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      Analysing nystagmus waveforms: a computational framework

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          Abstract

          We present a new computational approach to analyse nystagmus waveforms. Our framework is designed to fully characterise the state of the nystagmus, aid clinical diagnosis and to quantify the dynamical changes in the oscillations over time. Both linear and nonlinear analyses of time series were used to determine the regularity and complexity of a specific homogenous phenotype of nystagmus. Two-dimensional binocular eye movement recordings were carried out on 5 adult subjects who exhibited a unilateral, uniplanar, vertical nystagmus secondary to a monocular late-onset severe visual loss in the oscillating eye (the Heimann-Bielschowsky Phenomenon). The non-affected eye held a central gaze in both horizontal and vertical planes (± 10 min. of arc). All affected eyes exhibited vertical oscillations, with mean amplitudes and frequencies ranging from 2.0°–4.0° to 0.25–1.5 Hz, respectively. Unstable periodic orbit analysis revealed only 1 subject exhibited a periodic oscillation. The remaining subjects were found to display quasiperiodic ( n = 1) and nonperiodic ( n = 3) oscillations. Phase space reconstruction allowed attractor identification and the computation of a time series complexity measure—the permutation entropy. The entropy measure was found to be able to distinguish between a periodic oscillation associated with a limit cycle attractor, a quasiperiodic oscillation associated with a torus attractor and nonperiodic oscillations associated with higher-dimensional attractors. Importantly, the permutation entropy was able to rank the oscillations, thereby providing an objective index of nystagmus complexity (range 0.15–0.21) that could not be obtained via unstable periodic orbit analysis or attractor identification alone. These results suggest that our framework provides a comprehensive methodology for characterising nystagmus, aiding differential diagnosis and also permitting investigation of the waveforms over time, thereby facilitating the quantification of future therapeutic managements. In addition, permutation entropy could provide an additional tool for future oculomotor modelling.

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          Neural networks and physical systems with emergent collective computational abilities.

          J Hopfield (1982)
          Computational properties of use of biological organisms or to the construction of computers can emerge as collective properties of systems having a large number of simple equivalent components (or neurons). The physical meaning of content-addressable memory is described by an appropriate phase space flow of the state of a system. A model of such a system is given, based on aspects of neurobiology but readily adapted to integrated circuits. The collective properties of this model produce a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size. The algorithm for the time evolution of the state of the system is based on asynchronous parallel processing. Additional emergent collective properties include some capacity for generalization, familiarity recognition, categorization, error correction, and time sequence retention. The collective properties are only weakly sensitive to details of the modeling or the failure of individual devices.
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            Machine Learning in Medicine

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              Permutation entropy: a natural complexity measure for time series.

              We introduce complexity parameters for time series based on comparison of neighboring values. The definition directly applies to arbitrary real-world data. For some well-known chaotic dynamical systems it is shown that our complexity behaves similar to Lyapunov exponents, and is particularly useful in the presence of dynamical or observational noise. The advantages of our method are its simplicity, extremely fast calculation, robustness, and invariance with respect to nonlinear monotonous transformations.
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                Author and article information

                Contributors
                r.abadi@manchester.ac.uk
                o.e.akman@exeter.ac.uk
                Journal
                Sci Rep
                Sci Rep
                Scientific Reports
                Nature Publishing Group UK (London )
                2045-2322
                7 May 2021
                7 May 2021
                2021
                : 11
                : 9761
                Affiliations
                [1 ]Faculty of Biology, Medicine and Health, University of Manchester, Manchester, M13 9PT UK
                [2 ]College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK
                [3 ]Orthoptics Department, NHS Foundation Trust, Sheffield Teaching Hospitals, Sheffield, UK
                [4 ]Division of Ophthalmology and Orthoptics, Health Sciences School, University of Sheffield, Sheffield, UK
                Article
                89094
                10.1038/s41598-021-89094-7
                8105328
                33963228
                f4ebe1df-0f9c-40e5-9544-f319c3bbdbc1
                © The Author(s) 2021

                Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

                History
                : 23 February 2021
                : 21 April 2021
                Funding
                Funded by: FundRef http://dx.doi.org/10.13039/501100000266, Engineering and Physical Sciences Research Council;
                Award ID: EP/N017846/1
                Categories
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                © The Author(s) 2021

                Uncategorized
                computational biology and bioinformatics,neuroscience,systems biology,medical research

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