Coupled Neural P Systems

Reservoir computing models based on spiking neural P systems for time series classification

Nonlinear spiking neural P (NSNP) systems are neural-like membrane computing models with nonlinear spiking mechanisms. Because of this nonlinear spiking mechanism, NSNP systems can show rich nonlinear dynamics. Reservoir computing (RC) is a novel recurrent neural network (RNN) and can overcome some shortcomings of traditional RNNs. Based on NSNP systems, we developed two RC variants for time series classification, RC-SNP and RC-RMS-SNP, which are without and integrated with reservoir model space (RMS), respectively. The two RC variants use NSNP systems as the reservoirs and can be easily implemented in the RC framework. The proposed two RC variants were evaluated on 17 benchmark time series classification datasets and compared with 16 state-of-the-art or baseline classification models. The comparison results demonstrate the effectiveness of the proposed two RC variants for time series classification tasks.

Timed Tissue P Systems With Channel States

Tissue P systems with channel states are a variant of tissue P systems that can be employed as highly parallel computing devices, where the channel states can control the movements of objects. In a sense, the time-free approach can improve the robustness of P systems; hence, in this work, we introduce the time-free property into such P systems and explore their computational performances. Specifically, in a time-free manner, it is proved that this type of P systems have Turing universality by using two cells and four channel states with a maximum rule length of 2, or by using two cells and noncooperative symport rules with a maximum rule length of 1. Moreover, in terms of computational efficiency, it is proved that a uniform solution of the satisfiability ( SAT ) problem can be obtained in a time-free manner by applying noncooperative symport rules with a maximum rule length of 1. The research results of this paper show that a highly robust dynamic membrane computing system is constructed. Theoretically, relative to the existing system, our constructed system can enhance robustness and expand its application scope.

Spiking neural P systems with lateral inhibition

As a member of the third generation of artificial neural network models, spiking neural P systems (SN P systems) have gained a hot research spot in recent years. This work introduces the phenomenon of lateral inhibition in biological nervous systems into SN P systems, and proposes SN P systems with lateral inhibition (LISN P systems). LISN P systems add the property of synaptic length to portray the lateral distance between neurons, and adopt a new form of rules, lateral interaction rules, to describe the reception of spikes by postsynaptic neurons with different lateral distances from the presynaptic neuron. Specifically, an excited neuron produces lateral inhibition on surrounding postsynaptic neurons. Postsynaptic neurons close to the excited neuron, i.e., neurons with small lateral distances, are more susceptible to lateral inhibition and either receive a fewer number of spikes generated by the excited neuron or fail to receive spikes. As the lateral distance increases, the lateral inhibition weakens, and the number of spikes received by postsynaptic neurons increases. Based on the above mechanism, four specific LISN P systems are designed for generating arbitrary odd numbers, arbitrary even numbers, arbitrary natural numbers and arithmetic series, respectively, as examples. By designing working modules, LISN P systems provide equivalence in computational power to the universal register machines in both generating and accepting modes. This verifies the computational completeness of LISN P systems. A universal LISN P system using merely 65 neurons is devised for function computation. According to comparisons among several systems, universal LISN P systems require fewer computational resources.

Gated Spiking Neural P Systems for Time Series Forecasting

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.

An Attention-Aware Long Short-Term Memory-Like Spiking Neural Model for Sentiment Analysis

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.

Edge Detection Method Based on Nonlinear Spiking Neural Systems

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.

A Layered Spiking Neural System for Classification Problems

Biological brains have a natural capacity for resolving certain classification tasks. Studies on biologically plausible spiking neurons, architectures and mechanisms of artificial neural systems that closely match biological observations while giving high classification performance are gaining momentum. Spiking neural P systems (SN P systems) are a class of membrane computing models and third-generation neural networks that are based on the behavior of biological neural cells and have been used in various engineering applications. Furthermore, SN P systems are characterized by a highly flexible structure that enables the design of a machine learning algorithm by mimicking the structure and behavior of biological cells without the over-simplification present in neural networks. Based on this aspect, this paper proposes a novel type of SN P system, namely, layered SN P system (LSN P system), to solve classification problems by supervised learning. The proposed LSN P system consists of a multi-layer network containing multiple weighted fuzzy SN P systems with adaptive weight adjustment rules. The proposed system employs specific ascending dimension techniques and a selection method of output neurons for classification problems. The experimental results obtained using benchmark datasets from the UCI machine learning repository and MNIST dataset demonstrated the feasibility and effectiveness of the proposed LSN P system. More importantly, the proposed LSN P system presents the first SN P system that demonstrates sufficient performance for use in addressing real-world classification problems.

A Time Series Forecasting Approach Based on Nonlinear Spiking Neural Systems

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.

Numerical Spiking Neural P Systems

Spiking neural P (SN P) systems are a class of discrete neuron-inspired computation models, where information is encoded by the numbers of spikes in neurons and the timing of spikes. However, due to the discontinuous nature of the integrate-and-fire behavior of neurons and the symbolic representation of information, SN P systems are incompatible with the gradient descent-based training algorithms, such as the backpropagation algorithm, and lack the capability of processing the numerical representation of information. In this work, motivated by the numerical nature of numerical P (NP) systems in the area of membrane computing, a novel class of SN P systems is proposed, called numerical SN P (NSN P) systems. More precisely, information is encoded by the values of variables, and the integrate-and-fire way of neurons and the distribution of produced values are described by continuous production functions. The computation power of NSN P systems is investigated. We prove that NSN P is Turing universal as number generating devices, where the production functions in each neuron are linear functions, each involving at most one variable; as number accepting devices, NSN P systems are proved to be universal as well, even if each neuron contains only one production function. These results show that even if a single neuron is simple in the sense that it contains one or two production functions and the production functions in each neuron are linear functions with one variable, a network of simple neurons are still computationally powerful. With the powerful computation power and the characteristic of continuous production functions, developing learning algorithms for NSN P systems is potentially exploitable.

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.

Monodirectional Tissue P Systems With Promoters

Tissue P systems with promoters provide nondeterministic parallel bioinspired devices that evolve by the interchange of objects between regions, determined by the existence of some special objects called promoters. However, in cellular biology, the movement of molecules across a membrane is transported from high to low concentration. Inspired by this biological fact, in this article, an interesting type of tissue P systems, called monodirectional tissue P systems with promoters, where communication happens between two regions only in one direction, is considered. Results show that finite sets of numbers are produced by such P systems with one cell, using any length of symport rules or with any number of cells, using a maximal length 1 of symport rules, and working in the maximally parallel mode. Monodirectional tissue P systems are Turing universal with two cells, a maximal length 2, and at most one promoter for each symport rule, and working in the maximally parallel mode or with three cells, a maximal length 1, and at most one promoter for each symport rule, and working in the flat maximally parallel mode. We also prove that monodirectional tissue P systems with two cells, a maximal length 1, and at most one promoter for each symport rule (under certain restrictive conditions) working in the flat maximally parallel mode characterizes regular sets of natural numbers. Besides, the computational efficiency of monodirectional tissue P systems with promoters is analyzed when cell division rules are incorporated. Different uniform solutions to the Boolean satisfiability problem (SAT problem) are provided. These results show that with the restrictive condition of "monodirectionality," monodirectional tissue P systems with promoters are still computationally powerful. With the powerful computational power, developing membrane algorithms for monodirectional tissue P systems with promoters is potentially exploitable.

Homeostasis Tissue-Like P Systems

Tissue P systems provide distributed parallel devices inspired by actual biological reality, where communication rules are used for object exchange between cells (or between cells and the environment). In such systems, the environment continuously provides energy to cells, so the cells are very dependent on the objects in the environment. In biology, there is a mechanism called homeostasis, that is, an internal organism is independent from the external conditions, thus keeping itself relatively stable. Inspired by this biological fact, in this paper, we assume that the environment no longer provides energy for cells, introducing multiset rewriting rules into tissue P systems, thereby constructing a novel computational model called homeostasis tissue-like P systems. Based on the model, we construct two uniform solutions in feasible time. One solution is constructed to solve the 3-coloring problem in linear time in standard time, and the other solution is constructed to solve the SAT problem with communication rules and multiset rewriting rules of the length at most 3 in time-free mode. Moreover, we prove that the constructed system can generate any Turing computable set of numbers using communication rules and multiset rewriting rules with a maximal length 3, working in the mode of standard time and time-free, respectively. The results show that our constructed system does not rely on the environment and reflects the phenomenon of biological homeostasis. In addition, although the system runs in time-free way, it not only has Turing university, but also can effectively solve NP-complete problem.

Design and Implementation of a Spiking Neural Network with Integrate-and-Fire Neuron Model for Pattern Recognition

In contrast to the previous artificial neural networks (ANNs), spiking neural networks (SNNs) work based on temporal coding approaches. In the proposed SNN, the number of neurons, neuron models, encoding method, and learning algorithm design are described in a correct and pellucid fashion. It is also discussed that optimizing the SNN parameters based on physiology, and maximizing the information they pass leads to a more robust network. In this paper, inspired by the "center-surround" structure of the receptive fields in the retina, and the amount of overlap that they have, a robust SNN is implemented. It is based on the Integrate-and-Fire (IF) neuron model and uses the time-to-first-spike coding to train the network by a newly proposed method. The Iris and MNIST datasets were employed to evaluate the performance of the proposed network whose accuracy, with 60 input neurons, was 96.33% on the Iris dataset. The network was trained in only 45 iterations indicating its reasonable convergence rate. For the MNIST dataset, when the gray level of each pixel was considered as input to the network, 600 input neurons were required, and the accuracy of the network was 90.5%. Next, 14 structural features were used as input. Therefore, the number of input neurons decreased to 210, and accuracy increased up to 95%, meaning that an SNN with fewer input neurons and good skill was implemented. Also, the ABIDE1 dataset is applied to the proposed SNN. Of the 184 data, 79 are used for healthy people and 105 for people with autism. One of the characteristics that can differentiate between these two classes is the entropy of the existing data. Therefore, Shannon entropy is used for feature extraction. Applying these values to the proposed SNN, an accuracy of 84.42% was achieved by only 120 iterations, which is a good result compared to the recent results.

Evolution-Communication Spiking Neural P Systems

Spiking neural P systems (SNP systems) are a class of distributed and parallel computation models, which are inspired by the way in which neurons process information through spikes, where the integrate-and-fire behavior of neurons and the distribution of produced spikes are achieved by spiking rules. In this work, a novel mechanism for separately describing the integrate-and-fire behavior of neurons and the distribution of produced spikes, and a novel variant of the SNP systems, named evolution-communication SNP (ECSNP) systems, is proposed. More precisely, the integrate-and-fire behavior of neurons is achieved by spike-evolution rules, and the distribution of produced spikes is achieved by spike-communication rules. Then, the computational power of ECSNP systems is examined. It is demonstrated that ECSNP systems are Turing universal as number-generating devices. Furthermore, the computational power of ECSNP systems with a restricted form, i.e. the quantity of spikes in each neuron throughout a computation does not exceed some constant, is also investigated, and it is shown that such restricted ECSNP systems can only characterize the family of semilinear number sets. These results manifest that the capacity of neurons for information storage (i.e. the quantity of spikes) has a critical impact on the ECSNP systems to achieve a desired computational power.

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.

Turing Universality of Weighted Spiking Neural P Systems with Anti-spikes

Weighted spiking neural P systems with anti-spikes (AWSN P systems) are proposed by adding anti-spikes to spiking neural P systems with weighted synapses. Anti-spikes behave like spikes of inhibition of communication between neurons. Both spikes and anti-spikes are used in the rule expressions. An illustrative example is given to show the working process of the proposed AWSN P systems. The Turing universality of the proposed P systems as number generating and accepting devices is proved. Finally, a universal AWSN P system having 34 neurons is proved to work as a function computing device by using standard rules, and one having 30 neurons is proved to work as a number generator.

Medical Image Fusion Method Based on Coupled Neural P Systems in Nonsubsampled Shearlet Transform Domain

Coupled neural P (CNP) systems are a recently developed Turing-universal, distributed and parallel computing model, combining the spiking and coupled mechanisms of neurons. This paper focuses on how to apply CNP systems to handle the fusion of multi-modality medical images and proposes a novel image fusion method. Based on two CNP systems with local topology, an image fusion framework in nonsubsampled shearlet transform (NSST) domain is designed, where the two CNP systems are used to control the fusion of low-frequency NSST coefficients. The proposed fusion method is evaluated on 20 pairs of multi-modality medical images and compared with seven previous fusion methods and two deep-learning-based fusion methods. Quantitative and qualitative experimental results demonstrate the advantage of the proposed fusion method in terms of visual quality and fusion performance.

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.

Spiking Neural P Systems with Delay on Synapses

Based on the feature and communication of neurons in animal neural systems, spiking neural P systems (SN P systems) were proposed as a kind of powerful computing model. Considering the length of axons and the information transmission speed on synapses, SN P systems with delay on synapses (SNP-DS systems) are proposed in this work. Unlike the traditional SN P systems, where all the postsynaptic neurons receive spikes at the same instant from their presynaptic neuron, the postsynaptic neurons in SNP-DS systems would receive spikes at different instants, depending on the delay time on the synapses connecting them. It is proved that the SNP-DS systems are universal as number generators. Two small universal SNP-DS systems, with standard or extended rules, are constructed to compute functions, using 56 and 36 neurons, respectively. Moreover, a simulator has been provided, in order to check the correctness of these two SNP-DS systems, thus providing an experimental validation of the universality of the systems designed.

Nonlinear Spiking Neural P Systems

This paper proposes a new variant of spiking neural P systems (in short, SNP systems), nonlinear spiking neural P systems (in short, NSNP systems). In NSNP systems, the state of each neuron is denoted by a real number, and a real configuration vector is used to characterize the state of the whole system. A new type of spiking rules, nonlinear spiking rules, is introduced to handle the neuron’s firing, where the consumed and generated amounts of spikes are often expressed by the nonlinear functions of the state of the neuron. NSNP systems are a class of distributed parallel and nondeterministic computing systems. The computational power of NSNP systems is discussed. Specifically, it is proved that NSNP systems as number-generating/accepting devices are Turing-universal. Moreover, we establish two small universal NSNP systems for function computing and number generator, containing 117 neurons and 164 neurons, respectively.

Spiking neural P systems with multiple channels and polarizations

In this paper, we investigate a new variant of spiking neural P systems (SNP systems, in short), called spiking neural P systems with multiple channels and polarizations (SNP-MCP systems, in short). The variant integrates two interesting features: multiple channel and polarization. Each neuron can use its multiple channels to connect one or more subsequent sets of neurons. Moreover, both polarizations and regular expressions are used in rules to control the spiking of neurons. The computational power of the variant is discussed. The Turing universality of the variant as number generating/accepting devices is proven, and then a small universal system with 150 neurons is constructed to compute any Turing computable function.