• Elizabeth Bradley Professor, University of Colorado
  • Ryan James Postdoc, University of California
  • James Meiss Professor, University of Colorado

Prediction in Projection

Prediction models constructed from state-space dynamics have a long and rich history, dating back to roulette and beyond. A major stumbling block in the application of these models in real-world situations is the need to reconstruct the dynamics from scalar time-series data---e.g., via delay-coordinate embedding. This procedure, which is the topic of a large and active body of literature, involves estimation of two free parameters: the dimension of the reconstruction space and the delay, between the observations that make up the coordinates in that space. Estimating good values for these parameters is not trivial; it requires the proper mathematics, attention to the data requirements, computational effort, and expert interpretation of the results of the calculations. This is a major challenge if one is interested in real-time forecasting, especially when the systems involved operate on fast time scales. In this work, we have seen that the full effort of delay-coordinate embedding is not always necessary when one is building forecast models, and can indeed be overkill. Using synthetic time-series data generated from the Lorenz-96 atmospheric model and real data from a computer performance experiment, we have demonstrated that a two-dimensional embedding of scalar time-series data from a dynamical system gives simple forecast methods enough traction to generate accurate predictions of the future course of those dynamics---sometimes even more accurate than predictions created using the full embedding. Since incomplete embeddings do not preserve the topology of the full dynamics, this is interesting from a mathematical standpoint. It is also potentially useful in practice. This reduced-order forecasting strategy involves only one free parameter (time delay), good values for which, we believe, can be estimated 'on the fly' using information-theoretic and/or machine-learning algorithms. As such, it sidesteps much of the complexity of the embedding process---perhaps most importantly, the need for expert human interpretation---and this could enable automated, real-time dynamics-based forecasting in practical applications.

Related Publications

  • J. Garalnd, E. Bradley, J.D. Meiss “Exploring the Topology of Dynamical Reconstructions,” in Review at Physica D; submitted for review June 2, 2015. Preprint available at arXiv:1506.01128(2015).
  • J. Garland, E. Bradley, "Prediction in Projection," Currently in Review at Chaos; submitted for review March 6, 2015. Preprint available at arXiv:1503.01678 (2014).
  • J. Garland, R. James, E. Bradley, "Model-free quantification of time-series predictability," Physical Review E 90:052910 doi: 10.1103/PhysRevE.90.052910 (2014).
  • J. Garland, E. Bradley, "On the Importance of Nonlinear Modeling in Computer Performance Prediction," IDA-13 (Proceedings of the 12th International Symposium on Intelligent Data Analysis), Advances in Intelligent Data Analysis XII: Springer Lecture Notes in Computer Science. London, England, October 2013. Available here. IDA-13 Frontier Prize Recipient.
  • J. Garland, E. Bradley, "Predicting Computer Performance Dynamics," IDA-11 (Proceedings of the 10th International Symposium on Intelligent Data Analysis), Advances in Intelligent Data Analysis X: Springer Lecture Notes in Computer Science. London, England, October 2013. Available here.


  • Hiroshi Ashikaga PhD MD, John Hopkins University

Modeling the heart as a communication system

A human heart consists of a network of approximately five billion cardiomyocytes, connected by a lattice-like structure of low-resistance cell-to-cell gap junctions. The behaviors of individual cardiomyocytes on this network are orchestrated by electrical conduction between adjacent cells through these gap junctions. When the heart is functioning properly this cell-to-cell electrical propagation results in the heart beating normally. However, this process can break down during a phenomenon known as cardiac arrhythmia (abnormal heart rhythm)---a leading cause of sudden death in the world today.

Understanding when and why this electrical-transmission process breaks down is vitally important in developing actionable and effective treatment protocols. However, conventional electrocardiographic metrics simply measure the sequence of electrical excitations in small local regions of the heart, and effectively ignore cell-to-cell interactions. This means that traditional measures cannot quantify how arrhythmia impacts cell-to-cell wave propagation and the breakdown thereof, making it a real challenge to properly diagnose and treat cardiac arrhythmia.

In this work, we propose a novel approach to this problem: viewing the heart as a communication system in which electrical wave propagation allows information to transmit across this network of cardiomyocytes1. Under this paradigm, heart rhythm disorders can be viewed as the result of abnormal production or transmission of information. Processes that, we propose, are quantifiable using information-theoretic measures, such as Shannon entropy, mutual information and transfer entropy, and ignored by traditional electrocardiographic metrics. To this end, we developed a framework to quantify cardiac electrical communication during action potential propagation in normal and abnormal heart rhythms. We have shown that this paradigm allows for a deeper understanding of the electrical communication process present in the heart; in particular, when this communication system fails. In this work, we have obtained results with in silico experiments as well as in vivo observations. In silico experiments were performed with the FitzHugh-Nagumo model, a reaction-diffusion equation traditionally used to model cardiac activity. The in vivo observations were collected with a 64-lead basket catheter placed inside of patients’ left and right atria during episodes of cardiac arrhythmia.

We conjecture that information theory can be utilized to quantitatively assess electrical communication processes among cardiomyocytes during normal heartbeat and complex arrhythmias beyond electrocardiographic measures. Such information-theoretic metrics may find clinical application in the identification of rhythm-specific treatments which are currently unmet by traditional electrocardiographic techniques. We believe that this new paradigm provides a novel set of tools for practitioners and theorists to analyze the heart as a cellular information-processing unit.

Related Publications

  • H. Ashikaga, J. Aguilar-Rodrguez; S. Gorsky, E. Lusczek, F.M.D. Marquitti, B. Thompson, D. Wu, J. Garland, "Modeling the heart as a communication system," Journal of the Royal Society Interface 12 (105). doi:10.1098/rsif.2014.1201 (2015).