Research Background on Simon-Shlomo Poil

Introduction to Self-Organised Criticality

Mon, 20 Aug 2007 00:00:00 +0000

This essay is adapted from my MSc thesis (University of Copenhagen & VU University Amsterdam, 2007) and was first published on this site in two parts (2009 and 2012). The first sections give a short introduction; the later sections keep the more formal treatment from the thesis. The foundational concepts have remained stable, though the application of SOC to specific systems — particularly the brain — has matured considerably since then, with sharper debates about when criticality claims are warranted and improved tools for testing them. For the neuroscience application, see The Brain as a Critical System; for the propagation mechanism behind avalanches, see Branching Processes.

Branching Processes: How Cascades Propagate

Mon, 20 Aug 2007 00:00:00 +0000

This essay is adapted from my MSc thesis (University of Copenhagen & VU University Amsterdam, 2007). The mathematical framework described here — originally developed to understand activity propagation in neuronal networks — applies to any system where events can trigger further events: epidemic spread, error propagation, incident escalation, information cascades. The formalism has not changed; what has expanded is our understanding of where it applies. For the wider framework, see Introduction to Self-Organised Criticality; for the evidence in the brain, see The Brain as a Critical System.

The Brain as a Critical System

Sun, 14 Apr 2013 00:00:00 +0000

This essay was written in 2013 based on my PhD research at VU University Amsterdam. Since then, the brain criticality literature has developed further, including important debates about sub-critical regimes, improved statistical tests for power-law claims, and more careful discussion of when criticality language is warranted. The core concepts and evidence described here remain foundational to the background of my current work. The underlying concepts are introduced in Introduction to Self-Organised Criticality and Branching Processes, and the method behind the long-range temporal correlation results is in the DFA tutorial.

Detrended Fluctuation Analysis (DFA): Tutorial

Sat, 10 Nov 2012 00:00:00 +0000

This tutorial was originally published on nbtwiki.net as companion material to Hardstone et al. (2012). It has been migrated here with minor formatting updates. The MATLAB code uses functions from the Neurophysiological Biomarker Toolbox (NBT), available on GitHub. For why long-range temporal correlations matter, see The Brain as a Critical System.