Loss of grazing by large mammalian herbivores can destabilize the soil carbon pool.

Grazing by mammalian herbivores can be a climate mitigation strategy as it influences the size and stability of a large soil carbon (soil-C) pool (more than 500 Pg C in the world's grasslands, steppes, and savannas). With continuing declines in the numbers of large mammalian herbivores, the resultant loss in grazer functions can be consequential for this soil-C pool and ultimately for the global carbon cycle. While herbivore effects on the size of the soil-C pool and the conditions under which they lead to gain or loss in soil-C are becoming increasingly clear, their effect on the equally important aspect of stability of soil-C remains unknown. We used a replicated long-term field experiment in the Trans-Himalayan grazing ecosystem to evaluate the consequences of herbivore exclusion on interannual fluctuations in soil-C (2006 to 2021). Interannual fluctuations in soil-C and soil-N were 30 to 40% higher after herbivore exclusion than under grazing. Structural equation modeling suggested that grazing appears to mediate the stabilizing versus destabilizing influences of nitrogen (N) on soil-C. This may explain why N addition stimulates soil-C loss in the absence of herbivores around the world. Herbivore loss, and the consequent decline in grazer functions, can therefore undermine the stability of soil-C. Soil-C is not inert but a very dynamic pool. It can provide nature-based climate solutions by conserving and restoring a functional role of large mammalian herbivores that extends to the stoichiometric coupling between soil-C and soil-N.

Nonlinear analysis and recognition of epileptic EEG signals in different stages.

It is a hot problem in epilepsy research to detect and predict seizures by EEG signals. Clinically, it is generally observed that there are only sudden abnormal signals during the ictal stage, but there is no significant difference in the EEG signal between the interictal and preictal stages. To solve the problem that preictal signals are difficult to recognize clinically, and then effectively improve the recognition efficiency of epileptic seizures, so, in this paper, some nonlinear methods are comprehensively used to extract the hidden information in the EEG signals in different stages, namely, phase space reconstruction (PSR), Poincaré section (PS), synchroextracting transform (SET) and machine learning for EEG signal analysis. Firstly, PSR based on C-C method is used, and the results show that there are different diffuse attractor trajectories of the signals in different stages. Secondly, the confidence ellipse (CE) is constructed by using the scatter diagram of the corresponding trajectory on PS, and the aspect ratio and area of the ellipse are calculated. The results show that there is an interesting transitional phenomenon in preictal stage. To recognize ictal and preictal signals, time-frequency (TF) spectrums which are processed by SET are fed into the convolutional neural networks (CNN) classifier. The accuracy of recognize ictal and preictal signals reaches 99.7% and 93.7% respectively. To summarize, our results based on nonlinear method provide new research ideas for seizures detection and prediction.

Automatic classification of seizure and seizure-free EEG signals based on phase space reconstruction features.

Epilepsy is a type of brain disorder triggered by an abrupt electrical imbalance of neuronal networks. An electroencephalogram (EEG) is a diagnostic tool to capture the underlying brain mechanisms and detect seizure onset in epileptic patients. To detect seizures, neurologists need to manually monitor EEG recordings for long periods, which is challenging and susceptible to errors depending on expertise and experience. Therefore, automatic identification of seizure and seizure-free EEG signals becomes essential. This study introduces a method based on the features extracted from the phase space reconstruction for classifying seizure and seizure-free EEG signals. The computed features are derived from the elliptical area and interquartile range of the Euclidean distance by varying percentage values of data points ranging from 50 to 100%. We consider two public datasets and evaluate these features in each EEG epoch that includes the healthy, interictal, preictal, and ictal stages of epileptic subjects, utilizing the K-nearest neighbor classifier for classification. Results show that the features have higher values during the seizure than the seizure-free EEG signals and healthy subjects. Furthermore, the proposed features can effectively discriminate seizure EEG signals from the seizure-free and normal subjects with 100% accuracy, sensitivity, and specificity in both datasets. Likewise, the classification between the preictal stage and seizure EEG signals attains 98% accuracy. Overall, the reconstructed phase space features significantly enhance the accuracy of detecting epileptic EEG signals compared with existing methods. This advancement holds great potential in assisting neurologists in swiftly and accurately diagnosing epileptic seizures from EEG signals.

Phase Space Spin-Entropy.

Quantum physics is intrinsically probabilistic, where the Born rule yields the probabilities associated with a state that deterministically evolves. The entropy of a quantum state quantifies the amount of randomness (or information loss) of such a state. The degrees of freedom of a quantum state are position and spin. We focus on the spin degree of freedom and elucidate the spin-entropy. Then, we present some of its properties and show how entanglement increases spin-entropy. A dynamic model for the time evolution of spin-entropy concludes the paper.

A Nonlinear Local Approximation Approach for Catchment Classification.

Catchment classification plays an important role in many applications associated with water resources and environment. In recent years, several studies have applied the concepts of nonlinear dynamics and chaos for catchment classification, mainly using dimensionality measures. The present study explores prediction as a measure for catchment classification, through application of a nonlinear local approximation prediction method. The method uses the concept of phase-space reconstruction of a time series to represent the underlying system dynamics and identifies nearest neighbors in the phase space for system evolution and prediction. The prediction accuracy measures, as well as the optimum values of the parameters involved in the method (e.g., phase space or embedding dimension, number of neighbors), are used for classification. For implementation, the method is applied to daily streamflow data from 218 catchments in Australia, and predictions are made for different embedding dimensions and number of neighbors. The prediction results suggest that phase-space reconstruction using streamflow alone can provide good predictions. The results also indicate that better predictions are achieved for lower embedding dimensions and smaller numbers of neighbors, suggesting possible low dimensionality of the streamflow dynamics. The classification results based on prediction accuracy are found to be useful for identification of regions/stations with higher predictability, which has important implications for interpolation or extrapolation of streamflow data.

Distinction of Chaos from Randomness Is Not Possible from the Degree Distribution of the Visibility and Phase Space Reconstruction Graphs.

We investigate whether it is possible to distinguish chaotic time series from random time series using network theory. In this perspective, we selected four methods to generate graphs from time series: the natural, the horizontal, the limited penetrable horizontal visibility graph, and the phase space reconstruction method. These methods claim that the distinction of chaos from randomness is possible by studying the degree distribution of the generated graphs. We evaluated these methods by computing the results for chaotic time series from the 2D Torus Automorphisms, the chaotic Lorenz system, and a random sequence derived from the normal distribution. Although the results confirm previous studies, we found that the distinction of chaos from randomness is not generally possible in the context of the above methodologies.

Dynamical Tunneling in More than Two Degrees of Freedom.

Recent progress towards understanding the mechanism of dynamical tunneling in Hamiltonian systems with three or more degrees of freedom (DoF) is reviewed. In contrast to systems with two degrees of freedom, the three or more degrees of freedom case presents several challenges. Specifically, in higher-dimensional phase spaces, multiple mechanisms for classical transport have significant implications for the evolution of initial quantum states. In this review, the importance of features on the Arnold web, a signature of systems with three or more DoF, to the mechanism of resonance-assisted tunneling is illustrated using select examples. These examples represent relevant models for phenomena such as intramolecular vibrational energy redistribution in isolated molecules and the dynamics of Bose-Einstein condensates trapped in optical lattices.

Nonlinear analysis of heart rate variability signals in meditative state: a review and perspective.

INTRODUCTION: In recent times, an upsurge in the investigation related to the effects of meditation in reconditioning various cardiovascular and psychological disorders is seen. In majority of these studies, heart rate variability (HRV) signal is used, probably for its ease of acquisition and low cost. Although understanding the dynamical complexity of HRV is not an easy task, the advances in nonlinear analysis has significantly helped in analyzing the impact of meditation of heart regulations. In this review, we intend to present the various nonlinear approaches, scientific findings and their limitations to develop deeper insights to carry out further research on this topic. RESULTS: Literature have shown that research focus on nonlinear domain is mainly concentrated on assessing predictability, fractality, and entropy-based dynamical complexity of HRV signal. Although there were some conflicting results, most of the studies observed a reduced dynamical complexity, reduced fractal dimension, and decimated long-range correlation behavior during meditation. However, techniques, such as multiscale entropy (MSE) and multifractal analysis (MFA) of HRV can be more effective in analyzing non-stationary HRV signal, which were hardly used in the existing research works on meditation. CONCLUSIONS: After going through the literature, it is realized that there is a requirement of a more rigorous research to get consistent and new findings about the changes in HRV dynamics due to the practice of meditation. The lack of adequate standard open access database is a concern in drawing statistically reliable results. Albeit, data augmentation technique is an alternative option to deal with this problem, data from adequate number of subjects can be more effective. Multiscale entropy analysis is scantily employed in studying the effect of meditation, which probably need more attention along with multifractal analysis. METHODS: Scientific databases, namely PubMed, Google Scholar, Web of Science, Scopus were searched to obtain the literature on "HRV analysis during meditation by nonlinear methods". Following an exclusion criteria, 26 articles were selected to carry out this scientific analysis.

Monitor unit verification for Varian TrueBeam VMAT plans using Monte Carlo calculations and phase space data.

To use the open-source Monte Carlo (MC) software calculations for TPS monitor unit verification of VMAT plans, delivered with the Varian TrueBeam linear accelerator, and compare the results with a commercial software product, following the guidelines set in AAPM Task Group 219. The TrueBeam is modeled in EGSnrc using the Varian-provided phase-space files. Thirteen VMAT TrueBeam treatment plans representing various anatomical regions were evaluated, comprising 37 treatment arcs. VMAT plans simulations were performed on a computing cluster, using 107 -109 particle histories per arc. Point dose differences at five reference points per arc were compared between Eclipse, MC, and the commercial software, MUCheck. MC simulation with 5 × 107 histories per arc offered good agreement with Eclipse and a reasonable average calculation time of 9-18 min per full plan. The average absolute difference was 3.0%, with only 22% of all points exceeding the 5% action limit. In contrast, the MUCheck average absolute difference was 8.4%, with 60% of points exceeding the 5% dose difference. Lung plans were particularly problematic for MUCheck, with an average absolute difference of approximately 16%. Our EGSnrc-based MC framework can be used for the MU verification of VMAT plans calculated for the Varian TrueBeam; furthermore, our phase space approach can be adapted to other treatment devices by using appropriate phase space files. The use of 5 × 107 histories consistently satisfied the 5% action limit across all plan types for the majority of points, performing significantly better than a commercial MU verification system, MUCheck. As faster processors and cloud computing facilities become even more widely available, this approach can be readily implemented in clinical settings.

A Mechanical Defect Localization and Identification Method for High-Voltage Circuit Breakers Based on the Segmentation of Vibration Signals and Extraction of Chaotic Features.

To address the problem of mechanical defect identification in a high-voltage circuit breaker (HVCB), this paper studies the circuit breaker vibration signal and proposes a method of feature extraction based on phase-space reconstruction of the vibration substages. To locate mechanical defects in circuit breakers, vibration signals are divided into different substages according to the time sequence of the parts of the circuit breakers. The largest Lyapunov exponent (LLE) of the vibration signals' substages is calculated, and then the substages are reconstructed in high-dimensional phase space. The geometric features of the phase trajectory mean center distance (MCD) and vector diameter offset (VDO) are calculated, and the LLE, MCD, and VDO are selected as the three fault identification features of the vibration substages. The eigenvalue anomaly rate of each substage of the vibration signal under defect state are calculated and analyzed to locate the vibration substage of the mechanical defect. Finally, a fault diagnosis model is constructed by a support vector machine (SVM), and the common mechanical defects of circuit breakers simulated in the laboratory are effectively identified.

Convolutional Neural Network for Individual Identification Using Phase Space Reconstruction of Electrocardiogram.

Electrocardiogram (ECG) biometric provides an authentication to identify an individual on the basis of specific cardiac potential measured from a living body. Convolutional neural networks (CNN) outperform traditional ECG biometrics because convolutions can produce discernible features from ECG through machine learning. Phase space reconstruction (PSR), using a time delay technique, is one of the transformations from ECG to a feature map, without the need of exact R-peak alignment. However, the effects of time delay and grid partition on identification performance have not been investigated. In this study, we developed a PSR-based CNN for ECG biometric authentication and examined the aforementioned effects. Based on a population of 115 subjects selected from the PTB Diagnostic ECG Database, a higher identification accuracy was achieved when the time delay was set from 20 to 28 ms, since it produced a well phase-space expansion of P, QRS, and T waves. A higher accuracy was also achieved when a high-density grid partition was used, since it produced a fine-detail phase-space trajectory. The use of a scaled-down network for PSR over a low-density grid with 32 × 32 partitions achieved a comparable accuracy with using a large-scale network for PSR over 256 × 256 partitions, but it had the benefit of reductions in network size and training time by 10 and 5 folds, respectively.

Electric Bus Pedal Misapplication Detection Based on Phase Space Reconstruction Method.

Due to the environmental protection of electric buses, they are gradually replacing traditional fuel buses. Several previous studies have found that accidents related to electric vehicles are linked to Unintended Acceleration (UA), which is mostly caused by the driver pressing the wrong pedal. Therefore, this study proposed a Model for Detecting Pedal Misapplication in Electric Buses (MDPMEB). In this work, natural driving experiments for urban electric buses and pedal misapplication simulation experiments were carried out in a closed field; furthermore, a phase space reconstruction method was introduced, based on chaos theory, to map sequence data to a high-dimensional space in order to produce normal braking and pedal misapplication image datasets. Based on these findings, a modified Swin Transformer network was built. To prevent the model from overfitting when considering small sample data and to improve the generalization ability of the model, it was pre-trained using a publicly available dataset; moreover, the weights of the prior knowledge model were loaded into the model for training. The proposed model was also compared to machine learning and Convolutional Neural Networks (CNN) algorithms. This study showed that this model was able to detect normal braking and pedal misapplication behavior accurately and quickly, and the accuracy rate on the test dataset is 97.58%, which is 9.17% and 4.5% higher than the machine learning algorithm and CNN algorithm, respectively.

A Self-Coordinating Controller with Balance-Guiding Ability for Lower-Limb Rehabilitation Exoskeleton Robot.

The restricted posture and unrestricted compliance brought by the controller during human-exoskeleton interaction (HEI) can cause patients to lose balance or even fall. In this article, a self-coordinated velocity vector (SCVV) double-layer controller with balance-guiding ability was developed for a lower-limb rehabilitation exoskeleton robot (LLRER). In the outer loop, an adaptive trajectory generator that follows the gait cycle was devised to generate a harmonious hip-knee reference trajectory on the non-time-varying (NTV) phase space. In the inner loop, velocity control was adopted. By searching the minimum L2 norm between the reference phase trajectory and the current configuration, the desired velocity vectors in which encouraged and corrected effects can be self-coordinated according to the L2 norm were obtained. In addition, the controller was simulated using an electromechanical coupling model, and relevant experiments were carried out with a self-developed exoskeleton device. Both simulations and experiments validated the effectiveness of the controller.

Chaos and Predictability in Ionospheric Time Series.

Modelling the Earth's ionosphere is a big challenge, due to the complexity of the system. Different first principle models have been developed over the last 50 years, based on ionospheric physics and chemistry, mostly controlled by Space Weather conditions. However, it is not understood in depth if the residual or mismodelled component of the ionosphere's behaviour is predictable in principle as a simple dynamical system, or is conversely so chaotic to be practically stochastic. Working on an ionospheric quantity very popular in aeronomy, we here suggest data analysis techniques to deal with the question of how chaotic and how predictable the local ionosphere's behaviour is. In particular, we calculate the correlation dimension D2 and the Kolmogorov entropy rate K2 for two one-year long time series of data of vertical total electron content (vTEC), collected on the top of the mid-latitude GNSS station of Matera (Italy), one for the year of Solar Maximum 2001 and one for the year of Solar Minimum 2008. The quantity D2 is a proxy of the degree of chaos and dynamical complexity. K2 measures the speed of destruction of the time-shifted self-mutual information of the signal, so that K2-1 is a sort of maximum time horizon for predictability. The analysis of the D2 and K2 for the vTEC time series allows to give a measure of chaos and predictability of the Earth's ionosphere, expected to limit any claim of prediction capacity of any model. The results reported here are preliminary, and must be intended only to demonstrate how the application of the analysis of these quantities to the ionospheric variability is feasible, and with a reasonable output.

Restricted Phase Space Thermodynamics of Einstein-Power-Yang-Mills AdS Black Hole.

We consider the thermodynamics of the Einstein-power-Yang-Mills AdS black holes in the context of the gauge-gravity duality. Under this framework, Newton's gravitational constant and the cosmological constant are varied in the system. We rewrite the thermodynamic first law in a more extended form containing both the pressure and the central charge of the dual conformal field theory, i.e., the restricted phase transition formula. A novel phenomena arises: the dual quantity of pressure is the effective volume, not the geometric one. That leads to a new behavior of the Van de Waals-like phase transition for this system with the fixed central charge: the supercritical phase transition. From the Ehrenfest's scheme perspective, we check out the second-order phase transition of the EPYM AdS black hole. Furthermore the effect of the non-linear Yang-Mills parameter on these thermodynamic properties is also investigated.

The Typical Set and Entropy in Stochastic Systems with Arbitrary Phase Space Growth.

The existence of the typical set is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of dynamical constraints. However, given its central role underlying the emergence of stable, almost deterministic statistical patterns, a question arises whether typical sets exist in much more general scenarios. We demonstrate here that the typical set can be defined and characterized from general forms of entropy for a much wider class of stochastic processes than was previously thought. This includes processes showing arbitrary path dependence, long range correlations or dynamic sampling spaces, suggesting that typicality is a generic property of stochastic processes, regardless of their complexity. We argue that the potential emergence of robust properties in complex stochastic systems provided by the existence of typical sets has special relevance to biological systems.

Quantum-Classical Hybrid Systems and Ehrenfest's Theorem.

The conceptual analysis of quantum mechanics brings to light that a theory inherently consistent with observations should be able to describe both quantum and classical systems, i.e., quantum-classical hybrids. For example, the orthodox interpretation of measurements requires the transient creation of quantum-classical hybrids. Despite its limitations in defining the classical limit, Ehrenfest's theorem makes the simplest contact between quantum and classical mechanics. Here, we generalized the Ehrenfest theorem to bipartite quantum systems. To study quantum-classical hybrids, we employed a formalism based on operator-valued Wigner functions and quantum-classical brackets. We used this approach to derive the form of the Ehrenfest theorem for quantum-classical hybrids. We found that the time variation of the average energy of each component of the bipartite system is equal to the average of the symmetrized quantum dissipated power in both the quantum and the quantum-classical case. We expect that these theoretical results will be useful both to analyze quantum-classical hybrids and to develop self-consistent numerical algorithms for Ehrenfest-type simulations.

Correspondence between the Energy Equipartition Theorem in Classical Mechanics and Its Phase-Space Formulation in Quantum Mechanics.

In classical physics, there is a well-known theorem in which it is established that the energy per degree of freedom is the same. However, in quantum mechanics, due to the non-commutativity of some pairs of observables and the possibility of having non-Markovian dynamics, the energy is not equally distributed. We propose a correspondence between what is known as the classical energy equipartition theorem and its counterpart in the phase-space formulation in quantum mechanics based on the Wigner representation. Further, we show that in the high-temperature regime, the classical result is recovered.

Universality and beyond in Optical Microcavity Billiards with Source-Induced Dynamics.

Optical microcavity billiards are a paradigm of a mesoscopic model system for quantum chaos. We demonstrate the action and origin of ray-wave correspondence in real and phase space using far-field emission characteristics and Husimi functions. Whereas universality induced by the invariant-measure dominated far-field emission is known to be a feature shaping the properties of many lasing optical microcavities, the situation changes in the presence of sources that we discuss here. We investigate the source-induced dynamics and the resulting limits of universality while we find ray-picture results to remain a useful tool in order to understand the wave behaviour of optical microcavities with sources. We demonstrate the source-induced dynamics in phase space from the source ignition until a stationary regime is reached comparing results from ray, ray-with-phase, and wave simulations and explore ray-wave correspondence.

Dynamical Analyses Show That Professional Archers Exhibit Tighter, Finer and More Fluid Dynamical Control Than Neophytes.

Quantifying the dynamical features of discrete tasks is essential to understanding athletic performance for many sports that are not repetitive or cyclical. We compared three dynamical features of the (i) bow hand, (ii) drawing hand, and (iii) center of mass during a single bow-draw movement between professional and neophyte archers: dispersion (convex hull volume of their phase portraits), persistence (tendency to continue a trend as per Hurst exponents), and regularity (sample entropy). Although differences in the two groups are expected due to their differences in skill, our results demonstrate we can quantify these differences. The center of mass of professional athletes exhibits tighter movements compared to neophyte archers (6.3 < 11.2 convex hull volume), which are nevertheless less persistent (0.82 < 0.86 Hurst exponent) and less regular (0.035 > 0.025 sample entropy). In particular, the movements of the bow hand and center of mass differed more between groups in Hurst exponent analysis, and the drawing hand and center of mass were more different in sample entropy analysis. This suggests tighter neuromuscular control over the more fluid dynamics of the movement that exhibits more active corrections that are more individualized. Our work, therefore, provides proof of principle of how well-established dynamical analysis techniques can be used to quantify the nature and features of neuromuscular expertise for discrete movements in elite athletes.