Nonlinear Separation Research Articles

Modelling multivariate spatio-temporal data with identifiable variational autoencoders

Modelling multivariate spatio-temporal data with complex dependency structures is a challenging task but can be simplified by assuming that the original variables are generated from independent latent components. If these components are found, they can be modelled univariately. Blind source separation aims to recover the latent components by estimating the unknown linear or nonlinear unmixing transformation based on the observed data only. In this paper, we extend recently introduced identifiable variational autoencoder to the nonlinear nonstationary spatio-temporal blind source separation setting and demonstrate its performance using comprehensive simulation studies. Additionally, we introduce two alternative methods for the latent dimension estimation, which is a crucial task in order to obtain the correct latent representation. Finally, we illustrate the proposed methods using a meteorological application, where we estimate the latent dimension and the latent components, interpret the components, and show how nonstationarity can be accounted and prediction accuracy can be improved by using the proposed nonlinear blind source separation method as a preprocessing method.

Effects of nonlinearity on the crest shape of extreme irregular sea waves: Nonlinear harmonic separation and analysis

This work highlights the effects of nonlinearity on the crest shape of extreme directional water wave events in infinite and finite water depths. HOS-ocean, a High-Order Spectral code developed for solving the deterministic propagation of nonlinear wavefields in open ocean [Ducrozet et al., “HOS-ocean: Open-source solver for nonlinear waves in open ocean based on High-Order Spectral method,” Comput. Phys. Commun. 203, 245–254 (2016)], is used for comparisons with linear simulations. Nonlinear wave harmonics were extracted combining and extending previous methods [Fitzgerald et al., “Phase manipulation and the harmonic components of ringing forces on a surface-piercing column,” Proc. R. Soc. A 470, 20130847 (2014) and Hann et al., “A new set of focused wave linear combinations to extract non-linear wave harmonics,” in Proceedings of 29th International Workshop on Water Waves and Floating Bodies, 2014], showing the contribution of various orders of nonlinearity. The work shows that “walls of water,” [Adcock et al., “Nonlinear dynamics of wave-groups in random seas: Unexpected walls of water in the open ocean,” Proc. R. Soc. A 471, 20150660 (2015) and Adcock et al., “On the shape of large wave-groups on deep water—The influence of bandwidth and spreading,” Phys. Fluids 28, 106601 (2016)], a significant increase in the crest width, are also formulated in finite water depths. Mainly responsible for this is the first order harmonic, with significant energy transfers away from components propagating at an angle, which are more pronounced in finite water depths. As nonlinearity increases, higher order harmonics (>second) become, as expected, more significant. In deep water, rapid energy transfers lead to a broadening of the spectrum which is reflected in the increase in the first order amplitude sum and hence increased crest elevations at the point of the large event. However, in finite water depths, energy transfers are gradually leading to a narrowing of the spectrum around the spectral peak and to a general broadening of the spectrum at the higher harmonics; reflected in the significant decrease in the first order amplitude sum and hence a decrease in crest elevations at the point of the large event, also aided by the larger increase in the out-of-phase difference terms (zeroth harmonic).

Hydrodynamic performance of a high-Speed ship in waves using a fully nonlinear wave separation method

ABSTRACT A fully nonlinear time-domain simulation of a ship navigating in waves at high speed is realised by proposing a domain-split wave separation method. In the proposed method, a large distorted area of the free surface near the ship is split, on which the disturbed wave is separated by subtracting the incident wave from the total wave. For the rest of the free surface, the disturbed wave is traced by retaining the higher-order components. The present method is capable to simulate the strongly nonlinear interactions between the ship and waves, and can avoid unnecessary spurious waves. The present results are verified through comparison with experimental data. The steady VBM by navigation reaches its peak when the wavelength of the generated wave equals the ship length at the critical Froude number. The hydrodynamic behaviours of the S175 ship navigating in waves at this critical speed are investigated.

Predictably manipulating photoreceptor light responses to reveal their role in downstream visual responses.

Computation in neural circuits relies on the judicious use of nonlinear circuit components. In many cases, multiple nonlinear components work collectively to control circuit outputs. Separating the contributions of these different components is difficult, and this limits our understanding of the mechanistic basis of many important computations. Here, we introduce a tool that permits the design of light stimuli that predictably alter rod and cone phototransduction currents - including stimuli that compensate for nonlinear properties such as light adaptation. This tool, based on well-established models for the rod and cone phototransduction cascade, permits the separation of nonlinearities in phototransduction from those in downstream circuits. This will allow, for example, direct tests of how adaptation in rod and cone phototransduction affects downstream visual signals and perception.

Spatiotemporal Transformation-Based Neural Network With Interpretable Structure for Modeling Distributed Parameter Systems.

Many industrial processes can be described by distributed parameter systems (DPSs) governed by partial differential equations (PDEs). In this research, a spatiotemporal network is proposed for DPS modeling without any process knowledge. Since traditional linear modeling methods may not work well for nonlinear DPSs, the proposed method considers the nonlinear space-time separation, which is transformed into a Lagrange dual optimization problem under the orthogonal constraint. The optimization problem can be solved by the proposed neural network with good structural interpretability. The spatial construction method is employed to derive the continuous spatial basis functions (SBFs) based on the discrete spatial features. The nonlinear temporal model is derived by the Gaussian process regression (GPR). Benefiting from spatial construction and GPR, the proposed method enables spatially continuous modeling and provides a reliable output range under the given confidence level. Experiments on a catalytic reaction process and a battery thermal process demonstrate the effectiveness and superiority of the proposed method.

A kinetic Monte Carlo approach for Boolean logic functionality in gold nanoparticle networks

Nanoparticles interconnected by insulating organic molecules exhibit nonlinear switching behavior at low temperatures. By assembling these switches into a network and manipulating charge transport dynamics through surrounding electrodes, the network can be reconfigurably functionalized to act as any Boolean logic gate. This work introduces a kinetic Monte Carlo-based simulation tool, applying established principles of single electronics to model charge transport dynamics in nanoparticle networks. We functionalize nanoparticle networks as Boolean logic gates and assess their quality using a fitness function. Based on the definition of fitness, we derive new metrics to quantify essential nonlinear properties of the network, including negative differential resistance and nonlinear separability. These nonlinear properties are crucial not only for functionalizing the network as Boolean logic gates but also when our networks are functionalized for brain-inspired computing applications in the future. We address fundamental questions about the dependence of fitness and nonlinear properties on system size, number of surrounding electrodes, and electrode positioning. We assert the overall benefit of having more electrodes, with proximity to the network’s output being pivotal for functionality and nonlinearity. Additionally, we demonstrate an optimal system size and argue for breaking symmetry in electrode positioning to favor nonlinear properties.

Nonlinear strict cone separation theorems in real normed spaces

Nonlinear strict cone separation theorems in real normed spaces

Applicability Of Reflection Separation Algorithms To Nonlinear Irregular Waves Over Sloping Foreshores

In hydraulic model tests, it is common practice to relate the response of the tested structure to the incident wave parameters at the toe. Estimation of the incident wave parameters at the toe is thus an essential part of the analysis of hydraulic model testing. In many cases, the design conditions at the toe are given by waves that are highly nonlinear or even depth limited. Modelling such conditions requires reproducing the prototype foreshore slope in the model. The present paper provide guidelines on the accuracy of a nonlinear reflection separation algorithm when applied to nonlinear waves over sloping foreshores. A simple methodology has been established to estimate the expected errors on the incident wave parameters.

Nonlinear dynamic separation characteristics of friction pair and experimental analysis

This paper aims to reduce friction pair erosion of the clutch in the case of continuous shift; the dynamic separation process of the friction pair is investigated. The temperature of the friction pair, friction torque, and separation speed in the separation process are taken as the research objects, and the dynamics simulation model and finite element thermal coupling simulation model of the clutch separation process are established. The nonlinear dynamic separation characteristics of the friction pair are investigated by comparing and analyzing the effects of control parameters such as rotational speed difference, damping ratio, and lubricant viscosity on the friction torque, friction pair separation speed, separation gap, and contact stress during the separation process. The gap recovery coefficient is proposed as a response indicator for observing the separation process in response to the inability to observe the nonlinear dynamic motion of the friction pair during the separation process and to measure the end time of the separation. Finally, the clutch was subjected to a separation test. The results show that the proposed gap recovery coefficient accurately describes the separation process. The simulation model can simulate the clutch's separation and predict the trend of separation parameters.

Nonlinear Mixture Signal Separation With the Extended Slow Feature Analysis (xSFA) in Fiber-Optic Distributed Acoustic Sensor (DAS)

Nonlinear Mixture Signal Separation With the Extended Slow Feature Analysis (xSFA) in Fiber-Optic Distributed Acoustic Sensor (DAS)

Predictive functional control for separation processes by liquid-liquid extraction

A separation process by liquid-liquid extraction is a well-known and widespread industrial technology implemented to quantitatively recover valuable chemical elements. In the nuclear industry, such processes have been used for decades to recover uranium and plutonium from spent fuel. The process is non-linear and time constants vary over a wide range. Former studies on a simplified model showed linear controllers such as PID were not adapted to regulate these separation processes. The objective of this study is to propose process monitoring by using available physical models within the PAREX code and to validate the feasibility to monitor a separation process by using directly the PAREX code as a black box. The Predictive Functional Control (PFC) command law manages to monitor non-linear separation processes by liquid-liquid extraction, when using an existing physical model implemented in the PAREX code. An online alignment of the model on process values is necessary to keep the model sufficiently representative to predict the future behaviour of the process. As a reference benchmark, the PID control loop is also simulated with the physical model. The PFC and PID regulations are compared to evaluate the gain of using physical models implemented in the PAREX code. A simulation tool has been developed to implement the PID and Predictive Functional Control (PFC) controllers for separation processes by liquid-liquid extraction. The PFC command law manages to monitor non-linear separation processes, when using a physical model connected to the PAREX code. Even if the PID controller may be locally more efficient, the great strength of the PFC controller is to enable good performances on wider operating conditions, with an easier parametrization. The PFC algorithm is a mean to deal with the process characteristic features, like non-linearity and time constant change. The PFC controller appears to be a good candidate for experimental tests. A mid-term objective is to include the state estimator tool in the control loop to consolidate the controlled variable measurements. These developments may be regarded as an add-on module in a digital factory concept. Results shown in this article are only from simulation. For the sake of data confidentiality, studies with the PAREX code cannot be published and numerical parameters of the process are normalized. These simulations will be validated during further experimental tests.

Nonlinear Cone Separation Theorems in Real Topological Linear Spaces

Nonlinear Cone Separation Theorems in Real Topological Linear Spaces

Defect and interface/surface engineering synergistically modulated electron transfer and nonlinear absorption properties in MoX2 (X = Se, S, Te)@ZnO heterojunction.

Systematic interface and defect engineering strategies have been demonstrated to be an effective way to modulate the electron transfer and nonlinear absorption properties in semiconductor heterojunctions. However, the role played by defects and interfacial strain in electron transfer at the interface of the MoX2 (X = Se, S, Te)@ZnO heterojunction remains poorly understood. Herein, using the MoX2@ZnO heterojunction, we reveal that vacancies play a critical role in the interfacial electron transfer of heterojunctions. Specifically, we present the defect and interface engineering of the MoX2@ZnO heterojunction for controlled charge transfer and electron excitation-relaxation. The experimental characterization combined with first-principles calculations showed that the presence of defects promoted the transport of photogenerated carriers at the heterojunction interface, thereby inhibiting their rapid recombination. The DFT calculation confirmed that the electron band structure, density of states and charge density distribution in the system changed after the formation of Mo-O bonds. On the basis of defects and interfacial stress and the effective charge transfer, the MoX2@ZnO heterojunction exhibited excellent excitation and emission behaviors. The nonlinear optical regulation behavior of TMDs is expected to be realized with the help of the defects and interface/surface synergistically modulated effect of ZnO nanoparticles. The local strain generation on the MoX2@ZnO heterojunction boundary provides a new method for the design of new heterogeneous materials and will be of great significance to investigate the contact physical behavior and application of metals and two-dimensional (2D) semiconductors. This work provides some inspiration for the construction of heterojunctions with rich defects and surface/interface charge transfer channels to promote tunable electron transfer dynamics, thereby achieving a good nonlinear optical conversion efficiency and efficient charge separation in optoelectronic functional materials.

Forecasting the Magnitude Category Based on The Flores Sea Earthquake

Earthquakes are a phenomenon that is still a mystery in terms of predicting events, one of which is the magnitude. As technology develops, there are many algorithms that can be used as approaches in earthquake forecasting. In the context of magnitude forecasting, the application of GaussianNB, Random Forest, and SVM has the potential to reveal these patterns and relationships in the data. With the six main phases of this research, namely data acquisition, data pre-processing, feature selection, model training, forecast result evaluation, and performance analysis, this study is expected to contribute to the development of more accurate and effective earthquake forecasting methods. From these results we first obtain the result that the GaussianNB model has a relatively simple and fast method in training its model. However, the weakness lies in the assumption of a Gaussian distribution, which may not always suit the complex and diverse characteristics of earthquake data. Second, Random Forest, this method can increase accuracy and overcome the overfitting problem that occurs when forecasting magnitudes. In contrast to GaussianNB, it tends to result in models with greater complexity and requires more time to compute. The third option is SVM, which has both benefits and drawbacks that must be taken into account. The capacity of SVM to separate data that has both linear and nonlinear separation is one of its key advantages; nevertheless, the main drawback is that it is sensitive to hyperparameter adjustments.

A hybrid rotordynamic modeling method for a rotor system with flexible foundation and nonlinear support force: Numerical and experimental investigation

The dynamic characteristics of a flexible foundation would greatly affect the dynamic behavior of the rotor system. In this paper, a hybrid dynamic model method in time domain combines the finite element (FE) method and the subspace-based identification method to model a rotor system with the consideration of a flexible foundation and nonlinear support forces. The state-space model of flexible foundation is identified by the subspace state-space system identification algorithm with measured frequency response functions (FRFs). To solve the calculation problem of the hybrid dynamic model in time domain, a general algorithm named the hybrid model fusion solution (HMFS) method is proposed, which combines the linear and nonlinear nodes separation method used in the FE model and the trapezoidal rule used in the state-space model, improving the calculation efficiency of solving transient response with nonlinear forces. Simulations for the hybrid dynamic model under constant speed and speed-up cases were carried out, resulting that the dynamic characteristics of the entire system can be represented when the nonlinear factors of rolling bearings and gravity were also taken into consideration. Additionally, owe to the consideration of tested dynamic behaviors of flexible base, experimental results in the laboratory test rig are well agreed with the numerical ones under two different test configurations. The investigation provides a complete modeling and highly efficient solution framework for the rotor system with a flexible foundation and nonlinear rolling bearings, with the abilities of further consideration of more nonlinear components such as squeeze film dampers and rubbing forces.

Poster Session II: Light-adaptation clamp: A tool to predictably manipulate photoreceptor light responses.

Computation in neural circuits relies on judicious use of nonlinear circuit components. In many cases, multiple nonlinear components work collectively to control circuit outputs. Separating the contributions of these different components is difficult, and this hampers our understanding of the mechanistic basis of many important computations. Here, we introduce a tool that permits the design of light stimuli that predictably alter rod and cone phototransduction currents - including the compensation for nonlinear properties such as light adaptation. This tool, based on well-established models for the rod and cone phototransduction cascade, permits the separation of nonlinearities in phototransduction from those in downstream circuits. This will allow, for example, direct tests of the role of photoreceptor adaptation in downstream visual signals or in perception.

Competitive Perceptrons: The Relevance of Modeling New Bioinspired Properties Such as Intrinsic Plasticity, Metaplasticity, and Lateral Inhibition of Rate-Coding Artificial Neurons.

This article supports the relevance of modeling new bioinspired properties in rate-coding artificial neurons, focusing on fundamental neural properties rarely implemented thus far in artificial neurons, such as intrinsic plasticity, the metaplasticity of synaptic strength, and the lateral inhibition of neighborhood neurons. All these properties are bioinspired through empirical models developed by neurologists, and this in turn contributes to taking perceptrons to a higher potential level. Metaplasticity and intrinsic plasticity are different levels of plasticity and are believed by neurologists to have fundamental roles in memory and learning and therefore in the performance of neurons. Assuming that information about stimuli is contained in the firing rate of the connections among biological neurons, several models of artificial implementation have been tested. Analyzing their results and comparing them with learning and performance of state-of-the-art models, relevant advances are made in the context of the developing Industrial Revolution 4.0 based on advances in Machine Learning, and they may even initiate a new generation of artificial neural networks. As an example, a single-layer perceptron that includes the proposed advances is successfully trained to perform the XOR function, called the Competitive Perceptron, which is a new bioinspired artificial neuronal model with the potential of non-linear separability, continuous learning, and scalability, which is suitable to build efficient Deep Networks, overcoming the basic limitations of traditional perceptrons that have challenged scientists for half a century.

Bilinear differential game for competitive advertising with stochastic disturbance and abrupt impact

The estimated spending on online advertising worldwide will reach $520 billion during 2023, almost double compared with that in 2019. Due to the conjunction of huge expenditure and latent inefficiencies, competitive advertising has always been occupying a front-and-center place in marketing, among which research modeled as bilinear differential game is one of the most important. However, by the intrinsic difficulties of mathematics, there is no extant research to augment the analysis with Markov jump process, which is of particular significance to abrupt product-harm crisis or promotion interactions. Motivated by this requirement, iterative algorithm with convergence proof is developed to approximate bilinearity. Kalman filter and nonlinear separation theorem, which enable noise-contaminated sales data for analysis in the partial observation, are also introduce to hone in more actionable and focused in real business. The Simulink modeling in this paper provides a straightforward tool for rapid prototyping of these complex, time-varying, multilayer systems. The simulation model proposed allows automatically exploring competitions and finding the most efficient strategies. Moreover, six application examples, resulting from the permutations of four encounters with different time durations and abrupt impacts, have discovered eight implications. They not only complement the existing work on crisis, but also generalize to promotion, which imply that managers should anticipate the sales bump and optimally increase ad spending ex ante. Most importantly, they have revealed a number of new legal, advertising, competition and partly counterintuitive insights for those struggling to develop successful advertising strategies.

KIC 9845907: A δ Scuti Star with the First Overtone as the Dominant Frequency and with Many Equidistant Structures in Its Spectrum

In this paper, we present an analysis of the pulsating behavior of Kepler target KIC 9845907. Using the data from Kepler, we detected 85 significant frequencies, including the first overtone f 1 = 17.597 day−1 as the dominant frequency, the non-radial independent frequency f 3 = 31.428 day−1 (ℓ = 1), as well as two modulation terms f m1 = 0.065 day−1 and f m2 = 1.693 day−1. We found fourteen pairs of triplet structures with f m1 or f m2, four pairs of which can further form quintuplet structures. We note these are the most intriguing features discovered in this study and they were recognized for the first time in δ Scuti stars. We discussed several possible explanations, i.e., beating, the Blazhko effect, combination mode hypothesis, nonlinear mode coupling, large separation, and stellar rotational splitting for these equidistant structures. Our asteroseismic models indicate this modulation with f m1 might be related to the rotational splitting. The study of more δ Scuti stars with triplet and/or quintuplet structures using high-precision space photometry would be helpful to further explore its origin.

Entire Life Theoretical Model of Limestone under Unequal Cyclic Loading Based on the Expanding Theory of Thermodynamic System Analysis

Breakage, Helmholtz free energy, and nonlinearity are involved in many fundamental phenomena of complex systems across natural sciences. However, a mathematical equation that can express the entire life cycle of complex natural objects (such as rock-like quasi-brittle materials) is lacking. We expand the material body system to an isolated compound thermodynamic system to establish an innovative theoretical model induced by coupling nonlinear separation of Helmholtz free energy and breakage evolution that can be used to express the extreme entire life model of rock under unequal amplitude loading and unloading cycle. We gain crucial insights into the life essence of limestone, which is termed “Negative Dissipation.” This study first shows that the change in the mechanical properties of quasi-brittle materials caused by the timely evolution of breakage can be represented by the nonlinear separation of Helmholtz free energy and negative dissipation. An analytical solution to the nonlinear separation variables of Helmholtz free energy is provided by combining the method of solving nonlinear partial differential equations in mathematics and thermodynamic law. An analytical solution of Helmholtz free energy considering nonlinearity and breakage is proposed, and an equation that can reflect the constitutive mechanics law of the entire life cycle of rock in the theoretical model is presented. Theoretical results are consistent with the experimental data obtained from limestone samples with different prefabricated cracks. This original study provides a theoretical foundation for the life model of complex natural objects for nonlinear breakage and an early warning investigation of rocks under various unprecedented conditions.Practical ApplicationsThis study first found that the change in the mechanical properties of complex natural objects caused by the timely evolution of breakage can be represented by the nonlinear separation of Helmholtz free energy. We establish an innovative theoretical model induced by coupling nonlinear separation of Helmholtz free energy and breakage evolution. The innovative theory includes three parts: (1) an analytical solution to the nonlinear separation variables of Helmholtz free energy, (2) an analytical solution of Helmholtz free energy considering nonlinearity and breakage, and (3) an equation of the theoretical model that can reflect the constitutive mechanics’ law of the entire life of quasi-brittle rocks is presented for the first time. This original research result provides the foundation for a more in-depth life cycle of quasi-brittle rocks to develop the theoretical basis for the nonlinear breakage and early warning research of materials under various unprecedented conditions. We report a route to material microstructure composition, which may open an alternative pathway to quasi-brittle materials, which may, in turn, open a door into the mysterious world of science.