Perception of direction of motion reflects the early integration of first and second-order stimulus spatial properties

Neurons in the mammalian visual cortex have been found to respond to second-order features which are not defined by changes in luminance over the retina (Albright, 1992; Zhou & Baker, 1993, 1994, 1996; Mareschal & Baker, 1998a,b). The detection of these stimuli is most often accounted for by a separate nonlinear processing stream, acting in parallel to the linear stream in the visual system. Here we examine the two-dimensional spatial properties of these nonlinear neurons in area 18 using envelope stimuli, which consist of a high spatial-frequency carrier whose contrast is modulated by a low spatial-frequency envelope. These stimuli would fail to elicit a response in a conventional linear neuron because they are designed to contain no spatial-frequency components overlapping the neuron's luminance defined passband. We measured neurons' responses to these stimuli as a function of both the relative spatial frequencies and relative orientations of the carrier and envelope. Neurons' responses to envelope stimuli were narrowband to the carrier spatial frequency, with optimal values ranging from 8- to 30-fold higher than the envelope spatial frequencies. Neurons' responses to the envelope stimuli were strongly dependent on the orientation of the envelope and less so on the orientation of the carrier. Although the selectivity to the carrier orientation was broader, neurons' responses were clearly tuned, suggesting that the source of nonlinear input is cortical. There was no fixed relationship between the optimal carrier and envelope spatial frequencies or orientations, such that nonlinear neurons responding to these stimuli could perhaps respond to a variety of stimuli defined by changes in scale or orientation.

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Phragmén-Lindelöf Alternative Results for a Class of Thermoelastic Plate

Symmetry ◽

10.3390/sym13122256 ◽

2021 ◽

Vol 13 (12) ◽

pp. 2256

Author(s):

Shiguang Luo ◽

Jincheng Shi ◽

Baiping Ouyang

Keyword(s):

Energy Method ◽

Differential Inequality ◽

Second Order ◽

Biharmonic Operator ◽

Spatial Properties ◽

Energy Expression ◽

Coupling Equations ◽

Thermoelastic Plate

The spatial properties of solutions for a class of thermoelastic plate with biharmonic operator were studied. The energy method was used. We constructed an energy expression. A differential inequality which the energy expression was controlled by a second-order differential inequality is deduced. The Phragme´n-Lindelo¨f alternative results of the solutions were obtained by solving the inequality. These results show that the Saint-Venant principle is also valid for the hyperbolic–hyperbolic coupling equations. Our results can been seen as a version of symmetry in inequality for studying the Phragme´n-Lindelo¨f alternative results.

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Disappearance Voltage Determinations Using a Convergent Beam

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100064979 ◽

1971 ◽

Vol 29 ◽

pp. 184-185

Author(s):

W. L. Bell

Keyword(s):

Second Order ◽

Objective Method ◽

Uniform Thickness ◽

Rocking Curve ◽

Crystal Perfection ◽

Kikuchi Line ◽

Central Maximum ◽

Diffraction Patterns ◽

Convergent Beam ◽

Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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