Universal Nonlinear Spiking Neural P Systems with Delays and Weights on Synapses

The nonlinear spiking neural P systems (NSNP systems) are new types of computation models, in which the state of neurons is represented by real numbers, and nonlinear spiking rules handle the neuron’s firing. In this work, in order to improve computing performance, the weights and delays are introduced to the NSNP system, and universal nonlinear spiking neural P systems with delays and weights on synapses (NSNP-DW) are proposed. Weights are treated as multiplicative constants by which the number of spikes is increased when transiting across synapses, and delays take into account the speed at which the synapses between neurons transmit information. As a distributed parallel computing model, the Turing universality of the NSNP-DW system as number generating and accepting devices is proven. 47 and 43 neurons are sufficient for constructing two small universal NSNP-DW systems. The NSNP-DW system solving the Subset Sum problem is also presented in this work.

Parallel computing of fuzzy integrals: Performance and test

Fuzzy integral in data mining is an excellent information fusion tool. It has obvious advantages in solving the combination of features and has more successful applications in classification problems. However, with the increase of the number of features, the time complexity and space complexity of fuzzy integral will also increase exponentially. This problem limits the development of fuzzy integral. This article proposes a high-efficiency fuzzy integral—Parallel and Sparse Frame Based Fuzzy Integral (PSFI) for reducing time complexity and space complexity in the calculation of fuzzy integrals, which is based on the distributed parallel computing framework-Spark combined with the concept of sparse storage. Aiming at the efficiency problem of the Python language, Cython programming technology is introduced in the meanwhile. Our algorithm is packaged into an algorithm library to realize a more efficient PSFI. The experiments verified the impact of the number of parallel nodes on the performance of the algorithm, test the performance of PSFI in classification, and apply PSFI on regression problems and imbalanced big data classification. The results have shown that PSFI reduces the variable storage space requirements of datasets with aplenty of features by thousands of times with the increase of computing resources. Furthermore, it is proved that PSFI has higher prediction accuracy than the classic fuzzy integral running on a single processor.

Spiking Neural Membrane Computing Models

As third-generation neural network models, spiking neural P systems (SNP) have distributed parallel computing capabilities with good performance. In recent years, artificial neural networks have received widespread attention due to their powerful information processing capabilities, which is an effective combination of a class of biological neural networks and mathematical models. However, SNP systems have some shortcomings in numerical calculations. In order to improve the incompletion of current SNP systems in dealing with certain real data technology in this paper, we use neural network structure and data processing methods for reference. Combining them with membrane computing, spiking neural membrane computing models (SNMC models) are proposed. In SNMC models, the state of each neuron is a real number, and the neuron contains the input unit and the threshold unit. Additionally, there is a new style of rules for neurons with time delay. The way of consuming spikes is controlled by a nonlinear production function, and the produced spike is determined based on a comparison between the value calculated by the production function and the critical value. In addition, the Turing universality of the SNMC model as a number generator and acceptor is proved.

Novel Numerical Spiking Neural P Systems with a Variable Consumption Strategy

A novel variant of NSN P systems, called numerical spiking neural P systems with a variable consumption strategy (NSNVC P systems), is proposed. Like the spiking rules consuming spikes in spiking neural P systems, NSNVC P systems introduce a variable consumption strategy by modifying the form of the production functions used in NSN P systems. Similar to the delay feature of the spiking rules, NSNVC P systems introduce a postponement feature into the production functions. The execution of the production functions in NSNVC P systems is controlled by two, i.e., polarization and threshold, conditions. Multiple synaptic channels are used to transmit the charges and the production values in NSNVC P systems. The proposed NSNVC P systems are a type of distributed parallel computing models with a directed graphical structure. The Turing universality of the proposed NSNVC P systems is proved as number generating/accepting devices. Detailed descriptions are provided for NSNVC P systems as number generating/accepting devices. In addition, a universal NSNVC P system with 66 neurons is constructed as a function computing device.

Dynamic Threshold Neural P Systems with Multiple Channels and Inhibitory Rules

In biological neural networks, neurons transmit chemical signals through synapses, and there are multiple ion channels during transmission. Moreover, synapses are divided into inhibitory synapses and excitatory synapses. The firing mechanism of previous spiking neural P (SNP) systems and their variants is basically the same as excitatory synapses, but the function of inhibitory synapses is rarely reflected in these systems. In order to more fully simulate the characteristics of neurons communicating through synapses, this paper proposes a dynamic threshold neural P system with inhibitory rules and multiple channels (DTNP-MCIR systems). DTNP-MCIR systems represent a distributed parallel computing model. We prove that DTNP-MCIR systems are Turing universal as number generating/accepting devices. In addition, we design a small universal DTNP-MCIR system with 73 neurons as function computing devices.

Spiking Neural P Systems with Extended Channel Rules

This paper discusses a new variant of spiking neural P systems (in short, SNP systems), spiking neural P systems with extended channel rules (in short, SNP–ECR systems). SNP–ECR systems are a class of distributed parallel computing models. In SNP–ECR systems, a new type of spiking rule is introduced, called ECR. With an ECR, a neuron can send the different numbers of spikes to its subsequent neurons. Therefore, SNP–ECR systems can provide a stronger firing control mechanism compared with SNP systems and the variant with multiple channels. We discuss the Turing universality of SNP–ECR systems. It is proven that SNP–ECR systems as number generating/accepting devices are Turing universal. Moreover, we provide a small universal SNP–ECR system as function computing devices.