  We introduce new techniques to the analysis of neural spatiotemporal dynamics
via applying $\epsilon$-machine reconstruction to electroencephalography (EEG)
microstate sequences. Microstates are short duration quasi-stable states of the
dynamically changing electrical field topographies recorded via an array of
electrodes from the human scalp, and cluster into four canonical classes. The
sequence of microstates observed under particular conditions can be considered
an information source with unknown underlying structure. $\epsilon$-machines
are discrete dynamical system automata with state-dependent probabilities on
different future observations (in this case the next measured EEG microstate).
They artificially reproduce underlying structure in an optimally predictive
manner as generative models exhibiting dynamics emulating the behaviour of the
source. Here we present experiments using both simulations and empirical data
supporting the value of associating these discrete dynamical systems with
mental states (e.g. mind-wandering, focused attention, etc.) and with clinical
populations. The neurodynamics of mental states and clinical populations can
then be further characterized by properties of these dynamical systems,
including: i) statistical complexity (determined by the number of states of the
corresponding $\epsilon$-automaton); ii) entropy rate; iii) characteristic
sequence patterning (syntax, probabilistic grammars); iv) duration, persistence
and stability of dynamical patterns; and v) algebraic measures such as
Krohn-Rhodes complexity or holonomy length of the decompositions of these. The
potential applications include the characterization of mental states in
neurodynamic terms for mental health diagnostics, well-being interventions,
human-machine interface, and others on both subject-specific and
group/population-level.
