling framework and, to the best of our knowledge, it has never been performed. In order to account for accuracy, simulated data in realistic conditions are used to highlight the magnitude of pitfalls related to the model selection for estimation of the main kinetic parameters (K s , μ m and/or V m). Four scenarios related to model selection are compared for the first time and, diagnostic indicators able to anticipate relevant aspects related to accuracy and reliability are introduced. Moreover, first evidences of the impact of measurement errors in other intrinsic Monod parameters (the initial biomass concentration and the microbial yield coefficient, Y), as well as the impact of the simultaneous μ m , K s and Y estimation, on the accuracy and reliability of the estimations are reported. Despite the pitfalls shown, specific applicability of even unreliable models is highlighted, and suggestions for environmental and health risk modellers are provided accordingly. Image 1 • Pitfalls in biodegradation kinetic parameter estimations are identified by simulation. • Kinetic parameter accuracy and reliability elements are related for the first time. • Kinetic biodegradation model comparisons are developed. • Diagnostic statistics anticipate pitfall probabilities in real experiments. • Unreliable biodegradation models can still be useful to estimate persistence. Capsule : The accuracy degree of biodegradation parameter estimation from substrate depletion curves of organic pollutants is anticipated using diagnostic indicators calculated from models. [ABSTRACT FROM AUTHOR]

Abstract Estimating the parameters of an uncooperative space target is vital important in the on-orbit servicing missions (OOS). Considering the measurement failures caused by the complexed space environment during the measuring procedure, this paper proposes a novel dual vector quaternions based mixed artificial neural network estimating algorithm (DVQ-MANN) to estimate the parameters of the uncooperative space target. Firstly, the dual vector quaternions (DVQ) are utilized to set up the relative kinematics and dynamics model. When the measurements are available, an Extended Kalman Filter (EKF) of the DVQ-MANN will operate to accomplish parameter estimations. When the measurements failures occur, the artificial neural networks(ANN) of the DVQ-MANN will work. In the designed DVQ-MANN, the first ANN is a three-layer feedforward neural network to estimate the states of the uncooperative space target. Besides, a novel deep convolution neural network is designed to estimate the covariance matrix of the states for its advantages in processing high dimensional inputs. By training well off-board and updating onboard, the proposed ANNs of the proposed DVQ-MANN can make reliable estimations under measurements failures. Finally, the proposed DVQ-MANN is validated by mathematical simulations to show its robust performances. [ABSTRACT FROM AUTHOR]

In this study, it is aimed to estimate the regression parameters in case of measurement error in explanatory variables. In the study, data of March, June, September and December between the years 2003 and 2018 were used for the statistical analysis. Dollar values were taken to minimize the inflation effect of the data. To estimate the regression parameters, the least squares method, two group method and three group method were used to calculate the coefficients of the parameters. As a result of the study, it was seen that the three group methods gave better results than the other methods. In the study, the relationship between the multiple regression model and the variables was found to be functional. [ABSTRACT FROM AUTHOR]

We assess the relative performance of a suite of selected models to interpret three-phase oil relative permeability data and provide a procedure to determine identifiability of the model parameters. We ground our analysis on observations of Steady-State two- and three-phase relative permeabilities we collect on a water-wet Sand-Pack sample through series of core-flooding experiments. Three-phase experiments are characterized by simultaneous injection of water and gas into the core sample initiated at irreducible water saturation, a scenario which is relevant for modern enhanced oil recovery techniques. The selected oil relative permeability models include classical and recent formulations and we consider their performance when ( i ) solely two-phase data are employed and/or ( ii ) two- and three-phase data are jointly used to render predictions of three-phase oil relative permeability, k ro . We assess identifiability of model parameters through the Profile Likelihood (PL) technique. We rely on formal model discrimination criteria for a quantitative evaluation of the interpretive skill of each of the candidate models tested. We also evaluate the relative degree of likelihood associated with the competing models through a posterior probability weight and use Maximum Likelihood Bayesian model averaging to provide model-averaged estimate of k ro and the associated uncertainty bounds. Results show that assessing identifiability of uncertain model parameters on the basis of the available dataset can provide valuable information about the quality of the parameter estimates and can reduce computational costs by selecting solely identifiable models among available candidates. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of identification of Wiener systems with unknown integer time delay. This problem presents several difficulties, since it consists in estimating simultaneously the integer time delay, the parameters of the linear dynamic subsystem and the parameters of the non-linear static block. To overcome these difficulties, we propose a new approach to identify the Wiener time delay systems based on the Hierarchical gradient identification principle. This proposed method consists, first, in decoupling the original optimization problem into three simple separate criteria jointly optimized and second, in using the gradient algorithm to minimize each function. The analysis gives us insight into the properties of this algorithm and develops condition that must be satisfied to ensure the convergence and to guarantee the use of rounding property. Simulation results are presented to illustrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of nonlinear discrete fractional equations to model tumor growth rates in mice. For the data fitting purpose, we develop a new method which can be considered as an improved version of the partial sum method for parameter estimations. We demonstrate the goodness of fit by comparing the models with three statistical measures. [ABSTRACT FROM AUTHOR]

Simultaneous estimation of thermophysical and optical properties such as the thermal conductivity, the scattering albedo, and the emissivity of a 1-D planar porous matrix involving combined mode conduction and radiation heat transfer with heat generation is reported. Coupled energy equations for the gas and solid phase account for the nonlocal thermal equilibrium between the two phases. Performances of the genetic algorithm (GA) and the global search algorithm (GSA) in simultaneous estimation of three properties are analyzed. Both the GA and the GSA utilize a priori knowledge of the axial gas temperature distribution, and the magnitudes of the convective and the radiative heat fluxes at the outer surface of the porous matrix. With volumetric radiative information needed in the solid-phase energy equation computed using the discrete transfer method, the two energy equations are simultaneously solved using the finite volume method. GSA provides better estimation, and computationally, it is much faster than the GA. [ABSTRACT FROM AUTHOR]

An efficient approach to estimate model parameters from residual gravity data based on differential evolution (DE), a stochastic vector-based metaheuristic algorithm, has been presented. We have showed the applicability and effectiveness of this algorithm on both synthetic and field anomalies. According to our knowledge, this is a first attempt of applying DE for the parameter estimations of residual gravity anomalies due to isolated causative sources embedded in the subsurface. The model parameters dealt with here are the amplitude coefficient ( A ), the depth and exact origin of causative source ( zo and xo , respectively) and the shape factors ( q and ƞ ). The error energy maps generated for some parameter pairs have successfully revealed the nature of the parameter estimation problem under consideration. Noise-free and noisy synthetic single gravity anomalies have been evaluated with success via DE/best/1/bin, which is a widely used strategy in DE. Additionally some complicated gravity anomalies caused by multiple source bodies have been considered, and the results obtained have showed the efficiency of the algorithm. Then using the strategy applied in synthetic examples some field anomalies observed for various mineral explorations such as a chromite deposit (Camaguey district, Cuba), a manganese deposit (Nagpur, India) and a base metal sulphide deposit (Quebec, Canada) have been considered to estimate the model parameters of the ore bodies. Applications have exhibited that the obtained results such as the depths and shapes of the ore bodies are quite consistent with those published in the literature. Uncertainty in the solutions obtained from DE algorithm has been also investigated by Metropolis–Hastings (M–H) sampling algorithm based on simulated annealing without cooling schedule. Based on the resulting histogram reconstructions of both synthetic and field data examples the algorithm has provided reliable parameter estimations being within the sampling limits of M–H sampler. Although it is not a common inversion technique in geophysics, it can be stated that DE algorithm is worth to get more interest for parameter estimations from potential field data in geophysics considering its good accuracy, less computational cost (in the present problem) and the fact that a well-constructed initial guess is not required to reach the global minimum. [ABSTRACT FROM AUTHOR]

The principle of the thread fastenings have been known and used for decades with the purpose of joining one component to another. Threaded fastenings are popular because they permit easy disassembly for maintenance, repair, relocation and recycling. Screw insertions are typically carried out manually. It is a difficult problem to automat. As a result there is very little published research on automating threaded fastenings, and most research on automated assembly focus on the peg-in-hole assembly problem. This paper investigates the problem of automated monitoring of the screw insertion process. The monitoring problem deals with predicting integrity of a threaded insertion, based on the torque vs. insertion depth curve generated during the insertions. The authors have developed an analytical model to predict the torque signature signals during self-tapping screw insertions. However, the model requires parameters on the screw dimensions and plate material properties are difficult to measure. This paper presents a study on on-line identification during screw fastenings. An identification methodology for two unknown parameter estimation during a self-tapping screw insertion process is presented. It is shown that friction and screw properties required by the model can be reliably estimated on-line. Experimental results are presented to validate the identification procedure.

We consider parameter estimation for a single compartment model of a cerebrospinal fluid (CSF) infusion test using an inverse power law cerebral compliance depending on intracranial pressure (ICP). A least squares optimization is used to solve the inverse problem of estimating model parameter values from ICP observed during an infusion test. The optimization is applied to synthetic test data and to clinical ICP data from a number of infusion tests.We show that in tests that successfully reach a new plateau pressure, the resistance to CSF outflow and elastance can be reliably estimated using an automated least squares process. We find that a single infusion test does not provide enough resolution to distinguish between compliance models. [ABSTRACT FROM AUTHOR]

The accuracy of first-principle predictive models for the evolution of plasma profiles is sometimes limited by the lack of understanding of the plasma transport phenomena. It is possible then to develop approximate transport models for the prediction of plasma dynamics, which are consistent with the available diagnostic data. This data-driven approach, usually referred to as phenomenological modeling, arises as an alternative to the more classical theory-driven approach. In this paper, we propose a stochastic filtering approach based on an extended Kalman filter to provide real-time estimates of poorly known or totally unknown transport coefficients. We first assume that plasma dynamics is governed by tractable models obtained by first principles. However, the transport parameters are considered unknown and to be estimated. These estimates will be based solely on input/output diagnostic data and limited understanding of the transport physics. Numerical methods (e.g., finite differences) can be used to discretize the partial differential equation models both in space and time to obtain finite-dimensional discrete-time state-space representations. The system states and to-be-estimated parameters are then combined into an augmented state vector. The resulting nonlinear state-space model is used for the design of an extended Kalman filter that provides real-time estimations not only of the system states but also of the unknown transport coefficients. Simulation results demonstrate the effectiveness of the proposed method for a benchmark transport model in cylindrical coordinates. [ABSTRACT FROM AUTHOR]

Abstract: An increased interest has been directed towards the crystallization of pharmaceuticals and proteins in recent years, which have additional complications compared to the extensively studied inorganic batch and continuous crystallizations. Recent advances in process analytical technology have enabled the improved modeling and control of batch crystallization. This paper compares simulations and experiments between the classical temperature control approach developed in the 1970–1990s with the concentration-control approach developed more recently. The latter approach, which uses attenuated total reflection–Fourier transform infrared (ATR–FTIR) spectroscopy and feedback control to follow a setpoint trajectory in the solution concentration as a function of temperature, results in reduced sensitivity of the product quality to certain disturbances. The resulting guidelines from the simulations are applied to the experimental investigation of the crystallization of paracetamol in water. [Copyright &y& Elsevier]

Many pathologies are associated with abnormalities of glucose metabolism or with perturbations of its transport (type 2 diabetes or insulin-resistance). The pre-diabetic state is characterised by a state of insulin-resistance, in others words a defect of glucose transport in insulin-sensible tissues, such as muscles and adipose tissues. The mathematical modelling of experimental data can be an excellent method to explore the mechanisms implied in the studied biological phenomenon. Thus, starting from a symbolic formulation like the compartmental modelling, it can be possible to develop a theoretical basis for the observation and to consider the best-adapted experiments for the study. We showed with mathematical models that ⟦123I〉-6-deoxy-6-iodo-d-glucose (6-DIG), shown as a tracer of glucose transport in vitro, could point out this transport abnormality. To quantify the insulin resistance, we estimated the fractional transfer coefficients of 6-DIG from the blood to the organs. We realised many studies to lead to a satisfying model; special attention has been paid to the precision of the parameter to select the best model. The results showed that by associating experimental data obtained with 6-DIG activities and an adapted mathematical model, discriminating parameters (in and out fractional transfer coefficients) between the two groups (control and insulin-resistant rats) could be pointed out. [Copyright &y& Elsevier]