Two-scale eigenfunction methods with an application to the visual system
Authors:
L. Sirovich and B. W. Knight
Journal:
Quart. Appl. Math. 45 (1987), 749-768
MSC:
Primary 92A09; Secondary 92A27
DOI:
https://doi.org/10.1090/qam/917024
MathSciNet review:
917024
Full-text PDF Free Access
References |
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Additional Information
- Lawrence Sirovich and B. W. Knight, On the eigentheory of operators which exhibit a slow variation, Quart. Appl. Math. 38 (1980/81), no. 4, 469–488. MR 614554, DOI https://doi.org/10.1090/S0033-569X-1981-0614554-0
- L. Sirovich and B. W. Knight, Contributions to the eigenvalue problem for slowly varying operators, SIAM J. Appl. Math. 42 (1982), no. 2, 356–377. MR 650230, DOI https://doi.org/10.1137/0142028
- B. W. Knight and L. Sirovich, The Wigner transform and some exact properties of linear operators, SIAM J. Appl. Math. 42 (1982), no. 2, 378–389. MR 650231, DOI https://doi.org/10.1137/0142029
- Lawrence Sirovich and Bruce W. Knight, The eigenfunction problem in higher dimensions: asymptotic theory, Proc. Nat. Acad. Sci. U.S.A. 82 (1985), no. 24, 8275–8278. MR 820715, DOI https://doi.org/10.1073/pnas.82.24.8275
- Lawrence Sirovich and Bruce W. Knight, The eigenfunction problem in higher dimensions: asymptotic theory, Proc. Nat. Acad. Sci. U.S.A. 82 (1985), no. 24, 8275–8278. MR 820715, DOI https://doi.org/10.1073/pnas.82.24.8275
T. Cornsweet, Visual Perception, Academic Press, New York, 1970
F. Ratliff, Mach Bands: Qualitative Studies on Neural Networks in the Retina, Holden-Day, San Francisco, 1965
F. W. Campbell and J. G. Robson, Application of Fourier analysis to the visibility of gratings, J. Phys. (London) 197, 551–566 (1968)
N. Graham and J. Nachmias, Detecting of grating patterns containing two spatial frequencies: A comparison of single and multiple channel models, Vis. Res. 11, 251–261 (1971)
J. G. Robson and N. Graham, Probability summation and regional variation in contrast sensitivity across the visual field, Vis. Res. 21, 409–418 (1981)
H. R. Wilson and J. R. Bergen, A four mechanism model for threshold spatial vision, Vis. Res. 19, 19–32 (1979)
S. W. Kuffler, Discharge patterns and functional organization of mammalian retina, J. Neurophysiol. 16, 37–68 (1953)
R. W. Rodieck, Qualitative analysis of cat retinal cell response to visual stimuli, Vis. Res. 5, 583–601 (1965)
E. P. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev. 40, 749–759 (1932)
F. John, Partial Differential Equations, Springer-Verlag, New York, 1978
- J. Heading, An introduction to phase-integral methods, Methuen & Co., Ltd., London; John Wiley & Sons, Inc., New York, 1962. MR 0148995
- Carl M. Bender and Steven A. Orszag, Advanced mathematical methods for scientists and engineers, McGraw-Hill Book Co., New York, 1978. International Series in Pure and Applied Mathematics. MR 538168
- Joseph B. Keller, Corrected Bohr-Sommerfeld quantum conditions for nonseparable systems, Ann. Physics 4 (1958), 180–188. MR 99207, DOI https://doi.org/10.1016/0003-4916%2858%2990032-0
- Joseph B. Keller, Semiclassical mechanics, SIAM Rev. 27 (1985), no. 4, 485–504. MR 812451, DOI https://doi.org/10.1137/1027139
- Herbert Goldstein, Classical Mechanics, Addison-Wesley Press, Inc., Cambridge, Mass., 1951. MR 0043608
L. Sirovich and B. W. Knight, Characteristic patterns of an inhomogeneous imaging system with applications to vision, J. Op. Soc. Amer. A3, 358–364 (1986)
Y. T. So and R. Shapley, Spatial properties of X and Y cells in the lateral geniculate nucleus of the cat and conduction velocities of thin inputs, Exp. Brain Res. 36, 533–550 (1979)
B. G. Cleland, T. H. Harding, and U. Tulunay-Keesey, Visual resolution and receptive field size: examination of two kinds of retinal ganglion cells, Science 205, 1015–1017 (1979)
B. Fischer and H. V. May, Invarianzen in der katzen retina: gesetzmassig beziehungen zwischen empfindlichkeit, grosse und lage receptivier felder von ganglienzellen, Exp. Brain Res. 11, 448–464 (1970)
- Wilhelm Magnus, Fritz Oberhettinger, and Raj Pal Soni, Formulas and theorems for the special functions of mathematical physics, Third enlarged edition, Die Grundlehren der mathematischen Wissenschaften, Band 52, Springer-Verlag New York, Inc., New York, 1966. MR 0232968
L. Sirovich and B. W. Knight, On the eigentheory of operators which exhibit a slow variation, Quart Appl. Math. 38, 469–488 (1981)
L. Sirovich and B. W. Knight, Contributions to the eigenvalue problem for slowly varying operators, SIAM J. Appl. Math. 42, 356–377 (1982)
B. W. Knight and L. Sirovich, The Wigner transform and some exact properties of linear operators, SIAM J. Appl. Math. 42, 378–389 (1982)
L. Sirovich and B. W. Knight, The eigenfunction problem in higher dimensions, I. Asymptotic theory, Proc. Natl. Acad. Sci. USA 82, 8275–8278 (1985)
B. W. Knight and L. Sirovich, The eigenfunction problem in higher dimensions II. Exact Results, Proc. Natl. Acad. Sci. USA 83, 527–530 (1986)
T. Cornsweet, Visual Perception, Academic Press, New York, 1970
F. Ratliff, Mach Bands: Qualitative Studies on Neural Networks in the Retina, Holden-Day, San Francisco, 1965
F. W. Campbell and J. G. Robson, Application of Fourier analysis to the visibility of gratings, J. Phys. (London) 197, 551–566 (1968)
N. Graham and J. Nachmias, Detecting of grating patterns containing two spatial frequencies: A comparison of single and multiple channel models, Vis. Res. 11, 251–261 (1971)
J. G. Robson and N. Graham, Probability summation and regional variation in contrast sensitivity across the visual field, Vis. Res. 21, 409–418 (1981)
H. R. Wilson and J. R. Bergen, A four mechanism model for threshold spatial vision, Vis. Res. 19, 19–32 (1979)
S. W. Kuffler, Discharge patterns and functional organization of mammalian retina, J. Neurophysiol. 16, 37–68 (1953)
R. W. Rodieck, Qualitative analysis of cat retinal cell response to visual stimuli, Vis. Res. 5, 583–601 (1965)
E. P. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev. 40, 749–759 (1932)
F. John, Partial Differential Equations, Springer-Verlag, New York, 1978
J. Heading, An Introduction to Phase Integral Methods, Methuen & Co., Ltd., London, 1962
C. M. Bender and S. Orzag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, New York, 1978
J. B. Keller, Corrected Bohr-Sommerfeld quantum conditions for non-separable systems, Ann. Phys. 9, 180–188 (1958)
J. B. Keller, Semiclassical Mechanics, SIAM Review 27, 485–504 (1985)
H. Goldstein, Classical Mechanics, Addison-Wesley, Reading, Massachusetts, 1981
L. Sirovich and B. W. Knight, Characteristic patterns of an inhomogeneous imaging system with applications to vision, J. Op. Soc. Amer. A3, 358–364 (1986)
Y. T. So and R. Shapley, Spatial properties of X and Y cells in the lateral geniculate nucleus of the cat and conduction velocities of thin inputs, Exp. Brain Res. 36, 533–550 (1979)
B. G. Cleland, T. H. Harding, and U. Tulunay-Keesey, Visual resolution and receptive field size: examination of two kinds of retinal ganglion cells, Science 205, 1015–1017 (1979)
B. Fischer and H. V. May, Invarianzen in der katzen retina: gesetzmassig beziehungen zwischen empfindlichkeit, grosse und lage receptivier felder von ganglienzellen, Exp. Brain Res. 11, 448–464 (1970)
W. Magnus, F. Oberhettinger and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, Springer-Verlag, New York, 1966
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Article copyright:
© Copyright 1987
American Mathematical Society
