scholarly journals Three-dimensional space: locomotory style explains memory differences in rats and hummingbirds

2014 ◽  
Vol 281 (1784) ◽  
pp. 20140301 ◽  
Author(s):  
I. Nuri Flores-Abreu ◽  
T. Andrew Hurly ◽  
James A. Ainge ◽  
Susan D. Healy
Keyword(s):  
Horizontal Plane ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Vertical Component ◽  
Horizontal Component ◽  
Vertical Dimension ◽  
Three Dimensions ◽  
Two Dimensional ◽  
With Memory ◽  
Three Dimensional Space

While most animals live in a three-dimensional world, they move through it to different extents depending on their mode of locomotion: terrestrial animals move vertically less than do swimming and flying animals. As nearly everything we know about how animals learn and remember locations in space comes from two-dimensional experiments in the horizontal plane, here we determined whether the use of three-dimensional space by a terrestrial and a flying animal was correlated with memory for a rewarded location. In the cubic mazes in which we trained and tested rats and hummingbirds, rats moved more vertically than horizontally, whereas hummingbirds moved equally in the three dimensions. Consistent with their movement preferences, rats were more accurate in relocating the horizontal component of a rewarded location than they were in the vertical component. Hummingbirds, however, were more accurate in the vertical dimension than they were in the horizontal, a result that cannot be explained by their use of space. Either as a result of evolution or ontogeny, it appears that birds and rats prioritize horizontal versus vertical components differently when they remember three-dimensional space.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Navigating in a volumetric world: Metric encoding in the vertical axis of space

2013 ◽  
Vol 36 (5) ◽  
pp. 546-547 ◽  
Author(s):  
Theresa Burt de Perera ◽  
Robert Holbrook ◽  
Victoria Davis ◽  
Alex Kacelnik ◽  
Tim Guilford
Keyword(s):  
Spatial Information ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Vertical Component ◽  
Vertical Axis ◽  
Orthogonal Axis ◽  
Experimental Protocols ◽  
Three Dimensional Space ◽  
The Way

AbstractAnimals navigate through three-dimensional environments, but we argue that the way they encode three-dimensional spatial information is shaped by how they use the vertical component of space. We agree with Jeffery et al. that the representation of three-dimensional space in vertebrates is probably bicoded (with separation of the plane of locomotion and its orthogonal axis), but we believe that their suggestion that the vertical axis is stored “contextually” (that is, not containing distance or direction metrics usable for novel computations) is unlikely, and as yet unsupported. We describe potential experimental protocols that could clarify these differences in opinion empirically.

scholarly journals FOUR-DIMENSIONAL BALL IN A GRAPHIC REPRESENTATION

2021 ◽  
pp. 37-46
Author(s):  
Helena Bidnichenko
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Geometric Modelling ◽  
Vector Model ◽  
Original Position ◽  
Two Dimensional ◽  
Axis Of Rotation ◽  
Dimensional Ball ◽  
Three Dimensional Space ◽  
Horizontal Vector

The paper presents a method for geometric modelling of a four-dimensional ball. For this, the regularities of the change in the shape of the projections of simple geometric images of two-dimensional and three-dimensional spaces during rotation are considered. Rotations of a segment and a circle around an axis are considered; it is shown that during rotation the shape of their projections changes from the maximum value to the degenerate projection. It was found that the set of points of the degenerate projection belongs to the axis of rotation, and each n-dimensional geometric image during rotation forms a body of a higher dimension, that is, one that belongs to (n + 1) -dimensional space. Identified regularities are extended to the four-dimensional space in which the ball is placed. It is shown that the axis of rotation of the ball will be a degenerate projection in the form of a circle, and the ball, when rotating, changes its size from a volumetric object to a flat circle, then increases again, but in the other direction (that is, it turns out), and then in reverse order to its original position. This rotation is more like a deformation, and such a ball of four-dimensional space is a hypersphere. For geometric modelling of the hypersphere and the possibility of its projection image, the article uses the vector model proposed by P.V. Filippov. The coordinate system 0xyzt is defined. The algebraic equation of the hypersphere is given by analogy with the three-dimensional space along certain coordinates of the center a, b, c, d. A variant of hypersection at t = 0 is considered, which confirms by equations obtaining a two-dimensional ball of three-dimensional space, a point (a ball of zero radius), which coincides with the center of the ball, or an imaginary ball. For the variant t = d, the equation of a two-dimensional ball is obtained, in which the radius is equal to R and the coordinates of all points along the 0t axis are equal to d. The variant of hypersection t = k turned out to be interesting, in which the equation of a two-dimensional sphere was obtained, in which the coordinates of all points along the 0t axis are equal to k, and the radius is . Horizontal vector projections of hypersection are constructed for different values of k. It is concluded that the set of horizontal vector projections of hypersections at t = k defines an ellipse.  

scholarly journals Capacity of Inhomogeneous Hybrid Wireless Networks in Three-Dimensional Space

2015 ◽  
Vol 11 (9) ◽  
pp. 47
Author(s):  
Feng Wu ◽  
Jiang Zhu ◽  
Yilong Tian ◽  
Zhipeng Xi
Keyword(s):  
Sensor Node ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Network Capacity ◽  
Throughput Capacity ◽  
Two Dimensional ◽  
Hybrid Wireless Networks ◽  
Node Distribution ◽  
Analytical Expressions ◽  
Three Dimensional Space

Network capacity has been widely studied in recent years. However, most of the literatures focus on the networks where nodes are distributed in a two-dimensional space. In this paper, we propose a 3D hybrid sensor network model. By setting different sensor node distribution probabilities for cells, we divide all the cells in the network into dense cells and sparse cells. Analytical expressions of the aggregate throughput capacity are obtained. We also find that suitable inhomogeneity can increase the network throughput capacity.

Map fragmentation in two- and three-dimensional environments

2013 ◽  
Vol 36 (5) ◽  
pp. 569-570 ◽  
Author(s):  
Homare Yamahachi ◽  
May-Britt Moser ◽  
Edvard I. Moser
Keyword(s):  
Small Area ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Brain Circuits ◽  
Three Dimensional Space

AbstractThe suggestion that three-dimensional space is represented by a mosaic of neural map fragments, each covering a small area of space in the plane of locomotion, receives support from studies in complex two-dimensional environments. How map fragments are linked, which brain circuits are involved, and whether metric is preserved across fragments are questions that remain to be determined.

scholarly journals The Algorithm for Determining the Coordinates of a Point in Three-Dimensional Space by Using the Auxiliary Point

2013 ◽  
Vol 48 (4) ◽  
pp. 141-145 ◽  
Author(s):  
Bartlomiej Oszczak ◽  
Eliza Sitnik
Keyword(s):  
Fixed Point ◽  
Precise Measurement ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Satellite Navigation ◽  
Reference Points ◽  
Two Dimensional ◽  
Approximate Location ◽  
The Many ◽  
Three Dimensional Space

ABSTRACT During the process of satellite navigation, and also in the many tasks of classical positioning, we need to calculate the corrections to the initial (or approximate) location of the point using precise measurement of distances to the permanent points of reference (reference points). In this paper the authors have provided a way of developing Hausbrandt's equations, on the basis of which the exact coordinates of the point in two-dimensional space can be determined by using the computed correction to the coordinates of the auxiliary point. The authors developed generalised equations for threedimensional space introducing additional fixed point and have presented proof of derived formulas.

scholarly journals Filling of three-dimensional space by two-dimensional sheet growth

2015 ◽  
Vol 92 (4) ◽  
Author(s):  
Merlin A. Etzold ◽  
Peter J. McDonald ◽  
David A. Faux ◽  
Alexander F. Routh
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Space

scholarly journals Chaotic Attractor Generation via Space Function Controls

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Hong Shi ◽  
Guangming Xie ◽  
Desheng Liu
Keyword(s):  
Linear Systems ◽  
Chaotic Attractor ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Underlying Mechanism ◽  
Two Dimensional ◽  
One Dimensional ◽  
Suitable Space ◽  
Space Function ◽  
Three Dimensional Space

The analysis of chaotic attractor generation is given, and the generation of novel chaotic attractor is introduced in this paper. The underlying mechanism involves two simple linear systems with one-dimensional, two-dimensional, or three-dimensional space functions. Moreover, it is demonstrated by simulation that various attractor patterns are generated conveniently by adjusting suitable space functions' parameters and the statistic behavior is also discussed.

Estimating Three-Dimensional Space from Multiple Two-Dimensional Views

1993 ◽  
Vol 2 (1) ◽  
pp. 44-53 ◽  
Author(s):  
Kristinn R. Thorisson
Keyword(s):  
Visual Search ◽  
Eye Movement ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Three Dimensions ◽  
Limiting Factor ◽  
Single Subject ◽  
Search Performance ◽  
Two Dimensional

The most common visual feedback technique in teleoperation is in the form of monoscopic video displays. As robotic autonomy increases and the human operator takes on the role of a supervisor, three-dimensional information is effectively presented by multiple, televised, two-dimensional (2-D) projections showing the same scene from different angles. To analyze how people go about using such segmented information for estimations about three-dimensional (3-D) space, 18 subjects were asked to determine the position of a stationary pointer in space; eye movements and reaction times (RTs) were recorded during a period when either two or three 2-D views were presented simultaneously, each showing the same scene from a different angle. The results revealed that subjects estimated 3-D space by using a simple algorithm of feature search. Eye movement analysis supported the conclusion that people can efficiently use multiple 2-D projections to make estimations about 3-D space without reconstructing the scene mentally in three dimensions. The major limiting factor on RT in such situations is the subjects' visual search performance, giving in this experiment a mean of 2270 msec (SD = 468; N = 18). This conclusion was supported by predictions of the Model Human Processor (Card, Moran, & Newell, 1983), which predicted a mean RT of 1820 msec given the general eye movement patterns observed. Single-subject analysis of the experimental data suggested further that in some cases people may base their judgments on a more elaborate 3-D mental model reconstructed from the available 2-D views. In such situations, RTs and visual search patterns closely resemble those found in the mental rotation paradigm (Just & Carpenter, 1976), giving RTs in the range of 5-10 sec.

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