A Riemannian Geometry Theory of Synergy Selection for Visually-Guided Movement

Bringing together a Riemannian geometry account of visual space with a complementary account of human movement synergies we present a neurally-feasible computational formulation of visuomotor task performance. This cohesive geometric theory addresses inherent nonlinear complications underlying the match between a visual goal and an optimal action to achieve that goal: (i) the warped geometry of visual space causes the position, size, outline, curvature, velocity and acceleration of images to change with changes in the place and orientation of the head, (ii) the relationship between head place and body posture is ill-defined, and (iii) mass-inertia loads on muscles vary with body configuration and affect the planning of minimum-effort movement. We describe a partitioned visuospatial memory consisting of the warped posture-and-place-encoded images of the environment, including images of visible body parts. We depict synergies as low-dimensional submanifolds embedded in the warped posture-and-place manifold of the body. A task-appropriate synergy corresponds to a submanifold containing those postures and places that match the posture-and-place-encoded visual images that encompass the required visual goal. We set out a reinforcement learning process that tunes an error-reducing association memory network to minimize any mismatch, thereby coupling visual goals with compatible movement synergies. A simulation of a two-degrees-of-freedom arm illustrates that, despite warping of both visual space and posture space, there exists a smooth one-to-one and onto invertible mapping between vision and proprioception.

Appearance of a Solitary Wave Particle Concentration in Nanofluids under a Light Field

In this study, the nonlinear dynamics of nanoparticle concentration in a colloidal suspension (nanofluid) were theoretically studied under the action of a light field with constant intensity by considering concentration convection. The heat and nanoparticle transfer processes that occur in this case are associated with the phenomenon of thermal diffusion, which is considered to be positive in our work. Two exact analytical solutions of a nonlinear Burgers-Huxley-type equation were derived and investigated, one of which was presented in the form of a solitary concentration wave. These solutions were derived considering the dependence of the coefficients of thermal conductivity, viscosity, and absorption of radiation on the nanoparticle concentration in the nanofluid. Furthermore, an expression was obtained for the solitary wave velocity, which depends on the absorption coefficient and intensity of the light wave. Numerical estimates of the concentration wave velocity for a specific nanofluid—water/silver—are given. The results of this study can be useful in the creation of next-generation solar collectors.

Nonlinear analysis of scalp EEGs from normal and brain tumour subjects

Measurement of features from the chaos theory or as popularly known, the concept of nonlinear dynamics, as indicatives of several pathological conditions and cognition states using the electroencephalography (EEG) signal is very popular. In this paper, the analysis of scalp EEG signals of normal subjects and brain tumour patients using the nonlinear dynamic features has been presented. The nonlinear dynamic features that represent the dimensional and waveform complexities of the signal being analyzed have been considered. The statistical analysis of the selected nonlinear dynamic features has been presented. The results show that the nonlinear dynamic features significantly discriminate the brain tumour group from the normal group.

Large amplitude spin-Hall oscillations due to field-like torque

Large amplitude spin-Hall oscillations are identified in a ferromagnetic layer with two perpendicular in-plane easy axis in the presence of field-like torque without any polarizer and external field. The analytical study confirms the possibility of oscillations in the presence of field-like torque. The investigation shows that the oscillation frequency can be tuned from ∼2 GHz to ∼80 GHz by current and enhanced by field-like torque. Further, the enhancement of frequency along with theQ-factor by current and field-like torque is also observed.

A review of dynamical systems approaches for the detection of chaotic attractors in cancer networks

Cancers are complex dynamical systems. They remain the leading cause of disease-related pediatric mortality in North America. To overcome this burden, we must decipher the state-space attractor dynamics of gene expression patterns and protein oscillations orchestrated by cancer stemness networks. The review provides an overview of dynamical systems theory to steer cancer research in pattern science. While most of our current tools in network medicine rely on statistical correlation methods, causality inference remains primitively developed. As such, a survey of attractor reconstruction methods and machine algorithms for the detection of causal structures applicable in experimentally derived time series cancer datasets is presented. A toolbox of complex systems approaches are discussed for reconstructing the signaling state space of cancer networks, interpreting causal relationships in their time series gene expression patterns, and assisting clinical decision making in computational oncology. As a proof of concept, the applicability of some algorithms are demonstrated on pediatric brain cancer datasets and the requirement of their time series analysis is highlighted.

Farey Trees Explain Sequential Effects in Choice Response Time

The latencies of successive two-alternative, forced-choice response times display intricately patterned sequential effects, or dependencies. They vary as a function of particular trial-histories, and in terms of the order and identity of previously presented stimuli and registered responses. This article tests a novel hypothesis that sequential effects are governed by dynamic principles, such as those entailed by a discrete sine-circle map adaptation of the Haken Kelso Bunz (HKB) bimanual coordination model. The model explained the sequential effects expressed in two classic sequential dependency data sets. It explained the rise of a repetition advantage, the acceleration of repeated affirmative responses, in tasks with faster paces. Likewise, the model successfully predicted an alternation advantage, the acceleration of interleaved affirmative and negative responses, when a task’s pace slows and becomes more variable. Detailed analyses of five studies established oscillatory influences on sequential effects in the context of balanced and biased trial presentation rates, variable pacing, progressive and differential cognitive loads, and dyadic performance. Overall, the empirical patterns revealed lawful oscillatory constraints governing sequential effects in the time-course and accuracy of performance across a broad continuum of recognition and decision activities.

The Applicability of the Poincaré Plot in the Analysis of Variability of Reaction Time during Serial Testing

(1) Background: This study aims to put into evince the relationship between the variability of the reaction time (RT) during repeated testing, expressed through indicators extracted by the Poincaré plot method, and the age of the participants, their self-reported health (SRH), and level of perceived anxiety. (2) Methods: The study was performed using computerized RT testing software. An observational cross-sectional study was performed on a group of 120 subjects (mean age 42.33 ± 21.12 years), sex ratio men to women 1.14:1. Data were processed through descriptive and inferential statistics. The Poincaré plot method was applied in the analysis of the RT series of data, by calculating the indicators SD₁, SD₂, SD₁/SD₂, and area of the fitting ellipse (AFE) (3) Results: We provided evidence of the excellent reliability of the web-based RT serial testing (Cronbach’s Alpha 0.991) with this sample group. Our results showed that age is an important predictor for mean values of RT, while SD₁, SD₂, and AFE indicators are for SRH (p < 0.01). (4) Conclusions: the variability of RT, expressed by the Poincaré plot indicators, reflects the health status rather than the aging of the subjects and is barely influenced by their level of anxiety.

Coupled oscillators coordinate collective germline growth

Developing oocytes need large supplies of macromolecules and organelles. A conserved strategy for accumulating these products is to pool resources of oocyte-associated germline nurse cells. In Drosophila, these cells grow more than 100-fold to boost their biosynthetic capacity. No previously known mechanism explains how nurse cells coordinate growth collectively. Here, we report a cell cycle-regulating mechanism that depends on bidirectional communication between the oocyte and nurse cells, revealing the oocyte as a critical regulator of germline cyst growth. Transcripts encoding the cyclin-dependent kinase inhibitor, Dacapo, are synthesized by the nurse cells and actively localized to the oocyte. Retrograde movement of the oocyte-synthesized Dacapo protein to the nurse cells generates a network of coupled oscillators that controls the cell cycle of the nurse cells to regulate cyst growth. We propose that bidirectional nurse cell-oocyte communication establishes a growth-sensing feedback mechanism that regulates the quantity of maternal resources loaded into the oocyte.

A Novel Frequency Stabilization Approach for Mass Detection in Nonlinear Mechanically Coupled Resonant Sensors

Frequency stabilization can overcome the dependence of resonance frequency on amplitude in nonlinear microelectromechanical systems, which is potentially useful in nonlinear mass sensor. In this paper, the physical conditions for frequency stabilization are presented theoretically, and the influence of system parameters on frequency stabilization is analyzed. Firstly, a nonlinear mechanically coupled resonant structure is designed with a nonlinear force composed of a pair of bias voltages and an alternating current (AC) harmonic load. We study coupled-mode vibration and derive the expression of resonance frequency in the nonlinear regime by utilizing perturbation and bifurcation analysis. It is found that improving the quality factor of the system is crucial to realize the frequency stabilization. Typically, stochastic dynamic equation is introduced to prove that the coupled resonant structure can overcome the influence of voltage fluctuation on resonance frequency and improve the robustness of the sensor. In addition, a novel parameter identification method is proposed by using frequency stabilization and bifurcation jumping, which effectively avoids resonance frequency shifts caused by driving voltage. Finally, numerical studies are introduced to verify the mass detection method. The results in this paper can be used to guide the design of a nonlinear sensor.

Ischemic Preconditioning Blunts Loss of Knee Extensor Torque Complexity with Fatigue

INTRODUCTION

Neuromuscular fatigue reduces the temporal structure, or complexity, of muscle torque output, purportedly through an effect on motor unit behavior. Ischemic preconditioning (IPC), an emerging ergogenic aid, has been demonstrated to have a potent effect on muscular output and endurance. We therefore tested the hypothesis that IPC would attenuate the fatigue-induced loss of muscle torque complexity.

METHODS

Ten healthy participants (6 males/4 females) performed intermittent isometric knee extension contractions (6 s contraction, 4 s rest) to task failure at 40% maximal voluntary contraction. Contractions were preceded by either IPC (three bouts of 5 min proximal thigh occlusion at 225 mm Hg, interspersed with 5 min rest) or SHAM (as IPC, but occlusion at only 20 mm Hg) treatments. Torque and EMG signals were sampled continuously. Complexity and fractal scaling were quantified using approximate entropy (ApEn) and the detrended fluctuation analysis (DFA) α scaling exponent. Muscle oxygen consumption (mV˙O2) was determined using near-infrared spectroscopy.

RESULTS

IPC increased time to task failure by 43% ± 13% (mean ± SEM, P = 0.047). Complexity decreased in both trials (decreased ApEn, increased DFA α; both P < 0.001), although the rate of decrease was significantly lower after IPC (ApEn, -0.2 ± 0.1 vs -0.4 ± 0.1, P = 0.013; DFA α, 0.2 ± 0.1 vs 0.3 ± 0.1, P = 0.037). Similarly, the rates of increase in EMG amplitude (P = 0.022) and mV˙O2 (P = 0.043) were significantly slower after IPC.

CONCLUSION

These results suggest that the ergogenic effect of IPC observed here is of neural origin and accounts for the slowing of the rates of change in torque complexity, EMG amplitude, and mV˙O2 as fatigue develops.

Benchmarking of numerical integration methods for ODE models of biological systems

Ordinary differential equation (ODE) models are a key tool to understand complex mechanisms in systems biology. These models are studied using various approaches, including stability and bifurcation analysis, but most frequently by numerical simulations. The number of required simulations is often large, e.g., when unknown parameters need to be inferred. This renders efficient and reliable numerical integration methods essential. However, these methods depend on various hyperparameters, which strongly impact the ODE solution. Despite this, and although hundreds of published ODE models are freely available in public databases, a thorough study that quantifies the impact of hyperparameters on the ODE solver in terms of accuracy and computation time is still missing. In this manuscript, we investigate which choices of algorithms and hyperparameters are generally favorable when dealing with ODE models arising from biological processes. To ensure a representative evaluation, we considered 142 published models. Our study provides evidence that most ODEs in computational biology are stiff, and we give guidelines for the choice of algorithms and hyperparameters. We anticipate that our results will help researchers in systems biology to choose appropriate numerical methods when dealing with ODE models.

Complexity Measures of Heart-Rate Variability in Amyotrophic Lateral Sclerosis with Alternative Pulmonary Capacities

OBJECTIVE

the complexity of heart-rate variability (HRV) in amyotrophic lateral sclerosis (ALS) patients with different pulmonary capacities was evaluated.

METHODS

We set these according to their pulmonary capacity, and specifically forced vital capacity (FVC). We split the groups according to FVC (FVC > 50% (n = 29) and FVC < 50% (n = 28)). In ALS, the presence of an FVC below 50% is indicative of noninvasive ventilation with two pressure levels and with the absence of other respiratory symptoms. As the number of subjects per group was different, we applied the unbalanced one-way analysis of variance (uANOVA1) test after three tests of normality, and effect size by Cohen's d to assess parameter significance.

RESULTS

with regard to chaotic global analysis, CFP4 (p < 0.001; d = 0.91), CFP5 (p = 0.0022; d = 0.85), and CFP6 (p = 0.0009; d = 0.92) were enlarged. All entropies significantly increased. Shannon (p = 0.0005; d = 0.98), Renyi (p = 0.0002; d = 1.02), Tsallis (p = 0.0004; d = 0.99), approximate (p = 0.0005; d = 0.97), and sample (p < 0.0001; d = 1.22). Detrended fluctuation analysis (DFA) (p = 0.0358) and Higuchi fractal dimension (HFD) (p = 0.15) were statistically inconsequential between the two groups.

CONCLUSIONS

HRV complexity in ALS subjects with different pulmonary capacities increased via chaotic global analysis, especially CFP5 and 3 out of 5 entropies.

Bifurcation Analysis of a Micro-Machined Gyroscope with Nonlinear Stiffness and Electrostatic Forces

The bifurcation of the periodic response of a micro-machined gyroscope with cubic supporting stiffness and fractional electrostatic forces is investigated. The pull-in phenomenon is analyzed to show that the system can have a stable periodic response when the detecting voltage is kept within a certain range. The method of averaging and the residue theorem are employed to give the averaging equations for the case of primary resonance and 1:1 internal resonance. Transition sets on the driving/detecting voltage plane that divide the parameter plane into 12 persistent regions and the corresponding bifurcation diagrams are obtained via the singularity theory. The results show that multiple solutions of the resonance curves appear with a large driving voltage and a small detecting voltage, which may lead to an uncertain output of the gyroscope. The effects of driving and detecting voltages on mechanical sensitivity and nonlinearity are analyzed for three persistent regions considering the operation requirements of the micro-machined gyroscope. The results indicate that in the region with a small driving voltage, the mechanical sensitivity is much smaller. In the other two regions, the variations in the mechanical sensitivity and nonlinearity are analogous. It is possible that the system has a maximum mechanical sensitivity and minimum nonlinearity for an appropriate range of detecting voltages.

A quantitative model of cellular decision making in direct neuronal reprogramming

The direct reprogramming of adult skin fibroblasts to neurons is thought to be controlled by a small set of interacting gene regulators. Here, we investigate how the interaction dynamics between these regulating factors coordinate cellular decision making in direct neuronal reprogramming. We put forward a quantitative model of the governing gene regulatory system, supported by measurements of mRNA expression. We found that nPTB needs to feed back into the direct neural conversion network most likely via PTB in order to accurately capture quantitative gene interaction dynamics and correctly predict the outcome of various overexpression and knockdown experiments. This was experimentally validated by nPTB knockdown leading to successful neural conversion. We also proposed a novel analytical technique to dissect system behaviour and reveal the influence of individual factors on resulting gene expression. Overall, we demonstrate that computational analysis is a powerful tool for understanding the mechanisms of direct (neuronal) reprogramming, paving the way for future models that can help improve cell conversion strategies.

Coupling between Blood Pressure and Subarachnoid Space Width Oscillations during Slow Breathing

The precise mechanisms connecting the cardiovascular system and the cerebrospinal fluid (CSF) are not well understood in detail. This paper investigates the couplings between the cardiac and respiratory components, as extracted from blood pressure (BP) signals and oscillations of the subarachnoid space width (SAS), collected during slow ventilation and ventilation against inspiration resistance. The experiment was performed on a group of 20 healthy volunteers (12 females and 8 males; BMI =22.1±3.2 kg/m2; age 25.3±7.9 years). We analysed the recorded signals with a wavelet transform. For the first time, a method based on dynamical Bayesian inference was used to detect the effective phase connectivity and the underlying coupling functions between the SAS and BP signals. There are several new findings. Slow breathing with or without resistance increases the strength of the coupling between the respiratory and cardiac components of both measured signals. We also observed increases in the strength of the coupling between the respiratory component of the BP and the cardiac component of the SAS and vice versa. Slow breathing synchronises the SAS oscillations, between the brain hemispheres. It also diminishes the similarity of the coupling between all analysed pairs of oscillators, while inspiratory resistance partially reverses this phenomenon. BP–SAS and SAS–BP interactions may reflect changes in the overall biomechanical characteristics of the brain.

Molecular Diversity of Anesthetic Actions Is Evident in Electroencephalogram Effects in Humans and Animals

Anesthetic agents cause unique electroencephalogram (EEG) activity resulting from actions on their diverse molecular targets. Typically to produce balanced anesthesia in the clinical setting, several anesthetic and adjuvant agents are combined. This creates challenges for the clinical use of intraoperative EEG monitoring, because computational approaches are mostly limited to spectral analyses and different agents and combinations produce different EEG responses. Thus, testing of many combinations of agents is needed to generate accurate, protocol independent analyses. Additionally, most studies to develop new computational approaches take place in young, healthy adults and electrophysiological responses to anesthetics vary widely at the extremes of age, due to physiological brain differences. Below, we discuss the challenges associated with EEG biomarker identification for anesthetic depth based on the diversity of molecular targets. We suggest that by focusing on the generalized effects of anesthetic agents on network activity, we can create paths for improved universal analyses.

Altered Heart Rate Variability in Patients With Schizophrenia During an Autonomic Nervous Test

Reduced heart rate variability (HRV) and dysfunction of the autonomic nervous system (ANS) have been observed in schizophrenia patients. HRV parameters of schizophrenia patients in the resting state have been well-documented; however, these parameters of schizophrenia patients who experience continuous psychophysiological stress remain unclear. The objective of this study was to systematically explore the linear and nonlinear HRV parameters between schizophrenia patients and normal controls and to detect the adaptive capabilities of HRV of schizophrenia patients during the stimulation tests of autonomic nervous system. Forty-five schizophrenia patients and forty-five normal controls, matched for age, sex and body mass index, completed a 14 min ANS test. Thirteen linear and nonlinear HRV parameters of all subjects under the ANS test were computed and statistically analyzed between groups and between sessions. The STROBE checklist was adhered to in this study. All time-domain HRV features in the ANS test were significantly different between schizophrenia patients and normal controls (p < 0.01). The schizophrenia patients showed significantly low values in the Poincaré indices, which revealed significantly decreased heart rate fluctuation complexity compared with that of normal controls (p < 0.001). In addition, the normal controls, not schizophrenia patients, showed significant differences between the recovery and stress states in the parameters of low frequency, high frequency, and nonlinear dynamics. Schizophrenia patients showed autonomic dysfunction of the heart in a series of stimulation tests of the autonomic nervous system and could not regain normal physiological functions after stress cessation. Our findings revealed that the dynamic parameters of HRV in psychophysiological stress are sensitive and practical for a diagnosis of schizophrenia.

Differentiating fallers from nonfallers using nonlinear variability analyses of data from a low-cost portable footswitch device: a feasibility study

PURPOSE

Falls are one of the main causes of injuries in older adults. This study evaluated a low-cost footswitch device that was designed to measure gait variability and investigates whether there are any relationships between variability metrics and clinical balance tests for individuals with a history of previous falls.

METHODS

Sixteen older adults completed a history of falls questionnaire, three functional tests related to fall risk, and walked on a treadmill with the footswitch device. We extracted the stride times from the device and applied two nonlinear variability analyses: coefficient of variation and detrended fluctuation analysis.

RESULTS

The temporal variables and variability metrics from the footswitch device correlated with gold-standard measurements based on ground reaction force data. One variability metric (detrended fluctuation analysis) showed a significant relationship with the presence of past falls with a sensitivity of 43%.

CONCLUSION

This feasibility study demonstrates the basis for using low-cost footswitch devices to predict fall risk.

Fighting microbial pathogens by integrating host ecosystem interactions and evolution

Successful therapies to combat microbial diseases and cancers require incorporating ecological and evolutionary principles. Drawing upon the fields of ecology and evolutionary biology, we present a systems-based approach in which host and disease-causing factors are considered as part of a complex network of interactions, analogous to studies of "classical" ecosystems. Centering this approach around empirical examples of disease treatment, we present evidence that successful therapies invariably engage multiple interactions with other components of the host ecosystem. Many of these factors interact nonlinearly to yield synergistic benefits and curative outcomes. We argue that these synergies and nonlinear feedbacks must be leveraged to improve the study of pathogenesis in situ and to develop more effective therapies. An eco-evolutionary systems perspective has surprising and important consequences, and we use it to articulate areas of high research priority for improving treatment strategies.

Non-linear heart rate dynamics during and after three controlled exercise intensities in healthy men

We aimed to analyse the complexity and fractal nature of heartbeat during constant exercise, at three different intensities, and recovery.Fourteen healthy men underwent 4 separate sessions. The first session was an incremental treadmill test to determine ventilatory thresholds (VT1 and VT2) and maximal aerobic speed (MAS). Each subject ran at VT1 and VT2 speeds and MAS (second, third and fourth day). The duration of VT1 and VT2 loads were selected in such a way that the product intensity-duration (training load) was the same. Sample Entropy (SampEn) and slope of Detrended Fluctuation Analysis (DFA α1) were measured during the whole session.DFA α1 declines with exercise, being less in the VT1 trial than in the other two.SampEn shows no significant change during exercise. The three tests induce the same decline in SampEn, but at the highest intensity (MAS) tends to decline during the exercise itself, whereas at lower intensities (VT1, VT2) the decline is delayed (10 min of recovery). Subsequently, SampEn at VT1 gradually recovers, whereas at VT2 and MAS it remains stable during recovery.In conclusion, exercise produces a loss of heartbeat complexity, but not fractal nature, during recovery and it depends on intensity.

Awareness-driven behavior changes can shift the shape of epidemics away from peaks and toward plateaus, shoulders, and oscillations

The COVID-19 pandemic has caused more than 1,000,000 reported deaths globally, of which more than 200,000 have been reported in the United States as of October 1, 2020. Public health interventions have had significant impacts in reducing transmission and in averting even more deaths. Nonetheless, in many jurisdictions, the decline of cases and fatalities after apparent epidemic peaks has not been rapid. Instead, the asymmetric decline in cases appears, in most cases, to be consistent with plateau- or shoulder-like phenomena-a qualitative observation reinforced by a symmetry analysis of US state-level fatality data. Here we explore a model of fatality-driven awareness in which individual protective measures increase with death rates. In this model, fast increases to the peak are often followed by plateaus, shoulders, and lag-driven oscillations. The asymmetric shape of model-predicted incidence and fatality curves is consistent with observations from many jurisdictions. Yet, in contrast to model predictions, we find that population-level mobility metrics usually increased from low levels before fatalities reached an initial peak. We show that incorporating fatigue and long-term behavior change can reconcile the apparent premature relaxation of mobility reductions and help understand when post-peak dynamics are likely to lead to a resurgence of cases.

A Comprehensive Framework for Uncovering Non-Linearity and Chaos in Financial Markets: Empirical Evidence for Four Major Stock Market Indices

The presence of chaos in the financial markets has been the subject of a great number of studies, but the results have been contradictory and inconclusive. This research tests for the existence of nonlinear patterns and chaotic nature in four major stock market indices: namely Dow Jones Industrial Average, Ibex 35, Nasdaq-100 and Nikkei 225. To this end, a comprehensive framework has been adopted encompassing a wide range of techniques and the most suitable methods for the analysis of noisy time series. By using daily closing values from January 1992 to July 2013, this study employs twelve techniques and tools of which five are specific to detecting chaos. The findings show no clear evidence of chaos, suggesting that the behavior of financial markets is nonlinear and stochastic.

Dissecting Tether’s Nonlinear Dynamics during Covid-19

The present study is on the five cryptocurrency daily mean return time series linearity dynamics during the Covid-19 period. These cryptocurrencies were chosen based on their influence on the market, primarily driven by its market capitalisation. Tether is included as the most important stable coin on the market, nominally pegged to the U.S. dollar (USD). The reason to investigate it is that there are some inconsistencies in its behaviour as opposed to the other four cryptocurrencies. This study found that the behaviour of Tether cryptocurrency daily average return time series pattern is highly nonlinear and chaotic in nature, whereas the other four cryptocurrencies (namely Bitcoin, Ethereum, XRP and Bitcoin Cash) daily average return time series were found to be linear in nature. To further study Tether’s nonlinear time series rich dynamics, this study deployed one category of the regime switching models popularly known as the threshold regressions. The study estimates fairly suggest that both the threshold autoregression (TAR) and smooth transition autoregressive (STAR) models with lag 1 are adequate to capture the rich nonlinear and chaotic dynamics of Tether’s daily average return time series.

Synchronization Theory-Based Analysis of Coupled Vibrations of Dual-Tube Coriolis Mass Flowmeters

Certain nonlinear influences are found in dual-tube Coriolis mass flowmeters (CMFs). According to experimentation, a nonlinearity dominated by frequency-doubling signals can be observed in the measuring signal. In general, such nonlinear effects are simplified as linear systems or neglected through processing. In this paper, a simplified model has been constructed for dual-beam CMFs based on the theory of nonlinear dynamics, with the spring-damper system as the medium for the dual-beam coupled vibrations. Next, the dynamics differential equation of the coupled vibrations is set up on the basis of the Lagrangian equation. Furthermore, numerical solutions are obtained using the Runge-Kutta fourth-order method. The study then fits discrete points of the numerical solutions, which are converted into the frequency domain to observe the existence of frequency-doubling signal components. Our findings show that frequency-doubling components exist in the spectrogram, proving that these nonlinear influences are a result of the motions of coupled vibrations. In this study, non-linear frequency-doubling signal sources are qualitatively analyzed to formulate a theoretical basis for CMFs design.

Cooperate or Not Cooperate in Predictable but Periodically Varying Situations? Cooperation in Fast Oscillating Environment

In this work, the cooperation problem between two populations in a periodically varying environment is discussed. In particular, the two-population prisoner's dilemma game with periodically oscillating payoffs is discussed, such that the time-average of these oscillations over the period of environmental variations vanishes. The possible overlaps of these oscillations generate completely new dynamical effects that drastically change the phase space structure of the two-population evolutionary dynamics. Due to these effects, the emergence of some level of cooperators in both populations is possible under certain conditions on the environmental variations. In the domain of stable coexistence the dynamics of cooperators in each population form stable cycles. Thus, the cooperators in each population promote the existence of cooperators in the other population. However, the survival of cooperators in both populations is not guaranteed by a large initial fraction of them.