Research Tools and Paradigms
Abstract
Biology in the twenty-first century will be for Mathematics what Physics was in nineteenth and twentieth centuries. This is a well accepted belief among scientists with mathematical training. Some physicists can go even further and deplore the pre-Newtonian stage in which biology and in particular neuroscience find themselves (Mazzocchi F, EMBO Rep 9(1):10–14, 2008). Neuroscience is a data-rich field that needs for a theoretical framework that guides the model building and simulation processes. Biology, in opposition to physics which is quantitative and explanatory, may be perceived as a descriptive and qualitative field. However, to state that biology is descriptive and qualitative, while physics is mathematical and quantitative is a dichotomy too simplistic to be true (as all dichotomies usually are). Undoubtedly, biology today is quantitative in either its models and results. It is easily noticeable that in top scientific journals such as Nature or Science, though they are not devoted to any particular field, the studies in the field of biology, specifically molecular biology, are the overwhelming majority of the total of articles. The very dissimilar rate of production that these two prestigious publications display between disciplines other than biology is such, that one starts wondering if the non-life science community has anything left important to say. But the actual reason for this must be found in the scarcity of mathematized universal principles in biology compared to, for example, physics. Physics is built on formal theories embedded in universal laws, rendering particulars and details unnecessary. In biology, on the other hand, particular cases are relevant. Furthermore, variability, non linearity, noise or high dimensionality are biological features hardly generalizable in the standard mathematical forms (Gómez-Ramirez J, Sanz R, Prog Biophys Mol Biol 2013).
Keywords
Large Hadron Collider Category Theory Brain Science Associative Neural Network Biology TodayReferences
- 1.Eliot TS (2001) Four quartets: quartet no. 2: east coker. Faber and Faber, LondonGoogle Scholar
- 2.Jeannerod M (1999) A dichotomous visual brain? Psyche 5. Retrieved October 19, 2013, from www.theassc.org/files/assc/2443.pdf
- 3.Sokal A, Bricmont J (1999) Fashionable nonsense: postmodern intellectuals’ abuse of science, 1st edn. Picador, New YorkGoogle Scholar
- 4.Thompson DW (1992) On growth and form. Cambridge University Press, CambridgeGoogle Scholar
- 5.Kendrew J (1961) The three-dimensional structure of a protein molecule. Sci Am 205:96–110PubMedGoogle Scholar
- 6.Cull P (2007) The mathematical biophysics of nicolas rashevsky. Biosystems 88(3):178–184. BIOCOMP 2005: selected papers presented at the international conference – diffusion processes in neurobiology and subcellular biology, BIOCOMP2006: diffusion processes in neurobiology and subcellular biologyGoogle Scholar
- 7.Gerstein MB, Bruce C, Rozowsky JS, Zheng D, Du J, Korbel JO, Emanuelsson O, Zhang ZD, Weissman S, Snyder M (2007) What is a gene, post-ENCODE? history and updated definition. Genome Res 17(6):669–681. PMID: 17567988PubMedGoogle Scholar
- 8.White JG, Southgate E, Thomson JN, Brenner S (1986) The structure of the nervous system of the nematode caenorhabditis elegans. Philos Trans R Soc Lond B Biol Sci 314(1165):1–340PubMedGoogle Scholar
- 9.Schrödinger E (1944) What is life? Mind and matter. Cambridge University Press, CambridgeGoogle Scholar
- 10.Barr M, Wells C (1997) This is biology: the science of the living world. Belknap Press of Harvard University Press, CambridgeGoogle Scholar
- 11.Wikipedia () Action potential. http://en.wikipedia.org/wiki/Action_potential
- 12.Golubitsky M (2006) Symmetry and neuroscience. Bulletin of the AMS. American Mathematical Society (January 14)Google Scholar
- 13.Eilenberg S (Aug 2013) Page Version ID: 566981902Google Scholar
- 14.Mac Lane S (Aug 2013) Page Version ID: 550989403Google Scholar
- 15.Grothendieck A (Aug 2013) Page Version ID: 566771460Google Scholar
- 16.Lawvere W (Aug 2013) Page Version ID: 548025672Google Scholar
- 17.Healy J, Caudell T (2006) Ontologies and worlds in category theory: implications for neural systems. Axiomathes 16:165–214Google Scholar
- 18.Neuman Y, Nave O (2008) On the semio-mathematical nature of codes. Biosemiotics 1:99–111Google Scholar
- 19.Edelman G, Tononi G (2001) Consciousness: how matter becomes Imagination. Penguin, LondonGoogle Scholar
- 20.(2013) One and Three Chairs. June 2013. Page Version ID: 559080504Google Scholar
- 21.Ruth Lawson Otago Polytechnic (2007) Anatomy and physiology of animals relation btw sensory, relay & motor neurons. http://commons.wikimedia.org/wiki/File:Anatomy_and_physiology_of_animals_Relation_btw_sensory,_relay_%26_motor_neurons.jpg
- 22.Hubel DH, Wiesel TN (1977) Ferrier lecture. Functional architecture of macaque monkey visual cortex. Proc R Soc Lond Ser B. Containing papers of a Biological character Royal Society (Great Britain) 198(1130):1–59. PMID: 20635Google Scholar
- 23.Fuhs M, Touretzky D (2006) A spin glass model of path integration in rat medial entorhinal cortex. J Neurosci 26:4266–76PubMedGoogle Scholar
- 24.Taube J (2009) Head direction cells. Scholarpedia 4(12):1787Google Scholar
- 25.Mazzocchi F (2008) Complexity in biology. Exceeding the limits of reductionism and determinism using complexity theory. EMBO Rep 9(1):10–14. PMID: 18174892, PMCID: PMC2246621Google Scholar
- 26.Gómez-Ramirez J, Sanz R (2013) On the limitations of standard statistical modeling in biological systems: a full Bayesian approach for biology. Prog Biophys Mol Biol 113(1):80–91PubMedGoogle Scholar
- 27.Freeman WJ, Kozma R (2010) Freeman’s mass action. Scholarpedia 5(1):8040Google Scholar
- 28.Carnap R (1967) The logical structure of the world. Pseudoproblems in philosophy. University of California Press, BerkeleyGoogle Scholar
- 29.Kitano H (2002) Looking beyond the details: a rise in system-oriented approaches in genetics and molecular biology. Curr Genet 41(1):1–10. PMID: 12073094PubMedGoogle Scholar
- 30.Strange K (2005) The end of naive reductionism: rise of systems biology or renaissance of physiology? Am J Physiology Cell Physiol 288(5):C968–C974Google Scholar
- 31.Jacrot B (2006) Physique et biologie. Edp Sciences, Les UlisGoogle Scholar
- 32.Taylor JG (1999) Towards the networks of the brain: from brain imaging to consciousness. Neural Netw 12(7–8):943–959. PMID: 12662638PubMedGoogle Scholar
- 33.Bower JM (2005) Looking for Newton: realistic modeling in modern biology. In: Bower JM, Beeman D (eds) Special issue on realistic neural modeling - Wam-Bamm ’05 tutorials. Brains, minds and media, vol 1, bmm217Google Scholar
- 34.Noble D (2010) Biophysics and systems biology. Philos Trans R Soc A 368(1914):1125–1139Google Scholar
- 35.Brenner S (1999) Theoretical biology in the third millennium. Philos Trans R Soc Lond B 7:1963–1965Google Scholar
- 36.Smolin L (2003) The self-organization of space and time. Philos Trans Ser A Math Phys Eng Sci 361(1807):1081–8Google Scholar
- 37.Knight J (2002) Bridging the culture gap. Nature 419:244–246PubMedGoogle Scholar
- 38.Kuhn T (1962) The structure of scientific revolutions. University of Chicago Press, ChicagoGoogle Scholar
- 39.Kuhn T (2000) The road since structure: philosophical essays: 1970-1993. University of Chicago Press, ChicagoGoogle Scholar
- 40.Gatenby RA, Maini PK (2003) Mathematical oncology: cancer summed up. Nature 421(6921):321. PMID: 12540881PubMedGoogle Scholar
- 41.Polger T (2004) Natural minds. MIT, CambridgeGoogle Scholar
- 42.Bechtel W, Mundale J (1999) Multiple realizability revisited: linking cognitive and neural states. Philos Sci 66:175–207Google Scholar
- 43.Buzsaki G (2006) Rhythms of the brain. Oxford University Press, Oxford/New YorkGoogle Scholar
- 44.Nicolis G, Prigogine I (1977) Self-organization in nonequilibrium systems: from dissipative structures to order through fluctuations, 1st edn. Wiley, New YorkGoogle Scholar
- 45.Whishaw I, Vanderwolf C (1973) Hippocampal EEG and behavior: change in amplitude and frequency of RSA (theta rhythm) associated with spontaneous and learned movement patterns in rats and cats. Behav Biol 8(4):461–484PubMedGoogle Scholar
- 46.Pare D, Llinas R (1995) Conscious and pre-conscious processes as seen from the standpoint of sleep-waking cycle neurophysiology. Neuropsycholgia 33(9):1155–1168Google Scholar
- 47.Nunez PL (1995) Neocortical dynamics and human EEG rhythms. Oxford University Press, New YorkGoogle Scholar
- 48.Nunez P (2000) Toward a quantitative description of large-scale neocortical dynamic function and EEG. Behav Brain Sci 23(3):371–98PubMedGoogle Scholar
- 49.Chalmers D (1995) Facing up to the problem of consciousness. J Conscious Stud 2(3):200–219Google Scholar
- 50.Fell J (2004) Identifying neural correlates of consciousness: the state space approach. Conscious Cogn 13(4):709–729PubMedGoogle Scholar
- 51.Feldman J (2009) Ecological expected utility and the mythical neural code. Cogn Neurodyn 4(1):25–35PubMedGoogle Scholar
- 52.Gómez-Ramirez J (2012) Comments on aur’s “from neuroelectrodynamics to thinking machines”. Cogn Comput 4(4):563–565Google Scholar
- 53.Rosenblatt F (1958) The perceptron: a probabilistic model for information storage and organization in the brain. Cornell Aeronaut Lab Psychol Rev 65(6):386–408Google Scholar
- 54.Hodgkin A, Huxley A (1982) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500–544Google Scholar
- 55.Rall W (2009) Rall model. Scholarpedia 4(4):1369Google Scholar
- 56.De Schutter E (2008) Why are computational neuroscience and systems biology so separate? PLoS Comput Biol 4(5):e1000078PubMedGoogle Scholar
- 57.Solinas S, Maex R, De Schutter E (2006) Dendritic amplification of inhibitory postsynaptic potentials in a model Purkinje cell. Eur J Neurosci 23(4):1207–1218PubMedGoogle Scholar
- 58.Niebur E (2008) Neuronal cable theory. Scholarpedia 3(5):2674Google Scholar
- 59.Rall W (2011) Core conductor theory and cable properties of neurons. In: Comprehensive physiology. WileyGoogle Scholar
- 60.Segev I, London M (2000) Untangling dendrites with quantitative models. Science 290(5492):744–750PubMedGoogle Scholar
- 61.Segev I (2006) What do dendrites and their synapses tell the neuron? J Neurophysiol 95(3):1295–1297PubMedGoogle Scholar
- 62.Gerstner W, Kistler W (2002) Spiking neuron models. Single neurons, populations, plasticity. Cambridge University Press, Cambridge/New YorkGoogle Scholar
- 63.Bressloff P (2008) A Green’s function approach to analysing the effects of random synaptic background activity in a model neural network. J Phys A Math Gen 27(12):4097Google Scholar
- 64.Abbott L (1999) Lapique’s introduction of the integrate-and-fire model neuron. Brain Res Bull 50(5-6):303–304PubMedGoogle Scholar
- 65.Dayan P, Abbott L (2002) Theoretical neuroscience: computational and mathematical modeling of neural systems. MIT, Cambridge MAGoogle Scholar
- 66.Deco G, Jirsa V, Robinson P, Breakspear M, Friston K (2008) The dynamic brain: From spiking neurons to neural masses and cortical fields. PLoS Comput Biol 4(8):23–37Google Scholar
- 67.Gerstner W, Naud R (2009) Neuroscience: how good are neuron models? Science 326(5951):379–380PubMedGoogle Scholar
- 68.Meunier C, Segev I (2002) Playing the devil’s advocate: is the Hodgkin-Huxley model useful? Trends Neurosci 25(11):558–63PubMedGoogle Scholar
- 69.Herz AVM, Gollisch T, Machens CK, Jaeger D (2006) Modeling single-neuron dynamics and computations: a balance of detail and abstraction. Science 314(5796):80–85PubMedGoogle Scholar
- 70.Markram H (2006) The blue brain project. Nature Neurosci 7:153–158Google Scholar
- 71.Davie JT, Kole MHP, Letzkus JJ, Rancz EA, Spruston N, Stuart GJ, HÃusser M (2006) Dendritic patch-clamp recording. Nat Protoc 1(3):1235–1247Google Scholar
- 72.von der Malsburg C, Phillips WA, Singer W (eds) (2010) Dynamic coordination in the brain: from neurons to mind. MIT, CambridgeGoogle Scholar
- 73.McCulloch W, Pitts WH (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5:115–133Google Scholar
- 74.Searle J (1980) Minds, brains and programs. Behav Brain Sci 3(3):417–424Google Scholar
- 75.Harnad S (1990) The symbol grounding problem. Physica D 42(10):335–346Google Scholar
- 76.Cohen PR (2006) If not turing’s test, then what? AI Mag 26(4):335–346Google Scholar
- 77.Hoffman W (1998) Are neural networks a good model for cognition? Psycoloquy 9(12). Retrieved from http://www.cogsci.ecs.soton.ac.uk/cgi/psyc/newpsy?9.12
- 78.Fodor J, Pylyshyn Z (1983) Connectionism and cognitive architecture: a critical analysis. Cognition 28:3–71Google Scholar
- 79.Aizawa K (1995) The role of systematicity argument in classicism and connectionism. In: Ó Nuallaáin S, Mc Kevitt P, Mac Aogáin E (eds) Two sciences of mind: readings in cognitive science and consciousness. John Benjamims B.V, Amsterdam/PhiladelphiaGoogle Scholar
- 80.Eliasmith C (2007) Attractor network. Scholarpedia 2(10):1380Google Scholar
- 81.Izhikevich E (2006) Dynamical systems in neuroscience the geometry of excitability and bursting. MIT, CambridgeGoogle Scholar
- 82.Zhang D, Raichle ME (2010) Disease and the brain’s dark energy. Nat Rev Neurol 6(1):15–28PubMedGoogle Scholar
- 83.Biswal B, Yetkin FZ, Haughton VM, Hyde JS (1995) Functional connectivity in the motor cortex of resting human brain using echo-planar MRI. Magn Reson Med 34(4):537–541. PMID: 8524021PubMedGoogle Scholar
- 84.Damoiseaux JS, Rombouts SARB, Barkhof F, Scheltens P, Stam CJ, Smith SM, Beckmann CF (2006) Consistent resting-state networks across healthy subjects. Proc Natl Acad Sci USA 103(37):13848–13853. PMID: 16945915PubMedGoogle Scholar
- 85.Fox M, Raichle M (2007) Spontaneous fluctuation in brain activity observed with functional magnetic resonance imaging. Nat Neurosci Rev 8:700–711Google Scholar
- 86.West G, Brown J, Enquist B (1997) A general model for the origin of allometric scaling laws in biology. Science 276:122–126PubMedGoogle Scholar
- 87.Castellano C, Fortunato S, Loreto V (2009) Statistical physics of social dynamics. Rev Mod Phys 81:591–646Google Scholar
- 88.Willems JC (1972) Dissipative dynamical systems part i: General theory. Arch Ration Mech Anal 45(5):321–351Google Scholar
- 89.David O, Friston K (2003) A neural mass model for MEG/EEG coupling and neuronal dynamics. NeuroImage 20:102–109Google Scholar
- 90.Haskell E, Nykamp DQ, Tranchina D (2001) A population density method for large-scale modeling of neuronal networks with realistic synaptic kinetics. Neurocomputing 38-40:627–632Google Scholar
- 91.Breakspear M, Stam C (2005) Dynamics of a neural system with a multiscale architecture. Philos Trans R Soc B (360):1051–1074Google Scholar
- 92.Freeman W (1975) Mass action in the nervous system. Academic, New YorkGoogle Scholar
- 93.Freeman W, Schneider W (1982) Changes in spatial patterns of rabbit olfactory EEG with conditioning to odors. Psychophysiology 19(1):44–56PubMedGoogle Scholar
- 94.Strogatz S, Stewart I (1993) Coupled oscillators and biological synchronization. Sci Am 12(1993):102–109Google Scholar
- 95.Frank T, Daffertshofer A, Peper C, Beek P, Haken H (2000) Towards a comprehensive theory of brain activity: coupled oscillator systems under external forces. Physica D 14:62–86Google Scholar
- 96.Hoppensteadt F, Izhikevich E (1997) Weakly connected neural networks. Springer, New YorkGoogle Scholar
- 97.Collins J, Stewart I (1999) Coupled nonlinear oscillators and the symmetries of animal gaits. J Nonlinear Sci 349:349–392Google Scholar
- 98.Golubitsky M, Stewart I, Buono PL, Collins J (1999) Symmetry in locomotor central pattern generators and animal gaits. Nature 401:693–695PubMedGoogle Scholar
- 99.Buono P, Golubitsky M (2001) Models of central pattern generators for quadruped locomotion. J Math Biol 42(4):291–326PubMedGoogle Scholar
- 100.Stewart I (2004) Network opportunities. Nature 427:601–604PubMedGoogle Scholar
- 101.Theunissen F, Roddey J, Stufflebeam S, Clague H, Miller J (1996) Information theoretic analysis of dynamical encoding by four primary sensory interneurons in the cricket cercal system. J Neurophysiol 75:1345–1359PubMedGoogle Scholar
- 102.Strogatz H (1994) Nonlinear dynamics and chaos. Addison Wesley, ReadingGoogle Scholar
- 103.Abeles M (1991) Corticonics: neural circuits of the cerebral cortex. Cambridge University Press, Cambridge/New YorkGoogle Scholar
- 104.Manor Y, Rinzel J, Segev I, Yarom Y (1997) Low-amplitude oscillations in the inferior olive: a model based on electrical coupling of neurons with heterogeneous channel densities. J Neurophysiol 77:2736–2752PubMedGoogle Scholar
- 105.Steriade M, Domich L, Dakson G, Deschenes M (1987) The deafferented reticular thalamic nucleus generates spindle rhythmicity. J Neurophysiol 57:260–273PubMedGoogle Scholar
- 106.Caplan JB, Madsen JR, Schulze-Bonhage A, Aschenbrenner-Scheibe R, Newman EL, Kahana MJ (2003) Human theta oscillations related to sensorimotor integration and spatial learning. J Neurosci 23(11):4726–4736. PMID: 12805312PubMedGoogle Scholar
- 107.Garcia Dominguez L, Wennberg RA, Gaetz W, Cheyne D, Snead OC 3rd, Perez Velazquez JL (2005) Enhanced synchrony in epileptiform activity? Local versus distant phase synchronization in generalized seizures. J Neurosci 25(35):8077–8084. PMID: 16135765PubMedGoogle Scholar
- 108.Giaume C, McCarthy KD (1996) Control of gap-junctional communication in astrocytic networks. Trends Neurosci 19(8):319–325PubMedGoogle Scholar
- 109.Hutcheon B, Yarom Y (2000) Resonance, oscillation and the intrinsic frequency preferences of neurons. Trends Neurosci 23(5):216–222PubMedGoogle Scholar
- 110.Boehlen A, Heinemann U, Erchova I (2010) The range of intrinsic frequencies represented by medial entorhinal cortex stellate cells extends with age. J Neurosci 30(13):4585–9PubMedGoogle Scholar
- 111.Winfree AT (2001) The geometry of biological time, 2nd edn. Springer, New YorkGoogle Scholar
- 112.Acebrón JA, Bonilla LL, Pérez Vicente CJ, Ritort F, Spigler R (2005) The kuramoto model: a simple paradigm for synchronization phenomena. Rev Mod Phys 77(1):137–185Google Scholar
- 113.Ermentrout GB, Kopell N (1991) Multiple pulse interactions and averaging in systems of coupled neural oscillators. J Math Biol 29(3):195–217Google Scholar
- 114.Velazquez J (2007) Brain research: a perspective from the coupled oscillators field. NeuroQuantology 4(2):155–165Google Scholar
- 115.Buzsaki G (2010) Neural syntax: cell assemblies, synapsembles, and readers. Neuron 68(3):362–385PubMedGoogle Scholar
- 116.Freeman WJ (2008) A pseudo-equilibrium thermodynamic model of information processing in nonlinear brain dynamics. Neural Netw 21(2-3):257–265. PMID: 18249088PubMedGoogle Scholar
- 117.Prinz AA, Bucher D, Marder E (2004) Similar network activity from disparate circuit parameters. Nature Neurosci 7(12):1345–1352PubMedGoogle Scholar
- 118.Tsuda I (2001) Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems. Behav Brain Sci 24(05):793–810PubMedGoogle Scholar
- 119.Friston KJ (2001) Brain function, nonlinear coupling, and neuronal transients. Neurosci Rev J Bringing Neurobiol Neurol Psychiatry 7(5):406–418. PMID: 11597100Google Scholar
- 120.Harrison L, David O, Friston K (2005) Stochastic models of neuronal dynamics. Philos Trans R Soc B Biol Sci 360(1457):1075–1091. PMID: 16087449Google Scholar
- 121.Perez Velazquez J (2005) Brain, behaviour and mathematics: are we using the right approaches? Physica D 212:161–182Google Scholar
- 122.Griniasty M, Tsodyks M, Amit D (1999) Conversion of temporal correlations between stimuli to spatial correlations between attractors. In: Abbott LF, Sejnowski TJ (eds) Neural codes and distributed representations. MIT, CambridgeGoogle Scholar
- 123.Cossart R, Aromov D, Yuste R (2003) Attractor dynamics of network up states in the neocortex. Nature 423(5723):283–288PubMedGoogle Scholar
- 124.Hebb DO (2002) The organization of behavior: a neuropsychological theory, New edn. Psychology Press, MahwahGoogle Scholar
- 125.Wills TJ, Lever C, Cacucci F, Burgess N, O’Keefe J (2005) Attractor dynamics in the hippocampal representation of the local environment. Science 308(5723):873–876PubMedGoogle Scholar
- 126.Lopes da Silva F et al (2003) Epilepsies as dynamical diseases of brain systems: basic models of the transition between normal and epileptic activity. Epilepsia 44(12):72–83PubMedGoogle Scholar
- 127.Babloyantz A, Destexhe A (1986) Low-dimensional chaos in an instance of epilepsy. Babloyantz 83(12):3513–3517Google Scholar
- 128.Titcombe MS et al (2001) Dynamics of Parkinsonian tremor during deep brain stimulation. Chaos 11:766–773PubMedGoogle Scholar
- 129.Prinz A, Bucher D, Marder (2000) Similar network activity from disparate circuit parameters. Nat Neurosci 7:1345–1352Google Scholar
- 130.Gómez-Ramirez J, Sanz R (2012) What the escherichia coli tells neurons about learning. In: Simeonov PL, Smith LS, Ehresmann AC (eds) Integral biomathics. Springer, Berlin/Heidelberg, pp 41–55Google Scholar
- 131.Mizumori SJY (2008) Hippocampal place fields: relevance to learning and memory, 1st edn. Oxford University Press, New YorkGoogle Scholar
- 132.Mac Cormac E, Stamenov M (1996) Fractals of brain, fractals of mind: in search of a symmetry bond. John Benjamins B.V., Amsterdam/PhiladelphiaGoogle Scholar
- 133.Nunn C (2008) From neurons to notions: brains, mind and meaning. Floris Books, EdinburghGoogle Scholar
- 134.Haken H (1983) Synergetics: an introduction. Springer, BerlinGoogle Scholar
- 135.Haken H (2007) Synergetics. Scholarpedia 2(1):1400Google Scholar
- 136.Haken H (2006) Synergetics of brain function. Int J Psychophysiol 60(2):110–124PubMedGoogle Scholar
- 137.Haken H, Peper C, Beek P, Daffertshofer A (1996) A model for phase transitions in human hand movements during multifrequency tapping. Physica D Nonlinear Phenom 90(1–2): 179–196Google Scholar
- 138.Frank T, Daffertshofer A, Peper C, Beek P, Haken H (2000) Towards a comprehensive theory of brain activity: coupled oscillator systems under external forces. Physica D Nonlinear Phenom 144(1–2):62–86Google Scholar
- 139.Czaplicka A, Holyst JA, Sloot PMA (2013) Noise enhances information transfer in hierarchical networks. Sci Rep 3:1223PubMedGoogle Scholar
- 140.Pellionisz A, Llinás R (1985) Tensor network theory of the metaorganization of functional geometries in the CNS. Neuroscience 16:245–273PubMedGoogle Scholar
- 141.Makarenko V, Llinás R (1998) Experimentally determined chaotic phase synchronization in a neuronal system. Proc Natl Acad Sci USA 95:15747–15752PubMedGoogle Scholar
- 142.Leznik E, Makarenko V, Llinás R (2002) Electrotonically mediated oscillatory patterns in neuronal ensembles: an in vitro voltage-dependent dye imaging study in the inferior olive. J Neurosci 22(7):2804–2815PubMedGoogle Scholar
- 143.Roy S, Llinás R (2008) Dynamic geometry, brain function modeling, and consciousness. Prog Brain Res 168:133–144PubMedGoogle Scholar
- 144.Watts D, Strogatz S (1998) Collective dynamics of ‘small-world’ networks. Nature 393:244–442Google Scholar
- 145.Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U (2002) Network motifs: simple building blocks of complex networks. Science 298(5594):824–827. PMID: 12399590PubMedGoogle Scholar
- 146.Newman MEJ (2003) The structure and function of complex networks. SIAM Rev 45(2):167–256Google Scholar
- 147.Hopfield J (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci 79:2554–2558PubMedGoogle Scholar
- 148.Eliasmith C (2005) A unified approach to building and controlling spiking attractor networks. Neural Comput 17:1276–1314PubMedGoogle Scholar
- 149.Jaynes ET (1957) Information theory and statistical mechanics. Phys Rev 106:620–630Google Scholar
- 150.Jaynes ET (1957) Information theory and statistical mechanics. II. Phys Rev 108:171–190Google Scholar
- 151.Schneidman E, Berry MJ, Segev R, Bialek W (2006) Weak pairwise correlations imply strongly correlated network states in a neural population. Nature 440(7087):1007–1012. PMID: 16625187, PMCID: PMC1785327Google Scholar
- 152.Kaneko K (1992) Simulating spatiotemporal Chaos with coupled map lattices. In: Miyashita PDS, Imada PDM, Takayama PDH (eds) Computational approaches in condensed-matter physics. Springer, Berlin/Heidelberg, pp 260–271Google Scholar
- 153.Kaneko K, Tsuda I (2000) Complex systems: chaos and beyond, a constructive approach with applications in life sciences. Springer, Berlin/New YorkGoogle Scholar
- 154.Erdos P, Renyi A (1960) On the evolution of random graphs. Publ Math Inst Hung Acad Sci 5:17–61Google Scholar
- 155.Kozma R (2007) Neuropercolation. Scholarpedia 2(8):1360Google Scholar
- 156.Beggs JM (2007) Neuronal avalanche. Scholarpedia 2(1):1344Google Scholar
- 157.Beggs J, Plenz D (2003) Neuronal avalanches in neocortical circuits. J Neurosci 23(35):11167–11177PubMedGoogle Scholar
- 158.Breskin I et al (2006) Percolation in living neural networks. Phys Rev Lett 97(18):188102PubMedGoogle Scholar
- 159.Lee SY (ed) (2009) Systems biology and biotechnology of escherichia coli, 2009 edn. Springer, Dordrecht/LondonGoogle Scholar
- 160.Boden M (1972) What computers can’t do: the limits of artificial intelligence. Harper & Row, New YorkGoogle Scholar
- 161.Boden M (2006) Mind as machine. Oxford University Press, New YorkGoogle Scholar
- 162.Lichtman JW, Livet J, Sanes JR (2008) A technicolour approach to the connectome. Nat Rev Neurosci 9:417–422PubMedGoogle Scholar
- 163.Lehrer J (2009) Neuroscience: making connections. Nature 457:524–527PubMedGoogle Scholar
- 164.Gowers T, Barrow-Green, Leader I (2008) The Princeton companion to mathematics. Princeton University Press, PrincetonGoogle Scholar
- 165.Eilenberg S, MacLane S (1945) General theory of natural equivalences. Trans Am Math Soc 58(2):231Google Scholar
- 166.Barr M, Wells C (1999) Category theory for computing science. CRM Publications, Montreal.Google Scholar
- 167.Mac Lane S (1988) Concepts and categories in perspective. In: Duren P, A century of mathematics in America Part 3. American Mathematical Society, Providence 21:353–365Google Scholar
- 168.Pierce B (1991) Arrows, structures, and functors: the categorical imperative. MIT, Cambridge MAGoogle Scholar
- 169.Awodey S (2006) Category theory. Oxford University Press, Oxford/New YorkGoogle Scholar
- 170.Mac Lane S (1986) Mathematics form and function. Springer, New YorkGoogle Scholar
- 171.Mac Lane S (1998) Categories for the working mathematician. Springer, New YorkGoogle Scholar
- 172.Lawvere FW, Schanuel SH (1997) Conceptual mathematics: a first introduction to categories [...] [...]. Cambridge University Press, CambridgeGoogle Scholar
- 173.Arbib M, Manes E (1975) Arrows, structures, and functors: the categorical imperative. Academic, New YorkGoogle Scholar
- 174.Simmons H (2011) An introduction to category theory. Cambridge University Press, Cambridge/New YorkGoogle Scholar
- 175.Rydeheard DE, Burstall (1988) Computational category theory, 1st edn. Prentice Hall, New YorkGoogle Scholar
- 176.Borceux F (2008) Handbook of categorical algebra: volume 1, Basic category theory, 1st edn. Cambridge University Press, CambridgeGoogle Scholar
- 177.Pareigis B (1970) Categories and functors, 1st edn. Academic, New YorkGoogle Scholar
- 178.Schalk A, Simmons H (2005) Introduction to category theory in for easy movements. www.cs.man.ac.uk/mfg
- 179.Van Heijenoort J (1977) From Frege to Gödel: a source book in mathematical logic, 1879–1931. Harvard University Press, Cambridge/LondonGoogle Scholar
- 180.Macnamara J (1994) The logical foundations of cognition. Oxford University Press, New YorkGoogle Scholar
- 181.Hoffman W (2012) The dialectics of mind. J Mind Theory 1(1):1–27Google Scholar
- 182.Philips S, Wilson W, Hadford G (2009) What do transitive inference and class inclusion have in common? Categorical (co)products and cognitive development. PLoS Comput Biol 5(12):e1000599Google Scholar
- 183.Brown R, Porter T (2003) Category theory and higher dimensional algebra: potential descriptive tools in neuroscience. In: Singh N (ed) Proceedings of the international conference on theoretical neurobiology, Delhi, 2003. National Brain Research Centre, conference proceedings, vol 1, pp 80–92Google Scholar
- 184.Ehresmann A, Vanbremeersch JP (2007) Memory evolutive systems; hierarchy, emergence, cognition. Elsevier, Amsterdam/Boston/ParisGoogle Scholar
- 185.Zeeman EC (1962) The topology of the brain and visual perception. Prentice-Hall, New YorkGoogle Scholar
- 186.Spivak DI, Kent RE (2012) Ologs: a categorical framework for knowledge representation. PLoS ONE 7(1):e24274PubMedGoogle Scholar
- 187.Fidaeiro JL (2004) Categories for software engineering. Springer, Berlin HeidelbergGoogle Scholar
- 188.Haskell (programming language) (2013). Page Version ID: 551056925. http://en.wikipedia.org/wiki/Haskell_%28programming_language%29
- 189.Scala (programming language) (2013). Page Version ID: 551000017. http://en.wikipedia.org/wiki/Scala_%28programming_language%29
- 190.Clojure (2013). Page Version ID: 548200920. http://en.wikipedia.org/wiki/Clojure
- 191.Kary M (2009) (Math, science,?). Axiomathes 19:321–339Google Scholar
- 192.Simeonov PL (2010) Integral biomathics: a post-Newtonian view into the logos of bios. Prog Biophys Mol Biol 102(2-3):85–121. PMID: 20146929PubMedGoogle Scholar
- 193.Rosen R (2006) Autobiographical reminiscences of rober rosen. Axiomathes 16:1–23Google Scholar
- 194.Letelier JC, Soto-Andrade J, Abarzúa FG, Cornish-Bowden A, Cárdenas ML (2006) Organizational invariance and metabolic closure: analysis in terms of (m,r) systems. J Theor Biol 238(4):949–961PubMedGoogle Scholar
- 195.Arzi-Gonczarowski Z, Lehmann DJ (1998) From environments to representations: a mathematical theory of artificial perceptions. Artif Intell 102:187–247Google Scholar
- 196.Rashevsky N (1967) Organismic sets: outline of a general theory of biological and social organisms. Bull Math Biophys 29(1):139–152Google Scholar
- 197.Rashevsky N (1968) Organismic sets: II. Some general considerations. Bull Math Biophys 30(1):163–174Google Scholar
- 198.Healy M (2000) Category theory applied to neural modeling and graphical representations. In: Proceedings of IJCNN 2000, Como. IEEEGoogle Scholar
- 199.Neuman YN, Nave O (2008) A mathematical theory of sign-mediated concept formation. Appl Math Comput 201:72–81Google Scholar
- 200.Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:370–423Google Scholar
- 201.Tamarin RH (2002) Principles of genetics. McGraw-Hill, New YorkGoogle Scholar
- 202.Gomez J, Sanz R (2009) To cognize is to categorize revisited: category theory is where mathematics meets biology. AAAI fall symposium series, Washigton DC (Online)Google Scholar
- 203.Rosch E, Mervis CB (1975) Family resemblances: studies in the internal structure of categories. Cogn Psychol 7:573–605Google Scholar
- 204.Rosch E (1978) Cognition and categorization. Erlbaum, HillsdaleGoogle Scholar
- 205.Gómez-Ramirez J (2013) Naturalizing epistemology for autonomous systems. In: Talmont-Kaminski K, Milkowski M (eds) Regarding the mind, naturally: naturalist approaches to the sciences of the mental. Cambridge Scholars Publishing, Newcastle upon Tyne, pp 232–247Google Scholar
- 206.Philips S, Wilson WH (2010) Categorial compositionality: a category theory explanation for the systematicity of human cognition. PLoS Comput Biol 6(7):14Google Scholar
- 207.Dalton TC (2005) Challenging philosophical assumptions about mind. Trends Cogn Sci 9(8):365–366Google Scholar
- 208.Steels L (2006) Experiments on the emergence of human communication. Trends Cogn Sci 10(8):347–349PubMedGoogle Scholar
- 209.Ramus F (2006) Genes, brain, and cognition: a roadmap for the cognitive scientist. Cognition 101(2):247–269PubMedGoogle Scholar
- 210.Banerjee K, Bloom P (2013) Would Tarzan believe in God? Conditions for the emergence of religious belief. Trends Cogn Sci 17(1):7–8PubMedGoogle Scholar
- 211.Shiffrin RM (2010) Perspectives on modeling in cognitive science. Top Cogn Sci 2(4):736–750Google Scholar
- 212.Koblitz N (1988) A tale of three equations; or the emperors have no clothes. Math Intell 10(1):4–10Google Scholar
- 213.Huntington S (1968) Political order in changing societies. Yale University Press, New HavenGoogle Scholar
- 214.Brown J (1999) Philosophy of mathematics: an introduction to the world of proofs and pictures. Routledge, London/New YorkGoogle Scholar
- 215.Koblitz N (1981) Mathematics as propaganda. In: Steen DLA (ed) Mathematics tomorrow. Springer, New York, pp 111–120Google Scholar
- 216.Wille R, Wille U (1993) On the controversy over huntington’s equations: when are such equations meaningful? Math Soc Sci 25(2):173–180Google Scholar
- 217.Changeaux JP, Connes A (2000) Matière à pensée. Odile Jacob, ParisGoogle Scholar
- 218.Nagel E (1979) The structure of science: problems in the logic of scientific explanation. Hacket Publishing, IndianapolisGoogle Scholar
- 219.Bunge M (1969) La Investigación Científica. Ariel España, BarcelonaGoogle Scholar
- 220.Bunge M (2003) Emergence and convergence: qualitative novelty and the unity of knowledge. University of Toronto Press, TorontoGoogle Scholar
- 221.Bunge M (1979) Some topical problems in biophilosophy. J Soc Biol Syst 2(2):155–172Google Scholar
- 222.Ahn AC, Tewari M, Poon CS, Phillips RS (2006) The limits of reductionism in medicine: could systems biology offer an alternative? PLoS Med 3(6):e208PubMedGoogle Scholar
- 223.Gómez-Ramirez J, Wu J (2012) A new vision for biomedicine: a systems approach. In: 2012 ICME international conference on complex medical engineering (CME), Kobe, pp 479–484Google Scholar
- 224.Courant R, Robbins H, Stewart I (eds) (1996) What is mathematics? An elementary approach to ideas and methods. Oxford University Press, New YorkGoogle Scholar
- 225.Bohm D (2002) The essential David Bohm. Routledge, LondonGoogle Scholar
- 226.Dehaene E (2007) A few steps toward a science of mental life. Mind Brain Educ 1(1):28–47Google Scholar
- 227.Luce R (1995) Four tensions concerning mathematical modeling in psychology. Annu Rev Psychol 46:1–26PubMedGoogle Scholar
- 228.van Dalen D (1997) How connected is the intuitionistic continuum? J Symb Log 62(4):1147–1150Google Scholar
- 229.Fodor J (1983) The modularity of mind. MIT, CambridgeGoogle Scholar
- 230.Shannon CE, Weaver W (1949) The mathematical theory of communication, vol 27. University of Illinois Press, UrbanaGoogle Scholar
- 231.Kandel E (2000) Principles of neural science. McGraw-Hill, New YorkGoogle Scholar
- 232.Andersen P, Morris R, Amaral D, Bliss T, O’Keefe J (eds) (2006) The Hippocampus book, 1st edn. Oxford University Press, New YorkGoogle Scholar
- 233.Squire L, Berg D, Bloom FE, Lac Sd, Ghosh A, Spitzer NC (eds) (2012) Fundamental neuroscience, 4th edn. Academic, OxfordGoogle Scholar
- 234.Moore GP, Perkel DH, Segundo JP (1966) Statistical analysis and functional interpretation of neuronal spike data. Annu Rev Physiol 28(1):493–522. PMID: 5323104PubMedGoogle Scholar
- 235.Borst A, Theunissen FE (1999) Information theory and neural coding. Nat Neurosci 2(11):947–957PubMedGoogle Scholar
- 236.Rolls E (2007) Memory, attention, and decision-making: a unifying computational neuroscience approach, 1st edn. Oxford University Press, OxfordGoogle Scholar
- 237.Wang P (2007) Three fundamental misconceptions of artificial intelligence. J Exp Theor Artif Intell 19(3):249–268Google Scholar
- 238.Bays T (2012) Skolem’s paradox. In: Zalta EN (ed) The Stanford encyclopedia of philosophy, winter 2012. http://plato.stanford.edu/archives/win2012/entries/paradox-skolem/
- 239.Longo G (1997) Mathematical intelligence, infinity and machines: beyond the godelitis. J Conscious Stud 6:191–214Google Scholar
- 240.Dive LL (2003) An epistemic structuralist account of mathematical knowledge. PhD thesis, Department of Philosophy, Faculty of Arts, University of SydneyGoogle Scholar
- 241.Petitot J et al (1999) Naturalizing phenomenology: issues in contemporary phenomenology and cognitive science. Stanford University Press, StanfordGoogle Scholar
- 242.Arbib MA (1972) The metaphorical brain: introduction to cybernetics as artificial intelligence and brain theory, 1st edn. Wiley, New YorkGoogle Scholar
- 243.Pulvermüller F (1996) How and where are words represented and processed in the brain? In: International workshop on language, brain and verbal behavior: neurobiological aspects of linguistic capacities and language processing, Barcelona. Institut d’Estudis Catalans, pp 63–75Google Scholar
- 244.Feldman J (2008) From molecule to metaphor: a neural theory of language, 1st edn. A Bradford Book. The MIT Pess, Cambridge MAGoogle Scholar
- 245.Feldman J, Lakoff G, Bailey D, Narayanan S, Regier T, Stolcke A (1996) L0 – the first five years of an automated language acquisition project. Artif Intell Rev 10(1-2):103–129Google Scholar
- 246.Salthe S (2004) The spontaneous origin of new levels in a scalar hierarchy. Entropy 6:327–343Google Scholar
- 247.Salthe S (2009) A hierarchical framework for levels of reality: understanding through representation. Axiomathes (19):87–99Google Scholar
- 248.Baas N, Emmeche C (1997) On emergence and explanation. Intellectica (25):67–83Google Scholar
- 249.Putnam H (1981) Reason, truth and history. Cambridge University Press, CambridgeGoogle Scholar
- 250.Dummett M (2006) Thought and reality. Oxford University Press, New YorkGoogle Scholar
- 251.Holland J (1999) Emergence: from chaos to order. Basic Books, New YorkGoogle Scholar
- 252.Chalmers DJ (2007) Consciousness and its place in nature. In: Stich SP, Warfield TA (eds) The Blackwell guide to philosophy of mind. Blackwell, Malden, pp 102–142Google Scholar
- 253.Mack G (1996) Gauge theory of things alive: universal dynamics as a tool in parallel computing. Prog Theor Phys Suppl 122:201–212Google Scholar
- 254.Thom R (1988) Esquisse d’une sémiophysique. InterEditions, ParisGoogle Scholar
- 255.Mccarthy J, Hayes PJ (1969) Some philosophical problems from the standpoint of artificial intelligence. In: Michie D, Meltzer B (eds) Machine intelligence. Edinburgh University Press, Edinburgh, pp 463–502Google Scholar
- 256.Shanahan M (1997) Solving the frame problem: a mathematical investigation of the common sense law of inertia. MIT, CambridgeGoogle Scholar
- 257.Baianu IC et al (2007) Categorical ontology of complex spacetime structures: the emergence of life and human consciousness. Axiomathes (17):223–352Google Scholar
- 258.James W (1890) The principles of psychology. Henry Holt, New YorkGoogle Scholar
- 259.Rosen R (1985) Organisms as causal systems which are not mechanisms: an essay into the nature of complexity’. In: Rosen R (ed) Theoretical biology and complexity. Academic, Orlando, pp 165–203Google Scholar
- 260.Ehresmann AC, Vanbremeersch JP (2006) The memory evolutive systems as a model of Rosenâs organisms â (metabolic, replication) systems. Axiomathes 16(1–2):137–154Google Scholar
- 261.Pawlowitsch C (2008) Why evolution does not always lead to an optimal signaling system. Games Econ Behav 63:203–226Google Scholar
- 262.Wagner A (2007) Robustness and evolvability in living systems. Princeton University Press, Princeton/WoodstockGoogle Scholar
- 263.Alon U, Surette MG, Barkai N, Leibler S (1999) Robustness in bacterial chemotaxis. Nature 397(6715):168–171PubMedGoogle Scholar
- 264.Wagner A (2000) Robustness against mutations in genetic networks of yeast. Nat Genet 24(4):355–361. PMID: 10742097PubMedGoogle Scholar
- 265.Ay N, Krakauer DC (2007) Geometric robustness theory and biological networks. Theory Biosci (Theorie in den Biowissenschaften) 125:93–121Google Scholar
- 266.Tononi O Gand Sporns, Edelman G (1999) Measures of degeneracy and redundancy in biological networks. Proc Natl Acsd Sci 96(6):3257–3262Google Scholar
- 267.Holland JH (1999) Emergence: from chaos to order. Perseus Books, ReadingGoogle Scholar
- 268.Zee A (2007) Fearful symmetry: the search for beauty in modern physics. Princeton Science Library, PrincetonGoogle Scholar
- 269.Derrida J, Roudinesco E (2004) For what tomorrow: a dialogue. Stanford University Press, StanfordGoogle Scholar
- 270.Livingston E (1999) Cultures of proving. Soc Stud Sci 29(6):867–888Google Scholar
- 271.Miller GA (2007) Charge densities of the neutron and proton. Phys Rev Lett 99(11):112001PubMedGoogle Scholar
- 272.Elasser W (1958) The physical fundation of biology. Pergamon Press, LondonGoogle Scholar
- 273.Katz M (1986) Templets and complet patterns. Cambridge University Press, Cambridge MAGoogle Scholar
- 274.Arbib MA, Hesse MB (1986) The construction of reality. Cambridge University Press, Cambridge/New YorkGoogle Scholar
- 275.Corry L (2004) Modern algebra and the rise of mathematical structures, 2nd edn. Birkhauser, Basel/BostonGoogle Scholar
- 276.Shapiro S (1996) Space, number and structure: a tale of two debates. Philos Math 4(3):148–173Google Scholar
- 277.Skyttner L (2006) General systems theory: problems, perspectives, practice. World Scientific, SingaporeGoogle Scholar
- 278.Alon U (2006) An introduction to systems biology: design principles of biological circuits, 1st edn. Chapman and Hall/CRC, Boca Raton/LondonGoogle Scholar
- 279.Palsson BO (2006) Systems biology: properties of reconstructed networks, 1st edn. Cambridge University Press, Cambridge/New YorkGoogle Scholar
- 280.Mac Lane S (2006) Category theory as a framework for an in re interpretation of mathematical structuralism. Cah Topol Geom 21:163–179Google Scholar
- 281.Landry E (1998) Category theory: the language of mathematics. Philos Sci 66:14–27Google Scholar
- 282.Baez JC (1997) An introduction to n-categories. In: Moggi E, Rosolini G (eds) Category theory and computer science. No. 1290 in lecture notes in computer science. Springer, Berlin/Heidelberg, pp 1–33Google Scholar
- 283.Shapiro S (1996) Structure in mathematics and logic: a categorical perspective. Philos Math 4(4):209–237Google Scholar
- 284.Dragoi G, Tonegawa S (2011) Preplay of future place cell sequences by hippocampal cellular assemblies. Nature 469(7330):397–401PubMedGoogle Scholar
- 285.Goodrich R (1988) An agent-based conception of models and scientific representation. Br J Aesthet 28(1):48–58Google Scholar
- 286.Swoyer C (1991) Structural representation and surrogative reasoning. Synth 87(3):449–508Google Scholar
- 287.Teller P (2001) Twilight of the perfect model. Erkenntnis 55(3):393–415Google Scholar
- 288.Suarez M (2003) Scientific representation: against similarity and isomorphism. Int Stud Philos Sci 17(3):225–244Google Scholar
- 289.Carver C (2006) When mechanistic models explain. Synthese 153:355–376Google Scholar
- 290.Woodward J (2005) Making things happen: a theory of causal explanation. Oxford University Press, New York/OxfordGoogle Scholar
- 291.Giere RN (1990) Explaining science: a cognitive approach. University of Chicago Press, ChicagoGoogle Scholar
- 292.Giere RN (1999) Science without laws. University of Chicago Press, ChicagoGoogle Scholar
- 293.Giere R (2010) An agent-based conception of models and scientific representation. Synthese 172(2):269–281Google Scholar
- 294.Shapiro S (2000) Thinking about mathematics. Oxford University Press, New YorkGoogle Scholar
- 295.Shapiro S (2005) Oxford handbook of the philosophy of mathematics and logic. Oxford University Press, Oxford/New YorkGoogle Scholar
- 296.Birkhoff G, Mac Lane S (1946) A survey of modern algebra. Macmillan, New YorkGoogle Scholar
- 297.Geroch R (1985) Mathematical physics. University of Chicago Press, ChicagoGoogle Scholar
- 298.Bonsignorio F (2010) On the stochastic stability and observability of controlled serial kinematic chains. In: Proceedings of the ASME 2010 10th biennial conference on engineering systems design and analysis ESDA2010, TurkeyGoogle Scholar
- 299.von Helmholtz H (2005) Treatise on physiological optics. Dover, MineolaGoogle Scholar
- 300.Poincaré H (1952) Science and hypothesis. Dover, New YorkGoogle Scholar
- 301.Grant G (2007) How the 1906 Nobel Prize in physiology or medicine was shared between Golgi and Cajal. Brain Res Rev 55(2):490–498PubMedGoogle Scholar
- 302.Shepard RN, Chipman S (1970) Second-order isomorphism of internal representations: shapes of states. Cogn Psychol 1(1):1–17Google Scholar
- 303.Edelman S (1998) Representation is representation of similarities. Behav Brain Sci 21(4):449–467; discussion 467–498. PMID: 10097019Google Scholar
- 304.Churchland P (1986) Neurophilosophy toward a unified science of the mind-brain. MIT, CambridgeGoogle Scholar
- 305.Wiltschko W, Wiltschko R (1996) Collective dynamics of ‘small-world’ networks. J Exp Biol 199(1):29–38PubMedGoogle Scholar
- 306.Gray H, Standring S (2008) Gray’s anatomy: the anatomical basis of clinical practice, 40th edn. Churchill-Livingstone, ElsevierGoogle Scholar
- 307.Yildirim FB, Sarikcioglu L (2007) Marie Jean Pierre Flourens (1794–1867): an extraordinary scientist of his time. J Neurol Neurosurg Psychiatry 78(8):852. 17635978, PMCID: PMC2117745Google Scholar
- 308.York GK, Steinberg DA (2011) Hughlings Jackson’s neurological ideas. Brain 134(10):3106–3113. PMID: 21903729PubMedGoogle Scholar
- 309.Finger S (2001) Origins of neuroscience: a history of explorations into brain function. Oxford University Press, New YorkGoogle Scholar
- 310.Lashley K, Clark G (1946) The cytoarchitecture of the cerebral cortex of Ateles: a critical examination of the architectoic studies. J Comp Neurol 85:223–305PubMedGoogle Scholar
- 311.Wernicke C (1908) The symptom-complex of aphasia. Appleton, New YorkGoogle Scholar
- 312.Dykes RW, Ruest A (1986) What makes a map in somatosensory cortex? In: Jones EG, Peters A (eds) Sensory-motor areas and aspects of cortical connectivity. No. 5 in cerebral cortex, Springer, Boston, pp 1–29Google Scholar
- 313.Smith CUM (2008) Elementary units of cortical activity? The rise and fall of the cortical column. In: 12th annual meeting of the international society for the history of the neurosciences, Los AngelesGoogle Scholar
- 314.Mountcastle V (1997) The columnar organization of the cerebral cortex. Brain 120:701–722PubMedGoogle Scholar
- 315.Casanova MF (ed) (2005) Neocortical modularity and the cell minicolumn. Nova Biomedical Books, New YorkGoogle Scholar
- 316.Horton J, Adams D (2005) The cortical column: a structure without a function. Philos Trans R Soc B 360(1456):837–862Google Scholar
- 317.Blasdel G, Salama G (1986) Voltage-sensitive dyes reveal a modular organization in monkey striate cortex. Nature 321:579–585PubMedGoogle Scholar
- 318.Rakic P (1995) Radial versus tangential migration of neuronal clones in the developing cerebral cortex. Proc Natl Acad USA Sci 92(11):323–327Google Scholar
- 319.Rakic P (2000) Radial unit hypothesis of neocortical expansion. Novartis Found Symp 228:30–42; discussion 42–52. PMID: 10929315Google Scholar
- 320.Bressler S, Tognoli E (2006) Operational principles of neurocognitive networks. Int J Psychophysiol 60:139–148PubMedGoogle Scholar
- 321.Fuster J (2000) The module: crisis of a paradigm (book review, “the new cognitive neurosciences” 2nd edn, M.S. Gazzaniga, editor-in-chief, MIT Press). Neuron (26):51–53Google Scholar
- 322.Bechtel W (2001) The compatibility of complex systems and reduction: a case analysis of memory research. Minds Mach 11:83–502Google Scholar
- 323.Fiehn O (2001) Combining genomics, metabolome analysis, and biochemical modelling to understand metabolic networks. Comp Funct Genomics 2(3):155–168. PMID: 18628911PubMedGoogle Scholar
- 324.White J et al (1983) Factors that determine connectivity in the nervous system of Caenorhabditis elegans. Cold Spring Harb Symp Quant Biol 48(Pt 2):633–640PubMedGoogle Scholar
- 325.Smith J, Ellenberger H, Ballanyi K, Richter D, Feldman J (1991) Pre-Botzinger complex: a brainstem region that may generate respiratory rhythm in mammals. Science 254(5032):726–729PubMedGoogle Scholar
- 326.Horwitz B (2003) The elusive concept of brain connectivity. NeuroImage 19(2):466–470PubMedGoogle Scholar
- 327.Rodriguez P (2009) Neural decoding of goal locations in spatial navigation in humans with fMRI. Human Brain Mapp 31(3):3391–3397Google Scholar
- 328.Sharp D, Awad M, Warren J, Wise R, Vigliocco G, Scott S (2009) The neural response to changing semantic and perceptual complexity during language processing. Human Brain Mapp 31(3):365–377Google Scholar
- 329.Summerfield C, Egner T, Mangels J, Hirsch J (2006) Mistaking a house for a face: neural correlates of misperception in healthy humans. Cereb Cortex 16:500–508PubMedGoogle Scholar
- 330.Marian V, Shildkrot Y, Blumenfeld H, Kaushanskaya M, Faroqi-Shah Y, Hirsch J (1996) Cortical activation during word processing in late bilinguals: similarities and differences as revealed by functional magnetic resonance imaging. J Clin Exp Neuropsychol 29(3):247–265Google Scholar
- 331.Friston KJ (2009) Modalities, modes, and models in functional neuroimaging. Science 326(5951):399–403. PMID: 19833961PubMedGoogle Scholar
- 332.Friston KJ, Price CJ (2011) Modules and brain mapping. Cogn Neuropsychol 28(3–4): 241–250. PMID: 21416411, PMCID: PMC3335279Google Scholar
- 333.Muniz de Rezende A (1975) Le point de départ dans la philosophie de merleau-ponty. Revue Philosophique de Louvain 73(19):451–480Google Scholar
- 334.Bakker B (2005) The concept of circular causality should be discarded. Commentary on marc D. Lewis: Bridging emotion theory and neurobiology through dynamic system modeling. Behav Brain Sci 28:195–196Google Scholar
- 335.Granger CWJ (1969) Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37(3):424–38Google Scholar
- 336.Seth AK (2008) Causal networks in simulated neural systems. Cogn Neurodyn 2(1):49–64PubMedGoogle Scholar
- 337.Fuster JM (2005) Cortex and mind: unifying cognition, 1st edn. Oxford University Press, OxfordGoogle Scholar
- 338.Bressler SL (2007) The formation of global neurocognitive state. In: Perlovsky LI, Kozma R (eds) Neurodynamics of cognition and consciousness, understanding complex systems. Springer, Berlin/Heidelberg, pp 61–72Google Scholar
- 339.Freeman W (2000) Neurodynamics: an exploration in mesoscopic brain dynamics, 1st edn. Springer, London/New YorkGoogle Scholar
- 340.Goebel R, Linden DE, Lanfermann H, Zanella FE, Singer W (1998) Functional imaging of mirror and inverse reading reveals separate coactivated networks for oculomotion and spatial transformations. Neuroreport 9(4):713–719. PMID: 9559944PubMedGoogle Scholar
- 341.Cordes D, Haughton VM, Arfanakis K, Carew JD, Turski PA, Moritz CH, Quigley MA, Meyerand ME (2001) Frequencies contributing to functional connectivity in the cerebral cortex in “resting-state” data. AJNR Am J Neuroradiol 22(7):1326–1333. PMID: 11498421PubMedGoogle Scholar
- 342.Friston KJ, Frith CD, Liddle PF, Frackowiak RS (1993) Functional connectivity: the principal-component analysis of large (PET) data sets. J Cereb Blood Flow Metab 13(1):5–14. PMID: 8417010PubMedGoogle Scholar
- 343.Comon P (1994) Independent component analysis, a new concept? Signal Process 36(3):287–314Google Scholar
- 344.Bell AJ, Sejnowski TJ (1995) An information-maximization approach to blind separation and blind deconvolution. Neural Comput 7(6):1129–1159. PMID: 7584893PubMedGoogle Scholar
- 345.Hyvarinen A, Oja E (2000) Independent component analysis: algorithms and applications. Neural Netw 13(4-5):411–430. PMID: 10946390PubMedGoogle Scholar
- 346.Stone JV (2002) Independent component analysis: an introduction. Trends Cogn Sci 6(2):59–64PubMedGoogle Scholar
- 347.McKeown MJ, Hansen LK, Sejnowsk TJ (2003) Independent component analysis of functional MRI: what is signal and what is noise? Curr Opin Neurobiol 13(5):620–629. PMID: 14630228PubMedGoogle Scholar
- 348.van de Ven VG, Formisano E, Prvulovic D, Roeder CH, Linden DEJ (2004) Functional connectivity as revealed by spatial independent component analysis of fMRI measurements during rest. Human Brain Mapp 22(3):165–178. PMID: 15195284Google Scholar
- 349.Beckmann CF, DeLuca M, Devlin JT, Smith SM (2005) Investigations into resting-state connectivity using independent component analysis. Philos Trans R Soc Lond Ser B Biol Sci 360(1457):1001–1013. PMID: 16087444Google Scholar
- 350.Friston KJ (1998) Modes or models: a critique on independent component analysis for fMRI. Trends Cogn Sci 2(10):373–375PubMedGoogle Scholar
- 351.He Y, Evans A (2010) Graph theoretical modeling of brain connectivity. Curr Opin Neurol 23(4):341–350. PMID: 20581686PubMedGoogle Scholar
- 352.Erdös P, Rényi A (1960) On the evolution of random graphs. In: Publ Math Inst Hung Acad Sci 5:17–61Google Scholar
- 353.Schöner G, Kelso JA (1988) Dynamic pattern generation in behavioral and neural systems. Science (New York, NY) 239(4847):1513–1520. PMID: 3281253Google Scholar
- 354.Kelso JAS (1995) Dynamic patterns: the self-organization of brain and behavior [...] [...]. MIT, CambridgeGoogle Scholar
- 355.Kelso JAS (2012) Multistability and metastability: understanding dynamic coordination in the brain. Philos Trans R Soc B Biol Sci 367(1591):906–918. PMID: 22371613, PMCID: PMC3282307Google Scholar
- 356.Hartwell LH, Hopfield JJ, Leibler S, Murray AW (1999) From molecular to modular cell biology. Nature 402(6761 Suppl):C47–C52. PMID: 10591225PubMedGoogle Scholar
- 357.Ravasz E, Somera AL, Mongru DA, Oltvai ZN, Barabási AL (2002) Hierarchical organization of modularity in metabolic networks. Science 297(5586):1551–1555. PMID: 12202830PubMedGoogle Scholar
- 358.Humphries M, Gurney K, Prescott T (2006) The brainstem reticular formation is a small-world, not scale-free, network. Proc R Soc B Biol Sci 273(1585):503–511. PMID: 16615219, PMCID: PMC1560205Google Scholar
- 359.Vaessen MJ, Hofman PAM, Tijssen HN, Aldenkamp AP, Jansen JFA, Backes WH (2010) The effect and reproducibility of different clinical DTI gradient sets on small world brain connectivity measures. NeuroImage 51(3):1106–1116. PMID: 20226864PubMedGoogle Scholar
- 360.Honey CJ, Thivierge JP, Sporns O (2010) Can structure predict function in the human brain? NeuroImage 52(3):766–776. PMID: 20116438PubMedGoogle Scholar
- 361.Tononi G, Sporns O, Edelman GM (1994) A measure for brain complexity: relating functional segregation and integration in the nervous system. Proc Natl Acad Sci 91(11):5033–5037PubMedGoogle Scholar
- 362.Sporns O, Tononi G, Edelman GM (1991) Modeling perceptual grouping and figure-ground segregation by means of active reentrant connections. Proc Natl Acad Sci USA 88(1):129–133. PMID: 1986358PubMedGoogle Scholar
- 363.Srinivasan R, Russell DP, Edelman GM, Tononi G (1999) Increased synchronization of neuromagnetic responses during conscious perception. J Neurosci 19(13):5435–5448. PMID: 10377353PubMedGoogle Scholar
- 364.Varela F, Lachaux JP, Rodriguez E, Martinerie J (2001) The brainweb: phase synchronization and large-scale integration. Nat Rev Neurosci 2(4):229–239PubMedGoogle Scholar
- 365.Ermentrout B (1998) Neural networks as spatio-temporal pattern-forming systems. Rep Prog Phys 61(4):353Google Scholar
- 366.Achard S, Salvador R, Whitcher B, Suckling J, Bullmore E (2006) A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. J Neurosci 26(1):63–72. PMID: 16399673PubMedGoogle Scholar
- 367.Salvador R, Suckling J, Coleman MR, Pickard JD, Menon D, Bullmore E (2005) Neurophysiological architecture of functional magnetic resonance images of human brain. Cereb Cortex 15(9):1332–1342. PMID: 15635061PubMedGoogle Scholar
- 368.Salvador R, Anguera M, Gomar JJ, Bullmore ET, Pomarol-Clotet E (2010) Conditional mutual information maps as descriptors of net connectivity levels in the brain. Front Neuroinform 4:115PubMedGoogle Scholar
- 369.Barabasi AL, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509–512PubMedGoogle Scholar
- 370.Clauset A, Shalizi CR, Newman MEJ (2009) Power-law distributions in empirical data. SIAM Rev 51(4):661–703Google Scholar
- 371.Stumpf MPH, Porter MA (2012) Critical truths about power laws. Science 335(6069):665–666. PMID: 22323807PubMedGoogle Scholar
- 372.Wasserman S, Faust K (1994) Social network analysis: methods and applications. Cambridge University Press, Cambridge/New YorkGoogle Scholar
- 373.Latora V, Marchiori M (2001) Efficient behavior of small-world networks. Phys Rev Lett 87(19):198701PubMedGoogle Scholar
- 374.Supekar K, Musen M, Menon V (2009) Development of large-scale functional brain networks in children. PLoS Biol 7(7):e1000157PubMedGoogle Scholar
- 375.Travers J, Milgram S (1969) An experimental study of the small world problem. Sociometry 32(4):425Google Scholar
- 376.Albert R, Jeong H, Barabási AL (1999) Internet: diameter of the world-wide web. Nature 401(6749):130–131Google Scholar
- 377.Schmitt JE, Lenroot RK, Wallace GL, Ordaz S, Taylor KN, Kabani N, Greenstein D, Lerch JP, Kendler KS, Neale MC, Giedd JN (2008) Identification of genetically mediated cortical networks: a multivariate study of pediatric twins and siblings. Cereb Cortex (New York, NY: 1991) 18(8):1737–1747. PMID: 18234689Google Scholar
- 378.He Y, Chen ZJ, Evans AC (2007) Small-world anatomical networks in the human brain revealed by cortical thickness from MRI. Cereb Cortex (New York, NY: 1991) 17(10):2407–2419. PMID: 17204824Google Scholar
- 379.Watts DJ, Strogatz SH (1998) Collective dynamics of small-world networks. Nature 393(6684):440–442PubMedGoogle Scholar
- 380.Kleinberg JM (2000) Navigation in a small world. Nature 406(6798):845–845PubMedGoogle Scholar
- 381.Sporns O, Zwi JD (2004) The small world of the cerebral cortex. Neuroinformatics 2(2): 145–162. PMID: 15319512PubMedGoogle Scholar
- 382.Yu S, Huang D, Singer W, Nikolic D (2008) A small world of neuronal synchrony. Cereb Cortex (New York, NY: 1991) 18(12):2891–2901. PMID: 18400792Google Scholar
- 383.Bassett DS, Bullmore E (2006) Small-world brain networks. Neuroscientist 12(6):512–523PubMedGoogle Scholar
- 384.Supekar K, Menon V, Rubin D, Musen M, Greicius MD (2008) Network analysis of intrinsic functional brain connectivity in Alzheimer’s disease. PLoS Comput Biol 4(6):e1000100. PMID: 18584043, PMCID: PMC2435273Google Scholar
- 385.Liu Y, Liang M, Zhou Y, He Y, Hao Y, Song M, Yu C, Liu H, Liu Z, Jiang T (2008) Disrupted small-world networks in schizophrenia. Brain J Neurol 131(Pt 4):945–961. PMID: 18299296Google Scholar
- 386.Liao W, Zhang Z, Pan Z, Mantini D, Ding J, Duan X, Luo C, Lu G, Chen H (2010) Altered functional connectivity and small-world in mesial temporal lobe epilepsy. PLoS ONE 5(1):e8525PubMedGoogle Scholar
- 387.Costa LF, Rodrigues F, Travieso G, Boas V (2006) Characterization of complex networks: a survey of measurements. Adv Phys 56(1):167–242Google Scholar
- 388.Costa LF, Silva FN (2006) Hierarchical characterization of complex networks. J Stat Phys 125(4):841–872Google Scholar
- 389.Whitacre J, Bender A (2010) Degeneracy: a design principle for achieving robustness and evolvability. J Theor Biol 263(1):143–153. PMID: 19925810PubMedGoogle Scholar
- 390.Stevens AA, Tappon SC, Garg A, Fair DA (2012) Functional brain network modularity captures inter- and intra-individual variation in working memory capacity. PLoS ONE 7(1):e30468PubMedGoogle Scholar
- 391.Bullmore E, Sporns O (2012) The economy of brain network organization. Nat Rev Neurosci 13(5):336–349PubMedGoogle Scholar
- 392.Bullmore E, Sporns O (2009) Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 10(3):186–198. PMID: 19190637PubMedGoogle Scholar
- 393.Vaessen MJ, Hofman PAM, Tijssen HN, Aldenkamp AP, Jansen JFA, Backes WH (2010) The effect and reproducibility of different clinical DTI gradient sets on small world brain connectivity measures. NeuroImage 51(3):1106–1116. PMID: 20226864PubMedGoogle Scholar
- 394.Deuker L, Bullmore ET, Smith M, Christensen S, Nathan PJ, Rockstroh B, Bassett DS (2009) Reproducibility of graph metrics of human brain functional networks. NeuroImage 47(4):1460–1468. PMID: 19463959PubMedGoogle Scholar
- 395.Hayasaka S, Laurienti PJ (2010) Comparison of characteristics between region-and voxel-based network analyses in resting-state fMRI data. NeuroImage 50(2):499–508. PMID: 20026219PubMedGoogle Scholar
- 396.Kaiser M, Martin R, Andras P, Young MP (2007) Simulation of robustness against lesions of cortical networks. Eur J Neurosci 25(10):3185–3192.PubMedGoogle Scholar
- 397.Seeley WW, Crawford RK, Zhou J, Miller BL, Greicius MD (2009) Neurodegenerative diseases target large-scale human brain networks. Neuron 62(1):42–52. PMID: 19376066PubMedGoogle Scholar
- 398.Sanz-Arigita EJ, Schoonheim MM, Damoiseaux JS, Rombouts SARB, Maris E, Barkhof F, Scheltens P, Stam CJ (2010) Loss of ‘small-world’ networks in Alzheimer’s disease: graph analysis of FMRI resting-state functional connectivity. PloS One 5(11):e13788. PMID: 21072180PubMedGoogle Scholar
- 399.Sporns O, Kötter R (2004) Motifs in brain networks. PLoS Biol 2(11):e369PubMedGoogle Scholar
- 400.Alon U (2007) Network motifs: theory and experimental approaches. Nat Rev Genet 8(6):450–461PubMedGoogle Scholar
- 401.Cook SA (1971) The complexity of theorem-proving procedures. In: Proceedings of the third annual ACM symposium on theory of computing, STOC’71, Shaker Heights. ACM, New York, pp 151–158Google Scholar
- 402.Hagmann P, Cammoun L, Gigandet X, Meuli R, Honey CJ, Wedeen VJ, Sporns O (2008) Mapping the structural core of human cerebral cortex. PLoS Biol 6:e159PubMedGoogle Scholar
- 403.Artzy-Randrup Y, Fleishman SJ, Ben-Tal N, Stone L (2004) Comment on network motifs: simple building blocks of complex networks and superfamilies of evolved and designed networks. Science 305(5687):1107–1107. PMID: 15326338PubMedGoogle Scholar
- 404.Ingram PJ, Stumpf MP, Stark J (2006) Network motifs: structure does not determine function. BMC Genomics 7(1):108. PMID: 16677373PubMedGoogle Scholar
- 405.Knabe JF, Nehaniv CL, Schilstra MJ (2008) Do motifs reflect evolved function?–no convergent evolution of genetic regulatory network subgraph topologies. Bio Syst 94(1-2):68–74. PMID: 18611431Google Scholar
- 406.Hell P, Nesetril J (2004) Graphs and homomorphisms. Oxford University Press, Oxford/New YorkGoogle Scholar
- 407.Widom B, Rowlinson JS (1970) New model for the study of Liquid-Vapor phase transitions. J Chem Phys 52(4):1670–1684Google Scholar
- 408.Dyer M, Greenhill C (1999) The complexity of counting graph homomorphisms. In: 11th ACM/SIAM symposium on discrete algorithms. Press, San Francisco, pp 246–255Google Scholar
- 409.Strogatz SH (2001) Exploring complex networks. Nature 410(6825):268–276PubMedGoogle Scholar
- 410.Newman MEJ (2000) Models of the small world. J Stat Phys 101(3-4):819–841Google Scholar
- 411.Ehresmann A (1997) Colimits in free categories. Diagrammes 37:3–12Google Scholar
- 412.Mahalanobis PC (1936) On the generalised distance in statistics. Proc Natl Inst Sci India 2(1):49–55. Retrieved 2012-05-03Google Scholar
- 413.Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci 99(12):7821–7826. PMID: 12060727PubMedGoogle Scholar
- 414.Newman MEJ (2006) Modularity and community structure in networks. Proc Natl Acad Sci 103(23):8577–8582. PMID: 16723398PubMedGoogle Scholar
- 415.Onnela JP, Saramäki J, Kertész J, Kaski K (2005) Intensity and coherence of motifs in weighted complex networks. Phys Rev E Stat Nonlinear Soft Matter Phys 71(6 Pt 2):065103. PMID: 16089800Google Scholar
- 416.Song C, Havlin S, Makse HA (2005) Self-similarity of complex networks. Nature 433(7024):392–395PubMedGoogle Scholar
- 417.Kant I, Weigelt M, Müller FM (2007) Critique of pure reason. Penguin, London/New YorkGoogle Scholar
- 418.Polger T (1949) Philosophy of mathematics and natural science. Princeton University Press, PrincetonGoogle Scholar
- 419.Hull CL (1952) A behaviour system: an introduction to behavior theory concerning the individual organism. Yale University Press, New HavenGoogle Scholar
- 420.O’Keefe J, Nadel L (1978) The hippocampus as a cognitive map. Oxford University Press, New YorkGoogle Scholar
- 421.O’Keefe J, Dostrovsky J (1971) The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat. Brain Res 34(1):171–175. PMID: 5124915Google Scholar
- 422.Milford MJ (2008) Robot navigation from nature. Springer, BerlinGoogle Scholar
- 423.Redish A (2001) The hippocampal debate: are we asking the right questions? Behav Brain Res 127(935):81–98PubMedGoogle Scholar
- 424.Tolman E (1948) Cognitive maps in rats and men. Psychol Rev 55(4):189–208PubMedGoogle Scholar
- 425.Muller R, Kubie J, Ranck J (1987) Spatial firing patterns of hippocampal complex-spike cells in a fixed environment. J Neurosci 7:1935–1950PubMedGoogle Scholar
- 426.Fyhn M, Molden S, Witter M, Moser E, Moser MB (2004) Spatial representation in the entorhinal cortex. Science 305:1258–1264PubMedGoogle Scholar
- 427.Hafting T, Fyhn M, Molden S, Moser MB, Moser E (2005) Microstructure of a spatial map in the entorhinal cortex. Nature 436:801–806PubMedGoogle Scholar
- 428.Moser E, Kropff E, Moser M (2008) Place cells, grid cells, and the brain’s spatial representation system. Annu Rev Neurosci 31:69–89PubMedGoogle Scholar
- 429.Solstad T, Moser E, Einevoll G (2006) From grid cells to place cells: a mathematical model. Hippocampus 16:1026–1031PubMedGoogle Scholar
- 430.Zilli E, Yoshida M, Tahvildari B, Giocomo L, Hasselmo M (2009) Evaluation of the oscillatory interference model of grid cell firing through analysis and measured period variance of some biological oscillator. PLoS Comput Biol 5(11):e1000573PubMedGoogle Scholar
- 431.Ranck J (1984) Head-direction cells in the deep cell layers of dorsal presubiculum in freely moving rats. Soc Neurosci Abstr 10:599Google Scholar
- 432.Taube JS (1995) Head direction cells recorded in the anterior thalamic nuclei of freely moving rats. J Neurosci 15(1):70–86. PMID: 7823153PubMedGoogle Scholar
- 433.Mizumori SJ, Williams JD (1993) Directionally selective mnemonic properties of neurons in the lateral dorsal nucleus of the thalamus of rats. J Neurosci 13(9):4015–4028. PMID: 8366357PubMedGoogle Scholar
- 434.Wiener SI (1993) Spatial and behavioral correlates of striatal neurons in rats performing a self-initiated navigation task. J Neurosci 13(9):3802–3817. PMID: 8366346PubMedGoogle Scholar
- 435.O’Keefe J (1991) An allocentric spatial model for the hippocampal cognitive map. Hippocampus 1(3):230–235. PMID: 1669295PubMedGoogle Scholar
- 436.McNaughton BL, Barnes CA, Gerrard JL, Gothard K, Jung MW, Knierim JJ, Kudrimoti H, Qin Y, Skaggs WE, Suster M, Weaver KL (1996) Deciphering the hippocampal polyglot: the hippocampus as a path integration system. J Exp Biol 199(Pt 1):173–185. PMID: 8576689PubMedGoogle Scholar
- 437.Eichenbaum H (2002) The cognitive neuroscience of memory: an introduction. Oxford University Press, Oxford/New YorkGoogle Scholar
- 438.Adámek J, Gumm HP, Trnková V (2009) Presentation of set functors: a coalgebraic perspective. J Log Comput, 20(5), 991–1015Google Scholar
- 439.Touretzky D, Redish A (1996) Theory of rodent navigation based on interacting representations of space. Hippocampus 6(3):247–270PubMedGoogle Scholar
- 440.Burgess N, Recce M, O’Keefe J (1994) A model of hippocampal function. Neural Netw 7:1065–1081Google Scholar
- 441.Arleo A, Gerstner W (2000) Spatial cognition and neuro-mimetic navigation: a model of hippocampal place cell activity. Biol Cybern 83:287–299PubMedGoogle Scholar
- 442.Jung M, Wiener S, McNaughton B (1994) Comparison of spatial firing characteristics of units in dorsal and ventral hippocampus of the rat. J Neurosci 14:7347–56PubMedGoogle Scholar
- 443.Kjelstrup K et al (2007) Very large place fields at the ventral pole of the hippocampal CA3 area. Soc Neurosci Abstr 33(93):1Google Scholar
- 444.Wilson RA, Keil FC (eds) (1999) The MIT encyclopedia of the cognitive sciences. MIT, CambridgeGoogle Scholar
- 445.Scoville W, Milner B (1957) Loss of recent memory after bilateral hippocampal lesions. J Neurol Neurosurg Psychiatry 20:11–21PubMedGoogle Scholar
- 446.Jones EG, Mendell LM (1999) Assessing the decade of the brain. Science (New York, NY) 284(5415):739. PMID: 10336393Google Scholar
- 447.Raichle ME (2010) Two views of brain function. Trends Cogn Sci 14(4):180–190. PMID: 20206576PubMedGoogle Scholar
- 448.Cohen MA, Grossberg S (1987) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. In: Grossberg S (ed) Advances in psychology, vol 42. North-Holland, Amsterdam, pp 288–308Google Scholar