Three-Dimensional Scaling of EEG Coherence

2015 ◽  
pp. 109-116
Author(s):  
Richard W. Holler ◽  
Don M. Tucker
Keyword(s):  
Three Dimensional ◽  
Eeg Coherence ◽  
Dimensional Scaling

scholarly journals Bayesian Geographical Multi-Dimensional Scaling

2019 ◽  
Vol 1 ◽  
pp. 1-2
Author(s):  
Hayato Nishi ◽  
Yasushi Asami
Keyword(s):  
Three Dimensional ◽  
Geographical Location ◽  
Point Of View ◽  
Statistical Point ◽  
Dimensional Scaling ◽  
Regional Features ◽  
Geographical Distances ◽  
Strong Relation ◽  
Geographical Locations ◽  
Multi Dimensional Scaling

<p><strong>Abstract.</strong> Multi-dimensional scaling (MDS) is a popular method of visualizing the similarity of individuals in a dataset. When dissimilarities between individuals in a dataset are measured, MDS projects these individuals into the (typically two- or three-dimensional) map. In this map, because similar individuals are projected to be close to one another, distances between individuals correspond to their dissimilarities. In other words, MDS makes a similarity map of a dataset.</p><p>Some of the dissimilarities and distances have a strong relation to the geographical location. For example, time distances are similar to geographical distances, and regional features will be similar if the regions are close together. Therefore, it will be useful to compare the MDS projection and geographical locations. However, because MDS projection is not concerned with the rotation, parallel translation, and similarity expansion, it might be difficult to compare the projection to the actual geographical locations. When geographically related similarities are visualized, projected locations should be bound to the geographical locations.</p><p>In this article, we propose Bayesian Geographical Multidimensional Scaling (BGMDS), in which geographical restrictions of projections are given from a statistical point of view. BGMDS gives not only geographically bound projections, but also incorporates the uncertainty of the projections.</p>

High Rayleigh number convection in a three-dimensional porous medium

2014 ◽  
Vol 748 ◽  
pp. 879-895 ◽  
Author(s):  
Duncan R. Hewitt ◽  
Jerome A. Neufeld ◽  
John R. Lister
Keyword(s):  
Porous Medium ◽  
Three Dimensional ◽  
Field Measurements ◽  
Two Dimensions ◽  
Dimensional Scaling ◽  
Dynamical Flow ◽  
Background Temperature ◽  
Relationship Of ◽  
Rayleigh Numbers ◽  
Steady Convection

AbstractHigh-resolution numerical simulations of statistically steady convection in a three-dimensional porous medium are presented for Rayleigh numbers $Ra \leqslant 2 \times 10^4$. Measurements of the Nusselt number $Nu$ in the range $1750 \leqslant Ra \leqslant 2 \times 10^4$ are well fitted by a relationship of the form $Nu = \alpha _3 Ra + \beta _3$, for $\alpha _3 = 9.6 \times 10^{-3}$ and $\beta _3 = 4.6$. This fit indicates that the classical linear scaling $Nu \sim Ra$ is attained, and that $Nu$ is asymptotically approximately $40\, \%$ larger than in two dimensions. The dynamical flow structure in the range $1750 \leqslant Ra \leqslant 2\times 10^4$ is analysed, and the interior of the flow is found to be increasingly well described as $Ra \to \infty $ by a heat-exchanger model, which describes steady interleaving columnar flow with horizontal wavenumber $k$ and a linear background temperature field. Measurements of the interior wavenumber are approximately fitted by $k\sim Ra^{0.52 \pm 0.05}$, which is distinguishably stronger than the two-dimensional scaling of $k\sim Ra^{0.4}$.

Dissimilarity of yellow-blue surfaces under neutral light sources differing in intensity: Separate contributions of light intensity and chroma

2008 ◽  
Vol 25 (3) ◽  
pp. 395-398 ◽  
Author(s):  
RUMI TOKUNAGA ◽  
ALEXANDER D. LOGVINENKO ◽  
LAURENCE T. MALONEY
Keyword(s):  
Light Intensity ◽  
Three Dimensional ◽  
The Other ◽  
One Dimension ◽  
Light Sources ◽  
Point Scale ◽  
Illumination Condition ◽  
Dimensional Scaling ◽  
Three Dimensional Configuration ◽  
Multi Dimensional Scaling

Observers viewed two side-by-side arrays each of which contained three yellow Munsell papers, three blue, and one neutral Munsell. Each array was illuminated uniformly and independently of the other. The neutral light source intensities were 1380, 125, or 20 lux. All six possible combinations of light intensities were set as illumination conditions. On each trial, observers were asked to rate the dissimilarity between each chip in one array and each chip in the other by using a 30-point scale. Each pair of surfaces in each illumination condition was judged five times. We analyzed this data using non-metric multi-dimensional scaling to determine how light intensity and surface chroma contributed to dissimilarity and how they interacted. Dissimilarities were captured by a three-dimensional configuration in which one dimension corresponded to differences in light intensity.

scholarly journals Критический индекс восприимчивости 1D-изинговского ферромагнетика, замкнутого в кольцо

2018 ◽  
Vol 60 (7) ◽  
pp. 1318
Author(s):  
Ж.В. Дзюба ◽  
В.Н. Удодов
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Particle Interaction ◽  
Three Dimensional ◽  
One Dimensional ◽  
Dimensional Scaling ◽  
Finite Dimensional ◽  
The Monte Carlo Method ◽  
Ferromagnetic Ising Model ◽  
The One

AbstractUsing the Monte Carlo method, critical behavior of the one-dimensional ferromagnetic Ising model has been investigated with allowance for the interaction of the second and third neighbors and four-particle interaction. The obtained results on the critical temperature were compared with the critical temperature of the quasi-one-dimensional Ising magnetic [(СН_3)_3NH] · FeCl_3 · 2H_2O and with the magnitude of the exchange interaction J/k _B = 17.4 K. Within the scope of the finite-dimensional scaling theory, the critical susceptibility exponent has been calculated. It has been shown that values of the susceptibility exponent for the one-dimensional Ising model with periodic boundary conditions are considerably less than the known values of the exponents for three-dimensional systems. The critical susceptibility exponent strongly depends on energy parameters; namely, it decreases with an increase in them.

scholarly journals Scaling laws for the propulsive performance of three-dimensional pitching propulsors

2019 ◽  
Vol 871 ◽  
pp. 1117-1138 ◽  
Author(s):  
Fatma Ayancik ◽  
Qiang Zhong ◽  
Daniel B. Quinn ◽  
Aaron Brandes ◽  
Hilary Bart-Smith ◽  
...  
Keyword(s):  
Scaling Laws ◽  
Three Dimensional ◽  
Added Mass ◽  
Scaling Relations ◽  
The Novel ◽  
Vortex System ◽  
Propulsive Performance ◽  
Dimensional Scaling ◽  
Aspect Ratios ◽  
Thrust Production

Scaling laws for the thrust production and energetics of self-propelled or fixed-velocity three-dimensional rigid propulsors undergoing pitching motions are presented. The scaling relations extend the two-dimensional scaling laws presented in Moored & Quinn (AIAA J., 2018, pp. 1–15) by accounting for the added mass of a finite-span propulsor, the downwash/upwash effects from the trailing vortex system of a propulsor and the elliptical topology of shedding trailing-edge vortices. The novel three-dimensional scaling laws are validated with self-propelled inviscid simulations and fixed-velocity experiments over a range of reduced frequencies, Strouhal numbers and aspect ratios relevant to bio-inspired propulsion. The scaling laws elucidate the dominant flow physics behind the thrust production and energetics of pitching bio-propulsors, and they provide guidance for the design of bio-inspired propulsive systems.

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