{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T18:22:36Z","timestamp":1778523756971,"version":"3.51.4"},"reference-count":33,"publisher":"IOP Publishing","issue":"3","license":[{"start":{"date-parts":[[2023,7,14]],"date-time":"2023-07-14T00:00:00Z","timestamp":1689292800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,7,14]],"date-time":"2023-07-14T00:00:00Z","timestamp":1689292800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100010665","name":"H2020 Marie Sk\u0142odowska-Curie Actions","doi-asserted-by":"crossref","award":["861153"],"award-info":[{"award-number":["861153"]}],"id":[{"id":"10.13039\/100010665","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Neuromorph. Comput. Eng."],"published-print":{"date-parts":[[2023,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>To build neuromorphic hardware with self-assembled memristive networks, it is necessary to determine how the functional connectivity between electrodes can be adjusted, under the application of external signals. In this work, we analyse a model of a disordered memristor-resistor network, within the framework of graph theory. Such a model is well suited for the simulation of physical self-assembled neuromorphic materials where impurities are likely to be present. Two primary mechanisms that modulate the collective dynamics are investigated: the strength of interaction, i.e. the ratio of the two limiting conductance states of the memristive components, and the role of disorder in the form of density of Ohmic conductors (OCs) diluting the network. We consider the case where a fraction of the network edges has memristive properties, while the remaining part shows pure Ohmic behaviour. We consider both the case of poor and good OCs. Both the role of the interaction strength and the presence of OCs are investigated in relation to the trace formation between electrodes at the fixed point of the dynamics. The latter is analysed through an ideal observer approach. Thus, network entropy is used to understand the self-reinforcing and cooperative inhibition of other memristive elements resulting in the formation of a winner-take-all path. Both the low interaction strength and the dilution of the memristive fraction in a network provide a reduction of the steep non-linearity in the network conductance under the application of a steady input voltage. Entropy analysis shows enhanced robustness in selective trace formation to the applied voltage for heterogeneous networks of memristors diluted by poor OCs in the vicinity of the percolation threshold. The input voltage controls the diversity in trace formation.<\/jats:p>","DOI":"10.1088\/2634-4386\/acd6b3","type":"journal-article","created":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T22:25:33Z","timestamp":1684448733000},"page":"034001","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Conduction and entropy analysis of a mixed memristor-resistor model for neuromorphic networks"],"prefix":"10.1088","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4350-8691","authenticated-orcid":true,"given":"Davide","family":"Cipollini","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2351-930X","authenticated-orcid":true,"given":"Lambert R B","family":"Schomaker","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2023,7,14]]},"reference":[{"key":"nceacd6b3bib1","doi-asserted-by":"publisher","first-page":"434","DOI":"10.1038\/s41928-020-0448-2","article-title":"How we created neuromorphic engineering","volume":"3","author":"Mead","year":"2020","journal-title":"Nat. Electron."},{"key":"nceacd6b3bib2","doi-asserted-by":"publisher","DOI":"10.1088\/0957-4484\/24\/38\/384010","article-title":"Integration of nanoscale memristor synapses in neuromorphic computing architectures","volume":"24","author":"Indiveri","year":"2013","journal-title":"Nanotechnology"},{"key":"nceacd6b3bib3","doi-asserted-by":"publisher","DOI":"10.1088\/2634-4386\/ac4a83","article-title":"2022 roadmap on neuromorphic computing and engineering","volume":"2","author":"Christensen","year":"2022","journal-title":"Neuromorph. Comput. Eng."},{"key":"nceacd6b3bib4","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1038\/s41563-019-0291-x","article-title":"Memristive crossbar arrays for brain-inspired computing","volume":"18","author":"Qiangfei","year":"2019","journal-title":"Nat. Mater."},{"key":"nceacd6b3bib5","doi-asserted-by":"publisher","first-page":"2021","DOI":"10.1038\/s41467-021-21917-7","article-title":"Avalanches and edge-of-chaos learning in neuromorphic nanowire networks","volume":"12","author":"Hochstetter","year":"2021","journal-title":"Nat. Commun."},{"key":"nceacd6b3bib6","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1038\/s41563-021-01099-9","article-title":"In materia reservoir computing with a fully memristive architecture based on self-organizing nanowire networks","volume":"21","author":"Milano","year":"2021","journal-title":"Nat. Mater."},{"key":"nceacd6b3bib7","doi-asserted-by":"publisher","DOI":"10.1088\/2634-4386\/ac4d86","article-title":"Grid-graph modeling of emergent neuromorphic dynamics and heterosynaptic plasticity in memristive nanonetworks","volume":"2","author":"Montano","year":"2022","journal-title":"Neuromorph. Comput. Eng."},{"key":"nceacd6b3bib8","doi-asserted-by":"publisher","first-page":"5194","DOI":"10.1109\/TED.2017.2766063","article-title":"Stable self-assembled atomic-switch networks for neuromorphic applications","volume":"64","author":"Bose","year":"2017","journal-title":"IEEE Trans. Electron Devices"},{"key":"nceacd6b3bib9","doi-asserted-by":"publisher","first-page":"2022","DOI":"10.1038\/s41598-022-06122-w","article-title":"Dynamical stochastic simulation of complex electrical behavior in neuromorphic networks of metallic nanojunctions","volume":"12","author":"Mambretti","year":"2022","journal-title":"Sci. Rep."},{"key":"nceacd6b3bib10","doi-asserted-by":"publisher","DOI":"10.1002\/aisy.202200292","article-title":"Ferroelastic domain walls in BiFeO3 as memristive networks","volume":"5","author":"Rieck","year":"2022","journal-title":"Adv. Intell. Syst."},{"key":"nceacd6b3bib11","author":"Vourkas","year":"2016"},{"key":"nceacd6b3bib12","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1038\/nphys2566","article-title":"The parallel approach","volume":"9","author":"Di Ventra","year":"2013","journal-title":"Nat. Phys."},{"key":"nceacd6b3bib13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.84.046703","article-title":"Solving mazes with memristors: a massively parallel approach","volume":"84","author":"Pershin","year":"2011","journal-title":"Phys. Rev. E"},{"key":"nceacd6b3bib14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevApplied.10.064035","article-title":"Scalable method to find the shortest path in a graph with circuits of memristors","volume":"10","author":"Mizrahi","year":"2018","journal-title":"Phys. Rev. Appl."},{"key":"nceacd6b3bib15","doi-asserted-by":"publisher","first-page":"2018","DOI":"10.1038\/s41467-018-04378-3","article-title":"Emergence of winner-takes-all connectivity paths in random nanowire networks","volume":"9","author":"Manning","year":"2018","journal-title":"Nat. Commun."},{"key":"nceacd6b3bib16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.83.031105","article-title":"Electric currents in networks of interconnected memristors","volume":"83","author":"Oskoee","year":"2011","journal-title":"Phys. Rev. E"},{"key":"nceacd6b3bib17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.95.012305","article-title":"Conducting-insulating transition in adiabatic memristive networks","volume":"95","author":"Sheldon","year":"2017","journal-title":"Phys. Rev. E"},{"key":"nceacd6b3bib18","doi-asserted-by":"publisher","first-page":"504","DOI":"10.1109\/TCS.1975.1084079","article-title":"The modified nodal approach to network analysis","volume":"22","author":"Chung-Wen Ho","year":"1975","journal-title":"IEEE Trans. Circuits Syst."},{"key":"nceacd6b3bib19","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1016\/j.neunet.2018.07.003","article-title":"Evaluation of the computational capabilities of a memristive random network (MN3) under the context of reservoir computing","volume":"106","author":"Suarez","year":"2018","journal-title":"Neural Netw."},{"key":"nceacd6b3bib20","doi-asserted-by":"publisher","first-page":"771","DOI":"10.1038\/s42256-021-00376-1","article-title":"Learning function from structure in neuromorphic networks","volume":"3","author":"Su\u00e1rez","year":"2021","journal-title":"Nat. Machine Intell."},{"key":"nceacd6b3bib21","doi-asserted-by":"publisher","first-page":"2021","DOI":"10.1038\/s41598-021-81825-0","article-title":"Information dynamics in neuromorphic nanowire networks","volume":"11","author":"Zhu","year":"2021","journal-title":"Sci. Rep."},{"key":"nceacd6b3bib22","first-page":"pp 1","article-title":"Review of various available spice simulators","author":"Pratap","year":"2014"},{"key":"nceacd6b3bib23","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1016\/j.neunet.2022.02.022","article-title":"Connectome of memristive nanowire networks through graph theory","volume":"150","author":"Milano","year":"2022","journal-title":"Neural Netw."},{"key":"nceacd6b3bib24","doi-asserted-by":"publisher","first-page":"184","DOI":"10.3389\/fnins.2020.00184","article-title":"Topological properties of neuromorphic nanowire networks","volume":"14","author":"Loeffler","year":"2020","journal-title":"Front. Neurosci."},{"key":"nceacd6b3bib25","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1109\/TNANO.2020.3009734","article-title":"Modeling of short-term synaptic plasticity effects in ZnO nanowire-based memristors using a potentiation-depression rate balance equation","volume":"19","author":"Miranda","year":"2020","journal-title":"IEEE Trans. Nanotechnol."},{"key":"nceacd6b3bib26","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1038\/nmat4756","article-title":"Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing","volume":"16","author":"Wang","year":"2016","journal-title":"Nat. Mater."},{"key":"nceacd6b3bib27","doi-asserted-by":"publisher","first-page":"656","DOI":"10.1109\/LED.2018.2822047","article-title":"Switching voltage and time statistics of filamentary conductive paths in HfO2-based ReRAM devices","volume":"39","author":"Rodriguez-Fernandez","year":"2018","journal-title":"IEEE Electron Device Lett."},{"key":"nceacd6b3bib28","doi-asserted-by":"publisher","first-page":"6945","DOI":"10.1039\/c3cp50738f","article-title":"Switching kinetics of electrochemical metallization memory cells","volume":"15","author":"Menzel","year":"2013","journal-title":"Phys. Chem. Chem. Phys."},{"key":"nceacd6b3bib29","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.88.013305","article-title":"Self-organization and solution of shortest-path optimization problems with memristive networks","volume":"88","author":"Pershin","year":"2013","journal-title":"Phys. Rev. E"},{"key":"nceacd6b3bib30","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.6.041062","article-title":"Spectral entropies as information-theoretic tools for complex network comparison","volume":"6","author":"De Domenico","year":"2016","journal-title":"Phys. Rev. X"},{"key":"nceacd6b3bib31","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1038\/s41567-022-01866-8","article-title":"Laplacian renormalization group for heterogeneous networks","volume":"19","author":"Villegas","year":"2023","journal-title":"Nat. Phys."},{"key":"nceacd6b3bib32","author":"Stauffer","year":"2018"},{"key":"nceacd6b3bib33","article-title":"Memory capacity of neural network models","author":"Fusi","year":"2021"}],"container-title":["Neuromorphic Computing and Engineering"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/acd6b3","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/acd6b3\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/acd6b3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/acd6b3\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/acd6b3\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/acd6b3\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/acd6b3\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/acd6b3\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,11]],"date-time":"2023-10-11T09:01:16Z","timestamp":1697014876000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/acd6b3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,14]]},"references-count":33,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,7,14]]},"published-print":{"date-parts":[[2023,9,1]]}},"URL":"https:\/\/doi.org\/10.1088\/2634-4386\/acd6b3","relation":{},"ISSN":["2634-4386"],"issn-type":[{"value":"2634-4386","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,14]]},"assertion":[{"value":"Conduction and entropy analysis of a mixed memristor-resistor model for neuromorphic networks","name":"article_title","label":"Article Title"},{"value":"Neuromorphic Computing and Engineering","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2023 The Author(s). Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2023-02-10","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2023-05-18","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2023-07-14","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}