{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:27:03Z","timestamp":1760239623281,"version":"build-2065373602"},"reference-count":55,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2020,12,6]],"date-time":"2020-12-06T00:00:00Z","timestamp":1607212800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The Minister of Science and Higher Education of the Republic of Poland within the \u201cRegional Initiative of Excellence\u201d program for years 2019\u20132022","award":["Project number 027\/RID\/2018\/19, amount granted 11 999 900 PLN."],"award-info":[{"award-number":["Project number 027\/RID\/2018\/19, amount granted 11 999 900 PLN."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The paper aims to present modelling the sensor network operation based on the Potts model. The authors presented own approach based on three states in which each node can be. The change in the state of a given node depends on its current state, the impact of surrounding nodes on it, but also values of the parameters measured. Therefore, the Hamiltonian was introduced as a dependence of both exceeding the limit value of a measured parameter (corresponding to an alarm event), and the state of the battery powering a given node of a sensor. The simulations of the implemented algorithm based on the adopted model presented in the paper relate to the measurement of temperature by a network of sensors. However, this model is universal and can be applied to examine the behaviour of the sensor infrastructure performing various measurements. Moreover, it may simulate the functioning of the critical network infrastructure or sensor networks and industrial sensors supporting the functioning of Industry 4.0.<\/jats:p>","DOI":"10.3390\/s20236979","type":"journal-article","created":{"date-parts":[[2020,12,7]],"date-time":"2020-12-07T21:37:42Z","timestamp":1607377062000},"page":"6979","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Responsiveness of the Sensor Network to Alarm Events Based on the Potts Model"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7573-3856","authenticated-orcid":false,"given":"Andrzej","family":"Paszkiewicz","sequence":"first","affiliation":[{"name":"Department of Complex Systems, The Faculty of Electrical and Computer Engineering, Rzeszow University of Technology, 35-959 Rzesz\u00f3w, Poland"}]},{"given":"Jan","family":"W\u0119grzyn","sequence":"additional","affiliation":[{"name":"The Faculty of Electrical and Computer Engineering, Rzeszow University of Technology, 35-959 Rzesz\u00f3w, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,6]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Industry 4.0: A survey on technologies, applications and open research issues","volume":"6","author":"Lu","year":"2017","journal-title":"J. Ind. Inf. Integr."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"359","DOI":"10.5194\/jsss-7-359-2018","article-title":"Sensors 4.0\u2014Smart sensors and measurement technology enable Industry 4.0","volume":"7","author":"Helwig","year":"2018","journal-title":"J. Sens. Sens. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Silva, M., Vieira, E., Signoretti, G., Silva, I., Silva, D., and Ferrari, P. (2018). A Customer Feedback Platform for Vehicle Manufacturing Compliant with Industry 4.0 Vision. Sensors, 18.","DOI":"10.3390\/s18103298"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1016\/j.jpdc.2004.03.020","article-title":"Vehicle classification in distributed sensor networks","volume":"64","author":"Duarte","year":"2004","journal-title":"J. Parallel Distrib. Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7263","DOI":"10.3390\/su6107263","article-title":"Wireless Sensor Network Powered by a Terrestrial Microbial Fuel Cell as a Sustainable Land Monitoring Energy System","volume":"6","author":"Pietrelli","year":"2014","journal-title":"Sustainability"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.proeng.2014.10.551","article-title":"Wireless Sensor Networks Configurations for Applications in Construction","volume":"85","author":"Ibrahim","year":"2014","journal-title":"Procedia Eng."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Hughes-Riley, T., and Dias, T. (2018). Developing an Acoustic Sensing Yarn for Health Surveillance in a Military Setting. Sensors, 18.","DOI":"10.3390\/s18051590"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1109\/MCOM.2018.8291108","article-title":"Advanced Industrial Wireless Sensor Networks and Intelligent IoT","volume":"56","author":"Boubiche","year":"2018","journal-title":"IEEE Commun. Mag."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Furtak, J., Zieli\u0144ski, Z., and Chudzikiewicz, J. (2016, January 12\u201314). Security techniques for the WSN link layer within military IoT. Proceedings of the IEEE 3rd World Forum on Internet of Things (WF-IoT), Reston, VA, USA.","DOI":"10.1109\/WF-IoT.2016.7845508"},{"key":"ref_10","unstructured":"Ramson, S.R.J., and Moni, D.J. (2017, January 3\u20134). Applications of wireless sensor networks\u2014A survey. Proceedings of the International Conference on Innovations in Electrical, Electronics, Instrumentation and Media Technology (ICEEIMT), Coimbatore, India."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Auyang, S.Y. (1999). Foundation of Complex-System Theories, Cambridge University Press.","DOI":"10.1017\/CBO9780511626135"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Boccara, N. (2010). Modeling Complex Systems, Springer. [2nd ed.].","DOI":"10.1007\/978-1-4419-6562-2"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s13194-012-0056-8","article-title":"What is a complex system?","volume":"3","author":"Ladyman","year":"2013","journal-title":"Eur. J. Philos. of Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1002\/cplx.21438","article-title":"Nonextensive model of self-organizing systems","volume":"18","author":"Grabowski","year":"2013","journal-title":"Complexity"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2020.03.002","article-title":"Complex systems: Features, similarity and connectivity","volume":"861","author":"Comin","year":"2020","journal-title":"Phys. Rep."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Weisbuch, G. (2018). Complex Systems Dynamics, CRC Press.","DOI":"10.1201\/9780429494031"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1103\/RevModPhys.54.235","article-title":"The Potts model","volume":"54","author":"Wu","year":"1982","journal-title":"Rev. Mod. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1103\/PhysRev.64.178","article-title":"Statistics of Two-Dimensional Lattices with Four Components","volume":"64","author":"Ashkin","year":"1943","journal-title":"Phys. Rev."},{"key":"ref_19","first-page":"177","article-title":"Potts model on complex networks","volume":"38","author":"Dorogovtsev","year":"2004","journal-title":"Phys. Condens. Matter"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1007\/BF01009445","article-title":"The Ising model in a random magnetic field","volume":"34","author":"Fisher","year":"1984","journal-title":"J. Stat. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1080\/00029890.1987.12000742","article-title":"An Introduction to the Ising Model","volume":"87","author":"Cipra","year":"1987","journal-title":"Am. Math. Mon."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.jmst.2019.12.009","article-title":"Computational complexity of spin-glass three-dimensional (3D) Ising model","volume":"44","author":"Zhang","year":"2020","journal-title":"J. Mater. Sci. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Antol\u00edn, D., Medrano, N., Calvo, B., and P\u00e9rez, F. (2017). A Wearable Wireless Sensor Network for Indoor Smart Environment Monitoring in Safety Applications. Sensors, 17.","DOI":"10.3390\/s17020365"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"15848","DOI":"10.1109\/ACCESS.2017.2737078","article-title":"Energy Consumption Analysis of High Quality Multi-Tier Wireless Multimedia Sensor Network","volume":"5","author":"Mekonnen","year":"2017","journal-title":"IEEE Access"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1742","DOI":"10.1109\/TCSI.2008.922023","article-title":"An Adaptive System for Optimal Solar Energy Harvesting in Wireless Sensor Network Nodes","volume":"55","author":"Alippi","year":"2008","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_26","first-page":"757291","article-title":"Power-Management Techniques for Wireless Sensor Networks and Similar Low-Power Communication Devices Based on Nonrechargeable Batteries","volume":"2012","author":"Silva","year":"2012","journal-title":"J. Comput. Netw. Commun."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"La Rosa, R., Livreri, P., Trigona, C., Di Donato, L., and Sorbello, G. (2019). Strategies and Techniques for Powering Wireless Sensor Nodes through Energy Harvesting and Wireless Power Transfer. Sensors, 19.","DOI":"10.3390\/s19122660"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1109\/LCOMM.2018.2877317","article-title":"Learning-Based PHY-Layer Authentication for Underwater Sensor Networks","volume":"23","author":"Xiao","year":"2019","journal-title":"IEEE Commun. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1007\/s11036-017-0962-2","article-title":"Machine Learning and Intelligent Communications","volume":"23","author":"Huang","year":"2018","journal-title":"Mob. Netw. Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1007\/s11036-017-0888-8","article-title":"Robust Localization with Crowd Sensors: A Data Cleansing Approach","volume":"23","author":"Kan","year":"2018","journal-title":"Mob. Netw. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1109\/MNET.011.2000195","article-title":"Artificial Intelligence-Enabled Intelligent 6G Networks","volume":"34","author":"Yang","year":"2020","journal-title":"IEEE Netw."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Al-Turjman, F., and Baali, I. (2019). Machine learning for wearable IoT-based applications: A survey. Trans. Emerg. Telecommun. Technol., 3635.","DOI":"10.1002\/ett.3635"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Tsiropoulou, E.E., Paruchuri, S.T., and Baras, J.S. (2017, January 22\u201324). Interest, Energy and Physical-Aware Coalition Formation and Resource Allocation in Smart IoT Applications. Proceedings of the 51st Annual Conference on Information Sciences and Systems (CISS), Baltimore, MD, USA.","DOI":"10.1109\/CISS.2017.7926111"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Tefek, U., and Lim, T.J. (2016, January 3\u20136). Clustering and radio resource partitioning for machine-type communications in cellular networks. Proceedings of the IEEE Wireless Communications and Networking Conference, Doha, Qatar.","DOI":"10.1109\/WCNC.2016.7564740"},{"key":"ref_35","unstructured":"Luan, X., Wu, J., Wang, B., Cheng, Y., and Xiang, H. (2015, January 21\u201323). Distributed network topology formation and resource allocation for clustered Machine-to-Machine communication networks. Proceedings of the 11th International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM), Shanghai, China."},{"key":"ref_36","unstructured":"Stanley, H.E. (1989). Introduction to Phase Transitions and Critical Phenomena, Oxford University Press."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2803","DOI":"10.1016\/j.physleta.2016.06.017","article-title":"Phase transitions in models of human cooperation","volume":"380","author":"Perc","year":"2016","journal-title":"Phys. Lett. A"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1007\/978-3-642-02466-5_27","article-title":"Multiple Phase Transitions in the Culture Dissemination","volume":"4","author":"Wang","year":"2009","journal-title":"Complex Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1007\/s001910050048","article-title":"About some formalisms of interaction Phase transition models in economics?","volume":"7","author":"Hors","year":"1997","journal-title":"J. Evol. Econ."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Onuki, A. (2002). Phase Transition Dynamics, Cambridge University Press.","DOI":"10.1017\/CBO9780511534874"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Paszkiewicz, A., Bolanowski, M., and Zapa\u0142a, P. (2019). Phase Transitions in Wireless MESH Networks and Their Application in Early Detection of Network Coherence Loss. Appl. Sci., 9.","DOI":"10.3390\/app9245508"},{"key":"ref_42","unstructured":"Liu, S., Ying, L., and Shakkottai, S. (October, January 29). Influence maximization in social networks: An ising-model-based approach. Proceedings of the 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton, IL, USA."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"011122","DOI":"10.1103\/PhysRevE.74.011122","article-title":"Ising model on two connected Barabasi-Albert networks","volume":"74","author":"Suchecki","year":"2006","journal-title":"Phys. Rev. E"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Paszkiewicz, A., and Iwaniec, K. (2018, January 16\u201318). Use of Ising Model for Analysis of Changes in the Structure of the IT Network. Proceedings of the 39th International Conference on Information Systems Architecture and Technology (ISAT), Nysa, Poland.","DOI":"10.1007\/978-3-319-99981-4_7"},{"key":"ref_45","unstructured":"Antonio, K.E.S., Pinol, C.M.N., and Banzon, R.S. (2020, October 15). An Ising Model Approach to Malware Epidemiology. Available online: https:\/\/arxiv.org\/abs\/1007.4938."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"161682","DOI":"10.1109\/ACCESS.2020.3019379","article-title":"A Novel Medium Access Control Algorithm for Ad Hoc Networks Based on Ising Model","volume":"8","author":"Rahman","year":"2020","journal-title":"IEEE Access"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1038","DOI":"10.1109\/TCNS.2017.2673539","article-title":"I-CSMA: A link-scheduling algorithm for wireless networks based on Ising model","volume":"5","author":"Wang","year":"2018","journal-title":"IEEE Trans. Control Netw. Syst."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Li, X., Tolmachev, P., Pauley, M., and Manton, J.H. (2018, January 10\u201313). A distributed transmission scheduling algorithm for wireless networks based on the ising model. Proceedings of the IEEE Statistical Signal Processing Workshop (SSP), Freiburg, Germany.","DOI":"10.1109\/SSP.2018.8450715"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1080\/15501320802473250","article-title":"Adaptive Sensor Activity Scheduling in Distributed Sensor Networks: A Statistical Mechanics Approach","volume":"5","author":"Srivastav","year":"2009","journal-title":"Int. J. Distrib. Sens. Netw."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Perreau, S., Sigelle, M., Da Silva, P., and Jayasuriya, A. (2009, January 22\u201326). Sensor Networks Protocol Design Using Random Markov Field Theory. Proceedings of the 6th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks, Rome, Italy.","DOI":"10.1109\/SAHCN.2009.5168969"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/s11760-008-0101-4","article-title":"Self-organization of sensor networks for detection of pervasive faults","volume":"4","author":"Srivastav","year":"2010","journal-title":"Signal Image Video Process."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Assa, A., and Jahan, M.V. (2012, January 18\u201319). Adaptive scheduling in wireless sensor networks based on Potts model. Proceedings of the 2nd International eConference on Computer and Knowledge Engineering (ICCKE), Mashhad, Iran.","DOI":"10.1109\/ICCKE.2012.6395387"},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Hai, T.H., and Huh, E.N. (2008, January 6\u20138). Optimal Selection and Activation of Intrusion Detection Agents for Wireless Sensor Networks. Proceedings of the Future Generation Communication and Networking (FGCN 2007), Jeju, Korea.","DOI":"10.1109\/FGCN.2007.175"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1016\/j.physa.2016.11.065","article-title":"Degeneracy estimation in interference models on wireless networks","volume":"469","author":"McBride","year":"2017","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Singhal, C., and De, S. (2017). Resource Allocation in Next-Generation Broadband Wireless Access Networks, IGI Global.","DOI":"10.4018\/978-1-5225-2023-8"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/23\/6979\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:41:42Z","timestamp":1760179302000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/23\/6979"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,6]]},"references-count":55,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["s20236979"],"URL":"https:\/\/doi.org\/10.3390\/s20236979","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,12,6]]}}}