Causal Mathematical Logic as a guiding framework for the prediction of “Intelligence Signals” in brain simulations

Open access


A recent theory of physical information based on the fundamental principles of causality and thermodynamics has proposed that a large number of observable life and intelligence signals can be described in terms of the Causal Mathematical Logic (CML), which is proposed to encode the natural principles of intelligence across any physical domain and substrate. We attempt to expound the current definition of CML, the “Action functional” as a theory in terms of its ability to possess a superior explanatory power for the current neuroscientific data we use to measure the mammalian brains “intelligence” processes at its most general biophysical level. Brain simulation projects define their success partly in terms of the emergence of “non-explicitly programmed” complex biophysical signals such as self-oscillation and spreading cortical waves. Here we propose to extend the causal theory to predict and guide the understanding of these more complex emergent “intelligence Signals”. To achieve this we review whether causal logic is consistent with, can explain and predict the function of complete perceptual processes associated with intelligence. Primarily those are defined as the range of Event Related Potentials (ERP) which include their primary subcomponents; Event Related Desynchronization (ERD) and Event Related Synchronization (ERS). This approach is aiming for a universal and predictive logic for neurosimulation and AGi. The result of this investigation has produced a general “Information Engine” model from translation of the ERD and ERS. The CML algorithm run in terms of action cost predicts ERP signal contents and is consistent with the fundamental laws of thermodynamics. A working substrate independent natural information logic would be a major asset. An information theory consistent with fundamental physics can be an AGi. It can also operate within genetic information space and provides a roadmap to understand the live biophysical operation of the phenotype

Aftanas, L.; Varlamov, A.; and et al. 2001. Event-related synchronization and desynchronization during affective processing: emergence of valence-related time-dependent hemispheric asymmetries in theta and upper alpha band. Int J Neurosci. 110(3-4):197-219.

Anokhin, A.P.; Lutzenberger, W.; and Birbaumer, N., 1999. Spatiotemporal organization of brain dynamics and intelligence: an EEG study in adolescents. Int J Psychophysiol. 33, 259-73.

Arturo, M.; and Banachlocha, M. 2005. Magnetic storage of information in the human cerebral cortex: A hypothesis for memory, Int J Neuroscience. 115(3). 329-337

Askey, R. 1975. Orthogonal polynomials and special functions, Regional Conference Series in Applied Mathematics. 21,SIAM, pp. viii+110

Azizian, A.; Freitas, A. L.; and et al. 2006. Beware misleading cues: Perceptual similarity modulates the N2/P3 complex. Psychophysiology. 43, 253-260.

Baars, B.J.; Franklin, S.; and Zo, T. 2013. Global workspace dynamics: cortical “binding and propagation” enables conscious contents. Front. Psychol. doi: 10.3389/fpsyg.2013.00200

Balduzzi, D.; and Tononi, G. 2008. Integrated Information in Discrete Dynamical Systems: Motivation and Theoretical Framework. PLoS Comput Biol. 4(6) Banaclocha, M.A. 2002. Are neuronal activity-associated magnetic fields the physical base for memory? Med Hypotheses. 59, 555-9.

Banaclocha, M.A. 2004. Architectural organisation of neuronal activity-associated magnetic fields: a hypothesis for memory. MedHypotheses. 63(3):481-4.

Banaclocha, M.A.; 2007. Neuromagnetic dialogue between neuronal minicolumns and astroglial network: a new approach for memory and cerebral computation. Brain Res Bull. 73, 21-7.

Bartos, M.; Vida, I.; and Jonas, P. 2007. Synaptic mechanisms of synchronized gamma oscillations in inhibitory interneuron networks. Nat Rev Neurosci. 8(1):45-56

Basar-Eroglu, C.; Basar, E.; and et al. 1992. P300-response: possible psychophysiological correlates in delta and theta frequency channels. A review. Int J Psychophysiol. 13(2):161-79.

Bear, M.F.; Connors, B.W.; and Paradiso, M.A. 2006. Neuroscience: Exploring the Brain (3rd ed.). Philadelphia, PA: Lippincott Williams and Wilkins.

Buzsáki, G.; and Silva, F.L. 2012. High frequency oscillations in the intact brain. Prog Neurobiol. 98(3):241-9.

Berut, A.; Arakelyan, A.; and et al. 2012. Experimental verification of Landauer’s principle linking information and thermodynamics. Nature. 483:187-189.

Bevan, M.D.; Magill, P.J.; and et al. 2002. Move to the rhythm: oscillations in the subthalamic nucleus-external globus pallidus network. Trends Neurosci. 25(10):525-31.

Bolotin, Y.L.; Gonchar, V.Y.; and Granovsky, M.Y. 1995. The regularity-chaos regularity transition in a periodically driven harmonic oscillator. Physica D.Nonlinear Phenomena. 86, 500-507.

Brazier, M.; 1970. The Electrical Activity of the Nervous System, London: Pitman Brandt, M.E.;1997. Visual and auditory evoked phase resetting of the alpha EEG. Int J Psychophysiol. 26, 285-98.

Brown, L. M. 2005. Feynman's Thesis: The Principle of Least Action in Quantum Mechanics, World Scientific, Singapore. Burnett, G. J.; Coffman, Jr. E. G. 1973. A Combinatorial Problem Related to Interleaved Memory Systems. Journal of the ACM. 20 (1) 39-45

Buschman, T.J.; Siegel, M.; and et al. 2011. Neural substrates of cognitive capacity limitations. Proc Natl Acad Sci U S A. 5; 108(27): 11252-11255.

Buzsaki, G. 2006. Rhythms of the Brain. Oxford University Press.

Buzsáki, G.; and Xiao-Jing Wang, Xj. 2012. Mechanisms of Gamma Oscillations. Annual Review of Neuroscience. 35: 203-225

Buzsáki, G.; and Peyrache, A. 2013. A BOLD statement about the hippocampal-neocortical dialogue. Trends Cogn Sci. 17(2):57-9.

Buzsáki, G.; and Silva, F.L. 2012. High frequency oscillations in the intact brain. Prog Neurobiol. 98(3):241-9.

Campisi, M.; 2008. Increase of Boltzmann entropy in a quantum forced harmonic oscillator. Phys Rev E Stat Nonlin Soft Matter Phys. 78(5 Pt 1):051123

Chance, F.S. 2012. Hippocampal phase precession from dual input components. J Neurosci. 21;32(47):16693-703a Chang, Z. Li.; and MH. Li, X. 2010. Unification of Dark Matter and Dark Energy in a Modified Entropic Force Model. Available electronically

Clancy, B.; Darlington, R.B.; and Finlay, B.L. 2001. Translating developmental time across mammalian species. Neuroscience. 105(1):7-17.

Carhart-Harris, R.L.; Leech, R.; and et al. 2014. The entropic brain: a theory of conscious states informed by neuroimaging research with psychedelic drugs. Available electronically online at Collins, D.L.; Kabani, N.J.; and Evans A.C.1998. Automatic volume estimation of gross cerebral structures. Available electronically at 12/04/2005

Crick, F.; and Koch, C.2003. A framework for consciousness, Nature Neuroscience. 6(2), 119-26.

Cuntz, H.; Forstner, F.; and et al. 2010. One rule to grow them all: a general theory of neuronal branching and its practical application. PLoS Comput Biol. 5:6(8).

Cuntz, H.; Mathy A.; and Häusser M. 2012. A scaling law derived from optimal dendritic wiring. Proc Natl Acad Sci U S A. 109(27): 11014-11018.

Dalrymple, D. 2012. The principle of least action. Available electronically online at Daunizeau, J.; David, O.; and Stephan, K. E. 2011. Dynamic causal modeling: A critical review of the biophysical and statistical foundations. NeuroImage. 58:312-322.

Davis, T.; Love, B.C.; and Preston, A.R.; 2012. Striatal and hippocampal entropy and recognition signals in category learning: simultaneous processes revealed by model-based fMRI. J Exp Psychol Learn Mem Cogn. 38(4):821-39.

DeMarse, T.; Cadotte, A.; and et al. 2004. Computation Within Cultured Neural Networks. Proceedings of the 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society .7, 5340-5343.

Dewar, C.R. 2009. Maximum Entropy Production as an Inference Algorithm that Translates Physical Assumptions into Macroscopic Predictions: Don’t Shoot the Messenger. Entropy. 11(4), 931-944.

Di Caprio, D.; Badiali, J.P.; and Holovko, M. 2008. Simple field theoretical approach of Coulomb systems. Entropic effects. Available electronically from

Dutt, A.K.1999. Hysteresis in entropy production in a model chemical reaction exhibiting subcritical Hopf bifurcation. J. Chem. Phys. 110, 1061

Edmund T.R. 2013. The mechanisms for pattern completion and pattern separation in the hippocampus. Frontiers in Systems Neuroscience. 7:74.

Edwards, E.; Soltani, M.; and et al. 2005. High gamma activity in response to deviant auditory stimuli recorded directly from human cortex. J Neurophysiol 94, 4269-80.

Evans, A.C.; Collins, D.L.; and et al. 1996. Towards a probabilistic atlas of human neuroanatomy'' in Brain Mapping: The Methods.

England, J.L.; 2013. Statistical physics of self-replication. J. Chem. Phys. 139, 121923.

Engel, A. K.; Kreiter, A. K.; and et al. 1991. Synchronization of oscillatory neuronal responses between striate and extrastriate visual cortical areas of the cat. Proc. Natl. Acad. Sci. USA 88: 6048-6052.

Eriksen, N.; and Pakkenberg, B. 2007. Total neocortical cell number in the mysticete brain. Anat Rec. 290(1):83-95.

Farwell, L.A.; and Smith, S.S. 2001.Using brain MERMER testing to detect knowledge despite efforts to conceal. J Forensic Sci. 46 (1): 135-143.

Fiebelkorn, I.C.; Snyder, A.C.; and et al. 2013. Cortical cross-frequency coupling predicts perceptual outcomes. Neuroimage. 1;69:126-37. Fleury, V. 2011. A change in boundary conditions induces a discontinuity of tissue flow in chicken embryos and the formation of the cephalic fold. The European Physical Journal E. 34(7) Freeman, W. J.; and Kozma, R. 2010. Freeman's mass action Scholarpedia, 5(1):8040 Available electronically at's_mass_action Freund, P.G. 2010. Emergent Gauge Fields. Available electronically

Friston, K.J.; Daunizeau, J.; and et al. 2010. Action and behavior: a free-energy formulation. Biol Cybern. 102(3):227-60

Friston, K.J.; Harrison, L.; and Penny, W. 2003. Dynamic causal modelling. NeuroImage. 19(4):1273-302

Fründ, I.; Busch, N.A.; and et al. 2007. From perception to action: phase-locked gamma oscillations correlate with reaction times in a speeded response task. BMC Neurosci. 17;8:27

Folstein, J. R.; and Van Petten, C. 2008. Influence of cognitive control and mismatch on the N2 component of the ERP: A review. Psychophysiology. 45, 152-170.

Fuster, J.M. 2002. Cortex and Mind : Unifying Cognition: Oxford University Press.

Fuster, J.M. 2006. The cognit: a network model of cortical representation. Int J Psychophysiol. 60(2):125-32.

Gajewski, P. D.; Stoerig, P.; and Falkenstein, M. 2008. ERP - Correlates of response selection in a response conflict paradigm. Brain Research. 1189, 127-134.

Garrido, M.A. 2008. Causal Modelling of Evoked Brain Responses. Thesis submitted for the degree of Doctor of Philosophy University College London. Wellcome Trust Centre for Neuroimaging Institute of Neurology.

Geisler, C.; Robbe, D.; and et al. 2007. Hippocampal place cell assemblies are speed-controlled oscillators. Proc Natl Acad Sci U S A. 104(19):8149-54.

Gray, C.G. 2009. Principle of least action. Scholarpedia 4(12):8291.

Gzyl, H. 1995. The Method of Maximum Entropy. Series on Advances in Mathematics for Applied Sciences: Volume 29

Habib, R.; Nyberg, L.; and Tulving, E. 2003. Hemispheric asymmetries of memory: the HERA model revisited. Trends Cogn Sci. 7(6):241-245.

Hanslmayr, S.; Klimesch, W.; and Sauseng, P. 2007. Alpha phase Reset Contributes to the Generation of ERPs, Cereb Cortex. 17(1), 1-8 Han, X.; Chen, M.; and et al. 2013. Forebrain Engraftment by Human Glial Progenitor Cells Enhances Synaptic Plasticity and Learning in Adult Mice. Cell Stem Cell. 12 (3), 342-353, 7

Hartonen, T.; and Annila, A. 2012. Natural networks as thermodynamic systems. Complexity. 18(2)53-62.

Haufe, S.; Tomioka, R.; and et al. 2010. Localization of class-related mu-rhythm desynchronization in motor imagery based brain-computer interface sessions. Conf Proc IEEE Eng Med Biol. Soc 5137-40.

Hawkins, J. 2006. Hierarchical Temporal Memory (HTM) A new computational paradigm based on cortical theory. IBM Hawkins, J.; and Blakeslee, S. 2004. On Intelligence: How a New Understanding of the Brain will Lead to the Creation of Truly Intelligent Machines. Times Books: ISBN 0-8050-7456-2.

Hawrylycz, M.J.; Lein, E.S.; and et al. 2012. An anatomically comprehensive atlas of the adult human brain transcriptome. Nature. 20;489(7416):391-9.

Hill, S.L.; Wang, Y.; and et al. 2012. Statistical connectivity provides a sufficient foundation for specific functional connectivity in neocortical neural microcircuits. Proc Natl Acad Sci U S A. 109,42

Hinton, G.E. 2009. Deep belief networks Scholarpedia, 4(5):5947. Available electronically at Hoppensteadt, F.C.; and Izhikevich, E.M. 1996. Synaptic organizations and dynamical properties of weakly connected neural oscillators. II. Learning phase information. Biol Cybern. 75(2):129-35.

Ingber, L. 1983. Statistical mechanics of neocortical interactions. Dynamics of synaptic modification Phys. Rev. A. 28, 395-416

Ingber, L.; Nunez, P.L. 2010. Neocortical Dynamics at Multiple Scales: EEG Standing Waves, Statistical Mechanics, and Physical Analogs. Available electronically from

Ingber, L. 2011. Columnar electromagnetic influences on short-term memory at multiple scales.

Available electronically from on_calcium_momentum_waves/file/79e41505a243db793c.pdf Ingber, L. 2012. Influence of macrocolumnar EEG on Ca waves. Available electronically from

Isler, J.R.; Garland, M.; and et al. 2005. Local coherence oscillations in the EEG during development in the fetal baboon. Clin Neurophysiol. 116(9):2121-8. Jaynes, E. T. 1963. Information Theory and Statistical Mechanics. In Ford, K. (ed.). Statistical Physics. New York: Benjamin. p. 181.

Jaynes, E. T. 1968. Prior Probabilities. IEEE Transactions on Systems Science and Cybernetics. 4 (3): 227-241.

Jaynes, E. T. 2003. Probability Theory: The Logic of Science. Cambridge University Press. 351-355.

Jenkins, A. 2011. Self-oscillation. Available electronically at

Jensen,O.; Idiart, M.A.P.; and Lisman, J.E. 1996. Physiologically realistic formation of autoassociative memory in networks with theta/gamma oscillations: Role of fast NMDA channels. Learning and Memory 3:243-256, Jensen,. O.; and Lisman, J.E. 1996a. Novel lists of 7 p 2 known items can be reliably stored in an oscillatory short-term memory network: Interaction with long term memory. Learning and Memory. 3:257-263, Jensen, O.; Lisman, J.E.; 1996b. Hippocampal CA3 region predicts memory sequences: Accounting for the phase precession of place cells. Learning and Memory. 3:279-287.

Jin, X.; Lujan, M.; and et al. 2010. Efficient Parallel Implementation of Multilayer Backpropagation Network on Torus-connected CMPs. Proc. of the ACM International Conference on Computing Frontiers. 89-90.

Johnson, M.B.; Kawasawa, Y.I; and et al. 2009. Functional and evolutionary insights into human brain development through global transcriptome analysis. Neuron. 28;62(4):494-509.

Jones, S.R.; Pritchett, D.L.; and et al. 2009. Quantitative analysis and biophysically realistic neural modeling of the MEG mu rhythm: rhythmogenesis and modulation of sensory-evoked responses. J Neurophysiol. 102(6):3554-72.

Karlsen, A.S.; Pakkenberg, B. 2011. Total numbers of neurons and glial cells in cortex and basal ganglia of aged brains with Down syndrome--a stereological study. Cereb Cortex. 21(11):2519-24.

Karson, C.N.; Coppola, R.; and Daniel, D.G. 1988. alpha frequency in schizophrenia: an association with enlarged cerebral ventricles. Am J Psychiatry. 145, 861-4.

Kawamata, M.; Kirinom, E.; and et al. 2007. Event-related desynchronization of frontal-midline theta rhythm during preconscious auditory oddball processing. Clin EEG Neurosci. 38(4):193-202.

Klimesch, W.; Schack, B.; and et al. 2004. Phase-locked alpha and theta oscillations generate the P1-N1 complex and are related to memory performance. Brain Res Cogn Brain Res. 19, 302-16. Kocsis, B.; and Li, S.; 2004. In vivo contribution of h-channels in the septal pacemaker to theta rhythm generation. Eur J Neurosci. 20, 2149-58.

Koene, R. A. 2001. Functional requirements determine relevant ingredients to model for on-line acquisition of context dependent memory. Ph.D. Thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements of the degree of Doctor of Philosophy, McGill University, Montreal, Canada.

Landisman, C.E.; Long, M.A.; and et al. 2000. Electrical Synapses in the Thalamic Reticular Nucleus. The Journal of Neuroscience. 22(3): 1002-1009.

Lanzalaco, F.; and Zia, W. 2009a. Magnetic fields of radial glial in prenates : Mechanisms for a cortical dipole structure by VZ calcium waves. arNQ Eprints. 2011

Lanzalaco, F.; and Zia, W. 2009b. Dipole Neurology an electromagnetic multipole solution to brain structure, function and abnormality. Presentation to: Integrative approaches to brain complexity, Wellcome trust, Hinxton, Cambridge, UK.

Lawrence, J.J.; Grinspan, Z.M.; and et al. 2006. Muscarinic receptor activation tunes mouse stratum oriens interneurones to amplify spike reliability. J Physiol. 571, 555-62.

Lemm. S.; Müller, K.R.; and Curio, G. 2009. A generalized framework for qua ntifying the dynamics of EEG event-related desynchronization. PLoS Comput Biol. 5(8) Lerner, V. S. August 2012. Hidden information and regularities of information dynamics. Available electronically at

London, M.; and Häusser, M. 2005. Dendritic computation. Annu Rev Neurosci. 28:503-32.

Lytton, W.W.; and Lipton, P. 1999. Can the hippocampus tell time? The temporo-septal engram shift model. Neuroreport. 2;10(11):2301-6.

Malhotra, S.; Cross, R.W.; and Wan der Meer, M.A. 2012. Theta phase precession beyond the hippocampus. Rev Neurosci. 23(1):39-65.

Marino, L.; Conner, R.C.; and et al. 2007. Cetaceans have complex brains for complex cognition. PLoS Biol. 5(5):e139.

McCarthy, M.M.; Moore-Kochlacs, C.; and et al. 2011. Striatal origin of the pathologic beta oscillations in Parkinson's disease. Proc Natl Acad Sci U S A. 108(28) Mechelli, A.; Price, C.J.; and et al. 2003. A dynamic causal modeling study on category effects: bottom-up or top-down mediation? J Cogn Neurosci. 1:15(7):925-34.

Melloni, L.; Molina, C.,; and et al. 2007. Synchronization of neural activity across cortical areas correlates with conscious perception. J Neurosci. 27(11):2858-65.

Mi, Y.; Liao, X.; and et al. 2013. Long-period rhythmic synchronous firing in a scale-free network. Proc Natl Acad Sci U S A. 10;110(50) Mochizuk, Y.; and Shinomoto, S. 2013. Analog and digital codes in the brain. Available electronically at

Moran, R. J.; Stephan, K.E.; and et al. 2009. Dynamic causal models of steady-state responses. Neuroimage. 1;44(3):796-811.

Moss, F.; Ward, L.M.; and Sannita, W.G. 2004. Stochastic resonance and sensory information processing: a tutorial and review of application. Clin Neurophysiol. 115, 267-81.

Nachtergaele, B.; Sims, R.; and Stolz, G. 2012. Quantum harmonic oscillator systems with disorder. Available electronically from

Nunez, P.; Srinivasan, R. 1981. Electric Fields of the Brain. First Edition . Oxford University Press. 330-332, 232-298, 330.

Orosz, G.; Ashwin, P.; and et al. 2007. Cluster synchronization, switching and spatiotemporal coding in a phase oscillator network. Proc. Appl. Math. Mech. 7, 1030703-1030704

Owen, A.M. 2003. HERA today, gone tomorrow? Trends Cogn Sci. 7(9):383-384.

Papo, D. 2013. Why should cognitive neuroscientists study the brain’s resting state? Front Hum Neurosci. 7: 45

Patel, S. H.; and Azzam, P. N. 2005. Characterization of N200 and P300: Selected studies of the event related potential. International Journal of Medical Sciences. 2, 147-154.

Penny, W.D.; Litvak, V.; and et al. 2009. Dynamic Causal Models for phase coupling. J Neurosci Methods. 183(1):19-30.

Pereira, A. Jr.; and Furlan, F.A. 2010. Astrocytes and human cognition: modeling information integration and modulation of neuronal activity. Prog Neurobiol. 92(3):405-20.

Pereira, A. Jr. 2011. Biophysical Mechanisms Supporting Conscious Perception: Prospects for an Artificial Astrocyte. Available electronically from

Pfefferbaum, A.; Ford, J. M.; and et al. 1985. ERPs to response production and inhibition. Electroencephalography and Clinical Neurophysiology. 60, 423-434.

Pinotsis, D.A.; Moran, R.J.; and Friston, K.J. 2012. Dynamic causal modeling with neural fields. Neuroimage. 16;59(2):1261-74

Pissanetzky, S. 2009. A new Universal Model of Computation and its Contribution to Learning, Intelligence, Parallelism, Ontologies, Refactoring, and the Sharing of Resources. Int. J. of Information and Mathematical Sciences. 5:143-173.

Pissanetzky, S. 2010. Coupled Dynamics in Host-Guest Complex Systems Duplicates Emergent Behavior in the Brain. World Academy of Science, Engineering, and Technology 68:1-9. Available electronically from

Pissanetzky, S. 2011. Structural Emergence in Partially Ordered Sets is the Key to Intelligence. Artificial General Intelligence 92-101. Available electronically from

Pissanetzky, S.; and Lanzalaco, F. 2013. Black-box Brain Experiments, Causal Mathematical Logic, and the Thermodynamics of Intelligence. Under revision for Journal of Artificial General intelligence. Dec 2013.

Pissanetzky, S. 2013a. Reasoning with Computer Code: a new Mathematical Logic Journal of Artificial General Intelligence 3(3)11-42.

Pissanetzky, S. 2013b. Differential Euler Equations obtained derived from Casual Mathematical Logic. Available electronically from Polich, J., 2007. Updating P300: an integrative theory of P3a and P3b. Clin Neurophysiol. 118, 2128-48.

Potter, S.; DeMarse, T.; and et al. 2004. Hybrots Hybrids of living neurons and robots for studying neural computation. Available electronically from

Puttarprom, C.; Tanasittikisol, M.; and Yoo-Kong, S. 2013. Entanglement Entropy for a Coupled Harmonic Oscillator. Available electronically from

Ringach, D.L.; and Malone, B.J. 2007. The operating point of the cortex: neurons as large deviation detectors. J Neurosci. 27, 7673-83.

Rodriguez, A.; Whitson, J.; and Granger, R. 2004. Derivation and analysis of basic computational operations of thalamocortical circuits. J Cogn Neurosci. 16, 856-77

Sandersius, S.A.; Chuai, M.; and et al. 2011. A 'chemotactic dipole' mechanism for large-scale vortex motion during primitive streak formation in the chick embryo. Phys Biol. 8(4):045008.

Sardar, S.; Tewari, G.; and Babu, K.A. 2011. A Hardware/Software Co-design Model for Face Recognition using Cognimem Neural Network chip. Published in: Image Information Processing (ICIIP), 2011 International Conference on. 1 - 6. ISBN: 978-1-61284-859-4

Sauseng, P.; Klimesch, W.; and et al. 2008. Oscillatory phase synchronization: A brain mechanism of memory matching and attention. Neuroimage. 40, 308-317.

Sbyrnes321. 2013. Figure 3. Reference available electronically at Accessed 07/2013

Schiffer, A.M.; Ahlheim, C.; and et al. 2012. Surprised at all the entropy: hippocampal, caudate and midbrain contributions to learning from prediction errors. PLoS One. 7(5). Seung, S. 2012. Connectome: How the Brain's Wiring Makes Us Who We Are. Houghton Mifflin Harcourt.

Shapovalov, V. 2008. Entropy Oscillations. Available electronically at Sherwood, C.C.; and Stimpson, C.D.; and et al. 2006. Evolution of increased glia-neuron ratios in the human frontal cortex. Proc Natl Acad Sci U S A. 12;103(37):13606-11.

Sheykhi, A.; and Hendi, S.H. 2010. Entropic Corrections to Coulomb's Law. Available electronically from

Sotty, F.; Danik, M.; and et al. 2003. Distinct electrophysiological properties of glutamatergic, cholinergic and GABAergic rat septohippocampal neurons: novel implications for hippocampal rhythmicity. J Physiol. 551, 927-43.

Stephan, K.E.; Harrison, L.M.; and et al. 2007. Dynamic causal models of neural system dynamics: current state and future extensions. J Biosci. 32(1):129-44.

Staudacher, T.; Shi, F.; and et al. 2013. Nuclear Magnetic Resonance Spectroscopy on a (5- Nanometer)3 Sample Volume. Science. 2013; 339 (6119): 561

Still, S.; Sivak, D. A.; and et al. 2012. Thermodynamics of Prediction. Phys. Rev. Letters. 109, 120604

Striegel, D.A.; and Hurdal, M.K. 2009. Chemically based mathematical model for development of cerebral cortical folding patterns. PLoS Comput Biol. 5(9):e1000524.

Thompson, P.M.; Hayashi, K.M.; and et al. 2003. Dynamics of gray matter loss in Alzheimer's disease. J Neurosci. 23, 994-1005

Tiesinga, P.H.; and José, J,V. 2000. Robust gamma oscillations in networks of inhibitory hippocampal interneurons. Network. 11, 1-23

Tononi, G.; and Sporns O. 2003. Measuring information integration. BMC Neurosci. 2;4:31.

Tononi, G. 2008. Consciousness as integrated information: a provisional manifesto. Biol Bull. 215(3):216-42.

Ujfalussy, B.; Kiss, T.; and et al. 2007. Theta synchronization in the medial septum and the role of the recurrent connections. Available electronically at 30/11/2008.

Uhlhaas, P. J.; Roux, F.; and et al. 2010. Neural synchrony and the development of cortical networks. Trends Cogn. Sci. 14: 72-80.

Vianin, P.; Posada, A.; and et al. 2002. Reduced P300 amplitude in a visual recognition task in patients with schizophrenia. Neuroimage .17(2):911-21. Ward, L.M.; Doesburg, S.M.; and et al. 2006. Neural synchrony in stochastic resonance, attention, and consciousness. Can J Exp Psychol. 60, 319-26.

Wang, T. 2010. Coulomb Force as an Entropic Force. Available electronically from

Wang, Q.A. 2007. From virtual work principle to least action principle for stochastic dynamics. Available electronically from

Wang, Q.A. 2008a. Probability distribution and entropy as a measure of uncertainty. Available electronically from

Wang, Q.A. 2008b. Seeing maximum entropy from the principle of virtual work. Available electronically from

Wang, X.J. 2002. Pacemaker neurons for the theta rhythm and their synchronization in the septohippocampal reciprocal loop. J Neurophysiol. 87, 889-900.

Wedeen, V.J.; Rosene, D.L.; and et al. 2012. Response to comment on "the geometric structure of the brain fiber pathways". Science. 28;337(6102):1605.

Wilson, N.R.; Runyan, C.A.; and et al. 2012. Division and subtraction by distinct cortical inhibitory networks invivo. Nature. 488, 343-348

Wissner-Gross, A. D.; and Freer, C. E. 2013. Causal entropic forces. Physical Review Letters . 110, 168702.

Xu, W.; Huang, X.; and et al. 2007. Compression and reflection of visually evoked cortical waves. Neuron. 55, 119-29.

Yin, B.; and Troger, A.B. 2011. Exploring the 4th Dimension: Hippocampus, Time, and Memory Revisited Front Integr Neurosci. 5: 36.

Yordanova, J.; and Kolev, V. 1997. Developmental changes in the event-related EEG theta response and P300. Electroencephalography and clinical Neurophysiology. 104: 418-430.

Zhang, K.; and Sejnowski, T.J. 2000. A universal scaling law between gray matter and white matter of cerebral cortex. Proc Natl Acad Sci U S A. 9;97(10):5621-6.

Glossary of terms: Words in italics refer to other glossary terms Alpha: The 8-13 hz EEG oscillations primarily associated with the thalamus activity Alpha-beta. The range of oscillations in the alpha to beta range, 8-30 hz. Used to assist with the classification of Mu (8-30hz) in terms of mu-alpha (8-13hz) and mu-beta (12-30hz).

AMPA/KAINATE: One of the two primary classes of cortical neurons, these are the excitatory neurons. Astrocytes: Cortical Glial cells (support cells that outnumber neurons) that are primarily the most dense at the uppermost cortical layers. Previously considered just support cells, newer research suggest a role in computation function. Maybe gain capacitors for cortical columns.

Autobiographical processing: The brain processes which string together episodes into a sequence, that may for example tell a story.

Basal ganglia: A subcortical structure of various linked parts associated with a variety of functions, including voluntary motor control, procedural learning relating to routine behaviors or re-enforcement "habits" cognitive, emotional functions and action selection.

Beta: The 12-30hz EEG oscillations found in the striatum to cortex activity.

Central pacemaker: Areas in the centre of the brain which are thought to be the source clock for a wider range of neural oscillations.

Cingulate: Is the part of the cortex which wrap around the limbic system and is so highly integrated with it, and separate from the corpus callosum some propose it is part of the limbic system. Its function seems to be to integrate and resolve conflictions between cortex and limbic system.

Cortical surface gyration: The folds of the cortex. As neuron to glia ratio increases the gyrations increase. Increased gyration is thought to be linked to intelligence.

Corticolimbic: A reference to the cortex and limbic system in terms of its integrated function.

Delta: The 0-4hz EEG oscillation. Primarily subcortical, but also found in the cortex to thalamus cycle.

Dynamic attention allocation : Frontal cortex, executive control can suppress various signals in other areas of the brain to allow focus on other stimulus, which could originate as Spreading waves arising from lateral inhibition.

Dynamic Causal Modeling: The aim of dynamic causal modeling (DCM) is to infer the causal architecture of coupled or distributed dynamical neural systems. It is a Bayesian model comparison procedure that rests on comparing models of how data were generated Episodic encoding and recall: Episodes are memories which are a set of associations that cover many sensory modalities. e.g. The experience of being in a particular location with somebody.

Event Related Potential, ERP : is the brains EKG equivalent for the heart. It is where we look when we measure the brains perceptual operation at its highest and most integrated level.

Event related Desynchronization (ERD): This is the lowering of the brains ongoing stationary resting state energy. Mostly found as cortical lateral inhibition.

GABAA/GABAC : One of the two primary classes of cortical neurons, these are the inhibitory neurons. Gamma rhythm: The 30hz upwards oscillations generated in the cortex. Tend towards decoherence.

Glutamate: The primary excitatory neurotransmitter in the cortex.

Globus pallidus: The globus pallidus is a major component of the basal ganglia core along with the striatum “Greedy growth” principle: A mathematical term now used for neurons to describe each neurons dendrite growth in terms of a mathematical power law Grey to white matter ratios: (or the inverse). The ratio of grey to white matter either in individual brain areas, modules or the entire system.

Hippocampus: Primary roles is the consolidation of information from short-term memory to long-term memory, recall and spatial navigation.

Hippocampal theta: The 4-8hz EEG oscillations primarily associated with hippocampal activity.

Hopf bifurcation: A local bifurcation in which a fixed point of a dynamical system loses stability as a pair of complex conjugate eigenvalues of the linearization around the fixed point cross the imaginary axis of the complex plane.

Invariants: Both mathematical and computational neuroscience invariants have roughly the same general equivalence.

Lateral inhibition : an excited neuron or set of neurons such as cortical columns can reduce the activity of its neighbours. This can even extend to transcallosal inhibition across the two cortical hemispheres.

Limbic system. The set of subcortical structures which are separate from the brainstem and cerebellum.

Mu wave: EEG oscillation in the range 8-30 hz. It mirrors the alpha to beta range but has no known subcortical source, so maybe a cortical model of the alpha-beta range.

N1-P1 signal: An ERP composite signal associated with visual recognition in the time range of 100ms. There are also other types of N signal.. N just means the signal has a negative energy deviation to baseline, while P is positive. 1 is just an abbreviation so it could be called N100 on its own, just as P3 would also be P300

Non linear cortical activity: A reference to the manner in which most cortical activity is considered to be primarily non linear dynamical in nature.

Non explicit programming: For example programming all the neuronal components into a brain simulation wiring them together and seeing if ERS arises without programming that. But there are various levels of this. i.e. CML is first principle based, so if ERS/ERD arose from its program this would be considered a more pure example. P100-P300 or P600 etc: These are the various positive event related potentials with their onset time (see N1-P1 signal for more clarification) P300: Most well known ERP component occurring at 300ms as it is clearest in decision making and onset of conscious access. All ERP numbers describe the milliseconds of their onset after stimulus Phase coupling - coupled oscillation: Neural oscillations of various frequencies in the brain are found to lock together for a wide variety of neural sub processes, coding, recall and high level perceptual functions.

Phase-locked delta: the timing of spikes in the delta wave becomes phase coupled to the activity of other oscillations, such as alpha.

Phase reset: Neural oscillations may reset another set of neural activities, such as one set of oscillations, restarting the phase of another when coupled.

Re-enforcement learning: The brain processes associated with learning and repeating routines and habits.

Sensory routing: Allocation of inputs to outputs, mostly associated with thalamus function.

Septal areas: the region of the cerebral hemisphere, forming the medial wall of the lateral ventricle's frontal horn Spreading waves: There are many terms for this in neurodynamics, but basically it is mass attractor activity that is non linear dynamic in nature. Sporadic bursts across cortical areas that spread across columns, or even larger macroscopic areas.

Stationary dynamics - stationary resting state. The brain has continuous oscillations such as alpha, delta, beta and mu even when it is not processing information. i.e. just sitting doing nothing.

Striatum: The major input station of the basal ganglia system.

Subthalamic nucleus: The subthalamic nucleus is a small lens-shaped nucleus in the brain where it is, from a functional point of view, part of the basal ganglia system Symmetry: For disambiguation in cross discipline use in this paper, mathematical symmetry and asymmetry are different from biological e.g. radial symmetry or bilateral asymmetry. This is clarified as here we attempt to use CML to predict brain signals and structures that are using the biological definitions. So if we mention such terms in a neuroscience context it will not be mathematical. An example is we may say an alpha wave emerges with symmetrical spread over a symmetrical structure like the thalamus, but if we were to describe the computations the use of the term symmetry would not automatically infer a mathematical invariance.

System consolidation: The ability of the brain to filter out irrelevant information over longer term time periods. Thalamic reticular nucleus: A sheet of inhibitory neurons which surround the thalamus.

Thalamus: The brain module where nearly all incoming information passes through.

Thalamocortical: Refers to the interaction between thalamus and cortex which is usually an ongoing loop driven by locked Delta, Gamma and Alpha oscillations.

Third ventricle: The brain ventricle most central to the brain, in between the thalamus.