Dr. Peter beim Graben
Event-related Brain Potentials (ERP)
are commonly regarded to be tiny impulse responses in the
electroencephalogram (EEG) generated by neural networks that are
time-locked to the perception or processing of stimuli and blended
by the spontaneous EEG that reflects the ongoing, continuous
activity of the brain. In language processing, unexpected sentence
continuations, such as semantic anomalies or syntactic garden
paths, elicit characteristic ERP responses, such as the N400 and
P600 for semantic and syntactic processing problems, respectively
(REF, REF, REF, REF, REF, REF).
Event-related Brain Potentials in Language Processing
The plot shows ERP waves
obtained from the Symbolic Resonance Analysis (SRA) at a posterior
electode site for processing unlicensed negative polarity items.
The SRA reveals an early and a late subcomponent of the reanalysis
P600 that are not observable by means of voltage averages (REF).
Nonlinear Dynamical Automata
Transients in symbolic dynamics represent computational processes.
We have utilized this finding for the construction of
(context-free) grammar recognizers as Nonlinear Dynamical Automata
(REF, REF). The corresponding phase space
representation allows for determining processing costs such as
parsing entropy which has been related to language processing
ERPs. We have described processes of diagnosis and reanalysis by a
bifurcation-like tuning of the system’s control parameter.
Additionally, the autonomous parsing dynamics has been augmented
by an interactive counterpart (REF, REF).
The Figure shows the temporal
evolution of parsing states (from top to bottom) for an
interactive NDA with diagnosis and repair steps (indicated by
"*"). One interaction where a new input is scanned from the
environment into working memory is indicated by "o" (REF).
You may see an NDA animation by
clicking at the image.
Fock Space Models of Parsing
Symbolic structures such as linguistic phrase structure trees can
be represented through tensor products in Fock spaces. We use
finite- and infinite-dimensional Fock space representations to
model syntactic language processing in neural networks (REF, REF) and neural field theories (REF, REF, REF, REF), respectively.
Such models are able to describe language-related brain potentials
by trajectories exploring functionally different regions in phase
space during their transient evolution.
The plot depicts a snapshot
sequence of a Fock space parser represented by spherical
harmonics. The transient dynamics is governed by nonlinear order
parameter equations (REF, REF).
You may see an animation
by clicking at the image.
Pragmatic Information Theory
The concept of "pragmatic
information" has been introduced by stating three desiderata: i)
Pragmatic information assesses the impact of a message upon its
receiver. ii) In the limits of non-interpretable "novelty" and
complete "confirmation", the pragmatic information vanishes. iii)
Novelty and confirmation behave as Fourier-pairs of complementary
operators in quantum mechanics; pragmatic information should hence
exhibit some non-classical properties. We have shown how these
requirements can be naturally fulfilled within the framework of
the dynamic semantics of Bayesian belief models (REF).
The Figure illustrates the
property ii) above, the non-monotonic dependence of pragmatic
information on novelty (randomness) and confirmation. This is also
characteristic for measures of complexity (REF).
Symbolic Dynamics of Neurophysiological Data
ERP data are given as large
ensembles of short nonstationary (transient) and noisy time
series. Symbolic dynamics of ERPs describes intertrial coherence
of polarity deflections by running cylinder entropies and related
measures. We have provided heuristics for symbolic encoding of ERP
data, such as the median encoding (REF), the half-wave encoding (REF; REF; REF) and the stochastic resonance
analysis (SRA) based on the findings of threshold stochastic
resonance (REF). Especially the SRA allows to
discriminate ERPs for conditions where voltage averaging fails (REF, REF, REF, REF). Most recently, we have developed
a recurrence domain segmentation method (REF, REF).
The Figure shows a 3-symbol
encoding of a noisy signal exhibiting stochastic resonance at the
extrema of the signal.
A leaky integrator (LI) unit is the
most simple model neuron described by an ordinary differential
equation (REF). We have shown that at least two
recurrently connected LI units may form nonlinear neural
oscillators possessing limit cycles, which are known, e.g., in
thalamo-cortical pathways (REF). We studied networks of coupled LI
units in order to model global properties of the EEG (REF, REF). Moreover, we are also
investigating the issue of contextual emergence in neural networks
Emergence in Complex Neural Networks
The Figure shows simulated EEG
power spectra obtained from recurrent network of 20, 100, 200,
500, and 1000 LI units whose synaptic connections were randomly
drawn such that 80% excitatory and 20% inhibitory synapses have
been created. The spectra are computed for the oscillatory phase
transition where super-cycles emerge in the network's topology.
Very large networks of LI units can
be described by a continuum approximation (REF). Starting from the LI equation the
sum over the nodes connected with one unit has to be replaced by
an integral transformation of a neural field quantity, where the
continuous parameter now indicates the position of a unit in the
network. Correspondingly, the synaptic weights turn into a kernel
function. In addition, for large networks, the propagation
velocity of neural activation has to be taken into account. We
discuss the solvability and invertibility of neural field
equations for general synaptic kernels (REF, REF, REF, REF)
and their applicability to computational psycholinguistics (REF, REF) and cognitive science in general (REF).
The Figure should just
illustrate the continuum limit starting from a discrete neural
network and approaching a continuous neural tissue.
Epistemic Foundations of Symbolic Dynamics
The usefulness of symbolic
dynamics rests on finding “good partitions” of the phase space,
e.g. by construction of generating partitions which allow to
approximate individual points in phase space by sustained
measurements of coarse-graining devices. This is not possible for
“misplaced” partitions where an intrinsic grain remains which
makes certain states epistemically unaccessible. We have
demonstrated the emergence of quantum-like properties such as
complementary observables and contextual topologies (REF, REF).
The Figure shows the possibility
of complementary projectors in a chaotic dynamical system. As in
algebraic quantum theory, two observables A, B are complementary
if no eigenstate of A is eigenstate of B and vice versa. In
statistical mechanics, an eigenstate of an observable A can be
identified with a phase space domain R where A assumes a constant
value making all individual states in R epistemically
The concept of contextual emergence
(REF, REF) has been
proposed as a non-reductive relation between different levels of
description of physical and other systems where the lower level
description comprises necessary but not sufficient conditions for
the higher level description. These are supplied by contingent
contexts obeying particular stability conditions. We have shown
that Chalmers' definition of "neural correlates of consciousness"
(NCCs) can be complemented in terms of contextual emergence where
the sufficient conditions are provided by contextually given
"phenomenal families" partitioning the neural phase space (REF). Other examples for contextual
emergence are syntactic language processing (REF), the evolutionary formation of
categories (REF) macrostates in neural networks (REF, REF), or the
contextual emergence of intentionality (REF). Moreover, the
usefulness of quantum approaches for cognitive science ("Quantum
Cognition"), could be related to incompatible coarse-grainings
resulting from bounded rationality (REF, REF).
Emergence of Mental States and Cognitive Processes
The Figure illustrates
Descartes' "organ metaphor of the mind" (left) mounted together
with a brain synchronization map (right). Both portraits together
make up the "vase versus faces" ambiguity (REF).
- DFG Heisenberg Fellow for
- EUCogIII funding
for Special Session "Cognitive Architectures in Dynamic Field
Theory" (together with G. Schöner) at Second International Conference
on Neural Field Theory, University of Reading, April
19 – 21, 2012.
- Co-investigator of Fetzer Franklin Trust grant “Towards a
New Paradigmatic Framework: Weak Quantum Theory, Generalized
Entanglement and Generalized Complementarity– Explorations of
, 2014. Read Preface
Special theme issue “Brain Dynamics” of Bulletin of Mathematical Biology
Special theme issue “Language Dynamics” of Cognitive Neurodynamics
2009. Read Editorial
Special theme issue “Brain Waves” of Cognitive Neurodynamics
2(2), 2008. Read Editorial
Lectures in Supercomputational
, 2008. Read Chapt. 1 "Foundations
Special theme issue "Advanced Methods of Electrophysiological
Signal Analysis and Symbol Grounding? Dynamical Systems Approaches
to Language" of Chaos and
2(2/3), 2007. Read Editorial
Special theme issue “Pragmatic Information” of Mind and Matter
Special theme issue on “Cognition and Complex Brain Dynamics” of
the International Journal of
Bifurcation and Chaos
, 14(2), 2004. Read Editorial
- "Dynamic Cognitive Modeling" at Summer School for
Computational Linguistics, August 21 - 28, 2010, Zadar,
- Member of Program Commitee for 2nd International Conference on Cognitive Neurodynamics
(ICCN), Hangshou, China, November, 15 - 19, 2009.
- Minisymposium “Brain Waves and Cognitive Neurodynamics” at Waves 2007, The 8th
International Conference on Mathematical and Numerical
Aspects of Waves at the University of Reading, July,
23 – 27, 2007.
- Scientific Director of the Fifth Summer School of the Helmholtz Institute for
Supercomputational Physics on “Complex Networks in
Brain Dynamics” at the University of Potsdam, September, 05 –