Locality of interactions for planar memristive circuits
Abstract
The dynamics of purely memristive circuits has been shown to depend on a projection operator which expresses the Kirchhoff constraints, is naturally non-local in nature, and does represent the interaction between memristors. In the present paper we show that for the case of planar circuits, for which a meaningful Hamming distance can be defined, the elements of such projector can be bounded by exponentially decreasing functions of the distance. We provide a geometrical interpretation of the projector elements in terms of determinants of Dirichlet Laplacian of the dual circuit. For the case of linearized dynamics of the circuit for which a solution is known, this can be shown to provide a light cone bound for the interaction between memristors. Furthermore, this result establishes a finite speed of propagation of signals across the network, despite the non-local nature of the system.
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1410621
- Alternate Identifier(s):
- OSTI ID: 1408058
- Report Number(s):
- LA-UR-17-23533
Journal ID: ISSN 2470-0045; PLEEE8; TRN: US1800141
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review E
- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 5; Journal ID: ISSN 2470-0045
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; 30 DIRECT ENERGY CONVERSION; memristors, interaction, locality
Citation Formats
Caravelli, Francesco. Locality of interactions for planar memristive circuits. United States: N. p., 2017.
Web. doi:10.1103/PhysRevE.96.052206.
Caravelli, Francesco. Locality of interactions for planar memristive circuits. United States. https://doi.org/10.1103/PhysRevE.96.052206
Caravelli, Francesco. Wed .
"Locality of interactions for planar memristive circuits". United States. https://doi.org/10.1103/PhysRevE.96.052206. https://www.osti.gov/servlets/purl/1410621.
@article{osti_1410621,
title = {Locality of interactions for planar memristive circuits},
author = {Caravelli, Francesco},
abstractNote = {The dynamics of purely memristive circuits has been shown to depend on a projection operator which expresses the Kirchhoff constraints, is naturally non-local in nature, and does represent the interaction between memristors. In the present paper we show that for the case of planar circuits, for which a meaningful Hamming distance can be defined, the elements of such projector can be bounded by exponentially decreasing functions of the distance. We provide a geometrical interpretation of the projector elements in terms of determinants of Dirichlet Laplacian of the dual circuit. For the case of linearized dynamics of the circuit for which a solution is known, this can be shown to provide a light cone bound for the interaction between memristors. Furthermore, this result establishes a finite speed of propagation of signals across the network, despite the non-local nature of the system.},
doi = {10.1103/PhysRevE.96.052206},
journal = {Physical Review E},
number = 5,
volume = 96,
place = {United States},
year = {Wed Nov 08 00:00:00 EST 2017},
month = {Wed Nov 08 00:00:00 EST 2017}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 9 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
The missing memristor found
journal, May 2008
- Strukov, Dmitri B.; Snider, Gregory S.; Stewart, Duncan R.
- Nature, Vol. 453, Issue 7191
Universal Memcomputing Machines
journal, November 2015
- Traversa, Fabio Lorenzo; Di Ventra, Massimiliano
- IEEE Transactions on Neural Networks and Learning Systems, Vol. 26, Issue 11
Complex dynamics of memristive circuits: Analytical results and universal slow relaxation
journal, February 2017
- Caravelli, F.; Traversa, F. L.; Di Ventra, M.
- Physical Review E, Vol. 95, Issue 2
Sensory and short-term memory formations observed in a Ag 2 S gap-type atomic switch
journal, November 2011
- Ohno, Takeo; Hasegawa, Tsuyoshi; Nayak, Alpana
- Applied Physics Letters, Vol. 99, Issue 20
Memristive devices and systems
journal, January 1976
- Chua, L. O.
- Proceedings of the IEEE, Vol. 64, Issue 2
Emergent Criticality in Complex Turing B-Type Atomic Switch Networks
journal, October 2011
- Stieg, Adam Z.; Avizienis, Audrius V.; Sillin, Henry O.
- Advanced Materials, Vol. 24, Issue 2
Training and operation of an integrated neuromorphic network based on metal-oxide memristors
journal, May 2015
- Prezioso, M.; Merrikh-Bayat, F.; Hoskins, B. D.
- Nature, Vol. 521, Issue 7550
Nanobatteries in redox-based resistive switches require extension of memristor theory
journal, April 2013
- Valov, I.; Linn, E.; Tappertzhofen, S.
- Nature Communications, Vol. 4, Issue 1
The mise en scéne of memristive networks: effective memory, dynamics and learning
journal, February 2017
- Caravelli, Francesco
- International Journal of Parallel, Emergent and Distributed Systems, Vol. 33, Issue 4
The parallel approach
journal, April 2013
- Di Ventra, Massimiliano; Pershin, Yuriy V.
- Nature Physics, Vol. 9, Issue 4
Locality in Quantum and Markov Dynamics on Lattices and Networks
journal, September 2004
- Hastings, M. B.
- Physical Review Letters, Vol. 93, Issue 14
High-Density Crossbar Arrays Based on a Si Memristive System
journal, February 2009
- Jo, Sung Hyun; Kim, Kuk-Hwan; Lu, Wei
- Nano Letters, Vol. 9, Issue 2
Memory and Information Processing in Neuromorphic Systems
journal, August 2015
- Indiveri, Giacomo; Liu, Shih-Chii
- Proceedings of the IEEE, Vol. 103, Issue 8
Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing
journal, September 2016
- Wang, Zhongrui; Joshi, Saumil; Savel’ev, Sergey E.
- Nature Materials, Vol. 16, Issue 1
Trajectories Entropy in Dynamical Graphs with Memory
journal, April 2016
- Caravelli, Francesco
- Frontiers in Robotics and AI, Vol. 3
Memory effects in complex materials and nanoscale systems
journal, April 2011
- Pershin, Yuriy V.; Di Ventra, Massimiliano
- Advances in Physics, Vol. 60, Issue 2
Information propagation for interacting-particle systems
journal, September 2011
- Schuch, Norbert; Harrison, Sarah K.; Osborne, Tobias J.
- Physical Review A, Vol. 84, Issue 3
Data Clustering using Memristor Networks
journal, May 2015
- Choi, Shinhyun; Sheridan, Patrick; Lu, Wei D.
- Scientific Reports, Vol. 5, Issue 1
Scale-free networks as an epiphenomenon of memory
journal, January 2015
- Caravelli, F.; Hamma, A.; Di Ventra, M.
- EPL (Europhysics Letters), Vol. 109, Issue 2
Neuromorphic Atomic Switch Networks
journal, August 2012
- Avizienis, Audrius V.; Sillin, Henry O.; Martin-Olmos, Cristina
- PLoS ONE, Vol. 7, Issue 8
Memcomputing NP -complete problems in polynomial time using polynomial resources and collective states
journal, July 2015
- Traversa, Fabio Lorenzo; Ramella, Chiara; Bonani, Fabrizio
- Science Advances, Vol. 1, Issue 6
Memristive devices for computing
journal, January 2013
- Yang, J. Joshua; Strukov, Dmitri B.; Stewart, Duncan R.
- Nature Nanotechnology, Vol. 8, Issue 1, p. 13-24
Conducting-insulating transition in adiabatic memristive networks
journal, January 2017
- Sheldon, Forrest C.; Di Ventra, Massimiliano
- Physical Review E, Vol. 95, Issue 1
Sparse coding with memristor networks
journal, May 2017
- Sheridan, Patrick M.; Cai, Fuxi; Du, Chao
- Nature Nanotechnology, Vol. 12, Issue 8
Works referencing / citing this record:
Scalable Method to Find the Shortest Path in a Graph with Circuits of Memristors
journal, December 2018
- Mizrahi, Alice; Marsh, Thomas; Hoskins, Brian
- Physical Review Applied, Vol. 10, Issue 6
Memristors for the Curious Outsiders
journal, December 2018
- Caravelli, Francesco; Carbajal, Juan
- Technologies, Vol. 6, Issue 4
A scalable method to find the shortest path in a graph with circuits of memristors
text, January 2018
- Mizrahi, Alice; Marsh, Thomas; Hoskins, Brian
- arXiv