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In this paper, without assuming balanced network topologies, we address the weighted average consensus problem for discrete-time single-integrator multi-agent systems with logarithmic quantized information communication. By incorporating generalized quadratic Lyapunov function with the discrete-time Bellman-Gronwall inequality, a new upper bound about the quantization precision parameter of the infinite-level logarithmic quantizer is derived to design quantized protocol, under which agents in strongly connected directed networks can attain weighted average consensus. The obtained new upper bound clearly characterizes the intimate relation between the quantization precision parameter and the directed network topology. The proposed quantized protocol is particularly applicable to digital networks where balanced message passing among agents is not available.

Multiple-valued logic is an extended form of Boolean logic. In daily life, people often encounter the problem about the multiple-valued logic. With further study on Boolean logic, multiple-valued logic has been paid more and more attention by researchers. This paper achieves the operation of AND gate in three-valued logic by using the DNA hairpin structure. The experiment makes the DNA hairpin structure as the basic structure, and the molecular beacon as the input signal, and at last judges the logical results according to the intensity of fluorescence and gel electrophoresis. This method has the advantages that it has high sensitivity, good feasibility, and it is easy to observe. In addition, this method reduces the hybrid competition to a certain extent, and it is a new attempt to the research on multiple-valued logic.

Plasmid DNA algorithm of the minimal vertex covering problem is proposed upon the basic idea and operation of plasmid DNA computing model. In the plasmid DNA algorithm, though an appropriate encoding and the basic biological operation, we finish the generation and separation of solution. On the basis of the molecular biology methods, the algorithm is feasible.

About thirty years ago, the concept of the complexity of the problem was proposed. The most important complex class is P and NP class. Fruitful results of this concept are the existence of the so-called complex class complete problem. If the other issues of this class once solved in polynomial time, then the problem must exist polynomial time algorithms. Therefore, the complete problem is most difficult to solve, but because of their presence, we can choose any of them improved algorithm for a problem, so this kind of problem to get a good solution. DNA computing is a novel method that solving a class of intractable computational problems, in which the computing speeds up exponentially with the problem size. Up to now, many accomplishments have been made to improve its performance and increase its reliability. Maximum Independent Set problem (MIS) is a well-known NP-complete problem. Maximum Clique and Minimum Vertex Covering problem is equivalent to Maximum Independent Set problem. In this paper, we explore solving Maximum Independent Set problem by transforming it into equivalent 0-1 programming problem, and utilizing the surface computing model of that. The proposed method demonstrates universal nature of NP-complete problem.

The nullity of a graph is defined as the multiplicity of the eigenvalue zero in the spectrum of the adjacency matrix of the graph. We investigate a class of graphs with pendant trees, and express the nullity of such graph in terms of that of its subgraphs. As an application of our results, we characterize unicyclic graphs with a given nullity.

DNA computing is a novel method of solving a class of intractable computational problem, in which the computing speeds up exponentially with problem size. Up to now, many accomplishments have been made to improve its performance and increase its reliability. The positive integer linear programming is an NP-complete problem, in the paper, we solved the positive integer linear programming problem with fluorescence labeling techniques based on surface chemistry by attempted to apply DNA computing to programming problem. Our method has some significant advantages such as simple encoding, low cost, and short operating time.

DNA computing is being applied to solve problems in combinatorial optimization, logic and Boolean circuits. Breakthrough solutions in combinatorial optimization are the most impressive area of success but, in order to solve combinatorial optimization problems, problems related to the reliability of biological operators, stable DNA expressions, processing speed, expandability and the universality of evaluation criteria must be solved. This study implements a DNA sequence generation system that minimizes errors using DNA coding based on evolutionary models and performs simulation using biological experiment operators. The usefulness of this system is evaluated by applying the Hamiltonian Path Problem (HPP) in the form of a genetic algorithm. The proposed system generates sequences with minimal errors, as compared to existing systems, and identifies optimal solutions for combinatorial optimization problems in significantly reduced processing times.