# Peter Beim GrabenBernstein Center for Computational Neuroscience Berlin | BCCN

Peter Beim Graben

Dr. rer. nat.

## About

140

Publications

47,119

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1,762

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Introduction

My research fields are Computational Cognitive Neuroscience, particularly, Neurophysics, Computational Neurolinguistics, and Quantum Cognition (as applied in Mathematical Musicology).

Additional affiliations

December 2017 - December 2019

October 2017 - November 2017

September 2017 - September 2017

Education

December 1995 - July 2000

September 1987 - February 1995

## Publications

Publications (140)

Metastability refers to the fact that the state of a dynamical system spends a large amount of time in a restricted region of its available phase space before a transition takes place, bringing the system into another state from where it might recur into the previous one. beim Graben and Hutt (2013) suggested to use the recurrence plot (RP) techniq...

The concept of intelligent agents is—roughly speaking—based on an architecture and a set of behavioral programs that primarily serve to solve problems autonomously. Increasing the degree of autonomy and improving cognitive performance, which can be assessed using cognitive and behavioral tests, are two important research trends. The degree of auton...

After reviewing the physicalistic or metaphorical accounts to musical and visual forces by Arnheim and Larson, respectively, which were inspired by the basic tenets of gestalt psychology, I present a novel, naturalistic, mathematical framework, based on symmetry principles and gauge theory. In musicology, this approach has already been applied to t...

Computational modeling of neurodynamical systems often deploys neural networks and symbolic dynamics. One particular way for combining these approaches within a framework called vector symbolic architectures leads to neural automata. Specifically, neural automata result from the assignment of symbols and symbol strings to numbers, known as Gödel en...

Algebraic quantum theory, i.e. the theory of operator algebras and their representations is an important branch of modern functional analysis, connecting non-commutative algebra with topology, measure theory and lattice theory. In the past, many applications in statistical mechanics and quantum field theory have been developed. Yet most recently, a...

Motivated through recent applications of quantum theory to the music-theoretical conceptualisation of tonal attraction, the paper recapitulates basic facts about quantum wave functions over the finite configuration space \(\mathbb {Z}_n\), and proposes a particular musical application.After an introduction of position and momentum operators, the Fo...

Cognitive agents that act independently and solve problems in their environment on behalf of a user are referred to as autonomous. In order to increase the degree of autonomy, advanced cognitive architectures also contain higher-level psychological modules with which needs and motives of the agent are also taken into account and with which the beha...

Vector symbolic architectures (VSA) are a viable approach for the hyperdimensional representation of symbolic data, such as documents, syntactic structures, or semantic frames. We present a rigorous mathematical framework for the representation of phrase structure trees and parse trees of context-free grammars (CFG) in Fock space, i.e. infinite-dim...

Vector-symbolic architectures (VSA) provide viable techniques for the representation of complex symbolic data structures in high-dimensional embedding spaces (Gayler 2006, Kanerva 2009). In a VSA, symbols and variables are represented as filler and role vectors of some underlying linear spaces, respectively. When a symbol is assigned to a variable,...

Kurzfassung: Zunächst möchten wir in das Thema einführen, indem wir kurz auf gegenwärtige Probleme und zukünftige Möglichkeiten von Sprachassistenten ein-gehen. Es folgen grundlegende Überlegungen zur Semantik und zwei fundamentale Erkenntnisse aus der Biosemiotik und dem Konstruktivismus. Danach fokussieren wir uns auf den Spracherwerbsprozess. Hi...

In the last three decades, recurrence plot (RP) and quantification (RQA) techniques have become important research tools in the analysis of short, noisy, and non-stationary data. Theoretical work on RPs has reached considerable maturity, and the method's popularity in recent years continues to increase due to a large number of practical RP/RQA appl...

How can discrete pitches and chords emerge from the continuum of sound? Using a quantum cognition model of tonal music, we prove that the associated Schrödinger equation in Fourier space is invariant under continuous pitch transpositions. However, this symmetry is broken in the case of transpositions of chords, entailing a discrete cyclic group as...

Speech-controlled user interfaces facilitate the operation of devices and household functions to laymen. State-of-the-art language technology scans the acoustically analyzed speech signal for relevant keywords that are subsequently inserted into semantic slots to interpret the user's intent. In order to develop proper cognitive information and comm...

Metaphors involving motion and forces are a source of inspiration for understanding tonal music and tonal harmonies since ancient times. Starting with the rise of quantum cognition, the modern interactional conception of forces as developed in gauge theory has recently entered the field of theoretical musicology. We develop a gauge model of tonal a...

Speech-controlled user interfaces facilitate the operation of devices and household functions to laymen. State-of-the-art language technology scans the acoustically analyzed speech signal for relevant keywords that are subsequently inserted into semantic slots to interpret the user's intent. In order to develop proper cognitive information and comm...

Quantum cognition emerged as an important discipline of mathematical
psychology during the last two decades. Using abstract analogies
between mental phenomena and the formal framework of physical quantum
theory, quantum cognition demonstrated its ability to resolve several
puzzles from cognitive psychology. Until now, quantum cognition essentially...

Sprachgesteuerte Benutzerschnittstellen stehen oftmals vor der Aufgabe, physikalische Größenangaben und andere Zahlworte verstehen und äußern zu müssen. Wir beschränken uns hier auf die sprachliche Produktion und das Verstehen von Zahlworten. Um nicht sämtliche Zahlwörter in einer Datenbank (dem mentalen Lexikon) vorhalten zu müssen, sollen morphol...

Bereits in der Frühphase der Kybernetik stellte C. E. Shannon ein Labyrinthexperiment zur Problemlösung vor, das sich an der mythologischen Figur des Theseus orientierte. Seine Lösung kommt dabei ohne ein Bedeutungskonzept aus. Eine Problemanalyse aus psychologischer Sicht macht allerdings deutlich, dass bei diesem Experiment wesentliche kognitive...

Quantum cognition emerged as an important discipline of mathematical psychology during the last two decades. Using abstract analogies between mental phenomena and the formal framework of physical quantum theory, quantum cognition demonstrated its ability to resolve several puzzles from cognitive psychology. Until now, quantum cognition essentially...

Quantum theory emerged as the result of a successful resolution of
stringent empirical and profound conceptual conflicts within the
development of atomic physics at the beginning of the 20th century.
At a first glance, it seems to be bizarre to apply quantum physical
ideas to the philosophy of mind. However, a closer look shows that
there are indee...

We present a Matlab toolbox, called "FockBox", handling Fock spaces and objects associated with Fock spaces: scalars, ket and bra vectors, and linear operators. We give brief application examples from computational linguistics, semantics processing, and quantum logic, demonstrating the use of the toolbox.

Wir betrachten die syntaktische Sprachverarbeitung am Beispiel des Mouse–Maze–Problems, indem wir der Maus mitteilen, wo sie ein im Labyrinth verstecktes Käsestück auffinden kann. Wir definieren eine neuartige Art von Normalform für kontextfreie Grammatiken, die es erlaubt, Zustandsbeschreibungen eines aus psycholinguistischer Hinsicht besonders ge...

Recurrence structures in univariate time series are challenging to detect. We propose a combination of symbolic and recurrence analysis in order to identify recurrence domains in the signal. This method allows to obtain a symbolic representation of the data. Recurrence analysis produces valid results for multidimensional data, however, in the case...

See "readme.txt" for instruction.
Example files are "lorenzepl.m" for RSA of Lorenz attractor and "ensemblelorenzepl.m" for ensemble of Lorenz time series.

Metastable attractors and heteroclinic orbits are present in the dynamics of various complex systems. Although their occurrence is well-known, their identification and modeling is a challenging task. The present work reviews briefly the literature and proposes a novel combination of their identification in experimental data and their modeling by dy...

How well does a given pitch fit into a tonal scale or key, being either a major or minor key? This question addresses the well-known phenomenon of tonal attraction in music psychology. Metaphorically, tonal attraction is often described in terms of attracting and repelling forces that are exerted upon a probe tone of a scale. In modern physics, for...

How well does a given pitch fit into a tonal scale or key, being either a major or minor key? This question addresses the well-known phenomenon of tonal attraction in music psychology. Metaphorically, tonal attraction is often described in terms of attracting and repelling forces that are exerted upon a probe tone of a scale. In modern physics, for...

Computation is classically studied in terms of automata, formal languages and algorithms; yet, the relation between neural dynamics and symbolic representations and operations is still unclear in traditional eliminative connectionism. Therefore, we suggest a unique perspective on this central issue, to which we would like to refer as to transparent...

Hans Primas laid the groundwork for contextual emergence and also had a long-standing interest in issues of stochasticity and determinism and their consequences. In this contribution we describe contextual emergence and then turn to the question of whether determinism and stochasticity could be regarded as contextually emergent properties. In a fir...

We consider several puzzles of bounded rationality. These include the Allais- and Ellsberg paradox, the disjunction effect, and related puzzles. We argue that the present account of quantum cognition—taking quantum probabilities rather than classical probabilities—can give a more systematic description of these puzzles than the alternate treatments...

We consider several puzzles of bounded rationality. These include the Allais‐ and Ellsberg paradox, the disjunction effect, and related puzzles. We argue that the present account of quantum cognition – taking quantum probabilities rather than classical probabilities – can give a more systematic description of these puzzles than the alternate treatm...

Contextual emergence is an important methodological closed loop approach in the sciences. It involves the introduction of weak contextual topologies and their implementation as stability conditions. Guided by these principles, I discuss three applications of contextual emergence in the neurosciences. First, I show that relevant neural observables m...

In his study "What are the best hierarchical organizations for the success of a common endeavour" [Mathematical Anthropology and Cultural Theory 9, 1 (2016)] Gil uses coupled oscillator networks as a model for socially interacting individuals. In this commentary, I argue that such networks could also be related with lattice gauge theory. The most s...

Recurrence structures in univariate time series are challenging to detect. We propose a combination of symbolic and recurrence analysis in order to identify recurrence domains in the signal. This method allows to obtain a symbolic representation of the data. Recurrence analysis produces valid results for multidimensional data, however, in the case...

The present work proposes a solution of a pertinent problem for recurrence plots and recurrence quantification analysis of time series: the optimal selection of distance thresholds for estimating the recurrence structure of complex dynamic systems. We approximate this recurrence structure through Markov chains obtained from recurrence grammars. The...

The scientific description of any system depends on the target properties of that description. A detailed, fine-grained account of all individual constituents of a system differs from that of properties at larger scales of granularity, up to the system as a whole. All these level-specific descriptions can be compatible or incompatible with one anot...

For decades, research in neuroscience has supported the hypothesis that brain dynamics exhibits recurrent metastable states connected by transients, which together encode fundamental neural information processing. To understand the system's dynamics it is important to detect such recurrence domains, but it is challenging to extract them from experi...

We improve the results by Siegelmann & Sontag (1995) by providing a novel and
parsimonious constructive mapping between Turing Machines and Recurrent
Artificial Neural Networks, based on recent developments of Nonlinear Dynamical
Automata. The architecture of the resulting R-ANNs is simple and elegant,
stemming from its transparent relation with th...

Conventional neural field models describe well some experimental data, such as Local Field Potentials or electroencephalographic data. The work reviews recent extensions of neural field models and describes the activation and attenuation of spectral power in certain frequency bands subjected to the statistical properties of an external input and su...

The concept of complementarity in combination with a non-Boolean calculus of
propositions refers to a pivotal feature of quantum systems which has long been
regarded as a key to their distinction from classical systems. But a
non-Boolean logic of complementary features may also apply to classical
systems, if their states and observables are defined...

Nowadays, surgical operations are impossible to imagine without general anaesthesia, which involves loss of consciousness, immobility, amnesia and analgesia. Understanding mechanisms underlying each of these effects guarantees well-controlled medical treatment.
Our work focuses on analgesia effect of general anaesthesia, more specifically, on patie...

Transients, metastable states (MS) and their temporal recurrences encode fundamental information of biophysiological system dynamics. To understand the system’s temporal dynamics, it is important to detect such events. In neural experimental data, it is challenging to extract these features due to the large trial-to-trial variability. A proposed de...

We present numerical simulations of metastable states in heterogeneous neural fields that are connected along heteroclinic orbits. Such trajectories are possible representations of transient neural activity as observed, for example, in the electroencephalogram. Based on previous theoretical findings on learning algorithms for neural fields, we dire...

Quasistationarity is ubiquitous in complex dynamical systems. In brain
dynamics there is ample evidence that event-related potentials reflect such
quasistationary 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 quasistationary states as...

Biophysical modeling of brain activity has a long and illustrious history (Ermentrout, 1998; Deco et al., 2008; Coombes, 2010) and has recently profited from technological advances that furnish neuroimaging data at an unprecedented spatiotemporal resolution (Guillory and Bujarski, 2014; Sporns, 2014). Neuronal modeling is a very active area of rese...

The present work aims to reproduce certain changes observed experimentally in the EEG power spectrum over the frontal head region during general anesthesia induced by propofol. These observations include increased delta (0-4 Hz) and alpha (8-12 Hz) activities [1]. We extend a previous cortical model [2] and study a neuronal popula-tion model of a s...

Please look at http://www.springer.com/mathematics/analysis/book/978-3-642-54592-4

We present a microscopic approach for the coupling of cortical activity, as resulting from proper dipole currents of pyramidal neurons, to the electromagnetic field in extracellular fluid in presence of diffusion
and Ohmic conduction. Starting from a full-fledged three-compartment model of a single pyramidal neuron, including shunting and dendritic...

Turing machines and Gödel numbers are important pillars of the theory of computation. Thus, any computational architecture needs to show how it could relate to Turing machines and how stable implementations of Turing computation are possible. In this chapter, we implement universal Turing computation in a neural field environment. To this end, we e...

The tools of dynamical systems theory are having an increasing impact on our understanding of patterns of neural activity. In this tutorial chapter we describe how to build tractable tissue level models that maintain a strong link with biophysical reality. These models typically take the form of nonlinear integro-differential equations. Their non-l...

Background - We present analytical and numerical studies on the linear stability of spatially non-constant stationary states in heterogeneous neural fields for specific synaptic interaction kernels.
Methods - The work shows the linear stabiliy analysis of stationary states and the implementation of a nonlinear heteroclinic orbit.
Results - We find...

By means of an intriguing physical example, magnetic surface swimmers, that can be described in terms of Dennett's intentional stance, I reconstruct a hierarchy of necessary and sufficient conditions for the applicability of the intentional strategy. It turns out that the different levels of the intentional hierarchy are contextually emergent from...

In their target article, Wang & Busemeyer (2013) [A quantum question order model supported by empirical tests of an a priori and precise prediction. Topics in Cognitive Science] discuss question order effects in terms of incompatible projectors on a Hilbert space. In a similar vein, Blutner recently presented an orthoalgebraic query language essent...

Turing machines and G\"odel numbers are important pillars of the theory of
computation. Thus, any computational architecture needs to show how it could
relate to Turing machines and how stable implementations of Turing computation
are possible. In this chapter, we implement universal Turing computation in a
neural field environment. To this end, we...

We present a microscopic approach for the coupling of cortical activity, as
resulting from proper dipole currents of pyramidal neurons, to the
electromagnetic field in extracellular fluid in presence of diffusion and Ohmic
conduction. Starting from a full-fledged three-compartment model of a single
pyramidal neuron, including shunting and dendritic...

We propose a way in which Pothos and Busemeyer could strengthen their position. Taking a dynamic stance, we consider cognitive tests as functions that transfer a given input state into the state after testing. Under very general conditions, it can be shown that testable properties in cognition form an orthomodular lattice. Gleason’s theorem then yi...

We propose an algorithm for the detection of recurrence domains of complex dynamical systems from time series. Our approach exploits the characteristic checkerboard texture of recurrence domains exhibited in recurrence plots (RP). In phase space, RPs yield intersecting balls around sampling points that could be merged into cells of a phase space pa...

Quantum entanglement relies on the fact that pure quantum states are
dispersive and often inseparable. Since pure classical states are
dispersion-free they are always separable and cannot be entangled. However,
entanglement is possible for epistemic, dispersive classical states. We show
how such epistemic entanglement arises for epistemic states of...

We present a biophysical approach for the coupling of neural network activity
as resulting from proper dipole currents of cortical pyramidal neurons to the
electric field in extracellular fluid. Starting from a reduced threecompartment
model of a single pyramidal neuron, we derive an observation model for
dendritic dipole currents in extracellular...

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be...

We present a phenomenological modeling account to event-related brain
potentials (ERP) in syntactic language processing. For a paradigmatic ERP
experiment on the processing of phrase structure violations in German [Hahne
and Friederici (1999). Electrophysiological evidence for two steps in syntactic
analysis: Early automatic and late controlled pro...

Cognitive computation such as e.g. language processing, is conventionally
regarded as Turing computation, and Turing machines can be uniquely implemented
as nonlinear dynamical systems using generalized shifts and subsequent G\"odel
encoding of the symbolic repertoire. The resulting nonlinear dynamical automata
(NDA) are piecewise affine-linear map...

In this article we give a short introduction to the online method of event-related (brain) potentials (ERPs) and their importance for our understanding of language structure and grammar. This methodology places high demands on (technical) requirements for laboratory equipment as well as on the skills of the investigator. However, the high costs are...

Computational neurolinguistics integrates methods from computational (psycho-)linguistics and computational neuroscience in order to model neural correlates of linguistic behavior. We illustrate these techniques using an example of the language processing of German negative polarity items (NPI) in the event-related brain potential (ERP) paradigm. T...

Entanglement is a well-known and central concept in quantum theory, where it expresses a fundamental nonlocality (holism) of ontic quantum states, regarded as independent of epistemic means of gathering knowledge about them. An alternative, epistemic kind of entanglement is proposed for epistemic states (distributions) of dynamical systems represen...

We present a microscopic approach for the coupling of cortical activity, as
resulting from proper dipole currents of pyramidal neurons, to the
electromagnetic field in extracellular fluid in presence of diffusion and Ohmic
conduction. As a result, neural activity becomes represented by a continuous
neural field equation, while an observation model...

We discuss a specific way in which the notion of complementarity can be based on the dynamics of the system considered. This approach rests on an epis-temic representation of system states, reflecting our knowledge about a system in terms of coarse grainings (partitions) of its phase space. Within such an epistemic quantization of classical systems...