A comprehensive comparison and overview of R packages for calculating sample entropy

Sample entropy is a powerful tool for analyzing the complexity and irregularity of physiology signals which may be associated with human health. Nevertheless, the sophistication of its calculation hinders its universal application. As of today, the R language provides multiple open-source packages for calculating sample entropy. All of which, however, are designed for different scenarios. Therefore, when searching for a proper package, the investigators would be confused on the parameter setting and selection of algorithms. To ease their selection, we have explored the functions of five existing R packages for calculating sample entropy and have compared their computing capability in several dimensions. We used four published datasets on respiratory and heart rate to study their input parameters, types of entropy, and program running time. In summary, NonlinearTseries and CGManalyzer can provide the analysis of sample entropy with different embedding dimensions and similarity thresholds. CGManalyzer is a good choice for calculating multiscale sample entropy of physiological signal because it not only shows sample entropy of all scales simultaneously but also provides various visualization plots. MSMVSampEn is the only package that can calculate multivariate multiscale entropies. In terms of computing time, NonlinearTseries, CGManalyzer, and MSMVSampEn run significantly faster than the other two packages. Moreover, we identify the issues in MVMSampEn package. This article provides guidelines for researchers to find a suitable R package for their analysis and applications using sample entropy.

The Replication-Transmission Relativity Theory for Multiscale Modelling of Infectious Disease Systems

It is our contention that for multiscale modelling of infectious disease systems to evolve and expand in scope, it needs to be founded on a theory. Such a theory would improve our ability to describe infectious disease systems in terms of their scales and levels of organization, and their inter-relationships. In this article we present a relativistic theory for multiscale modelling of infectious disease systems, that can be considered as an extension of the relativity principle in physics, called the replication-transmission relativity theory. This replication-transmission relativity theory states that at any level of organization of an infectious disease system there is no privileged/absolute scale which would determine, disease dynamics, only interactions between the microscale and macroscale. Such a relativistic theory provides a scientific basis for a systems level description of infectious disease systems using multiscale modelling methods. The central idea of this relativistic theory is that at every level of organization of an infectious disease system, the reciprocal influence between the microscale and the macroscale establishes a pathogen replication-transmission multiscale cycle. We distinguish two kinds of reciprocal influence between the microscale and the macroscale based on systematic differences in their conditions of relevancy. Evidence for the validity of the replication-transmission relativity theory is presented using a multiscale model of hookworm infection that is developed at host level when the relationship between the microscale and the macroscale is described by one of the forms of reciprocal influence.

Harnessing tipping points in complex ecological networks

Complex and nonlinear ecological networks can exhibit a tipping point at which a transition to a global extinction state occurs. Using real-world mutualistic networks of pollinators and plants as prototypical systems and taking into account biological constraints, we develop an ecologically feasible strategy to manage/control the tipping point by maintaining the abundance of a particular pollinator species at a constant level, which essentially removes the hysteresis associated with a tipping point. If conditions are changing so as to approach a tipping point, the management strategy we describe can prevent sudden drastic changes. Additionally, if the system has already moved past a tipping point, we show that a full recovery can occur for reasonable parameter changes only if there is active management of abundance, again due essentially to removal of the hysteresis. This recovery point in the aftermath of a tipping point can be predicted by a universal, two-dimensional reduced model.

Resonant Doppler effect in systems with variable delay

We demonstrate that a time-varying delay in nonlinear systems leads to a rich variety of dynamical behaviour, which cannot be observed in systems with constant delay. We show that the effect of the delay variation is similar to the Doppler effect with self-feedback. We distinguish between the non-resonant and the resonant Doppler effect corresponding to the dichotomy between conservative delays and dissipative delays. The non-resonant Doppler effect leads to a quasi-periodic frequency modulation of the signal, but the qualitative properties of the solution are the same as for constant delays. By contrast, the resonant Doppler effect leads to fundamentally different solutions characterized by low- and high-frequency phases with a clear separation between them. This is equivalent to time-multiplexed dynamics and can be used to design systems with well-defined multistable solutions or temporal switching between different chaotic and periodic dynamics. We systematically study chaotic dynamics in systems with large dissipative delay, which we call generalized laminar chaos. We derive a criterion for the occurrence of different orders of generalized laminar chaos, where the order is related to the dimension of the chaotic attractor. The recently found laminar chaos with constant plateaus in the low-frequency phases is the zeroth-order case with a very low dimension compared to the known high dimension of turbulent chaos in systems with conservative delay. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

Class-C semiconductor lasers with time-delayed optical feedback

We perform a linear stability analysis and numerical bifurcation diagrams of a class-C laser with time-delayed optical feedback. We employ a rate equation system based on the Maxwell-Bloch equations, and study the influence of the dephasing time on the laser dynamics. We find a stabilizing effect of an intermediate dephasing time, i.e. when moving from a class-B to a class-C laser. At long dephasing times, a destabilization of the laser solution occurs by a feedback-induced unlocking of Rabi oscillations at the second laser threshold. We predict an optimum resistance to time-delayed optical feedback for dephasing times close to the photon cavity lifetime. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

Noise-induced bistability in the quasi-neutral coexistence of viral RNAs under different replication modes

Evolutionary and dynamical investigations into real viral populations indicate that RNA replication can range between the two extremes represented by so-called 'stamping machine replication' (SMR) and 'geometric replication' (GR). The impact of asymmetries in replication for single-stranded (+) sense RNA viruses has been mainly studied with deterministic models. However, viral replication should be better described by including stochasticity, as the cell infection process is typically initiated with a very small number of RNA macromolecules, and thus largely influenced by intrinsic noise. Under appropriate conditions, deterministic theoretical descriptions of viral RNA replication predict a quasi-neutral coexistence scenario, with a line of fixed points involving different strands' equilibrium ratios depending on the initial conditions. Recent research into the quasi-neutral coexistence in two competing populations reveals that stochastic fluctuations fundamentally alter the mean-field scenario, and one of the two species outcompetes the other. In this article, we study this phenomenon for viral RNA replication modes by means of stochastic simulations and a diffusion approximation. Our results reveal that noise has a strong impact on the amplification of viral RNAs, also causing the emergence of noise-induced bistability. We provide analytical criteria for the dominance of (+) sense strands depending on the initial populations on the line of equilibria, which are in agreement with direct stochastic simulation results. The biological implications of this noise-driven mechanism are discussed within the framework of the evolutionary dynamics of RNA viruses with different modes of replication.

Relationship between muscle metabolic rate and muscle torque complexity during fatiguing intermittent isometric contractions in humans

To test the hypothesis that a system's metabolic rate and the complexity of fluctuations in the output of that system are related, thirteen healthy participants performed intermittent isometric knee extensor contractions at intensities where a rise in metabolic rate would (40% maximal voluntary contraction, MVC) and would not (20% MVC) be expected. The contractions had a 60% duty factor (6 sec contraction, 4 sec rest) and were performed until task failure or for 30 min, whichever occurred sooner. Torque and surface EMG signals were sampled continuously. Complexity and fractal scaling of torque were quantified using approximate entropy (ApEn) and the detrended fluctuation analysis (DFA) α scaling exponent. Muscle metabolic rate was determined using near-infrared spectroscopy. At 40% MVC, task failure occurred after (mean ± SD) 11.5 ± 5.2 min, whereas all participants completed 30 min of contractions at 20% MVC. Muscle metabolic rate increased significantly after 2 min at 40% MVC (2.70 ± 1.48 to 4.04 ± 1.23 %·s-1 , P < 0.001), but not at 20% MVC. Similarly, complexity decreased significantly at 40% MVC (ApEn, 0.53 ± 0.19 to 0.15 ± 0.09; DFA α, 1.37 ± 0.08 to 1.60 ± 0.09; both P < 0.001), but not at 20% MVC. The rates of change of torque complexity and muscle metabolic rate at 40% MVC were significantly correlated (ApEn, ρ = -0.63, P = 0.022; DFA, ρ = 0.58, P = 0.037). This study demonstrated that an inverse relationship exists between muscle torque complexity and metabolic rate during high-intensity contractions.

Connecting empirical phenomena and theoretical models of biological coordination across scales

Coordination in living systems-from cells to people-must be understood at multiple levels of description. Analyses and modelling of empirically observed patterns of biological coordination often focus either on ensemble-level statistics in large-scale systems with many components, or on detailed dynamics in small-scale systems with few components. The two approaches have proceeded largely independent of each other. To bridge this gap between levels and scales, we have recently conducted a human experiment of mid-scale social coordination specifically designed to reveal coordination at multiple levels (ensemble, subgroups and dyads) simultaneously. Based on this experiment, the present work shows that, surprisingly, a single system of equations captures key observations at all relevant levels. It also connects empirically validated models of large- and small-scale biological coordination-the Kuramoto and extended Haken-Kelso-Bunz (HKB) models-and the hallmark phenomena that each is known to capture. For example, it exhibits both multistability and metastability observed in small-scale empirical research (via the second-order coupling and symmetry breaking in extended HKB) and the growth of biological complexity as a function of scale (via the scalability of the Kuramoto model). Only by incorporating both of these features simultaneously can we reproduce the essential coordination behaviour observed in our experiment.

Cellular and Network Mechanisms for Temporal Signal Propagation in a Cortical Network Model

The mechanisms underlying an effective propagation of high intensity information over a background of irregular firing and response latency in cognitive processes remain unclear. Here we propose a SSCCPI circuit to address this issue. We hypothesize that when a high-intensity thalamic input triggers synchronous spike events (SSEs), dense spikes are scattered to many receiving neurons within a cortical column in layer IV, many sparse spike trains are propagated in parallel along minicolumns at a substantially high speed and finally integrated into an output spike train toward or in layer Va. We derive the sufficient conditions for an effective (fast, reliable, and precise) SSCCPI circuit: (i) SSEs are asynchronous (near synchronous); (ii) cortical columns prevent both repeatedly triggering SSEs and incorrectly synaptic connections between adjacent columns; and (iii) the propagator in interneurons is temporally complete fidelity and reliable. We encode the membrane potential responses to stimuli using the non-linear autoregressive integrated process derived by applying Newton's second law to stochastic resilience systems. We introduce a multithreshold decoder to correct encoding errors. Evidence supporting an effective SSCCPI circuit includes that for the condition, (i) time delay enhances SSEs, suggesting that response latency induces SSEs in high-intensity stimuli; irregular firing causes asynchronous SSEs; asynchronous SSEs relate to healthy neurons; and rigorous SSEs relate to brain disorders. For the condition (ii) neurons within a given minicolumn are stereotypically interconnected in the vertical dimension, which prevents repeated triggering SSEs and ensures signal parallel propagation; columnar segregation avoids incorrect synaptic connections between adjacent columns; and signal propagation across layers overwhelmingly prefers columnar direction. For the condition (iii), accumulating experimental evidence supports temporal transfer precision with millisecond fidelity and reliability in interneurons; homeostasis supports a stable fixed-point encoder by regulating changes to synaptic size, synaptic strength, and ion channel function in the membrane; together all-or-none modulation, active backpropagation, additive effects of graded potentials, and response variability functionally support the multithreshold decoder; our simulations demonstrate that the encoder-decoder is temporally complete fidelity and reliable in special intervals contained within the stable fixed-point range. Hence, the SSCCPI circuit provides a possible mechanism of effective signal propagation in cortical networks.

Applying a Dynamical Systems Model and Network Theory to Major Depressive Disorder

Mental disorders like major depressive disorder can be modeled as complex dynamical systems. In this study we investigate the dynamic behavior of individuals to see whether or not we can expect a transition to another mood state. We introduce a mean field model to a binomial process, where we reduce a dynamic multidimensional system (stochastic cellular automaton) to a one-dimensional system to analyse the dynamics. Using maximum likelihood estimation, we can estimate the parameter of interest which, in combination with a bifurcation diagram, reflects the expectancy that someone has to transition to another mood state. After numerically illustrating the proposed method with simulated data, we apply this method to two empirical examples, where we show its use in a clinical sample consisting of patients diagnosed with major depressive disorder, and a general population sample. Results showed that the majority of the clinical sample was categorized as having an expectancy for a transition, while the majority of the general population sample did not have this expectancy. We conclude that the mean field model has great potential in assessing the expectancy for a transition between mood states. With some extensions it could, in the future, aid clinical therapists in the treatment of depressed patients.

Investigation of Linear and Nonlinear Properties of a Heartbeat Time Series Using Multiscale Rényi Entropy

The time series of interbeat intervals of the heart reveals much information about disease and disease progression. An area of intense research has been associated with cardiac autonomic neuropathy (CAN). In this work we have investigated the value of additional information derived from the magnitude, sign and acceleration of the RR intervals. When quantified using an entropy measure, these time series show statistically significant differences between disease classes of Normal, Early CAN and Definite CAN. In addition, pathophysiological characteristics of heartbeat dynamics provide information not only on the change in the system using the first difference but also the magnitude and direction of the change measured by the second difference (acceleration) with respect to sequence length. These additional measures provide disease categories to be discriminated and could prove useful for non-invasive diagnosis and understanding changes in heart rhythm associated with CAN.

The Therapy Process Questionnaire - Factor analysis and psychometric properties of a multidimensional self-rating scale for high-frequency monitoring of psychotherapeutic processes

Many outcome measures and session‐related questionnaires in psychotherapy are designed for weekly or biweekly administration. Yet, today, technical developments allow for higher frequency assessments to monitor human change dynamics more closely by daily assessments. For this purpose, the Therapy Process Questionnaire (TPQ) was developed, with a specific focus on inpatient psychotherapy. In this article, we present an explorative and confirmative factor analysis of the TPQ on the basis of the time series data of 150 patients collected during their hospital stay (mean time series length: 69.1 measurement points). A seven‐factor solution was identified, which explains 68.7% of variance and associates 43 items onto the factors, which are “well‐being and positive emotions,” “relationship with fellow patients,” “therapeutic relationship and clinical setting,” “emotional and problem intensity,” “insight/confidence/therapeutic progress,” “motivation for change,” and “mindfulness/self‐care.” The internal consistency (Cronbach's α), the inter‐item correlations of the subscales, and the discriminative power of the items are excellent. The TPQ can be applied in practice and research for creating time series with equidistant measurement points and time series lengths, which are appropriate for the application of nonlinear analysis methods. Especially in clinical practice, it is important to identify precursors of phase transitions, changing synchronization patterns, and critical or instable periods of a process, which now is possible by internet‐ or app‐based applications of this multidimensional questionnaire.

On the Robustness of Multiscale Indices for Long-Term Monitoring in Cardiac Signals

The identification of patients with increased risk of Sudden Cardiac Death (SCD) has been widely studied during recent decades, and several quantitative measurements have been proposed from the analysis of the electrocardiogram (ECG) stored in 1-day Holter recordings. Indices based on nonlinear dynamics of Heart Rate Variability (HRV) have shown to convey predictive information in terms of factors related with the cardiac regulation by the autonomous nervous system, and among them, multiscale methods aim to provide more complete descriptions than single-scale based measures. However, there is limited knowledge on the suitability of nonlinear measurements to characterize the cardiac dynamics in current long-term monitoring scenarios of several days. Here, we scrutinized the long-term robustness properties of three nonlinear methods for HRV characterization, namely, the Multiscale Entropy (MSE), the Multiscale Time Irreversibility (MTI), and the Multifractal Spectrum (MFS). These indices were selected because all of them have been theoretically designed to take into account the multiple time scales inherent in healthy and pathological cardiac dynamics, and they have been analyzed so far when monitoring up to 24 h of ECG signals, corresponding to about 20 time scales. We analyzed them in 7-day Holter recordings from two data sets, namely, patients with Atrial Fibrillation and with Congestive Heart Failure, by reaching up to 100 time scales. In addition, a new comparison procedure is proposed to statistically compare the poblational multiscale representations in different patient or processing conditions, in terms of the non-parametric estimation of confidence intervals for the averaged median differences. Our results show that variance reduction is actually obtained in the multiscale estimators. The MSE (MTI) exhibited the lowest (largest) bias and variance at large scales, whereas all the methods exhibited a consistent description of the large-scale processes in terms of multiscale index robustness. In all the methods, the used algorithms could turn to give some inconsistency in the multiscale profile, which was checked not to be due to the presence of artifacts, but rather with unclear origin. The reduction in standard error for several-day recordings compared to one-day recordings was more evident in MSE, whereas bias was more patently present in MFS. Our results pave the way of these techniques towards their use, with improved algorithmic implementations and nonparametric statistical tests, in long-term cardiac Holter monitoring scenarios.

Non-Linear Dynamical Analysis of Resting Tremor for Demand-Driven Deep Brain Stimulation

Parkinson's Disease (PD) is currently the second most common neurodegenerative disease. One of the most characteristic symptoms of PD is resting tremor. Local Field Potentials (LFPs) have been widely studied to investigate deviations from the typical patterns of healthy brain activity. However, the inherent dynamics of the Sub-Thalamic Nucleus (STN) LFPs and their spatiotemporal dynamics have not been well characterized. In this work, we study the non-linear dynamical behaviour of STN-LFPs of Parkinsonian patients using ε -recurrence networks. RNs are a non-linear analysis tool that encodes the geometric information of the underlying system, which can be characterised (for example, using graph theoretical measures) to extract information on the geometric properties of the attractor. Results show that the activity of the STN becomes more non-linear during the tremor episodes and that ε -recurrence network analysis is a suitable method to distinguish the transitions between movement conditions, anticipating the onset of the tremor, with the potential for application in a demand-driven deep brain stimulation system.

Using Video Processing for the Full-Field Identification of Backbone Curves in Case of Large Vibrations

Nonlinear modal analysis is a demanding yet imperative task to rigorously address real-life situations where the dynamics involved clearly exceed the limits of linear approximation. The specific case of geometric nonlinearities, where the effects induced by the second and higher-order terms in the strain–displacement relationship cannot be neglected, is of great significance for structural engineering in most of its fields of application—aerospace, civil construction, mechanical systems, and so on. However, this nonlinear behaviour is strongly affected by even small changes in stiffness or mass, e.g., by applying physically-attached sensors to the structure of interest. Indeed, the sensors placement introduces a certain amount of geometric hardening and mass variation, which becomes relevant for very flexible structures. The effects of mass loading, while highly recognised to be much larger in the nonlinear domain than in its linear counterpart, have seldom been explored experimentally. In this context, the aim of this paper is to perform a noncontact, full-field nonlinear investigation of the very light and very flexible XB-1 air wing prototype aluminum spar, applying the well-known resonance decay method. Video processing in general, and a high-speed, optical target tracking technique in particular, are proposed for this purpose; the methodology can be easily extended to any slender beam-like or plate-like element. Obtained results have been used to describe the first nonlinear normal mode of the spar in both unloaded and sensors-loaded conditions by means of their respective backbone curves. Noticeable changes were encountered between the two conditions when the structure undergoes large-amplitude flexural vibrations.

Black Swans of CRISPR: Stochasticity and Complexity of Genetic Regulation

Recent waves of controversies surrounding genetic engineering have spilled into popular science in Twitter battles between reputable scientists and their followers. Here, a cautionary perspective on the possible blind spots and risks of CRISPR and related biotechnologies is presented, focusing in particular on the stochastic nature of cellular control processes.

Recovery of signal loss adopting the residual bootstrap method in fetal heart rate dynamics

Fetal heart rate (FHR) data obtained from a non-stress test (NST) can be presented in a type of time series, which is accompanied by signal loss due to physical and biological causes. To recover or estimate FHR data, which is subjected to a high rate of signal loss, time series models [second-order autoregressive (AR(2)), first-order autoregressive conditional heteroscedasticity (ARCH(1)) and empirical mode decomposition and vector autoregressive (EMD-VAR)] and the residual bootstrap method were applied. The ARCH(1) model with the residual bootstrap technique was the most accurate [root mean square error (RMSE), 2.065] as it reflects the nonlinearity of the FHR data [mean absolute error (MAE) for approximate entropy (ApEn), 0.081]. As a result, the goal of predicting fetal health and identifying a high-risk pregnancy could be achieved. These trials may be effectively used to save the time and cost of repeating the NST when the fetal diagnosis is impossible owing to a large amount of signal loss.

Nonlinear dynamics of spherical shells buckling under step pressure

Dynamic buckling is addressed for complete elastic spherical shells subject to a rapidly applied step in external pressure. Insights from the perspective of nonlinear dynamics reveal essential mathematical features of the buckling phenomena. To capture the strong buckling imperfection-sensitivity, initial geometric imperfections in the form of an axisymmetric dimple at each pole are introduced. Dynamic buckling under the step pressure is related to the quasi-static buckling pressure. Both loadings produce catastrophic collapse of the shell for conditions in which the pressure is prescribed. Damping plays an important role in dynamic buckling because of the time-dependent nonlinear interaction among modes, particularly the interaction between the spherically symmetric 'breathing' mode and the buckling mode. In general, there is not a unique step pressure threshold separating responses associated with buckling from those that do not buckle. Instead, there exists a cascade of buckling thresholds, dependent on the damping and level of imperfection, separating pressures for which buckling occurs from those for which it does not occur. For shells with small and moderately small imperfections, the dynamic step buckling pressure can be substantially below the quasi-static buckling pressure.

Three-to-One Internal Resonance in MEMS Arch Resonators

We present an investigation of the nonlinear dynamics of a microelectromechanical system (MEMS) arch subjected to a combination of AC and DC loadings in the presence of three-to-one internal resonance. The axial force resulting from the residual stress or temperature variation is considered in the governing equation of motion. The method of multiple scales is used to solve the governing equation. A four first-order ordinary differential equation describing the modulation of the amplitudes and phase angles is obtained. The equilibrium solution and its stability of the modulation equations are determined. Moreover, we also obtain the reduced-order model (ROM) of the MEMS arch employing the Galerkin scheme. The dynamic response is presented in the form of time traces, Fourier spectrum, phase-plane portrait, and Poincare sections. The results show that when there is an internal resonance, the energy transfer occurs between the first and third modes. In addition, the response of the MEMS arch presents abundant dynamic behaviors, such as Hopf bifurcation and quasiperiodic motions.

Low-Intensity Pulsed Ultrasound Stimulation Modulates the Nonlinear Dynamics of Local Field Potentials in Temporal Lobe Epilepsy

Low-intensity pulsed ultrasound stimulation (LIPUS) can inhibit seizures associated with temporal lobe epilepsy (TLE), which is the most common epileptic syndrome in adults and accounts for more than half of the cases of intractable epilepsy. Electroencephalography (EEG) signal analysis is an important method for studying epilepsy. The nonlinear dynamics of epileptic EEG signals can be used as biomarkers for the prediction and diagnosis of epilepsy. However, how ultrasound modulates the nonlinear dynamic characteristics of EEG signals in TLE is still unclear. Here, we used low-intensity pulsed ultrasound to stimulate the CA3 region of kainite (KA)-induced TLE mice, simultaneously recorded local field potentials (LFP) in the stimulation regions before, during, and after LIPUS. The nonlinear characteristics, including complexity, approximate entropy of different frequency bands, and Lyapunov exponent of the LFP, were calculated. Compared with the control group, the experimental group showed that LIPUS inhibited TLE seizure and the complexity, approximate entropy of the delta (0.5–4 Hz) and theta (4–8 Hz) frequency bands, and Lyapunov exponent of the LFP significantly increased in response to ultrasound stimulation. The values before ultrasound stimulation were higher ∼1.87 (complexity), ∼1.39 (approximate entropy of delta frequency bands), ∼1.13 (approximate entropy of theta frequency bands) and ∼1.46 times (Lyapunov exponent) than that after ultrasound stimulation (p < 0.05). The above results demonstrated that LIPUS can alter nonlinear dynamic characteristics and provide a basis for the application of ultrasound stimulation in the treatment of epilepsy.

High-Frequency Stochastic Switching of Graphene Resonators Near Room Temperature

Stochastic switching between the two bistable states of a strongly driven mechanical resonator enables detection of weak signals based on probability distributions, in a manner that mimics biological systems. However, conventional silicon resonators at the microscale require a large amount of fluctuation power to achieve a switching rate in the order of a few hertz. Here, we employ graphene membrane resonators of atomic thickness to achieve a stochastic switching rate of 4.1 kHz, which is 100 times faster than current state-of-the-art. The (effective) temperature of the fluctuations is approximately 400 K, which is 3000 times lower than the state-of-the-art. This shows that these membranes are potentially useful to transduce weak signals in the audible frequency domain. Furthermore, we perform numerical simulations to understand the transition dynamics of the resonator and use analytical expressions to investigate the relevant scaling parameters that allow high-frequency, low-temperature stochastic switching to be achieved in mechanical resonators.

Nonlinear dynamics underlying sensory processing dysfunction in schizophrenia

Natural systems, including the brain, often seem chaotic, since they are typically driven by complex nonlinear dynamical processes. Disruption in the fluid coordination of multiple brain regions contributes to impairments in information processing and the constellation of symptoms observed in neuropsychiatric disorders. Schizophrenia (SZ), one of the most debilitating mental illnesses, is thought to arise, in part, from such a network dysfunction, leading to impaired auditory information processing as well as cognitive and psychosocial deficits. Current approaches to neurophysiologic biomarker analyses predominantly rely on linear methods and may, therefore, fail to capture the wealth of information contained in whole EEG signals, including nonlinear dynamics. In this study, delay differential analysis (DDA), a nonlinear method based on embedding theory from theoretical physics, was applied to EEG recordings from 877 SZ patients and 753 nonpsychiatric comparison subjects (NCSs) who underwent mismatch negativity (MMN) testing via their participation in the Consortium on the Genetics of Schizophrenia (COGS-2) study. DDA revealed significant nonlinear dynamical architecture related to auditory information processing in both groups. Importantly, significant DDA changes preceded those observed with traditional linear methods. Marked abnormalities in both linear and nonlinear features were detected in SZ patients. These results illustrate the benefits of nonlinear analysis of brain signals and underscore the need for future studies to investigate the relationship between DDA features and pathophysiology of information processing.

Pharmaceutical-based entrainment of circadian phase via nonlinear model predictive control

The widespread adoption of closed-loop control in systems biology has resulted from improvements in sensors, computing, actuation, and the discovery of alternative sites of targeted drug delivery. Most control algorithms for circadian phase resetting exploit light inputs. However, recently identified small-molecule pharmaceuticals offer advantages in terms of invasiveness and potency of actuation. Herein, we develop a systematic method to control the phase of biological oscillations motivated by the recently identified small molecule circadian pharmaceutical KL001. The model-based control architecture exploits an infinitesimal parametric phase response curve (ipPRC) that is used to predict the effect of control inputs on future phase trajectories of the oscillator. The continuous time optimal control policy is first derived for phase resetting, based on the ipPRC and Pontryagin's maximum principle. Owing to practical challenges in implementing a continuous time optimal control policy, we investigate the effect of implementing the continuous time policy in a sampled time format. Specifically, we provide bounds on the errors incurred by the physiologically tractable sampled time control law. We use these results to select directions of resetting (i.e. phase advance or delay), sampling intervals, and prediction horizons for a nonlinear model predictive control (MPC) algorithm for phase resetting. The potential of this ipPRC-informed pharmaceutical nonlinear MPC is then demonstrated in silico using real-world scenarios of jet lag or rotating shift work.

A Method for Detecting Dynamic Mutation of Complex Systems Using Improved Information Entropy

In this study, a nonlinear analysis method called improved information entropy (IIE) is proposed on the basis of constructing a special probability mass function for the normalized analysis of Shannon entropy for a time series. The definition is directly applied to several typical time series, and the characteristic of IIE is analyzed. This method can distinguish different kinds of signals and reflects the complexity of one-dimensional time series of high sensitivity to the changes in signal. Thus, the method is applied to the fault diagnosis of a rolling bearing. Experimental results show that the method can effectively extract the sensitive characteristics of the bearing running state and has fast operation time and minimal parameter requirements.

Mathematical modelling and application of frog choruses as an autonomous distributed communication system

Interactions using various sensory cues produce sophisticated behaviour in animal swarms, e.g. the foraging behaviour of ants and the flocking of birds and fish. Here, we investigate the behavioural mechanisms of frog choruses from the viewpoints of mathematical modelling and its application. Empirical data on male Japanese tree frogs demonstrate that (1) neighbouring male frogs avoid call overlaps with each other over a short time scale and (2) they collectively switch between the calling state and the silent state over a long time scale. To reproduce these features, we propose a mathematical model in which separate dynamical models spontaneously switch due to a stochastic process depending on the internal dynamics of respective frogs and also the interactions among the frogs. Next, the mathematical model is applied to the control of a wireless sensor network in which multiple sensor nodes send a data packet towards their neighbours so as to deliver the packet to a gateway node by multi-hop communication. Numerical simulation demonstrates that (1) neighbouring nodes can avoid a packet collision over a short time scale by alternating the timing of data transmission and (2) all the nodes collectively switch their states over a long time scale, establishing high network connectivity while reducing network power consumption. Consequently, this study highlights the unique dynamics of frog choruses over multiple time scales and also provides a novel bio-inspired technology that is applicable to the control of a wireless sensor network.