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.

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.

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.

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.

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.

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.

Unveiling the nonlinear dynamics of player performance in China's super league as a function of age.

To explore the dynamics in physical and technical performance of professional football players and changes across age groups. Match statistics were collected from 1900 games across ten seasons (2012-2021) in the Chinese Super League. Generalized additive models visualized age-related trends in 12 key performance indicators including technical and physical variables. Revealed nonlinear trajectories characterized by rapid early declines, stable peak periods and accelerated late decreases. Physical indicators decreased progressively from the early 20 s before stabilizing briefly then declining further after 30. Conversely, technical metrics gradually improved into the late 20 s and early 30 s prior to decreasing again. This study provides novel evidence that football performance changes nonlinearly across age. Targeted training and development strategies should be tailored to the specific needs of different career stages.

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.

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.

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.

Chaos and bifurcations of a two-dimensional hepatitis C virus model with hepatocyte homeostasis.

In this paper, we delve into the intricate local dynamics at equilibria within a two-dimensional model of hepatitis C virus (HCV) alongside hepatocyte homeostasis. The study investigates the existence of bifurcation sets and conducts a comprehensive bifurcation analysis to elucidate the system's behavior under varying conditions. A significant focus lies on understanding how changes in parameters can lead to bifurcations, which are pivotal points where the qualitative behavior of the system undergoes fundamental transformations. Moreover, the paper introduces and employs hybrid control feedback and Ott-Grebogi-Yorke strategies as tools to manage and mitigate chaos inherent within the HCV model. This chaos arises due to the presence of flip and Neimark-Sacker bifurcations, which can induce erratic behavior in the system. Through the implementation of these control strategies, the study aims to stabilize the system and restore it to a more manageable and predictable state. Furthermore, to validate the theoretical findings and the efficacy of the proposed control strategies, extensive numerical simulations are conducted. These simulations serve as a means of confirming the theoretical predictions and provide insight into the practical implications of the proposed control methodologies. By combining theoretical analysis with computational simulations, the paper offers a comprehensive understanding of the dynamics of the HCV model and provides valuable insights into potential strategies for controlling and managing chaos in such complex biological systems.

Disparate nonlinear neural dynamics measured with different techniques in macaque and human V1.

Diverse neuro-imaging techniques measure different aspects of neural responses with distinct spatial and temporal resolutions. Relating measured neural responses across different methods has been challenging. Here, we take a step towards overcoming this challenge, by comparing the nonlinearity of neural dynamics measured across methods. We used widefield voltage-sensitive dye imaging (VSDI) to measure neural population responses in macaque V1 to visual stimuli with a wide range of temporal waveforms. We found that stimulus-evoked VSDI responses are surprisingly near-additive in time. These results are qualitatively different from the strong sub-additive dynamics previously measured using fMRI and electrocorticography (ECoG) in human visual cortex with a similar set of stimuli. To test whether this discrepancy is specific to VSDI-a signal dominated by subthreshold neural activity, we repeated our measurements using widefield imaging of a genetically encoded calcium indicator (GcaMP6f)-a signal dominated by spiking activity, and found that GCaMP signals in macaque V1 are also near-additive. Therefore, the discrepancies in the extent of sub-additivity between the macaque and the human measurements are unlikely due to differences between sub- and supra-threshold neural responses. Finally, we use a simple yet flexible delayed normalization model to capture these different dynamics across measurements (with different model parameters). The model can potentially generalize to a broader set of stimuli, which aligns with previous suggestion that dynamic gain-control is a canonical computation contributing to neural processing in the brain.

Taxis-driven complex patterns of a plankton model.

This paper reports an important conclusion that self-diffusion is not a necessary condition for inducing Turing patterns, while taxis could establish complex pattern phenomena. We investigate pattern formation in a zooplankton-phytoplankton model incorporating phytoplankton-taxis, where phytoplankton-taxis describes the zooplankton that tends to move toward the high-densities region of the phytoplankton population. By using the phytoplankton-taxis sensitivity coefficient as the Turing instability threshold, one shows that the model exhibits Turing instability only when repulsive phytoplankton-taxis is added into the system, while the attractive-type phytoplankton-taxis cannot induce Turing instability of the system. In addition, the system does not exhibit Turing instability when the phytoplankton-taxis disappears. Numerically, we display the complex patterns in 1D, 2D domains and on spherical and zebra surfaces, respectively. In summary, our results indicate that the phytoplankton-taxis plays a pivotal role in giving rise to the Turing pattern formation of the model. Additionally, these theoretical and numerical results contribute to our understanding of the complex interaction dynamics between zooplankton and phytoplankton populations.

Force/position tracking control of fracture reduction robot based on nonlinear disturbance observer and neural network.

BACKGROUND: For the fracture reduction robot, the position tracking accuracy and compliance are affected by dynamic loads from muscle stretching, uncertainties in robot dynamics models, and various internal and external disturbances. METHODS: A control method that integrates a Radial Basis Function Neural Network (RBFNN) with Nonlinear Disturbance Observer is proposed to enhance position tracking accuracy. Additionally, an admittance control is employed for force tracking to enhance the robot's compliance, thereby improving the safety. RESULTS: Experiments are conducted on a long bone fracture model with simulated muscle forces and the results demonstrate that the position tracking error is less than ±0.2 mm, the angular displacement error is less than ±0.3°, and the maximum force tracking error is 26.28 N. This result can meet surgery requirements. CONCLUSIONS: The control method shows promising outcomes in enhancing the safety and accuracy of long bone fracture reduction with robotic assistance.

An efficient scheme for nonlinear shock wave model in a fractal domain under Caputo fractional operator.

This paper introduces a refined approach for obtaining the analytical solution of the nonlinear shock wave model incorporating fractal derivatives. The Fractal Yang Variational Iteration Strategy (FYVIS) is utilized to obtain the approximate solution of a fractal model in the form of a series under Caputo fractional operator. The suggested method is the composition of the fractal Yang transform and the variational iteration approach. By using the two-scale fractal theory, we transform the fractal model into its traditional problem and then apply the yang transform to generate a recurrence relation. The variational iteration approach is now suitable to handle this recurrence relation without imposing any hypotheses or restrictions on variables. The derived results by the proposed scheme are shown in terms of series solution. Numerical calculations verify the accuracy and consistency of the suggested approach, demonstrating its excellent performance. The dynamic behavior of fractal components is explored by evaluating absolute errors and presenting two-dimensional diagrams across the fractal domain. This investigation underscores that the suggested technique offers an efficient and user-friendly solution for solving the nonlinear shock wave model involving fractal derivatives.

Oscillations in Neuronal Activity: A Neuron-Centered Spatiotemporal Model of the Unfolded Protein Response in Prion Diseases.

Many neurodegenerative diseases (NDs) are characterized by the slow spatial spread of toxic protein species in the brain. The toxic proteins can induce neuronal stress, triggering the Unfolded Protein Response (UPR), which slows or stops protein translation and can indirectly reduce the toxic load. However, the UPR may also trigger processes leading to apoptotic cell death and the UPR is implicated in the progression of several NDs. In this paper, we develop a novel mathematical model to describe the spatiotemporal dynamics of the UPR mechanism for prion diseases. Our model is centered around a single neuron, with representative proteins P (healthy) and S (toxic) interacting with heterodimer dynamics (S interacts with P to form two S's). The model takes the form of a coupled system of nonlinear reaction-diffusion equations with a delayed, nonlinear flux for P (delay from the UPR). Through the delay, we find parameter regimes that exhibit oscillations in the P- and S-protein levels. We find that oscillations are more pronounced when the S-clearance rate and S-diffusivity are small in comparison to the P-clearance rate and P-diffusivity, respectively. The oscillations become more pronounced as delays in initiating the UPR increase. We also consider quasi-realistic clinical parameters to understand how possible drug therapies can alter the course of a prion disease. We find that decreasing the production of P, decreasing the recruitment rate, increasing the diffusivity of S, increasing the UPR S-threshold, and increasing the S clearance rate appear to be the most powerful modifications to reduce the mean UPR intensity and potentially moderate the disease progression.

Effects of nonlinear thermal radiation on the efficiency of building integrated photovoltaic systems with nanofluid cooling.

The nonlinear effects of thermal radiation on the free convection flow of certain nanofluids along a heated wall are studied numerically using an original finite-difference method. Nanofluids are used to improve the performance of flat and curved integrated photovoltaic modules. The partial differential equations governing the flow are difficult to solve due to the strong non-linearity of the radiative term. In contrast to previous studies, the problem is solved directly without linearization by Rosseland's nonlinear approximation. The proposed numerical method is validated with results from the literature. The effects of nonlinearity and various physical parameters such as time, volume fraction and radiation parameter on the velocity, temperature, Nusselt number and skin friction coefficient of the CuO-water nanofluid are analyzed and presented graphically. A comparative study between the solutions given by the linear and non-linear problems reveals that Rosseland's linear approximation is no longer valid when the effect of thermal radiation is significant. On the other hand, the non-linear model better reflects the physical phenomena involved in the cooling process. Finally, a comparison of the performance of five nanofluids (CuO, Ag, Al2O3, Cu and TiO2 in water) shows that the Cu-water nanofluid performs best, with a high heat transfer rate and low shear stresses.

Computation of soliton structure and analysis of chaotic behaviour in quantum deformed Sinh-Gordon model.

Soliton dynamics and nonlinear phenomena in quantum deformation has been investigated through conformal time differential generalized form of q deformed Sinh-Gordon equation. The underlying equation has recently undergone substantial amount of research. In Phase 1, we employed modified auxiliary and new direct extended algebraic methods. Trigonometric, hyperbolic, exponential and rational solutions are successfully extracted using these techniques, coupled with the best possible constraint requirements implemented on parameters to ensure the existence of solutions. The findings, then, are represented by 2D, 3D and contour plots to highlight the various solitons' propagation patterns such as kink-bright, bright, dark, bright-dark, kink, and kink-peakon solitons and solitary wave solutions. It is worth emphasizing that kink dark, dark peakon, dark and dark bright solitons have not been found earlier in literature. In phase 2, the underlying model is examined under various chaos detecting tools for example lyapunov exponents, multistability and time series analysis and bifurcation diagram. Chaotic behavior is investigated using various initial condition and novel results are obtained.

A Theoretical Approach to Understand the Nonlinear Processes in Enzymatic Electrochemical Biosensors.

The enzymatic biosensors' response can be monitored based on the results of nonlinear differential equations. The nonlinear reaction-diffusion equations proposed for this enzyme-based electrochemical biosensor include a nonlinear term associated with Michaelis-Menten kinetics. Herein, the system of nonlinear reaction-diffusion equations is solved using a modified homotopy perturbation method. For all values of the rate constants, the approximate analytical expressions for the concentration profiles, current, sensitivity, and gradient of biosensor have been determined. Performance factors of an enzymatic electrochemical biosensor, such as response time, sensitivity, accuracy, and resistance, are discussed. The analytical results and numerically simulated outcomes using Matlab software have been compared.

Chaos and extinction risks of sexually reproductive generalist top predator in a seasonally forced food chain system with Allee effect.

This paper investigates the dynamics of a tritrophic food chain model incorporating an Allee effect, sexually reproductive generalist top predators, and Holling type IV and Beddington-DeAngelis functional responses for interactions across different trophic levels. Analytically, we explore the feasible equilibria, their local stability, and various bifurcations, including Hopf, saddle-node, transcritical, and Bogdanov-Takens bifurcations. Numerical findings suggest that higher Allee intensity in prey growth leads to the inability of species coexistence, resulting in a decline in species density. Likewise, a lower reproduction rate and a higher strength of intraspecific competition among top predators also prevent the coexistence of species. Conversely, a rapid increase in the reproduction rate and a decrease in the strength of intraspecific competition among top predators enhance the densities of prey and top predators while decreasing intermediate predator density. We also reveal the presence of bistability and tristability phenomena within the system. Furthermore, we extend our autonomous model to its nonautonomous counterpart by introducing seasonally perturbed parameters. Numerical analysis of the nonautonomous model reveals that higher seasonal strength in the reproduction rate and intraspecific competition of top predators induce chaotic behavior, which is also confirmed by the maximum Lyapunov exponent. Additionally, we observe that seasonality may lead to the extinction of species from the ecosystem. Factors such as the Allee effect and growth rate of prey can cause periodicity in population densities. Understanding these trends is critical for controlling changes in population density within the ecosystem. Ecologists, environmentalists, and policymakers stand to benefit significantly from the invaluable insights garnered from this study. Specifically, our findings offer pivotal guidance for shaping future strategies aimed at safeguarding biodiversity and maintaining ecological stability amidst changing environmental conditions. By contributing to the existing body of knowledge, our study advances the field of ecological science, enhancing the comprehension of predator-prey dynamics across diverse ecological conditions.