Parameter estimation of the network of FitzHugh-Nagumo neurons based on the speed-gradient and filtering.

The paper is devoted to the parameter identification problem for two-neuron FitzHugh-Nagumo models under condition when only one variable, namely, the membrane potential, is measured. Another practical assumption is that both variable derivatives cannot be measured. Finally, it is assumed that the sensor measuring the membrane potential is imprecise, and all measurements have some unknown scaling factor. These circumstances bring additional difficulties to the parameters' estimation problem, and therefore, such case was not studied before. To solve the problem first, the model is transformed to a more simple form without unmeasurable variables. Variables obtained from applying a second-order real filter-differentiator are used instead of unmeasurable derivatives. Then, an adaptive system, parameters of which are estimates of original system parameters, is designed. The estimation (identification) goal is to properly adjust parameter estimates. To this end, the speed-gradient method is employed. The correctness of the obtained solution is proved theoretically and illustrated by computer simulation in the Simulink environment. The sufficient conditions of asymptotically correct identification for the speed-gradient method with integral objective function are formulated and proved. The novelty of the paper is that in contrast to existing solutions to the FitzHugh-Nagumo identification problem, we take into account a systematic error of the membrane potential measurement. Furthermore, the parameters are estimated for a system composed of two FitzHugh-Nagumo models, which open perspectives for using the proposed results for modeling and estimation of parameters for neuron population.

The paper is devoted to the problem of parameter identification of two FitzHugh-Nagumo neuron models. The FitzHugh-Nagumo model is a simplification of the Hodgkin-Huxley model and it is very valuable for using on practice thanks to its simplicity. However, within an experiment only one variable of the FitzHugh-Nagumo model, the membrane potential, is measured, while another variable of cumulative effects of all slow ion currents responsible for restoring the resting potential of the membranes and both variables’ derivatives cannot be measured. This circumstance brings additional difficulties to the parameters estimation problem and, therefore, this case needs special attention. Firstly, the model was transformed to more simple form without unmeasured variables. Variables obtained from applying second-order real filter-differentiator were used instead of unmeasured derivatives in model’s equations. As a result, a linear equation was gotten and for this equation the identification goal, which guarantees correct parameters’ adjustment, was formulated and an adaptive system, parameters of which are estimations of original system’s parameters and an output of which estimates the output of the linear equation, was constructed. Then, the integral objective function was defined and the algorithm for the original model parameters identification was designed with the speed-gradient method. The results of computer simulation in the Simulink environment are presented. These results demonstrate that estimates of the model’s state and parameters converge to their true values rather fast. Unlike existing solutions of the FitzHugh-Nagumo identification problem, we propose a much easier deterministic algorithm. Moreover, the parameters are estimated for a system collected from two FitzHugh-Nagumo models, which opens perspectives for using the proposed method in modeling neuron population activity.

P 215. A method for online correction of artifacts in EEG signals during transcranial electrical stimulation

Synchronous behavior in networks of coupled systems : with applications to neuronal dynamics

This work consists of two parts, both related with regression analysis for interval censored data. Interval censored data x have the property that their value cannot be observed exactly but only the respective interval [xL,xR] which contains the true value x with probability one. In the first part of this work I develop an estimation theory for the regression parameters of the linear model where both dependent and independent variables are interval censored. In doing so I use a semi-parametric maximum likelihood approach which determines the parameter estimates via maximization of the likelihood function of the data. Since the density function of the covariate is unknown due to interval censoring, the maximization problem is solved through an algorithm which frstly determines the unknown density function of the covariate and then maximizes the complete data likelihood function. The unknown covariate density is hereby determined nonparametrically through a modification of the approach of Turnbull (1976). The resulting parameter estimates are given under the assumption that the distribution of the model errors belong to the exponential familiy or are Weibull. In addition I extend my extimation theory to the case that the regression model includes both an interval censored and an uncensored covariate. Since the derivation of the theoretical statistical properties of the developed parameter estimates is rather complex, simulations were carried out to determine the quality of the estimates. As a result it can be seen that the estimated values for the regression parameters are always very close the real ones. Finally, some alternative estimation methods for this regression problem are discussed. In the second part of this work I develop a residual theory for the linear regression model where the covariate is interval censored, but the depending variable can be observed exactly. In this case the model errors appear to be interval censored, and so the residuals. This leads to the problem of not directly observable residuals which is solved in the following way: Since one assumption of the linear regression model is the N(0,2)-distribution of the model errors, it follows that the distribtuion of the interval censored errors is a truncated normal distribution, the truncation being determined by the observed model error intervals. Consequently, the distribution of the interval censored residuals is a -distribution, truncated in the respective residual interval, where the estimation of the residual variance is accomplished through the method of Gomez et al. (2002). In a simulation study I compare the behaviour of the so constructed residuals with those of Gomez et al. (2002) and a naive type of resiudals which considers the middle of the residual interval as the observed residual. The results show that my residuals can be used for most of the simulated scenarios, wheras this is not the case for the other two types of residuals. Finally, my new residual theory is applied to a data set from a clinical study.

A nonlinear oscillator differential equation model for EEG signals is linearized and discretized. The unknown parameters of this model are estimated using the EKF from noisy EEG signals. Likewise, the parameters of a linear difference equation model for speech are estimated using the EKF from noisy speech measurements. Based on the hypothesis that EEG and speech signals are correlated, a linear regression model that relates speech parameters to EEG parameters is proposed. By substituting this linear regression model into the speech differential equation, the EEG parameters for a fresh person are estimated from the speech signal alone using the EKF. This set up compares the generation of EEG data from speech data using a computer with training based on available EEG and speech signals from the BCI.

Since couple of decades, biomedical signal processing plays an important role to the improve the quality of human life. The recent research in the field of biomedical signal processing is carried out by using important biomedical signals like EEG, EMD, ECG, blood pressure and nasal signals. Thesis is divided into 5 chapters including summary. Chapter 1 gives the introduction about Epilepsy, sleep states, piecewise linear functions and metrics used for performance evaluation. In Chapter 2, we proposed a hybrid approach for seizure detection using EEG signals. We used two piecewise linear models namely Halfwave and Franklin transformation. The reason of preferring the linear models over other models is that linear models are simple, computationally fast, and efficient. The algorithm is tested on 23 different subjects having more than 100 hours long term EEG in the CHB-MIT database in several respects. It showed better performance compared to the state-of-the art methods for seizure detection tested on the given database. In 2017 Bhattacharyya et al. [68] proposed best method for seizure detection based on multichannel, which may not be used for real time applications efficiently, achieved average sensitivity, specificity, and accuracy of 97.91%, 99.57%, 99.41%. Whereas, our proposed method achieved an average sensitivity, specificity, accuracy, false alarm rate and kappa of 99.45%, 99.75%, 99.01%, 0.0039, 0.964 respectively and these results are comparatively good than [68] and other state of the art methods. In Chapter 3, various sleep states are detected by using the extended version of the method proposed in Chapter 2. The aim of the algorithm proposed in Chapter 3 is to detect the various sleep states by combining different biomedical signals like EEG, blood pressure, and nasal signals. Algorithm is tested on MIT-BIH Polysomnographic database having more than 70 hours long term EEG, blood pressure and respiratory (nasal) signals with six different sleep classes. Proposed method shows better performance than state of the art methods. Proposed algorithm achieved an average sensitivity, specificity, accuracy, and false alarm rate of 98.35% and 97.32%, 96.96%, 0.029 respectively for two randomly picked classes, 96.62% and 97.10%, 93.94%, 0.030 for randomly picked any 4 classes, 96.13% and 98.33%, 93.84%, 0.016 for all six classes, which is higher than the existing state of the art methods. To use the algorithm in real time scenario, and to increase the further accuracy of the method proposed in Chapter 3 we proposed a new approach for sleep states in Chapter 4. We used two biomedical signals i.e., blood pressure signal, in time domain and EEG signal, in frequency domain. In time domain, statistical and morphological features are extracted from the blood pressure signal and in frequency domain, a piecewise linear reduction namely Franklin transformation is applied on EEG signal. The Franklin coefficients are used as discriminatory features in frequency domain. The novelty of the proposed method is that we considered two cases, the blood pressure signal by itself, and the combination of it with EEG signal. The motivation behind the first one is that in certain cases, e.g., smart personal mobile devices, only the blood pressure signal is available. In both cases the algorithm is tested on MIT-BIH Polysomnographic database having more than 80 hours long term EEG and blood Pressure signals. In both cases we performed comparison tests with relevant state-of-the-art methods, and our algorithm showed better or equal performance in terms of sensitivity, specificity, accuracy, and false alarm rate. Our proposed algorithm in case of using only blood signal, achieved an average sensitivity, specificity, accuracy, false alarm rate and kappa of 95.45%, 98.27%, 93.78 %, 0.0170, 0.0224 respectively which is good or comparatively equal to the state-of-the-art methods. Whereas, an average sensitivity, specificity, accuracy, false alarm rate and kappa of 99.45%, 99.75%, 99.01%, 0.0039, 0.964 respectively is achieved using blood and EEG signals, which is higher than the existing state of the art methods so far.

Preface . Acknowledgements. 1 Introduction to designs . 1.1 Introduction. 1.2 Stages of the research process. 1.3 Research design. 1.4 Types of research designs. 1.5 Requirements for a 'good' design. 1.6 Ethical aspects of design choice. 1.7 Exact versus approximate designs. 1.8 Examples. 1.9 Summary. 2 Designs for simple linear regression . 2.1 Design problem for a linear model. 2.2 Designs for radiation-dosage example. 2.3 Relative efficiency and sample size. 2.4 Simultaneous inference. 2.5 Optimality criteria. 2.6 Relative efficiency. 2.7 Matrix formulation of designs for linear regression. 2.8 Summary. 3 Designs for multiple linear regression analysis . 3.1 Design problem for multiple linear regression. 3.2 Designs for vocabulary-growth study. 3.3 Relative efficiency and sample size. 3.4 Simultaneous inference. 3.5 Optimality criteria for a subset of parameters. 3.6 Relative efficiency. 3.7 Designs for polynomial regression model. 3.8 The Poggendorff and Ponzo illusion study. 3.9 Uncertainty about best fitting regression models. 3.10 Matrix notation of designs for multiple regression models. 3.11 Summary. 4 Designs for analysis of variance models . 4.1 A typical design problem for an analysis of variance model. 4.2 Estimation of parameters and efficiency. 4.3 Simultaneous inference and optimality criteria. 4.4 Designs for groups under stress study. 4.5 Specific hypotheses and contrasts. 4.6 Designs for the composite faces study. 4.7 Balanced designs versus unbalanced designs. 4.8 Matrix notation for Groups under Stress study. 4.9 Summary. 5 Designs for logistic regression models . 5.1 Design problem for logistic regression. 5.2 The design. 5.3 The logistic regression model. 5.4 Approaches to deal with local optimality. 5.5 Designs for calibration of item parameters in item response theory models. 5.6 Matrix formulation of designs for logistic regression. 5.7 Summary. 6 Designs for multilevel models . 6.1 Design problem for multilevel models. 6.2 The multilevel regression model. 6.3 Cluster versus subject randomization. 6.4 Cost function. 6.5 Example: Nursing home study. 6.6 Optimal design and power. 6.7 Design effect in multilevel surveys. 6.8 Matrix formulation of the multilevel model . 6.9 Summary. 7 Longitudinal designs for repeated measurement models . 7.1 Design problem for repeated measurements. 7.2 The design. 7.3 Analysis techniques for repeated measures. 7.4 The linear mixed effects model for repeated measurement data. 7.5 Variance-covariance structures. 7.6 Estimation of parameters and efficiency. 7.7 Bone mineral density example. 7.8 Cost function. 7.9 D-optimal designs for linear mixed effects models with autocorrelated errors. 7.10 Miscellanea. 7. 11 Matrix formulation of the linear mixed effects model. 7. 12 Summary. 8 Two-treatment crossover designs . 8.1 Design problem for crossover studies. 8.2 The design. 8.3 Confounding treatment effects with nuisance effects. 8.4 The linear model for crossover designs. 8.5 Estimation of parameters and efficiency. 8.6 Cost and efficiency of the crossover design. 8.7 Optimal crossover designs for two treatments. 8.8 Matrix formulation of the mixed model for crossover designs. 8.9 Summary. 9 Alternative optimal designs for linear models . 9.1 Introduction. 9.2 Information matrix. 9.3 D A - or Ds-optimal designs. 9.4 Extrapolation optimal design. 9.5 L-optimal designs. 9.6 Bayesian optimal designs. 9.7 Minimax optimal design. 9.8 Multiple-objective optimal designs. 9.9 Summary. 10 Optimal designs for nonlinear models . 10.1 Introduction. 10.2 Linear models versus nonlinear models. 10.3 Design issues for nonlinear models. 10.4 Alternative optimal designs with examples. 10.5 Bayesian optimal designs. 10.6 Minimax optimal design. 10.7 Multiple-objective optimal designs. 10.8 Optimal design for model discrimination. 10.9 Summary. 11 Resources for the construction of optimal designs . 11.1 Introduction. 11.2 Sequential construction of optimal designs. 11.3 Exchange of design points. 11.4 Other algorithms. 11.5 Optimal design software. 11.6 A web site for finding optimal designs. 11.7 Summary. References . Author Index. Subject Index.

This paper presents an adaptive fuzzy controller for Nonlinear in Parameters (NLP) chaotic systems with parametric uncertainties. In the proposed controller, the unknown parameters are estimated by the novel Improved Speed Gradient (ISG) method, which is a modification of Speed Gradient (SG) algorithm. ISG employs the Lagrangian of two suitable objective functionals for on-line estimation of system parameters. The most significant advantage of ISG is that it is applicable to NLP systems and it results in a faster rate of convergence for the estimated parameters than the SG method. Estimated parameters are used to design the fuzzy controller and to calculate the Lyapunov exponents of the chaotic system adaptively. Furthermore, established on the well-known Takagi–Sugeno (T-S) fuzzy model, a LMI (Linear Matrix Inequality)-based fuzzy controller is designed and is tuned using estimated parameters and Lyapunov exponents. Throughout the controller design procedure, several important issues in fuzzy control theory including relaxed stability analysis, control input performance specifications, and optimality are taken into account. Combination of ISG parameter estimation method and T-S-based fuzzy controller yields an adaptive fuzzy controller capable to suppress uncertainties in parameters and initial states of NLP chaotic systems. Finally, simulation results are provided to show the effectiveness of the ISG and adaptive fuzzy controller on chaotic Lorenz system and Duffing oscillator.

Editor's evaluation: Robust and Efficient Assessment of Potency (REAP) as a quantitative tool for dose-response curve estimation

The Ordinary Least Squares estimator estimates the parameter vectors in a linear regression model. However, it gives misleading results when the input variables are highly correlated, emanating the issue of multicollinearity. In light of multicollinearity, we wish to obtain more accurate estimators of the regression coefficients than the least square estimators. The main problem of least square estimation is to tackle multicollinearity so as to get more accurate estimates. In this paper, we introduce a New Modified Generalized Two Parameter Estimator by merging the Generalized Two Parameter Estimator and the Modified Two Parameter Estimator and compare it with other known estimators like Ordinary Least Squares Estimator, Ridge Regression Estimator, Liu estimator, Modified Ridge Estimator, Modified Liu Estimator and Modified Two Parameter Estimator. Mean Squared Error Matrix criterion was used to compare the new estimator over existing estimators. The estimation of the biased parameters is discussed. Necessary and sufficient conditions are derived to compare the proposed estimator with the existing estimators. The excellence of the new estimator over existing estimators is illustrated with the help of real data set and a Monte Carlo simulation study. The results indicate that the newly developed estimator is more efficient as it has lower mean square error.

Fast parameter estimation is required in several applications where unforeseen changes often occur in system characteristics. Quite often such parameter estimation must be accompanied by state estimation as well. A prime example of growing importance is battery management systems for Lithium-ion batteries.Without accurate knowledge of internal battery states and parameters we are left with a choice between safety and performance with regards to battery selection for a specific application. With the goal of simultaneous estimation of both states and parameters, and arbitrarily fast estimation of the latter, a new adaptive observer based on matrix regressors is introduced in this paper. In contrast to earlier work, this adaptive observer requires the regressors include filters of much lower order. Sufficient conditions for the exponential convergence of parameter estimates to their true values are stated and derived. Guidelines are provided for the selection of design parameters, minimizing the number of observer parameters that must be tuned to facilitate fast convergence. Two numerical simulations are included, demonstrating the performance of the proposed observer scheme as well as a comparison with existing matrix regressor based adaptive observers. Examples considered are a generic linear plant model as well as the dynamics representative of a single particle of a Lithium-ion battery cell.

Estimation, Prediction and Testing in Linear Models. Increments for (co)kriging with trend and pseudo-covariance estimation, L.C.A. Corsten. On the presentation of the minimax linear estimator in the convex linear model, H. Drygas, H. Lauter. Estimation of parameters in a special type of random effects model, J. Volaufova. Recent results in multiple testing - several treatments vs. a specified treatment, C.W. Dunnett. Multiple-multivariate-sequential T2-comparisons, C.P. Kitsos. On diagnosing collinearity-influential points in linear regression, H. Nyquist. Using nonnegative minimum biased quadratic estimation for variable selection in the linear regression model, S. Gnot, H. Knautz, G. Trenkler. Partial least squares and a linear model, D. von Rosen. Robustness. One-way analysis of variance under Tukey contamination - a small sample case simulation study, R. Zielinski. A note on robust estimation of parameters in mixed unbalanced models, T. Bednarski, S. Zontek. Optimal bias bounds for robust estimation in linear models, C.H. Muller. Estimation of Variance Components. Geometrical relations among variance component estimators, L.R. LaMotte. Asymptotic efficiencies of MINQUE and ANOVA variance component estimates in the nonnormal random model, P.H. Westfall. On asymptotic normality of admissible invariant quadratic estimators of variance components, S. Zontek. Admissible nonnegative invariant quadratic estimation in linear models with two variance components, S. Gnot, G. Trenkler, D. Stemann. About the multimodality of the likelihood function when estimating the variance components in a one-way classification by means of the ML or REML method, V. Guiard. Nonlinear Generalizations. Prediction domain in nonlinear models, S. Audrain, R. Tomassone. The geometry of nonlinear inference - accounting of prior and boundaries, A. Pazman. Design and Analysis of Experiments. General balance - artificial theory or practical relevance?, R.A. Bailey. Optimality of generally balanced experimental block designs, B. Bogacka, S. Mejza. Optimality of the orthogonal block design for robust estimation under mixed models, R. Zmyslony, S. Zontek. On generalized binary proper efficiency-balanced block designs, A. Das, S. Kageyama. Design of experiments and neighbour methods, J.-M. Azais. A new look into composite designs, S. Ghosh, W.S. Al-Sabah. Using the complex linear model to search for an optimal juxtaposition of regular fractions, H. Monod, A. Kobilinsky. Some directions in comparison of linear experiments - a review, C. Stepniak, Z. Otachel. Properties of comparison criteria of normal experiments, J. Hauke, A. Markiewicz. Miscellanea. Characterizations of oblique and orthogonal projectors, G. Trenkler. Asymptotic properties of least squares parameter estimators in a dynamic errors-in-variables model, J. ten Vregelaar. A generic look at factor analysis, M. Lejeune. On Q-covariance and its applications, A. Krajka, D. Szynal.

Towards Necessary and Sufficient Stability Conditions for NMPC

Viral kinetics in hepatitis C or hepatitis C/human immunodeficiency virus-infected patients