Research Background
Essays from my research in computational neuroscience and complex systems: measurement, criticality, branching processes and DFA.
These essays come from my MSc and PhD work in computational neuroscience (2007–2013) and from running biomarker analyses for pharmaceutical clinical trials at NBT Analytics. Each carries a note at the top on when and where it was written and, where the field has moved, what has changed since.
Two ideas run through this work. The first is measurement: how to infer the hidden state of a complex system from imperfect signals, and how to tell whether a signal is informative about that state at all. The second is propagation: how activity spreads through a connected system, and what changes as the system approaches a critical point.
Start with Introduction to Self-Organised Criticality and Branching Processes first; The Brain as a Critical System builds on both, and the DFA tutorial shows how the long-range temporal correlations in that essay are measured.
Background essays#
Introduction to Self-Organised Criticality
A short introduction to self-organised criticality and related ideas from complex systems theory, adapted from earlier thesis work.
Branching Processes
A background essay on activity propagation, critical branching, and why branching models matter for understanding scale-free dynamics in neuronal systems.
The Brain as a Critical System
An overview of the criticality hypothesis in neuroscience, long-range temporal correlations, and the question of whether temporal structure can reveal latent changes in system state.
Tutorials#
Detrended Fluctuation Analysis (DFA): Tutorial
A hands-on guide to computing DFA on neuronal oscillations in MATLAB using the Neurophysiological Biomarker Toolbox (NBT), including how to establish a safe fitting range and why signal-to-noise ratio can bias the exponent. Companion material to Hardstone et al. (2012).
Why this background matters#
A recurring problem in my research was how to understand a system when the most important properties were not directly observable. In the brain, this appeared as a question about temporal correlations, branching dynamics, oscillatory activity, and whether changes in system state could be detected before they became obvious in more conventional measures.
In my thesis work, this led to questions about the relation between spatial and temporal correlations, the limits of scale-free dynamics, and the mechanisms that might support long-range temporal structure in neuronal networks. It also led to a broader methodological question: which measurements are actually informative about hidden system state, and under what conditions?
Used carefully, this background provides a vocabulary for thinking about latent state, hidden degradation, and the limits of aggregate metrics. Used carelessly, it becomes mere metaphor. The aim here is the narrower and more practical one: to make the scientific background available in a form that is easy to read and to build on.
For a full list of academic publications, see Publications or my Google Scholar profile.