---
_id: '292'
abstract:
- lang: eng
  text: 'Retina is a paradigmatic system for studying sensory encoding: the transformation
    of light into spiking activity of ganglion cells. The inverse problem, where stimulus
    is reconstructed from spikes, has received less attention, especially for complex
    stimuli that should be reconstructed “pixel-by-pixel”. We recorded around a hundred
    neurons from a dense patch in a rat retina and decoded movies of multiple small
    randomly-moving discs. We constructed nonlinear (kernelized and neural network)
    decoders that improved significantly over linear results. An important contribution
    to this was the ability of nonlinear decoders to reliably separate between neural
    responses driven by locally fluctuating light signals, and responses at locally
    constant light driven by spontaneous-like activity. This improvement crucially
    depended on the precise, non-Poisson temporal structure of individual spike trains,
    which originated in the spike-history dependence of neural responses. We propose
    a general principle by which downstream circuitry could discriminate between spontaneous
    and stimulus-driven activity based solely on higher-order statistical structure
    in the incoming spike trains.'
article_number: e1006057
article_processing_charge: Yes
article_type: original
author:
- first_name: Vicent
  full_name: Botella Soler, Vicent
  id: 421234E8-F248-11E8-B48F-1D18A9856A87
  last_name: Botella Soler
  orcid: 0000-0002-8790-1914
- first_name: Stephane
  full_name: Deny, Stephane
  last_name: Deny
- first_name: Georg S
  full_name: Martius, Georg S
  last_name: Martius
- first_name: Olivier
  full_name: Marre, Olivier
  last_name: Marre
- first_name: Gasper
  full_name: Tkacik, Gasper
  id: 3D494DCA-F248-11E8-B48F-1D18A9856A87
  last_name: Tkacik
  orcid: 0000-0002-6699-1455
citation:
  ama: Botella Soler V, Deny S, Martius GS, Marre O, Tkačik G. Nonlinear decoding
    of a complex movie from the mammalian retina. <i>PLoS Computational Biology</i>.
    2018;14(5). doi:<a href="https://doi.org/10.1371/journal.pcbi.1006057">10.1371/journal.pcbi.1006057</a>
  apa: Botella Soler, V., Deny, S., Martius, G. S., Marre, O., &#38; Tkačik, G. (2018).
    Nonlinear decoding of a complex movie from the mammalian retina. <i>PLoS Computational
    Biology</i>. Public Library of Science. <a href="https://doi.org/10.1371/journal.pcbi.1006057">https://doi.org/10.1371/journal.pcbi.1006057</a>
  chicago: Botella Soler, Vicente, Stephane Deny, Georg S Martius, Olivier Marre,
    and Gašper Tkačik. “Nonlinear Decoding of a Complex Movie from the Mammalian Retina.”
    <i>PLoS Computational Biology</i>. Public Library of Science, 2018. <a href="https://doi.org/10.1371/journal.pcbi.1006057">https://doi.org/10.1371/journal.pcbi.1006057</a>.
  ieee: V. Botella Soler, S. Deny, G. S. Martius, O. Marre, and G. Tkačik, “Nonlinear
    decoding of a complex movie from the mammalian retina,” <i>PLoS Computational
    Biology</i>, vol. 14, no. 5. Public Library of Science, 2018.
  ista: Botella Soler V, Deny S, Martius GS, Marre O, Tkačik G. 2018. Nonlinear decoding
    of a complex movie from the mammalian retina. PLoS Computational Biology. 14(5),
    e1006057.
  mla: Botella Soler, Vicente, et al. “Nonlinear Decoding of a Complex Movie from
    the Mammalian Retina.” <i>PLoS Computational Biology</i>, vol. 14, no. 5, e1006057,
    Public Library of Science, 2018, doi:<a href="https://doi.org/10.1371/journal.pcbi.1006057">10.1371/journal.pcbi.1006057</a>.
  short: V. Botella Soler, S. Deny, G.S. Martius, O. Marre, G. Tkačik, PLoS Computational
    Biology 14 (2018).
date_created: 2018-12-11T11:45:39Z
date_published: 2018-05-10T00:00:00Z
date_updated: 2024-02-21T13:45:25Z
day: '10'
ddc:
- '570'
department:
- _id: GaTk
doi: 10.1371/journal.pcbi.1006057
ec_funded: 1
external_id:
  isi:
  - '000434012100002'
file:
- access_level: open_access
  checksum: 3026f94d235219e15514505fdbadf34e
  content_type: application/pdf
  creator: dernst
  date_created: 2019-02-13T11:07:15Z
  date_updated: 2020-07-14T12:45:53Z
  file_id: '5974'
  file_name: 2018_Plos_Botella_Soler.pdf
  file_size: 3460786
  relation: main_file
file_date_updated: 2020-07-14T12:45:53Z
has_accepted_license: '1'
intvolume: '        14'
isi: 1
issue: '5'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '05'
oa: 1
oa_version: Published Version
project:
- _id: 25CBA828-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '720270'
  name: Human Brain Project Specific Grant Agreement 1 (HBP SGA 1)
- _id: 254D1A94-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P 25651-N26
  name: Sensitivity to higher-order statistics in natural scenes
publication: PLoS Computational Biology
publication_status: published
publisher: Public Library of Science
quality_controlled: '1'
related_material:
  link:
  - description: News on IST Homepage
    relation: press_release
    url: https://ist.ac.at/en/news/video-of-moving-discs-reconstructed-from-rat-retinal-neuron-signals/
  record:
  - id: '5584'
    relation: research_data
    status: public
scopus_import: '1'
status: public
title: Nonlinear decoding of a complex movie from the mammalian retina
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 14
year: '2018'
...
---
_id: '1697'
abstract:
- lang: eng
  text: Motion tracking is a challenge the visual system has to solve by reading out
    the retinal population. It is still unclear how the information from different
    neurons can be combined together to estimate the position of an object. Here we
    recorded a large population of ganglion cells in a dense patch of salamander and
    guinea pig retinas while displaying a bar moving diffusively. We show that the
    bar’s position can be reconstructed from retinal activity with a precision in
    the hyperacuity regime using a linear decoder acting on 100+ cells. We then took
    advantage of this unprecedented precision to explore the spatial structure of
    the retina’s population code. The classical view would have suggested that the
    firing rates of the cells form a moving hill of activity tracking the bar’s position.
    Instead, we found that most ganglion cells in the salamander fired sparsely and
    idiosyncratically, so that their neural image did not track the bar. Furthermore,
    ganglion cell activity spanned an area much larger than predicted by their receptive
    fields, with cells coding for motion far in their surround. As a result, population
    redundancy was high, and we could find multiple, disjoint subsets of neurons that
    encoded the trajectory with high precision. This organization allows for diverse
    collections of ganglion cells to represent high-accuracy motion information in
    a form easily read out by downstream neural circuits.
acknowledgement: 'This work was supported by grants EY 014196 and EY 017934 to MJB,
  ANR OPTIMA, the French State program Investissements d’Avenir managed by the Agence
  Nationale de la Recherche [LIFESENSES: ANR-10-LABX-65], and by a EC grant from the
  Human Brain Project (CLAP) to OM, the Austrian Research Foundation FWF P25651 to
  VBS and GT. VBS is partially supported by contracts MEC, Spain (Grant No. AYA2010-
  22111-C03-02, Grant No. AYA2013-48623-C2-2 and FEDER Funds).'
article_number: e1004304
author:
- first_name: Olivier
  full_name: Marre, Olivier
  last_name: Marre
- first_name: Vicente
  full_name: Botella Soler, Vicente
  id: 421234E8-F248-11E8-B48F-1D18A9856A87
  last_name: Botella Soler
  orcid: 0000-0002-8790-1914
- first_name: Kristina
  full_name: Simmons, Kristina
  last_name: Simmons
- first_name: Thierry
  full_name: Mora, Thierry
  last_name: Mora
- first_name: Gasper
  full_name: Tkacik, Gasper
  id: 3D494DCA-F248-11E8-B48F-1D18A9856A87
  last_name: Tkacik
  orcid: 0000-0002-6699-1455
- first_name: Michael
  full_name: Berry, Michael
  last_name: Berry
citation:
  ama: Marre O, Botella Soler V, Simmons K, Mora T, Tkačik G, Berry M. High accuracy
    decoding of dynamical motion from a large retinal population. <i>PLoS Computational
    Biology</i>. 2015;11(7). doi:<a href="https://doi.org/10.1371/journal.pcbi.1004304">10.1371/journal.pcbi.1004304</a>
  apa: Marre, O., Botella Soler, V., Simmons, K., Mora, T., Tkačik, G., &#38; Berry,
    M. (2015). High accuracy decoding of dynamical motion from a large retinal population.
    <i>PLoS Computational Biology</i>. Public Library of Science. <a href="https://doi.org/10.1371/journal.pcbi.1004304">https://doi.org/10.1371/journal.pcbi.1004304</a>
  chicago: Marre, Olivier, Vicente Botella Soler, Kristina Simmons, Thierry Mora,
    Gašper Tkačik, and Michael Berry. “High Accuracy Decoding of Dynamical Motion
    from a Large Retinal Population.” <i>PLoS Computational Biology</i>. Public Library
    of Science, 2015. <a href="https://doi.org/10.1371/journal.pcbi.1004304">https://doi.org/10.1371/journal.pcbi.1004304</a>.
  ieee: O. Marre, V. Botella Soler, K. Simmons, T. Mora, G. Tkačik, and M. Berry,
    “High accuracy decoding of dynamical motion from a large retinal population,”
    <i>PLoS Computational Biology</i>, vol. 11, no. 7. Public Library of Science,
    2015.
  ista: Marre O, Botella Soler V, Simmons K, Mora T, Tkačik G, Berry M. 2015. High
    accuracy decoding of dynamical motion from a large retinal population. PLoS Computational
    Biology. 11(7), e1004304.
  mla: Marre, Olivier, et al. “High Accuracy Decoding of Dynamical Motion from a Large
    Retinal Population.” <i>PLoS Computational Biology</i>, vol. 11, no. 7, e1004304,
    Public Library of Science, 2015, doi:<a href="https://doi.org/10.1371/journal.pcbi.1004304">10.1371/journal.pcbi.1004304</a>.
  short: O. Marre, V. Botella Soler, K. Simmons, T. Mora, G. Tkačik, M. Berry, PLoS
    Computational Biology 11 (2015).
date_created: 2018-12-11T11:53:31Z
date_published: 2015-07-01T00:00:00Z
date_updated: 2021-01-12T06:52:35Z
day: '01'
ddc:
- '570'
department:
- _id: GaTk
doi: 10.1371/journal.pcbi.1004304
file:
- access_level: open_access
  checksum: 472b979f3f1cffb37b3e503f085115ca
  content_type: application/pdf
  creator: system
  date_created: 2018-12-12T10:16:25Z
  date_updated: 2020-07-14T12:45:12Z
  file_id: '5212'
  file_name: IST-2016-455-v1+1_journal.pcbi.1004304.pdf
  file_size: 4673930
  relation: main_file
file_date_updated: 2020-07-14T12:45:12Z
has_accepted_license: '1'
intvolume: '        11'
issue: '7'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 254D1A94-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P 25651-N26
  name: Sensitivity to higher-order statistics in natural scenes
publication: PLoS Computational Biology
publication_status: published
publisher: Public Library of Science
publist_id: '5447'
pubrep_id: '455'
quality_controlled: '1'
scopus_import: 1
status: public
title: High accuracy decoding of dynamical motion from a large retinal population
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2015'
...
---
_id: '2183'
abstract:
- lang: eng
  text: 'We describe a simple adaptive network of coupled chaotic maps. The network
    reaches a stationary state (frozen topology) for all values of the coupling parameter,
    although the dynamics of the maps at the nodes of the network can be nontrivial.
    The structure of the network shows interesting hierarchical properties and in
    certain parameter regions the dynamics is polysynchronous: Nodes can be divided
    in differently synchronized classes but, contrary to cluster synchronization,
    nodes in the same class need not be connected to each other. These complicated
    synchrony patterns have been conjectured to play roles in systems biology and
    circuits. The adaptive system we study describes ways whereby this behavior can
    evolve from undifferentiated nodes.'
acknowledgement: "V.B.S. is partially supported by contract MEC (Grant No. AYA2010-22111-C03-02).\r\n"
article_number: '062809'
article_processing_charge: No
author:
- first_name: Vicente
  full_name: Botella Soler, Vicente
  id: 421234E8-F248-11E8-B48F-1D18A9856A87
  last_name: Botella Soler
  orcid: 0000-0002-8790-1914
- first_name: Paul
  full_name: Glendinning, Paul
  last_name: Glendinning
citation:
  ama: Botella Soler V, Glendinning P. Hierarchy and polysynchrony in an adaptive
    network . <i>Physical Review E Statistical Nonlinear and Soft Matter Physics</i>.
    2014;89(6). doi:<a href="https://doi.org/10.1103/PhysRevE.89.062809">10.1103/PhysRevE.89.062809</a>
  apa: Botella Soler, V., &#38; Glendinning, P. (2014). Hierarchy and polysynchrony
    in an adaptive network . <i>Physical Review E Statistical Nonlinear and Soft Matter
    Physics</i>. American Institute of Physics. <a href="https://doi.org/10.1103/PhysRevE.89.062809">https://doi.org/10.1103/PhysRevE.89.062809</a>
  chicago: Botella Soler, Vicente, and Paul Glendinning. “Hierarchy and Polysynchrony
    in an Adaptive Network .” <i>Physical Review E Statistical Nonlinear and Soft
    Matter Physics</i>. American Institute of Physics, 2014. <a href="https://doi.org/10.1103/PhysRevE.89.062809">https://doi.org/10.1103/PhysRevE.89.062809</a>.
  ieee: V. Botella Soler and P. Glendinning, “Hierarchy and polysynchrony in an adaptive
    network ,” <i>Physical Review E Statistical Nonlinear and Soft Matter Physics</i>,
    vol. 89, no. 6. American Institute of Physics, 2014.
  ista: Botella Soler V, Glendinning P. 2014. Hierarchy and polysynchrony in an adaptive
    network . Physical Review E Statistical Nonlinear and Soft Matter Physics. 89(6),
    062809.
  mla: Botella Soler, Vicente, and Paul Glendinning. “Hierarchy and Polysynchrony
    in an Adaptive Network .” <i>Physical Review E Statistical Nonlinear and Soft
    Matter Physics</i>, vol. 89, no. 6, 062809, American Institute of Physics, 2014,
    doi:<a href="https://doi.org/10.1103/PhysRevE.89.062809">10.1103/PhysRevE.89.062809</a>.
  short: V. Botella Soler, P. Glendinning, Physical Review E Statistical Nonlinear
    and Soft Matter Physics 89 (2014).
date_created: 2018-12-11T11:56:11Z
date_published: 2014-06-16T00:00:00Z
date_updated: 2022-08-25T14:04:45Z
day: '16'
department:
- _id: GaTk
doi: 10.1103/PhysRevE.89.062809
ec_funded: 1
intvolume: '        89'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1403.3209
month: '06'
oa: 1
oa_version: Preprint
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '291734'
  name: International IST Postdoc Fellowship Programme
publication: Physical Review E Statistical Nonlinear and Soft Matter Physics
publication_status: published
publisher: American Institute of Physics
publist_id: '4798'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Hierarchy and polysynchrony in an adaptive network '
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 89
year: '2014'
...
---
_id: '2413'
abstract:
- lang: eng
  text: 'Progress in understanding the global brain dynamics has remained slow to
    date in large part because of the highly multiscale nature of brain activity.
    Indeed, normal brain dynamics is characterized by complex interactions between
    multiple levels: from the microscopic scale of single neurons to the mesoscopic
    level of local groups of neurons, and finally to the macroscopic level of the
    whole brain. Among the most difficult tasks are those of identifying which scales
    are significant for a given particular function and describing how the scales
    affect each other. It is important to realize that the scales of time and space
    are linked together, or even intertwined, and that causal inference is far more
    ambiguous between than within levels. We approach this problem from the perspective
    of our recent work on simultaneous recording from micro- and macroelectrodes in
    the human brain. We propose a physiological description of these multilevel interactions,
    based on phase–amplitude coupling of neuronal oscillations that operate at multiple
    frequencies and on different spatial scales. Specifically, the amplitude of the
    oscillations on a particular spatial scale is modulated by phasic variations in
    neuronal excitability induced by lower frequency oscillations that emerge on a
    larger spatial scale. Following this general principle, it is possible to scale
    up or scale down the multiscale brain dynamics. It is expected that large-scale
    network oscillations in the low-frequency range, mediating downward effects, may
    play an important role in attention and consciousness.'
alternative_title:
- Reviews of Nonlinear Dynamics and Complexity
author:
- first_name: Mario
  full_name: Valderrama, Mario
  last_name: Valderrama
- first_name: Vicente
  full_name: Botella Soler, Vicente
  id: 421234E8-F248-11E8-B48F-1D18A9856A87
  last_name: Botella Soler
  orcid: 0000-0002-8790-1914
- first_name: Michel
  full_name: Le Van Quyen, Michel
  last_name: Le Van Quyen
citation:
  ama: 'Valderrama M, Botella Soler V, Le Van Quyen M. Neuronal oscillations scale
    up and scale down the brain dynamics . In: Meyer M, Pesenson Z, eds. <i>Multiscale
    Analysis and Nonlinear Dynamics: From Genes to the Brain</i>. Wiley-VCH; 2013.
    doi:<a href="https://doi.org/10.1002/9783527671632.ch08">10.1002/9783527671632.ch08</a>'
  apa: 'Valderrama, M., Botella Soler, V., &#38; Le Van Quyen, M. (2013). Neuronal
    oscillations scale up and scale down the brain dynamics . In M. Meyer &#38; Z.
    Pesenson (Eds.), <i>Multiscale Analysis and Nonlinear Dynamics: From Genes to
    the Brain</i>. Wiley-VCH. <a href="https://doi.org/10.1002/9783527671632.ch08">https://doi.org/10.1002/9783527671632.ch08</a>'
  chicago: 'Valderrama, Mario, Vicente Botella Soler, and Michel Le Van Quyen. “Neuronal
    Oscillations Scale up and Scale down the Brain Dynamics .” In <i>Multiscale Analysis
    and Nonlinear Dynamics: From Genes to the Brain</i>, edited by Misha Meyer and
    Z. Pesenson. Wiley-VCH, 2013. <a href="https://doi.org/10.1002/9783527671632.ch08">https://doi.org/10.1002/9783527671632.ch08</a>.'
  ieee: 'M. Valderrama, V. Botella Soler, and M. Le Van Quyen, “Neuronal oscillations
    scale up and scale down the brain dynamics ,” in <i>Multiscale Analysis and Nonlinear
    Dynamics: From Genes to the Brain</i>, M. Meyer and Z. Pesenson, Eds. Wiley-VCH,
    2013.'
  ista: 'Valderrama M, Botella Soler V, Le Van Quyen M. 2013.Neuronal oscillations
    scale up and scale down the brain dynamics . In: Multiscale Analysis and Nonlinear
    Dynamics: From Genes to the Brain. Reviews of Nonlinear Dynamics and Complexity,
    .'
  mla: 'Valderrama, Mario, et al. “Neuronal Oscillations Scale up and Scale down the
    Brain Dynamics .” <i>Multiscale Analysis and Nonlinear Dynamics: From Genes to
    the Brain</i>, edited by Misha Meyer and Z. Pesenson, Wiley-VCH, 2013, doi:<a
    href="https://doi.org/10.1002/9783527671632.ch08">10.1002/9783527671632.ch08</a>.'
  short: 'M. Valderrama, V. Botella Soler, M. Le Van Quyen, in:, M. Meyer, Z. Pesenson
    (Eds.), Multiscale Analysis and Nonlinear Dynamics: From Genes to the Brain, Wiley-VCH,
    2013.'
date_created: 2018-12-11T11:57:31Z
date_published: 2013-08-01T00:00:00Z
date_updated: 2021-01-12T06:57:20Z
day: '01'
department:
- _id: GaTk
doi: 10.1002/9783527671632.ch08
editor:
- first_name: Misha
  full_name: Meyer, Misha
  last_name: Meyer
- first_name: Z.
  full_name: Pesenson, Z.
  last_name: Pesenson
language:
- iso: eng
month: '08'
oa_version: None
publication: 'Multiscale Analysis and Nonlinear Dynamics: From Genes to the Brain'
publication_identifier:
  eisbn:
  - '9783527671632'
  isbn:
  - '9783527411986 '
publication_status: published
publisher: Wiley-VCH
publist_id: '4513'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'Neuronal oscillations scale up and scale down the brain dynamics '
type: book_chapter
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2013'
...
---
_id: '2861'
abstract:
- lang: eng
  text: We consider a two-parameter family of piecewise linear maps in which the moduli
    of the two slopes take different values. We provide numerical evidence of the
    existence of some parameter regions in which the Lyapunov exponent and the topological
    entropy remain constant. Analytical proof of this phenomenon is also given for
    certain cases. Surprisingly however, the systems with that property are not conjugate
    as we prove by using kneading theory.
article_number: '125101'
author:
- first_name: Vicente
  full_name: Botella Soler, Vicente
  id: 421234E8-F248-11E8-B48F-1D18A9856A87
  last_name: Botella Soler
  orcid: 0000-0002-8790-1914
- first_name: José
  full_name: Oteo, José
  last_name: Oteo
- first_name: Javier
  full_name: Ros, Javier
  last_name: Ros
- first_name: Paul
  full_name: Glendinning, Paul
  last_name: Glendinning
citation:
  ama: 'Botella Soler V, Oteo J, Ros J, Glendinning P. Lyapunov exponent and topological
    entropy plateaus in piecewise linear maps. <i>Journal of Physics A: Mathematical
    and Theoretical</i>. 2013;46(12). doi:<a href="https://doi.org/10.1088/1751-8113/46/12/125101">10.1088/1751-8113/46/12/125101</a>'
  apa: 'Botella Soler, V., Oteo, J., Ros, J., &#38; Glendinning, P. (2013). Lyapunov
    exponent and topological entropy plateaus in piecewise linear maps. <i>Journal
    of Physics A: Mathematical and Theoretical</i>. IOP Publishing Ltd. <a href="https://doi.org/10.1088/1751-8113/46/12/125101">https://doi.org/10.1088/1751-8113/46/12/125101</a>'
  chicago: 'Botella Soler, Vicente, José Oteo, Javier Ros, and Paul Glendinning. “Lyapunov
    Exponent and Topological Entropy Plateaus in Piecewise Linear Maps.” <i>Journal
    of Physics A: Mathematical and Theoretical</i>. IOP Publishing Ltd., 2013. <a
    href="https://doi.org/10.1088/1751-8113/46/12/125101">https://doi.org/10.1088/1751-8113/46/12/125101</a>.'
  ieee: 'V. Botella Soler, J. Oteo, J. Ros, and P. Glendinning, “Lyapunov exponent
    and topological entropy plateaus in piecewise linear maps,” <i>Journal of Physics
    A: Mathematical and Theoretical</i>, vol. 46, no. 12. IOP Publishing Ltd., 2013.'
  ista: 'Botella Soler V, Oteo J, Ros J, Glendinning P. 2013. Lyapunov exponent and
    topological entropy plateaus in piecewise linear maps. Journal of Physics A: Mathematical
    and Theoretical. 46(12), 125101.'
  mla: 'Botella Soler, Vicente, et al. “Lyapunov Exponent and Topological Entropy
    Plateaus in Piecewise Linear Maps.” <i>Journal of Physics A: Mathematical and
    Theoretical</i>, vol. 46, no. 12, 125101, IOP Publishing Ltd., 2013, doi:<a href="https://doi.org/10.1088/1751-8113/46/12/125101">10.1088/1751-8113/46/12/125101</a>.'
  short: 'V. Botella Soler, J. Oteo, J. Ros, P. Glendinning, Journal of Physics A:
    Mathematical and Theoretical 46 (2013).'
date_created: 2018-12-11T11:59:59Z
date_published: 2013-03-29T00:00:00Z
date_updated: 2021-01-12T07:00:19Z
day: '29'
department:
- _id: GaTk
doi: 10.1088/1751-8113/46/12/125101
intvolume: '        46'
issue: '12'
language:
- iso: eng
month: '03'
oa_version: None
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_status: published
publisher: IOP Publishing Ltd.
publist_id: '3928'
quality_controlled: '1'
scopus_import: 1
status: public
title: Lyapunov exponent and topological entropy plateaus in piecewise linear maps
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 46
year: '2013'
...
