Next generation reservoir computing

Reservoir computing is a best-in-class machine learning algorithm for processing information generated by dynamical systems using observed time-series data. Importantly, it requires very small training data sets, uses linear optimization, and thus requires minimal computing resources. However, the algorithm uses randomly sampled matrices to define the underlying recurrent neural network and has a multitude of metaparameters that must be optimized. Recent results demonstrate the equivalence of reservoir computing to nonlinear vector autoregression, which requires no random matrices, fewer metaparameters, and provides interpretable results. Here, we demonstrate that nonlinear vector autoregression excels at reservoir computing benchmark tasks and requires even shorter training data sets and training time, heralding the next generation of reservoir computing.

A Note on the Generalized Nonlinear Vector Variational-Like Inequality Problem

In this paper, we discuss two variants of the generalized nonlinear vector variational-like inequality problem. We provide their solutions by adopting topological approach. Topological properties such as compactness, closedness, and net theory are used in the proof. The admissibility of the function space topology and KKM-Theorem have played important role in proving the results.

Regions of Reduced Dynamics in Dynamic Networks

We consider complex networks where the dynamics of each interacting agent is given by a nonlinear vector field and the connections between the agents are defined according to the topology of undirected simple graphs. The aim of the work is to explore whether the asymptotic dynamic behavior of the entire network can be fully determined from the knowledge of the dynamic properties of the underlying constituent agents. While the complexity that arises by connecting many nonlinear systems hinders us to analytically determine general solutions, we show that there are conditions under which the dynamical properties of the constituent agents are equivalent to the dynamical properties of the entire network. This feature, which depends on the nature and structure of both the agents and connections, leads us to define the concept of regions of reduced dynamics, which are subsets of the parameter space where the asymptotic solutions of a network behave equivalently to the limit sets of the constituent agents. On one hand, we discuss the existence of regions of reduced dynamics, which can be proven in the case of diffusive networks of identical agents with all-to-all topologies and conjectured for other topologies. On the other hand, using three examples, we show how to locate regions of reduced dynamics in parameter space. In simple cases, this can be done analytically through bifurcation analysis and in other cases we exploit numerical continuation methods.

Nonlinear vector model control of underactuated air cushion vehicle based on parameter reduction algorithm

Due to the serious drift phenomenon of underactuated air cushion vehicle, the actual trajectory is determined by the total speed and course angle. In this paper, the course angle and total speed model are derived from the general four degrees of freedom air cushion vehicle model and named nonlinear vector model. Nonlinear vector model can be used to directly design the course and total speed controllers for underactuated air cushion vehicle. Adaptive radial basis function neural network is introduced to deal with the strong nonlinearity and uncertainty of air cushion vehicle’s complex dynamics. However, the adaptive weights to be calculated and updated may be too many in each sampling period. For the relief of the burden caused by the online computing, parameter reduction algorithm is designed in this paper. It gives us a power to choose the number of online update parameters freely. Then the new trajectory tracking control method with independent total speed and course controller is designed based on nonlinear vector model and parameter reduction algorithm. The designed controller ensures that the tracking errors are uniformly ultimately bounded. Also, only a few weights need to be updated online. The effectiveness and superiority of the designed controller is verified by simulation results.

ECG Classification Framework for Cardiac Disease Prediction Using Nonlinear Vector Decomposed Neural Network

Early detection of heart disease may prevent myocardial infarction. Electrocardiogram (ECG) is the most widely used signal in clinical practice for the diagnosis of cardiovascular diseases such as arrhythmias and myocardial infarction. Human interpretation is time-consuming, and long-term ECG records are difficult to detect in small differences.Therefore, automated recognition of myocardial infarction using a Computer-Aided Diagnosis (CAD) system is the research interest, which can be used effectively to reduce mortality among cardiovascular disease patients. The most important step in the analysis of complex R-peak/QRS signals using an automated process of ECG signal. To automate the cardiovascular disease detection process, an adequate mechanism is required to characterize ECG signals, which are unknown features according to the similarities between ECG signals. If the classification can find similarities accurately and the probability of arrhythmia detection increases, the algorithm can become an effective method in the laboratory. In this research work, a new classification strategy is proposed to all the more precisely order ECG signals dependent on a powerful model of ECG signals. In this proposed method, a Nonlinear Vector Decomposed Neural Network (NVDN) is developed, and its simulation results show that this classifier can isolate the ECGs with high productivity. This proposed technique expands the exactness of the ECG classification concerning increasingly exact arrhythmia discovery.

Analysis of Time and Frequency Response for Single/Multi-Tone Stimulus Harmonic Phase-Reference Based on Prime Number Algorithm

We present a spectrally-dense phase-reference and its calibration for nonlinear vector network analyzers (NVNAs) using a step recovery diode (SRD) comb-generator with a multi-tone stimulus. Frequency selection for multi-tone stimulus based on prime number algorithms was used with the Digital Real-Time Oscilloscope (DRTO) to avoid the sub-Nyquist spurs components and to increase the effective sampling rate so that the waveform can be observed in greater detail. The measured results were calibrated to minimize drift and jitter and achieved excellent agreement between the prime number and the exact frequency strategies except at the sub-Nyquist frequencies. The analysis indicates that the prime number selected frequencies show significantly improved performance by avoiding the DRTO distortion components. We have verified the validity of the method described in this paper by experimental measurement results.

When is discretionary fiscal policy effective?

We investigate the effects of discretionary changes in government spending and taxes using a medium-scale nonlinear vector autoregressive model with policy shocks identified via sign restrictions. Tax cuts and spending increases have larger stimulative effects when there is excess slack in the economy, while they are much less effective, especially in the case of government spending increases, when the economy is close to potential. We find that contractionary shocks have larger effects than expansionary shocks across the business cycle, but this is much more pronounced during deep recessions and sluggish recoveries than in robust expansions. Notably, tax increases are highly contractionary and largely self-defeating in reducing the debt-to-GDP ratio when the economy is in a deep recession. The effectiveness of discretionary government spending, including its state dependence, appears to be almost entirely due to the response of consumption. The responses of both consumption and investment to discretionary tax changes are state dependent, but investment plays the larger quantitative role.