Assessment of Driver's Drowsiness Based on Fractal Dimensional Analysis of Sitting and Back Pressure Measurements

The most effective way of preventing motor vehicle accidents caused by drowsy driving is through a better understanding of drowsiness itself. Prior research on the detection of symptoms of drowsy driving has offered insights on providing drivers with advance warning of an elevated risk of crash. The present study measured back and sitting pressures during a simulated driving task under both high and low arousal conditions. Fluctuation of time series of center of pressure (COP) movement of back and sitting pressure was observed to possess a fractal property. The fractal dimensions were calculated to compare the high and low arousal conditions. The results showed that under low arousal (the drowsiness state) the fractal dimension was significantly lower than what was calculated with high arousal. Accumulated drowsiness thus contributed to the loss of self-similarity and unpredictability of time series of back and sitting pressure measurement. Drowsiness further reduces the complexity of the posture control system as viewed from back and sitting pressure. Thus, fractal dimension is a necessary and sufficient condition of a decreased arousal level. It further is a necessary condition for detecting the interval or point in time with high risk of crash.

Exploring comorbid depression and physical health trajectories: A case-based computational modelling approach

While comorbid depression/physical health is a major clinical concern, the conventional methods of medicine make it difficult to model the complexities of this relationship. Such challenges include cataloguing multiple trends, developing multiple complex aetiological explanations, and modelling the collective large-scale dynamics of these trends. Using a case-based complexity approach, this study engaged in a richly described case study to demonstrate the utility of computational modelling for primary care research. N = 259 people were subsampled from the Diamond database, one of the largest primary care depression cohort studies worldwide. A global measure of depressive symptoms (PHQ-9) and physical health (PCS-12) were assessed at 3, 6, 9, and 12 months and then annually for a total of 7 years. Eleven trajectories and 2 large-scale collective dynamics were identified, revealing that while depression is comorbid with poor physical health, chronic illness is often low dynamic and not always linked to depression. Also, some of the cases in the unhealthy and oscillator trends remain ill without much chance of improvement. Finally, childhood abuse, partner violence, and negative life events are greater amongst unhealthy trends. Computational modelling offers a major advance for health researchers to account for the diversity of primary care patients and for developing better prognostic models for team-based interdisciplinary care.

Lower limb joint angle variability and dimensionality are different in stairmill climbing and treadmill walking

The present study tested if the quadratic relationship which exists between stepping frequency and gait dynamics in walking can be generalized to stairmill climbing. To accomplish this, we investigated the joint angle dynamics and variability during continuous stairmill climbing at stepping frequencies both above and below the preferred stepping frequency (PSF). Nine subjects performed stairmill climbing at 80, 90, 100, 110 and 120% PSF and treadmill walking at preferred walking speed during which sagittal hip, knee and ankle angles were extracted. Joint angle dynamics were quantified by the largest Lyapunov exponent (LyE) and correlation dimension (CoD). Joint angle variability was estimated by the mean ensemble standard deviation (meanSD). MeanSD and CoD for all joints were significantly higher during stairmill climbing but there were no task differences in LyE. Changes in stepping frequency had only limited effect on joint angle variability and did not affect joint angle dynamics. Thus, we concluded that the quadratic relationship between stepping frequency and gait dynamics observed in walking is not present in stairmill climbing based on the investigated parameters.

Nano-electromechanical Drumhead Resonators from Two-Dimensional Material Bimorphs

Atomic membranes of monolayer 2D materials represent the ultimate limit in the size of nano-electromechanical systems. However, new properties and new functionalities emerge by looking at the interface between layers in heterostructures of 2D materials. Here, we demonstrate the integration of 2D heterostructures as tunable nano-electromechanical systems, exploring the competition between the mechanics of the ultrathin membrane and the incommensurate van der Waals interface. We fabricate electrically contacted 5 or 6 μm circular drumheads of suspended heterostructure membranes of monolayer graphene on monolayer molybdenum disulfide (MoS₂), which we call a 2D bimorph. We characterize the mechanical resonance through electrostatic actuation and laser interferometry detection. The 2D bimorphs have resonance frequencies of 5-20 MHz and quality factors of 50-700, comparable to resonators from monolayer or few-layer 2D materials. The frequencies and eigenmode shapes of the higher harmonics display split degenerate modes, showing that the 2D bimorphs behave as membranes with asymmetric tension. The devices display dynamic ranges of 44 dB, with an additional nonlinearity in the dissipation at small drive. Under electrostatic frequency tuning, devices display a small tuning of ∼20% compared with graphene resonators, which have >100%. In addition, the tuning shows a kink that deviates from the tensioned membrane model for atomic membranes and corresponds with a changing in stress of 14 mN/m. A model that accounts for this tuning behavior is the onset of interlayer slip in the heterostructure, allowing the tension in the membrane to relax. Using density functional theory simulations, we find that the change in stress at the kink is much larger than the predicted energy barrier for interlayer slip of 0.102 mN/m in an incommensurate 2D heterostructure but smaller than the energy barrier for an aligned graphene bilayer of 35 mN/m, suggesting a local pinning effect at ripples or folds in the heterostructure. Finally, we observe an asymmetry in tuning of the full width at half-maximum that does not exist in monolayer resonators. These findings demonstrate a new class of nano-electromechanical systems from 2D heterostructures and unravel the complex interaction of membrane morphology versus interlayer adhesion and slip on the mechanics of incommensurate van der Waals interfaces.

Investigations of the Effects of Geometric Imperfections on the Nonlinear Static and Dynamic Behavior of Capacitive Micomachined Ultrasonic Transducers

In order to investigate the effects of geometric imperfections on the static and dynamic behavior of capacitive micomachined ultrasonic transducers (CMUTs), the governing equations of motion of a circular microplate with initial defection have been derived using the von Kármán plate theory while taking into account the mechanical and electrostatic nonlinearities. The partial differential equations are discretized using the differential quadrature method (DQM) and the resulting coupled nonlinear ordinary differential equations (ODEs) are solved using the harmonic balance method (HBM) coupled with the asymptotic numerical method (ANM). It is shown that the initial deflection has an impact on the static behavior of the CMUT by increasing its pull-in voltage up to 45%. Moreover, the dynamic behavior is affected by the initial deflection, enabling an increase in the resonance frequencies and the bistability domain and leading to a change of the frequency response from softening to hardening. This model allows MEMS designers to predict the nonlinear behavior of imperfect CMUT and tune its bifurcation topology in order to enhance its performances in terms of bandwidth and generated acoustic power while driving the microplate up to 80% beyond its critical amplitude.

Sparse identification of nonlinear dynamics for model predictive control in the low-data limit

Data-driven discovery of dynamics via machine learning is pushing the frontiers of modelling and control efforts, providing a tremendous opportunity to extend the reach of model predictive control (MPC). However, many leading methods in machine learning, such as neural networks (NN), require large volumes of training data, may not be interpretable, do not easily include known constraints and symmetries, and may not generalize beyond the attractor where models are trained. These factors limit their use for the online identification of a model in the low-data limit, for example following an abrupt change to the system dynamics. In this work, we extend the recent sparse identification of nonlinear dynamics (SINDY) modelling procedure to include the effects of actuation and demonstrate the ability of these models to enhance the performance of MPC, based on limited, noisy data. SINDY models are parsimonious, identifying the fewest terms in the model needed to explain the data, making them interpretable and generalizable. We show that the resulting SINDY-MPC framework has higher performance, requires significantly less data, and is more computationally efficient and robust to noise than NN models, making it viable for online training and execution in response to rapid system changes. SINDY-MPC also shows improved performance over linear data-driven models, although linear models may provide a stopgap until enough data is available for SINDY. SINDY-MPC is demonstrated on a variety of dynamical systems with different challenges, including the chaotic Lorenz system, a simple model for flight control of an F8 aircraft, and an HIV model incorporating drug treatment.

Randomly distributed embedding making short-term high-dimensional data predictable

Future state prediction for nonlinear dynamical systems is a challenging task, particularly when only a few time series samples for high-dimensional variables are available from real-world systems. In this work, we propose a model-free framework, named randomly distributed embedding (RDE), to achieve accurate future state prediction based on short-term high-dimensional data. Specifically, from the observed data of high-dimensional variables, the RDE framework randomly generates a sufficient number of low-dimensional "nondelay embeddings" and maps each of them to a "delay embedding," which is constructed from the data of a to be predicted target variable. Any of these mappings can perform as a low-dimensional weak predictor for future state prediction, and all of such mappings generate a distribution of predicted future states. This distribution actually patches all pieces of association information from various embeddings unbiasedly or biasedly into the whole dynamics of the target variable, which after operated by appropriate estimation strategies, creates a stronger predictor for achieving prediction in a more reliable and robust form. Through applying the RDE framework to data from both representative models and real-world systems, we reveal that a high-dimension feature is no longer an obstacle but a source of information crucial to accurate prediction for short-term data, even under noise deterioration.

Parameters of Surface Electromyogram Suggest That Dry Immersion Relieves Motor Symptoms in Patients With Parkinsonism

Dry immersion (DI) is acknowledged as a reliable space flight analog condition. At DI, subject is immersed in water being wrapped in a waterproof film to imitate microgravity (μG). Microgravity is known to decrease muscle tone due to deprivation of the sensory stimuli that activate the reflexes that keep up the muscle tone. In contrary, parkinsonian patients are characterized by elevated muscle tone, or rigidity, along with rest tremor and akinesia. We hypothesized that DI can diminish the elevated muscle tone and/or the tremor in parkinsonian patients. Fourteen patients with Parkinson's disease (PD, 10 males, 4 females, 47-73 years) and 5 patients with vascular parkinsonism (VP, 1 male, 4 females, 65-72 years) participated in the study. To evaluate the effect of DI on muscles' functioning, we compared parameters of surface electromyogram (sEMG) measured before and after a single 45-min long immersion session. The sEMG recordings were made from the biceps brachii muscle, bilaterally. Each recording was repeated with the following loading conditions: with arms hanging freely down, and with 0, 1, and 2 kg loading on each hand with elbows flexed to 90°. The sEMG parameters comprised of amplitude, median frequency, time of decay of mutual information, sample entropy, correlation dimension, recurrence rate, and determinism of sEMG. These parameters have earlier been proved to be sensitive to PD severity. We used the Wilcoxon test to decide which parameters were statistically significantly different before and after the dry immersion. Accepting the p < 0.05 significance level, amplitude, time of decay of mutual information, recurrence rate, and determinism tended to decrease, while median frequency and sample entropy of sEMG tended to increase after the DI. The most statistically significant change was for the determinism of sEMG from the left biceps with 1 kg loading, which decreased for 84% of the patients. The results suggest that DI can promptly relieve motor symptoms of parkinsonism. We conclude that DI has strong potential as a rehabilitation method for parkinsonian patients.

Nonlinear effects induced in the normalized ion density in a linear trap system for a large ion cloud

In this work, we design, by means of a non-neutral plasma method, a linear trapping model for large ion clouds, which will become the core of an atomic clock. We first obtain the geometry and electromagnetic characteristics of the ion trap. We then perform a systematic analysis describing the main parameters of the ion cloud such as size, secular frequency, and ion number per unit length of temperature. The most appropriate operation point of the ion trap in a set of these specific parameters is evaluated, and a thorough discussion is performed about how minor perturbations introduced in these parameters affect, in a nonlinear response, the performance of the trapping system in sensibility, heating, and radiofrequency potential.

Do Complexity Measures of Frontal EEG Distinguish Loss of Consciousness in Geriatric Patients Under Anesthesia?

While geriatric patients have a high likelihood of requiring anesthesia, they carry an increased risk for adverse cognitive outcomes from its use. Previous work suggests this could be mitigated by better intraoperative monitoring using indexes defined by several processed electroencephalogram (EEG) measures. Unfortunately, inconsistencies between patients and anesthetic agents in current analysis techniques have limited the adoption of EEG as standard of care. In attempts to identify new analyses that discriminate clinically-relevant anesthesia timepoints, we tested 1/f frequency scaling as well as measures of complexity from nonlinear dynamics. Specifically, we tested whether analyses that characterize time-delayed embeddings, correlation dimension (CD), phase-space geometric analysis, and multiscale entropy (MSE) capture loss-of-consciousness changes in EEG activity. We performed these analyses on EEG activity collected from a traditionally hard-to-monitor patient population: geriatric patients on beta-adrenergic blockade who were anesthetized using a combination of fentanyl and propofol. We compared these analyses to traditional frequency-derived measures to test how well they discriminated EEG states before and after loss of response to verbal stimuli. We found spectral changes similar to those reported previously during loss of response. We also found significant changes in 1/f frequency scaling. Additionally, we found that our phase-space geometric characterization of time-delayed embeddings showed significant differences before and after loss of response, as did measures of MSE. Our results suggest that our new spectral and complexity measures are capable of capturing subtle differences in EEG activity with anesthesia administration-differences which future work may reveal to improve geriatric patient monitoring.

On the geometrically exact low-order modelling of a flexible beam: formulation and numerical tests

This paper proposes a low-order geometrically exact flexible beam formulation based on the utilization of generic beam shape functions to approximate distributed kinematic properties of the deformed structure. The proposed nonlinear beam shapes approach is in contrast to the majority of geometrically nonlinear treatments in the literature in which element-based—and hence high-order—discretizations are adopted. The kinematic quantities approximated specifically pertain to shear and extensional gradients as well as local orientation parameters based on an arbitrary set of globally referenced attitude parameters. In developing the dynamic equations of motion, an Euler angle parametrization is selected as it is found to yield fast computational performance. The resulting dynamic formulation is closed using an example shape function set satisfying the single generic kinematic constraint. The formulation is demonstrated via its application to the modelling of a series of static and dynamic test cases of both simple and non-prismatic structures; the simulated results are verified using MSC Nastran and an element-based intrinsic beam formulation. Through these examples, it is shown that the nonlinear beam shapes approach is able to accurately capture the beam behaviour with a very minimal number of system states.

Introduction to a topical issue 'nonlinear energy transfer in dynamical and acoustical Systems'

This topical issue is devoted to recent developments in the broader field of energy transfer across scales in nonlinear dynamical and acoustical systems. Nonlinear energy transfers are common in Nature, with perhaps the most famous example being energy cascading from large to small length scales in turbulent flows. Yet nonlinearity has been traditionally perceived either as an unavoidable nuisance or as an unwelcome design restriction in engineering systems. Nowadays, however, this trend is reversing, with nonlinear phenomena being intensely studied in diverse disciplines. Furthermore, strong nonlinearity is now intentionally used and explored in a variety of mechanical and physical settings, such as granular media, acoustic metamaterials, nonlinear energy sinks, essentially nonlinear and nonlocal lattices, vibro-impact oscillators, vibration and shock isolation systems, nanotechnology, biomimetic systems, microelectronics, energy harvesters and in other applications. This topical issue is an attempt to document in a single volume some of these recent research developments, in order to establish a common basis and provide motivation and incentive for further development. The aim is to discuss and compare theoretical and experimental approaches pursued by research groups in different areas, and describe the state of the art of nonlinear energy transfer phenomena in an as broad as possible range of applications of current interest.This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.

Tunable, synchronized frequency down-conversion in magnetic lattices with defects

We study frequency conversion in nonlinear mechanical lattices, focusing on a chain of magnets as a model system. We show that, by inserting mass defects at suitable locations, we can introduce localized vibrational modes that nonlinearly couple to extended lattice modes. The nonlinear interaction introduces an energy transfer from the high-frequency localized modes to a low-frequency extended mode. This system is capable of autonomously converting energy between highly tunable input and output frequencies, which need not be related by integer harmonic or subharmonic ratios. It is also capable of obtaining energy from multiple sources at different frequencies with a tunable output phase, due to the defect synchronization provided by the extended mode. Our lattice is a purely mechanical analogue of an opto-mechanical system, where the localized modes play the role of the electromagnetic field and the extended mode plays the role of the mechanical degree of freedom.This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.

The Maximum Lyapunov Exponent During Walking and Running: Reliability Assessment of Different Marker-Sets

The maximum Lyapunov exponent (MLE) has often been suggested as the prominent measure for evaluation of dynamic stability of locomotion in pathological and healthy population. Although the popularity of the MLE has increased in the last years, there is scarce information on the reliability of the method, especially during running. The purpose of the current study was, thus, to examine the reliability of the MLE during both walking and running. Sixteen participants walked and ran on a treadmill completing two measurement blocks (i.e., two trials per day for three consecutive days per block) separated by 2 months on average. Six different marker-sets on the trunk were analyzed. Intraday, interday and between blocks reliability was assessed using the intraclass correlation coefficient (ICC) and the root mean square difference (RMSD). The MLE was on average significantly higher (p < 0.001) in running (1.836 ± 0.080) compared to walking (1.386 ± 0.207). All marker-sets showed excellent ICCs (>0.90) during walking and mostly good ICCs (>0.75) during running. The RMSD ranged from 0.023 to 0.047 for walking and from 0.018 to 0.050 for running. The reliability was better when comparing MLE values between blocks (ICCs: 0.965–0.991 and 0.768–0.961; RMSD: 0.023–0.034 and 0.018–0.027 for walking and running respectively), and worse when considering trials of the same day (ICCs: 0.946–0.980 and 0.739–0.844; RMSD: 0.042–0.047 and 0.045–0.050 for walking and running respectively). Further, different marker-sets affect the reliability of the MLE in both walking and running. Our findings provide evidence that the assessment of dynamic stability using the MLE is reliable in both walking and running. More trials spread over more than 1 day should be considered in study designs with increased demands of accuracy independent of the locomotion condition.

Reducing nonlinear dynamical systems to canonical forms

A global framework for treating nonlinear differential dynamical systems is presented. It rests on the fact that most systems can be transformed into the quasi-polynomial format. Any system in this format belongs to an infinite equivalence class characterized by two canonical forms, the Lotka-Volterra (LV) and the monomial systems. Both forms allow for finding total or partial integrability conditions, invariants and dimension reductions of the original systems. The LV form also provides Lyapunov functions and systematic tools for stability analysis. An abstract Lie algebra is shown to underlie the whole formalism. This abstract algebra can be expressed in several realizations among which are the bosonic creation-destruction operators. One of these representations allows one to obtain the analytic form of the general coefficient of the Taylor series representing the solution of the original system. This generates a new class of special functions that are solutions of these nonlinear dynamical systems. From the monomial canonical form, one can prove an equivalence relationship between urn processes and dynamical systems. This establishes a new link between nonlinear dynamics and stochastic processes.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

A Pilot Study Investigating a Novel Non-Linear Measure of Eyes Open versus Eyes Closed EEG Synchronization in People with Alzheimer’s Disease and Healthy Controls

Background: The incidence of Alzheimer disease (AD) is increasing with the ageing population. The development of low cost non-invasive diagnostic aids for AD is a research priority. This pilot study investigated whether an approach based on a novel dynamic quantitative parametric EEG method could detect abnormalities in people with AD. Methods: 20 patients with probable AD, 20 matched healthy controls (HC) and 4 patients with probable fronto temporal dementia (FTD) were included. All had detailed neuropsychology along with structural, resting state fMRI and EEG. EEG data were analyzed using the Error Reduction Ratio-causality (ERR-causality) test that can capture both linear and nonlinear interactions between different EEG recording areas. The 95% confidence intervals of EEG levels of bi-centroparietal synchronization were estimated for eyes open (EO) and eyes closed (EC) states. Results: In the EC state, AD patients and HC had very similar levels of bi-centro parietal synchronization; but in the EO resting state, patients with AD had significantly higher levels of synchronization (AD = 0.44; interquartile range (IQR) 0.41 vs. HC = 0.15; IQR 0.17, p < 0.0001). The EO/EC synchronization ratio, a measure of the dynamic changes between the two states, also showed significant differences between these two groups (AD ratio 0.78 versus HC ratio 0.37 p < 0.0001). EO synchronization was also significantly different between AD and FTD (FTD = 0.075; IQR 0.03, p < 0.0001). However, the EO/EC ratio was not informative in the FTD group due to very low levels of synchronization in both states (EO and EC). Conclusion: In this pilot work, resting state quantitative EEG shows significant differences between healthy controls and patients with AD. This approach has the potential to develop into a useful non-invasive and economical diagnostic aid in AD.

Gait Dynamics in Parkinson's Disease: Short Gait Trials "Stitched" Together Provide Different Fractal Fluctuations Compared to Longer Trials

The fractal analysis of stride-to-stride fluctuations in walking has become an integral part of human gait research. Fractal analysis of stride time intervals can provide insights into locomotor function and dysfunction, but its application requires a large number of strides, which can be difficult to collect from people with movement disorders such as Parkinson's disease. It has recently been suggested that "stitching" together short gait trials to create a longer time series could be a solution. The objective of this study was to determine if scaling exponents from "stitched" stride time series were similar to those from continuous, longer stride time series. Fifteen young adults, fourteen older adults, and thirteen people with Parkinson's disease walked around an indoor track in three blocks: one time 15 min, five times 3 min, and thirty times 30 s. Stride time intervals were determined from gait events recorded with instrumented insoles, and the detrended fluctuation analysis was applied to each stride time series of 512 strides. There was no statistically significant difference between scaling exponents in the three blocks, but intra-class correlation revealed very low between-blocks reliability of scaling exponents. This result challenges the premise that the stitching procedure could provide reliable information about gait dynamics, as it suggests that fractal analysis of stitched time series does not capture the same dynamics as gait recorded continuously. The stitching procedure cannot be considered as a valid alternative to the collection of continuous, long trials. Further studies are recommended to determine if the application of fractal analysis is limited by its own methodological considerations (i.e., long time series), or if other solutions exists to obtain reliable scaling exponents in populations with movement disorders.

Application of cmOCT and continuous wavelet transform analysis to the assessment of skin microcirculation dynamics

Correlation mapping optical coherence tomography (cmOCT) is a powerful technique for the imaging of skin microvessels structure, based on the discrimination of the static and dynamic regions of the tissue. Although the suitability of cmOCT to visualize the microcirculation has been proved in humans and animal models, less evidence has been provided about its application to examine functional dynamics. Therefore, the goal of this research was validating the cmOCT method for the investigation into microvascular function and vasomotion. A spectral domain optical coherence tomography (SD-OCT) device was employed to image 90 sequential three-dimensional (3-D) OCT volumes from the forearm of 12 volunteers during a 25-min postocclusive reactive hyperemia (PORH) test. The volumes were processed using cmOCT to generate blood flow maps at selected cutaneous depths. The maps clearly trace flow variations during the PORH response for both capillaries and arterioles/venules microvascular layers. Continuous blood flow signals were reconstructed from cmOCT maps to study vasomotion by applying wavelet transform spectral analysis, which revealed fluctuations of flow during PORH, reflecting the regulation of microvascular tone mediated by endothelial cells and sympathetic nerves. The results clearly demonstrate that cmOCT allows the generation of functional information that may be used for diagnostic applications.

Force appropriation of nonlinear structures

Nonlinear normal modes (NNMs) are widely used as a tool for developing mathematical models of nonlinear structures and understanding their dynamics. NNMs can be identified experimentally through a phase quadrature condition between the system response and the applied excitation. This paper demonstrates that this commonly used quadrature condition can give results that are significantly different from the true NNM, in particular, when the excitation applied to the system is limited to one input force, as is frequently used in practice. The system studied is a clamped-clamped cross-beam with two closely spaced modes. This paper shows that the regions where the quadrature condition is (in)accurate can be qualitatively captured by analysing transfer of energy between the modes of the system, leading to a discussion of the appropriate number of input forces and their locations across the structure.

Bio-Signal Complexity Analysis in Epileptic Seizure Monitoring: A Topic Review

Complexity science has provided new perspectives and opportunities for understanding a variety of complex natural or social phenomena, including brain dysfunctions like epilepsy. By delving into the complexity in electrophysiological signals and neuroimaging, new insights have emerged. These discoveries have revealed that complexity is a fundamental aspect of physiological processes. The inherent nonlinearity and non-stationarity of physiological processes limits the methods based on simpler underlying assumptions to point out the pathway to a more comprehensive understanding of their behavior and relation with certain diseases. The perspective of complexity may benefit both the research and clinical practice through providing novel data analytics tools devoted for the understanding of and the intervention about epilepsies. This review aims to provide a sketchy overview of the methods derived from different disciplines lucubrating to the complexity of bio-signals in the field of epilepsy monitoring. Although the complexity of bio-signals is still not fully understood, bundles of new insights have been already obtained. Despite the promising results about epileptic seizure detection and prediction through offline analysis, we are still lacking robust, tried-and-true real-time applications. Multidisciplinary collaborations and more high-quality data accessible to the whole community are needed for reproducible research and the development of such applications.

Prediction of human gait trajectories during the SSP using a neuromusculoskeletal modeling: A challenge for parametric optimization

The parametric optimization techniques have been widely employed to predict human gait trajectories; however, their applications to reveal the other aspects of gait are questionable. The aim of this study is to investigate whether or not the gait prediction model is able to justify the movement trajectories for the higher average velocities. A planar, seven-segment model with sixteen muscle groups was used to represent human neuro-musculoskeletal dynamics. At first, the joint angles, ground reaction forces (GRFs) and muscle activations were predicted and validated for normal average velocity (1.55 m/s) in the single support phase (SSP) by minimizing energy expenditure, which is subject to the non-linear constraints of the gait. The unconstrained system dynamics of extended inverse dynamics (USDEID) approach was used to estimate muscle activations. Then by scaling time and applying the same procedure, the movement trajectories were predicted for higher average velocities (from 2.07 m/s to 4.07 m/s) and compared to the pattern of movement with fast walking speed. The comparison indicated a high level of compatibility between the experimental and predicted results, except for the vertical position of the center of gravity (COG). It was concluded that the gait prediction model can be effectively used to predict gait trajectories for higher average velocities.

A Novel Nonlinear Piezoelectric Energy Harvesting System Based on Linear-Element Coupling: Design, Modeling and Dynamic Analysis

This paper presents a novel nonlinear piezoelectric energy harvesting system which consists of linear piezoelectric energy harvesters connected by linear springs. In principle, the presented nonlinear system can improve broadband energy harvesting efficiency where magnets are forbidden. The linear spring inevitably produces the nonlinear spring force on the connected harvesters, because of the geometrical relationship and the time-varying relative displacement between two adjacent harvesters. Therefore, the presented nonlinear system has strong nonlinear characteristics. A theoretical model of the presented nonlinear system is deduced, based on Euler-Bernoulli beam theory, Kirchhoff’s law, piezoelectric theory and the relevant geometrical relationship. The energy harvesting enhancement of the presented nonlinear system (when n = 2, 3) is numerically verified by comparing with its linear counterparts. In the case study, the output power area of the presented nonlinear system with two and three energy harvesters is 268.8% and 339.8% of their linear counterparts, respectively. In addition, the nonlinear dynamic response characteristics are analyzed via bifurcation diagrams, Poincare maps of the phase trajectory, and the spectrum of the output voltage.

Cryptographic hashing using chaotic hydrodynamics

Fluids may store and manipulate information, enabling complex applications ranging from digital logic gates to algorithmic self-assembly. While controllable hydrodynamic chaos has previously been observed in viscous fluids and harnessed for efficient mixing, its application to the manipulation of digital information has been sparsely investigated. We show that chaotic stirring of a viscous fluid naturally produces a characteristic signature of the stirring process in the arrangement of particles in the fluid, and that this signature directly satisfies the requirements for a cryptographic hash function. This includes strong divergence between similar stirring protocols' hashes and avoidance of collisions (identical hashes from distinct stirs), which are facilitated by noninvertibility and a broad chaotic attractor that samples many points in the fluid domain. The hashing ability of the chaotic fluidic map implicates several unexpected mechanisms, including incomplete mixing at short time scales that produces a hyperuniform hash distribution. We investigate the dynamics of hashing using interparticle winding statistics, and find that hashing starts with large-scale winding of kinetically disjoint regions of the chaotic attractor, which gradually gives way to smaller scale braiding of single-particle trajectories. In addition to providing a physically motivated approach to implementing and analyzing deterministic chaotic maps for cryptographic applications, we anticipate that our approach has applications in microfluidic proof-of-work systems and characterizing large-scale turbulent flows from sparse tracer data.

Noise-induced transitions and shifts in a climate-vegetation feedback model

Motivated by the extremely important role of the Earth's vegetation dynamics in climate changes, we study the stochastic variability of a simple climate-vegetation system. In the case of deterministic dynamics, the system has one stable equilibrium and limit cycle or two stable equilibria corresponding to two opposite (cold and warm) climate-vegetation states. These states are divided by a separatrix going across a point of unstable equilibrium. Some possible stochastic scenarios caused by different externally induced natural and anthropogenic processes inherit properties of deterministic behaviour and drastically change the system dynamics. We demonstrate that the system transitions across its separatrix occur with increasing noise intensity. The climate-vegetation system therewith fluctuates, transits and localizes in the vicinity of its attractor. We show that this phenomenon occurs within some critical range of noise intensities. A noise-induced shift into the range of smaller global average temperatures corresponding to substantial oscillations of the Earth's vegetation cover is revealed. Our analysis demonstrates that the climate-vegetation interactions essentially contribute to climate dynamics and should be taken into account in more precise and complex models of climate variability.