Effects of Visual Angle on Perspective Reversal for Ambiguous Patterns

Perception ◽  
1982 ◽  
Vol 11 (3) ◽  
pp. 263-273 ◽  
Author(s):  
Antonio Borsellino ◽  
Franco Carlini ◽  
Massimo Riani ◽  
Maria Teresa Tuccio ◽  
Angelo De Marco ◽  
...  
Keyword(s):  
Gamma Distribution ◽  
Visual Angle ◽  
Necker Cube ◽  
Constant Term ◽  
Ambiguous Figure ◽  
Statistical Distributions ◽  
Reversal Time ◽  
Tentative Model ◽  
Pattern Size ◽  
The Mean

Reversal rates of an ambiguous figure (the Necker cube) were studied for different pattern sizes covering a range of visual angles θ from ∼1 to 62 deg. A large number of reversals was obtained for each observer and each pattern in order to examine the statistical distributions of reversal times. A pronounced flattening of the statistical distributions (represented throughout by a gamma distribution) and a growth of the mean duration of each percept, with increasing pattern size was found. A plateau in the range of θ between 5 and 20–30 deg was observed. For larger values of θ two kinds of observers have been identified: for ‘fast’ observers the inversion rate is little affected by θ, whilst for ‘slow’ observers, the mean reversal time increases strongly with θ. A tentative model, based on three different contributions to the duration of the alternation process, is proposed: a constant term, independent of θ, and two terms dependent on θ—a retinal term, and a cortical one. The last term is interpreted as due to the spreading of excitation with the characteristic of a filling-in process.

Smooth Periodic Eye Movements Can Entrain Perceptual Alternation

1991 ◽  
Vol 73 (3) ◽  
pp. 835-843 ◽  
Author(s):  
M. Scotto
Keyword(s):  
Eye Movements ◽  
Necker Cube ◽  
Oscillation Period ◽  
Mean Value ◽  
Sharp Reduction ◽  
Close Match ◽  
Reversal Time ◽  
Change In The Mean ◽  
Perceptual Alternation ◽  
The Mean

The reversal signals and eye movements of three subjects looking at a Necker cube that moved sinusoidally in the subject's field of view were recorded. The aim of the experiment was to provide evidence of possible synchronisation of perceptual alternation with smooth periodic eye movements. The occurrence of synchronisation was demonstrated for a proper choice of the eye oscillation period by both a sharp reduction in the fluctuations of the reversal time and a change in the mean value of this parameter. Such variations resulted in a close match of the mean reversal time to a multiple of the eye oscillation period. Further, inversions of the direction of eye movements elicited pattern reversals in a systematic way, characteristic for each subject. The described phenomenon, which is a typical example of nonlinear-resonant behaviour, stresses a new important aspect of the complex interaction pattern relating pursuit eye movements to visual perception.

Flows of liquid4He due to oscillating grids

2017 ◽  
Vol 832 ◽  
pp. 578-599 ◽  
Author(s):  
P. Švančara ◽  
M. La Mantia
Keyword(s):  
Turbulent Flows ◽  
Particle Tracking Velocimetry ◽  
Reynolds Numbers ◽  
Quantized Vortices ◽  
Viscous Fluids ◽  
Statistical Distributions ◽  
Small Particles ◽  
Oscillating Grids ◽  
The Mean ◽  
Cryogenic Flows

We investigate cryogenic flows of liquid4He between two grids oscillating in phase, at temperatures ranging from approximately 1.3 to 2.5 K, resulting in suitably defined Reynolds numbers up to$10^{5}$. We specifically study the flow-induced motions of small particles suspended in the fluid by using the particle tracking velocimetry technique. We focus on turbulent flows of superfluid4He that occur below approximately 2.2 K and are known to display, in certain conditions, features different from those observed in flows of classical viscous fluids, such as water. We find that, at large enough length scales, larger than the mean distance between quantized vortices, representing the quantum length scale of the flow, the shapes of the velocity and velocity increment statistical distributions are very similar to those obtained in turbulent flows of viscous fluids. The experimental outcome strongly supports the view that, in the range of investigated parameters, particles probing flows of superfluid4He behave as if they were tracking classical flows.

scholarly journals New Metallicity Calibration Down to [Fe/H] = −2.75 dex

2003 ◽  
Vol 20 (2) ◽  
pp. 165-172 ◽  
Author(s):  
S. Karaali ◽  
S. Bilir ◽  
Y. Karataş ◽  
S. G. Ak
Keyword(s):  
Least Squares Method ◽  
Constant Term ◽  
Colour Index ◽  
High Resolution Spectroscopy ◽  
Mean Deviation ◽  
Galactic Latitude ◽  
The Sun ◽  
Degree Polynomial ◽  
The Mean ◽  
Different Sources

AbstractWe have taken 88 dwarfs, covering the colour-index interval 0.37 ≤ (B–V)0 ≤ 1.07 mag, with metallicities –2.70 ≤ [Fe/H] ≤ +0.26 dex, from three different sources for new metallicity calibration. The catalogue of Cayrel de Stroble et al. (2001), which includes 65% of the stars in our sample, supplies detailed information on abundances for stars with determination based on high-resolution spectroscopy. In constructing the new calibration we have used as ‘corner stones’ 77 stars which supply at least one of the following conditions: (i) the parallax is larger than 10 mas (distance relative to the Sun less than 100 pc) and the galactic latitude is absolutely higher than 30°; (ii) the parallax is rather large, if the galactic latitude is absolutely low and vice versa. Contrary to previous investigations, a third-degree polynomial is fitted for the new calibration: [Fe/H] = 0.10 – 2.76δ – 24.04δ2 + 30.00δ3. The coefficients were evaluated by the least-squares method, without regard to the metallicity of Hyades. However, the constant term is in the range of metallicity determined for this cluster, i.e. 0.08 ≤ [Fe/H] ≤ 0.11 dex. The mean deviation and the mean error in our work are equal to those of Carney (1979), for [Fe/H] ≥ –1.75 dex where Carney's calibration is valid.

On population-size-dependent branching processes

1984 ◽  
Vol 16 (1) ◽  
pp. 30-55 ◽  
Author(s):  
F. C. Klebaner
Keyword(s):  
Stochastic Model ◽  
Asymptotic Behaviour ◽  
Rate Of Convergence ◽  
Population Size ◽  
Gamma Distribution ◽  
Branching Processes ◽  
Independent Random Variables ◽  
Size Dependent ◽  
Offspring Distribution ◽  
The Mean

We consider a stochastic model for the development in time of a population {Zn} where the law of offspring distribution depends on the population size. We are mainly concerned with the case when the mean mk and the variance of offspring distribution stabilize as the population size k grows to ∞, The process exhibits different asymptotic behaviour according to m < l, m = 1, m> l; moreover, the rate of convergence of mk to m plays an important role. It is shown that if m < 1 or m = 1 and mn approaches 1 not slower than n–2 then the process dies out with probability 1. If mn approaches 1 from above and the rate of convergence is n–1, then Zn/n converges in distribution to a gamma distribution, moreover a.s. both on a set of non-extinction and there are no constants an, such that Zn/an converges in probability to a non-degenerate limit. If mn approaches m > 1 not slower than n–α, α > 0, and do not grow to ∞ faster than nß, β <1 then Zn/mn converges almost surely and in L2 to a non-degenerate limit. A number of general results concerning the behaviour of sums of independent random variables are also given.

An Improved Interpretation of Recoil Compressive Failure Data for High-Performance Polymers

2001 ◽  
Vol 13 (4) ◽  
pp. 251-257 ◽  
Author(s):  
J A Newell ◽  
J M Gustafson
Keyword(s):  
High Performance ◽  
Weibull Model ◽  
Statistical Distributions ◽  
Compressive Failure ◽  
Accurate Approximation ◽  
Data Set ◽  
Data Intensive ◽  
Failure Data ◽  
The Mean ◽  
Sample Set

This paper describes an improved methodology for the accurate interpretation of recoil compressive failure data. This new procedure uses a wider portion of the data set in its interpretation than does the method of Allen and is far simpler and less data intensive than the Weibull model proposed by Hayes. Computer simulations using various statistical distributions for the intrinsic recoil compressive strength of a batch of filaments show that this method quickly and accurately converges to an accurate approximation of the mean for the sample set.

Stochastic Models and Fluctuations in Reversal Time of Ambiguous Figures

Perception ◽  
1977 ◽  
Vol 6 (6) ◽  
pp. 645-656 ◽  
Author(s):  
Angelo de Marco ◽  
Piero Penengo ◽  
Aurelia Trabucco ◽  
Antonio Borsellino ◽  
Franco Carlini ◽  
...  
Keyword(s):  
Random Walk ◽  
Gamma Distribution ◽  
Stochastic Models ◽  
Strong Correlation ◽  
Probability Distributions ◽  
Poisson Model ◽  
Ambiguous Figures ◽  
Underlying Process ◽  
Reversal Time ◽  
Low Efficiency

Five probability distributions for the description of temporal fluctuations in the perception of ambiguous figures were fitted to previously obtained experimental results and classified according to their efficiency in describing the data. The gamma, Wiener, and Capocelli-Ricciardi distributions showed the highest efficiency, while the χ2 and Taylor-Aldridge distributions showed a very low efficiency. Therefore the underlying process may be described either by a simple Poisson model or by a random-walk model. For the gamma distribution there was a strong correlation between the parameters, while for the Wiener distribution this correlation was lower.

scholarly journals Variability in rainfall dispersion in Madhya Pradesh

MAUSAM ◽  
2021 ◽  
Vol 43 (1) ◽  
pp. 29-36
Author(s):  
H.P. DAS ◽  
A. CHOWDHURY
Keyword(s):  
Gamma Distribution ◽  
Rainfall Variability ◽  
Probability Model ◽  
Regional Distribution ◽  
Madhya Pradesh ◽  
Regression Equations ◽  
Scale Parameters ◽  
Agronomic Practices ◽  
Distribution Probability ◽  
The Mean

An attempt has been made to examine distribution and dispersion in rainfall variability in Madhya Pradesh by applying Gamma distribution probability model, The spatial and regional distribution of shape and scale parameters of the Gamma distribution have been examined, Periods of water surpluses and deficiencies have been identified by comparing the probability rainfall with the water requirement. Regression equations have been developed to find probabilitistic rainfall from the mean rainfall. Agronomic practices have been evaluated for efficient utilization of water resources for crop planning.  

scholarly journals Gamma distributions for stationary Poisson flat processes

2009 ◽  
Vol 41 (4) ◽  
pp. 911-939 ◽  
Author(s):  
Volker Baumstark ◽  
Günter Last
Keyword(s):  
Poisson Process ◽  
Gamma Distribution ◽  
Shape Parameter ◽  
Voronoi Tessellation ◽  
Isotropic Case ◽  
Intensity Measure ◽  
First Case ◽  
Gamma Distributions ◽  
The Face ◽  
The Mean

We consider a stationary Poisson process X of k-flats in ℝd with intensity measure Θ and a measurable set S of k-flats depending on F1,…,Fn∈ X, x∈ℝd, and X in a specific equivariant way. If (F1,…,Fn,x) is properly sampled (in a ‘typical way’) then Θ(S) has a gamma distribution. This result generalizes and unifies earlier work by Miles (1971), Møller and Zuyev (1996), and Zuyev (1999). As a new example, we will show that the volume of the fundamental region of a typical j-face of a stationary Poisson–Voronoi tessellation is conditionally gamma distributed. This is true in the area-biased and the area-debiased cases. In the first case the shape parameter is not integer valued. As another new example, we will show that the generalized integral-geometric contents of the (area-biased and area-debiased) typical j-face of a Poisson hyperplane tessellation are conditionally gamma distributed. In the isotropic case the contents boil down to the mean breadth of the face.

scholarly journals Bayesian Estimation for Two Parameters of Gamma Distribution under Generalized Weighted Loss Function

2019 ◽  
Vol 60 (5) ◽  
pp. 1161-1171
Author(s):  
Loaiy F. Naji ◽  
Huda A. Rasheed
Keyword(s):  
Bayesian Estimation ◽  
Gamma Distribution ◽  
Loss Function ◽  
Maximum Likelihood Estimators ◽  
Simulation Method ◽  
Monte Carlo Simulation Method ◽  
Mean Squared Errors ◽  
Scale Parameters ◽  
The Mean ◽  
Two Parameters

This paper deals with, Bayesian estimation of the parameters of Gamma distribution under Generalized Weighted loss function, based on Gamma and Exponential priors for the shape and scale parameters, respectively. Moment, Maximum likelihood estimators and Lindley’s approximation have been used effectively in Bayesian estimation. Based on Monte Carlo simulation method, those estimators are compared in terms of the mean squared errors (MSE’s).

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