A Novel Radial Basis Function Neural Network with High Generalization Performance for Nonlinear Process Modelling

A radial basis function neural network (RBFNN), with a strong function approximation ability, was proven to be an effective tool for nonlinear process modeling. However, in many instances, the sample set is limited and the model evaluation error is fixed, which makes it very difficult to construct an optimal network structure to ensure the generalization ability of the established nonlinear process model. To solve this problem, a novel RBFNN with a high generation performance (RBFNN-GP), is proposed in this paper. The proposed RBFNN-GP consists of three contributions. First, a local generalization error bound, introducing the sample mean and variance, is developed to acquire a small error bound to reduce the range of error. Second, the self-organizing structure method, based on a generalization error bound and network sensitivity, is established to obtain a suitable number of neurons to improve the generalization ability. Third, the convergence of this proposed RBFNN-GP is proved theoretically in the case of structure fixation and structure adjustment. Finally, the performance of the proposed RBFNN-GP is compared with some popular algorithms, using two numerical simulations and a practical application. The comparison results verified the effectiveness of RBFNN-GP.

Simulation study on parametric dependence of whistler-mode hiss generation in the plasmasphere

We conduct electromagnetic particle simulations to examine the applicability of nonlinear wave growth theory to the generation process of plasmaspheric hiss. We firstly vary the gradient of the background magnetic field from a realistic model to a rather steep gradient model. Under such variation, the threshold amplitude in the nonlinear theory increases quickly and the overlap between threshold and optimum amplitude disappears correspondingly, the nonlinear process is suppressed. In the simulations, as we enlarge the gradient coefficient of the background magnetic field, waves generated near the equator do not grow through propagation. By examining the range of suitable values of inhomogeneity factor S (i.e., $$|S|<2$$ | S | < 2 ), we find the generation of wave packets is limited to the equatorial region when the background field is steep, showing a good agreement with what is indicated by critical distance in the theory. We then check the dependence of generation of hiss emissions on different hot electron densities. Since the overlap between threshold and optimum amplitude vanishes, the nonlinear process is weakened when hot electron density becomes smaller. In the simulation results, we find similar wave structures in all density cases, yet with different magnitudes. The existence of suitable S values implies that the nonlinear process occurs even at a low level of hot electron density. However, by examining $$J_E$$ J E that closely relates to the wave growth, we find energy conveyed from particles to waves is much limited in small density cases. Therefore, the nonlinear process is suppressed when hot electron density is small, which agrees with the theoretical analysis. Graphical Abstract

Similarity in evoked responses does not imply similarity in macroscopic network states across tasks

There is an ongoing debate as to whether cognitive processes arise from a group of functionally specialized brain modules (modularism) or as the result of a distributed nonlinear process (dynamical systems theory). The former predicts that tasks that recruit similar brain areas should have an equivalent degree of similarity in their connectivity. The latter allows for differential connectivity, even when the areas recruited are largely the same. Here we evaluated both views by comparing activation and connectivity patterns from a large sample of healthy subjects (N=242) that performed two executive control tasks, color-word Stroop task and Multi-Source Interference Task (MSIT), known to recruit similar brain areas. Using a measure of instantaneous connectivity based on edge time series as outcome variables, we estimated task-related network profiles as connectivity changes between incongruent and congruent information conditions. The degree of similarity of such profiles at the group level between both tasks was substantially smaller than their overlapping activation responses. A similar finding was observed at the subject level and when employing a different method for defining task-related connectivity. Our results are consistent with the perspective of the brain as a dynamical system, suggesting that task representations should be understood at both node and edge (connectivity) levels.

Nonlinear Analysis of Tropical Waves and Cyclogenesis Excited by Pressure Disturbance in Atmosphere

The horizontal equations of motion for an inviscid homogeneous fluid under the influence of pressure disturbance and waves are applied to investigate the nonlinear process of solitary waves and cyclone genesis forced by a moving pressure disturbance in atmosphere. Based on the reductive perturbation analysis, it is shown that the nonlinear evolution equation for the wave amplitude satisfies the Korteweg–de Vries equation with a forcing term (fKdV equation for short), which describes the physics of a shallow layer of fluid subject to external pressure forcing. Then, with the help of Hirota’s direct method, the analytic solutions of the fKdV equation are studied and some exact vortex solutions are given as examples, from which one can see that the solitary waves and vortex multi-pole structures can be excited by external pressure forcing in atmosphere, such as pressure perturbation and waves. It is worthy to point out that cyclone and waves can be excited by different type of moving atmospheric pressure forcing source.

Dispersion and damping rate of Langmuir wave in space plasma with regularized Kappa distributed electrons

The dispersion of Langmuir wave (LW) in an unmagnetized collisionless plasma with regularized Kappa distributed electrons is investigated from the kinetic theory. The frequency and damping rate of LW are analyzed for the parameters relating to the source region of a solar type III radio burst. It is found that the linear behavior of LW is greatly modified by the suprathermal index κ and the exponential cutoff parameter α. In the region κ<1.5, the damping rate of LW will be much larger than the one with Maxwellian distributed electrons. Hence, the nonlinear process of LW in low κ region may exhibit different properties in comparison with the one in large $\kappa$ region.

Avalanche transport of energetic-ions in magnetic confinement plasmas: Nonlinear multiple wave-number simulation

Large burst activity, identified as toroidal Alfv\'{e}n eigenmode (TAE) avalanche, occurs frequently in neutral-beam heated plasmas in National Spherical Torus Experiment (NSTX). Based on the typical experimental observation of TAE avalanche on NSTX, a self-consistent nonlinear multiple wave-number ($k_{\parallel}\simeq n/R$, where $n$ toroidal mode-number and $R$ major radius) simulation associated with TAE avalanches is performed using the experimental parameters and profiles before the occurrence of TAE avalanche as the M3D-K input. The wave-wave nonlinear coupling among different modes and the resonant interaction between different modes and energetic-ions during TAE avalanches are identified in the nonlinear multiple wave-number simulations. The resonance overlap during the TAE avalanche is clearly observed in the simulation. It is found that the effective wave-wave coupling and a sufficiently strong drive are two important ingredients for the onset of TAE avalanches. TAE avalanche is considered to be a strongly nonlinear process and it is always accompanied by the simultaneous rapid frequency-chirping and large amplitude bursting of multiple modes and significant energetic-ion losses. The experimental phenomenon is observed on NSTX and is qualitatively reproduced by the simulation results in this work. These findings indicate that the onset of avalanche is triggered by nonlinearity of the system, and are also conducive to understanding the underlying mechanism of avalanche transport of energetic particles in the future burning plasmas, such as ITER.