Skip to main content
SpringerLink
Log in

Tensorial Brain Theory in Cerebellar Modelling

  • Conference paper
Cerebellar Functions

Part of the book series: Proceedings in Life Sciences ((LIFE SCIENCES))

Abstract

For the last century and a half, the cerebellum (CB) has been known as the part of the brain that performs the most lucid global function: motor coordination (cf. classical treatises by Flourens, 1842; Sherrington, 1906; Holmes, 1939: Dow and Moruzzi, 1958; or recent review in Towe and Luschei, 1981). Experimentalists have also been enticed by the ”crystalline” elegance of the microarchitecture of this remarkable neuronal circuitry (cf. pioneering studies by Purkinje, 1837; Golgi, 1874; Ramon y Cajal, 1911; and modern analyses by Palkovits et al., 1972; Oscarsson, 1973; Palay and ChanPalay, 1974; Voogd and Bigare, 1980; and Hillman this volume). As a result, the CB has been studied by now in more detail than virtually any other part of the brain (cf. reviews in Eccles et al., 1967; Llinás, 1969a, 1981; Palay and Chan-Palay, 1982). Based on these pillars of general and detailed knowledge, attempts have also been made to erect a structure in order to show how knowledge of the functioning may be built into an understanding of neural function (cf. reviews in Szentagothai, 1968; Pellionisz, 1979a; Llinás and Simpson, 1981; Ito, 1984). Such understanding may ultimately be utilized in medicine (Mann, 1981; Dichgans this volume, Gilman this volume), as well as in novel applications, eg. in the construction of brain-like machines (Albus, 1981; Marr, 1982; Loeb, 1983; Pellionisz, 1983b).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Albert A (1972) Regression and the Moore-Penrose pseudoinverse. Academic Press, London New York

    Google Scholar 

  • Albus J (1971) A theory of cerebellar function. Math Biosci 10: 25–61

    Article  Google Scholar 

  • Albus JR (1981) Brains, behavior and robotics. McGraw-Hill, New York

    Google Scholar 

  • Anderson JA, Silverstein JW, Ritz SA, Randall JA (1977) Distinctive features, categorical percep- tion and probability learning: Some applications of a neural model. Psychol Rev 84: 413451

    Google Scholar 

  • Arbib MA, Boylls CC, Dev P (1974) Neural models of spatial perception and the control of movement. In: Keidel WD, Handler W, Spreng M (eds) Cybernetics and bionics. Oldenbourg, Munich, pp 216–231

    Google Scholar 

  • Armstrong DM (1974) Functional significance of connections of the inferior olive. Physiol Rev 54: 358–417

    PubMed  CAS  Google Scholar 

  • Bell CC, Grimm RJ (1969) Discharge properties of Purkinje cells recorded on single and double microelectrodes. J Neurophysiol 32: 1044–1055

    PubMed  CAS  Google Scholar 

  • Ben-Israel A, Greville THE (1980) Generalised inverses: theory and applications. Krieger Publ, New York

    Google Scholar 

  • Bernstein NA (1947) 0 Postroyenii Dvizheniy (On the construction of movements). Medgiz., Moscow (English translation: The coordination and regulation of movements. Pergamon, New York 1967 )

    Google Scholar 

  • Berthoz A, Llinás R (1974) Afferent neck projection to the cat cerebellar cortex Exp Brain Res 20: 385–401

    CAS  Google Scholar 

  • Bloedel JR, Ebner TJ, Qi-Xiang Yu (1983) Increased responsiveness of Purkinje cell associated with climbing fiber inputs to neighboring neurons. J Neurophysiol 50: 220–239

    PubMed  CAS  Google Scholar 

  • Bower J, Llinás R (1982) Simultaneous sampling and analysis of the activity of multiple, closely adjacent, cerebellar Purkinje cells. Soc Neurosci Abstr 8: 830

    Google Scholar 

  • Boylls CC Jr (1974) A theory of cerebellar function with applications to locomotion. PhD Thes, Stanford Univ

    Google Scholar 

  • Boylls CC Jr (1982) Climbing fibers and the spatial reference frame for motor coordination. In: Proceedings of the workshop on visuomotor coordination in frog and toad: Models and experiments. COINS Tech Rep 82–16. Univ Mass, Amherst, pp 2–23.

    Google Scholar 

  • Braitenberg V (1967) Is the cerebellar cortex a biological clock in the millisecond range? In: Fox CA, Snider RS (eds) Progress in brain research, vol 25. The cerebellum. Elsevier, Amsterdam, pp 334–346

    Google Scholar 

  • Braitenberg V, Atwood RP (1958) Morphological observations in the cerebellar cortex. J Comp Neurol 109: 1–34

    Article  PubMed  CAS  Google Scholar 

  • Brindley GS (1964) The use made by the cerebellum of the information that it receives from sense organs. IBRO Bull 3: 80

    Google Scholar 

  • Calvert TW, Meno F (1972) Neural systems modelling applied to the cerebellum. IEEE Trans., vol SMC-2(3):363–374

    Google Scholar 

  • Coburn N (1970) Vector and tensor analysis. Dover, New York

    Google Scholar 

  • Crick FHC (1979) Thinking about the brain. Sci 241: 219–232

    CAS  Google Scholar 

  • Demer JL, Robinson DA (1982) Effects of reversible lesions and stimulation of olivocerebellar system on vestibuloocular reflex plasticity. J Neurophysiol 47: 1084–1107

    PubMed  CAS  Google Scholar 

  • Dow RS (1970) Historical review of cerebellar investigation. In: Fields WS, Willis WD (eds) The cerebellum in health and disease, chap 1. Hilger, London, pp 5–38

    Google Scholar 

  • Dow RS, Moruzzi G (1958) The physiology and pathology of the cerebellum. Univ Minnesota Press, Minneapolis

    Google Scholar 

  • Dowling JE (1979) Information processing by local circuits: The vertebrate retina as a model system. In: Schmitt FO, Worden FG (eds) The neurosciences, IV study program. MIT Press, Cambridge, pp 163–182

    Google Scholar 

  • Dunin-Barkovsky VL (1978) Information processing in neuronal structures. Nauka, Moscow (in Russian)

    Google Scholar 

  • Ebner TJ, Qi-Xiang Yu, Bloedel JR (1983) Increase in Purkinje cell gain associated with naturally activated climbing fiber input. J Neurophysiol 50: 205–219

    PubMed  CAS  Google Scholar 

  • Eccles JC (1969) The dynamic loop hypothesis of movement control. In: Leibovic KN (ed) Information processing in the central nervous system. Springer Berlin Heidelberg New York, pp 245–269

    Google Scholar 

  • Eccles JC (1973) The cerebellum as a computer: Patterns in space and time. J Physiol 229: 1–32

    PubMed  CAS  Google Scholar 

  • Eccles JC (1982) The modular operation of the cerebral neocortex considered as the material basis of mental events. Neuroscience 6: 1839–1856

    Article  Google Scholar 

  • Eccles JC, Ito M, Szentágothai J (1967) The cerebellum as a neuronal machine. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Edelmann GM (1979) Group selection and phasic reentrant signaling: A theory of higher brain function. In: Schmitt FO, Worden FG (eds) The neurosciences vol, IV: study program. MIT Press, Cambridge, pp 1115–1139

    Google Scholar 

  • Einstein A (orig. 1916 ) The foundation of the general theory of relativity. In: Sommerfeld A (ed) The principle of relativity. ( 1952 ) Dover, New York, pp 111–164

    Google Scholar 

  • Ferin M, Grigorian RA, Strata P (1971) Mossy and climbing fiber activation in the cat cerebellum by stimulation of the labyrinth. Exp Brain Res 12: 1–17

    Article  PubMed  CAS  Google Scholar 

  • Flourens P (1842) Recherches experimentales sur les proprietes et les fonctions du systeme nerveux dans les animaux vertebres, 2nd edn. Bailliere

    Google Scholar 

  • Freeman JA (1969) The cerebellum as a timing device: An experimental study in the frog. In: Llinás R (ed) Neurobiology of cerebellar evolution and development. Am Med Assoc (Chicago) pp 397–420

    Google Scholar 

  • Fujita M (1982) Adaptive filter model of the cerebellum. Biol Cybernet 45: 195–206

    Article  CAS  Google Scholar 

  • Gelfand IM, Gurfinkel VS, Fomin SV, Tsetlin ML (1971) Models of the structural-functional organization of certain biological systems. MIT Press, Cambridge

    Google Scholar 

  • Gilbert PFC (1974) A theory of memory that explains the function and structure of the cerebellum. Brain Res 70: 1–18

    Article  PubMed  CAS  Google Scholar 

  • Gilbert PFC, Thatch WT (1977) Purkinje cell activity during motor learning. Brain Res 128: 309–328

    Article  PubMed  CAS  Google Scholar 

  • Goldberg J, Baker J, Hermann G, Peterson B (1983) Spatio-temporal convergence onto second order vestibular neurons. Abstr Soc Neurosci 9: 316

    Google Scholar 

  • Golgi C (1874) Sulla fine anatomia del cervelletto umano. Arch Ital Mal Nerv 1: 90–107

    Google Scholar 

  • Gonshor A, Melvill-Jones G (1973) Changes of human vestibulo-ocular response induced by vision-reversal during head rotation. J Physiol 234: 102–103

    Google Scholar 

  • Greene PH (1972) Problems of organization of motor system In: Rosen R, Snell FM (eds) Progr Theor Biol, vol II. Academic Press, London New York, pp 303–338

    Google Scholar 

  • Grossberg S (1969) On learning of spatiotemporal patterns by networks with ordered sensory and motor components. 1. Excitatory components of the cerebellum. Studies Appl Math 48: 105–132

    Google Scholar 

  • Hámori J, Szentágothai J (1966) Identification under the electron microscope of climbing fiber and their synaptic contacts. Exp Brain Res 1: 65–81

    Article  PubMed  Google Scholar 

  • Hebb DO (1949) The organization of behaviour. John Wiley, New York

    Google Scholar 

  • Hillman DE (1969) Neuronal organization of the cerebellar cortex in amphibia and reptilia. In: Llinás R (ed) Neurobiology of cerebellar evolution and development, Am Med Assoc (Chicago) pp 279–325

    Google Scholar 

  • Hillman DE (1979) Neuronal shape parameters and substructures as a basis of neuronal form. In: Schmitt FO, Worden FG (eds) The neurosciences, IVth study program. MIT Press, Cambridge, pp 477–499

    Google Scholar 

  • Holmes G (1939) The cerebellum in man. Brain 63: 1

    Article  Google Scholar 

  • Houk JC (1980) Principles of system theory as applied to physiology: systems and models. In: Mountcastle VB (ed) Medical physiology, 14th edn, chapt 7. Mosby, St. Louis

    Google Scholar 

  • Hubel DH, Wiesel T (1962) Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. J Physiol 160: 106–154

    PubMed  CAS  Google Scholar 

  • Ingle D, Sprague JM (1975) Sensorimotor function of the midbrain tectum. Neurosci Res Progr Bull 13 (2)

    Google Scholar 

  • Ito M (1970) Neurophysiological aspects of the cerebellar motor control system. Int J Neurol 7: 162–176

    PubMed  CAS  Google Scholar 

  • Ito M (1974) The control mechanism of cerebellar motor system. In: Schmitt FO, Worden FG (eds) The neurosciences, IIIrd study program. MIT Press, Cambridge, pp 293–303

    Google Scholar 

  • Ito M (1980) Experimental tests of constructive models of the cerebellum. In: Szkely G, Labos E, Damjanovich S (eds) Neural communication and control. Adv Physiol Sci, vol 30. Pergamon Press & Akadémiai Kiadô, New York

    Google Scholar 

  • Ito M (1984) The cerebellum and neural control. Raven Press, New York

    Google Scholar 

  • Ito M, Yoshida M, Obata K, Kawai N, Udo M (1970) Inhibitory control of intracerebellar nuclei by the Purkinje cell axons. Exp Brain Res 10: 64–80

    Article  PubMed  CAS  Google Scholar 

  • Ito M, Sakurai M, Tongroach P (1982) Climbing fibre induced depression of both mossy fibre responsiveness and glutamate sensitivity of cerebellar Purkinje cells. J Physiol 324: 113–134

    PubMed  CAS  Google Scholar 

  • Kohonen T (1977) Associative memory. A system-theoretical approach. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Kornhuber HH (1971) Motor functions of cerebellum and basal ganglia: the cerebello-cortical saccadic (ballistic) clock, the cerebello-nuclear hold regulator, and the basal ganglia ramp (voluntary speed smooth movement) generator. Kybernetik 8: 157–162

    Article  PubMed  CAS  Google Scholar 

  • Lashley KS (1942) The problem of cerebral organization in vision. In: Kluever H (ed) Visual mechanisms. Biol Symp, vol VII. Jacques Cattel Press, Lancaster, pp 301–322

    Google Scholar 

  • Levi-Civita T (1926) The absolute differential calculus (calculus of tensors) In: Persico E (ed) Dover, New York

    Google Scholar 

  • Lisberger SG, Fuchs AF (1978) Role of primate flocculus during rapid behavioral modification of vestibuloocular reflex. I. Purkinje cell acting during visually guided horizontal smooth-pursuit eye movements and passive head rotation. J Neurophysiol 41: 733–763

    Google Scholar 

  • Llinás R (ed) (1969a) Neurobiology of cerebellar evolution and development, Am Med Assoc (Chicago)

    Google Scholar 

  • Llinás R (1969b) Functional aspects of interneuronal evolution in the cerebellar cortex. In: Brazier

    Google Scholar 

  • MAB (ed) The interneuron. UCLA Forum Med, vol XI. Univ Cal Press, Los Angeles, pp 329–347

    Google Scholar 

  • Llinás R (1970) Neuronal operations in cerebellar transactions. In: Schmitt FO, Worden FG (eds) The neurosciences, Iind study program. MIT Press, Cambridge, pp 409–426

    Google Scholar 

  • Llinás R (1974)18th Bowditch Lecture: Motor aspects of cerebellar control. Physiologist 17:1946

    Google Scholar 

  • Llinás R (1979) The role of calcium in neuronal function. In: Schmitt FO, Worden FG (eds) The neurociences, IVth study program. MIT Press, Cambridge, pp 555–571

    Google Scholar 

  • Llinás R (1981) Electrophysiology of the cerebellum. In: Brooks VB (ed) Handbook of physiology, vol II. The nervous system, part II. Am Physiol Soc (Bethesda), pp 831–976

    Google Scholar 

  • Llinás R (1983) Possible role of tremor in the organization of the nervous system. In: Capildeo Findlay, Int Neurol Symp Tremor, MacMillan, New York (in press)

    Google Scholar 

  • Llinás R, Pellionisz A (1984) Cerebellar function and the adaptive feature of the central nervous system. In: Berthoz A, Melvill-Jones G (eds) Reviews of oculomotor research, vol I. Adaptive mechanisms in gaze control. Elsevier, Amsterdam

    Google Scholar 

  • Llinás R, Simpson JI (1981) Cerebellar control of movement. In: Towe AL, Luschei ES (eds) Handbook of behavioral neurobiology, vol V. Motor coordination. Plenum Press, New York, pp 231–302

    Google Scholar 

  • Llinás R, Volkind R (1973) The olivo-cerebellar system: Functional properties as revealed by harmaline-induced tremor. Exp Brain Res 18: 69–87

    Google Scholar 

  • Llinás R, Yarom Y (1981a) Electrophysiology of mammalian inferior olivary neurones in vitro.Different types of voltage-dependent ionic conductances. J Physiol 315: 549–567

    PubMed  Google Scholar 

  • Llinás R, Yarom Y (1981b) Properties and distribution of ionic conductances generating electro-responsiveness of mammalian inferior olivary neurones in vitro. J Physiol 315: 569–584

    PubMed  Google Scholar 

  • Llinás R, Precht w, Clarke M (1971) Cerebellar Purkinje cell responses to physiological stimulation of the vestibular system in the frog. Exp Brain Res 13: 408–431

    Google Scholar 

  • Llinás R, Walton K, Hillman DE, Sotelo C (1975) Inferior olive: Its role in motor learning. Science 190: 1230–1231

    Google Scholar 

  • Llinás R, Yarom Y, Sugimori M (1981) The isolated mammalian brain in vitro: A new technique for the analysis of the electrical activity of neuronal circuit function. Fed Proc 40: 2240–2245

    Google Scholar 

  • Loeb GE (1983) Finding common ground between robotics and physiology. Trends Neurosci 6: 203–204

    Article  Google Scholar 

  • Maekawa K, Simpson JI (1973) Climbing fiber responses evoked in vestibulo-cerebellum of rabbit from visual system. J Neurophys 36: 649–666

    CAS  Google Scholar 

  • Magendie F (1825) Precis elementaire de physiologie. Meguiguon-Marvis ( Paris ): I-II.

    Google Scholar 

  • Maisburg von C, Cowan JD (1982) Outline of a theory for the ontogenesis of iso-orientation domains in visual cortex. Biol Cybernet 45: 49–56

    Article  Google Scholar 

  • Mann RW (1981) Cybernetic limb prosthesis. Ann Biomed Eng 9: 1–43

    Article  Google Scholar 

  • Marr D (1969) A theory of cerebellar cortex. J Physiol 202: 437–470

    PubMed  CAS  Google Scholar 

  • Marr D (1982) Vision. A computational investigation into the human representation and processing of visual information. Freeman, San Francisco

    Google Scholar 

  • Miles FA (1980) Information processing at the cellular and systems levels in complex systems. Raven Press, New York

    Google Scholar 

  • Mortimer JA (1970) A cellular model for mammalian cerebellar cortex. Tech Rep. Univ. Mich, Ann Arbor

    Google Scholar 

  • Mountcastle V (1979) An organizing principle for cerebral function: The unit module and distributed system. In: Schmitt FO, Worden FG (eds) The neurosciences, IVth study program. MIT Press, Cambridge, pp 21–42

    Google Scholar 

  • Nering ED (1963) Linear algebra and matrix theory. John Wiley, New York

    Google Scholar 

  • Orbeli LA (1940) New notions on cerebellar functions. Usp Sovrem Biol 13: 207–220

    Google Scholar 

  • Oscarsson 0 (1969) The sagittal organization of the cerebellar anterior lobe as revealed by the projection patterns of the climbing fiber system. In: Llinás R (ed) Neurobiology of cerebellar evo-lution and development. Am Med Assoc (Chicago), pp 525–537

    Google Scholar 

  • Oscarsson 0 (1973) Functional organization of spinocerebellar paths. In: Iggo A (ed) Handbook of sensory physiology, vol II, Springer, Berlin Heidelberg New York, pp 320–328

    Google Scholar 

  • Palay SL, Chan-Palay V (1974) Cerebellar cortex: cytology and organization. Springer, Berlin Heidelberg New York

    Book  Google Scholar 

  • Palay SL, Chan-Palay V (eds) (1982) The cerebellum: New vistas. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Palkovits M, Magyar P, Szentágothai J (1972) Quantitative histological analysis of the cerebellar cortex in the cat: IV. Mossy fiber-Purkinje cell numerical transfer. Brain Res 45: 15–29

    Google Scholar 

  • Pellionisz A (1970) Computer simulation of the pattern transfer of large cerebellar neuronal fields. Acta Biochim Biophys Acad Sci Hung 5: 71–79

    PubMed  CAS  Google Scholar 

  • Pellionisz A (1976) Proposal for shaping the dynamism of Purkinje cells by climbing fiber activation. Brain Theor Newslett 2: 2–6

    Google Scholar 

  • Pellionisz A (1979a) Cerebellar control theory. In: Lissk K (ed) Recent developments of neurobiology in Hungary, vol VIII. Akadémiai Kiadb, Budapest, pp 211–243

    Google Scholar 

  • Pellionisz A (1979b) Modeling of neurons and neuronal networks. In: Schmitt FO, Worden FG (eds) The neurosciences, IVth study program. MIT Press, Cambridge, pp 525–550

    Google Scholar 

  • Pellionisz A (1983a) Sensorimotor transformations of natural coordinates via neuronal networks: conceptual and formal unification of cerebellar and tectal models. In: Lara R, Arbib MA (eds) H. Workshop on visuomotor coordination in frog and toad (Mexico City, Nov 1982 ), COINS Tech Rep, Amherst

    Google Scholar 

  • Pellionisz A (1983b) Brain theory: Connecting neurobiology to robotics. Tensor analysis: Utilizing intrinsic coordinates to describe, understand and engineer functional geometries of intelligent organisms. J Theor Neurobiol 2: 185–211

    Google Scholar 

  • Pellionisz A (1984a) Coordination: A vector-matrix description of transformations of overcomplete CNS coordinates and a tensorial solution using the Moore-Penrose generalized inverse. J Theor Biol 101: (in press)

    Google Scholar 

  • Pellionisz A (1984b) Tensorial aspects of the multidimensional approach to the vestibulo-oculomotor reflex and gaze. In: Berthoz A, Melvill-Jones G (eds) Reviews of oculomotor research, I. Adaptive mechanisms in gaze control. Elsevier, Amsterdam

    Google Scholar 

  • Pellionisz A, Llinás R (1977) A computer model of the cerebellar Purkinje cells. Neuroscience 2: 37–48

    Article  PubMed  CAS  Google Scholar 

  • Pellionisz A, Llinás R (1979) Brain modeling by tensor network theory and computer simulation.The cerebellum: Distributed processor for predictive coordination. Neuroscience 4: 323–348

    Google Scholar 

  • Pellionisz A, Llinás R (1980) Tensorial approach to the geometry of brain function. Cerebellar coordination via metric tensor. Neuroscience 5: 1125–1136

    Google Scholar 

  • Pellionisz A, Llinás R (1982a) Space-time representation in the brain. The cerebellum as a predictive space-time metric tensor. Neuroscience 7: 2949–2970

    Google Scholar 

  • Pellionisz A, Llinás R (1982b) Tensor theory of brain function. The cerebellum as a space-time metric. In: Arbib MA, Amari SI (eds) Competition and cooperation in neural nets. Proc US-Jpn Sem Kyoto. Lecture Notes Biomath, 45 Springer, Berlin Heidelberg New York, pp 394–417

    Google Scholar 

  • Pellionisz A, Szentágothai J (1973) Dynamic single unit simulation of a realistic cerebellar network model. Brain Res 49: 83–99

    Article  PubMed  CAS  Google Scholar 

  • Pellionisz A, Szentágothai J (1974) Dynamic single unit simulation of a realistic cerebellar network model, H. Brain Res 68: 19–40

    Article  PubMed  CAS  Google Scholar 

  • Pellionisz A, Llinás R, Perkel D (1977) A computer model of the cerebellar cortex of the frog. Neuroscience 2: 19–35

    Article  PubMed  CAS  Google Scholar 

  • Precht W (1978) Neuronal operations in the vestibular system. Studies on brain function, vol II Springer, Berlin Heidelberg New York

    Google Scholar 

  • Purkinje JE (1837) Bericht über die Versammlung deutscher Naturforscher und Ärzte in Prag, September 1837. 3. Sect. 5. Anat Physiol Verh, pp 177–180

    Google Scholar 

  • Ramon y Cajal S (1911) Histologie du Systeme nerveux de l’homme et des vertebres, vol 1–2. Maloine, Paris

    Google Scholar 

  • Robinson DA (1968) The oculomotor control system: A review. Proc IEEE 56: 1032–1049

    Article  Google Scholar 

  • Robinson DA (1975) How the oculomotor system repairs itself. Invest Ophthalmol 14: 413–415

    PubMed  CAS  Google Scholar 

  • Robinson DA (1982) The use of matrices in analyzing the three-dimensional behavior of the vestibulo-ocular reflex. Biol Cybernet 46: 53–66

    Article  CAS  Google Scholar 

  • Rolando L (1823) Experience sur les fonctions du systeme nerveux. J Physiol Exp 3: 113–114

    Google Scholar 

  • Sherrington C (1906) The integrative action of the nervous system. Scribner, New York

    Google Scholar 

  • Simpson JI (1979) Erroneous zones of the cerebellar flocculus. Soc Neurosci Abstr 5: 107

    Google Scholar 

  • Simpson JI, Alley KE (1974) Visual climbing fiber input to rabbit vestibulo-cerebellum: A source of direction-specific information. Brain Res 82: 302–308

    Google Scholar 

  • Simpson JI, Graf W, Leonard C (1981) The coordinate system of visual climbing fibers to the flocculus. In: Fuchs A, Becker WS (eds) Progress in oculomotor research. Elsevier/North Holland Biomedical Press, Amsterdam, pp 475–484

    Google Scholar 

  • Smolyaninov VA (1971) Some special features of organization of the cerebellar cortex. In: Gelfand IM, Gurfinkel VS, Fomin SV, Tsetlin, ML (eds) Models of the structural-functional organization of certain biological systems. MIT Press, Cambridge, pp 251–325

    Google Scholar 

  • Sotelo C, Llinás R, Baker R (1974) Structural study of inferior olivary nucleus of the morphological correlates of electrotonic oupling. J Neurophys 37: 541–559

    CAS  Google Scholar 

  • Sparks DL, Pollack JG (1977) The neural control of saccadic eye movements: the role of the superior colliculus. In: Brooks BA, Bajandas FJ (eds) Eye movements. Plenum Press, New York, pp 179–219

    Google Scholar 

  • Synge JL, Schild A (1949) Tensor calculus. Dover, New York

    Google Scholar 

  • Székely G (1973) Anatomy and synaptology of the tectum opticum. In: Jung R (ed) Handbook of sensory physiology, ud. VII. Springer, Berlin Heidelberg New York, pp 27–101

    Google Scholar 

  • Szentágothai J (1963) Ujabb adatok a synapsis functionális anatômiájához. Magyar Tud Akad Biol Ory Oszt Közl 6: 217–227

    Google Scholar 

  • Szentágothai J (1968) Structuro-functional considerations of the cerebellar neuron network. Proc IEEE 56: 960–968

    Article  Google Scholar 

  • Szentágothai J, Rajkovits KS (1959) Über den Ursprung der Kletterfasern des Kleinhirns. Z Anat Entwicklungsgesch 121: 130–141

    Article  Google Scholar 

  • Towe AI, Luschei ES (eds) (1981) Handbook of behavioral neurobiology, vol V: Motor coordination. Plenum Press, New York

    Google Scholar 

  • Voogd J, Bigare F (1980) Topographical distribution of olivary and cortico-nuclear fibers in the cerebellum. A review. In: Courville J, Montigny de C, Lamarre Y (eds) The inferior olivary nucleus. Anatomy and physiology. Raven Press, New York, pp 207–234

    Google Scholar 

  • Willis T (1664) Cerebri anatomae; Cui accessit nervorum descriptio et usus. Schagen, Amsterdam

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Physiology & Biophysics, New York University Medical Center, 550 First Ave, New York, NY, 10016, USA

    A. J. Pellionisz

Authors
  1. A. J. Pellionisz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Barrow Neurological Institute St. Joseph’s Hospital and Medical Center, 350 West Thomas Rd., 85013, Phoenix, Arizona, USA

    James R. Bloedel

  2. Neurologische Klinik, Universität Tübingen, Liebermeisterstraße 18-20, 7400, Tübingen, Germany

    Johannes Dichgans

  3. Institut für Hirnforschung, Universität Zürich, August-Forel-Straße 1, CH-8029, Zürich, Switzerland

    Wolfgang Precht

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pellionisz, A.J. (1984). Tensorial Brain Theory in Cerebellar Modelling. In: Bloedel, J.R., Dichgans, J., Precht, W. (eds) Cerebellar Functions. Proceedings in Life Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69980-1_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-69980-1_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-69982-5

  • Online ISBN: 978-3-642-69980-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation