Nonlinear Model Research Articles

Neural activity shaping in visual prostheses with deep learning.


The visual perception provided by retinal prostheses is limited by the overlapping current spread of adjacent electrodes. This reduces the spatial resolution attainable with unipolar stimulation. Conversely, simultaneous multipolar stimulation guided by the measured neural responses - Neural Activity Shaping (NAS) - can attenuate excessive spread of excitation allowing for more precise control over the pattern of neural activation. However, predicting the results of a multipolar stimulus pattern is a challenging task. Previous attempts focused on analytical solutions based on an assumed linear nonlinear model of retinal response; an Analytical Model Inversion (AMI) approach. Here, we propose a model-free solution for NAS, using Artificial Neural Networks (ANNs) that could be trained with data acquired from the implant. Our method consists of two ANNs trained sequentially. The Measurement Predictor Network (MPN) is trained on data from the implant and is used to predict how the retina responds to multipolar stimulation. The Stimulus Generator Network (STG) is trained on a large dataset of natural images and uses the trained MPN to determine efficient multipolar stimulus patterns by learning its inverse model. We validate our method in silico using a realistic model of retinal response to multipolar stimulation.
Main Results:
We show that our ANN-based NAS approach produces sharper retinal activations than the conventional unipolar stimulation strategy. As a theoretical bench-mark of optimal NAS results, we implemented AMI stimulation by inverting the model used to simulate the retina. Our ANN strategy produced equivalent results to AMI, while not being restricted to any specific type of retina model and being three orders of magnitude more computationally efficient. Our novel protocol provides a method for efficient and personalized retinal stimulation, which may improve the visual experience and quality of life of retinal prosthesis users.&#xD.

Exploring the chaotic structure and soliton solutions for (3 + 1)-dimensional generalized Kadomtsev–Petviashvili model

The study of the Kadomtsev–Petviashvili (KP) model is widely used for simulating several scientific phenomena, including the evolution of water wave surfaces, the processes of soliton diffusion, and the electromagnetic field of transmission. In current study, we explore some multiple soliton solutions of the (3+1)-dimensional generalized KP model via applying modified Sardar sub-equation approach (MSSEA). By extracting the novel soliton solutions, we can effectively obtain singular, dark, combo, periodic and plane wave solutions through a multiple physical regions. We also investigate the chaotic structure of governing model using the chaos theory. The behavior of the collected solutions is visually depicted to demonstrate the physical properties of the proposed model. The solutions obtained in this paper can expand the existing solutions of the (3+1)-dimensional KP model and enhance our understanding of the nonlinear dynamic behaviors. This approach allows for consistent and effective treatment of the computation process for nonlinear KP model.

Optical soliton solutions and modulation instability for unstable conformable Schrödinger model

The unstable time fractional Schrödinger model (UTFSM) is studied through the development of disturbances in marginally stable or unstable media. A modified Sardar-sub equation technique (MSSE) for a conformable fractional-order nonlinear evolution model is presented in this paper. The objective here is to construct new wave solutions for UTFSM. These solutions have particular relevance in quantum physics and assume several forms such as rational, exponential, trigonometric and hyperbolic functions, as well as combo solutions. This technique produces various shapes of dark, kink-type solitons and periodic solitary waves by setting proper parametric values. These discrete physical frameworks contribute to an understanding from analysis of unstable dynamical models. Additionally, we investigate modulation instability and stability analysis to ensure that obtained solutions are highly stable. The multiplicity of waves and solutions emphasizes how this technique can be used for different nonlinear fractional models in quantum physics and other areas.

Nonlinear similarity characterisation and validation of dynamic response of ship stiffened plate structure under explosion load impacts

The similarity test of ship stiffened plate structures under underwater explosions is a cost-effective and efficient method to evaluate the vitality of ships and guide the design of their shock resistance. This study focuses on the nonlinear impact response model tests of ship stiffened plate structures and their similarity laws with actual ships. The vertical motion of the ship stiffened plate structure is characterized by the Hurst index, and an equivalent relationship between the Hurst index of the model and the prototype is derived from classical similarity law. Based on the Hurst index, a similarity transformation relationship between the strain signals of the model and prototype is established. To verify the conclusions, similarity experiments of underwater explosions were conducted on both the model and the prototype. The original signals were grouped by the natural vibration period to determine the variation of the Hurst index over time. The model experiment strain signals for each natural vibration period were converted and compared with the prototype experiment results to verify the method's effectiveness. Simultaneously, the Hurst index of the stiffened plate structure under explosive shock load and its similarity transformation relationship with the prototype were simulated and analyzed. This provides theoretical and technical support for conducting analogous nonlinear response experiments for ship underwater explosions.

An improved dynamic bidirectional coupled hydrologic–hydrodynamic model for efficient flood inundation prediction

Abstract. To improve computational efficiency while maintaining numerical accuracy, coupled hydrologic–hydrodynamic models based on non-uniform grids are used for flood inundation prediction. In these models, a hydrodynamic model using a fine grid can be applied to flood-prone areas, and a hydrologic model using a coarse grid can be used for the remaining areas. However, it is challenging to deal with the separation and interface between the two types of areas because the boundaries of the flood-prone areas are time dependent. We present an improved Multigrid Dynamical Bidirectional Coupled hydrologic–hydrodynamic Model (IM-DBCM) with two major improvements: (1) automated non-uniform mesh generation based on the D-infinity algorithm was implemented to identify the flood-prone areas where high-resolution inundation conditions are needed and (2) ghost cells and bilinear interpolation were implemented to improve numerical accuracy in interpolating variables between the coarse and fine grids. A hydrologic model, the 2D nonlinear reservoir model, was bidirectionally coupled with a 2D hydrodynamic model that solves the shallow-water equations. Three cases were considered to demonstrate the effectiveness of the improvements. In all cases, the mesh generation algorithm was shown to efficiently and successfully generate high-resolution grids in those flood-prone areas. Compared to the original M-DBCM (OM-DBCM), the new model had lower root-mean square errors (RMSEs) and higher Nash–Sutcliffe efficiencies (NSEs), indicating that the proposed mesh generation and interpolation were reliable and stable. It can be adequately adapted to the real-life flood evolution process in watersheds and provide practical and reliable solutions for rapid flood prediction.

Hamiltonian shocks

AbstractWave propagation in the form of fronts or kinks, a common occurrence in a wide range of physical phenomena, is studied in the context of models defined by their Hamiltonian structure. Motivated, for dispersive wave evolution equations such as a strongly nonlinear model of two‐layer internal waves in the Boussinesq limit, by the symmetric properties of a class of front‐propagating solutions, known as conjugate states or solibores, a generalized formulation based purely on the dispersionless reduction of a system is introduced, and a class of undercompressive shock solutions, here referred to as “Hamiltonian shocks,” is defined. This analysis determines whether a Hamiltonian shock, representing locally a kink for the parent dispersive equations, will interact with a sufficiently smooth background wave without inducing loss of regularity, which would take the form of a classical dispersive shock for the parent equations. This property is also related to an infinitude of conservation laws, drawing a parallel to the case of completely integrable systems.

Dynamics of fractional solitonic profiles to multicomponent Gross–Pitaevskii system

The fractional multicomponent Gross-Pitaevskii system arising in the Bose-Einestein condensate is under consideration. The Gross-Pitaevskii equation plays a significant role in Bose-Einstein condensation and engineering, where it characterizes the dynamics of the condensate wave function. Superfluidity and superconductivity are two characteristics of the low-temperature phenomenon that are linked to the Bose–Einstein condensate, which is generated by a diluted atomic gas. The investigation of multi-component equations has garnered considerable attention because of their capacity to clarify intricate physical phenomena and reveal the dynamic configurations of localized wave solutions. A variety of solutions have been secured in various forms, including bright, dark, singular, and combo solitons, in addition to solutions of hyperbolic, periodic, and exponential functions. For the purpose of ensuring the solutions, recently developed integration tools called the modified Sardar subequation method and enhanced modified extended tanh-expansion method have been implemented. In nonlinear dispersive media, solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. The proposed approaches are certainly the most direct, efficient, and valuable method for dealing with multiple nonlinear models that arise in applied physics and mathematics, with the purpose of generating various types of exact solutions. In addition, 3D, 2D, contour, and density plots have been utilized to visually represent the obtained results, facilitating a greater understanding of the physical effects of the derived solutions. The solutions attained are of great importance with regard to their applicability across a wide range of quantum systems.

Construction of a non-linear analytical model for the rotation parts building up process using regression analysis

Construction of a non-linear analytical model for the rotation parts building up process using regression analysis

Structural response of half-scale pumice concrete masonry building: shake table/ambient vibration tests and FE analysis

AbstractSeismic performance evaluation of masonry structures is of paramount importance for ensuring the safety and resilience of buildings in earthquake-prone regions. There are limited number of studies on pumice elements in the literature. In addition, there are almost no studies investigating the earthquake behavior of pumice masonry building as a whole structure. In this context, a comprehensive understanding of their seismic response and dynamic characteristics has been lacking. To address this knowledge gap, a shake-table experimental campaign was undertaken, wherein half-scale pumice masonry building was exposed to simulated seismic forces. To enhance the experimental findings, numerical simulations were performed to confirm and expand our comprehension of how the pumice masonry structure responds to dynamic forces. Integrating both experimental and numerical outcomes provides a holistic understanding of how pumice masonry buildings behave during seismic events. At the end of the experimental study, the frequency values of the pumice model were observed to decrease up to 23.5% in the modes compared to the undamaged state. In the numerical model, this value decreases up to 19.85%. For the undamaged and damaged model, the first three experimental mode shapes were similar to the numerical mode shapes. Both experimental and numerical results show that the expected damages occur in the same regions. These results show that nonlinear FE models can be helpful in determining potential damage model locations. The findings have implications for the seismic design and retrofitting of similar traditional masonry buildings, facilitating the development of resilient and sustainable engineering solutions in seismic-prone regions.

The viscoelastic paradox in a nonlinear Kelvin–Voigt type model of dynamic fracture

In this paper, we consider a dynamic model of fracture for viscoelastic materials, in which the constitutive relation, involving the Cauchy stress and the strain tensors, is given in an implicit nonlinear form. We prove the existence of a solution to the associated viscoelastic dynamic system on a prescribed time-dependent cracked domain via a discretization-in-time argument. Moreover, we show that such a solution satisfies an energy-dissipation balance in which the energy used to increase the crack does not appear. As a consequence, in analogy to the linear case this nonlinear model exhibits the so-called viscoelastic paradox.

Research on Magnetic Levitation Control Method under Elastic Track Conditions Based on Backstepping Method

The vehicle–guideway coupled self-excited vibration of maglev systems is a common control instability problem in maglev traffic while the train is suspended above flexible girders, and it seriously affects the suspension stability of maglev vehicles. In order to solve this problem, a nonlinear dynamic model of a single-point maglev system with elastic track is established in this paper, and a new and more stable adaptive backstepping control method combined with magnetic flux feedback is designed. In order to verify the control effect of the designed control method, a maglev vehicle–guideway coupled experimental platform with elastic track is built, and experimental verifications under rigid and elastic conditions are carried out. The results show that, compared with the state feedback controller based on the feedback linearization controller, the adaptive backstepping control law proposed in this paper can achieve stable suspension under extremely low track stiffness, and that it shows good stability and anti-interference abilities under elastic conditions. This work has an important meaning regarding its potential to benefit the advancement of commercial maglev lines, which may significantly enhance the stability of the maglev system and reduce the cost of guideway construction.

Dynamic Modeling and Analysis of Flexible-Joint Robots with Clearance

The coupling effects of flexible joints and clearance on the dynamics of a robotic system were investigated. A numerical analysis was undertaken to reveal the coupling effects between flexible joints and clearance. The nonlinear spring-damping model and Coulomb model were applied to characterize the contact characteristics of the clearance, and a model for the flexible joint was formulated using the equivalent spring theory. An accurate robot model was established based on the clearance and joint flexibility characterization. The dynamic equation of a robot was obtained according to the Newton-Euler method. A comparative analysis was performed to assess the impacts of both the joint action of clearance and flexible joints and varying joint clearance values on the performance of the robot. The results showed that the coupling effects of flexible joints and clearance had a negative impact on the system dynamic performance. The amplitudes of the dynamic responses caused by the clearance are weakened by the flexible joint, but it leads to the lag of the system response. This study served as the theoretical foundation for exploring precise control techniques in robotics research.

Associations between long-term ambient PM2.5 exposure and the incidence of cardiopulmonary diseases and diabetes, attributable years lived with disability, and policy implication

Long-term exposure to ambient PM2.5 is known associated with cardiovascular and respiratory health effects. However, the heterogeneous concentrationresponse function (CRF) between PM2.5 exposure across different concentration range and cardiopulmonary disease and diabetes mellitus (DM) incidence, and their implications on attributable years lived with disability (YLD) and regulation policy has not been well-studied. In this retrospective longitudinal cohort study, disease-free participants (approximately 170,000 individuals, aged ≥ 30 years) from the MJ Health Database were followed up (2007–2017) regarding incidents of coronary heart disease (CHD), ischemic stroke, chronic obstructive pulmonary disease (COPD), lower respiratory tract infections (LRIs), and DM. We used a time-dependent nonlinear weight-transformation Cox regression model for the CRF with an address-matched 3-year mean PM2.5 exposure estimate. Town/district-specific PM2.5-attributable YLD were calculated by multiplying the disease incidence rate, population attributable fraction, disability weight, and sex-age group specific subpopulation for each disease separately. The estimated CRFs for cardiopulmonary diseases were heterogeneously with the hazard ratios (HRs) increased rapidly for CHD and ischemic stroke at PM2.5 concentration lower than 10 μg/m3, whereas the HRs for DM (LRIs) increased with PM2.5 higher than 15 (20) μg/m3. Women had higher HRs for ischemic stroke and DM but not CHD. Relative to the lowest observed PM2.5 concentration of 6 μg/m3 of the study population, the PM2.5 level with an extra risk of 0.1 % (comparable to the disease incidence) for CHD, ischemic stroke, DM, and LRIs were 8.59, 11.85, 22.09, and 24.23 μg/m3, respectively. The associated attributable YLD decreased by 51.4 % with LRIs reduced most (83.6 %), followed by DM (63.7 %) as a result of PM2.5 concentration reduction from 26.10 to 16.82 μg/m3 during 2011–2019 in Taiwan. The proportion of YLD due to CHD and ischemic stroke remained dominant (56.4 %-69.9 %). The cost-benefit analysis for the tradeoff between avoidable YLD and mitigation cost suggested an optimal PM2.5 exposure level at 12 μg/m3. CRFs for cardiopulmonary diseases, attributable YLD, and regulation level, may vary depending on the national/regional background and spatial distribution of PM2.5 concentrations, as well as demographic characteristics.

Symmetry-Optimized Dynamical Analysis of Optical Soliton Patterns in the Flexibly Supported Euler–Bernoulli Beam Equation: A Semi-Analytical Solution Approach

This study employs spatial optimization principles to investigate the nonlinear vibration of a flexibly supported Euler–Bernoulli beam, a (1 + 1)-dimensional system subjected to axial loads. The modified Khater method, a crucial tool in mechanical engineering, is utilized to analyze analytical solutions, which include a symmetric spatial representation of the waveform as an integral part of each solution. Notably, periodic soliton solutions for the nonlinear model closely align with numerical and approximate analytical solutions, demonstrating the accuracy of our modeling approach. Density diagrams, contour diagrams, and Poincaré maps depicting the obtained analytical solutions are presented to elucidate their accuracy and provide visual confirmation of the optimized engineering model’s physical significance. The planar dynamical system is derived through the Galilean transformation by employing mathematical models and appropriate parameter values, thereby further refining problem understanding. Sensitivity analysis is conducted, and phase portraits with equilibrium points are illustrated by analyzing a special case of the investigated dynamical system, emphasizing its symmetrical properties. Lastly, we perform a global analysis to identify periodic, quasi-periodic, and chaotic behaviors, with an extra weak forcing term confirmed by Poincaré maps and a two-dimensional symmetric basin of the largest Lyapunov exponent.

Linear control strategy of the dilution rate for stability in the anaerobic digestion process

Anaerobic digestion is a biochemical process of decomposition of organic matter, mediated by anaerobic bacteria, in an oxygen-free environment, from which biogas is produced. Biogas is used to generate thermal and electrical energy, where environmental conditions such as pH, temperature, concentration of volatile fatty acids, have a great influence on the efficiency and performance of the anaerobic digestion process, and can cause the process to be ruined. This document presents a control strategy that seeks to regulate the conditions of the anaerobic digestion process to keep it within the stability zone, using a linearization technique of the model in the state space for the design of controllers. In this work, a compensator is designed, for which the approximate linearization technique of the AM2 nonlinear model is proposed, to obtain the linearized model from which a classic lag-lead control strategy is proposed, using the dilution rate as a control variable. As a result, an improvement in system performance is obtained by reducing the maximum overshoot and reducing the settling time, evaluated at the operating point, which is validated through simulation and analysis of the response provided by the nonlinear model at the point of operation.

Evaluation of adherence to abiraterone therapy in prostate cancer patients based on a population pharmacokinetic model.

Abiraterone treatment requires regular drug intake under fasting conditions due to pronounced food effect, which may impact patient adherence. The aim of this prospective study was to evaluate adherence to abiraterone treatment in patients with prostate cancer. To achieve this aim, an abiraterone population pharmacokinetic model was developed and patients' adherence has been estimated by comparison of measured levels of abiraterone with population model-based simulations. A total of 1469 abiraterone plasma levels from 83 healthy volunteers collected in a bioequivalence study were analysed using a nonlinear mixed-effects model. Monte Carlo simulation was used to describe the theoretical distribution of abiraterone pharmacokinetic profiles at a dose of 1000 mg once daily. Adherence of 36 prostate cancer patients treated with abiraterone was then evaluated by comparing the real abiraterone concentration measured in each patient during follow-up visit with the theoretical distribution of profiles based on simulations. Patients whose abiraterone levels were ˂5th or ˃95th percentile of the distribution of simulated profiles were considered to be non-adherent. Based on this evaluation, 13 patients (36%) have been classified as non-adherent. We observed significant association (P = .0361) between richness of the breakfast and rate of non-adherence. Adherent patients reported significantly better overall condition in self-assessments (P = .0384). A trend towards a higher occurrence of adverse effects in non-adherent patients was observed. We developed an abiraterone population pharmacokinetic model and proposed an advanced approach to medical adherence evaluation. Due to the need for administration under fasting conditions, abiraterone therapy is associated with a relatively high rate of non-adherence.

Analyzing bifurcation, stability, and wave solutions in nonlinear telecommunications models using transmission lines, Hamiltonian and Jacobian techniques

This study presents a comprehensive analysis of a nonlinear telecommunications model, exploring bifurcation, stability, and wave solutions using Hamiltonian and Jacobian techniques. The investigation begins with a thorough examination of bifurcation behavior, identifying critical points and their stability characteristics, leading to the discovery of diverse bifurcation scenarios. The stability of critical points is further assessed through graphical and numerical methods, highlighting the sensitivity to parameter variations. The study delves into the derivation of both numerical and analytical wave solutions, aligning them with energy orbits depicted in phase portraits, revealing a spectrum of wave behaviors. Additionally, the analysis extends to traveling wave solutions, providing insights into wave propagation dynamics. Notably, the study underscores the efficacy of the planar dynamical approach in capturing system behavior in harmony with phase portrait orbits. The findings have significant implications for telecommunications engineers and researchers, offering insights into system behavior, stability, and signal propagation, ultimately advancing our understanding of complex nonlinear dynamics in telecommunications networks.

Counterion Release from Macroion Assemblies of Planar Geometry.

Macroions such as nanoparticles, polyelectrolytes, ionic gels, and amphiphiles can form condensed, often self-assembled, phases that are embedded in a solvent region. The condensed phase contains not only the partially or fully immobile charges of their macroions but also corresponding counterions that are mobile and thus free to migrate out of their confinement into the solvent region where they benefit from high translational entropy. Based on the nonlinear Poisson-Boltzmann model for monovalent ions, we quantify the corresponding fraction of released counterions for a planar slab geometry of the macroion phase. Slab thickness, extension of the solvent phase, fixed background charge density provided by the macroions, and dielectric constants inside slab and solvent combine into three dimensionless parameters that the fraction of released counterions depends on. We calculate that fraction and analyze the limits of a thin macroion phase, a large solvent phase, and linearized theory, where simple analytic results become available. Of particular interest is the presence of a single-planar interface that separates a bulk macroion phase from an extended solvent region. We calculate the apparent surface charge density that emerges due to the released counterions. Our model yields a comprehensive description of counterion partitioning between a planar macroion phase and a solvent region on the level of mean-field electrostatics in the absence of added salt ions.

Economy-wide rebound and the returns on investment in energy efficiency

In this paper we re-examine the relationship between global Gross Domestic Product (GDP), Primary Energy Use (PEU) and Economic Energy Efficiency (EEE) to explore how investment in energy efficiency causes rebound in energy use at the global scale. Assuming GDP is a measure of final useful work, we construct and fit a biophysics-inspired nonlinear dynamic model to global GDP, PEU and EEE data from 1900—2018 and use it to estimate how energy efficiency investments relate to output growth and hence economy-wide rebound effects. We illustrate the effects of future deployment of enhanced energy efficiency investments using two scenarios through to 2100. The first maximizes GDP growth, requiring energy efficiency investment to rise ~ twofold. Here there is no decrease in PEU growth because economy-wide rebound effects dominate. The second scenario minimizes PEU growth by increasing energy efficiency investment ~ 3.5 fold. Here PEU and GDP growth are near fully decoupled and rebound effects are minimal, although this results in a long run, zero output growth regime. We argue it is this latter regime that is compatible with the deployment of enhanced energy efficiency to meet climate objectives. However, while output growth maximising regimes prevail, efficiency-led pledges on energy use and emissions reduction appear at risk of failure at the global scale.

A Practical Approach to Tracking Estimation Using Object Trajectory Linearization

In the field of image processing and machine vision, object tracking is a significant and rapidly developing subfield. The numerous potential applications of object tracking have garnered much attention in recent years. The effectiveness of tracking and detecting moving targets is directly related to the quality of motion detection algorithms. This paper presents a new method for estimating the tracking of objects by linearizing their trajectories. Estimating the movement paths of objects in dynamic and complex environments is one of the fundamental challenges in various fields, such as surveillance systems, autonomous navigation, and robotics. Existing methods, such as the Kalman filter and particle filter, each have their strengths and weaknesses. The Kalman filter is suitable for linear systems but less efficient in nonlinear systems, while the particle filter can better handle system nonlinearity but requires more computations. The main goal of this research is to improve the accuracy and efficiency of estimating the movement paths of objects by combining path linearization techniques with existing advanced methods. In this method, the nonlinear model of the object's path is first transformed into a simpler linear model using linearization techniques. The Kalman filter is then used to estimate the states of the linearized system. This approach simplifies the calculations while increasing the estimation accuracy. In the subsequent step, a particle filter-based method is employed to manage noise and sudden changes in the object's trajectory. This combination of two different methods allows leveraging the advantages of both, resulting in a more accurate and robust estimate. Experimental results show that the proposed method performs better than traditional methods, achieving higher accuracy in various conditions, including those with high noise and sudden changes in the movement path. Specifically, the proposed approach improves movement forecasting accuracy by about 12% compared to existing methods. In conclusion, this research demonstrates that object trajectory linearization can be an effective tool for improving object tracking estimation. Combining this technique with existing advanced methods can enhance the accuracy and efficiency of tracking systems. Consequently, the results of this research can be applied to the development of advanced surveillance systems, self-driving cars, and other applications.