Relaxation and Noise-Driven Oscillations in a Model of Mitotic Spindle Dynamics.

During cell division, the mitotic spindle moves dynamically through the cell to position the chromosomes and determine the ultimate spatial position of the two daughter cells. These movements have been attributed to the action of cortical force generators which pull on the astral microtubules to position the spindle, as well as pushing events by these same microtubules against the cell cortex and plasma membrane. Attachment and detachment of cortical force generators working antagonistically against centring forces of microtubules have been modelled previously (Grill et al. in Phys Rev Lett 94:108104, 2005) via stochastic simulations and mean-field Fokker-Planck equations (describing random motion of force generators) to predict oscillations of a spindle pole in one spatial dimension. Using systematic asymptotic methods, we reduce the Fokker-Planck system to a set of ordinary differential equations (ODEs), consistent with a set proposed by Grill et al., which can provide accurate predictions of the conditions for the Fokker-Planck system to exhibit oscillations. In the limit of small restoring forces, we derive an algebraic prediction of the amplitude of spindle-pole oscillations and demonstrate the relaxation structure of nonlinear oscillations. We also show how noise-induced oscillations can arise in stochastic simulations for conditions in which the mean-field Fokker-Planck system predicts stability, but for which the period can be estimated directly by the ODE model and the amplitude by a related stochastic differential equation that incorporates random binding kinetics.

Control of complex systems with generalized embedding and empirical dynamic modeling.

Effective control requires knowledge of the process dynamics to guide the system toward desired states. In many control applications this knowledge is expressed mathematically or through data-driven models, however, as complexity grows obtaining a satisfactory mathematical representation is increasingly difficult. Further, many data-driven approaches consist of abstract internal representations that may have no obvious connection to the underlying dynamics and control, or, require extensive model design and training. Here, we remove these constraints by demonstrating model predictive control from generalized state space embedding of the process dynamics providing a data-driven, explainable method for control of nonlinear, complex systems. Generalized embedding and model predictive control are demonstrated on nonlinear dynamics generated by an agent based model of 1200 interacting agents. The method is generally applicable to any type of controller and dynamic system representable in a state space.

Robustness and exploration between the interplay of the nonlinear co-dynamics HIV/AIDS and pneumonia model via fractional differential operators and a probabilistic approach.

In this article, we considered a nonlinear compartmental mathematical model that assesses the effect of treatment on the dynamics of HIV/AIDS and pneumonia (H/A-P) co-infection in a human population at different infection stages. Understanding the complexities of co-dynamics is now critically necessary as a consequence. The aim of this research is to construct a co-infection model of H/A-P in the context of fractional calculus operators, white noise and probability density functions, employing a rigorous biological investigation. By exhibiting that the system possesses non-negative and bounded global outcomes, it is shown that the approach is both mathematically and biologically practicable. The required conditions are derived, guaranteeing the eradication of the infection. Furthermore, adequate prerequisites are established, and the configuration is tested for the existence of an ergodic stationary distribution. For discovering the system's long-term behavior, a deterministic-probabilistic technique for modeling is designed and operated in MATLAB. By employing an extensive review, we hope that the previously mentioned approach improves and leads to mitigating the two diseases and their co-infections by examining a variety of behavioral trends, such as transitions to unpredictable procedures. In addition, the piecewise differential strategies are being outlined as having promising potential for scholars in a range of contexts because they empower them to include particular characteristics across multiple time frame phases. Such formulas can be strengthened via classical techniques, power law, exponential decay, generalized Mittag-Leffler kernels, probability density functions and random procedures. Furthermore, we get an accurate description of the probability density function encircling a quasi-equilibrium point if the effect of H/A-P minimizes the propagation of the co-dynamics. Consequently, scholars can obtain better outcomes when analyzing facts using random perturbations by implementing these strategies for challenging issues. Random perturbations in H/A-P co-infection are crucial in controlling the spread of an epidemic whenever the suggested circulation is steady and the amount of infection eliminated is closely correlated with the random perturbation level.

Instabilities and self-organization in spatiotemporal epidemic dynamics driven by nonlinearity and noise.

Theoretical analysis of epidemic dynamics has attracted significant attention in the aftermath of the COVID-19 pandemic. In this article, we study dynamic instabilities in a spatiotemporal compartmental epidemic model represented by a stochastic system of coupled partial differential equations (SPDE). Saturation effects in infection spread-anchored in physical considerations-lead to strong nonlinearities in the SPDE. Our goal is to study the onset of dynamic, Turing-type instabilities, and the concomitant emergence of steady-state patterns under the interplay between three critical model parameters-the saturation parameter, the noise intensity, and the transmission rate. Employing a second-order perturbation analysis to investigate stability, we uncover both diffusion-driven and noise-induced instabilities and corresponding self-organized distinct patterns of infection spread in the steady state. We also analyze the effects of the saturation parameter and the transmission rate on the instabilities and the pattern formation. In summary, our results indicate that the nuanced interplay between the three parameters considered has a profound effect on the emergence of dynamical instabilities and therefore on pattern formation in the steady state. Moreover, due to the central role played by the Turing phenomenon in pattern formation in a variety of biological dynamic systems, the results are expected to have broader significance beyond epidemic dynamics.

Design Principles for Perfect Adaptation in Biological Networks with Nonlinear Dynamics.

Establishing a mapping between the emergent biological properties and the repository of network structures has been of great relevance in systems and synthetic biology. Adaptation is one such biological property of paramount importance that promotes regulation in the presence of environmental disturbances. This paper presents a nonlinear systems theory-driven framework to identify the design principles for perfect adaptation with respect to external disturbances of arbitrary magnitude. Based on the prior information about the network, we frame precise mathematical conditions for adaptation using nonlinear systems theory. We first deduce the mathematical conditions for perfect adaptation for constant input disturbances. Subsequently, we translate these conditions to specific necessary structural requirements for adaptation in networks of small size and then extend to argue that there exist only two classes of architectures for a network of any size that can provide local adaptation in the entire state space, namely, incoherent feed-forward (IFF) structure and negative feedback loop with buffer node (NFB). The additional positiveness constraints further narrow the admissible set of network structures. This also aids in establishing the global asymptotic stability for the steady state given a constant input disturbance. The proposed method does not assume any explicit knowledge of the underlying rate kinetics, barring some minimal assumptions. Finally, we also discuss the infeasibility of certain IFF networks in providing adaptation in the presence of downstream connections. Moreover, we propose a generic and novel algorithm based on non-linear systems theory to unravel the design principles for global adaptation. Detailed and extensive simulation studies corroborate the theoretical findings.

Global motion filtered nonlinear mutual information analysis: Enhancing dynamic portfolio strategies.

The complex financial networks, with their nonlinear nature, often exhibit considerable noises, inhibiting the analysis of the market dynamics and portfolio optimization. Existing studies mainly focus on the application of the global motion filtering on the linear matrix to reduce the noise interference. To minimize the noise in complex financial networks and enhance timing strategies, we introduce an advanced methodology employing global motion filtering on nonlinear dynamic networks derived from mutual information. Subsequently, we construct investment portfolios, focusing on peripheral stocks in both the Chinese and American markets. We utilize the growth and decline patterns of the eigenvalue associated with the global motion to identify trends in collective market movement, revealing the distinctive portfolio performance during periods of reinforced and weakened collective movements and further enhancing the strategy performance. Notably, this is the first instance of applying global motion filtering to mutual information networks to construct an investment portfolio focused on peripheral stocks. The comparative analysis demonstrates that portfolios comprising peripheral stocks within global-motion-filtered mutual information networks exhibit higher Sharpe and Sortino ratios compared to those derived from global-motion-filtered Pearson correlation networks, as well as from full mutual information and Pearson correlation matrices. Moreover, the performance of our strategies proves robust across bearish markets, bullish markets, and turbulent market conditions. Beyond enhancing the portfolio optimization, our results provide significant potential implications for diverse research fields such as biological, atmospheric, and neural sciences.

Global stability and optimal control of an age-structured SVEIR epidemic model with waning immunity and relapses.

The efficacy of vaccination, incomplete treatment and disease relapse are critical challenges that must be faced to prevent and control the spread of infectious diseases. Age heterogeneity is also a crucial factor for this study. In this paper, we investigate a new age-structured SVEIR epidemic model with the nonlinear incidence rate, waning immunity, incomplete treatment and relapse. Next, the asymptotic smoothness, the uniform persistence and the existence of interior global attractor of the solution semi-flow generated by the system are given. We define the basic reproduction number R 0 and prove the existence of the equilibria of the model. And we study the global asymptotic stability of the equilibria. Then the parameters of the model are estimated using tuberculosis data in China. The sensitivity analysis of R 0 is derived by the Partial Rank Correlation Coefficient method. These main theoretical results are applied to analyze and predict the trend of tuberculosis prevalence in China. Finally, the optimal control problem of the model is discussed. We choose to take strengthening treatment and controlling relapse as the control parameters. The necessary condition for optimal control is established.

A Least-Square Unified Framework for Spatial Filtering in SSVEP-Based BCIs.

The steady-state visual evoked potential (SSVEP) has become one of the most prominent BCI paradigms with high information transfer rate, and has been widely applied in rehabilitation and assistive applications. This paper proposes a least-square (LS) unified framework to summarize the correlation analysis (CA)-based SSVEP spatial filtering methods from a machine learning perspective. Within this framework, the commonalities and differences between various spatial filtering methods appear apparent, the interpretation of computational factors becomes intuitive, and spatial filters can be determined by solving a generalized optimization problem with non-linear and regularization items. Moreover, the proposed LS framework provides the foundation of utilizing the knowledge behind these spatial filtering methods in further classification/regression model designs. Through a comparative analysis of existing representative spatial filtering methods, recommendations are made for the superior and robust design strategies. These recommended strategies are further integrated to fill the research gaps and demonstrate the ability of the proposed LS framework to promote algorithmic improvements, resulting in five new spatial filtering methods. This study could offer significant insights in understanding the relationships between various design strategies in the spatial filtering methods from the machine learning perspective, and would also contribute to the development of the SSVEP recognition methods with high performance.

Nonlinear fusion is optimal for a wide class of multisensory tasks.

Animals continuously detect information via multiple sensory channels, like vision and hearing, and integrate these signals to realise faster and more accurate decisions; a fundamental neural computation known as multisensory integration. A widespread view of this process is that multimodal neurons linearly fuse information across sensory channels. However, does linear fusion generalise beyond the classical tasks used to explore multisensory integration? Here, we develop novel multisensory tasks, which focus on the underlying statistical relationships between channels, and deploy models at three levels of abstraction: from probabilistic ideal observers to artificial and spiking neural networks. Using these models, we demonstrate that when the information provided by different channels is not independent, linear fusion performs sub-optimally and even fails in extreme cases. This leads us to propose a simple nonlinear algorithm for multisensory integration which is compatible with our current knowledge of multimodal circuits, excels in naturalistic settings and is optimal for a wide class of multisensory tasks. Thus, our work emphasises the role of nonlinear fusion in multisensory integration, and provides testable hypotheses for the field to explore at multiple levels: from single neurons to behaviour.

Chaotic Transport of Solutes in Unsaturated Porous Media.

Unsaturated porous media, characterized by the combined presence of several immiscible fluid phases in the pore space, are highly relevant systems in nature, because they control the fate of contaminants and the availability of nutrients in the subsoil. However, a full understanding of the mechanisms controlling solute mixing in such systems is still missing. In particular, the role of saturation in the development of chaotic solute mixing has remained unexplored. Using three-dimensional numerical simulations of flow and transport at the pore scale, built upon X-ray tomograms of a porous medium at different degrees of liquid (wetting)-phase saturation, we show the occurrence of chaotic dynamics in both the deformation of the solute plume, as characterized by computed chaos metrics (Lyapunov exponents), and the mixing of the injected solute. Our results show an enhancement of these chaotic dynamics at lower saturation and their occurrence even under diffusion-relevant conditions over the medium's length, also being strengthened by larger flow velocities. These findings highlight the dominant role of the pore-scale spatial heterogeneity of the system, enhanced by the presence of an immiscible phase (e.g., air), on the mixing efficiency. This represents a stepping stone for the assessment of mixing and reactions in unsaturated porous media.

Topology degree results on a G-ABC implicit fractional differential equation under three-point boundary conditions.

This research manuscript aims to study a novel implicit differential equation in the non-singular fractional derivatives sense, namely Atangana-Baleanu-Caputo ([Formula: see text]) of arbitrary orders belonging to the interval (2, 3] with respect to another positive and increasing function. The major results of the existence and uniqueness are investigated by utilizing the Banach and topology degree theorems. The stability of the Ulam-Hyers ([Formula: see text]) type is analyzed by employing the topics of nonlinear analysis. Finally, two examples are constructed and enhanced with some special cases as well as illustrative graphics for checking the influence of major outcomes.

A Wild Horse Optimization algorithm with chaotic inertia weights and its application in linear antenna array synthesis.

Antennas play a crucial role in designing an efficient communication system. However, reducing the maximum sidelobe level (SLL) of the beam pattern is a crucial challenge in antenna arrays. Pattern synthesis in smart antennas is a major area of research because of its widespread application across various radar and communication systems. This paper presents an effective technique to minimize the SLL and thus improve the radiation pattern of the linear antenna array (LAA) using the chaotic inertia-weighted Wild Horse optimization (IERWHO) algorithm. The wild horse optimizer (WHO) is a new metaheuristic algorithm based on the social behavior of wild horses. The IERWHO algorithm is an improved Wild Horse optimization (WHO) algorithm that combines the concepts of chaotic sequence factor, nonlinear factor, and inertia weights factor. In this paper, the method is applied for the first time in antenna array synthesis by optimizing parameters such as inter-element spacing and excitation to minimize the SLL while keeping other constraints within the boundary limits, while ensuring that the performance is not affected. For performance evaluation, the simulation tests include 12 benchmark test functions and 12 test functions to verify the effectiveness of the improvement strategies. According to the encouraging research results in this paper, the IERWHO algorithm proposed has a place in the field of optimization.

On traveling wave solutions with stability and phase plane analysis for the modified Benjamin-Bona-Mahony equation.

The modified Benjamin-Bona-Mahony (mBBM) model is utilized in the optical illusion field to describe the propagation of long waves in a nonlinear dispersive medium during a visual illusion (Khater 2021). This article investigates the mBBM equation through the utilization of the rational [Formula: see text]-expansion technique to derive new analytical wave solutions. The analytical solutions we have obtained comprise hyperbolic, trigonometric, and rational functions. Some of these exact solutions closely align with previously published results in specific cases, affirming the validity of our other solutions. To provide insights into diverse wave propagation characteristics, we have conducted an in-depth analysis of these solutions using 2D, 3D, and density plots. We also investigated the effects of various parameters on the characteristics of the obtained wave solutions of the model. Moreover, we employed the techniques of linear stability to perform stability analysis of the considered model. Additionally, we have explored the stability of the associated dynamical system through the application of phase plane theory. This study also demonstrates the efficacy and capabilities of the rational [Formula: see text]-expansion approach in analyzing and extracting soliton solutions from nonlinear partial differential equations.

The comparisons of non-linear models to describe the growth performance of Lori-Bakhtiari sheep.

BACKGROUND: The study of growth traits is of interest to many animal scientists, regardless of specialization, due to the economic importance of growth rate, mature weight and other related traits. OBJECTIVE: This study aimed to compare six non-linear models for describing the growth of Lori-Bakhtiari sheep. METHODS: In order to collect weight data, 85 lambs (41 males and 44 females) were reared from birth to 140 days of age, and their growth patterns were recorded by measuring their body weight at 10-day intervals. Various mathematical functions, including the negative exponential, Brody, Gompertz, Logistic, Morgan-Mercer-Flodin (MMF) and Weibull, were used to model the relationship between body weight records and age. RESULTS: The results showed that the MMF and Gompertz models provided the best fit to the body weight data, whereas the negative exponential model exhibited the worst fit. In all models, the asymptotic weight of male lambs was higher than females. The research also revealed differences in growth patterns between male and female lambs. Overall, females had a lower absolute growth rate than males, but they reached their peak growth at an earlier period, and their growth rate declined faster. CONCLUSIONS: The differences in growth patterns between males and females indicate the importance of analysing male and female data separately when describing growth. As a result, Gompertz model can be recommended to Lori-Bakhtiari female and male lamb breeders to determine more accurate growth traits. In addition, it should be considered that feeding male and female lambs separately according to absolute growth rate values may increase growth performance.

Bifurcation, chaos, and stability analysis to the second fractional WBBM model.

This manuscript investigates bifurcation, chaos, and stability analysis for a significant model in the research of shallow water waves, known as the second 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) model. The dynamical system for the above-mentioned nonlinear structure is obtained by employing the Galilean transformation to fulfill the research objectives. Subsequent analysis includes planar dynamic systems techniques to investigate bifurcations, chaos, and sensitivities within the model. Our findings reveal diverse features, including quasi-periodic, periodic, and chaotic motion within the governing nonlinear problem. Additionally, diverse soliton structures, like bright solitons, dark solitons, kink waves, and anti-kink waves, are thoroughly explored through visual illustrations. Interestingly, our results highlight the importance of chaos analysis in understanding complex system dynamics, prediction, and stability. Our techniques' efficiency, conciseness, and effectiveness advance our understanding of this model and suggest broader applications for exploring nonlinear systems. In addition to improving our understanding of shallow water nonlinear dynamics, including waveform features, bifurcation analysis, sensitivity, and stability, this study reveals insights into dynamic properties and wave patterns.

CapsEnhancer: An Effective Computational Framework for Identifying Enhancers Based on Chaos Game Representation and Capsule Network.

Enhancers are a class of noncoding DNA, serving as crucial regulatory elements in governing gene expression by binding to transcription factors. The identification of enhancers holds paramount importance in the field of biology. However, traditional experimental methods for enhancer identification demand substantial human and material resources. Consequently, there is a growing interest in employing computational methods for enhancer prediction. In this study, we propose a two-stage framework based on deep learning, termed CapsEnhancer, for the identification of enhancers and their strengths. CapsEnhancer utilizes chaos game representation to encode DNA sequences into unique images and employs a capsule network to extract local and global features from sequence "images". Experimental results demonstrate that CapsEnhancer achieves state-of-the-art performance in both stages. In the first and second stages, the accuracy surpasses the previous best methods by 8 and 3.5%, reaching accuracies of 94.5 and 95%, respectively. Notably, this study represents the pioneering application of computer vision methods to enhancer identification tasks. Our work not only contributes novel insights to enhancer identification but also provides a fresh perspective for other biological sequence analysis tasks.

Relationship of Cycling Power and Non-Linear Heart Rate Variability from Everyday Workout Data: Potential for Intensity Zone Estimation and Monitoring.

The short-term scaling exponent alpha1 of detrended fluctuation analysis (DFA-a1) of heart rate variability (HRV) has been shown to be a sensitive marker for assessing global organismic demands. The wide dynamic range within the exercise intensity spectrum and the relationship to established physiologic threshold boundaries potentially allow in-field use and also open opportunities to provide real-time feedback. The present study expands the idea of using everyday workout data from the AI Endurance app to obtain the relationship between cycling power and DFA-a1. Collected data were imported between September 2021 and August 2023 with an initial pool of 3123 workouts across 21 male users. The aim of this analysis was to further apply a new method of implementing workout group data considering representative values of DFA-a1 segmentation compared to single workout data and including all data points to enhance the validity of the internal-to-external load relationship. The present data demonstrate a universal relationship between cycling power and DFA-a1 from everyday workout data that potentially allows accessible and regular tracking of intensity zone demarcation information. The analysis highlights the superior efficacy of the representative-based approach of included data in most cases. Validation data of the performance level and the up-to-date relationship are still pending.

Stability analysis of a nonlinear malaria transmission epidemic model using an effective numerical scheme.

Malaria is a fever condition that results from Plasmodium parasites, which are transferred to humans by the attacks of infected female Anopheles mosquitos. The deterministic compartmental model was examined using stability theory of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the disease-free, and the endemic equilibria were determined. More so, the qualitatively evaluated model incorporates time-dependent variable controls which was aimed at reducing the proliferation of malaria disease. The reproduction number R o was determined to be an asymptotically stable condition for disease free and endemic equilibria. In this paper, we used various schemes such as Runge-Kutta order 4 (RK-4) and non-standard finite difference (NSFD). All of the schemes produce different results, but the most appropriate scheme is NSFD. This is true for all step sizes. Various criteria are used in the NSFD scheme to assess the local and global stability of disease-free and endemic equilibrium points. The Routh-Hurwitz condition is used to validate the local stability and Lyapunov stability theorem is used to prove the global asymptotic stability. Global asymptotic stability is proven for the disease-free equilibrium when R 0 ≤ 1 . The endemic equilibrium is investigated for stability when R 0 ≥ 1 . All of the aforementioned schemes and their effects are also numerically demonstrated. The comparative analysis demonstrates that NSFD is superior in every way for the analysis of deterministic epidemic models. The theoretical effects and numerical simulations provided in this text may be used to predict the spread of infectious diseases.

Analyzing brain-activation responses to auditory stimuli improves the diagnosis of a disorder of consciousness by non-linear dynamic analysis of the EEG.

Although auditory stimuli benefit patients with disorders of consciousness (DOC), the optimal stimulus remains unclear. We explored the most effective electroencephalography (EEG)-tracking method for eliciting brain responses to auditory stimuli and assessed its potential as a neural marker to improve DOC diagnosis. We collected 58 EEG recordings from patients with DOC to evaluate the classification model's performance and optimal auditory stimulus. Using non-linear dynamic analysis (approximate entropy [ApEn]), we assessed EEG responses to various auditory stimuli (resting state, preferred music, subject's own name [SON], and familiar music) in 40 patients. The diagnostic performance of the optimal stimulus-induced EEG classification for vegetative state (VS)/unresponsive wakefulness syndrome (UWS) and minimally conscious state (MCS) was compared with the Coma Recovery Scale-Revision in 18 patients using the machine learning cascade forward backpropagation neural network model. Regardless of patient status, preferred music significantly activated the cerebral cortex. Patients in MCS showed increased activity in the prefrontal pole and central, occipital, and temporal cortices, whereas those in VS/UWS showed activity in the prefrontal and anterior temporal lobes. Patients in VS/UWS exhibited the lowest preferred music-induced ApEn differences in the central, middle, and posterior temporal lobes compared with those in MCS. The resting state ApEn value of the prefrontal pole (0.77) distinguished VS/UWS from MCS with 61.11% accuracy. The cascade forward backpropagation neural network tested for ApEn values in the resting state and preferred music-induced ApEn differences achieved an average of 83.33% accuracy in distinguishing VS/UWS from MCS (based on K-fold cross-validation). EEG non-linear analysis quantifies cortical responses in patients with DOC, with preferred music inducing more intense EEG responses than SON and familiar music. Machine learning algorithms combined with auditory stimuli showed strong potential for improving DOC diagnosis. Future studies should explore the optimal multimodal sensory stimuli tailored for individual patients.Trial registration: The study is registered in the Chinese Registry of Clinical Trials (Approval no: KYLL-2023-414, Registration code: ChiCTR2300079310).

Combining blood pressure variability and heart rate variability to analyze the autonomic nervous function of rotenone induced Parkinson's rat model.

BACKGROUND: Parkinson's patients have significant autonomic dysfunction, early detect the disorder is a major challenge. To assess the autonomic function in the rat model of rotenone induced Parkinson's disease (PD), Blood pressure and ECG signal acquisition are very important. NEW METHOD: We used telemetry to record the electrocardiogram and blood pressure signals from awake rats, with linear and nonlinear analysis techniques calculate the heart rate variability (HRV) and blood pressure variability (BPV). we applied nonlinear analysis methods like sample entropy and detrended fluctuation analysis to analyze blood pressure signals. Particularly, this is the first attempt to apply nonlinear analysis to the blood pressure evaluate in rotenone induced PD model rat. RESULTS: HRV in the time and frequency domains indicated sympathetic-parasympathetic imbalance in PD model rats. Linear BPV analysis didn't reflect changes in vascular function and blood pressure regulation in PD model rats. Nonlinear analysis revealed differences in BPV, with lower sample entropy results and increased detrended fluctuation analysis results in the PD group rats. COMPARISON WITH EXISTING METHODS AND CONCLUSIONS: our experiments demonstrate the ability to evaluate autonomic dysfunction in models of Parkinson's disease by combining the analysis of BPV with HRV, consistent with autonomic impairment in PD patients. Nonlinear analysis by blood pressure signal may help in early detection of the PD. It indicates that the fluctuation of blood pressure in the rats in the rotenone model group tends to be regular and predictable, contributes to understand the PD pathophysiological mechanisms and to find strategies for early diagnosis.