Detecting event-related recurrences by symbolic analysis: applications to human language processing

Abstract

Quasi-stationarity is ubiquitous in complex dynamical systems. In brain dynamics, there is ample evidence that event-related potentials (ERPs) reflect such quasi-stationary states. In order to detect them from time series, several segmentation techniques have been proposed. In this study, we elaborate a recent approach for detecting quasi-stationary states as recurrence domains by means of recurrence analysis and subsequent symbolization methods. We address two pertinent problems of contemporary recurrence analysis: optimizing the size of recurrence neighbourhoods and identifying symbols from different realizations for sequence alignment. As possible solutions for these problems, we suggest a maximum entropy criterion and a Hausdorff clustering algorithm. The resulting recurrence domains for single-subject ERPs are obtained as partition cells reflecting quasi-stationary brain states.

Sequences by Metastable Attractors: Interweaving Dynamical Systems and Experimental Data

“…In this representation the distinguished state 0 captures all transients, while m a is the number of detected MS [12].…”

“…Recurrent events (R ij = 1) of the dynamics lead to intersecting ε-balls B ε (x i ) ∩ B ε (x j ) = ∅ which can be merged together into equivalence classes of phase space X. By merging balls together into a set A j = B ε (x i ) ∪ B ε (x j ) when states x i and x j are recurrent and when i > j, we simply replace the larger time index i in the recurrence plot R by the smaller one j, symbolized as a rewriting rule i → j of a recurrence grammar [12,26,27].…”

“…In recent years, several experimental studies of biological systems have revealed that the systems' activities evolve between some equilibria [10][11][12]. Such HOs between MS may occur in neural responses in the insect olfactory bulb [13], in bird songs [14], in human scalp brain activity at rest [15], during cognitive tasks [16,17], in schizophrenia [18] and during emergence from unconsciousness [19].…”

“…Other methods consider MS as recurrence domains and transients between them as non-recurrent regimes. Then the recurrent and nonrecurrent states partition the underlying phase space into disjoint cells, thereby yielding a symbolic dynamics where all nonrecurrent transients are mapped to a single symbol, i.e., they are undistinguishable [12,26,27]. To determine such a symbolic dynamics, an underlying stochastic model on the temporal distribution of MS is mandatory.…”

“…Since a HO exhibits a temporal sequence of MS, in a first step these states are extracted by data analysis techniques identifying their location in phase space, their onset times and their durations as essential features [8,12,22,[25][26][27]. These features are assumed to fully describe the HO and typically are rather invariant in experimental repetitions.…”