•A radial space division based approach for many-objective optimization is proposed.•Radial projection is the first time to be adopted for diversity maintaining.•An adaptive grid division strategy in radial space is used for environmental selection.In evolutionary many-objective optimization, diversity maintenance plays an important role in pushing the population towards the Pareto optimal front. Existing many-objective evolutionary algorithms mainly focus on convergence enhancement, but pay less attention to diversity enhancement, which may fail to obtain uniformly distributed solutions or fall into local optima. This paper proposes a radial space division based evolutionary algorithm for many-objective optimization, where the solutions in high-dimensional objective space are projected into the grid divided 2-dimensional radial space for diversity maintenance and convergence enhancement. Specifically, the diversity of the population is emphasized by selecting solutions from different grids, where an adaptive penalty based approach is proposed to select a better converged solution from the grid with multiple solutions for convergence enhancement. The proposed algorithm is compared with five state-of-the-art many-objective evolutionary algorithms on a variety of benchmark test problems. Experimental results demonstrate the competitiveness of the proposed algorithm in terms of both convergence enhancement and diversity maintenance.Download high-res image (211KB)Download full-size image

P systems are a class of distributed parallel computing devices inspired by some basic behaviors of biological membranes, which have the restriction that each rule is executed in exactly one time unit. However, it is natural to consider the systems without the time restriction on each rule since biochemical reactions in biological systems are inherently parallel and have different reaction rates, and the execution time of biochemical reactions is unpredictably sensitive to environmental factors. In this work, we construct a family of P systems with proteins on membranes and membrane division that are “robust” against the execution time of rules. Specifically, we present a time-free uniform solution to the QSAT problem by using P systems with proteins on membranes and membrane division in the sense that the execution time of the involved rules has no influence on the correctness of the solution.

In this study, an aptamer-substrate strategy is introduced to control programmable DNA origami pattern. Combined with DNA aptamer-substrate binding and DNAzyme-cutting, small DNA tiles were specifically controlled to fill into the predesigned DNA origami frame. Here, a set of DNA logic gates (OR, YES, and AND) are performed in response to the stimuli of adenosine triphosphate (ATP) and cocaine. The experimental results are confirmed by AFM imaging and time-dependent fluorescence changes, demonstrating that the geometric patterns are regulated in a controllable and programmable manner. Our approach provides a new platform for engineering programmable origami nanopatterns and constructing complex DNA nanodevices.Keywords: aptamer; DNA origami; DNAzyme; logic gate; tile filling;

P systems are a class of distributed parallel computing models inspired by the structure and the functioning of a living cell, where the execution of each rule is completed in exactly one time unit (a global clock is assumed). However, in living cells, the execution time of different biological processes is difficult to know precisely and very sensitive to environmental factors that might be hard to control. Inspired from this biological motivation, in this work, timed polarization P systems with membrane creation are introduced and their computational efficiency and universality are investigated. Specifically, we give a time-free semi-uniform solution to the SAT problem by a family of P systems with membrane creation in the sense that the correctness of the solution is irrelevant to the times associated with the involved rules. We also prove that time-free P systems with membrane creation are computationally universal.

Recently, the toehold-mediated DNA strand displacement reaction has been widely used in detecting molecular signals. However, traditional strand displacement, without cooperative signaling among DNA inputs, is insufficient for the design of more complicated nanodevices. In this work, a logic computing system is established using the cooperative “binding-induced” mechanism, based on the AuNP-based beacons, in which five kinds of multiple-input logic gates have been constructed. This system can recognize DNA and protein streptavidin simultaneously. Finally, the manipulations of the logic system are also demonstrated by controlling programmed conjugate DNA/AuNP clusters. This study provides the possibility of detecting multiple input signals and designing complex nanodevices that can be potentially applied to the detection of multiple molecular targets and the construction of large-scale DNA-based computation.Keywords: binding-induced strand displacement; DNA self-assembly; fluorescent beacon; gold nanoparticle; logical computing

The design of DNA sequences is one of the most practical and important research topics in DNA computing. We adopt taboo search algorithm and improve the method for the systematic design of equal-length DNA sequences, which can satisfy certain combinatorial and thermodynamic constraints. Using taboo search algorithm, our method can avoid trapping into local optimization and can find a set of good DNA sequences satisfying required constraints.

•The notion of time-free solution to decision problem by P systems with proteins on membranes, in the sense that the correctness of the solution is irrelevant to the times associated with the involved rules, is defined.•A time-free uniform solution to the SAT problem by P systems with proteins on membranes is given.P systems with proteins on membranes are a class of bio-inspired computing models, where the execution of each rule completes in exactly one time unit. However, in living cells, the execution time of biochemical reactions is difficult to know precisely because of various uncontrollable factors. In this work, we present a time-free uniform solution to SAT problem by P systems with proteins on membranes in the sense that the correctness of the solution is irrelevant to the times associated with the involved rules, and the P systems are constructed from the sizes of instances.

To attack block cipher systems, it is inevitable to handle the bit-substitutions, such as S-box, cycle left shift, and expansion substitutions. In this paper, a DNA sticker algorithm for bit-substitution such as cycle left shift is proposed. The proposed algorithm requires two equal long memory strands. The first memory strand stores the original binary string, while the second memory strand stores the resulting binary string. With the proposed algorithm, cycle left shift is performed on a mass of equal long binary strings, and the computation complexity of the cycle left shift is O(n) for all n-bit binary strings. Furthermore, this work indicates that block cipher systems with a 64-bit key are perhaps insecure. This paper presents clear evidence of the ability of DNA computing to perform intractable computation problems.

Membrane systems, also called P systems, are biologically inspired theoretical models of distributed and parallel computing. This paper presents a new class of tissue-like P systems with cell separation, a feature which allows the generation of new workspace. We study the efficiency of the class of P systems and draw a conclusion that only tractable problems can be efficiently solved by using cell separation and communication rules with the length of at most 1. We further present an efficient (uniform) solution to SAT by using cell separation and communication rules with length at most 6. We conclude that a borderline between efficiency and non-efficiency exists in terms of the length of communication rules (assuming P≠NP). We discuss future research topics and open problems.

Looking for small universal computing devices is a natural and well investigated topic in computer science. Recently, this topic was also investigated in the framework of spiking neural P systems. One of the small universality results is that a small weakly universal extended spiking neural P system with 12 neurons was constructed. In this paper, a new way is introduced for simulating register machines by spiking neural P systems, where only one neuron is used for all instructions of the register machine; in this way, we can use less neurons to construct universal spiking neural P system. Specifically, we give a smaller weakly universal spiking neural P system that uses extended rules and has only 9 neurons.

Syntactic models constitute one of the main areas of mathematical studies on picture array generation. A number of 2D grammar models have been proposed motivated by a variety of applications. A P system is a biologically motivated new computing model, proposed by Păun in the area of membrane computing. It is a rich framework for dealing with different problems, including the problem of handling picture array generation. In this paper, the generative power of the array-rewriting P system with pure 2D context-free rules is investigated by comparing it with other 2D grammar models, thus bringing out the suitability of this P system model for picture array generation.

P systems are computing models inspired by some basic features of biological membranes. In this work, membrane division, which provides a way to obtain an exponential workspace in linear time, is introduced into (cell-like) P systems with communication (symport/antiport) rules, where objects are never modified but they just change their places. The computational efficiency of this kind of P systems is studied. Specifically, we present a (uniform) linear time solution to the NP-complete problem, Subset Sum by using division rules for elementary membranes and communication rules of length at most 3. We further prove that such P system allowing division rules for non-elementary membranes can efficiently solve the PSPACE-complete problem, QSAT in a uniform way.

In this paper we continue previous studies on the computational efficiency of spiking neural P systems, under the assumption that some pre-computed resources of exponential size are given in advance. Specifically, we give a deterministic solution for each of two well known PSPACE-complete problems: QSAT and Q3SAT. In the case of QSAT, the answer to any instance of the problem is computed in a time which is linear with respect to both the number n of Boolean variables and the number m of clauses that compose the instance. As for Q3SAT, the answer is computed in a time which is at most cubic in the number n of Boolean variables.

P systems are a class of computational models inspired by the structure and the functioning of a living cell. In the semantics of P systems, there exists a global clock, which marks the time for the system, and the execution time of each rule takes exactly one time unit. However, in living cells, the execution time of different biochemical reactions is dependent on many uncontrollable factors, and it is hard to know precisely the specific execution time of a reaction. In this work, with this biological inspiration, we consider the class of P systems with active membranes that are “robust” against the execution time of rules. Specifically, we give a time-free uniform solution to the SAT problem using P systems with active membranes, where the constructed P system can solve a family of instances with an arbitrarily given size, and the execution time of the involved rules has no influence on the correctness of the solution. We also prove that any Turing computable set of numbers can be generated by a time-free P system with active membranes in the sense that the set of numbers generated by the given P system with active membranes does not depend on the execution time of rules.

Numerical P systems are a class of P systems inspired both from the structure of living cells and from economics, where variables are associated with the membranes, and these associations are not changed during the computation. However, in the standard P systems, a crucial character for objects is that they can pass through membranes, between regions of the same cell, between cells, or between cells and their environment. We introduce this character also to numerical P systems, and call the new variant numerical P systems with migrating variables (MNP systems). The computational power of MNP systems is investigated both as number generators and as string generators, working in the one-parallel or the sequential modes. Specially, as number generators, MNP systems are proved to be universal working in the above two modes. As string generators, the generative capacity of such systems is investigated having as a reference the families of languages in the Chomsky hierarchy, and a characterization of recursively enumerable languages is obtained.

Tissue P systems are distributed parallel computing models inspired by the structure of tissue and the way of communicating substances between two cells or between a cell and the environment. In this work, we consider a variant of tissue P systems, called tissue P systems with promoters, where the application of rules is regulated by promoters. The computational power of such P systems is investigated. Specifically, it is proved that such P systems using only antiport rules of length 2 or using only symport rules of length 1 are able to compute only finite sets of non-negative integers. However, such P systems with one cell and using antiport rules of length 2 and symport rules of length 1 or only using symport rules of length 2 are Turing universal. Moreover, a uniform solution to the SAT problem is provided by tissue P systems with promoters and cell division using only antiport rules of length 2.

Spiking neural P systems, shortly called SN P systems, are a class of distributed and parallel neural-like computing models, inspired from the way of neurons spiking and communicating with each other by means of spikes. In this work, we propose a new variant of SN P systems, called SN P systems with request rules. In such a system, besides spiking and forgetting rules, a neuron can have request rules, with which the neuron can sense “stimulus” from the environment by receiving a certain number of spikes. We investigate the computation power of SN P systems with request rules. It is obtained that such systems are Turing universal, even with a small number of neurons. Specifically, (i) SN P systems with request rules having 4 neurons can compute any set of Turing computable natural numbers and (ii) with 47 neurons such systems can compute any Turing computable function.

With mathematical motivation, we consider a combination of basic features of multiset-rewriting P systems and of spiking neural P systems, that is, we consider cell-like P systems with spiking rules in their membranes (hence dealing with only one kind of objects, the spikes). The universality of these systems as number generating devices is proved for the two usual ways to define the output (internally or externally) and for various restrictions on the spiking rules. Several research topics are also pointed out.

In spite of the fact that many ways of using the evolution rules in a P system were already investigated, there is still a case, which we call the flat maximal parallelism, which appeared in several papers, but which deserves a more careful attention: in each step, in each membrane, a maximal set of applicable rules is chosen and each rule in the set is applied exactly once. In this work, flat maximal parallelism is studied for non-cooperating P systems with promoters. Specifically, we prove that non-cooperating P systems with at most one promoter associated with any rule, working in the flat maximally parallel way, are Turing universal (the Turing universality of such P systems is open if they work in the maximally parallel way). Moreover, a uniform solution to the SAT problem is provided by using non-cooperating P systems with promoters and membrane division, working in the flat maximal parallel way.

Tissue P systems with symport/antiport rules are a class of distributed parallel computing models inspired by the cell intercommunication in tissues, where objects are never modified in the process of communication, just changing their place within the system. In this work, a variant of tissue P systems, called tissue P systems with evolutional symport/antiport rules is introduced, where objects are moved from one region to another region and may be evolved during this process. The computational power of such P systems is studied. Specifically, it is proved that such P systems with one cell and using evolutional symport rules of length at most 3 or using evolutional antiport rules of length at most 4 are Turing universal (only the family of all finite sets of positive integers can be generated by such P systems if standard symport/antiport rules are used). Moreover, cell division rules are considered in tissue P systems with evolutional symport/antiport rules, and a limit on the efficiency of such P systems is provided with evolutional communication rules of length at most 2. The computational efficiency of this kind of models is shown when using evolutional communication rules of length at most 4.