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Computational Neuroscience: More Math Is Needed to Understand the Human Brain

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Mathematics Unlimited — 2001 and Beyond

Abstract

This short essay consists of two parts. A general introduction describes what neuroscience and computational neuroscience are and what the general problems facing these fields are. In the second part a few examples are given of areas where mathematicians can make important contributions.

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References

  • Abbott, L. F., Varela, J. A., Sen, K., and Nelson, S. B.: Synaptic depression and cortical gain control. Science 275 (1997) 220–224

    Article  Google Scholar 

  • Abeles, M.: Corticonics: Neural Structure of the Cerebral Cortex. Cambridge: Cambridge University Press, 1991

    Book  Google Scholar 

  • Arbib, M. A., Èrdi, P., and Szentagothai, J.: Neural Organization: Structure, Function, and Dynamics. Cambridge, Mass., USA: MIT Press, 1997

    MATH  Google Scholar 

  • Barinaga, M.: Brain mapping - Researchers get a sharper image of the human brain. Science 268 (1995) 803–804

    Article  Google Scholar 

  • Bormann, G., Brosens, F., and De Schutter, E.: Modeling molecular diffusion. In Computational Modeling of Genetic and Biochemical Networks, edited by J. M. Bower and H. Bolouri. Cambridge, Mass.: MIT Press, 2000 (in press)

    Google Scholar 

  • Churchland, P. S., and Sejnowski, T. J.: The computational brain. Cambridge, Mass.: MIT Press, 1992

    MATH  Google Scholar 

  • De Schutter, E.: A consumer guide to neuronal modeling software. Trends Neurosci. 15 (1992) 462–464

    Article  Google Scholar 

  • De Schutter, E.: Cerebellar long-term depression might normalize excitation of Purkinje cells: a hypothesis. Trends Neurosci. 18 (1995) 291–295

    Article  Google Scholar 

  • De Schutter, E., and Bower, J. M.: Simulated responses of cerebellar Purkinje cells are independent of the dendritic location of granule cell synaptic inputs. Proc. Natl. Acad. Sci. USA 91 (1994) 4736–4740

    Article  Google Scholar 

  • De Schutter, E., and Steuber, V.: Modeling simple and complex active neurons. In Computational Neuroscience: Realistic Modeling for Experimentalists, edited by E. De Schutter. Boca Raton, Florida: CRC Press, 2000, pp. 233–257

    Chapter  Google Scholar 

  • Denk, W., and Svoboda, K.: Photon upmanship: why multiphoton imaging is more than a gimmick. Neuron 18 (1997) 351–357

    Article  Google Scholar 

  • Fletcher, C. A. J.: Computational Techniques for Fluid Dynamics. Volume I. : Springer, Berlin Heidelberg 1991

    Google Scholar 

  • Gabso, M., Neher, E., and Spira, M. E.: Low mobility of the Ca2+ buffers in axons of cultured Aplysia neurons. Neuron 18 (1997) 473–481

    Article  Google Scholar 

  • Hille, B.: Ionic Channels of Excitable Membranes. Sunderland: Sinauer Associates, 1992

    Google Scholar 

  • Holt, G. R., and Koch, C: Electrical interactions via the extracellular potential near cell bodies. J. Comput. Neurosci. 6 (1999) 169–184

    Article  MATH  Google Scholar 

  • Hopfield, J. J.: Pattern recognition computation using action potential timing for stimulus representation. Nature 376 (1995) 33–36

    Article  Google Scholar 

  • Lunkes, A., Trottier, Y., and Mandel, J. L.: Pathological mechanisms in Huntington’s disease and other polyglutamine expansion diseases. Essays Biochem. 33 (1998) 149–163

    Article  Google Scholar 

  • Major, G.: Passive cable modeling - a practical introduction. In Computational Neuroscience: Realistic Modeling for Experimentalists, edited by E. De Schutter, Bota Racon, Florida: CRC Press, 2000, pp. 209–232

    Google Scholar 

  • Marder, E., and Calabrese, R. L.: Principles of rhythmic motor pattern generation. Physiol. Rev. 76 (1996) 687–717

    Google Scholar 

  • Markram, H., Gupta, A., Uziel, A., Wang, Y., and Tsodyks, M.: Information processing with frequency-dependent synaptic connections. Neurobiol. Learn. Mem. 70 (1998) 101–112

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Nicolelis, M. A., Ghazanfar, A. A., Stambaugh, C.R., Oliveira, L. M., Laubach, M., Chapin, J. K., Nelson, R. J., and Kaas, J. H.: Simultaneous encoding of tactile information by three primate cortical areas. Nature Neurosci. 1 (1998) 621–630

    Article  Google Scholar 

  • Nicolelis, M. A. L., Ghazanfar, A. A., Faggin, B. M., Votaw, S., and Oliveira, L. M. O.: Reconstructing the engram: simultaneous, multisite, many single neuron recordings. Neuron 18 (1997) 529–537

    Article  Google Scholar 

  • Qian, N., and Sejnowski, T. J.: When is an inhibitory synapse effective? Proc. Natl. Acad. Sci. USA 87 (1990) 8145–8149

    Article  Google Scholar 

  • Rall, W., and Agmon-Snir, H.: Cable theory for dendritic neurons. In Methods in Neuronal Modeling: From Ions to Networks, edited by C. Koch, and I. Segev, 2nd edn. Cambridge, Mass.: MIT Press, 1998, pp. 27–92

    Google Scholar 

  • Riehle, A., Grun, S., Diesmann, M., and Aertsen, A.: Spike synchronization and rate modulation differentially involved in motor cortical function. Science 278 (1997) 1950–1953

    Article  Google Scholar 

  • Rieke, F., Warland, D., de Ruyter van Steveninck, R. R., and Bialek, W.: Spikes. Exploring the Neural Code. Cambridge, Mass.: The MIT Press, 1997

    MATH  Google Scholar 

  • Sakmann, B., and Neher, E.: Single-channel recording. 2nd edn. New York: Plenum Press, 1995

    Book  Google Scholar 

  • Schneidman, E., Freedman, B., and Segev, I.: Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural Comput. 10 (1998) 1679–1703

    Article  Google Scholar 

  • Segev, I., Rinzel, J., and Shepherd, G. M. (eds.) The Theoretical Foundation of Dendritic Function. Selected Papers of Wilfrid Rall with Commentaries. Cambridge, Mass.:MIT Press, 1995

    Google Scholar 

  • Shadlen, M. N., and Newsome, W. T.: The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J. Neurosci. 18 (1998) 3870–3896

    Google Scholar 

  • Singer, W.: Consciousness and the structure of neuronal representations. Phil. Trans.Roy. Soc. London Ser. B 353 (1998) 1829–1840

    Article  Google Scholar 

  • Stiles, J. R., and Bartol, T. M.: Monte Carlo methods for simulating realistic synaptic microphysiology using MCell. In Computational Neuro science: Realistic Modeling for Experimentalists, edited by E. De Schutter. Boca Raton, Florida: CRC Press, 2000,pp. 87–122

    Google Scholar 

  • Stuart, G., Spruston, N., and Häusser, M. (eds.) Dendrites. Oxford: Oxford University Press, 1999.

    Google Scholar 

  • Stuart, G., Spruston, N., Sakmann, B., and Häusser, M.: Action potential inititation and backpropagation in neurons of the mammalian CNS. Trends Neurosci. 20 (1997) 125–131

    Article  Google Scholar 

  • Todorov, E.: Direct cortical control of muscle activation in voluntary arm movements: a model. Nature Neurosci. 4 (2000) 391–398

    Article  Google Scholar 

  • Wang, S. S.-H., and Augustine, G. J.: Confocal imaging and local photolysis of caged compounds: dual probes of synaptic function. Neuron 15 (1995) 755–760

    Article  Google Scholar 

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Authors
  1. Erik De Schutter
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Editor information

Editors and Affiliations

  1. Center for Parallel Computers, Royal Institute of Technology (KTH), Lindstedtsvägen 25, 10044, Stockholm, Sweden

    Björn Engquist

  2. Department of Mathematics, University of California at Los Angeles, 3148 Murphy Hall, 7619A MSB, 90095-1555, Los Angeles, CA, USA

    Björn Engquist

  3. Department of Mathematics, Harvard University, 02138-2901, Cambridge, MA, USA

    Wilfried Schmid

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© 2001 Springer-Verlag Berlin Heidelberg

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De Schutter, E. (2001). Computational Neuroscience: More Math Is Needed to Understand the Human Brain. In: Engquist, B., Schmid, W. (eds) Mathematics Unlimited — 2001 and Beyond. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56478-9_17

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  • DOI: https://doi.org/10.1007/978-3-642-56478-9_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-63114-6

  • Online ISBN: 978-3-642-56478-9

  • eBook Packages: Springer Book Archive

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