Narrow Results

We develop an autoregressive model framework based on the concept of Principal Dynamic Modes (PDMs) for the process of action potential (AP) generation in the excitable neuronal membrane described by the Hodgkin–Huxley (H–H) equations. The model's exogenous input is injected current, and whenever the membrane potential output exceeds a specified threshold, it is fed back as a second input. The PDMs are estimated from the previously developed Nonlinear Autoregressive Volterra (NARV) model, and represent an efficient functional basis for Volterra kernel expansion. The PDM-based model admits a modular representation, consisting of the forward and feedback PDM bases as linear filterbanks for the exogenous and autoregressive inputs, respectively, whose outputs are then fed to a static nonlinearity composed of polynomials operating on the PDM outputs and cross-terms of pair-products of PDM outputs. A two-step procedure for model reduction is performed: first, influential subsets of the forward and feedback PDM bases are identified and selected as the reduced PDM bases. Second, the terms of the static nonlinearity are pruned. The first step reduces model complexity from a total of 65 coefficients to 27, while the second further reduces the model coefficients to only eight. It is demonstrated that the performance cost of model reduction in terms of out-of-sample prediction accuracy is minimal. Unlike the full model, the eight coefficient pruned model can be easily visualized to reveal the essential system components, and thus the data-derived PDM model can yield insight into the underlying system structure and function.

We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown.

This paper proposes a realistic model of magnetizing branches for transient calculation of electric power circuits. The model represents the nonlinear relationship between flux linkage and exciting current of magnetizing branches with a major loop and a family of minor loop trajectories, which has the capability of simulating the multi-valued hysteresis behavior. By applying the proposed model to transient calculation, an efficient algorithm is developed for obtaining the transient responses in electric power circuits. In the algorithm, the electric power circuit is divided into the magnetizing branches and the remaining linear part. The nonlinear differential equations are set up for the magnetizing branches and solved by the semi-explicit Runge–Kutta method. The transient calculation for the remaining linear part is performed on the basis of the solution to the magnetizing branches. Then, a laboratory measurement is made with a reduced-scale experimental arrangement. The measured results are compared with the calculated ones and a reasonable agreement is shown between them.

Many models of the dynamics of nonlinear time series have large numbers of parameters and tend to overfit. This paper discusses algorithms for selecting the best basis functions from a dictionary for a model of a time series. Selecting the optimal subset of basis functions is typically an NP-hard problem which usually has to be solved by heuristic methods. In this paper, we propose a new heuristic that is a refinement of a previous one. We demonstrate with applications to artificial and real data. The results indicate that the method proposed in this paper is able to obtain better models in most cases.

In the past few years a new learning method called Support Vector Machines (SVMs) has enjoyed increasing popularity. Based on statistical learning theory it shows very good generalization abilities. Though SVMs are mainly used for classification tasks, they are also applicable to regression problems and thus to modeling the dynamics of a time series. However when regression techniques are used to build dynamical models caution is advisable if the data are noisy. Due to correlations between data points, estimates of model parameters deviate systematically from the true values. An approach is presented to reduce such bias in SVM parameters.

An ensemble approach is presented for the reconstruction of a phase synchronization diagram from time series. As an example system, we analyze a forced Colpitts oscillator to show that synchronization diagram reconstructed by a single nonlinear model depends sensitively upon the model parameters, which should be estimated with a considerable amount of care. This dependence can be crucial for a precise recovery of the synchronization phenomena. To overcome this weakness, an ensemble approach is introduced. Two types of techniques, namely, (I) ensemble regression and (II) ensemble classification, are developed to show that they provide much more robust and reliable reconstruction of the synchronization diagram compared to the conventional single modeling approach.

Whether or not the human cardiac system is chaotic has long been a subject of interest in the application of nonlinear time series analysis. The surrogate data method, which identifies an observed time series against three common kinds of hypotheses, does not provide sufficient evidence to confirm the existence of deterministic chaotic dynamics in cardiac time series, such as electrocardiogram data and pulse pressure propagation data. Moreover, these methods fail to exclude all but the most trivial hypothesis of linear noise. We present a recently suggested fourth algorithm for testing the hypotheses of a noise driven periodic orbit to decide whether these signals are consistent with deterministic chaos. Of course, we cannot exclude all other alternatives but our test is certainly stronger than the those applied previously. The algorithmic complexity is used as the discriminating statistic of the surrogate data method. We then perform nonlinear modeling for the short-term prediction between ECG and pulse data to provide further evidence that they conform to deterministic processes. We demonstrate the application of these methods to human electrocardiogram recordings and blood pressure propagation in the fingertip of seven healthy subjects. Our results indicate that bounded aperiodic determinism exists in both ECG and pulse time series. The addition of (the inevitable) dynamic noise means that it is not possible to conclude the underlying system is chaotic.

A nonlinear modeling of the protective effect of Quercetin (QCT) against various Mycotoxins (MTXs) has a high complexity and is conducted using artificial neural networks (ANNs). QCT is known to possess strong anti-oxidant, anti-inflammatory activity that can prevent many diseases. MTXs are highly toxic secondary metabolites that are capable of causing disease and death in humans and animals. The protective model of QCT against various MTXs (Citrinin, Patulin and Zearalenol) on HeLa cell is built accurately via learning of sparsely measured experimental data by the ANNs. It has shown that the neuro-model can predict the nonlinear protective effect of QCT against MTX-induced cytotoxicity for the measurement of percentage of inhibition of MTXs.

Lymphocyte recirculation plays an important role in controlling the spread of both pathogenic infections and tumor-producing cancer cells in the human body. We present a mathematical and computational framework that allows investigation of recirculating lymphocytes and estimation of model parameters using a genetic algorithm. The framework allows estimating parameters using data obtained from experiments performed in laboratory studies of rats as well as clinical studies of human subjects. Our computational model allows improved understanding of these data. Mathematical models enable investigators to obtain a quantitative picture of immune system kinetics and diversity in human health and disease outcomes. Our data-driven systems biology and immunological modeling approach contributes to a growing understanding of the dynamics of lymphocyte recirculation.

This paper tests for nonlinearities in the behavior of volatility expectations based on model-free implied volatility indices. Using Markov regime-switching models, the empirical evidence from the German, Japanese and U.S. markets suggests that there are indeed regime-specific levels of volatility expectations. Whereas the regimes seem to be governed by the degree of serial correlation and adjustment to forecast errors, there is no evidence of significant leverage effects. The frequency of regime shifts in volatility expectations is affected by the onset of financial crises, which have the effect of increasing the likelihood of regimes driven by lower autoregressive effects and faster speeds of adjustment. The evidence suggests that despite the heterogeneous beliefs of market participants, implied volatility indices provide a measure of consensus expectations that can be useful in understanding the nonlinear behavior of volatility expectations during periods of financial instability.

In 2006, a set of new correlation functions named combined ODACF and ODCCF was proposed for detecting nonlinear correltionships. In the present study, a new validation method which is based on the nonlinear correlation tests is proposed to check the quality of NARMAX data smoothers without detailed prior knowledge of the actual noise. A simulation example is implemented to demonstrate the effectiveness and efficiency of the new method.

Thermal dependency of material characteristics in MicroElectroMechanical Systems strongly affects their performance, design, and control. Hence, it is essential to understand and model that in MEMS devices to optimize their designs. Thermal dependency of material characteristics is one of the most important phenomena affecting the motion of Microresonator systems. A thermal phenomenon introduces two main effects: damping due to internal friction, and softening due to Young modulus-temperature relation. Based on some reported theoretical and experimental results, we qualitatively model the thermal phenomena and present two Lorentzian functions to describe the restoring and damping forces caused by thermal phenomena. In order to emphasize the thermal effects, a nonlinear model of the MEMS, by considering capacitor nonlinearity and midplane stretching, have been used. The response of the system is developed by employing multiple time scales perturbation method on nondimensionalized form of equations. Frequency response, resonant frequency and peak amplitude are examined for variation of dynamic parameters involved.