Nonlinear Techniques Research Articles

Bioclimatic similarity between species locations and their environment revealed by dimensionality reduction analysis

Species distribution modeling is an active research topic with applications in conservation management, pest risk assessment, and population ecology. Several machine-learning methods have been applied to estimate species distribution. Non-linear dimensionality reduction techniques aim to preserve the similarity among objects at a reduced dimension for visualization, clustering, and feature selection. We propose a framework that uses Uniform Manifold Approximation and Projection (UMAP) to analyze bioclimatic variables associated with environmental (background) and species samples. Our objective was to identify geographic areas similar to those inhabited by the species. We hypothesize that the similarity between species locations and their environment in the reduced dimension will reflect similarity in the multivariate bioclimatic space. We estimated the probability of background points near a species point utilizing the latent nearest neighbor distance distribution. We tested this procedure with ten insect pest species of global importance and found that UMAP was able to generate a gradient of similarity between geographic areas and species occurrence. We also found that background-species latent distance tends to have a convergent non-linear relationship with the mean value of bioclimatic variables, thus supporting our key assumption. The performance of UMAP as a binary classifier and comparison with MaxEnt supports its use in modeling of species distribution. Potential applications are discussed for multi-species and multi-scenario analysis, as well as projection to new regions.

Optimizing Nonlinear Control Strategies for Autonomous Vehicles

Maximizing the effectiveness of nonlinear control techniques (NCT) is crucial for the broad acceptance and smooth integration of autonomous vehicles. Navigating the intricacies of real-world settings, boosting vehicle stability, and enhancing overall performance are all greatly impacted by these tactics. For manufacturers to successfully deploy autonomous cars in environments that are both dynamic and unpredictable, it is crucial to strike a balance between rigid control and flexibility. Autonomous vehicles confront a number of obstacles when trying to optimize nonlinear control systems, including changing road conditions, unpredictable traffic, and the requirement to make decisions in real-time. Because of the complexity of these problems, traditional control methods are frequently not up to the task, thus one need to find new ways to make control strategies more resilient and flexible. A Nonlinear Control Optimization Framework (NCOF) is suggested in this research; it makes use of adaptive control mechanisms, high-level optimization methods, and machine learning approaches. NCOF is engineered to enhance the vehicle's performance in a variety of situations by continuously adapting and optimizing control parameters using environmental data and real-time feedback. Beyond conventional navigation, the NCOF finds use in situations including emergency response, complicated urban surroundings, and bad weather. Improved decision-making, navigating, and passenger safety in a variety of situations are all outcomes of NCOF's optimization of nonlinear control techniques for autonomous cars. Thorough simulation assessments are carried out across several virtual scenarios to verify the efficacy of the suggested NCOF. Displaying the flexibility, stability, and efficacy of NCOF in various contexts, the simulations evaluate the optimal nonlinear control schemes' effectiveness in contrast to conventional methods.

Optimizing Communication Systems with Applied Nonlinear Analysis Techniques

The introduction of applied nonlinear analytic techniques is a disruptive force in the field of modern communication systems, revolutionising the methodology for system optimisation. This investigation into nonlinear approaches provides a deep grasp of the complex dynamics in communication networks and opens a realm beyond the confines of conventional linear models. This paper has become a beacon, illuminating the potential of nonlinear optimisation to tackle issues inherent in linear frameworks by exploring the intricacies of nonlinear systems. Nonlinear analytic integration has impacted concrete implementations in various communication domains, surpassing theoretical limitations. The application of nonlinear optimisation has produced robust error correction schemes, optimised signal processing algorithms, and adaptive modulation techniques that can dynamically adapt to the unpredictable network landscape. These innovations span wireless and optical communication, error correction coding, and adaptive modulation techniques. But there are obstacles on this journey of transformation. Implementation challenges in real-time and computational complexity still exist. However, communication systems strengthened by nonlinear analysis have a bright future ahead of them. With new technologies like artificial intelligence (AI) and machine learning positioned to be powerful partners that may accelerate and simplify nonlinear optimisation, the field of communication systems seems set for a period of intelligent, responsive, and adaptive networks. In conclusion, a new age for communication systems is being heralded by the integration of applied nonlinear analytic techniques, which promises resilience, efficiency, and adaptability. With new technologies and methods emerging to overcome obstacles, it seems that communication systems will continue to evolve in the future, ushering in a new era of network architecture.

Unraveling the Complexity with Applications of Nonlinear Analysis in Signal Processing and Communication Engineering

Nonlinear analysis is an essential area of signal and communication engineering. Many different kinds of nonlinear analysis can be used in this study. Linear signal processing techniques had previously struggled to accurately capture complex data pattern and communication signals. However, the development of non-linear analysis is a game-changing advancement since it provides a solid framework for understanding and manipulating these complex and non-trivial dynamics. In order to understand the behaviour of a wide variety of signals, from financial market trends to biological and environmental data, non-linear techniques are essential in signal processing. Improved understanding of system behaviour and predictive models may result from the use of such techniques to extract complex data patterns that are not often used. Non-linear approaches also contribute to the development of image and video processing by easing the development of advanced compression, tracking, and object recognition algorithms. Non-linear analysis is crucial in communication engineering as it aids in comprehending and optimising the flow of information across various channels. A greater understanding of signal distortion is made possible by the nonlinear perspective, which makes it possible to build reliable communication systems that can withstand interference and noise. By facilitating the creation of sophisticated modulation systems, adaptive equalisation methods, and error control coding, it raises the communication networks' dependability and effectiveness. Designing complex systems that can handle the complexities of today's data and communication demands is made possible by the paradigm-shifting synergy of nonlinear analysis, signal processing, and communication engineering. This abstract highlights the role that nonlinear analysis plays in transforming various fields and highlights how it can be used to solve changing problems related to information comprehension, processing, and transmission in a technologically sophisticated world.

Exploring the dynamics of a multistable general model of discrete memristor-based map featuring an exponentially varying memristance

Chua’s groundbreaking discovery in 1971 introduced the memristor as the fourth essential electrical component, joining resistance, capacitance, and inductance. Over the past few years, numerous discrete memristor models have been developed following its formal proposal, expanding our understanding of this subject. However, there is limited discussion about multistable discrete memristor models. This research combines a comprehensive methodology for generating memristive maps using the modulo function and an exponential memristance, resulting in the development of a multistable discrete memristor model. Nonlinear techniques, such as bifurcation diagrams, Lyapunov spectrum diagrams, and phase portraits were utilized to analyze the dynamic characteristics of the system. The findings uncovered a range of captivating phenomena associated with chaos theory, including regular orbits, chaotic orbits, the mechanism of period doubling leading to chaos, crisis phenomena, and the presence of multistability.

Command filter‐based adaptive event‐triggered control for switched nonlinear systems with full state constraints

AbstractAn adaptive event‐triggered control issue based on command filter and dynamic surface control is studied for switched nonlinear systems with full state time‐varying constraints in this article. To handle state constraints, the nonlinear mapping conversion technique is used. Radial basis function neural networks (RBFNNs) are utilized to approximate unknown nonlinear continuous functions. Adaptive control algorithm is designed based on command filtered backstepping technology. Novel even triggered control is constructed for two different cases in the switching interval. Furthermore, all signals in the switched system are proved to be semi‐globally uniformly ultimate bounded (SGUUB) by the aid of dynamic surface control method under arbitrary switching. Meanwhile, all states do not violate the preset constraints and Zeno phenomenon is avoided. The validity of the presented approach is confirmed through a numerical simulation result.

Event‐triggered adaptive tracking control for nonlinear systems with input saturation and unknown control directions

AbstractThis article is concerned with event‐triggered adaptive tracking control design of strict‐feedback nonlinear systems, which are subject to input saturation and unknown control directions. In the design procedure, a smooth nonlinear function is employed to approximate the saturation function so that the controller can be designed under the framework of backstepping. The Nussbaum gain technique is employed to address the issue of the unknown control directions. A predetermined time convergent performance function and a nonlinear mapping technique are introduced to guarantee that the tracking error can converge in the predetermined time with a fast convergence rate and a high accuracy. Then the event‐triggered adaptive prescribed performance tracking control strategy is proposed, which not only ensures the boundedness of all the closed‐loop signals and the convergence of tracking error but also reduces the communication burden from the controller to the actuator. At last, the simulation study further tests the availability of the proposed control strategy.

Theoretical study of excitation profiles of coherent anti-stokes Raman Scattering (CARS) and applications to carotenoids

Coherent anti-Stokes Raman Scattering (CARS) spectroscopy is a nonlinear optical technique that is used to investigate many different chemical and biological systems. This tool is very efficient and essentially completely rejects fluorescence. As is well known, the excitation profiles of resonance CARS are mostly used to estimate the origin shift parameters with electronic excitation for vibrations with resonantly enhanced Raman components that give information about the molecular structure and its changes in an excited electronic state. Certainly, it is necessary to have an appropriate theoretical model for pragmatically representing these processes and considering the joint (simultaneous) impact of different broadening mechanisms. The theoretical model presented in the paper is the most general and is free from a priori assumptions. Also, the mathematical algorithm created on its basis is flexible and fast for quantitative calculations.

An Overview of Mathematical Methods Applied in the Biomechanics of Foot and Ankle–Foot Orthosis Models

Ankle–foot orthoses (AFOs) constitute medical instruments designed for patients exhibiting pathological gait patterns, notably stemming from conditions such as stroke, with the primary objective of providing support and facilitating rehabilitation. The present research endeavors to conduct a comprehensive review of extant scholarly literature focusing on mathematical techniques employed for the examination of AFO models. The overarching aim is to gain deeper insights into the biomechanical intricacies underlying these ankle–foot orthosis models from a mathematical perspective, while concurrently aiming to advance novel models within the domain. Utilizing a specified set of keywords and their configurations, a systematic search was conducted across notable academic databases, including ISI Web of Knowledge, Google Scholar, Scopus, and PubMed. Subsequently, a total of 23 articles were meticulously selected for in-depth review. These scholarly contributions collectively shed light on the utilization of nonlinear optimization techniques within the context of ankle–foot orthoses (AFOs), specifically within the framework of fully Cartesian coordinates, encompassing both kinematic and dynamic dimensions. Furthermore, an exploration of a two-degree-of-freedom AFO design tailored for robotic rehabilitation, which takes into account the interplay between foot and orthosis models, is delineated. Notably, the review article underscores the incorporation of shape memory alloy (SMA) elements in AFOs and overviews the constitutive elastic, viscoelastic, and hyperelastic models. This comprehensive synthesis of research findings stands to provide valuable insights for orthotists and engineers, enabling them to gain a mathematical understanding of the biomechanical principles underpinning AFO models and fostering the development of innovative AFO designs.

Existence theory and Ulam’s stabilities for switched coupled system of implicit impulsive fractional order Langevin equations

In this work, a system of nonlinear, switched, coupled, implicit, impulsive Langevin equations with two Hilfer fractional derivatives is introduced. The suitable conditions and results are established to discuss existence, uniqueness, and Ulam-type stability results of the mentioned model, with the help of nonlinear functional analysis techniques and Banach’s fixed-point theorem. Furthermore, we examine our results with the help of example.

Mathematical Camera Array Optimization for Face 3D Modeling Application.

Camera network design is a challenging task for many applications in photogrammetry, biomedical engineering, robotics, and industrial metrology, among other fields. Many driving factors are found in the camera network design including the camera specifications, object of interest, and type of application. One of the interesting applications is 3D face modeling and recognition which involves recognizing an individual based on facial attributes derived from the constructed 3D model. Developers and researchers still face difficulty in reaching the required high level of accuracy and reliability needed for image-based 3D face models. This is caused among many factors by the hardware limitations and imperfection of the cameras and the lack of proficiency in designing the ideal camera-system configuration. Accordingly, for precise measurements, we still need engineering-based techniques to ascertain the specific level of deliverables quality. In this paper, an optimal geometric design methodology of the camera network is presented by investigating different multi-camera system configurations composed of four up to eight cameras. A mathematical nonlinear constrained optimization technique is applied to solve the problem and each camera system configuration is tested for a facial 3D model where a quality assessment is applied to conclude the best configuration. The optimal configuration is found to be a 7-camera array, comprising a pentagon shape enclosing two additional cameras, offering high accuracy. For those who prioritize point density, a 9-camera array with a pentagon and quadrilateral arrangement in the X-Z plane is a viable choice. However, a 5-camera array offers a balance between accuracy and the number of cameras.

Non-linear dimension reduction in factor-augmented vector autoregressions

This paper introduces non-linear dimension reduction in factor-augmented vector autoregressions to analyze the effects of different economic shocks. I argue that controlling for non-linearities between a large-dimensional dataset and the latent factors is particularly useful during turbulent times of the business cycle. In simulations, I show that non-linear dimension reduction techniques yield good forecasting performance, especially when data is highly volatile. In an empirical application, I identify a monetary policy as well as an uncertainty shock excluding and including observations of the COVID-19 pandemic. Those two applications suggest that the non-linear FAVAR approaches are capable of dealing with the large outliers caused by the COVID-19 pandemic and yield reliable results in both scenarios.

Simple pseudo-steady state productivity index correlations for infinite-conductivity horizontal wells based on a rigorous, semi-analytical model

Simple pseudo-steady state (PSS) productivity index (PI) correlations are developed for horizontal wells producing at a constant rate from a closed, rectangular reservoir based on a rigorous infinite-conductivity model (ICM). The main three correlations are functions of the half-length wellbore segments number (mt) only and mt can be determined by the general correlation, which is a function of dimensionless well length (LD). The correlations are developed by using a nonlinear regression technique (with zero error) based on over thousand semi-analytical runs for a rigorous ICM covering 90 cases of different well and reservoir configurations. The 90 cases are averaged with less than 5% error in the total pressure drop calculation for the most of them to reduce the number of correlations and to remove the slight effect of well penetration ratio (PR). The PSS PI correlations are simply used to calculate mt, average pressure drop at transient-state, average starting time of PSS, and average total pressure drop at the beginning of PSS. At PSS, the reservoir outer boundaries are dominant, and the pressure drop will depend on the temporal and the spatial time-independent functions. The simple PSS PI correlations have been verified, and can be easily implemented in a standard spreadsheet code.The results show that LD is directly proportional to PSS PI and more significant than reservoir thickness (h) on horizontal-well productivity evaluation, which confirms the principle of the economic feasibility for drilling horizontal well in the oil industry. The results also show that the horizontal-well productivity by this study is several times higher than its counterparts by the methods reported in the literature because the method used by this study is based on a rigorous infinite-conductivity solution where no significant pressure drop occurs, while the previous methods are based on approximate infinite-conductivity solutions (AICSs). Therefore, there is a big underestimation in productivity calculation by using the previous methods which crucially reflect on reservoir evaluation. The new correlations give accurate PSS PI for over 3000 cases of diverse well and reservoir configurations, besides giving a rough PSS PI for the other cases.

Role of technology management for carbon neutrality in Gulf economies: the role of social globalization and financial development.

This study is founded on the United Nations' Sustainable Development Goals (SDGs) for 2030, particularly SDGs 8, 11, 12, and 13, among others. Investigating the impact of nonrenewable energy, social globalization, financial development, and ICT on CO2 emissions in the Gulf nations, data from 1992 to 2019 was employed using advanced panel methodologies. Both linear and nonlinear autoregressive distributed lag techniques, along with a panel causality approach, were utilized for a comprehensive analysis. These extensive investigations offer robust insights into the ecological sustainability dynamics within the Gulf nations. The empirical findings highlight that positive (negative) shifts in social globalization, economic growth, ICT, and nonrenewable energy correlate with an increase (decrease) in CO2 emissions, while positive (negative) shifts in financial development contribute to a decrease (increase) in CO2 emissions. These results emphasize the need for a policy framework aligned with the SDGs, advocating an inclusive policy framework tailored for the Gulf nations, aiming to drive progress towards achieving SDGs 7, 8, 9, 13, and 16.

Information maximization-based clustering of histopathology images using deep learning

Pancreatic cancer is one of the most adverse diseases and it is very difficult to treat because the cancer cells formed in the pancreas intertwine themselves with nearby blood vessels and connective tissue. Hence, the surgical procedure of treatment becomes complicated and it does not always lead to a cure. Histopathological diagnosis is the usual approach for cancer diagnosis. However, the pancreas remains so deep inside the body that experts sometimes struggle to detect cancer in it. Computer-aided diagnosis can come to the aid of pathologists in this scenario. It assists experts by supporting their diagnostic decisions. In this research, we carried out a deep learning-based approach to analyze histopathology images. We collected whole-slide images of KPC mice to implement this work. The pancreatic abnormalities observed in KPC mice develop similar histological features to human beings. We created random patches from whole-slide images. Then, a convolutional autoencoder framework was used to embed these patches into an integrated latent space. We applied ‘information maximization’, a deep learning clustering technique to cluster the identical patches in an unsupervised manner since our dataset does not have annotation. Moreover, Uniform manifold approximation and projection, a nonlinear dimension reduction technique was utilized to visualize the embedded patches in a 2-dimensional space. Finally, we calculated a few internal cluster validation metrics to determine the optimal cluster set. Our work concentrated on patch-based anomaly detection in the whole slide histopathology images of KPC mice.

Predicting Bordeaux red wine origins and vintages from raw gas chromatograms

Connecting chemical properties to various wine characteristics is of great interest to the science of olfaction as well as the wine industry. We explored whether Bordeaux wine chemical identities and vintages (harvest year) can be inferred from a common and affordable chemical analysis, namely, a combination of gas chromatography (GC) and electron ionization mass spectrometry. Using 12 vintages (within the 1990–2007 range) from 7 estates of the Bordeaux region, we report that, remarkably, nonlinear dimensionality reduction techniques applied to raw gas chromatograms recover the geography of the Bordeaux region. Using machine learning, we found that we can not only recover the estate perfectly from gas chromatograms, but also the vintage with up to 50% accuracy. Interestingly, we observed that the entire chromatogram is informative with respect to geographic location and age, thus suggesting that the chemical identity of a wine is not defined by just a few molecules but is distributed over a large chemical spectrum. This study demonstrates the remarkable potential of GC analysis to explore fundamental questions about the origin and age of wine.

Comparison of dimensionality reduction techniques for multi-variable spatiotemporal flow fields

In the field of fluid mechanics, it is a potential consensus that nonlinear dimensionality reduction (DR) techniques outperform linear methods. However, this conclusion has been obtained based on simple fluid phenomena and an incomplete evaluation system of dimensionality reduction algorithms. In this study, we use an improved evaluation system of DR methods to compare and evaluate the performance of four DR methods, including two linear techniques: Principal Component Analysis (PCA) and Independent Component Analysis (ICA), and two non-linear techniques: Isometric Mapping (ISOMAP) and Locally Linear Embedding (LLE). The four methods are applied to analyze a complex hydrodynamic flow field with cavitation by considering the joint features of multiple variables. Results show that LLE can capture redundant features that do not contribute to understanding the characteristics of flow fields, while ISOMAP is more suitable for handling datasets with multiple scales than LLE. PCA and ISOMAP can successfully capture the characteristics and evolution of flow fields. In addition, 3D supplementary information can assist ICA in improving the problem of identifying unstable flow field states.

Wavefield imaging of nonlinear ultrasonic Lamb waves for visualizing fatigue micro-cracks

The traditional nonlinear ultrasonic technique, as typified by the second-harmonic generation and the frequency mixing response, can be employed to identify and characterize the micro-damage. However, the research on micro-damage characterization using nonlinear Lamb wave imaging technique remains an ongoing challenge and is rarely reported. A method called standardized amplitude difference is proposed for nonlinear feature enhancement, and further for fatigue crack imaging based on the wavefield data. Wavefield data contain abundant information on the spatial and temporal variation of propagating waves in the damaged structure. The nonlinearity index β′ of the signal difference under the high and low incident wave amplitudes is calculated for fatigue crack imaging. Two scanning methods, including local scanning and global scanning, are introduced to image the fatigue crack tip and visualize the wave field of the harmonics respectively. The experimental validation, based on the imaging results of an aluminum alloy plate specimen with a barely visible fatigue crack and a steel plate with a blind hole, manifests that the proposed method can be used to enhance and extract the nonlinear features and suppress the fundamental frequency, so as to improve the signal-to-noise ratio (SNR) of the micro-damage imaging results.

Applied Nonlinear Analysis for Efficient Communication Signal Processing and Network Management

The use of nonlinear analysis in network management and communication signal processing is a revolutionary strategy that is redefining contemporary networking paradigms. The goal of this project is to improve communication systems' resilience, efficiency, and agility by integrating cutting-edge nonlinear techniques. This study investigates the complex relationship between signal processing and network management using nonlinear analysis techniques in order to meet the growing needs of modern networks. Nonlinear approaches provide dynamic signal processing methods, enabling in-the-moment modifications that maximise data transfer under variable network circumstances. Prioritising data streams is made easier by this integration, which also improves network speed and efficiently allocates resources to guarantee Quality of Service (QoS). The study explores the complexities of interdisciplinary ideas, using the concepts of nonlinear analysis to comprehend phase transitions, emergent network architectures, and networks' inherent ability to self-organize. By deciphering the complexity of network behaviours and their evolution, this understanding aids in the creation of more effective management techniques. However, there are difficulties with computing complexity, interoperability, and skill adaption when using nonlinear analysis in network management. To properly utilise nonlinear approaches for network management and communication signal processing optimisation, these obstacles must be overcome. The research is important because it may lead to game-changing advancements in communication systems by introducing cutting-edge ways that go beyond the constraints of conventional, linear methods. The findings show potential for more effective and secure communication systems, which can meet the increasing needs of modern networking.

Adaptive-Critic-Based Event-Triggered Intelligent Cooperative Control for a Class of Second-Order Constrained Multiagent Systems

An event-based intelligent cooperative control policy is developed in this paper for a class of second-order multiagent systems (MASs). The followers are subject to external disturbances and output constraints, in which the constraint ranges are asymmetric and time-varying. By using one-to-one nonlinear mapping technique to obtain equivalent unconstrained systems and designing a distributed observer to estimate the leader's states, a simplified unconstrained tracking control task is established for each follower. After that, event-driven distributed optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> controllers are designed to mitigate the effects of external disturbances, which are obtained from a set of decoupled Hamilton-Jacobi-Isaacs (HJI) equations, where the proposed event-triggered strategy is dynamic. Aiming at solving the HJI equations more efficiently, an event-based adaptive dynamic programming (ADP) learning algorithm applying only critic neural networks (NNs) is developed. And the critic NN weights are convergent by using stored data under finite excitation condition. Finally, the validity of the developed control scheme is demonstrated by multiple single-link robot arm systems.