Minimum Number of Probes for Brain Dynamics Observability
Sergio Pequito, Paul Bogdan, George Pappas

Citation
Sergio Pequito, Paul Bogdan, George Pappas. "Minimum Number of Probes for Brain Dynamics Observability". 54th IEEE Conference on Decision and Control, 306-311, 15, December, 2015.

Abstract
In this paper, we address the problem of placing sensor probes in the brain such that the system dynamics' are generically observable. The system dynamics whose states can encode for instance the fire-rating of the neurons or their ensemble following a neural-topological (structural) approach, and the sensors are assumed to be dedicated, i.e., can only measure a state at each time. Even though the mathematical description of brain dynamics is (yet) to be discovered, we build on its observed fractal characteristics and assume that the a good model of the brain activity satisfies the following properties: (i) linear time-varying, or (ii) fractional-order dynamics. Although the sensor placement explored in this paper is particularly considering the observability of brain dynamics, the proposed methodology applies to any fractional-order linear system. Thus, the main contributions of this paper are twofold: (i) we show how to place the minimum number of dedicated sensors for continuous-time linear switching systems, i.e., a sequential description of the dynamics by a finite collection of linear time-invariant systems that can change over time, that ensures the system to be generically observable; and (ii) we show how to place the minimum number of dedicated sensors to ensure generic observability in discrete-time fractional-order systems for a specified finite interval of time. Finally, an illustrative example of the main results is provided using brain activity data.

Electronic downloads


Internal. This publication has been marked by the author for TerraSwarm-only distribution, so electronic downloads are not available without logging in.
Citation formats  
  • HTML
    Sergio Pequito, Paul Bogdan, George Pappas. <a
    href="http://www.terraswarm.org/pubs/531.html"
    >Minimum Number of Probes for Brain Dynamics
    Observability</a>, 54th IEEE Conference on Decision
    and Control, 306-311, 15, December, 2015.
  • Plain text
    Sergio Pequito, Paul Bogdan, George Pappas. "Minimum
    Number of Probes for Brain Dynamics Observability".
    54th IEEE Conference on Decision and Control, 306-311, 15,
    December, 2015.
  • BibTeX
    @inproceedings{PequitoBogdanPappas15_MinimumNumberOfProbesForBrainDynamicsObservability,
        author = {Sergio Pequito and Paul Bogdan and George Pappas},
        title = {Minimum Number of Probes for Brain Dynamics
                  Observability},
        booktitle = {54th IEEE Conference on Decision and Control},
        pages = {306-311},
        day = {15},
        month = {December},
        year = {2015},
        abstract = {In this paper, we address the problem of placing
                  sensor probes in the brain such that the system
                  dynamics' are generically observable. The system
                  dynamics whose states can encode for instance the
                  fire-rating of the neurons or their ensemble
                  following a neural-topological (structural)
                  approach, and the sensors are assumed to be
                  dedicated, i.e., can only measure a state at each
                  time. Even though the mathematical description of
                  brain dynamics is (yet) to be discovered, we build
                  on its observed fractal characteristics and assume
                  that the a good model of the brain activity
                  satisfies the following properties: (i) linear
                  time-varying, or (ii) fractional-order dynamics.
                  Although the sensor placement explored in this
                  paper is particularly considering the
                  observability of brain dynamics, the proposed
                  methodology applies to any fractional-order linear
                  system. Thus, the main contributions of this paper
                  are twofold: (i) we show how to place the minimum
                  number of dedicated sensors for continuous-time
                  linear switching systems, i.e., a sequential
                  description of the dynamics by a finite collection
                  of linear time-invariant systems that can change
                  over time, that ensures the system to be
                  generically observable; and (ii) we show how to
                  place the minimum number of dedicated sensors to
                  ensure generic observability in discrete-time
                  fractional-order systems for a specified finite
                  interval of time. Finally, an illustrative example
                  of the main results is provided using brain
                  activity data.},
        URL = {http://terraswarm.org/pubs/531.html}
    }
    

Posted by Sergio Pequito on 27 Mar 2015.
Groups: services

Notice: This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright.