Narrow Results

Membrane systems (currently called P systems) are parallel computing devices inspired by the structure and the functioning of living cells. A standard feature of P systems is that each rule is executed in exactly one time unit. Actually, in living cells different chemical reactions might take different times to be executed; moreover, it might be hard to know precisely such time of execution. For this reason, in [7] two models of P systems (time-free and clock-free P systems) have been defined and investigated, where the time of execution of the rules is arbitrary and the output produced by the system is always the same, independently of this time. Preliminary results concerning time-free and clock-free P system have been obtained in [6, 7, 8]. In this paper we continue these investigations by considering different combinations of possible ingredients. In particular, we present the universality of time-free P systems using bi-stable catalysts. Then, we prove that this result implies that is not possible to decide whether an arbitrary bi-stable catalytic P system is time-free. We present several results about time-free evolution-communication P systems, where the computation is a mixed application of evolution and symport/antiport rules. In this case we obtain the universality even by using non-cooperative evolution rules and antiports of weight one. Finally, we formulate several open problems.

We discuss aspects of biological relevance to the modelling of bio-computation in a multiset rewriting system context: turnover, robustness against perturbations, and the dataflow programming paradigm. The systems under consideration are maximally parallel and asynchronous parallel membrane systems, the latter corresponding to computation in which the notion of time is operationally meaningless.

A natural geometrical setting which seems promising for the study of computational processes in general multiset rewriting systems is presented. Configuration space corresponds to a subset of the lattice , d ∈ N, and state transitions correspond to vector addition. The similarities and differences with Vector Addition Systems and Petri nets are discussed. Symbolic dynamics are introduced on special partitions of configuration space and we indicate different notions of complexity for membrane systems based on this and related concepts such as graph complexity and minimal automata. Some examples of synchronized, pipelined dataflow computations are given and decompositions into functional subunits are briefly commented on.

Computer modeling of molecular signaling cascades can provide useful insight into the underlying complexities of biological systems. We present a refined approach for the discrete modeling of protein interactions within the environment of a single cell. The technique we offer utilizes the Membrane Systems paradigm which, due to its hierarchical structure, lends itself readily to mimic the behavior of cells. Since our approach is nondeterministic and discrete, it provides an interesting contrast to the standard deterministic ordinary differential equations techniques. We argue that our approach may outperform ordinary differential equations when modeling systems with relatively low numbers of molecules – a frequent occurrence in cellular signaling cascades.

Refinements over our previous modeling efforts include the addition of nondeterminism for handling reaction competition over limited reactants, increased efficiency in the storing and sorting of reaction waiting times, and modifications of the model reactions. Results of our discrete simulation of the type I and type II Fas-mediated apoptotic signaling cascade are illustrated and compared with two approaches: one based on ordinary differential equations and another based on the well-known Gillespie algorithm.

In this paper we provide a summary on important results concerning P automata and their distributed systems, dP automata. Since these constructs combine properties of classical automata and membrane systems being in interaction with their environments, we also discuss their non-standard features, compared them to characteristics of classical automata.

Spiking neural membrane systems (or spiking neural P systems, SNP systems) are a new type of computation model which have attracted the attention of plentiful scholars for parallelism, time encoding, interpretability and extensibility. The original SNP systems only consider the time delay caused by the execution of rules within neurons, but not caused by the transmission of spikes via synapses between neurons and its adaptive adjustment. In view of the importance of time delay for SNP systems, which are a time encoding computation model, this study proposes SNP systems with adaptive synaptic time delay (ADSNP systems) based on the dynamic regulation mechanism of synaptic transmission delay in neural systems. In ADSNP systems, besides neurons, astrocytes that can generate adenosine triphosphate (ATP) are introduced. After receiving spikes, astrocytes convert spikes into ATP and send ATP to the synapses controlled by them to change the synaptic time delays. The Turing universality of ADSNP systems in number generating and accepting modes is proved. In addition, a small universal ADSNP system using 93 neurons and astrocytes is given. The superiority of the ADSNP system is demonstrated by comparison with the six variants. Finally, an ADSNP system is constructed for credit card fraud detection, which verifies the feasibility of the ADSNP system for solving real-world problems. By considering the adaptive synaptic delay, ADSNP systems better restore the process of information transmission in biological neural networks, and enhance the adaptability of SNP systems, making the control of time more accurate.

In this paper, a new evolutionary algorithm based on a membrane system is proposed to solve the dynamic or uncertain optimization problems. The proposed algorithm employs objects, a dynamical membrane structure and several reaction rules of the membrane systems. The object represents a candidate solution of the optimization problems. The dynamical structure consists of the nested membranes where a skin membrane contains several membranes, which is useful for the proposed algorithm that finds optimal solutions. The reaction rules are designed to locate and track the optimal solutions of the dynamic optimization problems (DOPs), which are inspired by processing the chemical compounds in the region of cellular membranes. Experimental study is conducted based on the moving peaks benchmark to evaluate the performance of the proposed algorithm in comparison with three state-of-the-art dynamic optimization algorithms. The results indicate the proposed algorithm is effective to solve the DOPs.