This dissertation was partially supported by the European Union grant GRIDMAP, Future in Emerging Technologies (FET) project 600725, funded under Framework Programme 7 ”Information and communication technologies” (FP7-ICT). Several valuable discussions with participants and examiners of the project lead to the development of the novel concepts. Most notably were meetings in person and written communications with Alessandro Treves to help improve the understanding of existing models for grid cells, especially his rate adaptation model [196]. Furthermore, discussions with were discussions with Richard Morris and Edvard Moser lead to the realization that the grid cell system is supportive but not sufficient for behavior expressed by rodents during spatial navigation. They also helped to clarify the interactions between several areas of the entorhinal-hippocampal loop on a synaptic level. Additional important insight into transition systems and how they can be used in terms of neural modelling were gained during discussions with Philippe Gaussier, who is one of the authors of a transition model of the entorhinal-hippocampal loop which is closely related to the model presented in this thesis [73, 74, 146].
The overviews of neural networks, modelling, and the representation of space in the rodent brain, presented in the final two chapters of Part I, are reviews of research conducted by others. Particularly influential work is clearly stated in these chapters, for instance when discussing the modelling approach adopted in the thesis, which was inspired by David Marr [230].
The thesis contributes an entirely novel perspective on grid cells in Part II in which it is proposed that grid cells form an optimal encoding of a multi-transition system. This perspective and the associated formalisms, models, and simulations presented in that part of the thesis were derived and developed by the author of this thesis. Note however that transition systems as such are a well-known formal concept from computer science to examine automata [345]. In addition, this thesis combines the logic of transition systems with notations used by Tony Hoare in his formulation of Communicating Sequential Processes (CSP) [147]. Furthermore, the temporal interpretation of events in a neural system was inspired by the analysis of time in distributed systems, introduced primarily by Lesslie Lamport [203]. The proposed model states grid cells in multiple scales form a scale-space representation of transitions. Scale-space theory itself is well-known, especially in the computer vision community [213]. However, it has not been applied to the concept of transitions and neural spatial navigation previously in the form it was used in this thesis. Influential other or related work is clearly marked at the appropriate places.
At the time of writing, the results presented in Part II have not been reported in a peer-reviewed publication yet. However, valuable feedback was collected during and after a presentation of the matter at Ludwig-Maximilians-Universit¨at M¨unchen on 14th of Februrary 2017, hosted by Andreas Herz. Furthermore, a preprint that outlines the results presented in Part II is available as
N. Waniek. Multi-Transition Systems: A theory for spatial navigation.
1.4 Contributions to and of the thesis 11
The manuscript uses several parts of the thesis verbatim due to the technicality of the content. For instance, theorems and proofs are taken as-is. In addition, several figures are reproduced.
The algorithms and data structures presented in Part III, Chapter 8, were developed in collaboration with Edvarts Berzs. They were conceived and evaluated during his Master’s thesis [22]. Several figures of the chapter were reprinted from his thesis with permission. Furthermore, the pseudo-code for the algorithms given in Appendix D and the complexity analysis which was derived collaboratively and reprinted in Appendix E, are taken as-is, also with permission. The results were submitted for peer-review as
N. Waniek, E. Berzs, and J. Conradt. Data structures for locally distributed routing.
Figures that are displayed in this thesis and reprinted or adapted from others, for instance from the Master’s thesis [22] or the submitted manuscript [372], are clearly marked as such. Any other figure is the work of the author.
1.4.1 List of Publications
The following list contains publications that were accepted at the time of writing and submitted or prepared during the phase of the dissertation. In addition, submitted but pending publications and manuscripts still in preparation are listed.
Accepted peer-reviewed journal papers
1. M. Mulas, N. Waniek, and J. Conradt. Hebbian plasticity realigns grid cell activity with external sensory cues in continuous attractor models. Front Comput Neurosci, 10:13, Feb 2016.
Accepted peer-reviewed conference papers
1. N. Waniek, J. Biedermann, and J. Conradt. Cooperative SLAM on small mobile robots.In 2015 IEEE International Conference on Robotics and Biomimetics (ROBIO), pages 1810–1815, Dec 2015.
2. N. Waniek, S. Bremer, and J. Conradt. Real-time anomaly detection with a growing neural gas. In Artificial Neural Networks and Machine Learning – ICANN 2014, volume 8681 of Lecture Notes in Computer Science, pages
97–104. Springer International Publishing, 2014.
3. R. Ara´ujo, N. Waniek, and J. Conradt. Development of a dynamically ex-tendable spinnaker chip computing module.In Artificial Neural Networks and Machine Learning – ICANN 2014, volume 8681 of Lecture Notes in Computer Science, pages 821–828. Springer International Publishing, 2014.
Accepted conference and workshop posters
1. N. Waniek, J. von Stetten, and J. Conradt. Event-based graph cuts, 2016.
Poster presented atNeurocomputing Systems Workshop, Frauenw¨orth, 2016.
2. M. Mulas, N. Waniek, and J. Conradt. Exploiting grid cell properties for robotic spatial navigation. Poster presented atBCCN Retreat, Tutzing, 2015.
3. N. Waniek, M. Mulas, and J. Conradt. Self-organization of grid cell networks.
Poster presented at Bernstein Conference on Computational Neuroscience, Heidelberg, 2015.
4. M. Mulas, N. Waniek, and J. Conradt. Neuromorphic architecture for robotic spatial navigation. Poster presented atBernstein Conference on Computational Neuroscience, G¨ottingen, 2014.
5. N. Waniek, M. Mulas, and J. Conradt. Grid cell realignment based on idiothetic head direction cues. Poster presented atBernstein Conference on Computational Neuroscience, G¨ottingen, 2014.
6. N. Waniek, C. Denk, and J. Conradt. GRIDMAP – from brains to technical implementations. Poster presented at Bernstein Conference on Computational Neuroscience, T¨ubingen, 2013.
7. N. Waniek and J. Conradt. From brains to technical implementations, 2013.
Poster presented atBCCN Sparks Workshop, Tutzing, 2013.
Submitted publications and manuscripts in preparation
1. N. Waniek, E. Berzs, and J. Conradt. Data structures for locally distributed routing. submitted.
2. N. Waniek, J. von Stetten, and J. Conradt. Graph cuts for asynchronous event-based vision sensors. submitted.
3. N. Waniek. Multi-Transition Systems: A theory for spatial navigation. in preparation.