recurrence quantification analysis

14. Darovic GO, Zbilut JP (2002). Fluid-filled monitoring systems (Chap. 6). In: Darovic GO (ed), Hemodynamic Monitoring: Invasive and Noninvasive Clinical Applications (3 rd ed). Philadelphia, W.B. Saunders, pp 113-131. 15. Webber Jr Cl , Zbilut JP (2001). Recurrence Quantification Analysis. In:

Let us attempt to give a detailed answer. Surface electromyography has been considered for years an electro- physiological signal having noise as basic components. Also according to some previous results that have been recently obtained in literature and that we have properly quoted, this interpretation is not correct. This signal, due to extremely complex network of interacting components, is intrinsically nonlinear and generating a com- plex dynamics that is fundamentally chaotic, fractal and also noise corrupted. As a consequence, the analysis of the sEMG requires the detailed application of the basic methods of the nonlinear analysis and in particular of chaos and fractal analysis and of the Recurrence Quantification Analysis (RQA) that is a fundamental method- ology since it enables us to look at the inner structure of the investigated signal and quantify with detailed vari- ables. The first merit is thus to have studied in detail a case of muscular dystrophy and to have confirmed with unquestionable results that this is really the dynamics of this signal. The second merit is that, using chaos, fractal and RQA analysis, we have given new indexes that are of immediate clinical application. In each case we have given the standard values in the case of normal subjects and we have compared these results with the case of the investigated pathology. It is evident that we have now new indexes of evaluation which are so sensitive to be able to characterize in detail the severity of the pathological condition of the case of muscular dystrophy that we have in examination. The third merit is that we have also given the modality of investigation. We have created a standard protocol of examination of the data that clinicians have, starting with the present paper, to follow in detail. We have attempted to standardize the frequency of sEMG recording and the epochs or windows to frag- ment the recorded

Background: Autism spectrum disorder (ASD) is a neurodevelopmental disorder with a worldwide prevalence of 1 – 2%. In low-resource environments, in particular, early identification and diagnosis is a significant challenge. Therefore, there is a great demand for ‘ language-free, culturally fair ’ low-cost screening tools for ASD that do not require highly trained professionals. Electroencephalography (EEG) has seen growing interest as an investigational tool for biomarker development in ASD and neurodevelopmental disorders. One of the key challenges is the identification of appropriate multivariate, next-generation analytical methodologies that can characterise the complex, nonlinear dynamics of neural networks in the brain, mindful of technical and demographic confounders that may influence biomarker findings. The aim of this study was to evaluate the robustness of recurrence quantification analysis (RQA) as a potential biomarker for ASD using a systematic methodological exploration of a range of potential technical and demographic confounders. Methods: RQA feature extraction was performed on continuous 5-second segments of resting state EEG (rsEEG) data and linear and nonlinear classifiers were tested. Data analysis progressed from a full sample of 16 ASD and 46 typically developing (TD) individuals (age 0 – 18 years, 4802 EEG segments), to a subsample of 16 ASD and 19 TD children (age 0 – 6 years, 1874 segments), to an age-matched sample of 7 ASD and 7 TD children (age 2 – 6 years, 666 segments) to prevent sample bias and to avoid misinterpretation of the classification results attributable to technical and demographic confounders. A clinical scenario of diagnosing an unseen subject was simulated using a leave-one-subject-out

These small-scale structures are the base for recurrence quantification analysis (RQA) [20]. RQA attempts to capture and quantify the amount and distribution of points on the RP. The basis of the RQA approach is phase-space reconstruction through time-delayed embedding. A phase space is a space in which all possible states of a system under study can be charted. If full determination of the state of a system re- quires N independent variables, then the phase space has N dimensions. The method of time-delayed embedding allows the reconstruction of phase-space profiles from a single, one-dimensional variable, in this case CBT, according to Takens ’ theorem [21]. Briefly, if a system is comprised of multiple interdependent variables and one has access only to a single observable x from the system (i.e., CBT), then the multidimensional dy- namics of that system can be reconstructed from the single measured dimension by plotting the variable x against itself a certain number of times and at a certain time delay. This variable is called Takens vector ’ s index, and in our case, plotting was 24 number of times with a time delay of 1 h. The following features were calculated from the matrix, with NonlinearTseries R package (https://cran.r-project.org/web/packages/ nonlinearTseries/index.html), as described below:

Mental health disorders affect approximately 20% of children and adolescents worldwide (Belfer, 2008; de Vries et al., 2013). Autism spectrum disorder (ASD) is one of the most common neurodevelopmental disorders (NDD), with a global prevalence estimate of 1 to 2% in children (Baird et al., 2006; Kim et al., 2011; Elsabbagh et al., 2012; American Psychiatric Association, 2013; CDC, 2014). 90% of people with ASD live in low- and middle-income countries (LMICs) where there is a significant demand for screening tools that do not require highly trained professionals (Tomlinson and Swartz, 2003). There has been growing interest in electroencephalography (EEG) as an investigational tool for biomarker development in NDD. However, one of the key challenges lies in the identification of appropriate multivariate, next-generation analytical methodologies that can characterise the complex, nonlinear dynamics of neural networks in the brain (Natarajan et al., 2004; Acharya et al., 2011; Bosl et al., 2011; Jeste et al., 2015). The ultimate goal of this research is to develop a robust and reliable early marker of ASD risk that can be implemented as a simple laboratory-type test by community healthcare workers in low-resource environments where expert knowledge and skilled staff are often not accessible. In this dissertation the application of recurrence quantification analysis (RQA) to resting state EEG (rsEEG) is investigated as a potentially robust and reliable biomarker for ASD risk.

Cross-recurrence quantification analysis (CRQA), an analysis using cross-recurrence plots (CRP), was used to determine whether there are significant differences in the gaze collaboration patterns between these pair categories. Results showed that successful and unsuccessful pairs can be characterized distinctively based on their CRPs and CRQA metrics. This study also attempted to interpret the CRQA metrics in relation to how the pairs collaborated in order to provide a somewhat clear picture of their relevance and meaning. The analysis results could serve as a precursor in helping us understand what makes a programming pair more successful over other pairs and what behaviors exhibited by unsuccessful pairs that should be avoided.

Abstract—A methodology based on Recurrence Quantification Analysis (RQA) for the clustering of generator dynamic behavior is presented. RQA is a nonlinear data analysis method, which is used in this paper to extract features from measured generator rotor angle responses that can be used to cluster generators in groups with similar oscillatory behavior. The possibility of extracting features relevant to damping and frequency of oscillations present in power systems is studied. The k-Means clustering algorithm is further used to cluster the generator responses in groups exhibiting well or poorly damped oscillations, based on the extracted features from RQA. The effectiveness of RQA is investigated using simulated responses from a modified version of the IEEE 68 bus network, including renewable energy resources.

regarding the analyses of nonstationary, low-frequency kinetic signals [10,11]. Some dynamical measures (e.g. fractal dimensions or Lyapunov exponents) were devel- oped for univariate signals with long-range variability, but are limited in quantifying nonlinear interrelations from short bivariate and nonstationary time series [12]. Recently, the cross recurrence quantification analysis (CRQA) has been introduced as an advanced technique for nonlinear, neurophysiological signals. CRQA pro- vides a group of statistical parameters to analyze the structures of a cross recurrence plot (CRP). The CRP is a graphical representation of a matrix whose elements correspond to all the moments when phase-space trajec- tories of one system pass through the neighborhoods of trajectories of another system [13]. CRQA is particularly suitable for the study of interdigit coordination as it is capable of revealing the interactions of two dynamical systems with robustness against model presumption, nonstationarity transients, outliers, and noise that often limit the use of other methods [14]. In addition, CRQA is an effective tool to analyze the phase synchronization (PS) of two coupled dynamical systems [15]. PS means that phases or frequencies of two chaotic systems be- come locked, even though their amplitudes remain uncorrelated [13]. PS has been observed in human cog- nition and behaviors, such as neuron activities [16], corticomuscular coupling [17], or binocular eye move- ments [13]. However, it has yet to be determined whether the thumb and index finger synchronize in their kinetic signals during a precision grip.

This paper presents the application of recurrence plots (RPs) and recurrence quantification analysis (RQA) in the diagnostics of various faults in a gear-train system. For this study, multiple test gears with different health con- ditions (such as a healthy gear, and defective gears with a root crack on one tooth, multiple cracks on five teeth and missing tooth) are studied. The vibra- tion data of a gear-train is measured by a triaxial accelerometer installed on the test. Two different support vector machine classifiers are trained and compared. Mutual information is used to rank the extracted features in order to select an optimal subset that provides as much information as possible about the intrinsic dynamics of the system. Results indicate that our approach is quite efficient in diagnosing the status of the health of the gear system and characterizing the dynamic behavior.

Chaos theory may be considered for surface height fluctuations treatment, as it takes phenomena, which in spite of their apparent random nature, they are governed by deterministic laws which produce complex results as they are mutually combined. Among different chaotic signals analysis methodologies, Echmann et al. proposed the so called Recursive Plots (RPs) method [5]. This kind of signal graphic analysis reveals characteristics where heterogeneities and complicated contributions of the system are highlighted, impossible to detect by means of other different methodologies. In order to quantify the complex structure observed on RPs, Webber et al. proposed the Recurrence Quantification Analysis (RQA), which is based on quantification of the diagonal line structures of RPs [6]. Later, Norbert Marwan succesfully added quantifications based on vertical line structures [7]. On the other hand, Kolmogorov Entropy (K) is a quantitative measure of the rate of information loss of a system dynamics, where information loss in chaotic systems arises from the exponential divergence of very close trajectories. For periodic system its value is zero; for pure random system its value is positive infinity, making it impossible to predict the state of the system, and for the case of chaotic system, its value is finite and positive [8]. More recently, Pincus [9] introduced the Approximate Entropy (ApEn) to quantify the regularity and complexity of time series; its computing is based on the probability that patterns on a time series continue to be similar to the next ones on incremental comparisons; ApEn has been applied as a tool to detect changes on regularities [10], characterization of rotatory machines [11] and identification of dynamical unstabilities on machinary processes [12] [13].

This paper provides a practical, hands-on introduction to cross-recurrence quantification analysis (CRQA), diagonal cross-recurrence profiles (DCRP), and multidimensional recurrence quantification analysis (MdRQA) in R. These methods have enjoyed increasing popularity in the cognitive and social sciences since a recognition that many behavioral and neurophysiological processes are intrinsically time dependent and reliant on environmental and social context has emerged. Recurrence-based methods are particularly suited for time-series that are non-stationary or have complicated dynamics, such as longer recordings of continuous physiological or movement data, but are also useful in the case of time-series of symbolic data, as in the case of text/verbal transcriptions or categorically coded behaviors. In the past, they have been used to assess changes in the dynamics of, or coupling between physiological and behavioral measures, for example in joint action research to determine the co-evolution of the behavior between individuals in dyads or groups, or for assessing the strength of coupling/correlation between two or more time-series. In this paper, we provide readers with a conceptual introduction, followed by a step-by-step explanation on how the analyses are performed in R with a summary of the current best practices of their application.

20. Zbilut JP, Webber Jr., CL, Zak M (1998). Quantification of heart rate variability using methods derived from nonlinear dynamics. In: Drzewiecki G, and Li J K-J, (eds.) Assessment and Analysis of Cardiovascular Function. Springer Verlag, NY, Chapter 19, pp 324-334.

Dynamical systems display two fundamental properties - determinism and recurrence [2]. A deterministic dynamical system can be defined as a system whose future behavior can be accurately predicted, given that sufficient knowledge for the current state of the system exists. Recurrence is another property which can be used to characterize the nonlinear dynamics of a system. In 1890, Henri Poincar´e introduced the concept of recurrence, while addressing the three body problem [12]. Nearly a century later, in 1987, J.-P.Eckman introduced recurrence plots (RPs) [13], a two-dimensional graphical plot to visualize recurrent behavior of dynamical systems. RPs have been successfully applied to characterize the underlying dynamical properties of wide variety of systems [2]. A further important contribution made in the field of recurrence plots was the introduction of recurrence quantification analysis (RQA) tool to objectively quantify the structure of recurrence plots [14]. Recently, by integrating the approach from complex network theory and nonlinear dynamical systems theory, network-based nonlinear time series analysis has been proposed. Such networks constructed from time series are based on the recurrences in phase space and are known as recurrence networks (RNs). Topological characterization of such networks using tools from graph theory allows us to analyze the dynamically relevant structural properties of the time series data [15–17]. In particular, RNs encode the geometric information about the underlying system which can be characterized (for example using graph theoretical measures) to extract information on the geometric properties of the attractor [18]. Thus, RNs provide useful and complementary insights into phase space structures that are otherwise not provided by other methods of nonlinear time series analysis [16]. Methods based on RNs are particularly advantageous over some other nonlinear measures due to their applicability to short and non-stationary data [15].

A few years following the introduction of RPs, Webber and Zbilut proposed several quantification measures in order to standardize and facilitate the interpretation of these graphical tools (Webber and Zbilut, 1994; Zbilut and Webber, 1992). These measures made the RP method more rigorous since they enhanced it with well de- fined quantitative descriptions. Recurrence quantification analysis (RQA) is applied to estimate the complexity of the nonlinear system. These measures are related to the RP’s recurrence density, diagonal and vertical lines. Here, we introduce the RQA formulas with a brief explanation for each one (Marwan et al., 2007). It should be mentioned that the LOI is usually excluded form RQA analyses. In the following, N is defined as the number of data points which is the number of phase space points.

The goal of any nonlinear dynamical analysis of a data series is to extract features of the dynamics of the underlying physical and chemical processes that produce that spatial pattern or time series; a by-product is to characterise the signal in terms of quantitative measures. In this paper, we briefly review the methodology involved in nonlinear analysis and explore time series for GNSS crustal displacements with a view to constraining the dynamics of the underlying tectonic processes responsible for the kinematics. We use recurrence plots and their quantification to extract the invariant measures of the tectonic system including the embedding dimension, the maximum Lyapunov exponent and the entropy and characterise the system using recurrence quantification analysis (RQA). These measures are used to develop a data model for some GNSS data sets in New Zealand. The resulting dynamical model is tested using nonlinear prediction algorithms. The behaviours of some RQA measures are shown to act as precursors to major jumps in crustal displacement rate. We explore synchronisation using cross- and joint-recurrence analyses between stations and show that generalised synchronisation occurs between GNSS time series separated by up to 600 km. Synchronisation between stations begins up to 250 to 400 days before a large displacement event and decreases immediately before the event. The results are used to speculate on the coupled processes that may be responsible for the tectonics of the observed crustal deformations and that are compatible with the results of nonlinear analysis. The overall aim is to place constraints on the nature of the global attractor that describes plate motions on the Earth.

Supplementary Figure SN1 shows some screenshots from a sleuth analysis of the Bottomly data [?]. Supplementary Figure 1a shows the principal component analysis of the data set colored by the different conditions. One can see that the first two principal components do not segregate the data by experimental condition (mouse strain). Supplementary Figure 1b shows how one can use the drop-down menu to change the coloring, revealing that the first two principal components seem to explain some of the variation due to the batch. In addition, there are many other features assisting in exploring the data, such as the ability to view, sort and search the table of differential expression results. For example, sorting by the inferential variability and then by largest p-values, we find transcript Ppip5k1-004 (ENSMUST00000110625), which is not reported as differentially expressed by sleuth, but is reported as differentially expressed by both voom and DESeq2. This is likely due to the high inferential variability which is not being properly assessed and adjusted for by those programs. The transcript name can be pasted into the “transcript view” window and the distribution of inferential variability can be explored with boxplots describing the variability within each sample (Supplementary Figure SN1c).

The workload analysis is divided into two primary sections; cluster analysis and distribution analysis. The objective of the cluster analysis is to classify users and tasks, quantify their respective statistical properties, and study their temporal and spatial behavioural patterns across the entire system timespan as well as selected time observation periods as discussed in Chapter 3.3. Specifically, the cluster analysis studies the characteristics and behaviour of the created clusters and the statistical properties of each identified attribute within the workload model, including the Mean, Standard Deviation and Coefficient of Variation (Cv). In the context of the Google trace log, we investigate the variance of task and user clusters and their respective attributes over three additional observational periods of Day 2, Day 18 and Day 26 in order to inspect patterns that exist within the Cloud and to explore the variability and dynamicity over the system lifespan. The objective of the distribution analysis is to study the internal data distributions of attributes in each task and user cluster in order to better understand intra-cluster behaviour and diversity, as well extract model parameters of practical use for researchers. This requires fitting the data to the closest theoretical distribution using a GoF test to obtain the parameters of their Probabilistic Distribution Functions (PDF). The data of each cluster is fitted to a parametric distribution by using the Anderson-Darling (AD) GoF statistical test, with the theoretical distribution with the lowest AD-value selected to represent the data distribution of each cluster attribute. The parameters of the PDFs for each workload model attribute described in Equations 3 and 4 are extracted and can be by other researchers in evaluating energy-efficient mechanisms and developing realistic simulation environments.

recorded with the corresponding results to verify that the individual linear measurements, location and orientation of the tumor was the same with respect to both modalities [3]. In another study by T. Jobling, Narayan and R.J. Hicks aimed to assess whether positron emission tomography (PET) or Magnetic Resource Imaging (MRI) could obviate the need for surgical staging in patients with locally cervical carcinoma being planned for radiotherapy (RT). They concluded that positive predictive value of PET in the pelvis and para aortic region were sufficient to obviate lymph nodal sampling. Still requirement of sampling is needed to exclude small volume disease cranial to sites of abnormality on PET.MRI was not sufficient accurate for the staging of nodal. [4]. Sang-Young Ryu, Moon- Hong Kim and others worked on the detection of early recurrence with 18 F-FDG PET in patients with Cervical cases. They observed that 82 percent of recurrence was detected within 6-18 months after diagnosis, and 89 percent of recurrence occurred in FIGO stage IIB and Stage patients. It was concluded that 18-FDG PET was effective in detecting early recurrences in cervical cancer patients with no evidence of disease [5].In another study by James B Unger, Joseph, aimed to detect the recurrence of Cervical carcinoma in both symptomatic and asymptomatic women through FDG and PET scan test. 44 records of cervical patients were reviewed out of which 47 underwent post treatment whole body FDG scan in an attempt to detect recurrent disease. 26 scans were performed in asymptomatic women and 21 with symptoms of recurrence. As a result 30.8% of asymptomatic women had recurrent disease detected by PET compared with 66.7% of women in the symptomatic ones [6].

Above 6 characteristic were introduced into multivariate analysis, gender, age, extracolonic tumor history, alcohol history and adenomas’ number at baseline status were the inde- pendent prognostic factors for adenoma recurrence (Table 4). Patients older the 60 years had high adenoma recurrence risk than patients younger than 60 (HR 1.359, P=0.011), patients with extracolonic tumor history had high adenoma recurrence risk than patients without extracolonic tumor history (HR 5.180, P<0.001), patients with alcohol history had high risk than patients without alcohol history (HR 2.022, P=0.001), patients had more than 3 colonic adenomas at initial colonscopy had high adenoma recurrence risk than patients had ≤2 adenomas (HR 1.811, P<0.001), the female patients had lower recurrence risk than male patients (HR 0.632, P=0.001). The median recurrence time for male patients, patients older than 60 years, patients with extracolonic tumor his-tory, patients with alco- hol history and patients with ≥3 adenomas at baseline status were 19 ± 1.28 months, 22 ± According to the definition, advanced adeno-

This meta-analysis of published studies demonstrates that an individual ’ s risk of having an early (within 24 to 48 hours) recurrent intussusception after a successful enema reduction is low. In addition, the risk of recurrence is in- dependent of enema type, study loca- tion, year of study completion, and study quality. The risk of recurrence in the fi rst 24 hours post reduction is 2.2% to 3.9% and 2.7% to 6.6% in the fi rst 48 hours. Assuming a 24-hour re- currence risk of 3.9%, it would require hospitalizing 26 patients for 24 hours to identify a single recurrence. This suggests that the vast majority of recurrences will not be identi fi ed by overnight hospitalization. In addition, recurrent intussusceptions can be safely and successfully reduced via repeat en- ema, and signi fi cant complications as- sociated with enema reduction are rare. Multiple studies supporting outpatient management after successful enema reduction have demonstrated high rates of success with repeat enema reduction without delayed complications. 16 – 20 In