Impact of time-history terms on reservoir dynamics and prediction accuracy in echo state networks.

The echo state network (ESN) is an excellent machine learning model for processing time-series data. This model, utilising the response of a recurrent neural network, called a reservoir, to input signals, achieves high training efficiency. Introducing time-history terms into the neuron model of the reservoir is known to improve the time-series prediction performance of ESN, yet the reasons for this improvement have not been quantitatively explained in terms of reservoir dynamics characteristics. Therefore, we hypothesised that the performance enhancement brought about by time-history terms could be explained by delay capacity, a recently proposed metric for assessing the memory performance of reservoirs. To test this hypothesis, we conducted comparative experiments using ESN models with time-history terms, namely leaky integrator ESNs (LI-ESN) and chaotic echo state networks (ChESN). The results suggest that compared with ESNs without time-history terms, the reservoir dynamics of LI-ESN and ChESN can maintain diversity and stability while possessing higher delay capacity, leading to their superior performance. Explaining ESN performance through dynamical metrics are crucial for evaluating the numerous ESN architectures recently proposed from a general perspective and for the development of more sophisticated architectures, and this study contributes to such efforts.

Photoplethysmogram Recording Length: Defining Minimal Length Requirement from Dynamical Characteristics.

Photoplethysmography is a widely used technique to noninvasively assess heart rate, blood pressure, and oxygen saturation. This technique has considerable potential for further applications-for example, in the field of physiological and mental health monitoring. However, advanced applications of photoplethysmography have been hampered by the lack of accurate and reliable methods to analyze the characteristics of the complex nonlinear dynamics of photoplethysmograms. Methods of nonlinear time series analysis may be used to estimate the dynamical characteristics of the photoplethysmogram, but they are highly influenced by the length of the time series, which is often limited in practical photoplethysmography applications. The aim of this study was to evaluate the error in the estimation of the dynamical characteristics of the photoplethysmogram associated with the limited length of the time series. The dynamical properties were evaluated using recurrence quantification analysis, and the estimation error was computed as a function of the length of the time series. Results demonstrated that properties such as determinism and entropy can be estimated with an error lower than 1% even for short photoplethysmogram recordings. Additionally, the lower limit for the time series length to estimate the average prediction time was computed.

Dynamical Characteristics of Wild-Type Mouse Spontaneous Pupillary Fluctuations.

Spontaneous pupil size fluctuations in humans and mouse models are noninvasively measured data that can be used for early detection of neurodevelopmental spectrum disorders. While highly valuable in such applied studies, pupillometry dynamics and dynamical characteristics have not been fully investigated, although their understanding may potentially lead to the discovery of new information, which cannot be readily uncovered by conventional methods. Properties of pupillometry dynamics, such as determinism, were previously investigated for healthy human subjects; however, the dynamical characteristics of pupillometry data in mouse models, and whether they are similar to those of human subjects, remain largely unknown. Therefore, it is necessary to establish a thorough understanding of the dynamical properties of mouse pupillometry dynamics and to clarify whether it is similar to that of humans. In this study, dynamical pupillometry characteristics from 115 wild-type mouse datasets were investigated by methods of nonlinear time series analysis. Results clearly demonstrated a strong underlying determinism in the investigated data. Additionally, the data's trajectory divergence rate and predictability were estimated.

Human photoplethysmogram through the Morse graph: Searching for the saddle point in experimental data.

Photoplethysmogram (PPG) is one of the noninvasive biological signals widely used for the estimation of physiological parameters, such as heart rates in human health monitoring. Methods of its processing, its applications, and dynamics have been extensively investigated over the last several decades. However, there is still lack of the knowledge related to the fundamental structure of the PPG dynamics such as saddle equilibrium points, which have crucial importance to achieve the full understanding of the PPG dynamics and might provide useful information for establishing a mathematical model of the PPG. In this study, Morse graph theory was applied to the experimental PPG data in an attempt to verify the existence of saddle equilibrium and estimate its location with respect to the time-delay-reconstructed PPG attractor. The results demonstrated evidence that a saddle equilibrium point can be found in a neighborhood of the reconstructed PPG trajectory; moreover, it was found to be in the same reconstructed attractor's region for healthy subjects from different age groups that points toward fundamental importance of the found saddle equilibrium for a general understanding of the PPG dynamics.

Reconstructed Dynamics of the Imaging Photoplethysmogram.

Human photoplethysmogram (PPG) is one of the signals widely applied for health monitoring. Development of the new techniques made possible evolution of traditional contact PPG which was measured at red and near-infrared light (NIR) to the contactless, imaging PPG (iPPG) that can be recorded at various light wavelengths, including ambient visible light. However, despite the numerous advantages of iPPG its applications demonstrated so far are quite limited. The NIR PPG was previously found to be useful for various applications in the area of physiological and mental health monitoring by utilizing advanced methods of nonlinear time-series analysis applied on its reconstructed dynamics. The main purpose of this study is to demonstrate data-driven approach with time-delay-reconstructed attractor obtained from the iPPG. The results of this study demonstrated that the iPPG dynamics can be reconstructed with fine data resolution, and its time-delay-reconstructed trajectory is almost deterministic, though contains noise. The obtained results might be useful for further applied studies on the iPPG.

Chaos emerging in soil failure patterns observed during tillage: Normalized deterministic nonlinear prediction (NDNP) and its application.

Real-world processes are often combinations of deterministic and stochastic processes. Soil failure observed during farm tillage is one example of this phenomenon. In this paper, we investigated the nonlinear features of soil failure patterns in a farm tillage process. We demonstrate emerging determinism in soil failure patterns from stochastic processes under specific soil conditions. We normalized the deterministic nonlinear prediction considering autocorrelation and propose it as a robust way of extracting a nonlinear dynamical system from noise contaminated motion. Soil is a typical granular material. The results obtained here are expected to be applicable to granular materials in general. From a global scale to nano scale, the granular material is featured in seismology, geotechnology, soil mechanics, and particle technology. The results and discussions presented here are applicable in these wide research areas. The proposed method and our findings are useful with respect to the application of nonlinear dynamics to investigate complex motions generated from granular materials.

Local noise sensitivity: Insight into the noise effect on chaotic dynamics.

Noise contamination in experimental data with underlying chaotic dynamics is one of the significant problems limiting the application of many nonlinear time series analysis methods. Although numerous studies have been devoted to the investigation of different aspects of noise-nonlinear dynamics interactions, the effects produced by noise on chaotic dynamics are not fully understood. This study sought to analyze the local effects produced by noise on chaotic dynamics with a smooth attractor. Local Wayland test translation errors were calculated for noise-induced Lorenz and Rössler chaotic models, and for experimental green light photoplethysmogram data. Results demonstrated that under noise induction, local regions on the chaotic attractor with high values of local translation error can be observed. This phenomenon was defined as the local noise sensitivity. It was found that for both models, local noise-sensitive regions were located close to the system's equilibrium points. Additionally, it was found that the reconstructed dynamics represent well the local noise sensitivity of the original dynamics. The concept of local noise sensitivity is expected to contribute to various applied studies, as it reveals regions of chaotic attractors that are sensitive to the presence of noise.

Outcome of anatomic ganglionated plexi ablation to treat paroxysmal atrial fibrillation: a 3-year follow-up study.

AIMS: A new strategy for anatomically based ganglionated plexi (GP) ablation for the treatment of paroxysmal atrial fibrillation (AF) has been proposed recently. We aimed to assess the long-term outcome of patients undergoing anatomic GP ablation for paroxysmal AF, in comparison with circumferential pulmonary vein (PV) isolation. METHODS AND RESULTS: The study population consisted of 70 patients (mean age 56.6 ± 10.9 years; 41 males) with paroxysmal AF and no history of structural heart disease: 35 subjects underwent anatomic GP ablation, while 35 consecutive patients had circumferential PV isolation (CPVI) (control group). The groups were not different in demographic and clinical parameters. Anatomic GP ablation required more ablation points (85.6 ± 5.5 vs. 74.4 ± 6.2, P < 0.05) and equal duration of total procedure and fluoroscopy times. During a mean follow-up period of 36.3 ± 2.3 months, freedom from any atrial tachyarrhythmia without antiarrhythmics was achieved in 34.3% patients after anatomic GP ablation and 65.7% patients after CPVI (log-rank test P = 0.008). Early arrhythmia recurrences and anatomic GP ablation were independent predictors of late recurrence [HR 6.44 (CI 95%; 3.14-13.18; P < 0.001) and HR 2.08 (CI 95%; 1.03-4.22; P = 0.04), respectively]. Six patients in the group of GP ablation underwent subsequent CPVI, plus peri-mitral flutter ablation in two of them, with no further arrhythmia episodes in five patients. CONCLUSION: Anatomic GP ablation yields a significantly lower success rate over the long-term follow-up period, when compared with CPVI. Recurrences include AF and macro re-entrant atrial tachycardias.