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Membrane Computing and Its Applications

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Computing and Artificial Intelligence".

Deadline for manuscript submissions: 30 April 2025 | Viewed by 13993

Special Issue Editors


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Guest Editor
College of Computer Science, Chongqing University, Chongqing 400044, China
Interests: biological computing; evolutionary computing; intelligent information systems

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Guest Editor
School of Automation, Chengdu University of Information Technology, Chengdu 610225, China
Interests: membrane computing; natural computing; artificial intelligence
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
Interests: membrane computing; bioinformatics

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Guest Editor
College of Computer Science and Technology, China University of Petroleum, Qingdao 266580, China
Interests: deep learning; membrane computing

Special Issue Information

Dear Colleagues,

Membrane computing (MC) is a computing paradigm inspired by the structure and functionality of living cells. The theory, method, simulation, and application of membrane computing have developed rapidly since it was proposed by Professor Gheorghe Păun in 1998. The computing system based on membrane computing idea is called the P system, which has been widely combined with computer science, neural computing, natural heuristic optimization, and other disciplines, and has produced a lot of theoretical and application achievements.

This Special Issue aims to publish new ideas and original research results of membrane computing from theory to application, hoping to promote membrane computing to a wider computer science community and promote its wider research and application. Theoretical results, application methods, system design, and simulation implementation are all welcome. The list of topics includes, but is not limited to, the following:

  • New architecture and computing model of the P system;
  • Computing power of the P system;
  • Problem solving method based on the P system;
  • Optimization theory and method based on the P system;
  • Analysis and design of the P system for NP-hard problems;
  • Application of the P system in engineering problems;
  • Modeling, verification and simulation tools for membrane systems.

Prof. Dr. Ping Guo
Prof. Dr. Gexiang Zhang
Dr. Bosheng Song
Prof. Dr. Tao Song
Guest Editors

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Keywords

  • membrane computing
  • P system
  • membrane computing model
  • cell-like P system
  • tissue-like P system
  • spiking neural P systems
  • P system application
  • P system simulation
  • optimization algorithm
  • NP hard problem

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Published Papers (8 papers)

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Research

14 pages, 3294 KiB  
Article
Research on Detection of Rice Pests and Diseases Based on Improved yolov5 Algorithm
by Hua Yang, Dang Lin, Gexiang Zhang, Haifeng Zhang, Junxiong Wang and Shuxiang Zhang
Appl. Sci. 2023, 13(18), 10188; https://doi.org/10.3390/app131810188 - 11 Sep 2023
Cited by 10 | Viewed by 2529
Abstract
Rice pests and diseases have a significant impact on the quality and yield of rice, and even have a certain impact on and cause a loss in the national agricultural industry and economy. The timely and accurate detection of pests and diseases is [...] Read more.
Rice pests and diseases have a significant impact on the quality and yield of rice, and even have a certain impact on and cause a loss in the national agricultural industry and economy. The timely and accurate detection of pests and diseases is the basic premise of formulating effective rice pest control and prevention programs. However, the complexity and diversity of pests and diseases and the high similarity between some pests and diseases make the detection and classification task of pests and diseases extremely difficult without detection tools. The existing target detection algorithms can barely complete the task of detecting pests and diseases, but the detection effect is not ideal. In the actual situation of rice disease and insect pest detection, the detection algorithm is required to have fast speed, high accuracy, and good performance for small target detection, and so this paper improved the popular yolov5 algorithm to achieve an ideal detection performance suitable for rice disease and insect pest detection. This paper briefly introduces the current status and influence of rice pests and diseases and several target detection algorithms based on deep learning. Based on the yolov5 algorithm, the RepVGG network structure is introduced, 3*3 convolution is combined with ReLU, a training time model with multi-branch topology is adopted, and the inference time is reduced through layer merging. To improve algorithm detection speed, the SK attention mechanism is introduced to improve the receptive field of the convolution kernel to obtain more information and improve accuracy. In addition, Adaptive NMS is replaced by Adaptive NMS, the dynamic suppression strategy is adopted, and scores for learning density are set, which greatly improves the problems of missing detection and the false detection of small targets. Finally, the improved algorithm model is combined with membrane calculation to further improve the accuracy and speed of the algorithm. According to the experimental results, the accuracy of the improved algorithm is increased by about 2.7 percentage points, and the mAP is increased by 4.3 percentage points, up to 94.4%. The speed is improved by about 2.8 percentage points, and indicators such as recall rate and AP are improved. Full article
(This article belongs to the Special Issue Membrane Computing and Its Applications)
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Figure 1
<p>Flowchart of the Faster R-CNN algorithm.</p>
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<p>Structure of the yolov1 algorithm.</p>
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<p>Structure of the yolov5 algorithm.</p>
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<p>conv_3*3 process diagram.</p>
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<p>RepVGG network structure.</p>
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<p>Schematic diagram of SK attention mechanism.</p>
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<p>Performance counters of the yolov5-RSAN algorithm.</p>
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<p>Effect of yolov5-RSAN algorithm on rice pest detection.</p>
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18 pages, 2188 KiB  
Article
Conversion between Number Systems in Membrane Computing
by Hai Nan, Jiqiao Jiang, Jie Zhang, Ran Liu and Aijuan Wang
Appl. Sci. 2023, 13(17), 9945; https://doi.org/10.3390/app13179945 - 2 Sep 2023
Cited by 2 | Viewed by 1787
Abstract
The number system is the representation method of numbers, and number system conversion is the most basic function of a computing system. The decimal system is the most commonly used number system; however, it may not necessarily be the most suitable number system [...] Read more.
The number system is the representation method of numbers, and number system conversion is the most basic function of a computing system. The decimal system is the most commonly used number system; however, it may not necessarily be the most suitable number system in a computing system. This paper investigates the conversion methods between different number systems and designs corresponding cells, such as P systems, to implement them. The P systems we designed include Π10_2 and Π2_10 to implement conversion between decimal and binary, Π10_m and Πm_10 to implement conversion between decimal and m-base. The operation process of each P system was explained through examples, and their feasibility and effectiveness were verified through simulation software, UPSimulator. Full article
(This article belongs to the Special Issue Membrane Computing and Its Applications)
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Figure 1
<p>The structure of a cell-like P system.</p>
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<p>P system for decimal to binary.</p>
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<p>P system for binary to decimal.</p>
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<p>P system for decimal to m-binary.</p>
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<p>P system for n-bit m deciaml to decimal.</p>
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<p>P system for 4-bit 3 decimal to decimal.</p>
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<p>Simulation process from decimal number ‘10’ to binary number ‘1010’.</p>
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<p>Simulation process from decimal number ‘10’ to binary number ‘1010’.</p>
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<p>Simulation result of the 4-bit 3-decimal number ‘1021’.</p>
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20 pages, 3134 KiB  
Article
P System Design for Integer Factorization
by Hai Nan, Zhijian Xue, Chaoyue Li, Mingqiang Zhou and Xiaoyang Liu
Appl. Sci. 2023, 13(15), 8910; https://doi.org/10.3390/app13158910 - 2 Aug 2023
Viewed by 1347
Abstract
Membrane computing is a natural computing branch inspired by the structure of biological cells. The mathematical abstract model of a membrane computing system is called a P System, which is one of the main topics in membrane computing research for the design and [...] Read more.
Membrane computing is a natural computing branch inspired by the structure of biological cells. The mathematical abstract model of a membrane computing system is called a P System, which is one of the main topics in membrane computing research for the design and verification of a P System. Integer factorization is still a world-class problem and a very important research direction. If a fast method can be found to solve the integer factorization problem, several important cryptographic systems including the RSA public key algorithm will be broken. The aim of this paper is to design a P System capable of implementing integer decomposition, taking advantage of the characteristics of parallelism of P Systems. We construct a process with a main goal to study the modal exponential function f(x) = ax mod N and explore the possible periodic behavior for different values of a. We attempt to compute nontrivial prime factors by the period found and constrain the operation of the P System in polynomial time. Full article
(This article belongs to the Special Issue Membrane Computing and Its Applications)
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Figure 1
<p>An example of membrane structure.</p>
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<p>The relation between the roles of <span class="html-italic">δ</span> and <span class="html-italic">τ</span>.</p>
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<p>Flow chart of the system execution. (<b>a</b>): The first stage splits the process of computing the sub-task membranes of the different values of <span class="html-italic">a</span>; (<b>b</b>): The second stage shows the execution flow of calculating the membrane corresponding to a certain <span class="html-italic">a</span>. The value of <span class="html-italic">N</span> in <span class="html-italic">ξ<sup>N</sup></span> is the number to decompose, not the exponential order. The value of <span class="html-italic">a</span> in <span class="html-italic">z<sup>a</sup></span><sup>−1</sup> will not be greater than <span class="html-italic">N</span> itself (the number of digits to be decomposed <span class="html-italic">N</span>). The * in the figure represents a random sample of the generated Com membranes.</p>
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<p>Steps for solving a large number of decompositions using the P system.</p>
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<p>Membrane structure diagram at T<sub>0</sub> to T<sub>5</sub> (in the figure, the label names of some membranes are abbreviated, such as how Computer is abbreviated as Com, the same applies below).</p>
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<p>Membrane structure diagram at T<sub>6</sub> to T<sub>11</sub>, the membrane behind T<sub>6</sub> only displays the first split membrane.</p>
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<p>Partial membrane structure diagram of T<sub>14</sub> toT<sub>26</sub>.</p>
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<p>Partial membrane structure diagram of T<sub>27</sub> toT<sub>43</sub>.</p>
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<p>Partial membrane structure diagram of T<sub>44</sub> to end.</p>
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<p>Simulation results using UPSimulator, where (<b>a</b>) experimental results with <span class="html-italic">N</span> = 15, which factored into 5 and 3 marked with the red square; (<b>b</b>) experimental results with <span class="html-italic">N</span> = 39, which factored into 13 and 3 marked with the red square.</p>
Full article ">
45 pages, 6695 KiB  
Article
P System with Fractional Reduction
by Hai Nan, Yumeng Kong, Jie Zhan, Mingqiang Zhou and Ling Bai
Appl. Sci. 2023, 13(14), 8514; https://doi.org/10.3390/app13148514 - 23 Jul 2023
Cited by 1 | Viewed by 1324
Abstract
Membrane computing is a branch of natural computing, which is a new computational model abstracted from the study of the function and structure of living biological cells. The study of numerical computation based on membrane computation has received increasing attention in recent years, [...] Read more.
Membrane computing is a branch of natural computing, which is a new computational model abstracted from the study of the function and structure of living biological cells. The study of numerical computation based on membrane computation has received increasing attention in recent years, where maximum parallelism in the execution of evolutionary rules plays an important role in improving the efficiency of numerical computation. Numbers in numerical computation are usually represented as decimals or fractions, and this paper investigates the fundamental problem in fraction representation and operations—fraction simplification. By improving the parallelization of two traditional fractional reduction algorithms, we design the corresponding fractional reduction class cells P System Π1 and P System Π2. Combining these two P Systems, this paper designs P System Π3. The feasibility and effectiveness of the P System designed in this paper are verified experimentally with the simulation software UPSimulator, and the characteristics and application scenarios of the three P Systems are analyzed. Full article
(This article belongs to the Special Issue Membrane Computing and Its Applications)
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Figure 1
<p>Structure of the cell-like P System. (<b>a</b>) Cell membrane; (<b>b</b>) Abstraction of membranes.</p>
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<p>Initial Pattern of the More Phase Derogation Algorithm P System.</p>
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<p>Flowchart of the fraction simplification solution of the more phase derogation algorithm P System. (<b>a</b>) Flowchart of the sequence <math display="inline"><semantics><mrow><mfenced open="{" close="}" separators="|"><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced><mo>,</mo><mfenced open="{" close="}" separators="|"><mrow><msub><mrow><mi>y</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow></semantics></math> by more phase derogation algorithm; (<b>b</b>) Flowchart of the sequence <math display="inline"><semantics><mrow><mo>{</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>}</mo></mrow></semantics></math>, <math display="inline"><semantics><mrow><mo>{</mo><msub><mrow><mi>q</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>}</mo></mrow></semantics></math> by more phase derogation algorithm.</p>
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<p>Flowchart of the more phase derogation algorithm example.</p>
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<p>Initial pattern of the P System in the division algorithm.</p>
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<p>Flow diagram of the division algorithm P System.</p>
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<p>Process diagram for solving the example of the division algorithm P System. (<b>a</b>) Flowchart for finding the greatest common divisor x in the division algorithm; (<b>b</b>) Flowchart for simplifying the result of the division algorithm example.</p>
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<p>Process diagram for solving the example of the rolling phase division P System.</p>
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<p>Flow chart for solving the combined method P System. (<b>a</b>) Flow chart for the combination of the two methods to find the intermediate values m, n; (<b>b</b>) Flow chart for finding the maximum common divisor by the division algorithm; (<b>c</b>) Flow chart for the sequence <math display="inline"><semantics><mrow><mo>{</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>}</mo></mrow></semantics></math>, <math display="inline"><semantics><mrow><mo>{</mo><msub><mrow><mi>q</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>}</mo></mrow></semantics></math> by the more phase derogation algorithm.</p>
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<p>Simplified flow chart for approximate differentiation of the two combined examples.</p>
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<p>Software structure of UPS.</p>
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<p>Initial state of the instance.</p>
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<p>Example simulation results.</p>
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<p>Four-digit parameter comparison line chart.</p>
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<p>Five-digit parameter comparison line chart.</p>
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<p>Six-digit parameter comparison line chart.</p>
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<p>Step number comparison of three methods in a line chart.</p>
Full article ">
33 pages, 1614 KiB  
Article
Performing Arithmetic Operations with Locally Homogeneous Spiking Neural P Systems
by Xu Zhang, Zongrong Hu, Jingyi Li and Ran Liu
Appl. Sci. 2023, 13(14), 8460; https://doi.org/10.3390/app13148460 - 21 Jul 2023
Viewed by 1101
Abstract
The parallelism of rule execution in membrane computing provides support for improving computational efficiency. Membrane computing models have been applied in many fields. In arithmetic operations, designing basic arithmetic operation spiking neural P systems using fewer neurons and rule types has been an [...] Read more.
The parallelism of rule execution in membrane computing provides support for improving computational efficiency. Membrane computing models have been applied in many fields. In arithmetic operations, designing basic arithmetic operation spiking neural P systems using fewer neurons and rule types has been an important field of membrane computing application research in recent years. We discuss the application of locally homogeneous spiking neural P systems in arithmetic operations. The purpose is to design a spiking neural P system with fewer neurons and rule types to perform arithmetic operations. We designed the addition and subtraction of a locally homogeneous spiking neural P system without weight and delay. They include two input neurons to achieve any two binary number subtraction, one input neuron to achieve any two binary number addition and subtraction, and one input neuron to achieve any n binary number addition and subtraction. This is an attempt to apply the locally homogeneous spiking neural P system in arithmetic operations. Compared with the current excellent spiking neural P system performing arithmetic operations, our designed locally homogeneous spiking neural P system is more concise. The system we designed reduces the number of neurons required for n number addition operations by k − 6 and reduces the number of rule types by 5k − 14. Full article
(This article belongs to the Special Issue Membrane Computing and Its Applications)
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Figure 1
<p>The LHSNP system П<span class="html-italic"><sub>Add</sub></span><sub>2</sub> with 1 input neuron for 2 <span class="html-italic">k</span>-bit binary numbers addition.</p>
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<p>The LHSNP system П<span class="html-italic"><sub>Add</sub></span><sub>3</sub> with 1 input neuron for <span class="html-italic">n k</span>-bit binary numbers addition.</p>
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<p>The LHSNP system П<span class="html-italic"><sub>Sub</sub></span><sub>1</sub> with 2 input neurons for two <span class="html-italic">k</span>-bit binary numbers subtraction.</p>
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<p>The LHSNP system П<span class="html-italic"><sub>Sub</sub></span><sub>2</sub> with 1 input neuron for 2 <span class="html-italic">k</span>-bit binary numbers subtraction.</p>
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<p>The LHSNP system П<span class="html-italic"><sub>Sub</sub></span><sub>3</sub> with 1 input neuron for <span class="html-italic">n k</span>-bit binary numbers subtraction.</p>
Full article ">
30 pages, 4525 KiB  
Article
Q-MeaMetaVC: An MVC Solver of a Large-Scale Graph Based on Membrane Evolutionary Algorithms
by Chunmei Liao, Ping Guo, Jiaqi Gu and Qiuju Deng
Appl. Sci. 2023, 13(14), 8021; https://doi.org/10.3390/app13148021 - 9 Jul 2023
Viewed by 1269
Abstract
In recent years, the rapid development of the internet and the advancement of information technology have produced a large amount of large-scale data, some of which are presented in the form of large-scale graphs, such as social networks and sensor networks. Minimum vertex [...] Read more.
In recent years, the rapid development of the internet and the advancement of information technology have produced a large amount of large-scale data, some of which are presented in the form of large-scale graphs, such as social networks and sensor networks. Minimum vertex cover (MVC) is an important problem in large-scale graph research. This paper proposes a solver Q-MeaMetaVC based on the MVC framework PEAF and the membrane evolution algorithm framework MEAF. First, the graph is reduced and divided into two types of connected components (bipartite graph and non-bipartite graph) to reduce the scale of the problem. Second, different membrane structures are designed for different types of connected components to better represent the connected component features and facilitate solutions. Third, a membrane evolution algorithm (MEA), which includes fusion, division, cytolysis, and selection operators, is designed to solve the connected components. Then, Q-MeaMetaVC is compared with the best MVC solver in recent years on the test set, and good experimental results that are obtained verify the feasibility and effectiveness of Q-MeaMetaVC in solving the MVC of large-scale graphs. Full article
(This article belongs to the Special Issue Membrane Computing and Its Applications)
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<p>Example of the fusion operator.</p>
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<p>Example of the division operator.</p>
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<p>The initial membrane structure of the MEAF.</p>
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<p>The base membrane structure of Q-MeaMetaVC.</p>
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<p>The non-bipartite graph-connected component C<span class="html-italic"><sub>i</sub></span> membrane structure.</p>
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<p>CB<span class="html-italic"><sub>j</sub></span> membrane structure for processing the bipartite graph-connected component.</p>
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<p>The original bipartite graph.</p>
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<p>Bipartite graph solution example.</p>
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<p>Bipartite graph solution example.</p>
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<p>An instance of the original graph and its result after preprocessing.</p>
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<p>An example of how Q-MeaMetaVC solves a minimum vertex cover problem.</p>
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<p>An example about how division and fusion work.</p>
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<p>An example of how Selection and Cytolysis works.</p>
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<p>An example of what to do in the inverse processing stage.</p>
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<p>Compares the minimum and the average size of the solutions obtained by Q-MeaMetaVC with different N.</p>
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<p>The number of instances in which the minimum and the average size of the solutions obtained by Q-MeaMetaVC reach the optimal values under different iterCounts.</p>
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<p>The number of instances in which each solver performs the best.</p>
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<p>Instance distribution based on the differences between the sizes of the solutions in the testing set.</p>
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<p>Instance distribution based on the differences between the sizes of the solutions in the testing set.</p>
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25 pages, 8862 KiB  
Article
An Extended Membrane System with Monodirectional Tissue-like P Systems and Enhanced Particle Swarm Optimization for Data Clustering
by Lin Wang, Xiyu Liu, Jianhua Qu, Yuzhen Zhao, Liang Gao and Qianqian Ren
Appl. Sci. 2023, 13(13), 7755; https://doi.org/10.3390/app13137755 - 30 Jun 2023
Viewed by 1052
Abstract
In order to establish a highly efficient P system for resolving clustering problems and overcome the computation incompleteness and implementation difficulty of P systems, an attractive clustering membrane system, integrated with enhanced particle swarm optimization (PSO) based on environmental factors and crossover operators [...] Read more.
In order to establish a highly efficient P system for resolving clustering problems and overcome the computation incompleteness and implementation difficulty of P systems, an attractive clustering membrane system, integrated with enhanced particle swarm optimization (PSO) based on environmental factors and crossover operators and a distributed parallel computing model of monodirectional tissue-like P systems (MTP), is constructed and proposed, which is simply named ECPSO-MTP. In the proposed ECPSO-MTP, two kinds of evolution rules for objects are defined and introduced to rewrite and modify the velocity of objects in different elementary membranes. The velocity updating model uses environmental factors based on partitioning information and randomly replaces global best to improve the clustering performance of ECPSO-MTP. The crossover operator for the position of objects is based on given objects and other objects with crossover probability and is accomplished through the hybridization of the global best of elementary membranes to reject randomness. The membrane structure of ECPSO-MTP is abstracted as a network structure, and the information exchange and resource sharing between different elementary membranes are accomplished by evolutional symport rules with promoters for objects of MTP, including forward and backward communication rules. The evolution and communication mechanisms in ECPSO-MTP are executed repeatedly through iteration. At last, comparison experiments, which are conducted on eight benchmark clustering datasets from artificial datasets and the UCI Machine Learning Repository and eight image segmentation datasets from BSDS500, demonstrate the effectiveness of the proposed ECPSO-MTP. Full article
(This article belongs to the Special Issue Membrane Computing and Its Applications)
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<p>The membrane structure of the proposed ECPSO-MTP.</p>
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<p>The communication relationship in the proposed ECPSO-MTP.</p>
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<p>Comparison of convergence results from six test clustering approaches on eight datasets. (<b>a</b>) Data_9_2; (<b>b</b>) Square4; (<b>c</b>) Iris; (<b>d</b>) Newthyroid; (<b>e</b>) Seeds; (<b>f</b>) Yeast; (<b>g</b>) Glass; (<b>h</b>) Wine.</p>
Full article ">Figure 3 Cont.
<p>Comparison of convergence results from six test clustering approaches on eight datasets. (<b>a</b>) Data_9_2; (<b>b</b>) Square4; (<b>c</b>) Iris; (<b>d</b>) Newthyroid; (<b>e</b>) Seeds; (<b>f</b>) Yeast; (<b>g</b>) Glass; (<b>h</b>) Wine.</p>
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<p>Eight test images. (<b>a</b>) Lawn; (<b>b</b>) Agaric; (<b>c</b>) Church; (<b>d</b>) Castle; (<b>e</b>) Elephants; (<b>f</b>) Lane; (<b>g</b>) Starfish; (<b>h</b>) Pyramid.</p>
Full article ">Figure 4 Cont.
<p>Eight test images. (<b>a</b>) Lawn; (<b>b</b>) Agaric; (<b>c</b>) Church; (<b>d</b>) Castle; (<b>e</b>) Elephants; (<b>f</b>) Lane; (<b>g</b>) Starfish; (<b>h</b>) Pyramid.</p>
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<p>The labels of eight test images. (<b>a</b>) Lawn; (<b>b</b>) Agaric; (<b>c</b>) Church; (<b>d</b>) Castle; (<b>e</b>) Elephants; (<b>f</b>) Lane; (<b>g</b>) Starfish; (<b>h</b>) Pyramid.</p>
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<p>Segmentation results obtained by SLIC for eight test images. (<b>a</b>) Lawn; (<b>b</b>) Agaric; (<b>c</b>) Church; (<b>d</b>) Castle; (<b>e</b>) Elephants; (<b>f</b>) Lane; (<b>g</b>) Starfish; (<b>h</b>) Pyramid.</p>
Full article ">Figure 6 Cont.
<p>Segmentation results obtained by SLIC for eight test images. (<b>a</b>) Lawn; (<b>b</b>) Agaric; (<b>c</b>) Church; (<b>d</b>) Castle; (<b>e</b>) Elephants; (<b>f</b>) Lane; (<b>g</b>) Starfish; (<b>h</b>) Pyramid.</p>
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<p>Comparison of clustering results on the Lawn image. (<b>a</b>) K-means; (<b>b</b>) SC; (<b>c</b>) PSO; (<b>d</b>) ECPSO-MTP.</p>
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<p>Comparison of clustering results on the Agaric image. (<b>a</b>) K-means; (<b>b</b>) SC; (<b>c</b>) PSO; (<b>d</b>) ECPSO-MTP.</p>
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<p>Comparison of clustering results on the Church image. (<b>a</b>) K-means; (<b>b</b>) SC; (<b>c</b>) PSO; (<b>d</b>) ECPSO-MTP.</p>
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<p>Comparison of clustering results on the Castle image. (<b>a</b>) K-means; (<b>b</b>) SC; (<b>c</b>) PSO; (<b>d</b>) ECPSO-MTP.</p>
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<p>Comparison of clustering results on the Elephants image. (<b>a</b>) K-means; (<b>b</b>) SC; (<b>c</b>) PSO; (<b>d</b>) ECPSO-MTP.</p>
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<p>Comparison of clustering results on the Lane image. (<b>a</b>) K-means; (<b>b</b>) SC; (<b>c</b>) PSO; (<b>d</b>) ECPSO-MTP.</p>
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<p>Comparison of clustering results on the Starfish image. (<b>a</b>) K-means; (<b>b</b>) SC; (<b>c</b>) PSO; (<b>d</b>) ECPSO-MTP.</p>
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<p>Comparison of clustering results on the Pyramid image. (<b>a</b>) K-means; (<b>b</b>) SC; (<b>c</b>) PSO; (<b>d</b>) ECPSO-MTP.</p>
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19 pages, 7883 KiB  
Article
Density Peaks Clustering Algorithm Based on a Divergence Distance and Tissue—Like P System
by Fuhua Ge and Xiyu Liu
Appl. Sci. 2023, 13(4), 2293; https://doi.org/10.3390/app13042293 - 10 Feb 2023
Cited by 1 | Viewed by 1829
Abstract
Density Peaks Clustering (DPC) has recently received much attention in many fields by reason of its simplicity and efficiency. Nevertheless, empirical studies have shown that DPC has some shortfalls: (i) similarity measurement based on Euclidean distance is prone to misclassification. When dealing with [...] Read more.
Density Peaks Clustering (DPC) has recently received much attention in many fields by reason of its simplicity and efficiency. Nevertheless, empirical studies have shown that DPC has some shortfalls: (i) similarity measurement based on Euclidean distance is prone to misclassification. When dealing with clusters of non-uniform density, it is very difficult to identify true clustering centers in the decision graph; (ii) the clustering centers need to be manually selected; (iii) the chain reaction; an incorrectly assigned point will affect the clustering outcome. To settle the above limitations, we propose an improved density peaks clustering algorithm based on a divergence distance and tissue—like P system (TP-DSDPC in short). In the proposed algorithm, a novel distance measure is introduced to accurately estimate the local density and relative distance of each point. Then, clustering centers are automatically selected by the score value. A tissue—like P system carries out the entire algorithm process. In terms of the three evaluation metrics, the improved algorithm outperforms the other comparison algorithms using multiple synthetic and real-world datasets. Full article
(This article belongs to the Special Issue Membrane Computing and Its Applications)
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<p>The basic membrane structure of the tissue—like P system.</p>
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<p>The initial configuration of the tissue—like P system.</p>
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<p>The workflow of the TP-DSDPC algorithm.</p>
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<p>The realization process of the tissue—like P system.</p>
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<p>The original data of the nine synthetic datasets.</p>
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<p>Clustering results on Flame.</p>
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<p>Clustering results on Jain.</p>
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<p>Clustering results on Spiral.</p>
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<p>Clustering results on Threecircles.</p>
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<p>Clustering results on Smile.</p>
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<p>Clustering results on Fourlines.</p>
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<p>Clustering results on Aggregation.</p>
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<p>Clustering results on R15.</p>
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<p>The ACC of the six algorithms on six real-world datasets.</p>
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<p>The NMI of the six algorithms on six real-world datasets.</p>
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<p>The ARI of the six algorithms on six real-world datasets.</p>
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