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Electroencephalographic (EEG) recordings are receiving growing attention in the field of emotion recognition, since they monitor the brain’s first response to an external stimulus. Traditionally, EEG signals have been studied from a linear viewpoint by means of statistical and frequency features. Nevertheless, given that the brain follows a completely nonlinear and nonstationary behavior, linear metrics present certain important limitations. In this sense, the use of nonlinear methods has recently revealed new information that may help to understand how the brain works under a series of emotional states. Hence, this paper summarizes the most recent works that have applied nonlinear methods in EEG signal analysis for emotion recognition. This paper also identifies some nonlinear indices that have not been employed yet in this research area.

Recently, the recognition of emotions with electroencephalographic (EEG) signals has received increasing attention. Furthermore, the nonstationarity of brain has intensified the application of nonlinear methods. Nonetheless, metrics like quadratic sample entropy (QSE), amplitude-aware permutation entropy (AAPE) and permutation min-entropy (PME) have never been applied to discern between more than two emotions. Therefore, this study computes for the first time QSE, AAPE and PME for recognition of four groups of emotions. After preprocessing the EEG recordings, the three entropy metrics were computed. Then, a tenfold classification approach based on a sequential forward selection scheme and a support vector machine classifier was implemented. This procedure was applied in a multi-class scheme including the four groups of study simultaneously, and in a binary-class approach for discerning emotions two by two, regarding their levels of arousal and valence. For both schemes, QSE+AAPE and QSE+PME were combined. In both multi-class and binary-class schemes, the best results were obtained in frontal and parietal brain areas. Furthermore, in most of the cases channels from QSE and AAPE/PME were selected in the classification models, thus highlighting the complementarity between those different types of entropy indices and achieving global accuracy results higher than 90% in multi-class and binary-class schemes. The combination of regularity- and predictability-based entropy indices denoted a high degree of complementarity between those nonlinear methods. Finally, the relevance of frontal and parietal areas for recognition of emotions has revealed the essential role of those brain regions in emotional processes., Facultad de Ingeniería, Centro de Investigaciones Ópticas

Current design codes have prepared linear analysis methods instead of nonlinear ones in order to reduce time, cost and other factors such as less need of these methods for expert knowledge. In linear analysis method, elastic strength demand of structure is decreased by applying a response modification factor called behavior factor (R) and by considering the design code regulations, structure members will be permitted to experience nonlinear response (in the time of middle-to-severe earthquakes). Because of different assumptions for linear (force-based method that has deficiencies) and nonlinear methods and whereas seismic stability or instability is not merely related to the strength of structure, rather it depends largely on the capability of structure to resist drifts, seismic performance evaluation of structures designed by linear procedure appears to be necessary using standards for evaluation. In this research, seismic performance of steel moment frames once designed based on 3rd edition of 2800-Iranian seismic code and allowable stress design (ASD) method and another time based on new ones, the 4th edition of 2800 seismic code and load and resistance factor design (LRFD) method, are compared with each other through nonlinear pushover and time-history analyses according to ASCE/SEI 41–13. Results showed positive change of design codes procedure with respect to alteration of design method in both types of ductile design, intermediate and special. Since mean of overstrength values and mean of ductility values have increased a little, mean of behavior factor values has become closer to the recommended values of the new seismic code. Also, a small number of structures met total collapse during nonlinear time-history analyses.

This paper presents relations between real-world phenomena, sensors and measurement methods that without applied simplifications are generally nonlinear. The article is built upon real-world examples which directly affect quality of human life or straightforwardly refer to life itself. First, the health of a human being is investigated. Next, attention is moved towards measurements of water and air quality. We conclude with an observation that commonly demanded linear characteristics of a measurement system are feasible with nonlinear methods of signal and data processing.

Purpose: Yoga is known as a type of exercise that combines physical, mental and spiritual aspects. There has not been much research on the postural control in various yoga poses. The aim of this study was to examine CoP regularity in both yoga instructors and novices during the performance of four yoga poses, and to verify the sensitivity of linear and nonlinear methods for assessing postural stability. Methods: The dynamic characteristics of CoP fluctuations were examined using linear and nonlinear methods on a group of 22 yoga instructors (Y) and 18 age-matched non-practitioners of yoga (NY). The study involved maintaining a balance for 20 seconds while performing four yoga poses. Results: Conventional analysis of CoP trajectories showed that NY and Y exhibited similar control of postural sway, as indicated by similar CoP path-length and area values observed in both groups. These results suggest that the special balance yoga training received by Y may not have an impact on less challenging balance conditions, such as the poses used in this experiment. Interestingly, nonlinear dynamical analysis of CoP showed that Y exhibited less CoP regularity and more complex signal than NY, as evidenced by higher values of sample entropy and fractal dimension. Conclusions: The results shed light on the surplus values of CoP trajectories in the nonlinear dynamical analysis to gain further insight into the mechanisms involved in posture control.

This paper presents the results of a study of total and intrinsic nonlinearities in inverse problems of the dynamics of Jupiter’s Outer Satellites, observed on very short orbital arcs. The relationship between nonlinearity and the conditions of satellite observations is revealed. In particular, it is shown that a very strong total nonlinearity occurs when the observation period is less than 0.1 of the orbital period. In addition, it is shown that the intrinsic nonlinearity is rather weak for all the satellites. This indicates the possibility of using nonlinear methods for adequate simulating their orbital uncertainty.

Dairy commodity prices have become more volatile over the last 10–11 yr. The aim of this paper was to produce reliable price forecasts for the most frequently traded dairy commodities. Altogether five linear and nonlinear time series models were applied. The analysis reveals that prices of dairy commodities reached a structural breakpoint in 2006/2007. The results also show that a combination of linear and nonlinear models is useful in forecasting commodity prices. In this study, the price of cheese is the most difficult to forecast, but a simple autoregressive (AR) model performs reasonably well after 12 mo. Similarly, for butter the AR model performs the best, while for skimmed milk powder (Smp), whole milk powder (Wmp) and whey powder (Whp) the nonlinear methods are the most accurate. However, few of the differences between models are significant according to the Diebold–Mariano (DM) test. The findings could be of interest to the whole dairy industry.

Respiratory sinus arrhythmia (RSA) is a form of cardiorespiratory coupling. It is observed as changes in the heart rate in synchrony with the respiration. RSA has been hypothesized to be due to a combination of linear and nonlinear effects. The quantification of the latter, in turn, has been suggested as a biomarker to improve the assessment of several conditions and diseases. In this study, a framework to quantify RSA using support vector machines is presented. The methods are based on multivariate autoregressive models, in which the present samples of the heart rate variability are predicted as combinations of past samples of the respiration. The selection and tuning of a kernel in these models allows to solve the regression problem taking into account only the linear components, or both the linear and the nonlinear ones. The methods are tested in simulated data as well as in a dataset of polysomnographic studies taken from 110 obstructive sleep apnea patients. In the simulation, the methods were able to capture the nonlinear components when a weak cardiorespiratory coupling occurs. When the coupling increases, the nonlinear part of the coupling is not detected and the interaction is found to be of linear nature. The trends observed in the application in real data show that, in the studied dataset, the proposed methods captured a more prominent linear interaction than the nonlinear one. ispartof: FRONTIERS IN PHYSIOLOGY vol:12 ispartof: location:Switzerland status: published

Aim: In many cases, the dynamics of psychotherapeutic change processes is characterized by sudden and critical transitions. In theoretical terms, these transitions may be "phase transitions" of self-organizing nonlinear systems. Meanwhile, a variety of methods is available to identify phase transitions even in short time series. However, it is still an open question if different methods for timeseries analysis reveal convergent results indicating the moments of critical transitions and related precursors.Methods and Procedures: Seven concepts which are commonly used in nonlinear time series analysis were investigated in terms of their ability to identify changes in psychological time series: Recurrence Plots, Change Point Analysis, Dynamic Complexity, Permutation Entropy, Time Frequency Distributions, Instantaneous Frequency, and Synchronization Pattern Analysis, i.e., the dynamic inter-correlation of the system's variables. Phase transitions were simulated by shifting control parameters in the Hénon map dynamics, in a simulation model of psychotherapy processes (one by an external shift of the control parameter and one created by a simulated control parameter shift), and three sets of empirical time series generated by daily self-ratings of patients during the treatment.Results: The applied methods showed converging results indicating the moments of dynamic transitions within an acceptable tolerance. The convergence of change points was confirmed statistically by a comparison to random surrogates. In the three simulated dynamics with known phase transitions, these could be identified, and in the empirical cases, the methods converged indicating one and the same transition (possibly the phase transitions of the cases). Moreover, changes that did not manifest in a shift of mean or variance could be detected.Conclusion: Changes can occur in many different ways in the psychotherapeutic process. For instance, there can be very slow and small transitions or very high and sudden ones. The results show the validity and stability of different measures indicating pattern transitions and/or early warning signals of those transitions. This has profound implications for real-time monitoring in psychotherapy, especially in cases where a transition is not obvious to the eye. Reliably identifying points of change is mandatory also for research on precursors, which in turn can help improving treatment.

Modern mathematical methods for analysis of heart rate variability (HRV), such as rescaled range analysis, detrended fluctuation analysis, and phase-rectified signal averaging were considered. Algorithms for calculating novel nonlinear HRV indices were described in detail. Mathematical models for simulating artificial cardiac Beat-to-beat intervals that take into account various noise processes were created. A state model of the cardiovascular system based on HRV analysis was developed. The sensitivity of HRV indices to changes in the state of the cardiovascular system was theoretically estimated using artificially simulated data.

Sparse modeling representative selection (SMRS) has been recently introduced for selecting the most relevant examples in data sets. SMRS exploits data self-representativeness coding in order to infer a coding matrix with block sparsity constraint. The relevance scores of samples are then derived from the estimated matrix of coefficients. Since SMRS is based on a linear model for data self-representation, it cannot always provide good relevant samples. Besides, most of its selected samples can be found in dense areas in input space. In this paper, we propose to overcome the SMRS method’s shortcomings that are related to the coding matrix estimation. We introduce two nonlinear data self-representativeness coding schemes that are based on Hilbert space and column generation. Experimental evaluation is carried out on summarizing a video movie and on summarizing training image data sets used for classification tasks. These experiments demonstrated that the proposed nonlinear methods can outperform state-of-the art selection methods.

The paper considers the problem of motion correction in fMRI data by different methods existing in standard packages: SPM, AFNI, BROCCOLI. Method of rigid body correction is too poor for using in real world cases, because of registration of a single 3D fMRI snapshot is not instantaneous, but sequentially by slices. Comparison of methods in the case controlled artificially of nonlinear and partial shifts and rotations of slices of fMRI records and made recommendations of using methods for different cases is a goal of this paper.

This paper applies the surrogate data method to investigate the presence of nonlinearity in neonatal electroencephalogram (EEG) burst suppression (B/S) patterns in order to rationalize the use of nonlinear methods for automated detection of such patterns. To generate surrogate data, the statically transformed autoregressive process (STAP) algorithm is deployed, and, the correlation dimension (CD) and asymmetry due to time reversal (REV) are applied as discriminating statistics. The results of the surrogate data test demonstrate the nonlinearity characteristic of real neonatal EEG signals during both burst and suppression phases at the 0.05 significance level. The evidence of nonlinearity is found in 90% and 87% of bursts and suppressions respectively. Furthermore, the ability of nonlinear tools in detecting B/S patterns in multichannel neonatal EEG signals is investigated using receiver operating characteristic analysis. The experimental results show that the CD outperforms existing methods based on the nonlinear energy operator. The newborn EEG datasets were obtained from the University of Queensland Center for Clinical Research (UQCCR), The University of Queensland, Brisbane, Australia, as part of two QNRF grants, and the Christian-Albrechts-University, Kiel, Germany. Prof. Boashash thanks Prof. Paul Colditz for his assistance in collecting the relevant data as part of the two QNRF grants NPRP 4-1303-2-517 and 6-885-2-364. The second and last authors acknowledge funding from the two QNRF grants NPRP 4-1303-2-517 and 6-885-2-364. Scopus

Using a Linear Discriminant Analysis (LDA), we aimed to distinguish positive and negative emotions through EEG signals. The emotions were elicited using a set of six videos to express happiness and disgust. We adopted two different signal pre-processing techniques, verifying the importance of artifacts removal, assuming a linear and a PostNonlinear mixture (PNL) model. In the first case, we applied the SOBI algorithm and in the second a mutual information minimization based algorithm. Without the artifacts removal, the classifier had an accuracy of 67.39%. With SOBI, there was an increase to 71.74%, while with PNL accuracy was 77.54%. These results point to the importance of artifacts removal in EEG signal analysis and show that nonlinear models may be better suited to deal with EEG signals.

The increasing penetration of renewable energy is altering concern about the stability of the renewable grid- connected system. Photovoltaic (PV) output characteristic should be considered when modelling for N-paralleled PV grid- connected systems, where nonlinear methods are required. In this paper, N-paralleled PV grid-connected DC systems are modelled and simplified firstly. Then for a single PV system, describing function method is adopted to model the nonlinear part of the power control part based on P&O method. Finally, the influence of the grid inductance and the number of paralleled systems are analyzed. Theoretical analysis shows that the increscent grid inductance and the number destabilizes the system, and RTLAB simulation is conducted to verify the analysis.

In the last three decades, the analysis of heart rate variability by nonlinear methods demonstrated the complexity of cardiovascular regulation. Additionally to the observations of periodic heart rate regulation by the autonomic nervous system, the long-term statistics of the heart rate has been determined to reminisce a tempered Levy process. A number of heuristic arguments have previously been made to support a tempering conjecture, using exponentially truncated waiting times for the time intervals between heart beats. Herein we use the fractional probability calculus to frame our arguments and to parameterize the control process that tempers the Levy process through a collective-induced potential. We also determine that the hypothesis of a self-induced nonlinear potential control resulting in such a tempered Levy process is consistent with the hypothesis of disease being the loss of physiologic complexity made over 25 years ago.

We propose using the nonlinear method of smoothing splines in conjunction with forecast combination to predict the market equity premium. The smooth splines are flexible enough to capture the possible nonlinear relationship between the equity premium and predictive variables while controlling for complexity, overcoming the difficulties often attached to nonlinear methods such as computational cost, overfitting and interpretation. Our empirical results show that when used with forecast combination, the smoothing spline forecasts outperform many competing methods such as the adaptive combinations, shrinkage estimators and technical indicators, in delivering statistical and economic gains consistently.

Driving fatigue is a common occupational hazard for any long distance or professional driver, and fatigue detecting has major implications for transportation safety. Monitoring physiological signal while driving can provide the possibility to detect the fatigue and give the necessary warning. In this paper, fifty subjects participated in driving simulations experiment with their recorded EEG signals to induce two kinds of fatigue states: Alert and drowsy. Two nonlinear methods, approximate Entropy (AE) and Sample Entropy (SE), were used to characterize irregularity and complexity of EEG data. Subsequently Support Vector Machine (SVM) was applied to classify these two fatigue states. The experimental result shows that two complexity parameters are significantly decreased as the fatigue level increases. The result indicates that both of two nonlinear indicators can be used to characterize driver fatigue level. Furthermore, the combined measure feature results in higher classification accuracy, indicating the proposed classification method is more robust and effective, compared with single complexity measure.

The application of performance-based design and assessment procedures requires an accurate estimation of local component deformation demands. In the case of steel moment-resisting frames, these are usually defined in terms of plastic rotations. A rigorous estimation of this response parameter is not straightforward, requiring not only the adoption of complex nonlinear structural models, but also of time-consuming numerical integration calculations. Moreover, the majority of existing codes and guidelines do not provide any guidance in terms of how these response parameters should be estimated. Part 3 of Eurocode 8 (EC8-3) requires the quantification of plastic rotations even when linear methods of analysis are used. Therefore, the aim of the research presented in this paper is to evaluate different methods of quantifying local component demands and also to answer the question of how reliable are the estimates obtained using the EC8-3 linear analysis procedures in comparison to more accurate nonlinear methods of analysis, particularly when the linear analysis applicability criterion proposed by EC8-3 is verified. An alternative methodology to assess the applicability of linear analysis is proposed which overcomes the important limitations identified in the EC8-3 criterion.

Background Body weight variability (BWV) is common in the general population and may act as a risk factor for obesity or diseases. The correct identification of these patterns may have prognostic or predictive value in clinical and research settings. With advancements in technology allowing for the frequent collection of body weight data from electronic smart scales, new opportunities to analyze and identify patterns in body weight data are available. Objective This study aims to compare multiple methods of data imputation and BWV calculation using linear and nonlinear approaches Methods In total, 50 participants from an ongoing weight loss maintenance study (the NoHoW study) were selected to develop the procedure. We addressed the following aspects of data analysis: cleaning, imputation, detrending, and calculation of total and local BWV. To test imputation, missing data were simulated at random and using real patterns of missingness. A total of 10 imputation strategies were tested. Next, BWV was calculated using linear and nonlinear approaches, and the effects of missing data and data imputation on these estimates were investigated. Results Body weight imputation using structural modeling with Kalman smoothing or an exponentially weighted moving average provided the best agreement with observed values (root mean square error range 0.62%-0.64%). Imputation performance decreased with missingness and was similar between random and nonrandom simulations. Errors in BWV estimations from missing simulated data sets were low (2%-7% with 80% missing data or a mean of 67, SD 40.1 available body weights) compared with that of imputation strategies where errors were significantly greater, varying by imputation method. Conclusions The decision to impute body weight data depends on the purpose of the analysis. Directions for the best performing imputation methods are provided. For the purpose of estimating BWV, data imputation should not be conducted. Linear and nonlinear methods of estimating BWV provide reasonably accurate estimates under high proportions (80%) of missing data.

This paper presents a comparison of near and far-fault ground motion effects on the seismic response of masonry structures, using nonlinear methods. To compare the influence on low to moderate rise buildings, a detailed field investigation and archive study were executed in Albania. Based on the archive and detailed field investigation over a hundred real residential masonry buildings constructed between 1963-1978, seven masonry buildings of 2-5 stories were selected to reflect the commonly constructed template designs. Analytical models of each building were prepared following the experimental data on the quality of the masonry constitutive components of the selected buildings. Seismic deformation capacities of each building were obtained by nonlinear static analyses. Inelastic time history analysis was used to predict the seismic displacement demands of the studied buildings. The significance of the findings is further investigated by examining the nonlinear behavior of a group of realistic buildings subjected to near and far-fault ground recordings. Results indicate that there is a remarkable difference in the seismic response of masonry structures between near and far-fault records. It can therefore be concluded that near-fault earthquakes may have significantly more damage potential on masonry structures than far-fault records.

Despite the widespread diffusion of nonlinear methods for heart rate variability (HRV) analysis, the presence and the extent to which nonlinear dynamics contribute to short-term HRV are still controversial. This work aims at testing the hypothesis that different types of nonlinearity can be observed in HRV depending on the method adopted and on the physiopathological state. Two entropy-based measures of time series complexity (normalized complexity index, NCI) and regularity (information storage, IS), and a measure quantifying deviations from linear correlations in a time series (Gaussian linear contrast, GLC), are applied to short HRV recordings obtained in young (Y) and old (O) healthy subjects and in myocardial infarction (MI) patients monitored in the resting supine position and in the upright position reached through head-up tilt. The method of surrogate data is employed to detect the presence and quantify the contribution of nonlinear dynamics to HRV. We find that the three measures differ both in their variations across groups and conditions and in the percentage and strength of nonlinear HRV dynamics. NCI and IS displayed opposite variations, suggesting more complex dynamics in O and MI compared to Y and less complex dynamics during tilt. The strength of nonlinear dynamics is reduced by tilt using all measures in Y, while only GLC detects a significant strengthening of such dynamics in MI. A large percentage of detected nonlinear dynamics is revealed only by the IS measure in the Y group at rest, with a decrease in O and MI and during T, while NCI and GLC detect lower percentages in all groups and conditions. While these results suggest that distinct dynamic structures may lie beneath short-term HRV in different physiological states and pathological conditions, the strong dependence on the measure adopted and on their implementation suggests that physiological interpretations should be provided with caution.

The linear hydroelastic theory has been widely used in engineering applications in the past. However, the increasing demand for larger merchant ships makes it necessary to evaluate the influences of second-order nonlinear fluid forces on ship response in seas. In this study, the second-order nonlinear responses induced by sea waves are calculated using generalized second-order wave force theory in the frequency domain. The Fluid-Structure Interaction (FSI) method is presented first in this paper which is used for the assessment of ship response and loads, including both linear and second-order nonlinear methods in the frequency domain. Subsequently, the effects of linear forces on the wave-induced responses and loads for a 180k DWT large bulk carrier with and without forward speed are calculated using pulsating source Green's function and translating-pulsating source Green's function. The second-order nonlinear responses are predicted mainly based on pulsating source Green's function. The numerical results show that the ship responses change significantly at high speed, and there are extra vertical bending moments caused by second-order fluid forces acting on the ship in large-amplitude waves compared to linear results. It indicates that both the speed of the ship and the second-order nonlinear wave forces acting on the ship could amplify the wave-induced responses and vertical bending moments.

The problem of detecting anomalies in time series has attracted much attention recently due to its numerous applications. In this paper, we proposed a novel framework based on nonlinear methods. Firstly, we use time-dependent URP (Unthreholded Recurrence Plots) to represent time series, so as to capture the nonlinear characteristic of time series. Secondly, we present ELM-AE (Extreme Learning Machine Auto-Encoder) based algorithm to learn the main features of URPs. Finally, we compute residual errors as anomaly score for each time series points. This framework can perform well on complex nonlinear systems using unlabeled datasets.

a b s t r a c t The aim of our research was to find out if the time irreversibility as a sign of specific class of nonlinear dynamics is present even in the newborn's heart rate oscillations. Multiscale irreversibility indices (Porta's index P%, Guzik index G% and Ehlers index E) of the heart rate signals were computed in 20 healthy neonates. The presence of system nonlinearity was assessed by surrogate data analysis. The results of our analysis revealed asymmetrical nature of heart rate oscillations present in the majority of neonatal heart rate recordings. Moreover, time irreversibility index P% was able to detect shift of sympathovagal balance toward sympathetic dominance in newborns. Our findings support the concept of nonlinearity as a universal feature of the biological control system even in the early stage of the system maturation. This finding supports the application of nonlinear methods to heart rate variability analysis. © 2015 Published by Elsevier Ltd.

The earthquake analysis of multistorey structure is done by linear and nonlinear methods. Response spectrum method of analysis is linear dynamic analysis. For nonlinear dynamic analysis time history method is used. In this paper, response spectrum method is used for linear analysis. For nonlinear analysis, time history method is used. For time history method, time history function of Bhuj earthquake is used. Both the analyses are done using ETABs software. To study seismic behaviour, base shear, time period, storey displacement parameters are studied

Practical engineering structures commonly display nonlinear dynamic response when damage is present in the system. Hence, the studies on nonlinear system identification have increased within these past few years. Current study is aimed on the structural identification of nonlinear systems based on the extraction of underlying linear frequency response function (FRF). The methods chosen to obtain the FRF are the Conditioned Reverse Path (CRP) and the Orthogonalised Reverse Path (ORP) method. The well-known frequency-domain CRP method has been recognised for its ability in solving nonlinear problems; detecting and quantifying nonlinearities in structures. In contrary, the ORP is a new algorithm developed in time-domain which gives simpler formulation for describing the underlying linear dynamics of nonlinear systems. Results show that the performance of the new ORP algorithm in handling nonlinearities is as good as the CRP method. The ability of ORP method has become the aim of the current study to assess the robustness of both algorithms towards nonlinear system identification of structures with multi-degree-of-freedom (MDOF) system.

This paper investigates the dynamic causal link between exports and economic growth using both linear and nonlinear Granger causality tests. We use annual South African data on real exports and real gross domestic product from 1911-2011. The linear Granger causality result shows no evidence of significant causality between exports and GDP. The relevant VAR is unstable, which undermines our confidence in the causality result identified by the linear Granger causality test. Accordingly we turn to the nonlinear methods to evaluate Granger causality between exports and GDP. First, we use Hiemstra and Jones (1994) nonlinear Granger causality test and find a unidirectional causality from GDP to exports. However, using a more powerful and less biased nonlinear test, the Diks and Panchenko (2006) test, we find evidence of significant bi-directional causality. These results highlight the risk of misleading conclusions based on the standard linear Granger causality tests which neither accounts for structural breaks nor uncover nonlinearities in the dynamic relationship between exports and GDP.

This paper discusses the possibilities of the Linear and Quadratic Discriminant analysis for diagnosing arterial hypertension patients. For this purpose, electrocardiogram was recorded while performing the tilt testing in two distinct groups: 30 healthy volunteers and 40 patients suffering from the arterial hypertension of II-III degree. Further analysis includes the extraction of 64 features, obtained by statistical, geometric, spectral (Fourier and wavelet) and nonlinear methods. In order to find the best feature combination, a Semi-optimal search of the non-correlated features space is proposed. All calculations were performed in the in-house software written on Python. The results suggest that a 4-features combination of statistical, spectral and nonlinear features provide the most robust classifiers.

The authors investigate linear and nonlinear methods of reducing noise while preserving information in spectra, optical and otherwise. The optimum linear and nonlinear approaches are Gauss–Hermite and maximum-entropy, respectively. However, intelligent processing still requires an initial assessment of the data in reciprocal space.The authors investigate linear and nonlinear methods of reducing noise while preserving information in spectra, optical and otherwise. The optimum linear and nonlinear approaches are Gauss–Hermite and maximum-entropy, respectively. However, intelligent processing still requires an initial assessment of the data in reciprocal space.

Several seismic events are calculated by an iterative, linear algorithm relocated in a nonlinear, grid-search with a maximum-likelihood hypocenter method. The same simultaneous events separately registered by regional and local seismological networks have also been used. A verified 1D (one dimensional) velocity crustal structure model is used in both methods and in all datasets for better comparisons. Some rock quarry blasts registered by the local receiver stations as ground truths are examined by both methods. This study's main objectives were: (i) to carry out a comparative examination of the error estimates in both techniques and (ii) to generalize location assessment of the permanent low-density regional network in Central Alborz. The regional network operates under Iranian Seismological Center and its seismic data are massively applied. To reach the research goals, the dataset–method correlation matrix and the location variables were statistically processed. It was shown that the estimated earthquake epicenters by the linear and nonlinear methods are approximately similar for well-located events in each network. For dense-proper distribution of the seismic stations, the elliptical error estimates have lower amounts and consequently the seismicity pattern is more reliable. The difference between subsurface seismicity patterns resulting from the above-mentioned approaches in the studied area is presented. Some depth calculation errors for the same recorded events are higher in the regional network. The correlation comparisons demonstrated that the nonlinear approach and the locally-constrained data may be closer to reality and more convincing. The nonlinear application is more plausible due to all of the possible solutions and less elliptical error estimates under the Gaussian distribution assumption. Subsequently, the combination of the nonlinear method, proper location criteria, and appropriate crustal velocity structure can effectively improve some of the earthquake location estimates in the regional catalogue. As a result, this procedure can be useful in seismicity concept evaluations.

In recent years, nonlinear calculation methods can be easily carried out by means of developing computer technologies. In this way, comparisons of the nonlinear methods have started to increase rapidly and more studies are carried out on regular and irregular buildings. However, it is most important to compare consistency of the methods on buildings. In this study, most common nonlinear static (pushover) and nonlinear dynamic analysis (time history analysis) methods were compared on an asymmetric planned reinforced concrete (R/C) building. Building having horizontal and vertical irregularities was 5-story. Analyses were carried out by using SAP2000 program. The results are discussed in terms of base shear, lateral displacements and top displacement ratios.

This study investigates if deeper understanding is achieved when combining nonlinear and linear chromatographic column characterization methods. As test systems, two hybrid columns (Phenomenex Gemini-NX C18 and Kromasil Eternity C18) and one classic one (Kromasil-C18) were selected. The nonlinear methods were based on firm adsorption theory and involved determination of adsorption isotherms followed by calculations with a new numerical tool, adsorption energy distribution, on probe components at different pH values. The linear methods involved the hydrophobic subtraction model and selected probe components retention factors as a function of pH. The combined analysis indicated that both complementary and confirmative information can be achieved regarding the actual model systems.

The objective of this paper is to analyze the use of nonlinear models to predict the CPU frequency that reaches the lowest power consumption of a smartphone based on Android OS context variables. Artificial neural networks (ANNs) and k-nearest neighbors (k-NN) techniques are investigated, and their results are compared to those obtained by the linear method (LM). Experimental results indicate the k-NN technique is the best option in terms of model accuracy and performance when compared to the other prediction models.

Although protein folding is a simple outcome of the underlying thermodynamics, arriving at a quantitative and predictive understanding of how proteins fold nevertheless poses huge challenges. Therefore, both advanced experimental and computational methods are continuously being developed and refined to probe and reveal the atomistic details of protein folding dynamics and mechanisms. Herein, we provide a concise review of recent developments in spectroscopic studies of protein folding, with a focus on new triggering and probing methods. In particular, we describe several laser-based techniques for triggering protein folding/unfolding on the picosecond and/or nanosecond timescales and various linear and nonlinear spectroscopic techniques for interrogating protein conformations, conformational transitions, and dynamics.

Interferential electromyogram (iEMG) was analyzed in healthy newborns (n = 29) during the first 24 h of life as a model of transition from hypogravity (intrauterine immersion) to Earth’s gravity (the postnatal period). Nonlinear methods of iEMG analysis (correlation dimension, entropy, and fractal dimension) reflecting the complexity, chaotic character, and predictability of signals from the leg and arm antagonistic muscles were used. The iEMG fractal dimension was shown to grow in all the muscles as the postnatal period extended, except the m. gastrocnemius during the first 24 h of life. Lower fractal and correlation dimensions and entropy were found to be characteristic of the flexors, especially at a low iEMG amplitude suggesting better congenital programming of the flexors compared to the extensors. It was concluded that the early ontogenesis model can be potentially useful for studying the evolution and the states of antigravity functions.

Quantitative relationships between molecular structures and bioactivities of a set of CCR5 inhibitor derivatives were discovered. We have demonstrated the detailed application of two efficient nonlinear methods, general regression and radial basis function neural networks, for evaluation of quantitative structure–activity relationships of the studied compounds. Components produced by principal component analysis were used as input of the developed nonlinear models. Comparison between predictability of PC-GRNNs and PC-RBFNNs indicated that later method has higher ability to predict the activity of the studied molecules. In order to design novel derivatives of inhibitors with high activity and low side effects, and because experimental and calculated activities of molecules employed in the model development step, shown a good correlation, developed PC-RBFNNs QSAR model was used to calculate inhibitory activities of some suggested compounds.

Nonlinear methods of fractal analysis and recurrence quantification analysis are becoming more commonplace in the cognitive and behavioral sciences. These methods are illustrated here in a tutorial style using self-paced reading data. Self-paced reading was performed in which each spacebar press revealed a story word-by-word or else sentence-by-sentence. Participant readers were either Ph.D. candidates in English literature or undergraduates from an introductory psychology course and the same story was read by all, either one time only or reread another time on another occasion. The nonlinear analyses revealed crucial differences between the word unit and sentence unit conditions. Performance in the word unit condition was dominated by a task specific strategy, yielding data patterns more like those observed in tapping tasks. Nonlinear analyses of the sentence unit condition, however, discriminated between graduate and undergraduate readers, and first readings of the story from re-reading. From these analyses, the repeated reading of the same story reveals a kind of über-fluency, in a manner of speaking, of the Ph.D. candidates in English literature, whose performance stayed at or closer to a performance ceiling in both readings.

Based on chaotic characteristics in vertical direction of vibrating screen sides, nonlinear methods were proposed to diagnose crack of vibrating screen. First phase space maps were got in different conditions of vibrating screen, and the correlation dimension of signals were calculated. Through the comparison, the author proved that the equipment had different nonlinear characteristics in different work condition. Meanwhile, a three-dimensional spectral analysis method was proposed and validated based on neural network identification model.

Given the increasing use of nonlinear analysis in earthquake resistant design via performance-based design, and ongoing research in simplified nonlinear methods, a software tool was developed for use in the teaching of nonlinear as well as linear structural dynamics. The program caters for single-degree-of-freedom (SDOF) nonlinear systems and emphasizes degrading response as in-cycle strength degradation, progressive cycle strength degradation, general stiffness degradation, and pinching degradation, or combinations of these, under earthquake ground motions. This is achieved using the smoothly varying endochronic plasticity Da hysteresis model. Utilizing numerical integration, the program also provides approximate solutions for many problems from SDOF linear dynamics such as free undamped or damped vibration, and forced periodic or non-periodic damped or undamped vibration. As such, the VB6 program is named ENGLTHA—Earthquake Nonlinear and General Linear Time History Analysis, and also calculates elastic and inelastic displacement and acceleration response spectra. This article describes ENGLTHA and how it can be used, via a set of nine experiments, for teaching structural dynamics as a thread trough several courses spanning from the undergraduate to postgraduate levels. © 2009 Wiley Periodicals, Inc. Comput Appl Eng Educ 19: 97–106, 2011

In this paper, we show that geo-anomalies can be delineated for mineral deposit prediction according to singularity theories developed to characterize nonlinear mineralization processes. Associating singularity and geo-anomalies makes it possible to quantitatively study geo-anomalies with modern nonlinear theories and methods. This paper introduces a newly developed singularity analysis of nonlinear mineralization processes and nonlinear methods for characterizing and mapping geo-anomalies for mineral deposit prediction. Mineral deposits, as the products of singular mineralization processes caused by geo-anomalies, can be characterized by means of fractal or multifractal models. It has been shown that singularity can characterize the degree of geo-abnormality, and this has been demonstrated to be useful for mapping anomalies of undiscovered mineral deposits. The study of mineralization and mineral deposits from a nonlinear process point of view is a new but promising research direction. This study emphasizes the relationships between geo-anomalies and singularity, including singular processes resulting in singularity and geo-anomalies, the characterization of singularity and geo-anomalies and the identification of geo-anomalies for mineral deposit prediction. The concepts and methods are demonstrated using a case study of Sn mineral deposit prediction in the Gejiu mineral district in Yunnan, China.

Rainstorm is one of the major natural disasters in the world. Because of the complexity and non-linearity, using the current methods to correctly monitor and predict rainfalls is difficult. In recent years, with the rapid developments of nonlinear science, nonlinear time series analysis has been widely used in many scientific and technological fields. In this study two kinds of nonlinear methods, i.e., the robust symbolic dynamics and information entropy, are used for nonlinear time series analysis of rainstorms. The theoretical bases on symbolic dynamics, information entropy and nonlinear time series analysis are introduced, first. Then, a new algorithm for rainstorm monitoring, including data preprocessing, time series symbolizing, symbolic time series segmentation and information entropy calculations, is described. Finally, 45 cases of heavy rainstorms around the world are analyzed. The preliminary results show that the method developed in this paper is promising for rainstorm monitoring.

This review discusses nonlinear chromatographic methods of importance for proper characterization of the adsorption processes in analytical chromatographic systems, with focus on reversed-phase liquid chromatography. Linear methods such as the linear solvation energy relationship (LSER) method and the Snyder-Dolan hydrophobic-subtraction model will also be reviewed briefly. The nonlinear methods for adsorption isotherm determination and the tools for further treatment of the nonlinear adsorption data will be extensively treated in a way suitable for the general chromatographer. Applications of the various methods will be given and the outcome and conclusions will be discussed. Special emphasis will be placed on discussing the possibilities of combining linear and nonlinear methods in order to obtain a deeper and more complete investigation of the interactions in the actual phase system.

Oscillations of heart rate and blood pressure are related to the activity of the underlying control mechanism. They have been investigated mostly with linear methods in the time and frequency domains. Also, in recent years, many different nonlinear analysis methods have been applied for the evaluation of cardiovascular variability. This review presents the most commonly used nonlinear methods. Physiological understanding is obtained from various results from small animals.

Single-storey models are widely adopted because they are able to describe the main aspects of the torsional coupling of asymmetric buildings and, at the same time, they are simple enough to enable extensive parametric analysis. Generally, single-story systems are constituted by a rigid deck, where the mass is lumped, supported by vertical resisting elements with lateral stiffness and strength in their plane only (uni-axial resisting elements). Thus, these models neglect the interaction phenomena that can be observed in actual framed structures, where the vertical resisting elements provide lateral stiffness and strength in all the horizontal directions. In this chapter, the influence of the interaction phenomena on the torsional coupling of the seismic response of asymmetric buildings predicted by nonlinear methods of analysis is investigated. Single storey systems with bi- and uni-axial resisting elements are used to simulate structures whose seismic response is affected or not by interaction phenomena. Finally, both nonlinear dynamic and nonlinear static methods of analysis are investigated.

Cardiotocography (CTG) is widely used in pregnant women for fetal monitoring and has provided extensive knowledge on the pathophysiology of fetal hypoxia. Computer analyses of CTG tracings were developed to reduce intraobserver and interobserver disagreement inherent to visual analyses, but commonly rely on the use of simple linear time-domain indices, providing a limited understanding of fetal heart rate (FHR) variability. Additional information can be obtained from linear analysis of FHR in the frequency-domain and from nonlinear methods such as measures of entropy. Such indices are able to characterize fetal behavioral states, different gestational ages, and to identify situations of fetal acidemia. However, the technical specifications of fetal monitoring equipment and fetal presentation should be considered in order to ensure an adequate application of these indices. In addition to these, the inclusion of fetal gender may improve the identification of fetal acidemia and intrauterine growth-restriction. In conclusion, linear and nonlinear analysis of FHR variability is likely to improve the performance of existing computer systems for CTG analysis, justifying more extensive clinical trials with these methods.

The nonlinear non-local elliptic equation governing the deflection of charged plates in electrostatic actuators is studied under the pinned and the clamped boundary conditions. Results concerning the existence, construction and approximation, and behaviour of classical and singular solutions with respect to the variation of physical parameters of the equation in various situations are presented.

In this work we compare the predictive power of some of the most popular algorithms used for gene network inference, seen as an unsupervised graph learning problem. The data, generated by an artificial model of a gene regulatory network, are taken in different conditions, like at equilibrium or during a time course, and different numbers of samples are considered in the reconstruction. For these data, we see that the performances of the algorithms are neatly superior for steady state data than for time series. Furthermore, we obtain that linear measures are better suited to capture linear behavior (like steady state conditions), while nonlinear measures are more effective for intrinsically nonlinear data (like the time course of our artificial network).

Geotechnical earthquake engineers have been trying to determine the most appropriate solution techniques for ground response analysis under earthquake loadings. This paper presents the importance of the adequate soil behavior model to simulate earthquake site response analysis. The influence of nonlinearity and linearity of soils on the site response is also investigated. Many methods have been proposed for the analysis of one-dimensional ground response such as nonlinear methods and equivalent linear with reduced modulus. Using 13 well known earthquake records and geotechnical information of sand in the Qeshm Island (Iran) and classification of earthquakes based on seismic parameters, the influence of each parameter on the Response spectra and Fourier Spectrum of surface of ground becomes evident. Analysis was done using two softwares; EERA (equivalent linear analysis) and NERA (nonlinear analysis) and compared. Finally, output of the software is compared with the reference result on site.