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The dynamics of cardiac signals can be studied using methods for nonlinear analysis of heart rate variability (HRV). The methods that are used in the article to investigate the fractal, multifractal and informational characteristics of the intervals between heartbeats (RR time intervals) are: Rescaled Range, Detrended Fluctuation Analysis, Multifractal Detrended Fluctuation Analysis, Poincaré plot, Approximate Entropy and Sample Entropy. Two groups of people were studied: 25 healthy subjects (15 men, 10 women, mean age: 56.3 years) and 25 patients with arrhythmia (13 men, 12 women, mean age: 58.7 years). The results of the application of the methods for nonlinear analysis of HRV in the two groups of people studied are shown as mean ± std. The effectiveness of the methods was evaluated by t-test and the parameter Area Under the Curve (AUC) from the Receiver Operator Curve (ROC) characteristics. The studied 11 parameters have statistical significance (p < 0.05); therefore, they can be used to distinguish between healthy and unhealthy subjects. It was established by applying the ROC analysis that the parameters Hq=2(MFDFA), F(α)(MFDFA) and SD2(Poincaré plot) have a good diagnostic value; H(R/S), α1(DFA), SD1/SD2(Poincaré plot), ApEn and SampEn have a very good score; α2(DFA), αall(DFA) and SD1(Poincaré plot) have an excellent diagnostic score. In conclusion, the methods used for nonlinear analysis of HRV have been evaluated as effective, and with their help, new perspectives are opened in the diagnosis of cardiovascular diseases.

Recent developments in the probabilistic and statistical analysis of probability density functions are reviewed. Density functions are treated as data objects for which suitable notions of the center of distribution and variability are discussed. Special attention is given to nonlinear methods that respect the constraints density functions must obey. Regression, time series and spatial models are discussed. The exposition is illustrated with data examples. A supplementary vignette contains expanded versions of data analyses with accompanying codes.

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.

Uterine contractions monitoring is essential during pregnancy progression for due date prediction and the screening of preterm deliveries, i.e., those related to labour contractions occurring before 37 weeks of gestation. As there are different kinds of uterine contraction, distinguishing between true labour ones and normal physiological ones during pregnancy is not trivial. Thus, early identification is necessary for the effective and efficient care of pregnant women to avoid unnecessary and costly hospitalization. In this regard, while classical clinical methods proved their limitations, real-time monitoring of uterine contractions is now possible thanks to a new technique called ElectroHysteroGraphy which measures the uterine electrical activity that is a proxy for the mechanical activity of the muscles of the uterus. An exhaustive and comprehensive literature review was conducted to retrieve and report the state-of-the-art of the methods to distinguish labour contractions from pregnancy contractions. A systematic search was run on different search engines using a search string. A snowball sampling approach was applied to the references of the retrieved articles to identify further appropriate papers. According to this, the relevant references included in the bibliography of each analysed article led to other appropriate articles. Thus, papers dealing with the methods to distinguish labour from pregnancy (normal physiological) contractions and published between 2001 and 2020 were selected. Linear and nonlinear methods have been developed for uterine contractions signals (EHG/EMG) analysis to distinguish labour from pregnancy contractions. Nonlinear methods yielded better results compared to the linear methods, but not all nonlinear methods are promising in terms of clinical application.

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

The evaluation of second-order effects of steel framed structures can provide different analysis results than using linear analysis methods. In various structural engineering literature were distinguished different methods of analysis: taking or without taking into account second-order effects. It depends on the sensitivity to the horizontal actions. The slenderer the structure, the more sensitive it is to horizontal actions. Using nonlinear methods, the sensitivity of steel frame to second-order impact is considered. This paper shows the importance of evaluations of the second-order effects in behaviour of steel frame structures. Performed investigations reveal the influence of the rotational stiffness of the joints to the behaviour of whole framed structure. Calculation results show that decreased flexibility of the semi-rigid joints increase sensitivity of the framed structure to the second-order effects and vice versa. The identified interdependence between the sensitivity to the second-order effects and the flexibility of the semi-rigid joints highlights the importance of evaluation of such dependencies.

The article shows the results of the implementation of the first stage of the project "Study of the application of new mathematical methods for analysis of cardiac data", funded by the Research Fund. The results are related to the creation of a portable information system for individual monitoring of the cardiovascular system, which includes a portable device for recording photoplethysmographic (PPG) signals and software for processing, mathematical analysis and assessment of heart rate variability. An important advantage of the portable device is the ability to constantly monitor and record the functioning and parameters of the cardiovascular system of the individual. This allows more accurate diagnosis of patients in different life situations in normal life, which is based on subsequent scientific analysis of the registered cardiac information through developed specialized software using linear and nonlinear mathematical methods. The article also shows the results for validation of the created new device, by means of an experimental scheme with which electrocardiographic (ECG) and PPG signals are registered simultaneously. The obtained two types of signals are compared in terms of the accuracy parameter of the registered signals. The results show that the two types of registered signals are identical; therefore the developed portable device can be used as an alternative to the currently widely used ECG and Holter devices. Научното изследване е проведено като част от проекта „Изследване на приложението на нови математически методи за анализ на кардиологични данни“ по договор № КП-06-Н22/5 от 07.12.2018 г., финансиран от Фонд „Научни Изследвания“.

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.

The article presents possibility of defects detection from milling time series using nonlinear methods: recurrence plots and recurrence quantifications. The defects are modeled as the holes with different diameters and depths. This allows estimation of the minimal size of defect possible to detect. Based on the conducted research, it has been shown that some of the recurrence indicators enable detection of defects. These recurrence indicators have been tested on the reals damage. Additionally, we show influence of the defect depth on the recurrence indicator values.

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.

Nowadays, nonlinear vibration methods are increasingly used for the detection of damage mechanisms in polymer matrix composite (PMC) materials, which are anisotropic and heterogeneous. The originality of this study was the use of two nonlinear vibration methods to detect different types of damage within PMC through an in situ embedded polyvinylidene fluoride (PVDF) piezoelectric sensor. The two used methods are nonlinear resonance (NLR) and single frequency excitation (SFE). They were first tested on damage introduced during the manufacturing of the smart PMC plates, and second, on the damage that occurred after the manufacturing. The results show that both techniques are interesting, and probably a combination of them will be the best choice for SHM purposes. During the experimentation, an accelerometer was used, in order to validate the effectiveness of the integrated PVDF sensor.

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.

The ability to monitor the physiological effect of the analgesic agent is of interest in clinical practice. Nonstationary changes would appear in photoplethysmography (PPG) during the analgesics-driven transition to analgesia. The present work studied the properties of nonlinear methods including approximate entropy (ApEn) and sample entropy (SampEn) derived from PPG responding to a nociceptive stimulus under various opioid concentrations. Forty patients with ASA I or II were randomized to receive one of the four possible remifentanil effect-compartment target concentrations (Ceremi) of 0, 1, 3, and 5 ng·ml−1 and a propofol effect-compartment target-controlled infusion to maintain the state entropy (SE) at 50 ± 10. Laryngeal mask airway (LMA) insertion was applied as a standard noxious stimulation. To optimize the performance of ApEn and SampEn, different coefficients were carefully evaluated. The monotonicity of ApEn and SampEn changing from low Ceremi to high Ceremi was assessed with prediction probabilities (PK). The result showed that low Ceremi (0 and 1 ng·ml−1) could be differentiated from high Ceremi (3 and 5 ng·ml−1) by ApEn and SampEn. Depending on the coefficient employed in algorithm: ApEn with k = 0.15 yielded the largest PK value (0.875) whereas SampEn gained its largest PK of 0.867 with k = 0.2. Thus, PPG-based ApEn and SampEn with appropriate k values have the potential to offer good quantification of analgesia depth under general anesthesia.

Although alcohol use and partner violence are consistently associated, the nature of the alcohol–violence relationship is still unclear. The purpose of this pilot study was to use longitudinal daily assessments of male partners’ alcohol use and violent events to identify the nature of the alcohol–violence relationship, employing both linear and nonlinear analyses. The participants were 20 adult heterosexual couples of whom the woman reported experiencing partner violence in the prior 30 days. Each partner provided a separate daily telephone report for 8 weeks via an automated interactive voice response (IVR), concerning the previous day’s violence, alcohol use, stressors, emotional reactions, and concerns for children. Individual IVR databases were merged to form a combined couple’s IVR time series. Time series were analyzed using graphic, linear, and nonlinear methods. Graphic analysis using state space grids found no consistent pattern across couples. Similarly, linear analysis using same-day cross-correlation and prior-day beta statistics found no significant group-level alcohol–violence relationship. Using cross-approximate entropy statistics and differential structural equation modeling, no nonlinear relationships between alcohol use and violence were noted either. Whether applying linear or nonlinear analytic methods, there is no group-level relationship between alcohol use by male perpetrators and their violent acts. The implications are significant. First, the alcohol–violence relationship may differ among subgroups. Second, couples need to be assessed thoroughly to determine their unique relationship with alcohol use, so that couple-specific interventions can be designed. Third, if perpetrators believe that their violence is facilitated by their alcohol use, then alcohol reduction should be encouraged despite any evidence suggesting a different alcohol–violence relationship. Finally, the accepted alcohol-causes-violence belief held by many providers needs to be reconsidered. Because the nature of the alcohol–violence relationship varies considerably across couples, clinicians should seek to understand their unique relationship applying across-the-board management approaches.

Attention-deficit/hyperactivity disorder (ADHD) is a neuro-developmental and psychiatric disorder, which affects 11% of children around the world. Several linear and nonlinear biomarkers from electroencephalogram (EEG) signals have been proposed for diagnosis of ADHD to date. However, the determination of which type of analysis gives us the best feature and biomarker to diagnose ADHD is still controversial. In this study, we aimed to evaluate and compare several categories of features, extracted from EEG signals, for diagnosis of ADHD. Thirty 7–12-year-old children fulfilling the DSM5 criteria for ADHD and thirty healthy children underwent a noninvasive EEG evaluation at resting-state. After preprocessing, five categories of features including morphological, time, frequency, time-frequency, and nonlinear features were extracted from EEGs. The efficacy of each feature category in ADHD diagnosis was determined using statistical analysis, receiver operating characteristic (ROC) curves, and evidential K-nearest neighbor (EKNN) classifier. Statistical analyses showed that 13.15, 13.68, 14.47, 14.03, and 34.73% of extracted features were significant (p

It is common to characterize fluidized bed dynamics using spectral analysis and nonlinear methods such as correlation entropy (Kolmogorov entropy). In this paper, an alternative method, the Hilbert...

This work aims the study chemometric methods for the classification of the origin of coffee samples. Samples of finely pulverized coffee grains were analyzed by synchronous molecular fluorescence spectroscopy to carry out the classification. The spectral data of the samples were obtained in triplicate in two offsets: 10 nm (with emission wavelengths from 240 nm to 600 nm) and 40 nm (from 240 nm to 560 nm), all with 1 nm resolution. Different strategies were performed using the spectra obtained with the offsets of 10 nm and 40 nm and fused data at mid-level (10 nm + 40 nm). The performances of linear and nonlinear methods were compared, the best results were obtained from the raw data from the fusion at low-level of the 10 nm and 40 nm offset spectra with the Pareto optimization criterion.

Autism spectrum disorder (ASD) is a heterogeneous neuropsychiatric disorder with a complex genetic background. Analysis of altered molecular processes in ASD patients requires linear and nonlinear methods that provide interpretable solutions. Interpretable machine learning provides legible models that allow explaining biological mechanisms and support analysis of clinical subgroups. In this work, we investigated several case-control studies of gene expression measurements of ASD individuals. We constructed a rule-based learning model from three independent datasets that we further visualized as a nonlinear gene-gene co-predictive network. To find dissimilarities between ASD subtypes, we scrutinized a topological structure of the network and estimated a centrality distance. Our analysis revealed that autism is the most severe subtype of ASD, while pervasive developmental disorder-not otherwise specified and Asperger syndrome are closely related and milder ASD subtypes. Furthermore, we analyzed the most important ASD-related features that were described in terms of gene co-predictors. Among others, we found a strong co-predictive mechanism between EMC4 and TMEM30A, which may suggest a co-regulation between these genes. The present study demonstrates the potential of applying interpretable machine learning in bioinformatics analyses. Although the proposed methodology was designed for transcriptomics data, it can be applied to other omics disciplines.

Considerable disagreement exists on the linearity of the development of standing balance in children. This study aimed to use different traditional and nonlinear methods to investigate age-related changes in standing balance in preschoolers. A sample of 118 preschoolers took part in this study. A force platform was used to record the center of pressure during standing balance over 15 s in three conditions: eyes open, eyes closed, and/or head extended backward. Detrended fluctuation analysis (DFA), recurrence quantification analysis (RQA), and traditional measures were used to evaluate standing balance. The main results are as follows: (1) Higher range and SD in the anterior-posterior (AP) direction were observed for 5-year-old than for 4-year-old children, while higher DFA coefficient (at shorter time scales) and higher determinism and laminarity in the AP direction were found for 5-year-old children compared to 3- and 4-year-old children; and (2) as sensory conditions became more challenging, all traditional measures increased and DFA coefficients (at shorter and longer time scales) decreased in the AP and mediolateral directions, while determinism and laminarity significantly declined in the AP direction. In conclusion, although increased postural sway, 5-year-old preschool children’s balance performance improved, and their control strategy changed significantly compared with the younger preschoolers. Sensory perturbation (eye closure and/or head extension) changed preschoolers’ balance performance and control strategy. Moreover, both traditional and nonlinear methods provided complementary information on the control of standing balance in preschoolers.

Nowadays, piled raft foundation is increasingly being used not only in developed countries but also in developing countries like India. This paper is based on the study of piled raft foundation constructed in Uttarakhand, India, with the help of finite element software ELPLA and finite difference software GROUP. In analysis with ELPLA methods considered are linear as well as nonlinear methods such as hyperbolic stress–strain function and method as per DIN (4014) standard. The software is validated with results of the on-site pile load–settlement test conducted on individual pile. The results are compared also with analysis performed using PLAXIS 3D.

The financial liberalization that began in the last quarter of the twentieth century caused sudden movements in the currencies and financial assets of the countries. These sudden movements are called volatility. Sudden price changes in financial assets made it difficult to predict the future and increased the risks of financial assets. Investors wishing to invest in financial assets wanted to estimate the price of assets correctly to minimize their risks; this has revealed the need for accurate determination of volatility. Since the changes in asset prices are not linear, volatilities in prices are determined by nonlinear methods. This chapter discusses the GARCH models (GARCH, GJR, EGARCH), which are nonlinear models, and tests the validity of these models through a Turkey application on exchange rate volatility. The findings of the study have indicated that the GARCH (1,1) model successfully explained the volatility in the exchange rate.

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.

Russian Abstract: В данной работе проведен анализ возможностей использования сверточных и рекуррентных нейронных сетей для прогнозирования индексов промышленного производства экономики России. Поскольку индексы имеют асимметрию в периодах роста и падения, была выдвинута гипотеза о том, что нелинейные методы позволят улучшить качество прогноза относительно линейных. English Abstract: This paper analyzes the possibilities of using convolutional and recurrent neural networks to predict the indices of industrial production of the Russian economy. Since the indices are asymmetric in periods of growth and decline, it was hypothesized that nonlinear methods will improve the quality of the forecast relative to linear ones.

High-dynamic-range (HDR) imaging applications are increasing rapidly due to their advantages to increase the color quality of the pictures that can be accessed now even from the cellphones. Combining HDR with multispectral images could give us the opportunity to not only have great color information but also to analyze different compositions of materials. However, the use of these techniques is still limited due to portability and costs. In this work, we present linear and nonlinear methods to generate HDR images using a novel single capture multispectral camera based on nanowires sensors. The results presented here show an error reduction in color estimation compared to previous methods.

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.

BACKGROUND: Spatial normalization plays an essential role in multi-subject MRI and functional MRI (fMRI) experiments by facilitating a common space in which group analyses are performed. Although many prominent adult templates are available, their use for pediatric data is problematic. Generalized templates for pediatric populations are limited or constructed using older methods that result in less ideal normalization. OBJECTIVE: The Haskins pediatric templates and atlases aim to provide superior registration and more precise accuracy in labeling of anatomical and functional regions essential for all fMRI studies involving pediatric populations. MATERIALS AND METHODS: The Haskins pediatric templates and atlases were generated with nonlinear methods using structural MRI from 72 children (age range 7–14 years, median 10 years), allowing for a detailed template with corresponding parcellations of labeled atlas regions. The accuracy of these templates and atlases was assessed using multiple metrics of deformation distance and overlap. RESULTS: When comparing the deformation distances from normalizing pediatric data between this template and both the adult templates and other pediatric templates, we found significantly less deformation distance for the Haskins pediatric template (P

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

Modeling of experimental biosorption isotherm data is a fundamental step in the screening of the biosorption process and provides useful information about the mechanisms involved and the ability of biosorbents to remove the heavy metals ions. This paper focuses on modeling $Cd^{2+}$ biosorption by dead biomass of B. megaterium and Rhodotorula sp. by applying non-linear and linear forms of Langmuir, Freundlich, Jovanovic and Hill isotherm models. In order to determine the best fit isotherm model for each biosorbent, the results of linear methods have been compared with the results of nonlinear analysis. For both biosorbents, the non-linear forms of isotherms fit well with the experimental data, the regression coefficients (R2) being over 0.85. $Cd^{2+}$ biosorption by B. megaterium is described better by the non-linear Hill model, while the non-linear Langmuir model fits better with experimental data of Rhodotorula sp. biosorption. The maximum biosorption capacities calculated by these models are 15.59 mg/g for B. megaterium and 10.94 mg/g for Rhodotorula sp. These models also confirm that the surfaces of the biosorbents are homogeneous.

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.

In recent years, political activists have taken to social media platforms to rapidly reach broad audiences. Despite the prevalence of micro-blogging in these sociopolitical movements, the degree to which virtual mobilization reflects or drives real-world movements is unclear. Here, we explore the dynamics of real-world events and Twitter social cohesion in Syria during the Arab Spring. Using the nonlinear methods cross-recurrence quantification analysis and windowed cross-recurrence quantification analysis, we investigate if frequency of events of different intensities are coupled with social cohesion found in Syrian tweets. Results indicate that online social cohesion is coupled with the counts of all, positive, and negative events each day but shows a decreased connection to negative events when outwardly directed events (i.e., source events) were considered. We conclude with a discussion of implications and applications of nonlinear methods in political science research.

There is a growing interest in the development of models and methods of analysis aimed to recognize in the geomagnetic field signals the different contributions coming from the various sources both internal and external to the Earth. Many models describing the geomagnetic field of internal and external origin have been developed. Here, we investigate the possibility to recognize in the magnetic field of external origin the different contributions coming from external sources. We consider the measurements of the vertical component of the geomagnetic field recorded by the European Space Agency (ESA) Swarm A and B satellites at low and mid latitudes during a geomagnetically quiet period. We apply two different methods of analysis: a linear method, that is, the empirical orthogonal function (EOF), and a nonlinear one, that is, the multivariate empirical mode decomposition (MEMD). Due to the high nonlinear behavior of the different external contributions to the magnetic signal the MEMD seems to recognize better than EOF the main intrinsic modes capable of describing the different magnetic spatial structures embedded in the analyzed signal. By applying the MEMD only five modes and a residue are necessary to recognize the different contributions coming from the external sources in the magnetic signal against the 26 modes that are necessary in the case of the EOF. This study is an example of the potential of the MEMD to give new insights into the analysis of the geomagnetic field of external origin and to separate the ionospheric signal from the magnetospheric one in a simple and rapid way.

Accurate forecasting of lake level time series (LLTS) is an important but challenging problem with major economic, social and environmental implications. However, in recent years, the level of uncertainty in the existing LLTS forecast methods has increased significantly due to climate change, therefore, the need to develop more accurate models. The main research question for this study is whether it is necessary to use nonlinear methods in LLTS modeling or if linear methods can produce as accurate and reliable forecast tools. We introduce a new linear-based forecast method for LLTS using spectral analysis, seasonal standardization, and stochastic terms. The application of the new LLTS forecast method is tested on two case study Lakes, including the Van Lake, in Turkey and the Michigan-Huron Lake, in North America. A two-step preprocessing techniques based on standardization and differencing was used for the Van Lake, and spectral analysis and differencing was employed for the Michigan-Huron Lake. We then compared the accuracy and uncertainty of the proposed linear method with an artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) methods. The uncertainty of the new linear LLTS forecast model was ±0.00455 and ±0.00264 for the Van Lake and the Michigan-Huron Lake, respectively, compared to ±0.00625 and ±0.00766 for the ANN and the ANFIS (respectively) at the Van Lake and ±0.00312 and ±0.00319 for the ANN and the ANFIS (respectively) at the Michigan-Huron Lake.

While tropical cyclone (TC) track forecasts have become increasingly accurate over recent decades, intensity forecasts from both numerical models and statistical schemes have been trailing behind. Most operational statistical–dynamical forecasts of TC intensity use linear regression to relate the initial TC characteristics and most relevant large-scale environmental parameters along the TC track to the TC intensification rate. Yet, many physical processes involved in TC intensification are nonlinear, hence potentially hindering the skill of those linear schemes. Here, we develop two nonlinear TC intensity hindcast schemes, for the first time globally. These schemes are based on either support vector machine (SVM) or artificial neural network (ANN) algorithms. Contrary to linear schemes, which perform slightly better when trained individually over each TC basin, nonlinear methods perform best when trained globally. Globally trained nonlinear schemes improve TC intensity hindcasts relative to regionally trained linear schemes in all TC-prone basins, especially the SVM scheme for which this improvement reaches ~10% globally. The SVM scheme, in particular, partially corrects the tendency of the linear scheme to underperform for moderate intensity (category 2 and less on the Saffir–Simpson scale) and decaying TCs. Although the TC intensity hindcast skill improvements described above are an upper limit of what could be achieved operationally (when using forecasted TC tracks and environmental parameters), it is comparable to that achieved by operational forecasts over the last 20 years. This improvement is sufficiently large to motivate more testing of nonlinear methods for statistical TC intensity prediction at operational centers.

In coupled reaction-diffusion systems, modes with two different length scales can interact to produce a wide variety of spatiotemporal patterns. Three-wave interactions between these modes can explain the occurrence of spatially complex steady patterns and time-varying states including spatiotemporal chaos. The interactions can take the form of two short waves with different orientations interacting with one long wave, or vice-versa. We investigate the role of such three-wave interactions in a coupled Brusselator system. As well as finding simple steady patterns when the waves reinforce each other, we can also find spatially complex but steady patterns, including quasipatterns. When the waves compete with each other, time varying states such as spatiotemporal chaos are also possible. The signs of the quadratic coefficients in three-wave interaction equations distinguish between these two cases. By manipulating parameters of the chemical model, the formation of these various states can be encouraged, as we confirm through extensive numerical simulation. Our arguments allow us to predict when spatiotemporal chaos might be found: standard nonlinear methods fail in this case. The arguments are quite general and apply to a wide class of pattern-forming systems, including the Faraday wave experiment., 35 pages, 11, figures. For associated data files and movies, see https://doi.org/10.5518/768

The mathematical analysis and the assessment of heart rate variability (HRV) based on computer systems can assist the diagnostic process with determining the cardiac status of patients. The new cardio-diagnostic assisting computer system created uses the classic Time-Domain, Frequency-Domain, and Time-Frequency analysis indices, as well as the nonlinear methods (Poincar&eacute, plot, Recurrence plot, Hurst R/S method, Detrended Fluctuation Analysis (DFA), Multi-Fractal DFA, Approximate Entropy and Sample Entropy). To test the feasibility of the software developed, 24-hour Holter recordings of four groups of people were analysed: healthy subjects and patients with arrhythmia, heart failure and syncope. Time-Domain (SDNN &lt, 50 ms, SDANN &lt, 100 ms, RMSSD &lt, 17 ms) and Frequency-Domain (the spectrum of HRV in the LF &lt, 550 ms2, and HF &lt, 540 ms2) parameter values decreased in the cardiovascular disease groups compared to the control group as a result of lower HRV due to decreased parasympathetic and increased sympathetic activity. The results of the nonlinear analysis showed low values of (SD1 &lt, 56 ms, SD2 &lt, 110 ms) at Poincar&eacute, plot (Alpha &lt, 90 ms) at DFA in patients with diseases.Significantly reducing these parameters are markers of cardiac dysfunction. The examined groups of patients showed an increase in the parameters (DET% &gt, 95, REC% &gt, 38, ENTR &gt, 3.2) at the Recurrence plot. This is evidence of a pathological change in the regulation of heart rhythm. The system created can be useful in making the diagnosis by the cardiologist and in bringing greater accuracy and objectivity to the treatment.

This paper examines the response of the U.S. labor market to a large and persistent job separation rate shock, motivated by the ongoing economic effects of the COVID-19 pandemic. We use nonlinear methods to analytically and numerically characterize the responses of vacancy creation and unemployment. Vacancies decline in response to the shock when firms expect persistent job destruction and the number of unemployed searching for work is low. Quantitatively, under our baseline forecast the unemployment rate peaks at 19.7%, 2 months after the shock, and takes 1 year to return to 5%. Relative to a scenario without the shock, unemployment uncertainty rises by a factor of 11. Nonlinear methods are crucial. In the linear economy, the unemployment rate “only” rises to 9.2%, vacancies increase, and uncertainty is unaffected. In both cases, the severity of the COVID-19 shock depends on the separation rate persistence.

Previous research that applied the new nonlinear methods to Japan’s trade balance with the rest of the world or between Japan and its major partner, the U.S., could not discover any asymmetric effects of exchange rate changes. Suspecting that aggregation bias could play a role, in this paper we concentrate on the Japan-U.S. trade balance but disaggregate their trade flows by commodity and consider the response of the trade balance of each of the 56 industries to industry-specific real exchange rate changes. We find short-run asymmetric effects of exchange rate changes in 44 industries and short-run impact asymmetric effects in 19 industries. However, the short-run effects lasted into long-run asymmetric effects in 18 industries. Small as well as large industries are included. Our approach identifies industries that will benefit from a yen depreciation or that will be hurt from a yen appreciation.

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 objectives of this paper are to empirically identify business cycles in a small open EU-candidate country such as the Republic of Macedonia and to assess the degree of synchronization of the country’s business cycle with the cycle of the EU economy. Towards the first objective, we apply linear and nonlinear methods for delineating the production gap cycle in the Macedonian economy. As for the second objective, we apply autoregressive methods to assess the size and speed of cyclical adjustment of the Macedonian economy to output shocks to the Euro-zone economy. The results of our analysis suggest a high degree of synchronization of the Macedonian business cycles with the cycles of the EU economy. Also, the shocks in economic activity in the Euro-zone economy are transmitted almost instantaneously, and with a large magnitude, to the Macedonian economy. Finally, the impact of the Euro-zone output contraction is less pronounced than the impact of the Euro-zone output expansion, suggesting an impact of the country’s autonomous countercyclical economic policies. Key words: Business cycles, Exogenous shocks, Potential output, Filter methods, Asymmetric adjustment.JEL: E32, F41, F62, C13, C22. Sinhronizacija poslovnog ciklusa ekonomije male otvorene zemlje kandidata za Evropsku uniju sa ekonomijom Evropske unije Cilj rada je da se empirijski identifikuju poslovni ciklusi u maloj otvorenoj zemlji kandidatkinji EU kao sto je Republika Makedonija kao i procena stepena sinhronizacije poslovnog ciklusa zemlje sa ciklusom ekonomije EU. Prema prvom cilju, primenjujemo linearne i nelinearne metode za određivanje ciklusa proizvodnog jaza u Makedonskoj ekonomiji. Sto se tice drugog cilja, primjenjujemo autoregresivne metode za procenu velicine i brzine ciklicnog prilagođavanja Makedonske ekonomije na sokove proizvodnje u ekonomiji eurozone. Rezultati nase analize ukazuju na visok stepen sinhronizacije Makedonskih poslovnih ciklusa sa ciklusima ekonomije EU. Takođe, sokovi u privrednim aktivnostima u ekonomiji evrozone prenose se skoro trenutacno i u velikoj meri na Makedonsku ekonomiju. Na kraju, uticaj smanjenja proizvodnje u evrozoni je manje izražen nego uticaj ekspanzije proizvodnje u evrozoni, sto ukazuje na uticaj autonomnih kontraciklicnih ekonomskih politika u zemlji. Kljucne reci: Poslovni ciklusi, egzogeni sokovi, potencijalna proizvodnja, metode filtriranja, asimetricno podesavanje.

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.

Land surface temperature (LST) is an essential parameter in land–atmosphere interaction. However, it is still poorly understood about the effects of seasonal LST on the interannual LST change and the dominant driving force for the variation in LST. In this study, trends of time-series LST were analyzed by using both linear and nonlinear methods. Two indices were developed to evaluate the effects of seasonal LST trends on interannual LST change. The main driving factor of LST was identified based on each pixel. Two turning points were founded in 2007 and 2011 during the study period of 2003–2019. A significant cooling trend of LST appeared from 2007 to 2011/2012 with the rates of −0.2237 K/year (daytime) and −0.1239 K/year (nighttime). LST increased in almost all seasons except the daytime in autumn. The warming effect in spring and winter contributed 69.43% to interannual warming of daytime LST, and accounted for 59.02% of interannual warming of nighttime LST. In most regions of China, air temperature and vegetation were the dominant factors influencing the change of LST. The current research improved our understanding of changes of LST and the results can serve for mitigating and adapting to climate change.