Skip to main content
SpringerLink
Log in

Optimality in mono- and multisensory map formation

  • Prospects
  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

In the struggle for survival in a complex and dynamic environment, nature has developed a multitude of sophisticated sensory systems. In order to exploit the information provided by these sensory systems, higher vertebrates reconstruct the spatio-temporal environment from each of the sensory systems they have at their disposal. That is, for each modality the animal computes a neuronal representation of the outside world, a monosensory neuronal map. Here we present a universal framework that allows to calculate the specific layout of the involved neuronal network by means of a general mathematical principle, viz., stochastic optimality. In order to illustrate the use of this theoretical framework, we provide a step-by-step tutorial of how to apply our model. In so doing, we present a spatial and a temporal example of optimal stimulus reconstruction which underline the advantages of our approach. That is, given a known physical signal transmission and rudimental knowledge of the detection process, our approach allows to estimate the possible performance and to predict neuronal properties of biological sensory systems. Finally, information from different sensory modalities has to be integrated so as to gain a unified perception of reality for further processing, e.g., for distinct motor commands. We briefly discuss concepts of multimodal interaction and how a multimodal space can evolve by alignment of monosensory maps.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alais D, Burr D (2004) The ventriloquist effect results from near-optimal bimodal integration. Curr Biol 14: 257–262

    PubMed  CAS  Google Scholar 

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

    Google Scholar 

  • Anastasio TJ, Patton PE, Belkacem-Boussaid K (2000) Using bayes’ rule to model multisensory enhancement in the superior collic ulus. Neural Comput 12: 1165–1187

    Article  PubMed  CAS  Google Scholar 

  • Bartels M, Münz H, Claas B (1990) Representation of the lateral line and electrosensory systems in the midbrain of the axolotl, Ambystoma mexicanum. J Comp Physiol A 167: 347–356

    Article  Google Scholar 

  • Ben-Israel A, Greville TNE (2003) Generalized inverses: t lications, 2nd edn. Springer, New York, NY

    Google Scholar 

  • Bi GQ, Poo MM (1998) Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. J Neurosci 18: 10,464–10,472

    CAS  Google Scholar 

  • Bi GQ, Poo MM (2001) Synaptic modification by correlated activity: Hebb’s postulate revisited. Annu Rev Neurosci 24: 139–166

    Article  PubMed  CAS  Google Scholar 

  • Brand A, Behrend O, Marquardt T, McAlpine D, Grothe B (2002) Precise inhibition is essential for microsecond interaural time difference coding. Nature 417: 543–547

    Article  PubMed  CAS  Google Scholar 

  • Breiman L (1968) Probability. Addison-Wesley, Reading, MA

    Google Scholar 

  • Bresciani JP, Ernst MO, Drewing K, Bouyer G, Maury V, Kheddar A (2005) Feeling what you hear: auditory signals can modulate tactile taps perception. Exp Brain Res 162: 172–180

    Article  PubMed  Google Scholar 

  • Calvert G, Spence C, Stein BE (2004) The handbook of multisensory processes. MIT, Cambridge, MA

    Google Scholar 

  • Carr CE, Konishi M (1988) Axonal delay lines for time measurement in the owl’s brainstem. Proc Natl Acad Sci USA 85: 8311–8315

    Article  PubMed  CAS  Google Scholar 

  • Carr CE, Konishi M (1990) A circuit for detection of interaural time differences in the brain stem of the barn owl. J Neurosci 10: 3227–3246

    PubMed  CAS  Google Scholar 

  • Carr CE, Maler L, Sas E (1982) Peripheral organization and cetral projections of the electrosensory nerves in gymnotiform fish. J Comp Neurol 211: 139–153

    Article  PubMed  CAS  Google Scholar 

  • Carriere BN, Royal DW, Perrault TJ, Morrison SP, Vaughan JW, Stein BE, Wallace MT (2007) Visual deprivation alters the development of cortical multisensory integration. J Neurophysiol 98: 2858–2867

    Article  PubMed  Google Scholar 

  • Claas B (1994) Removal of eyes in early larval stages alters the response of the clawed toad, Xenopus laevis, to surface waves. Physiol Behav 56: 423–428

    Article  PubMed  CAS  Google Scholar 

  • Clegg JC (1968) Calculus of variations. Oliver and Boyd, Edinburgh

    Google Scholar 

  • Copelli M, Roque AC, Oliveira RF, Kinouchi O (2002) Physics of psychophysics: Stevens and Weber-Fechner laws are transfer functions of excitable media. Phys Rev E 65: 60,901

    Article  CAS  Google Scholar 

  • Dan Y, Poo MM (2004) Spike timing-dependent plasticity of neural circuits. Neuron 44: 23–30

    Article  PubMed  CAS  Google Scholar 

  • Davison AP, Frégnac Y (2006) Learning cross-modal spatial transformations through spike timing-dependent plasticity. J Neurosci 26: 5604–5615

    Article  PubMed  CAS  Google Scholar 

  • Denève S, Pouget A (2004) Bayesian multisensory integration and cross-modal spatial links. J Physiol (Paris) 98: 249–258

    Article  Google Scholar 

  • Denève S, Latham PE, Pouget A (1999) Reading population codes: a neural implementation of ideal observers. Nat Neurosci 2(8): 740–745

    Article  PubMed  Google Scholar 

  • Denève S, Latham PE, Pouget A (2001) Efficient computation and cue integration with noisy population codes. Nat Neurosci 4(8): 826–831

    Article  PubMed  Google Scholar 

  • Dräger UC, Hubel DH (1975) Responses to visual stimulation and relationship between visual, auditory, and somatosensory inputs in mouse superior colliculus. J Neurophysiol 38: 690–713

    PubMed  Google Scholar 

  • Durrett R (2004) Probability: theory and examples, 3rd edn. Duxbury Press, Belmont, MA

    Google Scholar 

  • Eckhorn R, Bauer R, Jordan W, Brosch M, Kruse W, Munk M, Reitboeck HJ (1988) Coherent oscillations: a mechanism of feature linking in the visual cortex. Biol Cybern 60: 121–130

    Article  PubMed  CAS  Google Scholar 

  • Ernst MO, Banks MS (2002) Humans integrate visual and haptic information in a statistically optimal fashion. Nature 415: 429–433

    Article  PubMed  CAS  Google Scholar 

  • Ernst MO, Banks MS, Bülthoff H (2000) Touch can change visual slant perception. Nat Neurosci 3: 69–73

    Article  PubMed  CAS  Google Scholar 

  • Etemadi N (1981) An elementary proof of the strong law of large numbers. Z Wahrscheinlichkeitstheorie verw Geb 55: 119–122

    Article  Google Scholar 

  • Faisal AA, Selen LPJ, Wolpert DM (2008) Noise in the nervous system. Nat Rev Neurosci 9: 292–303

    Article  PubMed  CAS  Google Scholar 

  • Franosch JMP, Sobotka MC, Elepfandt A, van Hemmen JL (2003) Minimal model of prey localization through the lateral-line system. Phys Rev Lett 91: 158101

    Article  PubMed  CAS  Google Scholar 

  • Franosch JMP, Lingenheil M, van Hemmen JL (2005a) How a frog can learn what is where in the dark. Phys Rev Lett 95: 78,106

    Article  CAS  Google Scholar 

  • Franosch JMP, Sichert AB, Suttner MD, van Hemmen JL (2005b) Estimating position and velocity of a submerged moving object by the clawed frog Xenopus and by fish—a cybernetic approach. Biol Cybern 93: 231–238

    Article  PubMed  Google Scholar 

  • Frens MA, van Opstal AJ (1998) Visual-auditory interactions modulate saccade-related activity in monkey superior colliculus. Brain Res 46: 211–224

    CAS  Google Scholar 

  • Friedel P, van Hemmen JL (2008) Inhibition, not excitation, is the key to multimodal sensory integration. Biol Cybern 98: 597–618

    Article  PubMed  Google Scholar 

  • Geisler CD (1990) From sound to synapse: physiology of the mammalian ear. Oxford University, Oxford

    Google Scholar 

  • Gelfand IM, Fomin SV (1963) Calculus of variations. Prentice-Hall, Englewood Cliffs, NY

    Google Scholar 

  • Gerstner W, Kempter R, van Hemmen JL, Wagner H (1996) A neuronal learning rule for sub-millisecond temporal coding. Nature 383: 76–78

    Article  PubMed  CAS  Google Scholar 

  • Gnedenko B, Kolmogorov A (1968) Limit distributions for sums of independent random variables. Addison-Wesley, Reading, MA

    Google Scholar 

  • Goulet J, Engelmann J, Chagnaud BP, Franosch JMP, Suttner MD, van Hemmen JL (2008) Object localization through the lateral line system of fish: theory and experiment. J Comp Physiol A 194: 1–17

    Article  Google Scholar 

  • Grace MS, Woodward OM, Church DR, Calisch G (2001) Prey targeting by the infrared-imaging snake Python: effects of experimental and congenital visual deprivation. Behav Brain Res 119: 23–31

    Article  PubMed  CAS  Google Scholar 

  • Gray CM, König P, Engel AK, Singer W (1989) Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature 338: 334–337

    Article  PubMed  CAS  Google Scholar 

  • Gu Y, Angelaki DE, DeAngelis GC (2008) Neural correlates of multisensory cue integration in macaque MSTd. Nat Neurosci 11: 1201–1210

    Article  PubMed  CAS  Google Scholar 

  • Gutfreund Y, Zheng W, Knudsen EI (2002) Gated visual input to the central auditory system. Science 297: 1556–1559

    Article  PubMed  CAS  Google Scholar 

  • Hafed ZM, Goffart L, Krauzlis RJ (2008) Superior colliculus inactivation causes stable offsets in eye position during tracking. J Neurosci 28: 8124–8137

    Article  PubMed  CAS  Google Scholar 

  • Halmos PR (1956) Ergodic theory. Chelsea, New York

    Google Scholar 

  • Hartline PH, Kass L, Loop MS (1978) Merging of modalities in the optic Tectum: infrared and visual integration in rattlesnakes. Science 199: 1225–1229

    Article  PubMed  CAS  Google Scholar 

  • Helbig HB, Ernst MO (2007) Optimal integration of shape information from vision and touch. Exp Brain Res 179: 595–606

    Article  PubMed  Google Scholar 

  • Helmholtz H (1879) Die Thatsachen in der Wahrnehmung. August Hirschwald, Berlin

    Google Scholar 

  • Hötting K, Rösler F, Röder B (2004) Altered auditory-tactile interactions in congenitally blind humans: an event-related potential study. Exp Brain Res 159: 370–381

    Article  PubMed  Google Scholar 

  • Hubel DH, Wiesel TN (1977) Functional architecture of macaque monkey visual cortex. Proc Roy Soc Lond B 198: 1–59

    Article  CAS  Google Scholar 

  • Hughes A (1977) The topography of vision in mammals of contrasting life style: comparative optics and retinal organization. In: Crescitelli F (ed) Handbook of sensory physiology, vol VII/5, chap. 8. Springer, Berlin, Heidelberg, New York, pp 613–756

  • Hürlimann F, Kiper DC, Carandini M (2002) Testing the bayesian model of perceived speed. Vis Res 42:2253–2257

    Article  PubMed  Google Scholar 

  • Hyde PS, Knudsen EI (2001) A topographic instructive signal guides the adjustment of the auditory space map in the optic tectum. J Neurosci 21: 8586–8593

    PubMed  CAS  Google Scholar 

  • Itti L, Koch C (2001) Computational modeling of visual attention. Nat Rev Neurosci 2(3): 194–203

    Article  PubMed  CAS  Google Scholar 

  • Järvilehto M (1985) The eye: vision and perception. In: Kerkut GA, Gilbert LI (eds) Nervous system: sensory, comprehensive insect physiology, biochemistry, and pharmacology, vol 6. Pergamon, Oxford, pp 355–429

    Google Scholar 

  • Jazayeri M, Movshon (2006) Optimal representation of sensory information by neural populations. Nat Neurosci 9: 690–696

    Article  PubMed  CAS  Google Scholar 

  • Jiang B, Treviño M, Kirkwood A (2007) Sequential development of long-term potentiation and depression in different layers of the mouse visual cortex. J Neurosci 27: 9648–9652

    Article  PubMed  CAS  Google Scholar 

  • Johnson DH, Dudgeon DE (1993) Array signal processing: concepts and techniques. Prentice-Hall, Upper Saddle River, NJ

    Google Scholar 

  • Johnson KO, Hsiao SS, Yoshioka T (2002) Neural coding and the basic law of psychophysics. Neuroscientist 8: 111–121

    Article  PubMed  Google Scholar 

  • Jost J, Li-Jost X (1998) Calculus of variations. Cambridge University, Cambridge

    Google Scholar 

  • Kaas JH, Collins CE (2004) The resurresction of multisensory cortex in primates: connection patterns that integrate modalities. In: Calvert G, Spence C, Stein BE (eds) The handbook of multisensory processes, chap 17. MIT, Cambridge, MA, pp 285–293

  • Kandel ER, Schwartz JH, Jessell TM (2000) Principles of neural science, 4th (international) edn. McGraw-Hill, New York

    Google Scholar 

  • Kay SM (1993) Fundamentals of statistical signal processing. Prentice Hall, Upper Saddle River, NJ

    Google Scholar 

  • Kempter R, Gerstner W, van Hemmen JL (1999) Hebbian learning and spiking neurons. Phys Rev E 59: 4498–4514

    Article  CAS  Google Scholar 

  • Kempter R, Leibold C, Wagner H, van Hemmen JL (2001) Formation of temporal-feature maps by axonal propagation of synaptic learning. Proc Natl Acad Sci USA 98: 4166–4171

    Article  PubMed  CAS  Google Scholar 

  • King AJ (1999) Sensory experience and the formation of a computational map of auditory space in the brain. Bioessays 21: 900–911

    Article  PubMed  CAS  Google Scholar 

  • King AJ (2009) Visual influences on auditory spatial learning. Phil Trans R Soc B 364: 331–339

    Article  PubMed  Google Scholar 

  • King AJ, Hutchings ME (1987) Spatial response properties of acoustically responsive neurons in the superior colliculus of the ferret: a map of auditory space. J Neurophysiol 57: 596–624

    PubMed  CAS  Google Scholar 

  • King AJ, Palmer AR (1983) Cells responsive to free-field auditory stimuli in guinea-pig superior colliculus: distribution and response properties. J Physiol 342: 361–381

    PubMed  CAS  Google Scholar 

  • King AJ, Hutchings ME, Moore DR, Blakemore C (1988) Developmental plasticity in the visual and auditory representations in the mammalian superior colliculus. Nature 332: 73–76

    Article  PubMed  CAS  Google Scholar 

  • Knierim JJ, van Essen DC (1992) Neuronal responses to static texture patterns in area V1 of the alert macaque monkey. J Neurophysiol 67: 961–980

    PubMed  CAS  Google Scholar 

  • Knudsen EI (1982) Auditory and visual maps of space in the optic tectum of the owl. J Neurosci 2: 1177–1194

    PubMed  CAS  Google Scholar 

  • Knudsen EI (2002) Instructed learning in the auditory localization pathway of the barn owl. Nature 417: 322–328

    Article  PubMed  CAS  Google Scholar 

  • Knudsen EI, Brainard MS (1991) Visual instruction of the neural map of auditory space in the developing optic tectum. Science 253: 85–87

    Article  PubMed  CAS  Google Scholar 

  • Knudsen EI, Knudsen PF (1985) Vision guides the adjustment of auditory localization in young barn owls. Science 230: 545–548

    Article  PubMed  CAS  Google Scholar 

  • Knudsen EI, Lac Sd, Esterly SD (1987) Computational maps in the brain. Annu Rev Neurosci 10: 41–65

    Article  PubMed  CAS  Google Scholar 

  • Körding K, Wolpert DM (2004) Bayesian integration in sensorimotor learning. Nature 427:244–247

    Article  PubMed  CAS  Google Scholar 

  • Krauzlis RJ, Basso MA, Wurtz RH (1997) Shared motor error for multiple eye movements. Science 276: 1693–1695

    Article  PubMed  CAS  Google Scholar 

  • Krauzlis RJ, Liston D, Carello CD (2004) Target selection and the superior colliculus: goals, choices and hypotheses. Vision Res 44: 1445–1451

    Article  PubMed  Google Scholar 

  • Krueger LE (1989) Reconciling Fechner and Stevens: toward a unified psychophysical law. Behav Brain Sci 12: 251–320

    Article  Google Scholar 

  • Laming D (1997) The measurement of sensation. Oxford University, Oxford

    Book  Google Scholar 

  • Lamperti J (1966) Probability. Benjamin, New York

    Google Scholar 

  • Leibold C, van Hemmen JL (2005) Spiking neurons learning phase delays: how mammels may develop auditory time-difference sensitivity. Phys Rev Lett 94: 168102

    Article  PubMed  CAS  Google Scholar 

  • Li Z (2002) A saliency map in primary visual cortex. Trends Cogn Neurosci 6(1):9–16

    Article  Google Scholar 

  • Lingenheil M (2004) Theorie der Beuteortung beim Krallenfrosch. Master’s thesis, Technische Universität München

  • Luksch H (2008) Sensorimotor integration: optic tectum. In: Binder MD, Hirokawa N, Windhorst U, Hirsch MC (eds) Encyclopedia of neuroscience. Springer, New York

    Google Scholar 

  • Mach E (1866) Über die physiologische Wirkung räumlich vertheilter Lichtreize. Sitzungsber Akad Wiss Wien II 54: 393–408

    Google Scholar 

  • Magosso E, Cuppinia C, Serino A, Di Pellegrino G, Ursino M (2008) A theoretical study of multisensory integration in the superior colliculus by a neural network model. Neural Netw 21: 817–829

    Article  PubMed  Google Scholar 

  • Manley GA, Köppl C, Konishi M (1988) A neural map of interaural intensity differences in the brainstem of the barn owl. J Neurosci 8: 2665–2676

    PubMed  CAS  Google Scholar 

  • Markram H, Lübke J, Frotscher M, Sakmann B (1997) Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science 275: 213–215

    Article  PubMed  CAS  Google Scholar 

  • Middlebrooks JC, Knudsen EI (1984) A neural code for auditory space in the cat’s superior colliculus. J Neurosci 4: 2621–2634

    PubMed  CAS  Google Scholar 

  • Miller K (1970) Least squares methods for ill-posed problems with a prescribed bound. SIAM J Math Anal 1: 52–74

    Article  Google Scholar 

  • Mooney RD, Klein BG, Rhoades RW (1987) Effects of altered visual input upon the development of the visual system and somatosensory representations in the hamster’s superior colliculus. Neurosci 20: 537–555

    Article  CAS  Google Scholar 

  • Moore EH (1920) On the reciprocal of the general algebraic matrix. Bull Am Math Soc 26: 394–395

    Google Scholar 

  • Morgan ML, DeAngelis GC, Angelaki DE (2008) Multisensory integration in macaque visual cortex depends on cue reliability. Neuron 59: 662–673

    Article  PubMed  CAS  Google Scholar 

  • Mosegaard K, Tarantola A (2002) Probabilistic approach to inverse problems. In: Lee WHK, Kanamori H, Jennings PC, Kisslinger C (eds) International handbook of earthquake and engineering seismology, chap 16. Academic, San Diego, CA, pp 237–265

  • Murphey RK (1973) Mutual inhibition and the organization of a non-visual orientation in Notonecta. J Comp Physiol A 84: 31–40

    Article  Google Scholar 

  • Newman EA, Hartline PH (1981) Integration of visual and infrared information in bimodal neurons of the rattlesnake optic tectum. Science 213: 789–791

    Article  PubMed  CAS  Google Scholar 

  • Newman EA, Hartline PH (1982) The infrared “vision” of snakes. Sci Am 246(3): 98–107

    Article  Google Scholar 

  • Norwich KH, Wong W (1997) Unification of psychological phenomena: the complete form of Fechner’s law. Percept Psychophys 59: 929–940

    PubMed  CAS  Google Scholar 

  • Oǧuztöreli MN, Caelli TM (1985) An inverse problem in neural processing. Biol Cybern 53: 239–245

    Article  Google Scholar 

  • Olsen JF, Knudsen EI, Esterly SD (1989) Neural maps of interaural time and intensity differences in the optic tectum of the barn owl. J Neurosci 9: 2591–2605

    PubMed  CAS  Google Scholar 

  • Patton PE, Belkacem-Boussaid K, Anastasio TJ (2002) Multimodality in the superior colliculus: an information theoretic analysis. Cogn Brain Res 14: 10–19

    Article  Google Scholar 

  • Penrose R (1955) A generalized inverse for matrices. Camb Philos Soc 51: 406–413

    Article  Google Scholar 

  • Pickles JO (1988) An introduction to the physiology of hearing, 2nd ed. Academic Press, London

    Google Scholar 

  • Pouget A, Dayan P, Zemel RS (2003) Inference and computation with population codes. Annu Rev Neurosci 26: 381–410

    Article  PubMed  CAS  Google Scholar 

  • Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes: the art of scientific computing, 3rd ed. Cambridge University, Cambridge

    Google Scholar 

  • Puetter RC, Gosnell TR, Yahil A (2005) Digital image reconstruction: deblurring and denoising. Annu Rev Astron Astrophys 43: 139–194

    Article  Google Scholar 

  • Putzar L, Goerendt I, Lange K, Rösler F, Röder B (2007) Early visual deprivation impairs multisensory interactions in humans. Nat Neurosci 10: 1243–1245

    Article  PubMed  CAS  Google Scholar 

  • Röder B, Rösler F, Spence C (2004) Early vision impairs tactile perception in the blind. Curr Biol 14: 121–124

    PubMed  Google Scholar 

  • Rosenfeld D (2002) New approach to gridding using regularization. Magn Reson Med 48: 193–202

    Article  PubMed  Google Scholar 

  • Rowland BA, Quessy S, Stanford TR, Stein BE (2007a) Multisensory integration shortens physiological response latencies. J Neurosci 27: 5879–5884

    Article  PubMed  CAS  Google Scholar 

  • Rowland BA, Stanford TR, Stein BE (2007b) A bayesian model unifies multisensory spatial localization with the physiological properties of the superior colliculus. Exp Brain Res 180: 153–161

    Article  PubMed  Google Scholar 

  • Rowland BA, Stanford TR, Stein BE (2007c) A model of the neural mechanisms underlying multisensory integration in the superior colliculus. Perception 36(10): 1431–1443

    Article  PubMed  Google Scholar 

  • Sarkar TK, Weiner DD, Jain VK (1981) Some mathematical considerations in dealing with the inverse problem. IEEE Trans Antennas Propag 29: 373–379

    Article  Google Scholar 

  • Schreiner CE, Langner G (1988) Periodicity coding in the inferior colliculus of the cat. II. Topograhical organization. J Neurophysiol 60: 1823–1840

    PubMed  CAS  Google Scholar 

  • Scott DJ (1973) Central limit theorems for martingales and for processes with stationary independent increments using Skorohod representation approach. Adv App Probab 5: 119–137

    Article  Google Scholar 

  • Seung HS, Sompolinsky H (1993) Simple models for reading neuronal population codes. Proc Natl Acad Sci USA 90: 10,749–10,753

    Article  CAS  Google Scholar 

  • Shams L, Kamitani Y, Shimojo S (2000) What you see is what you hear. Nature 408: 788

    Article  PubMed  CAS  Google Scholar 

  • Shumway CA (1989) Multiple electrosensory maps in the medulla of weakly electric gymnotiform fish. I. Physiological differences. J Neurosci 9: 4388–4399

    PubMed  CAS  Google Scholar 

  • Sichert AB, Friedel P, van Hemmen JL (2006) Snake’s perspective on heat: reconstruction of input using an imperfect detection system. Phys Rev Lett 97: 68,105

    Article  CAS  Google Scholar 

  • Sichert AB, Bamler R, van Hemmen JL (2009) Hydrodynamic object recognition: when multipoles count. Phys Rev Lett 102: 058,104

    Article  CAS  Google Scholar 

  • Song S, Miller KD, Abbott LF (2000) Competitive hebbian learning through spike-timing-dependent plasticity. Nat Neurosci 3: 919–926

    Article  PubMed  CAS  Google Scholar 

  • Stanford LR, Hartline PH (1980) Spatial sharpening by second-order trigeminal neurons in crotaline infrared system. Brain Res 185: 115–123

    Article  PubMed  CAS  Google Scholar 

  • Stavenga DG (2002) Reflections on colourful ommatidia of butterfly eyes. J Exp Biol 205: 1077–1085

    PubMed  Google Scholar 

  • Steenken R, Colonius H, Diederich A, Rach S (2008) Visual and auditory interaction in saccadic reaction time: effects of auditory masker level. Brain Res 1220: 150–156

    Article  PubMed  CAS  Google Scholar 

  • Stein BE, Gaither NS (1981) Sensory representations in reptilian optic tectum: some comparisons with mammals. J Comp Neurol 202: 69–87

    Article  PubMed  CAS  Google Scholar 

  • Stein BE, Meredith MA (1993) The merging of the senses. MIT Press, Cambridge, MA

    Google Scholar 

  • Stein BE, Stanford TR (2008) Multisensory integration: current issues from the perspective of the single neuron. Nat Rev Neurosci 9: 255–266

    Article  PubMed  CAS  Google Scholar 

  • Stein BE, Jiang W, Stanford TR (2004) Multisensory integration in single neurons of the midbrain. In: Calvert G, Spence C, Stein BE (eds) The handbook of multisensory processes, chap 15. MIT, Cambridge, MA, pp 243–264

  • Sullivan WE, Konishi M (1986) Neural map of interaural phase difference in the owl’s brainstem. Proc Natl Acad Sci USA 83: 8400–8404

    Article  PubMed  CAS  Google Scholar 

  • Takahashi T, Konishi M (1986) Selectivity for interaural time difference in the owl’s midbrain. J Neurosci 6: 3413–3422

    PubMed  CAS  Google Scholar 

  • Takeda M, Goodman JW (1986) Neural networks for computation: number representations and programming complexity. Appl Optics 25: 3033–3046

    Article  CAS  Google Scholar 

  • Tikhonov AN, Arsenin VY, John F (1977) Solution of ill-posed problems. V. H. Winston & Sons, Washington, DC. English translation of the original Russian text

  • Tikhonov AN, Goncharsky AV, Stepanov VV, Yagola AG (1995) Numerical methods for the solution of ill-posed problems. Kluwer Academic Publishers, Dordrecht. English translation of the original Russian text

  • Udin S, Fawcett J (1988) Formation of topographic maps. Annu Rev Neurosci 11: 289–327

    Article  PubMed  CAS  Google Scholar 

  • Ursino M, Cuppinia C, Magosso E, Serino A, Di Pellegrino G (2009) Multisensory integration in the superior colliculus: a neural network model. J Comput Neurosci 26(1): 55– 73

    Article  PubMed  Google Scholar 

  • Van Brunt B (2000) The calculus of variations. Springer, Heidelberg

    Google Scholar 

  • van der Waerden BL (1957) Mathematische Statistik. Springer, Berlin

    Google Scholar 

  • van Hemmen JL (2001) Theory of synaptic plasticity. In: Moss F, Gielen S (eds) Neuro-informatics, neural modelling, handbook of biological physics, vol 4. Elsevier, Amsterdam, pp 771– 823

    Google Scholar 

  • van Hemmen JL (2002) The map in your head: how does the brain represent the outside world?. Chem Phys Chem 3: 291–298

    PubMed  Google Scholar 

  • van Opstal AJ, Munoz DP (2004) Auditory-visual interactions subserving primate gaze orienting. In: Calvert G, Spence C, Stein BE (eds) The handbook of multisensory processes, chap 23. MIT, Cambridge, MA, pp 373–393

  • Wallace MT, Stein BE (1997) Development of multisensory neurons and multisensory integration in cat superior colliculus. J Neurosci 17: 2429–2444

    PubMed  CAS  Google Scholar 

  • Wallace MT, Stein BE (2007) Early experience determines how the senses will interact. J Neurophysiol 97: 921–926

    Article  PubMed  Google Scholar 

  • Wallace MT,Perrault TJ Jr, Hairston WD,Stein BE (2004) Visual experience is necessary for the development of multisensory integration. J Neurosci 24:9580–9584

    Article  PubMed  CAS  Google Scholar 

  • Wallace MT, Carriere BN, Perrault TJ Jr, Vaughan JW, Stein BE (2006) The development of cortical multisensory integration. J Neurosci 26(46):11,844–11,849

    Article  CAS  Google Scholar 

  • Wandell BA (1995) Foundations of vision. Sinauer Associates, Sunderland, MA

    Google Scholar 

  • Willshaw DJ, Malsburg C (1976) How patterned neural connections can be set up by self-organization. Proc Roy Soc Lond B 194: 431–445

    Article  CAS  Google Scholar 

  • Winkowski DE, Knudsen EI (2006) Top-down gain control of the auditory space map by gaze control circuitry in the barn owl. Nature 439: 336–339

    Article  PubMed  CAS  Google Scholar 

  • Zeil J, Hemmi JM (2006) The visual ecology of fiddler crabs. J Comp Physiol A 192: 1–25

    Article  Google Scholar 

  • Zhang LL, Huizong WT, Holt CE, Harris WA, Poo MM (1998) A critical window for cooperation and competition among developing retinotectal synapses. Nature 395: 37–44

    Article  PubMed  CAS  Google Scholar 

  • Zhou YT, Chellappa R, Vaid A, Jenkins BK (1988) Image restoration using a neural network. IEEE Trans Acoust Speech Sign Process 36: 1141–1151

    Article  Google Scholar 

  • Zittlau KE, Claas B, Münz H (1988) Horseradish peroxidase study of tectal afferents in Xenopus laevis with special emphasis on their relationship to the lateral-line system. Brain Behav Evol 32: 208–219

    Article  PubMed  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technical University of Munich, Munich, Germany

    Moritz Bürck, Paul Friedel, Andreas B. Sichert, Christine Vossen & J. Leo van Hemmen

Authors
  1. Moritz Bürck
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul Friedel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andreas B. Sichert
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Christine Vossen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. J. Leo van Hemmen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Moritz Bürck.

Additional information

Moritz Bürck, Paul Friedel, Andreas B. Sichert and Christine Vossen have contributed equally to this work.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bürck, M., Friedel, P., Sichert, A.B. et al. Optimality in mono- and multisensory map formation. Biol Cybern 103, 1–20 (2010). https://doi.org/10.1007/s00422-010-0393-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00422-010-0393-7

Keywords

Search

Navigation