scholarly journals Perceptual insensitivity to higher-order statistical moments of coherent random dot motion

2018 ◽  
Author(s):  
Michael L. Waskom ◽  
Janeen Asfour ◽  
Roozbeh Kiani
Keyword(s):  
Visual Processing ◽  
Probability Distributions ◽  
Higher Order ◽  
Statistical Moments ◽  
Coherent Motion ◽  
It Use ◽  
Higher Order Moments ◽  
Dynamic Stimuli ◽  
Dot Motion ◽  
The Individual

ABSTRACTWhen the visual system analyses distributed patterns of sensory inputs, what features of those distributions does it use? It has been previously demonstrated that higher-order statistical moments of luminance distributions influence perception of static surfaces and textures. Here, we tested whether the brain also represents higher-order moments of dynamic stimuli. We constructed random dot kinematograms where dots moved according to probability distributions that selectively differed in terms of their mean, variance, skewness, or kurtosis. When viewing these stimuli, human observers were sensitive to the mean direction of coherent motion and to the variance of the individual dot displacement angles, but they were insensitive to skewness and kurtosis. Observer behavior accorded with a model of directional motion energy, suggesting that information about higher-order moments is discarded early in the visual processing hierarchy. These results demonstrate that use of higher-order moments is not a general property of visual perception.

scholarly journals Classroom note: An inductive derivation of Stirling numbers of the second kind and their applications in statistics

1997 ◽  
Vol 1 (2) ◽  
pp. 151-157 ◽  
Author(s):  
Anwar H. Joarder ◽  
Munir Mahmood
Keyword(s):  
Probability Distributions ◽  
Stirling Numbers ◽  
Higher Order ◽  
Inductive Method ◽  
Higher Order Moments ◽  
Discrete Probability ◽  
Discrete Probability Distributions

An inductive method has been presented for finding Stirling numbers of the second kind. Applications to some discrete probability distributions for finding higher order moments have been discussed.

scholarly journals Some Moment Relations for the Hipp approximation

1996 ◽  
Vol 26 (1) ◽  
pp. 117-121 ◽  
Author(s):  
Jan Dhaene ◽  
Bjørn Sundt ◽  
Nelson De Pril
Keyword(s):  
Finite Number ◽  
Present Note ◽  
Order Approximation ◽  
Probability Distributions ◽  
Higher Order ◽  
Exact Distribution ◽  
Higher Order Moments ◽  
The Moment

AbstractIn the present note we consider the Hipp approximation to the convolution of a finite number of probability distributions on the non-negative integers. It is shown that the moment up to and including order r of the rth order approximation are equal to the corresponding moments of the exact distribution. We also give a relation between the exact and approximated (r + 1)th order moments and indicate how similar relations can be obtained for higher order moments.

scholarly journals Perceptual insensitivity to higher-order statistical moments of coherent random dot motion

2018 ◽  
Vol 18 (6) ◽  
pp. 9 ◽  
Author(s):  
Michael L. Waskom ◽  
Janeen Asfour ◽  
Roozbeh Kiani
Keyword(s):  
Higher Order ◽  
Statistical Moments ◽  
Dot Motion ◽  
Random Dot Motion

scholarly journals The Effects of Gridding Algorithms on the Statistical Moments and Their Trends of Daily Surface Air Temperature*

2015 ◽  
Vol 28 (23) ◽  
pp. 9188-9205 ◽  
Author(s):  
Nicholas R. Cavanaugh ◽  
Samuel S. P. Shen
Keyword(s):  
Climate Change ◽  
Air Temperature ◽  
Climate Models ◽  
Decadal Variability ◽  
Surface Air Temperature ◽  
Higher Order ◽  
Statistical Moments ◽  
Weighted Sums ◽  
Higher Order Moments ◽  
Station Data

Abstract This paper explores the effects from averaging weather station data onto a grid on the first four statistical moments of daily minimum and maximum surface air temperature (SAT) anomalies over the entire globe. The Global Historical Climatology Network–Daily (GHCND) and the Met Office Hadley Centre GHCND (HadGHCND) datasets from 1950 to 2010 are examined. The GHCND station data exhibit large spatial patterns for each moment and statistically significant moment trends from 1950 to 2010, indicating that SAT probability density functions are non-Gaussian and have undergone characteristic changes in shape due to decadal variability and/or climate change. Comparisons with station data show that gridded averages always underestimate observed variability, particularly in the extremes, and have altered moment trends that are in some cases opposite in sign over large geographic areas. A statistical closure approach based on the quasi-normal approximation is taken to explore SAT’s higher-order moments and point correlation structure. This study focuses specifically on relating variability calculated from station data to that from gridded data through the moment equations for weighted sums of random variables. The higher-order and nonlinear spatial correlations up to the fourth order demonstrate that higher-order moments at grid scale can be determined approximately by functions of station pair correlations that tend to follow the usual Kolmogorov scaling relation. These results can aid in the development of constraints to reduce uncertainties in climate models and have implications for studies of atmospheric variability, extremes, and climate change using gridded observations.

Associations Between Higher-Order Values Vary with Age, Education, and Income

2020 ◽  
Author(s):  
Maksim Rudnev
Keyword(s):  
Cognitive Abilities ◽  
Developed Countries ◽  
European Social Survey ◽  
Higher Order ◽  
Group Differences ◽  
Social Survey ◽  
Value Structures ◽  
Younger Age ◽  
The Individual ◽  
Representative Samples

A theory of basic human values relies on the similarity of value structures across countries. It has been well established that the quasi-circumplex value structure as a whole is indeed universal. However, less attention has been paid to the associations between specific values. This study investigated associations between four higher-order values across age, education, and income groups. We analyzed the data from national representative samples collected in 29 countries as part of the fourth round of the European Social Survey with a series of multilevel regressions. Younger age, higher levels of education and income coincided with higher independence of the four adjacent higher-order values, whereas among older, less educated, and less wealthy groups, values tended to merge into a single dimension of Social versus Person Focus. These differences were slightly weaker in more economically developed countries. The group differences in value associations may follow from corresponding differences in the degree of societal and individual empowerment, cognitive abilities, and socialization experiences. Accounting for the individual differences in relations between values may bring deeper understanding and higher predictive power to the studies of links between values and various behaviors or attitudes. , value structure, value interactions, European Social Survey

scholarly journals Alzheimer’s Disease Progressively Reduces Visual Functional Network Connectivity

2021 ◽  
pp. 1-14
Author(s):  
Jie Huang ◽  
Paul Beach ◽  
Andrea Bozoki ◽  
David C. Zhu
Keyword(s):  
Visual Cortex ◽  
Lower Order ◽  
Resting State ◽  
Visual Processing ◽  
Network Connectivity ◽  
Higher Order ◽  
Functional Network ◽  
Functional Networks ◽  
The Face ◽  
Processing Network

Background: Postmortem studies of brains with Alzheimer’s disease (AD) not only find amyloid-beta (Aβ) and neurofibrillary tangles (NFT) in the visual cortex, but also reveal temporally sequential changes in AD pathology from higher-order association areas to lower-order areas and then primary visual area (V1) with disease progression. Objective: This study investigated the effect of AD severity on visual functional network. Methods: Eight severe AD (SAD) patients, 11 mild/moderate AD (MAD), and 26 healthy senior (HS) controls undertook a resting-state fMRI (rs-fMRI) and a task fMRI of viewing face photos. A resting-state visual functional connectivity (FC) network and a face-evoked visual-processing network were identified for each group. Results: For the HS, the identified group-mean face-evoked visual-processing network in the ventral pathway started from V1 and ended within the fusiform gyrus. In contrast, the resting-state visual FC network was mainly confined within the visual cortex. AD disrupted these two functional networks in a similar severity dependent manner: the more severe the cognitive impairment, the greater reduction in network connectivity. For the face-evoked visual-processing network, MAD disrupted and reduced activation mainly in the higher-order visual association areas, with SAD further disrupting and reducing activation in the lower-order areas. Conclusion: These findings provide a functional corollary to the canonical view of the temporally sequential advancement of AD pathology through visual cortical areas. The association of the disruption of functional networks, especially the face-evoked visual-processing network, with AD severity suggests a potential predictor or biomarker of AD progression.

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