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.
- Authors:
-
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- 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}
}
Web of Science
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