**AUTHORS:**Xiyu Liu, Jie Xue

**Download as PDF**

**ABSTRACT:**
The purpose of this paper is to propose a new kind of P system on chain structure. We present the basic discrete Morse structure, membrane structures on complexes, objects with positive and negative charges and communication rules on chains. The computation completeness of Morse P system is proved by simulation of register machine. The process of Boltzmann Machines are implemented by Morse P system. A new clustering technique is described on Morse P system based Boltzmann Machines. Examples are given to show the effect of the algorithm.

**KEYWORDS:**
Cluster analysis, membrane computing, discrete Morse theory, chain structure

**REFERENCES:**

[1] Rozenberg G. Paun and A. Salomaa (eds.), ˘ Handbook of Membrane Computing, Oxford University Press, Cambridge, 2010.

[2] Xiangxiang Zeng, Tao Song, Xingyi Zhang and Linqiang Pan, Performing Four Basic Arithmetic Operations With Spiking Neural P Systems, IEEE transactions on nanoscience, 11:4, 2012, pp.366–374.

[3] Tao Song, Linqiang Pan and G. Paun, Asyn- ˘ chronous spiking neural P systems with local synchronization, Information Sciences, 219, 2012, pp.197-C207.

[4] Krithivasan Rama R. Kamala, Introduction to Formal Languages, Automata Theory and Computation, Pearson Education India, 2009.

[5] G. Paun and R. P ˘ aun, Membrane computing and ˘ economics: numerical P systems, Fundamenta Informaticae, 73(122), 2006, pp.213–227.

[6] Bogdan Aman and Gabriel Ciobanu, Behavioural Equivalences in Real-Time P Systems, CMC14, Chisinau, Moldova, 2013, pp.49–62.

[7] H. Adorna, Gh. Paun and M. Prez Jimnez, ˘ On Communication Complexity in EvolutionCommunication P systems, Romanian Journal of Information Science and Technology, 13(2), 2010, pp.113–130.

[8] Ciprian Dragomir, Florentin Ipate, Savas Konur, Raluca Lefticaru and Laurentiu Mierla, Model Checking Kernel P Systems, CMC14, Chisinau, Moldova, 2013, pp.131–152.

[9] E.H.L. Aarts and Jan H.M. Korst, Boltzmann machines and their applications, Lecture Notes in Computer Science, Volume 258, 1987, pp.34– 50.

[10] Cardona Monica, M. Angels Colomer, Mario J. ´ Perez-Jim ´ enez, and Alba Zaragoza, Hierarchical ´ clustering with membrane computing, Computing and Informatics, vol.27(3+), 2008, pp.497– 513.

[11] Jianwen Feng, Jingyi Wang, Chen Xu, and Francis Austin, Cluster Synchronization of Nonlinearly Coupled Complex Networks via Pinning Control, Discrete Dynamics in Nature and Society, Volume 2011, Article ID 262349, doi:10.1155/2011/262349.

[12] Forman Robin, Morse Theory for Cell Complexes, Advances in Mathematics, vol.134, 1998, pp.90–145.

[13] D.H. Ackley, G.E. Hinton and T.J. Sejnowski, A Learning Algorithm for Boltzmann Machines, Cognitive Science, 9, 1985, pp.147.

[14] D.H. Ackley, G.E. Hinton and T.J. Sejnowski, A learning algorithm for Boltzmann machine, Cognitive Science, vol. 9, 1985, pp.147–169.

[15] J. Han and M. Kamber, Data Mining, Concepts and Techniques, Higher Education Press, Morgan Kaufmann Publishers, Beijing, 2002.

[16] Yusuke Hosoi, Yuta Taniguchi and Daisuke Ikeda, Replacing Log-Based Profiles to Context Profiles and Its Application to Context-aware Document Clustering, WSEAS Transactions on Information Science and Applications, vol.11, 2014, pp.51–60.

[17] Z.H. Jiang, Introduction to Topology, Shanghai Science and Technology Press, Shanghai, 1978.

[18] Paun Gheorghe, A quick introduction to mem- ˘ brane computing, The Journal of Logic and Algebraic Programming, vol.79, 2010, pp.291– 294.

[19] G. Paun, G. Rozenberg, and A. Salomaa, ˘ Membrane Computing, Oxford University Press, New York, 2010.

[20] J.H. Xiao, X.Y. Zhang and J. Xu, A membrane evolutionary algorithm for DNA sequence design in DNA computing, Chinese Science Bulletin, vol.57:6, 2012, pp.698–706.

[21] Liping Zhang and Haibo Jiang, Impulsive Cluster Anticonsensus of Discrete Multiagent Linear Dynamic Systems, Discrete Dynamics in Nature and Society, vol.2012, Article ID 857561, doi:10.1155/2012/857561.

[22] I. Korec, Small universal register machines, Theor Comput Sci, 168, 1996, pp.267–301.