@misc{HuttBeimGraben, author = {Hutt, Axel and Beim Graben, Peter}, title = {Sequences by metastable attractors: interweaving dynamical systems and experimental data}, series = {Frontiers in applied mathematics and statistics}, volume = {3}, journal = {Frontiers in applied mathematics and statistics}, issn = {2297-4687}, doi = {10.3389/fams.2017.00011}, pages = {14}, abstract = {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 dynamical systems. This combination applies recurrence structure analysis permitting the derivation of an optimal symbolic representation of metastable states and their dynamical transitions. To derive heteroclinic sequences of metastable attractors in various experimental conditions, the work introduces a Hausdorff clustering algorithm for symbolic dynamics. The application to brain signals (event-related potentials) utilizing neural field models illustrates the methodology.}, language = {en} } @misc{CarmantiniBeimGrabenDesrochesetal., author = {Carmantini, Giovanni S. and Beim Graben, Peter and Desroches, Mathieu and Rodrigues, Serafim}, title = {A modular architecture for transparent computation in recurrent neural networks}, series = {Neural Networks}, volume = {85}, journal = {Neural Networks}, issn = {1879-2782}, doi = {10.1016/j.neunet.2016.09.001}, pages = {85 -- 105}, abstract = {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 connectionism, by proposing accounts of how symbolic computation can be implemented in neural substrates. In this study we first introduce a new model of dynamics on a symbolic space, the versatile shift, showing that it supports the real-time simulation of a range of automata. We then show that the G{\"o}delization of versatile shifts defines nonlinear dynamical automata, dynamical systems evolving on a vectorial space. Finally, we present a mapping between nonlinear dynamical automata and recurrent artificial neural networks. The mapping defines an architecture characterized by its granular modularity, where data, symbolic operations and their control are not only distinguishable in activation space, but also spatially localizable in the network itself, while maintaining a distributed encoding of symbolic representations. The resulting networks simulate automata in real-time and are programmed directly, in absence of network training. To discuss the unique characteristics of the architecture and their consequences, we present two examples: i) the design of a Central Pattern Generator from a finite-state locomotive controller, and ii) the creation of a network simulating a system of interactive automata that supports the parsing of garden-path sentences as investigated in psycholinguistics experiments.}, language = {en} } @inproceedings{BeimGrabenBlutner, author = {Beim Graben, Peter and Blutner, Reinhard}, title = {Toward a gauge theory of musical forces}, series = {Quantum Interaction, 10th International Conference, QI 2016, San Francisco, CA, USA, July 20-22, 2016}, booktitle = {Quantum Interaction, 10th International Conference, QI 2016, San Francisco, CA, USA, July 20-22, 2016}, editor = {Barros, Jose Acacio de and Coecke, Bob and Pothos, Emmanuel}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-52289-0}, doi = {10.1007/978-3-319-52289-0_8}, pages = {99 -- 111}, abstract = {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, forces are related to gauge fields expressing fundamental symmetries of a theory. In this study we address the intriguing relationship between musical symmetries and gauge forces in the framework of quantum cognition.}, language = {en} } @inproceedings{FedotenkovaBeimGrabenSleighetal., author = {Fedotenkova, Mariia and Beim Graben, Peter and Sleigh, Jamie and Hutt, Axel}, title = {Time-frequency representations as phase space reconstruction in symbolic recurrence structure analysis}, series = {Advances in time series analysis and forecasting, selected contributions from ITISE 2016}, booktitle = {Advances in time series analysis and forecasting, selected contributions from ITISE 2016}, editor = {Rojas, Ignacio and Pomares, Hector and Valenzuela, Olga}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-55789-2}, doi = {10.1007/978-3-319-55789-2_7}, pages = {89 -- 102}, abstract = {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 of univariate time series one should perform phase space reconstruction first. In this chapter, we propose a new method of phase space reconstruction based on the signal's time-frequency representation and compare it to the delay embedding method. We argue that the proposed method outperforms the delay embedding reconstruction in the case of oscillatory signals. We also propose to use recurrence complexity as a quantitative feature of a signal. We evaluate our method on synthetic data and show its application to experimental EEG signals.}, language = {en} } @inproceedings{BeimGrabenHuberRoemeretal., author = {Beim Graben, Peter and Huber, Markus and R{\"o}mer, Ronald and Schmitt, Ingo and Wolff, Matthias}, title = {Der Fockraum als Labyrinth: Wissensrepr{\"a}sentation und Probleml{\"o}sungen am Beispiel des Mouse-Maze-Problems}, series = {Elektronische Sprachsignalverarbeitung, Tagungsband der 29. Konferenz, Ulm, 7.-9. M{\"a}rz 2018}, booktitle = {Elektronische Sprachsignalverarbeitung, Tagungsband der 29. Konferenz, Ulm, 7.-9. M{\"a}rz 2018}, editor = {Berton, Andr{\´e} and Haiber, Udo and Minker, Wolfgang}, publisher = {TUDpress}, address = {Dresden}, isbn = {978-3-95908-128-3}, pages = {167 -- 174}, language = {de} } @inproceedings{WolffWirschingHuberetal., author = {Wolff, Matthias and Wirsching, G{\"u}nther and Huber, Markus and Beim Graben, Peter and R{\"o}mer, Ronald and Schmitt, Ingo}, title = {A Fock Space Toolbox and Some Applications in Computational Cognition}, series = {Speech and computer : 20th International Conference, SPECOM 2018, Leipzig, Germany, September 18-22, 2018, proceedings}, booktitle = {Speech and computer : 20th International Conference, SPECOM 2018, Leipzig, Germany, September 18-22, 2018, proceedings}, editor = {Karpov, Alexey and Jokisch, Oliver and Potapova, Rodmonga}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-99578-6}, doi = {10.1007/978-3-319-99579-3}, abstract = {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.}, language = {en} } @inproceedings{WolffHuberWirschingetal., author = {Wolff, Matthias and Huber, Markus and Wirsching, G{\"u}nther and R{\"o}mer, Ronald and Beim Graben, Peter and Schmitt, Ingo}, title = {Towards a Quantum Mechanical Model of the Inner Stage of Cognitive Agents}, series = {9th IEEE International Conference on Cognitive Infocommunications (CogInfoCom 2018), proceedings, Aug. 22-24, 2018, Budapest, Hungary}, booktitle = {9th IEEE International Conference on Cognitive Infocommunications (CogInfoCom 2018), proceedings, Aug. 22-24, 2018, Budapest, Hungary}, publisher = {IEEE}, address = {Piscataway, NJ}, isbn = {978-1-5386-7094-1}, doi = {10.1109/CogInfoCom.2018.8639892}, pages = {147 -- 152}, abstract = {We present a model, inspired by quantum field theory, of the so-called inner stage of technical cognitive agents. The inner stage represents all knowledge of the agent. It allows for planning of actions and for higher cognitive functions like coping and fantasy. By the example of a cognitive mouse agent living in a maze wold, we discuss learning, action planning, and attention in a fully deterministic setting and assuming a totally observable world. We explain the relevance of our approach to cognitive infocommunications.}, language = {en} } @misc{BeimGrabenBlutner, author = {Beim Graben, Peter and Blutner, Reinhard}, title = {Quantum approaches to music cognition}, series = {Journal of Mathematical Psychology}, volume = {91}, journal = {Journal of Mathematical Psychology}, issn = {0022-2496}, doi = {10.1016/j.jmp.2019.03.002}, pages = {38 -- 50}, abstract = {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 exploited ideas from projective (Hilbert space) geometry, such as quantum probability or quantum similarity. However, many powerful tools provided by physical quantum theory, e.g., symmetry groups have not been utilized in the field of quantum cognition research sofar. Inspired by seminal work by Guerino Mazzola on the symmetries of tonal music, our study aims at elucidating and reconciling static and dynamic tonal attraction phenomena in music psychology within the quantum cognition framework. Based on the fundamental principles of octave equivalence, fifth similarity and transposition symmetry of tonal music that are reflected by the structure of the circle of fifths, we develop different wave function descriptions over this underlying tonal space. We present quantum models for static and dynamic tonal attraction and compare them with traditional computational models in musicology. Our approach replicates and also improves predictions based on symbolic models of music perception.}, language = {en} } @techreport{HuberRoemerMeyeretal., author = {Huber, Markus and R{\"o}mer, Ronald and Meyer, Werner and beim Graben, Peter and Wolff, Matthias}, title = {Struktur und Bedeutung-Theseus reloaded}, pages = {10}, abstract = {Bereits in der Fr{\"u}hphase der Kybernetik stellte C. E. Shannon ein Labyrinthexperiment zur Probleml{\"o}sung vor, das sich an der mythologischen Figur des Theseus orientierte. Seine L{\"o}sung kommt dabei ohne ein Bedeutungskonzept aus. Eine Problemanalyse aus psychologischer Sicht macht allerdings deutlich, dass bei diesem Experiment wesentliche kognitive Aspekte nicht ber{\"u}cksichtigt wurden. Um diese Aspekte herauszustellen, befassen wir uns kurz mit den mythologischen und historischen Hintergr{\"u}nden des Labyrinthproblems und erl{\"a}utern anschließend, warum wir {\"u}ber Shannons Modellvorstellungen hinausgehen m{\"u}ssen und Verfahren ben{\"o}tigen, mit denen wir zu semantischen Datentr{\"a}gern gelangen k{\"o}nnen. Zur Veranschaulichung unserer Methode modifizieren wir die Problemstellung, in dem wir "Theseus" die Befriedigung der Bed{\"u}rfnisse Hunger und Durst erm{\"o}glichen. Die Grundlage des Verfahrens ist die Festlegung von Zielmerkmalen und daran anschließend die Identifikation von l{\"o}sungsrelevanten Steuermerkmalen, welche "Theseus" zur Probleml{\"o}sung nutzen kann. Wir verwenden dabei den mathematischen Formalismus der Quantenmechanik, da er uns die Ableitung von semantischen Strukturen auf eine sehr elegante Weise erlaubt. Zun{\"a}chst exploriert "Theuseus" die Umgebung und erh{\"a}lt eine kompakte Repr{\"a}sentation in Form eines Weltvektors in einem Hilbertraum, der durch Tensorverkn{\"u}pfungen verschiedener Merkmalsr{\"a}ume entsteht. Die Kombination dieser Merkmalsr{\"a}ume f{\"u}hrt auf die mathematische Struktur eines Verbandes. Ausgehend vom gefundenen Weltvektor stellen wir ein Verfahren vor, mit dem "Theseus" Unterstrukturen des Verbandes bestimmen kann, welche semantischen Strukturen entsprechen und anschließend f{\"u}r die Probleml{\"o}sung verwendet werden k{\"o}nnen. Wir demonstrieren das Verfahren an verschiedenen Weltkonfigurationen. Den dabei abgeleiteten semantischen Strukturen kann man entnehmen, welche Merkmale ber{\"u}cksichtigt werden m{\"u}ssen, um die Zielmerkmale einer gegebenen Konfiguration manipulieren zu k{\"o}nnen.}, language = {de} } @inproceedings{BeimGrabenMeyerRoemeretal., author = {Beim Graben, Peter and Meyer, Werner and R{\"o}mer, Ronald and Wolff, Matthias}, title = {Bidirektionale Utterance-Meaning-Transducer f{\"u}r Zahlworte durch kompositionale minimalistische Grammatiken}, series = {Elektronische Sprachsignalverarbeitung 2019, Tagungsband der 30. Konferenz Dresden, 3.-8. M{\"a}rz 2019}, booktitle = {Elektronische Sprachsignalverarbeitung 2019, Tagungsband der 30. Konferenz Dresden, 3.-8. M{\"a}rz 2019}, editor = {Birkholz, Peter and Stone, Simon}, publisher = {TUDpress}, address = {Dresden}, isbn = {978-3-95908-157-3}, pages = {76 -- 82}, abstract = {Sprachgesteuerte Benutzerschnittstellen stehen oftmals vor der Aufgabe, physikalische Gr{\"o}ßenangaben und andere Zahlworte verstehen und {\"a}ußern zu m{\"u}ssen. Wir beschr{\"a}nken uns hier auf die sprachliche Produktion und das Verstehen von Zahlworten. Um nicht s{\"a}mtliche Zahlw{\"o}rter in einer Datenbank (dem mentalen Lexikon) vorhalten zu m{\"u}ssen, sollen morphologische Komposita durch eine geeignete Grammatik ableitbar sein. Wir kodieren sprachliche Zeichen als geordnete Tripel von Exponenten, syntaktischen Typen und Semantiken. Der syntaktische Typ wird durch eine minimalistische Grammatik (MG) beschrieben. F{\"u}r die Semantik verwenden wir den Lambda-Kalk{\"u}l der arithmetischen Termalgebra. Auf dem MG-Lexikon operieren syntaktische Erzeugungsfunktionen, die durch linguistische Inferenzregeln vorgegeben sind. Sprachproduktion und Sprachverstehen lassen sich dann durch einen bidirektionalen Utterance-Meaning-Transducer (UMT) beschreiben. Bei der Sprachproduktion gehen wir von einer semantischen Repr{\"a}sentation einer Zahl als arithmetische Termstruktur aus. Durch Datenbankabfrage wird daraus eine Zeichenfolge, welche die passenden Lexikon-Eintr{\"a}ge enth{\"a}lt. Daraus berechnet der UMT die Morphologie der {\"A}ußerung. Beim Sprachverstehen wird zur Eingabe die abgefragte Zeichenfolge auf dem Stack eines Priority-Queue-Parsers abgespeichert. Durch Anwendung der minimalistischen Inferenzregeln erzeugt der UMT dann schrittweise die semantische Termstruktur.}, language = {de} }