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Title: Asymptotic Behavior of Memristive Circuits

Abstract

The interest in memristors has risen due to their possible application both as memory units and as computational devices in combination with CMOS. This is in part due to their nonlinear dynamics, and a strong dependence on the circuit topology. We provide evidence that also purely memristive circuits can be employed for computational purposes. In the present paper we show that a polynomial Lyapunov function in the memory parameters exists for the case of DC controlled memristors. Such a Lyapunov function can be asymptotically approximated with binary variables, and mapped to quadratic combinatorial optimization problems. This also shows a direct parallel between memristive circuits and the Hopfield-Little model. In the case of Erdos-Renyi random circuits, we show numerically that the distribution of the matrix elements of the projectors can be roughly approximated with a Gaussian distribution, and that it scales with the inverse square root of the number of elements. This provides an approximated but direct connection with the physics of disordered system and, in particular, of mean field spin glasses. Using this and the fact that the interaction is controlled by a projector operator on the loop space of the circuit. We estimate the number of stationary points ofmore » the approximate Lyapunov function and provide a scaling formula as an upper bound in terms of the circuit topology only.« less

Authors:
ORCiD logo [1]
  1. 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:
1557331
Alternate Identifier(s):
OSTI ID: 1558046
Report Number(s):
LA-UR-18-24748
Journal ID: ISSN 1099-4300; ENTRFG
Grant/Contract Number:  
89233218CNA000001; AC52-06NA25396
Resource Type:
Journal Article: Published Article
Journal Name:
Entropy
Additional Journal Information:
Journal Volume: 21; Journal Issue: 8; Journal ID: ISSN 1099-4300
Publisher:
MDPI
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; memristive circuits; spin models; disordered systems

Citation Formats

Caravelli, Francesco. Asymptotic Behavior of Memristive Circuits. United States: N. p., 2019. Web. doi:10.3390/e21080789.
Caravelli, Francesco. Asymptotic Behavior of Memristive Circuits. United States. doi:10.3390/e21080789.
Caravelli, Francesco. Tue . "Asymptotic Behavior of Memristive Circuits". United States. doi:10.3390/e21080789.
@article{osti_1557331,
title = {Asymptotic Behavior of Memristive Circuits},
author = {Caravelli, Francesco},
abstractNote = {The interest in memristors has risen due to their possible application both as memory units and as computational devices in combination with CMOS. This is in part due to their nonlinear dynamics, and a strong dependence on the circuit topology. We provide evidence that also purely memristive circuits can be employed for computational purposes. In the present paper we show that a polynomial Lyapunov function in the memory parameters exists for the case of DC controlled memristors. Such a Lyapunov function can be asymptotically approximated with binary variables, and mapped to quadratic combinatorial optimization problems. This also shows a direct parallel between memristive circuits and the Hopfield-Little model. In the case of Erdos-Renyi random circuits, we show numerically that the distribution of the matrix elements of the projectors can be roughly approximated with a Gaussian distribution, and that it scales with the inverse square root of the number of elements. This provides an approximated but direct connection with the physics of disordered system and, in particular, of mean field spin glasses. Using this and the fact that the interaction is controlled by a projector operator on the loop space of the circuit. We estimate the number of stationary points of the approximate Lyapunov function and provide a scaling formula as an upper bound in terms of the circuit topology only.},
doi = {10.3390/e21080789},
journal = {Entropy},
issn = {1099-4300},
number = 8,
volume = 21,
place = {United States},
year = {2019},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.3390/e21080789

Figures / Tables:

Figure 1 Figure 1: Dynamics of the memory is shown in Figure (a) and the corresponding evolution of the Lyapunov function of Equation (A1) ((b), continuous line) for 8750 memristors and for the asymptotic function of Equation (6) Figure ((b)-dashed line). We considered α = 0.1, β = 1 and ξ =more » 10, for Ωij from a random circuit of the Erdos-Renyi type with p = 0.9. The sources $\vec{S}$’s elements were chosen at random between [−0.05, 0.05].« less

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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
  • DOI: 10.1038/nature06932

Neural networks and physical systems with emergent collective computational abilities.
journal, April 1982

  • Hopfield, J. J.
  • Proceedings of the National Academy of Sciences, Vol. 79, Issue 8
  • DOI: 10.1073/pnas.79.8.2554

Universal Memcomputing Machines
journal, November 2015

  • Traversa, Fabio Lorenzo; Di Ventra, Massimiliano
  • IEEE Transactions on Neural Networks and Learning Systems, Vol. 26, Issue 11
  • DOI: 10.1109/TNNLS.2015.2391182

Complex dynamics of memristive circuits: Analytical results and universal slow relaxation
journal, February 2017


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
  • DOI: 10.1063/1.3662390

Solving mazes with memristors: A massively parallel approach
journal, October 2011


Memristive devices and systems
journal, January 1976


Memristive networks: From graph theory to statistical physics
journal, January 2019


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
  • DOI: 10.1002/adma.201103053

The mise en scéne of memristive networks: effective memory, dynamics and learning
journal, February 2017


Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing
journal, August 2017

  • Kumar, Suhas; Strachan, John Paul; Williams, R. Stanley
  • Nature, Vol. 548, Issue 7667
  • DOI: 10.1038/nature23307

A sequence of approximated solutions to the S-K model for spin glasses
journal, April 1980


Cycle bases in graphs characterization, algorithms, complexity, and applications
journal, November 2009


Self-organization and solution of shortest-path optimization problems with memristive networks
journal, July 2013


Heuristics for cardinality constrained portfolio optimisation
journal, November 2000


Ant colonies for the travelling salesman problem
journal, July 1997


Spin-glass models of neural networks
journal, August 1985


Memory and Information Processing in Neuromorphic Systems
journal, August 2015


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
  • DOI: 10.1038/nmat4756

Trajectories Entropy in Dynamical Graphs with Memory
journal, April 2016


Associative memory realized by a reconfigurable memristive Hopfield neural network
journal, June 2015

  • Hu, S. G.; Liu, Y.; Liu, Z.
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms8522

Memristors for the Curious Outsiders
journal, December 2018


Optimization by Simulated Annealing
journal, May 1983


Scale-free networks as an epiphenomenon of memory
journal, January 2015


Neuromorphic Atomic Switch Networks
journal, August 2012


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
  • DOI: 10.1038/nnano.2012.240

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
  • DOI: 10.1126/sciadv.1500031

The existence of persistent states in the brain
journal, February 1974


Locality of interactions for planar memristive circuits
journal, November 2017


Computing with neural circuits: a model
journal, August 1986


    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.