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Modelling dynamics of electrical responses in plants

Modelling dynamics of electrical responses in plants. Sanmitra Ghosh Supervisor: Dr Srinandan Dasmahapatra & Dr Koushik Maharatna Electronics and Software Systems, School of Electronics & Computer Science University of Southampton. Introduction

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Modelling dynamics of electrical responses in plants

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  1. Modelling dynamics of electrical responses in plants SanmitraGhosh Supervisor: Dr SrinandanDasmahapatra & Dr KoushikMaharatna Electronics and Software Systems, School of Electronics & Computer Science University of Southampton

  2. Introduction • Black Box models (System Identification) • Modelling plant responses as ODEs • Calibration of Models (Parameter Estimation in ODE using ABC-SMC) • ABC-SMC using Gaussian processes • Future work • References

  3. Experiments Models ???

  4. Typical electrical responses Light Ozone (sprayed for 2 minutes)

  5. Generalized least-square estimator • {A,B,F,C,D} are rational polynomials Linear estimator

  6. Nonlinear Hammerstein-Wiener model structure System output Cost function This cost function is minimized using optimization

  7. Proposed model: (v) is a chosen non-linear function of voltage V(t) (t) models a latent stimulus Voltage time

  8. (v) is chosen as Micheles-Menten (sigmoidal) and Fitzhugh-Nagumo (cubic) type non-linear function of v(t) (voltage)

  9. Approximate Bayesian Computation posterior Prior Likelihood

  10. ABC Rejection Sampler (Pickard, 1999) • Given , π(θ), (x|) • Sample a parameter ∗ from the prior distribution π(). • Simulate a dataset xfrom model (x|∗) with parameter θ∗. • if ∆(, ) ≤ then • 5. Accept ∗ otherwise reject. Note: to generate data x from model (x|∗) we have to solve the ODE

  11. ABC-Sequential Monte Carlo (Toni et al, 1999) … Limitation: extremely slow due to large number of explicit ODE solving for generating simulated data

  12. The Gaussian process trick = = + noise Data Gaussian Process ≤

  13. Model needs to be extended to capture the variability seen among different electrical responses. • More models are required to represent other stimuli.

  14. 1. J K Pritchard, M T Seielstad, a Perez-Lezaun, and M W Feldman. Population growth of human Y chromosomes: a study of Y chromosome microsatellites. Mol. Biol. Evol., 16(12):1791–8, December 1999. 2. T. Toni, D. Welch, N. Strelkowa, a. Ipsen, and M. P.H Stumpf. Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J. R. Soc. Interface, 6(31):187–202, February 2009.

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