Bridges Between Spiking Neural Membrane Systems and Virus Machines.

Spiking Neural P Systems (SNP) are well-established computing models that take inspiration from spikes between biological neurons; these models have been widely used for both theoretical studies and practical applications. Virus machines (VMs) are an emerging computing paradigm inspired by viral transmission and replication. In this work, a novel extension of VMs inspired by SNPs is presented, called Virus Machines with Host Excitation (VMHEs). In addition, the universality and explicit results between SNPs and VMHEs are compared in both generating and computing mode. The VMHEs defined in this work are shown to be more efficient than SNPs, requiring fewer memory units (hosts in VMHEs and neurons in SNPs) in several tasks, such as a universal machine, which was constructed with 18 hosts less than the 84 neurons in SNPs, and less than other spiking models discussed in the work.

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.

Nonlinear Spiking Neural Systems With Autapses for Predicting Chaotic Time Series.

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.

How mutation accumulation depends on the structure of the cell lineage tree.

All the cells of a multicellular organism are the product of cell divisions that trace out a single binary tree, the so-called cell lineage tree. Because cell divisions are accompanied by replication errors, the shape of the cell lineage tree is a key determinant of how somatic evolution, which can potentially lead to cancer, proceeds. Carcinogenesis requires the accumulation of a certain number of driver mutations. By mapping the accumulation of mutations into a graph theoretical problem, we present an exact numerical method to calculate the probability of collecting a given number of mutations and show that for low mutation rates it can be approximated with a simple analytical formula, which depends only on the distribution of the lineage lengths, and is dominated by the longest lineages. Our results are crucial in understanding how natural selection can shape the cell lineage trees of multicellular organisms and curtail somatic evolution.

The structure of the hematopoietic system can explain chronic myeloid leukemia progression.

Almost all cancer types share the hallmarks of cancer and a similar tumor formation: fueled by stochastic mutations in somatic cells. In case of chronic myeloid leukemia (CML), this evolutionary process can be tracked from an asymptomatic long-lasting chronic phase to a final rapidly evolving blast phase. Somatic evolution in CML occurs in the context of healthy blood production, a hierarchical process of cell division; initiated by stem cells that self-renew and differentiate to produce mature blood cells. Here we introduce a general model of hierarchical cell division explaining the particular progression of CML as resulting from the structure of the hematopoietic system. Driver mutations confer a growth advantage to the cells carrying them, for instance, the BCR::ABL1 gene, which also acts as a marker for CML. We investigated the relation of the BCR::ABL1 mutation strength to the hematopoietic stem cell division rate by employing computer simulations and fitting the model parameters to the reported median duration for the chronic and accelerated phases. Our results demonstrate that driver mutations (additional to the BCR::ABL1 mutation) are necessary to explain CML progression if stem cells divide sufficiently slowly. We observed that the number of mutations accumulated by cells at the more differentiated levels of the hierarchy is not affected by driver mutations present in the stem cells. Our results shed light on somatic evolution in a hierarchical tissue and show that the clinical hallmarks of CML progression result from the structural characteristics of blood production.

Using Virus Machines to Compute Pairing Functions.

Virus machines are computational devices inspired by the movement of viruses between hosts and their capacity to replicate using the resources of the hosts. This behavior is controlled by an external graph of instructions that opens different channels of the system to make viruses capable of moving. This model of computation has been demonstrated to be as powerful as turing machines by different methods: by generating Diophantine sets, by computing partial recursive functions and by simulating register machines. It is interesting to investigate the practical use cases of this model in terms of possibilities and efficiency. In this work, we give the basic modules to create an arithmetic calculator. As a practical application, two pairing functions are calculated by means of two different virus machines. Pairing functions are important resources in the field of cryptography. The functions calculated are the Cantor pairing function and the Gödel pairing function.

Attacking cryptosystems by means of virus machines.

The security that resides in the public-key cryptosystems relies on the presumed computational hardness of mathematical problems behind the systems themselves (e.g. the semiprime factorization problem in the RSA cryptosystem), that is because there is not known any polynomial time (classical) algorithm to solve them. The paper focuses on the computing paradigm of virus machines within the area of Unconventional Computing and Natural Computing. Virus machines, which incorporate concepts of virology and computer science, are considered as number computing devices with the environment. The paper designs a virus machine that solves a generalization of the semiprime factorization problem and verifies it formally.

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.

Attention-enabled gated spiking neural P model for aspect-level sentiment classification.

Gated spiking neural P (GSNP) model is a recently developed recurrent-like network, which is abstracted by nonlinear spiking mechanism of nonlinear spiking neural P systems. In this study, a modification of GSNP is combined with attention mechanism to develop a novel model for sentiment classification, called attention-enabled GSNP model or termed as AGSNP model. The AGSNP model has two channels that process content words and aspect item respectively, where two modified GSNPs are used to obtain dependencies between content words and between aspect words. Moreover, two attention components are used to establish semantic correlation between content words and aspect item. Comparative experiments on three real data sets and several baseline models are conducted to verify the effectiveness of the AGSNP model. The comparison results demonstrate that the AGSNP model is competent for aspect-level sentiment classification tasks.

Simulation of P systems with active membranes on CUDA.

P systems or Membrane Systems provide a high-level computational modelling framework that combines the structure and dynamic aspects of biological systems in a relevant and understandable way. They are inherently parallel and non-deterministic computing devices. In this article, we discuss the motivation, design principles and key of the implementation of a simulator for the class of recognizer P systems with active membranes running on a (GPU). We compare our parallel simulator for GPUs to the simulator developed for a single central processing unit (CPU), showing that GPUs are better suited than CPUs to simulate P systems due to their highly parallel nature.

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.

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.

A Complete Arithmetic Calculator Constructed from Spiking Neural P Systems and its Application to Information Fusion.

Several variants of spiking neural P systems (SNPS) have been presented in the literature to perform arithmetic operations. However, each of these variants was designed only for one specific arithmetic operation. In this paper, a complete arithmetic calculator implemented by SNPS is proposed. An application of the proposed calculator to information fusion is also proposed. The information fusion is implemented by integrating the following three elements: (1) an addition and subtraction SNPS already reported in the literature; (2) a modified multiplication and division SNPS; (3) a novel storage SNPS, i.e. a method based on SNPS is introduced to calculate basic probability assignment of an event. This is the first attempt to apply arithmetic operation SNPS to fuse multiple information. The effectiveness of the presented general arithmetic SNPS calculator is verified by means of several examples.

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.

Dendrite P Systems Toolbox: Representation, Algorithms and Simulators.

Dendrite P systems (DeP systems) are a recently introduced neural-like model of computation. They provide an alternative to the more classical spiking neural (SN) P systems. In this paper, we present the first software simulator for DeP systems, and we investigate the key features of the representation of the syntax and semantics of such systems. First, the conceptual design of a simulation algorithm is discussed. This is helpful in order to shade a light on the differences with simulators for SN P systems, and also to identify potential parallelizable parts. Second, a novel simulator implemented within the P-Lingua simulation framework is presented. Moreover, MeCoSim, a GUI tool for abstract representation of problems based on P system models has been extended to support this model. An experimental validation of this simulator is also covered.

Spiking neural P systems with weights.

A variant of spiking neural P systems with positive or negative weights on synapses is introduced, where the rules of a neuron fire when the potential of that neuron equals a given value. The involved values-weights, firing thresholds, potential consumed by each rule-can be real (computable) numbers, rational numbers, integers, and natural numbers. The power of the obtained systems is investigated. For instance, it is proved that integers (very restricted: 1, -1 for weights, 1 and 2 for firing thresholds, and as parameters in the rules) suffice for computing all Turing computable sets of numbers in both the generative and the accepting modes. When only natural numbers are used, a characterization of the family of semilinear sets of numbers is obtained. It is shown that spiking neural P systems with weights can efficiently solve computationally hard problems in a nondeterministic way. Some open problems and suggestions for further research are formulated.

Dendrite P systems.

It was recently found that dendrites are not just a passive channel. They can perform mixed computation of analog and digital signals, and therefore can be abstracted as information processors. Moreover, dendrites possess a feedback mechanism. Motivated by these computational and feedback characteristics, this article proposes a new variant of neural-like P systems, dendrite P (DeP) systems, where neurons simulate the computational function of dendrites and perform a firing-storing process instead of the storing-firing process in spiking neural P (SNP) systems. Moreover, the behavior of the neurons is characterized by dendrite rules that are abstracted by two characteristics of dendrites. Different from the usual firing rules in SNP systems, the firing of a dendrite rule is controlled by the states of the corresponding source neurons. Therefore, DeP systems can provide a collaborative control capability for neurons. We discuss the computational power of DeP systems. In particular, it is proven that DeP systems are Turing-universal number generating/accepting devices. Moreover, we construct a small universal DeP system consisting of 115 neurons for computing functions.

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.

Modelling gene expression control using P systems: The Lac Operon, a case study.

In this paper P systems are used as a formal framework for the specification and simulation of biological systems. In particular, we will deal with gene regulation systems consisting of protein-protein and protein-DNA interactions that take place in different compartments of the hierarchical structure of the living cell or in different individual cells from a colony. We will explicitly model transcription and translation as concurrent and discrete processes using rewriting rules on multisets of objects and strings. Our approach takes into account the discrete character of the components of the system, its random behaviour and the key role played by membranes in processes involving signalling at the cell surface and selective uptake of substances from the environment. Our systems will evolve according to an extension of Gillespie's algorithm, called Multicompartmental Gillespie's Algorithm. The well known gene regulation system in the Lac Operon in Escherichia coli will be modelled as a case study to benchmark our approach.