Spiking neural P (SNP) systems are a class of distributed and parallel neural-like computing models that are inspired by the mechanism of spiking neurons and are 3rd-generation neural networks. Chaotic time series forecasting is one of the most challenging problems for machine learning models. To address this challenge, we first propose a nonlinear version of SNP systems, called nonlinear SNP systems with autapses (NSNP-AU systems). In addition to the nonlinear consumption and generation of spikes, the NSNP-AU systems have three nonlinear gate functions, which are related to the states and outputs of the neurons. Inspired by the spiking mechanisms of NSNP-AU systems, we develop a recurrent-type prediction model for chaotic time series, called the NSNP-AU model. As a new variant of recurrent neural networks (RNNs), the NSNP-AU model is implemented in a popular deep learning framework. Four datasets of chaotic time series are investigated using the proposed NSNP-AU model, five state-of-the-art models, and 28 baseline prediction models. The experimental results demonstrate the advantage of the proposed NSNP-AU model for chaotic time series forecasting.

LSTM-SNP model is a recently developed long short-term memory (LSTM) network, which is inspired from the mechanisms of spiking neural P (SNP) systems. In this paper, LSTM-SNP is utilized to propose a novel model for aspect-level sentiment analysis, termed as ALS model. The LSTM-SNP model has three gates: reset gate, consumption gate and generation gate. Moreover, attention mechanism is integrated with LSTM-SNP model. The ALS model can better capture the sentiment features in the text to compute the correlation between context and aspect words. To validate the effectiveness of the ALS model for aspect-level sentiment analysis, comparison experiments with 17 baseline models are conducted on three real-life data sets. The experimental results demonstrate that the ALS model has a simpler structure and can achieve better performance compared to these baseline models.

Nonlinear spiking neural P (NSNP) systems are a class of neural-like computational models inspired from the nonlinear mechanism of spiking neurons. NSNP systems have a distinguishing feature: nonlinear spiking mechanism. To handle edge detection of images, this paper proposes a variant, nonlinear spiking neural P (NSNP) systems with two outputs (TO), termed as NSNP-TO systems. Based on NSNP-TO system, an edge detection framework is developed, termed as ED-NSNP detector. The detection ability of ED-NSNP detector relies on two convolutional kernels. To obtain good detection performance, particle swarm optimization (PSO) is used to optimize the parameters of the two convolutional kernels. The proposed ED-NSNP detector is evaluated on several open benchmark images and compared with seven baseline edge detection methods. The comparison results indicate the availability and effectiveness of the proposed ED-NSNP detector.

Nonlinear spiking neural P (NSNP) systems are one of neural-like membrane computing models, abstracted by nonlinear spiking mechanisms of biological neurons. NSNP systems have a nonlinear structure and can show rich nonlinear dynamics. In this paper, we introduce a variant of NSNP systems, called gated nonlinear spiking neural P systems or GNSNP systems. Based on GNSNP systems, a recurrent-like model is investigated, called GNSNP model. Moreover, exchange rate forecasting tasks are used as the application background to verify its ability. For the purpose, we develop a prediction model based on GNSNP model, called ERF-GNSNP model. In ERF-GNSNP model, the GNSNP model is followed by a "dense" layer, which is used to capture the correlation between different sub-series in multivariate time series. To evaluate the prediction performance, nine groups of exchange rate data sets are utilized to compare the proposed ERF-GNSNP model with 25 baseline prediction models. The comparison results demonstrate the effectiveness of the proposed ERF-GNSNP model for exchange rate forecasting tasks.

Spiking neural P (SNP) systems are a class of neural-like computing models, abstracted by the mechanism of spiking neurons. This article proposes a new variant of SNP systems, called gated spiking neural P (GSNP) systems, which are composed of gated neurons. Two gated mechanisms are introduced in the nonlinear spiking mechanism of GSNP systems, consisting of a reset gate and a consumption gate. The two gates are used to control the updating of states in neurons. Based on gated neurons, a prediction model for time series is developed, known as the GSNP model. Several benchmark univariate and multivariate time series are used to evaluate the proposed GSNP model and to compare several state-of-the-art prediction models. The comparison results demonstrate the availability and effectiveness of GSNP for time series forecasting.

Nonlinear spiking neural P (NSNP) systems are a recently developed theoretical model, which is abstracted by nonlinear spiking mechanism of biological neurons. NSNP systems have a nonlinear structure and the potential to describe nonlinear dynamic systems. Based on NSNP systems, a novel time series forecasting approach is developed in this paper. During the training phase, a time series is first converted to frequency domain by using a redundant wavelet transform, and then according to the frequency data, an NSNP system is automatically constructed and adaptively trained in frequency domain. Then, the well-trained NSNP system can automatically generate sequence data for future time as the prediction results. Eight benchmark time series data sets and two real-life time series data sets are utilized to compare the proposed approach with several state-of-the-art forecasting approaches. The comparison results demonstrate availability and effectiveness of the proposed forecasting approach.

Abstracted from the nested structure of biological cells with application on the modeling of economical processes, numerical P systems (in short, NP systems) as a kind of distributed parallel computation systems have been proposed. It has been proven that NP systems and variants are Turing universal for number accepting/generating devices and language generating device. However, universality of NP systems as function computing devices has not been established. Aiming at numerical P systems with thresholds (in short, TNP systems), small universality for computing functions is discussed in this paper. Six small universal function computing devices of TNP systems for two threshold cases and working on three different modes are constructed, respectively.