Exploring and Statistically Learning an Excitable Stochastic-Dynamical Model

Objective

A collaboration with the core Nextjournal team to publish work on the statistical procedure for the FitzHugh-Nagumo model as an explorable, data driven, reproducible article.

Problem Statement

The interplay between the noise coming from outside factors interacting with the system in a random or non-predictable way and the rhythm created by the delayed interaction between excitatory and inhibitory components of the system create a manifold of possible recurrence patterns.

The methodologies appearing in the literature are difficult to implement and difficult to tune. An easy to use procedure has not appeared yet. Providing automatic solutions for the inference problem is not of much use if the results are not easily understood. This is why it is important to allow scientists to visually explore the estimated FitzHugh-Nagumo models and make the estimation results tangible.

Input

An observed trajectory (a curve showing the change of the modeled quantity over time)

Output

The procedure returns likely intervals of the parameters which govern the dynamics of the model. The statistical analysis of this data will be explorable using an interface aimed at visualizing the behavior of the models best describing the data.

Existing Assets

Exploring and Statistically Learning an Excitable Stochastic-Dynamical Model currently includes these assets:

These existing assets and research will form the foundation of an interactive article. Our goal is to change how people engage research. To paraphrase Bret Victor, rather than "information to be consumed," the resulting notebook will be "used as an environment to think in."

This will be accomplished using Nextjournal's existing technologies and collaborative efforts with the Nextjournal team where appropriate, e.g. specialty graphics, user experience components, or back end services.

Deliverables

The project should roughly take 2 months to implement and begins upon receipt of the first paid installment of the award. This includes:

  • A Bayesian statistical procedure which provides the range of likely parameters given the data

  • The visualizations of any given model's behavior

  • The interface to explore the visualizations via a set of parameters

The collaboration with Nextjournal will primarily concern the second two deliverables.

The creation of the corresponding Nextjournal components is initially disentangled from the statistical methodology so that two groups can work simultaneously. Only in a second stage, the two groups will converge in order to make the statistical procedure available online in Nextjournal and embed it together with the graphical interface created for the visualisation of the model.

The work will primarily take place in Julia.

Administration

  • $1,500 will be awarded upon receiving the initial invoice from the awardee.

  • $1,500 upon receiving the second invoice from the awardee at the completion of the project.

  • The awardee is responsible for bank transfer and currency exchange fees.

  • All individuals in the project's group will be provided a Private Research plan and receive all related benefits plus unlimited cloud compute resources.

The awardees intend to dedicate part of the scholarship to refund travels to Berlin that will facilitate our work together with Nextjournal.

Team

A collaboration between Nextjournal and the Lobatto group:

  • Sebastiano Grazzi, Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands
  • Dr.ir. Frank van der Meulen, Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands
  • Marcin Mider, Department of Statistics, University of Warwick, United Kingdom
  • Dr. Moritz Schauer, Mathematical Institute, Leiden University, The Netherlands

Glossary

  • The FitzHugh-Nagumo model - a versatile yet simple model for the evolution of excitable or oscillatory physical processes.
  • Awardee - the winning individual or team of Nextjournal's Scholarship for Explorable Research.
  • Article: a published, version controlled document that includes data, code, commentary, and execution environment.

  • Notebook - a published or unpublished human-readable document that combines code, commentary, and results.

  • Reproducibility - the ability to generate the same results at some point in the future given the same data and code.

  • Remix - an exact copy of a published Nextjournal article. With remixing, it is easy to take fully accredited work, reproduce its results, and experiment with variants.

  • Explorable explanations is a term that is best illustrated in Bret Victor’s essays Ten Brighter Ideas and Explorable Explanations.