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Complex dynamics of memristive circuits: Analytical results and universal slow relaxation

Overview of attention for article published in arXiv, February 2017
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About this Attention Score

  • In the top 25% of all research outputs scored by Altmetric
  • High Attention Score compared to outputs of the same age (91st percentile)
  • High Attention Score compared to outputs of the same age and source (97th percentile)

Mentioned by

news
1 news outlet
twitter
11 tweeters
wikipedia
2 Wikipedia pages

Citations

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6 Dimensions

Readers on

mendeley
21 Mendeley
Title
Complex dynamics of memristive circuits: Analytical results and universal slow relaxation
Published in
arXiv, February 2017
DOI 10.1103/physreve.95.022140
Pubmed ID
Authors

F. Caravelli, F. L. Traversa, M. Di Ventra

Abstract

Networks with memristive elements (resistors with memory) are being explored for a variety of applications ranging from unconventional computing to models of the brain. However, analytical results that highlight the role of the graph connectivity on the memory dynamics are still few, thus limiting our understanding of these important dynamical systems. In this paper, we derive an exact matrix equation of motion that takes into account all the network constraints of a purely memristive circuit, and we employ it to derive analytical results regarding its relaxation properties. We are able to describe the memory evolution in terms of orthogonal projection operators onto the subspace of fundamental loop space of the underlying circuit. This orthogonal projection explicitly reveals the coupling between the spatial and temporal sectors of the memristive circuits and compactly describes the circuit topology. For the case of disordered graphs, we are able to explain the emergence of a power-law relaxation as a superposition of exponential relaxation times with a broad range of scales using random matrices. This power law is also universal, namely independent of the topology of the underlying graph but dependent only on the density of loops. In the case of circuits subject to alternating voltage instead, we are able to obtain an approximate solution of the dynamics, which is tested against a specific network topology. These results suggest a much richer dynamics of memristive networks than previously considered.

Twitter Demographics

The data shown below were collected from the profiles of 11 tweeters who shared this research output. Click here to find out more about how the information was compiled.

Mendeley readers

The data shown below were compiled from readership statistics for 21 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Unknown 21 100%

Demographic breakdown

Readers by professional status Count As %
Student > Master 5 24%
Researcher 4 19%
Professor 3 14%
Student > Bachelor 2 10%
Student > Postgraduate 2 10%
Other 5 24%
Readers by discipline Count As %
Physics and Astronomy 4 19%
Unspecified 4 19%
Computer Science 3 14%
Engineering 2 10%
Chemistry 2 10%
Other 6 29%

Attention Score in Context

This research output has an Altmetric Attention Score of 20. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 02 November 2018.
All research outputs
#672,309
of 12,352,410 outputs
Outputs from arXiv
#10,771
of 481,944 outputs
Outputs of similar age
#23,447
of 261,680 outputs
Outputs of similar age from arXiv
#402
of 17,103 outputs
Altmetric has tracked 12,352,410 research outputs across all sources so far. Compared to these this one has done particularly well and is in the 94th percentile: it's in the top 10% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 481,944 research outputs from this source. They receive a mean Attention Score of 3.5. This one has done particularly well, scoring higher than 97% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 261,680 tracked outputs that were published within six weeks on either side of this one in any source. This one has done particularly well, scoring higher than 91% of its contemporaries.
We're also able to compare this research output to 17,103 others from the same source and published within six weeks on either side of this one. This one has done particularly well, scoring higher than 97% of its contemporaries.