A Pedestal Blocks the Perception of Non-Fourier Motion

Perception ◽  
1997 ◽  
Vol 26 (1_suppl) ◽  
pp. 17-17 ◽  
Author(s):  
O I Ukkonen ◽  
A M Derrington
Keyword(s):  
Modulation Depth ◽  
Discrimination Performance ◽  
Spatial Variations ◽  
Second Order ◽  
First Order ◽  
Direction Discrimination ◽  
Forced Choice Task ◽  
The Mean ◽  
Texture Contrast ◽  
Moving Pattern

We wanted to know whether the mechanisms that discriminate the motion of first-order patterns (defined by spatial variations of luminance) differ from those that detect the motion of non-Fourier or second-order patterns (defined by spatial variations of contrast). To address this question we tested whether motion discrimination performance of first-order and second-order patterns was affected by a pedestal (Lu and Sperling, 1995 Vision Research35 2697 – 2722). A pedestal is a static replica of a moving pattern. We used pedestals with contrast or modulation depth twice the value at which it becomes possible to discriminate the direction of a moving pattern. A two-interval forced-choice task was used to determine how direction discrimination varies with contrast of sine gratings (1 cycle deg−1) and modulation depth of amplitude-modulated gratings presented either alone or with a pedestal. The amplitude-modulated gratings had a 5 cycles deg−1 carrier modulated at 1 cycle deg−1. Three different temporal frequencies (1, 3, and 12 Hz) were studied. Performance with sine gratings was unaffected by the pedestal at all temporal frequencies tested. For amplitude-modulated gratings the pedestal raised the modulation depth at which it became possible to discriminate the direction of motion. This elevation in threshold decreased when the mean contrast of the pattern was high. This result shows that immunity to pedestals of texture-contrast patterns (Lu and Sperling, 1996 Journal of the Optical Society of America13 2305 – 2318) does not generalise to other non-Fourier motion stimuli.

Asymmetric Masking: Luminance Gratings Mask Second-Order Gratings, but Not Vice Versa

Perception ◽  
1997 ◽  
Vol 26 (1_suppl) ◽  
pp. 345-345
Author(s):  
A J Schofield ◽  
M A Georgeson
Keyword(s):  
Modulation Depth ◽  
Broad Band ◽  
Gain Control ◽  
High Amplitude ◽  
Second Order ◽  
Human Vision ◽  
First Order ◽  
Contrast Gain ◽  
Spatiotemporal Information ◽  
The Mean

Human vision can detect spatiotemporal information conveyed by first-order modulations of luminance and by second-order, non-Fourier modulations of image contrast. Models for second-order motion have suggested two filtering stages separated by a rectifying nonlinearity. We explore here the encoding of stationary first-order and second-order gratings, and their interaction. Stimuli consisted of 2-D broad-band static visual noise sinusoidally modulated in luminance (first-order, LM) or contrast (second-order, CM). Modulation thresholds were measured in a two-interval forced-choice staircase procedure. With increasing noise contrast, first-order sensitivity decreased (owing to masking) but sensitivity to contrast modulation increased. Weak background gratings present in both intervals produced order-specific facilitation: LM background facilitated LM detection (the ‘dipper function’) and CM facilitated CM detection. LM did not facilitate CM, nor vice versa, and this is strong evidence that LM and CM are detected via different mechanisms. Nevertheless, suprathreshold LM gratings masked CM detection, but not vice versa. High-amplitude CM masks had little or no effect on CM or LM detection. A broadly tuned divisive gain-control mechanism applied to the first-order filtering stage has been proposed by Foley (1994 Journal of the Optical Society of America A11 1710 – 1719) to account for masking of luminance gratings, and this might also explain the masking of second-order by first-order stimuli. First-order maskers would drive down the effective contrast of the carrier, thus reducing second-order sensitivity. But for second-order maskers the mean contrast, and hence contrast gain, remained constant, independent of modulation depth. Thus second-order gratings would produce no masking effects, as observed.

The Second-Order Master Equation

2019 ◽  
pp. 128-158
Author(s):  
Pierre Cardaliaguet ◽  
François Delarue ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions
Keyword(s):  
Master Equation ◽  
Mean Field ◽  
Second Order ◽  
Well Posedness ◽  
Mean Field Game ◽  
First Order ◽  
Common Noise ◽  
System P ◽  
The Mean

This chapter investigates the second-order master equation with common noise, which requires the well-posedness of the mean field game (MFG) system. It also defines and analyzes the solution of the master equation. The chapter explains the forward component of the MFG system that is recognized as the characteristics of the master equation. The regularity of the solution of the master equation is explored through the tangent process that solves the linearized MFG system. It also analyzes first-order differentiability and second-order differentiability in the direction of the measure on the same model as for the first-order derivatives. This chapter concludes with further description of the derivation of the master equation and well-posedness of the stochastic MFG system.

Second-Order Mach Bands, Chevreul, and Craik-O’Brien-Cornsweet Illusions

2017 ◽  
Author(s):  
Zhong-Lin Lu ◽  
George Sperling
Keyword(s):  
Second Order ◽  
Spatial Interactions ◽  
Apparent Brightness ◽  
Concomitant Change ◽  
Brightness Perception ◽  
First Order ◽  
Mach Bands ◽  
Texture Contrast

Second-order texture illusions, corresponding to Mach bands, Chevreul, and Craik-O’Brien-Cornsweet illusions in brightness perception, are generated by replacing luminance modulations in the classic stimuli with modulations of texture contrast. Whereas the classic (first-order) illusions exhibit changes in lightness or darkness near boundaries, the second-order stimuli exhibit analogous perceptual effects that are increases or decreases in apparent texture contrast with no concomitant change in apparent brightness. The magnitudes of the second-order texture-contrast changes are comparable to brightness changes in the classic first-order illusions. These results indicate that second-order (texture) illusions involve spatial interactions that are remarkably similar to those in first-order (luminance) processing.

Perturbation Analysis of Texture Effects on Lubricated Devices

2005 ◽  
Author(s):  
Gustavo C. Buscaglia ◽  
Mohammed Jai ◽  
Sorin Ciuperca
Keyword(s):  
Friction Coefficient ◽  
Friction Force ◽  
Perturbation Analysis ◽  
Mathematical Analysis ◽  
Load Capacity ◽  
Second Order ◽  
Numerical Investigations ◽  
First Order ◽  
The Mean

Given a bearing of some specified shape, what is the effect of texturing its surfaces uniformly? Experimental and numerical investigations on this question have recently been pursued, which we complement here with a mathematical analysis. Assuming the texture length to be much smaller than the bearing’s length, we combine homogenization techniques with perturbation analysis. This allows us to consider arbitrary, 2D texture shapes. The results show that both the load capacity and the friction force depend, to first order in the amplitude, just on the mean depth/height of the texture. The dependence of the friction coefficient is thus of second order.

A Stochastic Model for Primary Settlers

1970 ◽  
Vol 5 (1) ◽  
pp. 129-170
Author(s):  
D.P. Singh ◽  
A.W. Bryson ◽  
P.L. Silveston
Keyword(s):  
Stochastic Model ◽  
Stochastic Models ◽  
Suspended Solids ◽  
Sewage Treatment ◽  
Sewage Treatment Plant ◽  
Treatment Plant ◽  
Second Order ◽  
Order Model ◽  
First Order ◽  
The Mean

Abstract Stochastic models of process units are useful where the flow and concentrations in a feed stream vary appreciably over long time periods in a random way. Models yield not only the mean, but provide a measure of the variation around the mean. Assuming sedimentation can be described by a rate equation, stochastic models are developed for zero, first and second order rate processes. The zero order model can be rejected because it cannot be made to fit plant data, while the second order model was not developed further because of its complexity. The rate parameter for the first order model was evaluated from 1968 suspended solids data for the Kitchener Sewage Treatment Plant and found to have zero variance. Testing the model against 1966 and 1967 data and shorter period for 1968 showed that the model predicted suspended solids and BOD removals differing on the average from plant results by 10%. The first order stochastic model gives, thus, a satisfactory representation of primary settler performance.

The mean drift force and yaw moment on marine structures in waves and current

1993 ◽  
Vol 250 ◽  
pp. 121-142 ◽  
Author(s):  
John Grue ◽  
Enok Palm
Keyword(s):  
Momentum Flux ◽  
Wave Spectrum ◽  
Second Order ◽  
The Body ◽  
Far Field ◽  
Marine Structures ◽  
First Order ◽  
The Mean ◽  
Yaw Moment ◽  
Drift Forces

The effect of the steady second-order velocities on the drift forces and moments acting on marine structures in waves and a (small) current is considered. The second-order velocities are found to arise due to first-order evanescent modes and linear body responses. Their contributions to the horizontal drift forces and yaw moment, obtained by pressure integration at the body, and to the yaw drift moment, obtained by integrating the angular momentum flux in the far field, are expressed entirely in terms of the linear first-order solution. The second-order velocities may considerably increase the forward speed part of the mean yaw moment on realistic marine structures, with the most important contribution occurring where the wave spectrum often has its maximal value. The contribution to the horizontal forces obtained by pressure integration is, however, always found to be small. The horizontal drift forces obtained by the linear momentum flux in the far field are independent of the second-order velocities, provided that there is no velocity circulation in the fluid.

scholarly journals Note About a New Evaluation of the Direct Perturbations of the Planets on the Moon’s Motion

1981 ◽  
Vol 63 ◽  
pp. 265-266
Author(s):  
D. Standaert
Keyword(s):  
Order Theory ◽  
Second Order ◽  
Point Of View ◽  
Internal Point ◽  
First Order ◽  
Keplerian Orbits ◽  
First Order Theory ◽  
External Point ◽  
Constants Of Motion ◽  
The Mean

The aim of this paper is to present the principal features of a new evaluation of the direct perturbations of the planets on the Moon’s motion. Using the method already published in Celestial Mechanics (Standaert, 1980), we compute “a first-order theory” aiming at an accuracy of the order of the meter for all periodic terms of period less than 3 500 years.From an external point of view, we mean by that: a)keplerian orbits for the planets,b)the ELP-2000 solution of the Main Problem proposed by Mrs. Chapront (Chapront-Touzë, 1980),c)the first-order derivatives with respect to the constants of motion of the SALE theory of Henrard (Henrard, 1979).On the other hand, from an internal point of view, the computations include: d)the development in Legendre polynomials not only to the first-order in (a/a'), but also the following ones (up to the sixth-order for Venus, for example),e)the contributions of the second-order in the Lie triangle,f)second-order contributions coming from the corrections of the mean motions due to the planetary action.

scholarly journals Second-Order Inference for the Mean of a Variable Missing at Random

2016 ◽  
Vol 12 (1) ◽  
pp. 333-349 ◽  
Author(s):  
Iván Díaz ◽  
Marco Carone ◽  
Mark J. van der Laan
Keyword(s):  
Coverage Probability ◽  
Convergence Rates ◽  
Kernel Smoothing ◽  
Missing At Random ◽  
Second Order ◽  
Finite Sample ◽  
Case Scenario ◽  
First Order ◽  
Order Expansion ◽  
The Mean

Abstract We present a second-order estimator of the mean of a variable subject to missingness, under the missing at random assumption. The estimator improves upon existing methods by using an approximate second-order expansion of the parameter functional, in addition to the first-order expansion employed by standard doubly robust methods. This results in weaker assumptions about the convergence rates necessary to establish consistency, local efficiency, and asymptotic linearity. The general estimation strategy is developed under the targeted minimum loss-based estimation (TMLE) framework. We present a simulation comparing the sensitivity of the first and second-order estimators to the convergence rate of the initial estimators of the outcome regression and missingness score. In our simulation, the second-order TMLE always had a coverage probability equal or closer to the nominal value 0.95, compared to its first-order counterpart. In the best-case scenario, the proposed second-order TMLE had a coverage probability of 0.86 when the first-order TMLE had a coverage probability of zero. We also present a novel first-order estimator inspired by a second-order expansion of the parameter functional. This estimator only requires one-dimensional smoothing, whereas implementation of the second-order TMLE generally requires kernel smoothing on the covariate space. The first-order estimator proposed is expected to have improved finite sample performance compared to existing first-order estimators. In the best-case scenario of our simulation study, the novel first-order TMLE improved the coverage probability from 0 to 0.90. We provide an illustration of our methods using a publicly available dataset to determine the effect of an anticoagulant on health outcomes of patients undergoing percutaneous coronary intervention. We provide R code implementing the proposed estimator.

Low-Frequency Phenomena Associated With Vessels Moored at Sea

1975 ◽  
Vol 15 (06) ◽  
pp. 487-494 ◽  
Author(s):  
J.A. Pinkster
Keyword(s):  
Wave Height ◽  
Low Frequency ◽  
Second Order ◽  
Irregular Waves ◽  
Ship Motions ◽  
Wave Forces ◽  
Mooring System ◽  
Frequency Wave ◽  
First Order ◽  
The Mean

Abstract The influence of the low-frequency-wave-drifting force on the motions of moored vessels and the loads in the mooring system is demonstrated from results of model tests in irregular waves. The origin of the wave drifting force is discussed and methods for calculating the mean drifting force are reviewed. To facilitate calculation of the low-frequency-wave drifting force on an object in irregular waves, an existing method using the mean drifting force in regular waves is generalized. The results of calculations using the method introduced in this paper are compared with previously published test results. Finally, some remarks are added concerning effects that have not been accounted for in existing calculation methods. Introduction A vessel moored at sea in stationary conditions with regard to waves, wind, and current is subjected to forces that tend to shift it from the desired position. For a given vessel and position in the position. For a given vessel and position in the horizontal plane, the motions depend on both the mooring system and the external forces acting on the vessel. In steady conditions, the forces caused by a constant wind and current are constant quantities for a given heading angle of the vessel. The forces caused by a stationary irregular sea are of an irregular nature and may be split into two parts: first-order oscillatory forces with wave parts: first-order oscillatory forces with wave frequency, and second-order, slowly varying forces with frequencies much lower than the wave frequency.The first-order oscillatory wave forces on a vessel cause the well known ship motions whose frequencies equal the frequencies present in the spectrum of the irregular waves. These are the linear motions of surge, sway, and heave and the three angular motions of roll, pitch, and yaw. In general, the first-order wave forces are proportional to the wave height, as are the ensuing motions. The magnitude of the linear oscillatory motions is in the order of the height of the waves.The second-order wave forces, perhaps better known as the wave drifting forces, have been shown to be proportional to the square of the wave height. These forces, though small in magnitude, are the cause of the low-frequency, large-amplitude, horizontal motions sometimes observed in large vessels moored in irregular waves. Tests run in irregular waves in wave tanks of the Netherlands Ship Model Basin revealed a number of properties and effects of the low-frequency-wave properties and effects of the low-frequency-wave drifting force that are discussed here using the results of two test programs.The first of these programs concerns tests run with the model of a 125,000-cu m LNG carrier moored in head seas with an ideal linear mooring system. The second program deals with a 300,000-DWT VLCC moored with a realistic nonlinear bow hawser to a single-buoy mooring in waves, wind, and current coming from different directions.The results of the tests with the LNG carrier are shown in Figs. 1 through 3, while the results of the tests with the 300,000-DWT VLCC are shown in Fig. 4. All results are given in full-scale values. Fig. 1 shows the wave trace and the surge motion of the LNG carrier to a base of time. SPEJ P. 487

Effects of Adaptation on Perceived Location for First-Order and Second-Order Visual Stimuli

Perception ◽  
1996 ◽  
Vol 25 (1_suppl) ◽  
pp. 180-180
Author(s):  
D Whitaker ◽  
P V McGraw ◽  
D M Levi
Keyword(s):  
Test Stimulus ◽  
Contrast Ratio ◽  
Central Element ◽  
Second Order ◽  
Stimulus Contrast ◽  
Low Contrast ◽  
First Order ◽  
Ratio Data ◽  
Alignment Task ◽  
Texture Contrast

Observers adapted to a stimulus consisting of two vertically separated antisymmetric Gaussian blobs. This was immediately followed by a 3-Gaussian-blob alignment task, whose outer two elements were spatially coincident with those of the adapting stimulus. The adapting antisymmetric stimulus resulted in a perceived misalignment of the central element of the test stimulus, and the magnitude of this perceived offset was established by the method of constant stimuli. The apparent offset increased as a power function of the adapting stimulus contrast at all test contrast levels. Perceived offset was greater for low-contrast test stimuli, although dependence upon the contrast of the adapting stimulus was less pronounced. When expressed as a function of adapting/test contrast ratio, data for all conditions collapsed together to form a single, saturating function which was well described by the formula k/[ k'+(1/ratio)], where k and k' are constants. Thus, at high adapting/test ratios, the function saturated at an offset of k/ k'. Adaptation effects were measured for luminance-defined first-order stimuli, and also stimuli defined by variations in texture contrast, which can be termed second-order. The effects of adaptation on perceived offset for second-order stimuli were at least as large as those for first-order, but little or no crossover adaptation occurred, ie adapting to a second-order antisymmetric stimulus produced no effect on a first-order test stimulus and vice versa. This suggests that the mechanisms involved in the localisation of first-order and second-order stimuli are independent.

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