Investigation of a Camera-Based Contactless Pulse Oximeter with Time-Division Multiplex Illumination Applied on Piglets for Neonatological Applications.

(1) Objective: This study aims to lay a foundation for noncontact intensive care monitoring of premature babies. (2) Methods: Arterial oxygen saturation and heart rate were measured using a monochrome camera and time-division multiplex controlled lighting at three different wavelengths (660 nm, 810 nm and 940 nm) on a piglet model. (3) Results: Using this camera system and our newly designed algorithm for further analysis, the detection of a heartbeat and the calculation of oxygen saturation were evaluated. In motionless individuals, heartbeat and respiration were separated clearly during light breathing and with only minor intervention. In this case, the mean difference between noncontact and contact saturation measurements was 0.7% (RMSE = 3.8%, MAE = 2.93%). (4) Conclusions: The new sensor was proven effective under ideal animal experimental conditions. The results allow a systematic improvement for the further development of contactless vital sign monitoring systems. The results presented here are a major step towards the development of an incubator with noncontact sensor systems for use in the neonatal intensive care unit.

Reminiscences of Half a Century of Life in the World of Theoretical Physics.

Selma Lagerlöf said that culture is what remains when one has forgotten everything we had learned. Without any warranty, through ongoing research tasks, that I will ever attain this high level of wisdom, I simply share here reminiscences that have played, during my life, an important role in my incursions in science, mainly in theoretical physics. I end by presenting some perspectives for future developments.

Characterization of differential susceptibility and differential infectivity epidemic models.

Heterogeneity in susceptibility and infectivity is a central issue in epidemiology. Although the latter has received some attention recently, the former is often neglected in modeling of epidemic systems. Moreover, very few studies consider both of these heterogeneities. This paper is concerned with the characterization of epidemic models with differential susceptibility and differential infectivity under a general setup. Specifically, we investigate the global asymptotic behavior of equilibria of these systems when the network configuration of the Susceptible-Infectious interactions is strongly connected. These results prove two conjectures by Bonzi et al. (J Math Biol 62:39-64, 2011) and Hyman and Li (Math Biosci Eng 3:89-100, 2006). Moreover, we consider the scenario in which the strong connectivity hypothesis is dropped. In this case, the model exhibits a wider range of dynamical behavior, including the rise of boundary and interior equilibria, all based on the topology of network connectivity. Finally, a model with multidirectional transitions between infectious classes is presented and completely analyzed.

The Dynamics of Pasture-Herbivores-Carnivores with Sigmoidal Density Dependent Harvesting.

We investigate biomass-herbivore-carnivore (top predator) interactions in terms of a tritrophic dynamical systems model. The harvesting rates of the herbivores and the top predators are described by means of a sigmoidal function of the herbivores density and the top predator density, respectively. The main focus in this study is on the dynamics as a function of the natural mortality and the maximal harvesting rate of the top predators. We identify parameter regimes for which we have non-existence of equilibrium points as well as necessary conditions for the existence of such states of the modelling framework. The system does not possess any finite equilibrium states in the regime of high herbivore mortality. In the regime of a high consumption rate of the herbivores and low mortality rates of the top predator, an asymptotically stable finite equilibrium state exists. For this positive equilibrium to exist the mortality of the top predator should not exceed a certain threshold level. We also detect regimes producing coexistence of equilibrium states and their respective stability properties. In the regime of negligible harvesting of the top predator level, we observe a finite window of the natural top predator mortality rates for which oscillations in the top predator-, the herbivore- and the biomass level take place. The lower and upper bound of this window correspond to two Hopf bifurcation points. We also identify a bifurcation diagram using the top predator harvesting rate as a control variable. Using this diagram we detect several saddle node- and Hopf bifurcation points as well as regimes for which we have coexistence of interior equilibrium states, bistability and relaxation type of oscillations.

Playing HAVOK on the Chaos Caused by Internet Trolls.

Trump supporting Twitter posting activity from right-wing Russian trolls active during the 2016 United States presidential election was analyzed at multiple timescales using a recently developed procedure for separating linear and nonlinear components of time series. Trump supporting topics were extracted with DynEGA (Dynamic Exploratory Graph Analysis) and analyzed with Hankel Alternative View of Koopman (HAVOK) procedure. HAVOK is an exploratory and predictive technique that extracts a linear model for the time series and a corresponding nonlinear time series that is used as a forcing term for the linear model. Together, this forced linear model can produce surprisingly accurate reconstructions of nonlinear and chaotic dynamics. Using the R package havok, Russian troll data yielded well-fitting models at several timescales, not producing well-fitting models at others, suggesting that only a few timescales were important for representing the dynamics of the troll factory. We identified system features that were timescale-universal versus timescale-specific. Timescale-universal features included cycles inherent to troll factory governance, which identified their work-day and work-week organization, later confirmed from published insider interviews. Cycles were captured by eigen-vector basis components resembling Fourier modes, rather than Legendre polynomials typical for HAVOK. This may be interpreted as the troll factory having intrinsic dynamics that are highly coupled to nearly stationary cycles. Forcing terms were timescale-specific. They represented external events that precipitated major changes in the time series and aligned with major events during the political campaign. HAVOK models specified interactions between the discovered components allowing to reverse-engineer the operation of Russian troll factory. Steps and decision points in the HAVOK analysis are presented and the results are described in detail.

Evidence of Chaos in Electroencephalogram Signatures of Human Performance: A Systematic Review.

(1) Background: Chaos, a feature of nonlinear dynamical systems, is well suited for exploring biological time series, such as heart rates, respiratory records, and particularly electroencephalograms. The primary purpose of this article is to review recent studies using chaos theory and nonlinear dynamical methods to analyze human performance in different brain processes. (2) Methods: Several studies have examined chaos theory and related analytical tools for describing brain dynamics. The present study provides an in-depth analysis of the computational methods that have been proposed to uncover brain dynamics. (3) Results: The evidence from 55 articles suggests that cognitive function is more frequently assessed than other brain functions in studies using chaos theory. The most frequently used techniques for analyzing chaos include the correlation dimension and fractal analysis. Approximate, Kolmogorov and sample entropy account for the largest proportion of entropy algorithms in the reviewed studies. (4) Conclusions: This review provides insights into the notion of the brain as a chaotic system and the successful use of nonlinear methods in neuroscience studies. Additional studies of brain dynamics would aid in improving our understanding of human cognitive performance.

An improved sparse identification of nonlinear dynamics with Akaike information criterion and group sparsity.

A crucial challenge encountered in diverse areas of engineering applications involves speculating the governing equations based upon partial observations. On this basis, a variant of the sparse identification of nonlinear dynamics (SINDy) algorithm is developed. First, the Akaike information criterion (AIC) is integrated to enforce model selection by hierarchically ranking the most informative model from several manageable candidate models. This integration avoids restricting the number of candidate models, which is a disadvantage of the traditional methods for model selection. The subsequent procedure expands the structure of dynamics from ordinary differential equations (ODEs) to partial differential equations (PDEs), while group sparsity is employed to identify the nonconstant coefficients of partial differential equations. Of practical consideration within an integrated frame is data processing, which tends to treat noise separate from signals and tends to parametrize the noise probability distribution. In particular, the coefficients of a species of canonical ODEs and PDEs, such as the Van der Pol, Rössler, Burgers' and Kuramoto-Sivashinsky equations, can be identified correctly with the introduction of noise. Furthermore, except for normal noise, the proposed approach is able to capture the distribution of uniform noise. In accordance with the results of the experiments, the computational speed is markedly advanced and possesses robustness.

A systematic exploration of reservoir computing for forecasting complex spatiotemporal dynamics.

A reservoir computer (RC) is a type of recurrent neural network architecture with demonstrated success in the prediction of spatiotemporally chaotic dynamical systems. A further advantage of RC is that it reproduces intrinsic dynamical quantities essential for its incorporation into numerical forecasting routines such as the ensemble Kalman filter-used in numerical weather prediction to compensate for sparse and noisy data. We explore here the architecture and design choices for a "best in class" RC for a number of characteristic dynamical systems. Our analysis points to the importance of large scale parameter optimization. We also note in particular the importance of including input bias in the RC design, which has a significant impact on the forecast skill of the trained RC model. In our tests, the use of a nonlinear readout operator does not affect the forecast time or the stability of the forecast. The effects of the reservoir dimension, spinup time, amount of training data, normalization, noise, and the RC time step are also investigated. Finally, we detail how our investigation leads to optimal design choices for a parallel RC scheme applied to the 40 dimensional spatiotemporally chaotic Lorenz 1996 dynamics.

A Comprehensive Evaluation of Spine Kinematics, Kinetics, and Trunk Muscle Activities During Fatigue-Induced Repetitive Lifting.

OBJECTIVE: Spine kinematics, kinetics, and trunk muscle activities were evaluated during different stages of a fatigue-induced symmetric lifting task over time. BACKGROUND: Due to neuromuscular adaptations, postural behaviors of workers during lifting tasks are affected by fatigue. Comprehensive aspects of these adaptations remain to be investigated. METHOD: Eighteen volunteers repeatedly lifted a box until perceived exhaustion. Body center of mass (CoM), trunk and box kinematics, and feet center of pressure (CoP) were estimated by a motion capture system and force-plate. Electromyographic (EMG) signals of trunk/abdominal muscles were assessed using linear and nonlinear approaches. The L5-S1 compressive force (Fc) was predicted via a biomechanical model. A two-way multivariate analysis of variance (MANOVA) was performed to examine the effects of five blocks of lifting cycle (C1 to C5) and lifting trial (T1 to T5), as independent variables, on kinematic, kinetic, and EMG-related measures. RESULTS: Significant effects of lifting trial blocks were found for CoM and CoP shift in the anterior-posterior direction (respectively p < .001 and p = .014), trunk angle (p = .004), vertical box displacement (p < .001), and Fc (p = .005). EMG parameters indicated muscular fatigue with the extent of changes being muscle-specific. CONCLUSION: Results emphasized variations in most kinematics/kinetics, and EMG-based indices, which further provided insight into the lifting behavior adaptations under dynamic fatiguing conditions. APPLICATION: Movement and muscle-related variables, to a large extent, determine the magnitude of spinal loading, which is associated with low back pain.

External Stimuli on Neural Networks: Analytical and Numerical Approaches.

Based on the behavior of living beings, which react mostly to external stimuli, we introduce a neural-network model that uses external patterns as a fundamental tool for the process of recognition. In this proposal, external stimuli appear as an additional field, and basins of attraction, representing memories, arise in accordance with this new field. This is in contrast to the more-common attractor neural networks, where memories are attractors inside well-defined basins of attraction. We show that this procedure considerably increases the storage capabilities of the neural network; this property is illustrated by the standard Hopfield model, which reveals that the recognition capacity of our model may be enlarged, typically, by a factor 102. The primary challenge here consists in calibrating the influence of the external stimulus, in order to attenuate the noise generated by memories that are not correlated with the external pattern. The system is analyzed primarily through numerical simulations. However, since there is the possibility of performing analytical calculations for the Hopfield model, the agreement between these two approaches can be tested-matching results are indicated in some cases. We also show that the present proposal exhibits a crucial attribute of living beings, which concerns their ability to react promptly to changes in the external environment. Additionally, we illustrate that this new approach may significantly enlarge the recognition capacity of neural networks in various situations; with correlated and non-correlated memories, as well as diluted, symmetric, or asymmetric interactions (synapses). This demonstrates that it can be implemented easily on a wide diversity of models.

On the Mathematical Modelling of Competitive Invasive Weed Dynamics.

We explore the dynamics of invasive weeds by partial differential equation (PDE) modelling and applying dynamical system and phase portrait techniques. We begin by applying the method of characteristics to a preexisting PDE model of the spreading of T. fluminensis, an invasive weed which has been responsible for native forest depletion. We explore the system both at particular points in space and over all of space, in one dimension, as a function of time. Our model suggests that an increase in the rate of spread of the weed through space will increase the efficacy of control measures taken at the weed's spatial boundary. We then propose new competition models based on the previous model and explore the existence of travelling wave solutions. These models represent both the cases with (i) a competing native plant species which spreads through the forest and (ii) a non-mobile, established native plant species. In the former case, the model suggests that an increased mass-action coefficient between the competing species is sufficient and necessary for the transition of the forest into a state of coexistence. In the latter case, the result is not as strong: a sufficiently large rate of competition between the species excludes the possibility of native plant extinction and hence suggests that forest depletion will not occur, but does not imply coexistence. We perform some numerical simulations to support our analytic results. In all cases, we give a discussion on the physical and biological interpretations of our results. We conclude with some suggestions for future work and with a discussion of the advantages and disadvantages of the methods.

Physical principle used in reliability.

An effective approach based on the principle of maximum entropy is developed to analyze reliability in systems with dynamics of electric circuits and infectious diseases like coronavirus disease 2019 (COVID-19).

Dimensionality reduction of complex dynamical systems.

One of the outstanding problems in complexity science and engineering is the study of high-dimensional networked systems and of their susceptibility to transitions to undesired states as a result of changes in external drivers or in the structural properties. Because of the incredibly large number of parameters controlling the state of such complex systems and the heterogeneity of its components, the study of their dynamics is extremely difficult. Here we propose an analytical framework for collapsing complex N-dimensional networked systems into an S+1-dimensional manifold as a function of S effective control parameters with S << N. We test our approach on a variety of real-world complex problems showing how this new framework can approximate the system's response to changes and correctly identify the regions in the parameter space corresponding to the system's transitions. Our work offers an analytical method to evaluate optimal strategies in the design or management of networked systems.

Can motor function uncertainty and local instability within upper-extremity dual-tasking predict amnestic mild cognitive impairment and early-stage Alzheimer's disease?

In this study, we examined the uncertainty and local instability of motor function for cognitive impairment screening using a previously validated upper-extremity function (UEF). This approach was established based upon the fact that elders with an impaired executive function have trouble in the simultaneous execution of a motor and a cognitive task (dual-tasking). Older adults aged 65 years and older were recruited and stratified into 1) cognitive normal (CN), 2) amnestic MCI of the Alzheimer's type (aMCI), and 3) early-stage Alzheimer's Disease (AD). Participants performed normal-paced repetitive elbow flexion without counting and while counting backward by ones and threes. The influence of cognitive task on motor function was measured using uncertainty (measured by Shannon entropy), and local instability (measured by the largest Lyapunov exponent) of elbow flexion and compared between cognitive groups using ANOVAs, while adjusting for age, sex, and BMI. We developed logistic ordinal regression models for predicting cognitive groups based on these nonlinear measures. A total of 81 participants were recruited, including 35 CN (age = 83.8 ± 6.9), 30 aMCI (age = 83.9 ± 6.9), and 16 early AD (age = 83.2 ± 6.6). Uncertainty of motor function demonstrated the strongest associations with cognitive impairment, with an effect size of 0.52, 0.88, and 0.51 for CN vs. aMCI, CN vs. AD, and aMCI vs. AD comparisons, respectively. Ordinal logistic models predicted cognitive impairment (aMCI and AD combined) with a sensitivity and specificity of 0.82. The findings accentuate the potential of employing nonlinear dynamical features of motor functions during dual-tasking, especially uncertainty, in detecting cognitive impairment.

Distinguishing Two Types of Variability in a Sit-to-Stand Task.

Variability is commonly observed in complex behavior, such as the maintenance of upright posture. The current study examines the value added by using nonlinear measures of variability to identify dynamic stability instead of linear measures that reflect average fluctuations about a mean state. The largest Lyapunov exponent (λ1) and SD were calculated on mediolateral movement as participants performed a sit-to-stand task on a stable and unstable platform. Both measures identified changes in movement across postures, but results diverged when participants stood on the unstable platform. Large SD indicated an increase in movement variability, but small λ1 identified those movements as stable and controlled. The results suggest that a combination of linear and nonlinear analyses is useful in identifying the proportion of observed variability that may be attributed to structured, controlled sources. Nonlinear measures of variability, like λ1, can further be used to make predictions about transitions between stable postures and to identify a system's resistance to disruption from external perturbations. Those features make nonlinear analyses highly applicable to both human movement research and clinical practice.

Nonlinear models of distribution of talking in small groups.

This paper develops a mathematical model of the distribution over time of talking in discussion groups. Researchers of small group processes and social inequality have long recognized that interaction in small discussion groups is usually not equally distributed and that being a person who talks more than others is associated with having higher status outside the group and greater prestige and influence within the group. There is also a history of mathematical approaches to describing this phenomenon. As an addition to this literature, here a nonlinear dynamical system model is presented and used to develop computer simulations that are compared with data from a laboratory study of real four-person discussion groups. The model is based on theoretical assumptions about group processes including individual differences in volubility, status generalization, deference hierarchies and norms of taking turns and of fairness. While none of these alone make predictions that match the data, when they are all combined simulations are produced that closely match the data in both changes over time and differentiation among members. The dynamical system using the parameters as estimated for these data reaches a fixed point, which may help understand how groups structures become stable under some conditions but not others.

Control of multilayer biological networks and applied to target identification of complex diseases.

BACKGROUND: Networks have been widely used to model the structures of various biological systems. The ultimate aim of research on biological networks is to steer biological system structures to desired states by manipulating signals. Despite great advances in the linear control of single-layer networks, it has been observed that many complex biological systems have a multilayer networked structure and extremely complicated nonlinear processes. RESULT: In this study, we propose a general framework for controlling nonlinear dynamical systems with multilayer networked structures by formulating the problem as a minimum union optimization problem. In particular, we offer a novel approach for identifying the minimal driver nodes that can steer a multilayered nonlinear dynamical system toward any desired dynamical attractor. Three disease-related biology multilayer networks are used to demonstrate the effectiveness of our approaches. Moreover, in the set of minimum driver nodes identified by the algorithm we proposed, we confirmed that some nodes can act as drug targets in the biological experiments. Other nodes have not been reported as drug targets; however, they are also involved in important biological processes from existing literature. CONCLUSIONS: The proposed method could be a promising tool for determining higher drug target enrichment or more meaningful steering nodes for studying complex diseases.

Recent advances in physical reservoir computing: A review.

Reservoir computing is a computational framework suited for temporal/sequential data processing. It is derived from several recurrent neural network models, including echo state networks and liquid state machines. A reservoir computing system consists of a reservoir for mapping inputs into a high-dimensional space and a readout for pattern analysis from the high-dimensional states in the reservoir. The reservoir is fixed and only the readout is trained with a simple method such as linear regression and classification. Thus, the major advantage of reservoir computing compared to other recurrent neural networks is fast learning, resulting in low training cost. Another advantage is that the reservoir without adaptive updating is amenable to hardware implementation using a variety of physical systems, substrates, and devices. In fact, such physical reservoir computing has attracted increasing attention in diverse fields of research. The purpose of this review is to provide an overview of recent advances in physical reservoir computing by classifying them according to the type of the reservoir. We discuss the current issues and perspectives related to physical reservoir computing, in order to further expand its practical applications and develop next-generation machine learning systems.

Characteristic, completion or matching timescales? An analysis of temporary boundaries in enzyme kinetics.

Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions, it is often overlooked that the characteristic timescales used for the scaling the rate equations are not ideal for determining when concentrations and reaction rates reach their maximum values. In this work, we first illustrate this point by considering the classic example of the single-enzyme, single-substrate Michaelis-Menten reaction mechanism. We then extend this analysis to a more complicated reaction mechanism, the auxiliary enzyme reaction, in which a substrate is converted to product in two sequential enzyme-catalyzed reactions. In this case, depending on the ordering of the relevant timescales, several dynamic regimes can emerge. In addition to the characteristic timescales for these regimes, we derive matching timescales that determine (approximately) when the transitions from transient to quasi-steady-state kinetics occurs. The approach presented here is applicable to a wide range of singular perturbation problems in nonlinear dynamical systems.

Inferring Gene Regulatory Networks from Multiple Datasets.

Gaussian process dynamical systems (GPDS) represent Bayesian nonparametric approaches to inference of nonlinear dynamical systems, and provide a principled framework for the learning of biological networks from multiple perturbed time series measurements of gene or protein expression. Such approaches are able to capture the full richness of complex ODE models, and can be scaled for inference in moderately large systems containing hundreds of genes. Related hierarchical approaches allow for inference from multiple datasets in which the underlying generative networks are assumed to have been rewired, either by context-dependent changes in network structure, evolutionary processes, or synthetic manipulation. These approaches can also be used to leverage experimentally determined network structures from one species into another where the network structure is unknown. Collectively, these methods provide a comprehensive and flexible platform for inference from a diverse range of data, with applications in systems and synthetic biology, as well as spatiotemporal modelling of embryo development. In this chapter we provide an overview of GPDS approaches and highlight their applications in the biological sciences, with accompanying tutorials available as a Jupyter notebook from https://github.com/cap76/GPDS .