Nonlinear Integration Research Articles

Rapid invisible frequency tagging reveals nonlinear integration of auditory and visual information.

During communication in real‐life settings, the brain integrates information from auditory and visual modalities to form a unified percept of our environment. In the current magnetoencephalography (MEG) study, we used rapid invisible frequency tagging (RIFT) to generate steady‐state evoked fields and investigated the integration of audiovisual information in a semantic context. We presented participants with videos of an actress uttering action verbs (auditory; tagged at 61 Hz) accompanied by a gesture (visual; tagged at 68 Hz, using a projector with a 1,440 Hz refresh rate). Integration difficulty was manipulated by lower‐order auditory factors (clear/degraded speech) and higher‐order visual factors (congruent/incongruent gesture). We identified MEG spectral peaks at the individual (61/68 Hz) tagging frequencies. We furthermore observed a peak at the intermodulation frequency of the auditory and visually tagged signals (fvisual − fauditory = 7 Hz), specifically when lower‐order integration was easiest because signal quality was optimal. This intermodulation peak is a signature of nonlinear audiovisual integration, and was strongest in left inferior frontal gyrus and left temporal regions; areas known to be involved in speech‐gesture integration. The enhanced power at the intermodulation frequency thus reflects the ease of lower‐order audiovisual integration and demonstrates that speech‐gesture information interacts in higher‐order language areas. Furthermore, we provide a proof‐of‐principle of the use of RIFT to study the integration of audiovisual stimuli, in relation to, for instance, semantic context.

A Simple and Accurate Apollo-Trained Neural Network Controller for Mars Atmospheric Entry

We present a new method to design the controller for Mars capsule atmospheric entry using deep neural networks and flight-proven Apollo entry data. The controller is trained to modulate the bank angle with data from the Apollo entry simulations. The neural network controller reproduces the classical Apollo results over a variation of entry state initial conditions. Compared to the Apollo controller as a baseline, the present approach achieves the same level of accuracy for both linear and nonlinear entry dynamics. The Apollo-trained controller is then applied to Mars entry missions. As in Earth environment, the controller achieves the desired level of accuracy for Mars missions using both linear and nonlinear entry dynamics with higher uncertainties in the entry states and the atmospheric density. The deep neural network is only trained with data from Apollo reentry simulation in an Earth model and works in both Earth and Mars environments. It achieves the desired landing accuracy for a Mars capsule. This method works with both linear and nonlinear integration and can generate the bank angle commands in real-time without a prestored trajectory.

Persistence and efficiency of OECD stock markets: linear and nonlinear fractional integration approaches

The analysis of the dynamics of the share price series using the fractional integration technique that accommodates nonlinear deterministic trend based on the Chebyshev polynomials in time is considered in this study. It is important to account for the nonlinear behavior and autoregressive structure of the error disturbance term of the share price indices if correct estimates of the integration order are to be obtained. The findings of this study show that it is important to put the autoregressive order into consideration following the significant effect it imposes on the fractional integration estimates, and there are evidences of nonlinearities in nine countries. The nonlinear effect significantly imparts on the degree of persistence of the nine countries by either inducing more or less persistence. However, it is more profound for Belgium, Japan and Hungary whose share market statuses change from efficient to inefficient, as their d estimates under the linearity case, respectively, fall from 0.9715, 0.9998 and 0.9344 to 0.3230, 0.3112 and 0.8579 under the nonlinearity case. For the sake of policy, these findings have important implications for portfolio management and diversification, investment choices, and policy making and forecast.

Power-efficient neural network with artificial dendrites.

In the nervous system, dendrites, branches of neurons that transmit signals between synapses and soma, play a critical role in processing functions, such as nonlinear integration of postsynaptic signals. The lack of these critical functions in artificial neural networks compromises their performance, for example in terms of flexibility, energy efficiency and the ability to handle complex tasks. Here, by developing artificial dendrites, we experimentally demonstrate a complete neural network fully integrated with synapses, dendrites and soma, implemented using scalable memristor devices. We perform a digit recognition task and simulate a multilayer network using experimentally derived device characteristics. The power consumption is more than three orders of magnitude lower than that of a central processing unit and 70 times lower than that of a typical application-specific integrated circuit chip. This network, equipped with functional dendrites, shows the potential of substantial overall performance improvement, for example by extracting critical information from a noisy background with significantly reduced power consumption and enhanced accuracy.

Vibration reduction of rotating frame structure based on quadratic performance index

An efficient method based on quadratic performance index and Lyapunov's second method is developed for the vibration reduction optimization of frame structure rotating at a constant angular velocity. Four optimization formulations and algorithms are studied for both low and high angular velocity. These formulations consider both linear vs nonlinear dynamic models as well as direct integration and Lypunov method to evaluate performance index. Three numerical examples are presented to compare the effectiveness of the four algorithms. Numerical results show that all the four optimization methods can reduce vibration at low rotating speed and find very similar optimal designs. However, at high rotating speed, dynamic model of rotating structure must consider nonlinear axial strain in order to obtain correct dynamic response. Since the Lyapunov's second method is not applicable for the nonlinear model and the NFTI (nonlinear dynamic model with nonlinear axial strain and time integration) method is very inefficient, the present study develops a perturbation method, linearizes the nonlinear dynamic model and establishes the LNFLA(linearized dynamic model with nonlinear axial strain, the Lyapunov's second method). Numerical examples show the optimization method LNFLA provides an efficient numerical method for vibration reduction of rotating frame structure with both low and high rotating speed.

Speed Control for the Pitching Axis of a Remote Sensing Camera Using an Improved Active Disturbance Rejection Controller

This paper proposes the theoretical framework and the experimental application of an improved active disturbance rejection controller (ADRC) to speed control for the pitching axis of a remote sensing camera. Mechanical model of the pitching axis, mechatronics model of the speed control system for the pitching axis, and speed algorithm model of a permanent magnet synchronous motor are established. Control rates of the extended state observer (ESO) and the nonlinear state error feedback (NSEF) of the traditional ADRC are improved using a new nonlinear function. The nonlinear dynamics, model uncertainty, and external disturbances of the speed control system are extended to a new state, and the improved ESO is implemented to observe this state. The overtime variation of the speed control system is predicted and compensated for in real time using the improved ESO. The nonlinear integration method is adopted to nonlinearly combine the differential and the error differential by the improved NSEF. Subsequently, high-quality control is provided to the system. Simulation and experimental verification for the speed control system for the pitching axis of a remote sensing camera are conducted. Results show the effectiveness of the proposed controller.

Assimilation of radar radial velocity data with the WRF hybrid 4DEnVar system for the prediction of hurricane Ike (2008)

Four dimensional ensemble-variation data assimilation (4DEnVar) is the method that considers the flow dependent background error covariance (BEC) and asynchronous observations throughout the assimilation window, which avoids the maintenance of the adjoint model. The impacts of assimilation of radial velocity (Vr) data using hybrid-4DEnVar for the analyses and forecasts of hurricane Ike are investigated using Weather Research and Forecasting and Data Assimilation model (WRFDA). 4DEnVar is coupled with Ensemble Transform Kalman Filter (ETKF) by updating the ensemble mean by the hybrid scheme and the ensemble perturbations are updated by the ETKF. Single observation tests for typical Jet cast and tropical cyclone (TC) case are conducted before the real hurricane Ike (2008) case. It is found that the analysis increment moves downstream by the end of the assimilation window. The linear propagation represented by the 4DEnVar method is close to the full nonlinear model integration. For the real IKE case, it is found that positive and spiral temperature increments, best track and intensity forecast are found in 4DEnVar experiment, indicating a more realistic thermal structure of hurricane Ike. 3DEnVar and 3DVar-FGAT are limited due to the lack of the BEC description spatially and temporally. 3DVar experiment produces much smoother and weaker increments with cold temperature increments at the hurricane vortex center at lower levels.

Estimation of long-term fatigue damage of fixed substructures using fully-coupled models and non-linear dynamic analysis

Typical industry models for Offshore Wind Turbines with fixed substructures are based on decoupled models between the wind turbine and the substructure. It is proved that the complete dynamic response of the structure can only be captured with coupled models. In this paper a fully-coupled model for Offshore Wind Turbines with jacket support is presented. The computational model allows to obtain an accurate response of the whole structure and the dynamic interaction between all the elements. It also allows to reproduce particular effects such as the aerodynamic damping without the need for artificial damping ratios which would be needed in decoupled models. Typical environmental offshore conditions are integrated in the model and the response of the structure is obtained by means of a non-linear time integration algorithm in order to include the effect of the continuous rotation of the blades. A cost-efficient approach for the determination of fatigue-damage in the joints of the jackets is proposed. It is based on short-time simulations which allow to accurately estimate the long-term damage in general. The estimation shows a good agreement when compared to the damage values obtained by performing the whole time-interval simulation.

Artificial intelligence algorithm for optimal time series data model

In order to solve the limitation of a large number of literatures on the study of modeling, simulation and prediction of time series data, there is no model selection, and a certain model is directly used for analysis. For three types of artificial intelligence models often applied to time series analysis: hidden Markov Carrier model, artificial neural network model and autoregressive moving average model are used to study model selection based on simulation comparison method. The study of nonlinear integration methods, using intelligent system methods to learn the weighting mode, has made the model's generalization ability and the degree is of fit to the sample data have been significantly improved. At the same time, numerical simulations are performed on various models, and the characteristics of the time series generated by various models are investigated. Based on the characteristics, the theory and algorithm of model selection are proposed. The model selection theory and algorithm in this paper is used for empirical analysis. For the artificial intelligence models commonly used in time series analysis such as autoregressive moving average model, artificial neural network model, hidden Markov model, etc., when selecting the research model, the method of simulation comparison can be used. The experimental results show that the time series data generated by various models have different mathematical and physical characteristics, which provide a basis for model selection. At the same time, the selection theory is practical. The model selected by the theory has a good fit and prediction effect. The generation of different models has different mathematical characteristics of time series data, which also provides a basis for selecting models.

Research on Hybrid Wind Speed Prediction System Based on Artificial Intelligence and Double Prediction Scheme

Wind energy analysis and wind speed modeling have a significant impact on wind power generation systems and have attracted significant attention from many researchers in recent decades. Based on the inherent characteristics of wind speed, such as nonlinearity and randomness, the prediction of wind speed is considered to be a challenging task. Previous studies have only considered point prediction or interval measurement of wind speed separately and have not combined these two methods for prediction and analysis. In this study, we developed a novel hybrid wind speed double prediction system comprising a point prediction module and interval prediction module to compensate for the shortcomings of existing research. Regarding point prediction in the developed double prediction system, a novel nonlinear integration method based on a backpropagation network optimized using the multiobjective evolutionary algorithm based on decomposition was successfully implemented to derive the final prediction results, which enable further improvement of the accuracy of point prediction. Based on point prediction results, we propose an interval prediction method that constructs different intervals according to the classification of different data features via fuzzy clustering, which provides reliable interval prediction results. The experimental results demonstrate that the proposed system outperforms existing methods in engineering applications and can be used as an effective technology for power system planning.

A Hybrid Double Forecasting System of Short Term Power Load Based on Swarm Intelligence and Nonlinear Integration Mechanism

Accurate and reliable power load forecasting not only takes an important place in management and steady running of smart grid, but also has environmental benefits and economic dividends. Accurate load point forecasting can provide a guarantee for the daily operation of the power grid, and effective interval forecasting can further quantify the uncertainty of power load on this basis to provide dependable and precise load information. However, most of the previous work focuses on the deterministic point prediction of power load and rarely considers the interval prediction of power load, which makes the prediction of power load not comprehensive. In this study, a new double hybrid load forecasting system including point forecasting module and interval forecasting module is developed, which can make up for the shortcomings of incomplete analysis for the existing research. The point forecasting module adopts a nonlinear integration mechanism based on Back Propagation (BP) network optimized by Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D) to improve the accuracy of point prediction. A fuzzy clustering interval prediction method based on different data feature classification is successfully proposed which provides an effective tool for load uncertainty analysis. The experiment results show that the system not only has a good effect in accurately predicting power load, but also can analyze the uncertainty of the power load, which can be used as an effective technology of power system planning.

Effects of synaptic integration on the dynamics and computational performance of spiking neural network

Neurons in the brain receive thousands of synaptic inputs from other neurons. This afferent information is processed by neurons through synaptic integration, which is an important information processing mechanism in biological neural networks. Synaptic currents integrated from spiking trains of presynaptic neurons have complex nonlinear dynamics which endow neurons with significant computational abilities. However, in many computational studies of neural networks, external input currents are often simply taken as a direct current that is static. In this paper, the influences of synaptic and noise external currents on the dynamics of spiking neural network and its computational capability have been investigated in detail. Our results show that due to the nonlinear synaptic integration, both of fast and slow excitatory synaptic currents have much more complex and oscillatory fluctuations than the noise current with the same average intensity. Thus network driven by synaptic external current exhibits remarkably more complex dynamics than that driven by noise external current. Interestingly, the enhancement of network activity is beneficial for information transmission, which is further supported by two computational tasks conducted on the liquid state machine (LSM) network. LSM with synaptic external current displays considerably better performance in both nonlinear fitting and pattern classification than that with noise external current. Synaptic integration can significantly enhance the entropy of activity patterns and computational performance of LSM. Our results demonstrate that the complex dynamics of nonlinear synaptic integration play a critical role in the computational abilities of neural networks and should be more broadly considered in the modelling studies of spiking neural networks.

Quantification of heavy metal pollution for environmental assessment of soil condition

The aim of this study was to quantify heavy metal pollution for environmental assessment of soil quality using a flexible approach based on multivariate analysis. The study was conducted using 241 soil samples collected from agricultural, urban and rangeland areas in northwestern Iran. The heavy metals causing soil pollution (SP) in the study area were determined. The efficiency of principal component analysis (PCA) and discriminate analysis (DA) were compared to identify the critical heavy metals causing SP. Fourteen soil pollution indices were developed using non-linear and linear scoring equations and different integration methods. The indices were validated using the integrated pollution and potential ecological risk indices and by comparing their ability to detect soil pollution risk levels. Chromium (Cr), lead (Pb), Zinc (Zn) and copper (Cu) were identified as the significant pollutant elements using PCA, and the main pollutant elements identified using DA comprised cadmium (Cd), Zn and Pb. DA yielded a better data set for indexing SP and indicated high pollution risks for Cd > Pb > Zn. Sources of heavy metals were reliably identified using PCA, variation assessment and interrelationship evaluation of soil variables. Cr, nickel (Ni) and cobalt (Co) were found to have geogenic sources, and anthropogenic sources controlled the accumulation of Pb, Zn, Cd and Cu in soil. Linear function and additive integration were the best scoring and integrating methods for indexing HMP. The multivariate analysis provided a reliable and rapid method for indexing and mapping soil HMP.

Multi-domain stability and modal analysis applied to Gas Foil Bearings: Three approaches

The dynamic characteristics of rotors supported by Gas Foil Bearings (GFBs) are commonly assessed using linear force coefficients, which are usually derived from an analytical perturbation in combination with an implicit compliance model. This remains common practice even though discrepancies have been reported between the Onset Speed of Instability (OSI) predicted using such linear coefficients and observations from non-linear time integration. For the first time, the present paper pinpoints the root cause of this discrepancy by demonstrating an extended perturbation, akin to that used for tilting pad journal bearings, to predict exactly the same OSIs as obtained from an eigenvalue analysis based on the Jacobian of the full non-linear system of equations. To demonstrate this, the OSIs predicted using (i) the classical perturbation, (ii) the extended perturbation, and (iii) the Jacobian eigenvalues are compared over a range of compliance levels covering essentially rigid bearings to modern heavily loaded industrial GFBs. Using carefully aligned implementations, the deficiency of the classical method is demonstrated to increase with the compliance level (up to 13% for the benchmark case), while the extended perturbation provides OSIs in agreement with the Jacobian eigenvalues for all compliance levels. Furthermore, the mode shapes attainable from the three approaches, encompassing only the rotor, the rotor and foil, and the rotor, foil and pressure respectively, are compared.

EVALUATION OF RIGID BODY SLIDING ANALYSIS FOR MODULAR STEEL STRUCTURES SUBJECTED TO BLAST LOADING

Blast resistant modular steel (BRMS) buildings are prefabricated cost-effective and explosion-proof structures used to shelter personal near hazardous-material handling or storage facilities, in facilities handling high-pressure processes, and within designed blast zones in mining, petrochemical, and military industries. Typically, BRMS buildings are designed to be fixed (anchored) to their foundation. However, this design approach can result in very large anchorage and foundation reactions, which result in very large and high-cost foundations. Therefore, an alternative foundation approach which minimize foundation reactions and known as unanchored or free-to-slide foundation has recently attracted much attention for BRMS buildings. In this study, dynamic behavior of a typical BRMS building under blast loading with unanchored foundation was determined using 3D nonlinear dynamic finite element and a simplified numerical analysis method. The developed numerical analysis method is based on nonlinear numerical integration scheme, and it was verified using the finite element results. Applicability of the proposed numerical analysis method was evaluated using finite element results for a typical unachored BRMS building subjected to blast loads. Several values of coefficient of friction between the foundation and BRMS building were considered. The computed building sliding, horizontal velocity, acceleration, and horizontal foundation reaction histories were used to evaluate applicability of the proposed numerical method. The overall results show that the proposed simple numerical analysis method based on rigid-body dynamics is suitable to predict building sliding and sliding velocity, but unconservative in terms of foundation vertical reaction and horizontal acceleration.

A Simplified Model for Investigation on the Effects of Seismic Actions on Masonry Arch Bridges

Masonry bridges are vulnerable structural systems to the ground motion excitation and their survival in case of such incidents has to be studied in detail. In this work, a simplified model for dynamic analysis of masonry bridges based on rocking motion of rigid blocks is proposed. Using this model, nonlinear time integration analysis on these bridges can be done with ease and in a short time. The proposed model was used in evaluation of seismic performances of a monumental masonry bridge subjected to both horizontal and vertical seismic actions. The study shows the importance of vertical component of ground motion in determination of internal forces and shear sliding deformation at bottom of the bridge’s pier. The proposed model has also shown its ability in defining the effectiveness of a seismic retrofit approach for the same bridge system in a comparative study. According to this investigation, seismic performances of the bridge can be significantly improved in case of adding ductility to its deck assembly.

Synaptic Clustering and Memory Formation.

In the study of memory engrams, synaptic memory allocation is a newly emerged theme that focuses on how specific synapses are engaged in the storage of a given memory. Cumulating evidence from imaging and molecular experiments indicates that the recruitment of synapses that participate in the encoding and expression of memory is neither random nor uniform. A hallmark observation is the emergence of groups of synapses that share similar response properties and/or similar input properties and are located within a stretch of a dendritic branch. This grouping of synapses has been termed “synapse clustering” and has been shown to emerge in many different memory-related paradigms, as well as in in vitro studies. The clustering of synapses may emerge from synapses receiving similar input, or via many processes which allow for cross-talk between nearby synapses within a dendritic branch, leading to cooperative plasticity. Clustered synapses can act in concert to maximally exploit the nonlinear integration potential of the dendritic branches in which they reside. Their main contribution is to facilitate the induction of dendritic spikes and dendritic plateau potentials, which provide advanced computational and memory-related capabilities to dendrites and single neurons. This review focuses on recent evidence which investigates the role of synapse clustering in dendritic integration, sensory perception, learning, and memory as well as brain dysfunction. We also discuss recent theoretical work which explores the computational advantages provided by synapse clustering, leading to novel and revised theories of memory. As an eminent phenomenon during memory allocation, synapse clustering both shapes memory engrams and is also shaped by the parallel plasticity mechanisms upon which it relies.

Passing the Message: Representation Transfer in Modular Balanced Networks.

Neurobiological systems rely on hierarchical and modular architectures to carry out intricate computations using minimal resources. A prerequisite for such systems to operate adequately is the capability to reliably and efficiently transfer information across multiple modules. Here, we study the features enabling a robust transfer of stimulus representations in modular networks of spiking neurons, tuned to operate in a balanced regime. To capitalize on the complex, transient dynamics that such networks exhibit during active processing, we apply reservoir computing principles and probe the systems' computational efficacy with specific tasks. Focusing on the comparison of random feed-forward connectivity and biologically inspired topographic maps, we find that, in a sequential set-up, structured projections between the modules are strictly necessary for information to propagate accurately to deeper modules. Such mappings not only improve computational performance and efficiency, they also reduce response variability, increase robustness against interference effects, and boost memory capacity. We further investigate how information from two separate input streams is integrated and demonstrate that it is more advantageous to perform non-linear computations on the input locally, within a given module, and subsequently transfer the result downstream, rather than transferring intermediate information and performing the computation downstream. Depending on how information is integrated early on in the system, the networks achieve similar task-performance using different strategies, indicating that the dimensionality of the neural responses does not necessarily correlate with nonlinear integration, as predicted by previous studies. These findings highlight a key role of topographic maps in supporting fast, robust, and accurate neural communication over longer distances. Given the prevalence of such structural feature, particularly in the sensory systems, elucidating their functional purpose remains an important challenge toward which this work provides relevant, new insights. At the same time, these results shed new light on important requirements for designing functional hierarchical spiking networks.

A tutorial-driven introduction to the parallel finite element library FEMPAR v1.0.0

This work is a user guide to the FEMPAR scientific software library. FEMPAR is an open-source object-oriented framework for the simulation of partial differential equations (PDEs) using finite element methods on distributed-memory platforms. It provides a rich set of tools for numerical discretization and built-in scalable solvers for the resulting linear systems of equations. An application expert that wants to simulate a PDE-governed problem has to extend the framework with a description of the weak form of the PDE at hand (and additional perturbation terms for non-conforming approximations). We show how to use the library by going through three different tutorials. The first tutorial simulates a linear PDE (Poisson equation) in a serial environment for a structured mesh using both continuous and discontinuous Galerkin finite element methods. The second tutorial extends it with adaptive mesh refinement on octree meshes. The third tutorial is a distributed-memory version of the previous one that combines a scalable octree handler and a scalable domain decomposition solver. The exposition is restricted to linear PDEs and simple geometries to keep it concise. The interested user can dive into more tutorials available in the FEMPAR public repository to learn about further capabilities of the library, e.g., nonlinear PDEs and nonlinear solvers, time integration, multi-field PDEs, block preconditioning, or unstructured mesh handling. Program summaryProgram Title:FEMPARProgram Files doi:http://dx.doi.org/10.17632/dtx487wp57.1Licensing provisions: GNU General Public License 3Programming language: MPI, Fortran2003/2008 (Object-Oriented Programming features)Nature of problem: Computational simulation of a broad range of large-scale application problems governed by Partial Differential EquationsSolution method: Arbitrary-order grad-, curl-, and div-conforming finite elements on n-cube and n-simplex meshes. Continuous and Discontinuous Galerkin FEM. Adaptive Mesh Refinement and Coarsening via forests-of-octrees. Diagonally Implicit Runge–Kutta time integrators. Newton–Raphson linearization. Block preconditioning for multiphysics applications. Multilevel Balancing Domain Decomposition by Constraints preconditioning. Krylov subspace iterative solvers. Sparse direct solvers.Additional comments: Program Github repository https://github.com/fempar/fempar Program website http://www.fempar.org

Numerical and analytical investigation of the effects of dimensional parameters on mutual inductance of helical-shaped YBCO superconducting variable inductors

High-temperature superconducting coils (HTSCs) have an applied feature in reduction of power air-core inductors losses. This paper presents an analytical method for calculating the mutual inductance of an air-core superconducting variable inductor and investigates the impact of dimensional parameters on the mutual inductance. The proposed method is based on changing the position of a movable inner coil inside an outer coil. A variable inductor may consist of two finite length coaxial helical-shaped coils that their mutual inductance can be changed to achieve a variable inductance. The proposed variable inductor may be further optimized for high-power and high frequency applications and has the potential to be realized in matching circuits technology. To calculate the mutual inductance, a direct and fast method has been employed to solve nonlinear double integration of Neumann’s formula along the current-carrying path that offers two advantages. Firstly, it reduces the computational time comparing to the area-integration methods, especially for complex geometries. Secondly, it can split coil turns accurately as well as other design details that violate axial symmetry. In the end, the Finite Element (FEM) and the loop model methods have been used to verify the results of the analytical method. The analytical and FEM results showed an error of less than 0.064% in the least compatible case.