POWER LAW MAPPING IN HUMAN AREA PERCEPTION

2011 ◽  
Vol 22 (05) ◽  
pp. 495-503 ◽  
Author(s):  
ANTHONY LONGJAS ◽  
ERIKA FILLE LEGARA ◽  
CHRISTOPHER MONTEROLA
Keyword(s):  
Power Law ◽  
Goodness Of Fit ◽  
Formal Education ◽  
Reference Area ◽  
Length Perception ◽  
Monitor Screen ◽  
Space Allocation ◽  
Length Estimation ◽  
Computer Mouse ◽  
Cultural Interventions

We investigate how humans visually perceive and approximate area or space allocation through visual area experiments. The participants are asked to draw a circle concentric to the reference circle on the monitor screen using a computer mouse with area measurements relative to the area of the reference circle. The activity is repeated for triangle, square and hexagon. The area estimated corresponds to the area estimates of a participant (perceived) for a corresponding requested area to be drawn (stimulus). The area estimated fits very well (goodness of fit R2 > 0.97) to a power law given by r2α where r is the radius of the circle or the distance of the edge for triangle, square and hexagon. The power law fit demonstrates that for all shapes sampled, participants underestimated area for stimulus that are less than ~100% of the reference area and overestimated area for stimulus greater than ~100% of the reference area. The value of α is smallest for the circle (α∘ ≈ 1.33) and largest for triangle (α△ ≈ 1.56) indicating that in the presence of a reference area with the same shape, circle is perceived to be smallest among the figures considered when drawn bigger than the reference area, but largest when drawn smaller than the reference area. We also conducted experiments on length estimation and consistent with the results of Dehaene et al., Science 2008, we recover a linear relationship between the perceived length and the stimulus. We show that contrary to number mapping into space and/or length perception, human's perception of area is not corrected by the introduction of cultural interventions such as formal education.

scholarly journals Influence of the physical dimension of leaf size measures on the goodness of fit for Taylor's power law using 101 bamboo taxa

2019 ◽  
Vol 19 ◽  
pp. e00657 ◽  
Author(s):  
Peijian Shi ◽  
Lei Zhao ◽  
David A. Ratkowsky ◽  
Karl J. Niklas ◽  
Weiwei Huang ◽  
...  
Keyword(s):  
Power Law ◽  
Goodness Of Fit ◽  
Leaf Size ◽  
Taylor’S Power Law ◽  
Taylor's Power Law

scholarly journals Investigating the Complexity of Spatial Interactions between Different Administrative Units in China Using Flickr Data

2020 ◽  
Vol 12 (22) ◽  
pp. 9778
Author(s):  
Wei Zhu ◽  
Ding Ma ◽  
Zhigang Zhao ◽  
Renzhong Guo
Keyword(s):  
Power Law ◽  
Goodness Of Fit ◽  
Human Mobility ◽  
Scaling Analysis ◽  
Spatial Interactions ◽  
Mobility Patterns ◽  
Spatial And Temporal Scales ◽  
Movement Trajectories ◽  
Geotagged Photos ◽  
Great Complexity

Location-based social media have facilitated us to bridge the gap between virtual and physical worlds through the exploration of human online dynamics from a geographic perspective. This study uses a large collection of geotagged photos from Flickr to investigate the complexity of spatial interactions at the country level. We adopted three levels of administrative divisions in mainland China—province, city, and county—as basic geographic units and established three types of topology—province–province network, city–city network, and county–county network—from the extracted user movement trajectories. We conducted the scaling analysis based on heavy-tailed distribution statistics including power law exponents, goodness of fit index, and ht-index, by which we characterized a great complexity of the trajectory lengths, spatial distribution of geotagged photos, and the related metrics of built networks. The great complexity indicates the highly imbalanced ratio of populated-to-unpopulated areas or large-to-small flows between areas. More interestingly, all power law exponents were around 2 for the networks at various spatial and temporal scales. Such a recurrence of scaling statistics at multiple resolutions can be regarded a statistical self-similarity and could thus help us to reveal the fractal nature of human mobility patterns.

scholarly journals The Louder, the Longer: Object Length Perception Is Influenced by Loudness, but Not by Pitch

Vision ◽  
2019 ◽  
Vol 3 (4) ◽  
pp. 57 ◽  
Author(s):  
Pia Hauck ◽  
Heiko Hecht
Keyword(s):  
Sound Pressure Level ◽  
Visual Information ◽  
Visual Cues ◽  
Sound Pressure ◽  
Pressure Level ◽  
Acoustic Properties ◽  
Size Estimation ◽  
Length Perception ◽  
Length Estimation ◽  
Reliable Source

Sound by itself can be a reliable source of information about an object’s size. For instance, we are able to estimate the size of objects merely on the basis of the sound they make when falling on the floor. Moreover, loudness and pitch are crossmodally linked to size. We investigated if sound has an effect on size estimation even in the presence of visual information, that is if the manipulation of the sound produced by a falling object influences visual length estimation. Participants watched videos of wooden dowels hitting a hard floor and estimated their lengths. Sound was manipulated by (A) increasing (decreasing) overall sound pressure level, (B) swapping sounds among the different dowel lengths, and (C) increasing (decreasing) pitch. Results showed that dowels were perceived to be longer with increased sound pressure level (SPL), but there was no effect of swapped sounds or pitch manipulation. However, in a sound-only-condition, main effects of length and pitch manipulation were found. We conclude that we are able to perceive subtle differences in the acoustic properties of impact sounds and use them to deduce object size when visual cues are eliminated. In contrast, when visual cues are available, only loudness is potent enough to exercise a crossmodal influence on length perception.

scholarly journals Galaxy disc scaling relations: A tight linear galaxy–halo connection challenges abundance matching

2019 ◽  
Vol 629 ◽  
pp. A59 ◽  
Author(s):  
Lorenzo Posti ◽  
Antonino Marasco ◽  
Filippo Fraternali ◽  
Benoit Famaey
Keyword(s):  
Angular Momentum ◽  
Galaxy Formation ◽  
Power Law ◽  
Goodness Of Fit ◽  
Dark Matter Halo ◽  
Monotonic Functions ◽  
Stellar Component ◽  
Matching Priors ◽  
Matching Models ◽  
Formation Efficiency

In ΛCDM cosmology, to first order, galaxies form out of the cooling of baryons within the virial radius of their dark matter halo. The fractions of mass and angular momentum retained in the baryonic and stellar components of disc galaxies put strong constraints on our understanding of galaxy formation. In this work, we derive the fraction of angular momentum retained in the stellar component of spirals, fj, the global star formation efficiency fM, and the ratio of the asymptotic circular velocity (Vflat) to the virial velocity fV, and their scatter, by fitting simultaneously the observed stellar mass-velocity (Tully–Fisher), size–mass, and mass–angular momentum (Fall) relations. We compare the goodness of fit of three models: (i) where the logarithm of fj, fM, and fV vary linearly with the logarithm of the observable Vflat; (ii) where these values vary as a double power law; and (iii) where these values also vary as a double power law but with a prior imposed on fM such that it follows the expectations from widely used abundance matching models. We conclude that the scatter in these fractions is particularly small (∼0.07 dex) and that the linear model is by far statistically preferred to that with abundance matching priors. This indicates that the fundamental galaxy formation parameters are small-scatter single-slope monotonic functions of mass, instead of being complicated non-monotonic functions. This incidentally confirms that the most massive spiral galaxies should have turned nearly all the baryons associated with their haloes into stars. We call this the failed feedback problem.

scholarly journals Normative human brain volume growth

2018 ◽  
Vol 21 (5) ◽  
pp. 478-485 ◽  
Author(s):  
Mallory Peterson ◽  
Benjamin C. Warf ◽  
Steven J. Schiff
Keyword(s):  
Human Brain ◽  
Power Law ◽  
Goodness Of Fit ◽  
Brain Volume ◽  
Volume Growth ◽  
Growth Charts ◽  
Brain Growth ◽  
Statistical Measures ◽  
Curve Fit ◽  
Males And Females

OBJECTIVEWhile there is a long history of interest in measuring brain growth, as of yet there is no definitive model for normative human brain volume growth. The goal of this study was to analyze a variety of candidate models for such growth and select the model that provides the most statistically applicable fit. The authors sought to optimize clinically applicable growth charts that would facilitate improved treatment and predictive management for conditions such as hydrocephalus.METHODSThe Weibull, two-term power law, West ontogenic, and Gompertz models were chosen as potential models. Normative brain volume data were compiled from the NIH MRI repository, and the data were fit using a nonlinear least squares regression algorithm. Appropriate statistical measures were analyzed for each model, and the best model was characterized with prediction bound curves to provide percentile estimates for clinical use.RESULTSEach model curve fit and the corresponding statistics were presented and analyzed. The Weibull fit had the best statistical results for both males and females, while the two-term power law generated the worst scores. The statistical measures and goodness of fit parameters for each model were provided to assure reproducibility.CONCLUSIONSThe authors identified the Weibull model as the most effective growth curve fit for both males and females. Clinically usable growth charts were developed and provided to facilitate further clinical study of brain volume growth in conditions such as hydrocephalus. The authors note that the homogenous population from which the normative MRI data were compiled limits the study. Gaining a better understanding of the dynamics that underlie childhood brain growth would yield more predictive growth curves and improved neurosurgical management of hydrocephalus.

Contributions of the Computer-Administered Neuropsychological Screen for Mild Cognitive Impairment (CANS-MCI) for the diagnosis of MCI in Brazil

2014 ◽  
Vol 26 (9) ◽  
pp. 1483-1491 ◽  
Author(s):  
Cláudia M. Memória ◽  
Mônica S. Yassuda ◽  
Eduardo Y. Nakano ◽  
Orestes V. Forlenza
Keyword(s):  
Cognitive Impairment ◽  
Mild Cognitive Impairment ◽  
Goodness Of Fit ◽  
Formal Education ◽  
Factor Model ◽  
Characteristic Curve ◽  
Reliability And Validity ◽  
Cognitive Status ◽  
Cognitive Screening ◽  
Extensive Evaluation

ABSTRACTBackground:The Computer-Administered Neuropsychological Screen for Mild Cognitive Impairment (CANS-MCI) is a computer-based cognitive screening instrument that involves automated administration and scoring and immediate analyses of test sessions. The objective of this study was to translate and culturally adapt the Brazilian Portuguese version of the CANS-MCI (CANS-MCI-BR) and to evaluate its reliability and validity for the diagnostic screening of MCI and dementia due to Alzheimer's disease.Methods:The test was administered to 97 older adults (mean age 73.41 ± 5.27 years) with at least four years of formal education (mean education 12.23 ± 4.48 years). Participants were classified into three diagnostic groups according to global cognitive status (normal controls, n = 41; MCI, n = 35; AD, n = 21) based on clinical data and formal neuropsychological assessments.Results:The results indicated high internal consistency (Cronbach's α = 0.77) in the total sample. Three-month test-retest reliability correlations were significant and robust (0.875; p < 0.001). A moderate level of concurrent validity was attained relative to the screening test for MCI (MoCA test, r = 0.76, p < 0.001). Confirmatory factor analysis supported the three-factor model of the original test, i.e., memory, language/spatial fluency, and executive function/mental control. Goodness of fit indicators were strong (Bentler Comparative Fit Index = 0.96, Root Mean Square Error of Approximation = 0.09). Receiver operating characteristic curve analyses suggested high sensitivity and specificity (81% and 73% respectively) to screen for possible MCI cases.Conclusions:The CANS-MCI-BR maintains adequate psychometric characteristics that render it suitable to identify elderly adults with probable cognitive impairment to whom a more extensive evaluation by formal neuropsychological tests may be required.

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