Kjeldsen, H 14.Pdf

Delta rhythms as a substrate for holographic processing in sleep and wakefulness Henrik Daniel Kjeldsen Thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy Newcastle University Faculty of Medical Sciences Institute of Neuroscience Systems Neuroscience: From Networks to Behaviour September 2013 Abstract We initially considered the theoretical properties and benefits of so-called holographic processing in a specific type of computational problem implied by the theories of synaptic rescaling processes in the biological wake-sleep cycle. This raised two fundamental questions that we attempted to answer by an experimental in vitro electrophysiological approach. We developed a comprehensive experimental paradigm based on a pharmacological model of the wake-sleep-associated delta rhythm measured with a Utah micro-electrode array at the interface between primary and associational areas in the rodent neocortex. We first verified that our in vitro delta rhythm model possessed two key features found in both in vivo rodent and human studies of synaptic rescaling processes in sleep: The first property being that prior local synaptic potentiation in wake leads to increased local delta power in subsequent sleep. The second property is the reactivation in sleep of neural firing patterns observed prior to sleep. By reproducing these findings we confirmed that our model is arguably an adequate medium for further study of the putative sleep-related synaptic rescaling process. In addition we found important differences between neural units that reactivated or deactivated during delta; these were differences in cell types based on unit spike shapes, in prior firing rates and in prior spike-train-to-local-field-potential coherence. Taken together these results suggested a mechanistic chain of explanation of the two observed properties, and set the neurobiological framework for further, more computationally driven analysis. Using the above experimental and theoretical substrate we developed a new method of analysis of micro-electrode array data. The method is a generalization to the electromagnetic case of a well-known technique for processing acoustic microphone array data. This allowed calculation of: The instantaneous spatial energy flow and dissipation in the neocortical areas under the array; The spatial energy source density in analogy to well-known current source density analysis. We then refocused our investigation on the two theoretical questions that we hoped to achieve experimental answers for: Whether the state of the neocortex during a delta ii rhythm could be described by ergodic statistics, which we determined by analyzing the spectral properties of energy dissipation as a signature of the state of the dynamical system; A more explorative approach prompting an investigation of the spatiotemporal interactions across and along neocortical layers and areas during a delta rhythm, as implied by energy flow patterns. We found that the in vitro rodent neocortex does not conform to ergodic statistics during a pharmacologically driven delta or gamma rhythm. We also found a delta period locked pattern of energy flow across and along layers and areas, which doubled the processing cycle relative to the fundamental delta rhythm, tentatively suggesting a reciprocal, two-stage information processing hierarchy similar to a stochastic Helmholtz machine with a wake-sleep training algorithm. Further, the complex valued energy flow might suggest an improvement to the Helmholtz machine concept by generalizing the complex valued weights of the stochastic network to higher dimensional multi-vectors of a geometric algebra with a metric particularity suited for holographic processes. Finally, preliminary attempts were made to implement and characterize the above network dynamics in silico. We found that a qubit valued network does not allow fully holographic processes, but tentatively suggest that an ebit valued network may display two key properties of general holographic processing. iii Acknowledgements I would like to thank my supervisors: Miles Whittington, Marcus Kaiser, Jennifer Simonotto and Mark Cunningham. Their patience, open-mindedness and willingness to allow me to pursue my own course, balanced with timely guidance, input and supervision has made this time particularly enjoyable and well-spend. I would also like to thank all the remaining members of the respective labs, without whose help and support on a daily basis, I would simply not have been able to carry the physical workload. I thank my family and friends, especially Lars Bredvig who over the years has put in thousands of hours discussing the fundamental issues forming the starting point for this work. iv Publications Kjeldsen, H. D., Traub, R. D., Whittington, M. A. (2012). “A neocortical delta frequency generator modulates layer2/3 sparse spiking via nested theta rhythms.” Society for Neuroscience. Carracedo, L. M., Kjeldsen, H. D., Cunnington, L.,Jenkins, A.,Schofield, I.,Cunningham, M. O., Davies, C. H., Traub, R. D., Whittington, M. A. (2013). "A Neocortical Delta Rhythm Facilitates Reciprocal Interlaminar Interactions via Nested Theta Rhythms." The Journal of Neuroscience 33(26): 10750-10761. v Table of Contents Abstract ......................................................................................................................... ii Acknowledgements ...................................................................................................... iv Publications ................................................................................................................... v Table of Contents ......................................................................................................... vi List of Figures .............................................................................................................. xi Chapter 1. Introduction defining the problem and scope of investigation ................... 1 1.1 The issue of intractable problems ....................................................................... 1 1.1.1 Interpreting Gödel’s theorems..................................................................... 3 1.1.2 The Gödel letter and the modern Millennium Prize problem of P vs. NP .. 5 1.2 Does the brain somehow solve intractable problems? ....................................... 7 1.2.1 Gödel’s theorems imply that the brain solves intractable problems ........... 8 1.2.2 The Bayesian brain is intractable ................................................................ 9 1.2.3 Associative memory is intractable ............................................................ 10 1.2.4 Vision is intractable................................................................................... 10 1.2.5 Natural language is at least intractable...................................................... 11 1.3 How does the brain solve intractable problems? .............................................. 11 1.3.1 Friston’s ergodic suggestion ..................................................................... 12 1.3.2 Penrose’s interpretation (but not his suggested solution) ......................... 14 1.3.3 The brain is too cold to be a classical computer ....................................... 19 1.3.4 Is the brain really too hot to be a quantum computer? .............................. 20 1.3.5 For now define a holographic computer to be just right ........................... 22 1.4 A reverse-engineering perspective on the brain ............................................... 22 1.4.1 The two concurrent and complementary approaches of this thesis .......... 23 Chapter 2. The Wake-Sleep Cycle neurophysiological background and framework 24 2.1 Is sleep the price of tractability? ....................................................................... 24 vi 2.2 The wake-sleep cycle and the synaptic rescaling hypothesis ........................... 24 2.2.1 Delta rhythms and the wake-sleep cycle ................................................... 26 2.2.2 Replay and rescaling ................................................................................. 28 2.2.3 Delta orchestrated interaction looks like a Helmholtz machine................ 30 2.3 Electrophysiological aims ................................................................................ 34 2.3.1 Establish a simplified model of the wake-sleep cycle .............................. 34 2.3.2 Investigate the influence of prior activation on delta power ..................... 34 2.3.3 Investigate reactivation in delta of stimulated units .................................. 34 2.3.4 Investigate possible ergodic dynamics in the wake-sleep model .............. 35 2.3.5 Expand on Helmholtz machine interaction ............................................... 35 Chapter 3. Holographic Processes computational background and framework ........ 36 3.1 Gabor’s discovery of the holographic process ................................................. 36 3.2 Holographic processes in the brain? ................................................................. 37 3.2.1 Holographic interpretations allow tractable processes .............................. 37 3.3 Potential loop-holes in Gödel’s theorems ........................................................ 38 3.3.1 Gödel’s loop-hole in this own theorems ................................................... 38 3.3.2 Holographic computation as the interaction of past and future ................ 41 3.4 Holographic processes in

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