2 results
Harmonic basis functions for spatial coding in the cat striate cortex
- V. D. Glezer, V. V. Yakovlev, V. E. Gauzelman
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- Journal:
- Visual Neuroscience / Volume 3 / Issue 4 / October 1989
- Published online by Cambridge University Press:
- 02 June 2009, pp. 351-363
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The number of subregions in the activity profiles of simple cells varies in different cells from 2–8; that is, the number of cycles in the weighting function varies from 1–4. The distribution of receptive-field (RF) sizes at eccentricities of 0-6 deg are clustered at half-octave intervals and form a discrete distribution with maxima at 0.62, 0.9, 1.24, 1.8, 2.48, and 3.4 deg. The spatial frequencies to which the cells are tuned are also clustered at half-octave intervals, forming a discrete distribution peaking at 0.45, 0.69, 0.9, 1.35, 1.88, 2.7, 3.8, and 5.6 cycles/deg. If we divide the RF sizes by the size of the period of the subregions, then the average indices of complexity (really existing) or the number of cycles in the weighting function form (after normalization) the sequences: 1, 1.41, 2.0, 2.9, 4.15.
The relation between the bandwidth of the spatial-frequency characteristic and the optimal spatial frequency is in accordance with predictions of the Fourier hypothesis. The absolute bandwidth does not change with the number of cycles/module. This means that inside the module the absolute bandwidth does not change with the number of the harmonic. The results allow us to suggest the following. A module of the striate cortex, which is a group of cells with RFs of equal size projected onto the same area of central visual field, accounts for the Fourier description of the image. The basis functions of the module are composed of four harmonics only, irrespective of size and position of the module.
Besides linear cells (sinusoidal and cosinusoidal elements), the module contains nonlinear cells, performing a nonlinear summation of the responses of sinusoidal and cosinusoidal elements. Such cells are characterized by an index of complexity which is more than the number of cycles in the weighting function and by marked overlap of ON and OFF zones. The analysis of organization suggests that the cells can measure the amplitude and phase of the stimulus.
3 - Patterns
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- By G. E. Koppenwallner, D. Etling, C.-W. Leong, J. M. Ottino, E. Villermaux, J. Duplat, P. D. Weidman, V. O. Afenchenko, A. B. Ezersky, S. V. Kiyashko, M. I. Rabinovich, E. Bodenschatz, S. W. Morris, J. R. De bruyn, D. S. Cannell, G. Ahlers, C. F. Chen, F. Zoueshtiagh, P. J. Thomas, G. Gauthier, P. Gondret, F. Moisy, M. Rabaud, M. Fermigier, P. Jenffer, E. Tan, S. T. Thoroddsen, B. Vukasinovic, A. Glezer, M. K. Smith, N. J. Zabusky, W. Townsend, R. A. Hess, N. J. Brock, B. J. Weber, L. W. Carr, M. S. Chandrasekhara
- M. Samimy, Ohio State University, K. S. Breuer, Brown University, Rhode Island, L. G. Leal, University of California, Santa Barbara, P. H. Steen, Cornell University, New York
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- Book:
- A Gallery of Fluid Motion
- Published online:
- 25 January 2010
- Print publication:
- 12 January 2004, pp 28-41
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Summary
Vortex flows paint themselves
The artistlike pictures of vortex flows presented here have been produced by the flow itself. The method of this “natural” flow visualization can be described briefly as follows: The working fluid is water mixed with some paste in order to increase the viscosity. Vortex flows are produced by pulling a stick or similar devices through the fluid or by injecting fluid through a nozzle into the working tank.
The flow visualization is performed in the following way: the surface of the fluid at rest is sparkled with oil paint of different colors diluted with some evaporating chemical. After the vortex structures have formed due to wakes or jets, a sheet of white paper is placed on the surface of the working fluid, where the oil color is attached to the paper immediately. The final results are artistlike paintings of vortex flows which exhibit a rich variety of flow structures.
Mixing in regular and chaotic flows
These photographs show the time evolution of two passive tracers in a low Reynolds number two-dimensional timeperiodic flow. The initial condition corresponds to two blobs of dye, green and orange, located below the free surface of a cavity filled with glycerine. The flow is induced by moving the top and bottom walls of the cavity while the other two walls are fixed. In this experiment the top wall moves from left to right and the bottom wall moves from right to left; both velocities are of the form Usin2(2πt/T), with the same U and the same period T, but with a phase shift of 90°.