Noncommutative Updating of Perceived Self-Orientation in Three Dimensions

2007 ◽  
Vol 97 (4) ◽  
pp. 2958-2964 ◽  
Author(s):  
Stefan Glasauer ◽  
Thomas Brandt
Keyword(s):  
Vestibular System ◽  
Horizontal Plane ◽  
Three Dimensional ◽  
Vertical Axis ◽  
Three Dimensions ◽  
Whole Body ◽  
The Earth ◽  
Angular Velocities ◽  
Velocity Information ◽  
Final Orientation

After whole body rotations around an earth-vertical axis in darkness, subjects can indicate their orientation in space with respect to their initial orientation reasonably well. This is possible because the brain is able to mathematically integrate self-velocity information provided by the vestibular system to obtain self-orientation, a process called path integration. For rotations around multiple axes, however, computations are more demanding to accurately update self-orientation with respect to space. In such a case, simple integration is no longer sufficient because of the noncommutativity of rotations. We investigated whether such updating is possible after three-dimensional whole body rotations and whether the noncommutativity of three-dimensional rotations is taken into account. The ability of ten subjects to indicate their spatial orientation in the earth-horizontal plane was tested after different rotational paths from upright to supine positions. Initial and final orientations of the subjects were the same in all cases, but the paths taken were different, and so were the angular velocities sensed by the vestibular system. The results show that seven of the ten subjects could consistently indicate their final orientation within the earth-horizontal plane. Thus perceived final orientation was independent of the path taken, i.e., the noncommutativity of rotations was taken into account.

scholarly journals Three-dimensional tuning of head direction cells in rats

2019 ◽  
Vol 121 (1) ◽  
pp. 4-37 ◽  
Author(s):  
Michael E. Shinder ◽  
Jeffrey S. Taube
Keyword(s):  
Horizontal Plane ◽  
Reference Frames ◽  
Three Dimensional ◽  
Vertical Axis ◽  
Ventral Surface ◽  
Three Dimensions ◽  
Head Direction ◽  
Horizontal Canal ◽  
Cell Responses ◽  
The Earth

Head direction (HD) cells fire when the animal faces that cell’s preferred firing direction (PFD) in the horizontal plane. The PFD response when the animal is oriented outside the earth-horizontal plane could result from cells representing direction in the plane of locomotion or as a three-dimensional (3D), global-referenced direction anchored to gravity. To investigate these possibilities, anterodorsal thalamic HD cells were recorded from restrained rats while they were passively positioned in various 3D orientations. Cell responses were unaffected by pitch or roll up to ~90° from the horizontal plane. Firing was disrupted once the animal was oriented >90° away from the horizontal plane and during inversion. When rolling the animal around the earth-vertical axis, cells were active when the animal’s ventral surface faced the cell’s PFD. However, with the rat rolled 90° in an ear-down orientation, pitching the rat and rotating it around the vertical axis did not produce directionally tuned responses. Complex movements involving combinations of yaw-roll, but usually not yaw-pitch, resulted in reduced directional tuning even at the final upright orientation when the rat had full visual view of its environment and was pointing in the cell’s PFD. Directional firing was restored when the rat’s head was moved back-and-forth. There was limited evidence indicating that cells contained conjunctive firing with pitch or roll positions. These findings suggest that the brain’s representation of directional heading is derived primarily from horizontal canal information and that the HD signal is a 3D gravity-referenced signal anchored to a direction in the horizontal plane. NEW & NOTEWORTHY This study monitored head direction cell responses from rats in three dimensions using a series of manipulations that involved yaw, pitch, roll, or a combination of these rotations. Results showed that head direction responses are consistent with the use of two reference frames simultaneously: one defined by the surrounding environment using primarily visual landmarks and a second defined by the earth’s gravity vector.

Dynamic Analysis of Explosive-Metal Interaction in Three Dimensions

1981 ◽  
Vol 48 (1) ◽  
pp. 30-34 ◽  
Author(s):  
G. R. Johnson
Keyword(s):  
Three Dimensional ◽  
Three Dimensions ◽  
Double Pass ◽  
Sliding Surfaces ◽  
Metal Interaction ◽  
Angular Velocities ◽  
Explosive Device ◽  
Metal Interfaces ◽  
Metal Liner ◽  
Explosive Devices

This paper demonstrates the capability to perform three-dimensional computations for explosive-metal interaction problems with complex sliding surfaces. An analysis is performed for an explosive device which accelerates a metal liner known as a self-forging fragment. Results are presented to show the effects of off-center detonation, asymmetric liner thickness, and asymmetric explosive density for an otherwise axisymmetric device. These three-dimensional conditions have little effect on the linear velocities, but they do introduce significant angular velocities to the self-forging fragment. Unlike projectile-target impact computations, which require only a single sliding surface between the projectile and the target, the explosive devices have multiple, intersecting, three-dimensional sliding surfaces between the expanding explosive gases and the various metal portions of the devices. Included are descriptions of the specialized “search routines” and the “double-pass” approach used for the explosive-metal interfaces.

Spatial Alignment of Rotational and Static Tilt Responses of Vestibulospinal Neurons in the Cat

1999 ◽  
Vol 82 (2) ◽  
pp. 855-862 ◽  
Author(s):  
S. I. Perlmutter ◽  
Y. Iwamoto ◽  
J. F. Baker ◽  
B. W. Peterson
Keyword(s):  
Horizontal Plane ◽  
Dimensional Space ◽  
Body Position ◽  
Three Dimensional ◽  
Whole Body ◽  
Angular Difference ◽  
Spatial Alignment ◽  
Minimum Sensitivity ◽  
Alert Cats ◽  
Vestibulospinal Neurons

The responses of vestibulospinal neurons to 0.5-Hz, whole-body rotations in three-dimensional space and static tilts of whole-body position were studied in decerebrate and alert cats. The neurons’ spatial properties for earth-vertical rotations were characterized by maximum and minimum sensitivity vectors ( R max and R min) in the cat’s horizontal plane. The orientation of a neuron’s R max was not consistently related to the orientation of its maximum sensitivity vector for static tilts ( T max). The angular difference between R max and T max was widely distributed between 0° and 150°, and R max and T max were aligned (i.e., within 45° of each other) for only 44% (14/32) of the neurons. The alignment of R max and T max was not correlated with the neuron’s sensitivity to earth-horizontal rotations, or to the orientation of R max in the horizontal plane. In addition, the extent to which a neuron exhibited spatiotemporal convergent (STC) behavior in response to vertical rotations was independent of the angular difference between R max and T max. This suggests that the high incidence of STC responses in our sample (56%) reflects not only canal-otolith convergence, but also the presence of static and dynamic otolith inputs with misaligned directionality. The responses of vestibulospinal neurons reflect a complex combination of static and dynamic vestibular inputs that may be required by postural reflexes that vary depending on head, trunk, and limb orientation, or on the frequency of stimulation.

Adaptation of the vestibulo-ocular reflex, subjective tilt, and motion sickness to head movements during short-radius centrifugation

2003 ◽  
Vol 13 (2-3) ◽  
pp. 65-77
Author(s):  
Laurence R. Young ◽  
Kathleen H. Sienko ◽  
Lisette E. Lyne ◽  
Heiko Hecht ◽  
Alan Natapoff
Keyword(s):  
Motion Sickness ◽  
Body Position ◽  
Rest Period ◽  
Vertical Axis ◽  
Head Movements ◽  
Whole Body ◽  
Slow Phase ◽  
Ocular Reflex ◽  
Vestibulo Ocular Reflex ◽  
Angular Velocities

Head movements made while the whole body is rotating at unusually high angular velocities (here with supine body position about an earth-vertical axis) result in inappropriate eye movements, sensory illusions, disorientation, and frequently motion sickness. We investigated the acquisition and retention of sensory adaptation to cross-coupled components of the vestibulo-ocular reflex (VOR) by asking eight subjects to make headturns while being rotated at 23 rpm on two consecutive days, and again a week later. The dependent measures were inappropriate vertical VOR, subjective tilt, and motion sickness in response to 90° yaw out-of-plane head movements. Motion sickness was evaluated during and following exposure to rotation. Significant adaptation effects were found for the slow phase velocity of vertical nystagmus, the reported magnitude of the subjective tilt experienced during head turns, and motion-sickness scores. Retention of adaptation over a six-day rest period without rotation occurred, but was not complete for all measures. Adaptation of VOR was fully maintained while subjective tilt was only partially maintained and motion-sickness scores continued to decrease. Practical implications of these findings are discussed with particular emphasis on artificial gravity, which could be produced in weightlessness by means of a short-radius (2 m) rotator.

Responses of Neurons in the Nucleus of the Basal Optic Root to Translational and Rotational Flowfields

1999 ◽  
Vol 81 (1) ◽  
pp. 267-276 ◽  
Author(s):  
Douglas R. W. Wylie ◽  
Barrie J. Frost
Keyword(s):  
Optic Flow ◽  
Horizontal Plane ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Vertical Axis ◽  
Mesencephalic Reticular Formation ◽  
Companion Paper ◽  
Direction Selectivity ◽  
Large Field ◽  
Adjacent Area

Wylie, Douglas R. W. and Barrie J. Frost. Responses of Neurons in the nucleus of the basal optic root to translational and rotational flowfields. J. Neurophysiol. 81: 267–276, 1999. The nucleus of the basal optic root (nBOR) receives direct input from the contralateral retina and is the first step in a pathway dedicated to the analysis of optic flowfields resulting from self-motion. Previous studies have shown that most nBOR neurons exhibit direction selectivity in response to large-field stimuli moving in the contralateral hemifield, but a subpopulation of nBOR neurons has binocular receptive fields. In this study, the activity of binocular nBOR neurons was recorded in anesthetized pigeons in response to panoramic translational and rotational optic flow. Translational optic flow was produced by the “translator” projector described in the companion paper, and rotational optic flow was produced by a “planetarium projector” described by Wylie and Frost. The axis of rotation or translation could be positioned to any orientation in three-dimensional space. We recorded from 37 cells, most of which exhibited a strong contralateral dominance. Most of these cells were located in the caudal and dorsal aspects of the nBOR complex and many were localized to the subnucleus nBOR dorsalis. Other units were located outside the boundaries of the nBOR complex in the adjacent area ventralis of Tsai or mesencephalic reticular formation. Six cells responded best to rotational flowfields, whereas 31 responded best to translational flowfields. Of the rotation cells, three preferred rotation about the vertical axis and three preferred horizontal axes. Of the translation cells, 3 responded best to a flowfield simulating downward translation of the bird along a vertical axis, whereas the remaining 28 responded best to flowfields resulting from translation along axes in the horizontal plane. Seventeen of these cells preferred a flowfield resulting from the animal translating backward along an axis oriented ∼45° to the midline, but the best axes of the remaining eleven cells were distributed throughout the horizontal plane with no definitive clustering. These data are compared with the responses of vestibulocerebellar Purkinje cells.

scholarly journals The Life Mission Theory III. Theory of Talent

2003 ◽  
Vol 3 ◽  
pp. 1286-1293 ◽  
Author(s):  
Soren Ventegodt ◽  
Niels Jorgen Andersen ◽  
Joav Merrick
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Vertical Axis ◽  
Three Dimensions ◽  
Natural State ◽  
Human Form ◽  
The World ◽  
Sex And Sexuality ◽  
And Gender ◽  
Third Dimension

When we acknowledge our purpose as the essence of our self, when we take all our power into use in an effortless way, and when we fully accept our own nature — including sex and sexuality, our purpose of life takes the form of a unique talent. Using this talent gives the experience of happiness. A person in his natural state of being uses his core talent in a conscious, joyful, and effortless way, contributing to the world the best he or she has to offer. Full expression of self happens when a person, in full acceptance of body and life, with whole-hearted intension, uses all his personal powers to realize his core talent and all associated talents, to contribute to his beloved and to the world. Thus, self-actualisation is a result of a person fully expressing and realizing his core talent.The theory of talent states that a core talent can be expressed optimally when a human being takes possession of a three-dimensional space with the axis of purpose, power and gender, as we have a threefold need: 1-Acknowledging our core talent (our purpose of life) and intending it 2-Understanding our potential powers and manifesting them 3-Accepting our human form including our sex and expressing itThe first dimension is spiritual, the next dimension is mental, emotional and physical, and the third dimension is bodily and sexual. We manifest our talents in a giving movement from the bottom of our soul trough our biological nature onto the subject and object of the outer world. These three dimensions can be drawn as three axes, one saggital axis called purpose or love or me-you, one vertical axis called power or consciousness (light) or heaven-earth, and one horizontal axis called gender or joy or male-female. The three core dimensions of human existence are considered of equal importance for expression of our life purpose, life mission, or core talent. Each of the dimensions is connected to special needs. When these needs are not fulfilled, we suffer and if this suffering becomes unbearable we deny the dimension or a part of is. This is why the dimensions of purpose, power and gender become suppressed from our consciousness.

scholarly journals Navigating in a three-dimensional world

2013 ◽  
Vol 36 (5) ◽  
pp. 523-543 ◽  
Author(s):  
Kathryn J. Jeffery ◽  
Aleksandar Jovalekic ◽  
Madeleine Verriotis ◽  
Robin Hayman
Keyword(s):  
Spatial Cognition ◽  
Horizontal Plane ◽  
Spatial Representation ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Complex Topography ◽  
Orthogonal Axis ◽  
Fully Integrated ◽  
Insight Into ◽  
Considerable Insight

AbstractThe study of spatial cognition has provided considerable insight into how animals (including humans) navigate on the horizontal plane. However, the real world is three-dimensional, having a complex topography including both horizontal and vertical features, which presents additional challenges for representation and navigation. The present article reviews the emerging behavioral and neurobiological literature on spatial cognition in non-horizontal environments. We suggest that three-dimensional spaces are represented in a quasi-planar fashion, with space in the plane of locomotion being computed separately and represented differently from space in the orthogonal axis – a representational structure we have termed “bicoded.” We argue that the mammalian spatial representation in surface-travelling animals comprises a mosaic of these locally planar fragments, rather than a fully integrated volumetric map. More generally, this may be true even for species that can move freely in all three dimensions, such as birds and fish. We outline the evidence supporting this view, together with the adaptive advantages of such a scheme.

scholarly journals Everything Is A Circle: A New Universal Orbital Model

2021 ◽  
Author(s):  
AslıPınar Tan
Keyword(s):  
Solar System ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Ecliptic Plane ◽  
The Sun ◽  
The Moon ◽  
Circular Orbits ◽  
Orbital Parameters ◽  
The Earth ◽  
Angular Velocities

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other. According to Kepler’s 1st Law, “orbit of a planet with respect to the Sun is an ellipse, with the Sun at one of the two foci.” Orbit of the Moon with respect to Earth is also distinctly elliptical, but this ellipse has a varying eccentricity as the Moon comes closer to and goes farther away from the Earth in a harmonic style along a full cycle of this ellipse. In this paper, our research results are summarized, where it is first mathematically shown that the “distance between points around any two different circles in three dimensional space” is equivalent to the “distance of points around a vector ellipse to another fixed or moving point, as in two dimensional space”. What is done is equivalent to showing that bodies moving on two different circular orbits in space vector wise behave as if moving on an elliptical path with respect to each other, and virtually seeing each other as positioned at an instantaneously stationary point in space on their relative ecliptic plane, whether they are moving with the same angular velocity, or different but fixed angular velocities, or even with different and changing angular velocities with respect to their own centers of revolution. This mathematical revelation has the potential to lead to far reaching discoveries in physics, enabling more insight into forces of nature, with a formulation of a new fundamental model regarding the motions of bodies in the Universe, including the Sun, Planets, and Satellites in the Solar System and elsewhere, as well as at particle and subatomic level. Based on the demonstrated mathematical analysis, as they exhibit almost fixed elliptic orbits relative to one another over time, the assertion is made that the Sun, the Earth, and the Moon must each be revolving in their individual circular orbits of revolution in space. With this expectation, individual orbital parameters of the Sun, the Earth, and the Moon are calculated based on observed Earth to Sun and Earth to Moon distance data, also using analytical methods developed as part of this research to an approximation. This calculation and analysis process have revealed additional results aligned with observation, and this also supports our assertion that the Sun, the Earth, and the Moon must actually be revolving in individual circular orbits.

Three-dimensional organization of optokinetic responses in the rabbit

1993 ◽  
Vol 69 (2) ◽  
pp. 303-317 ◽  
Author(s):  
H. S. Tan ◽  
J. van der Steen ◽  
J. I. Simpson ◽  
H. Collewijn
Keyword(s):  
Control System ◽  
Horizontal Plane ◽  
Three Dimensional ◽  
Vertical Axis ◽  
Horizontal Axis ◽  
Constant Speed ◽  
Slow Phase ◽  
Optokinetic Stimulation ◽  
Axis Orientation ◽  
Maximum Gain

1. Three-dimensional rotations of both eyes were measured in alert rabbits during optokinetic stimulation about axes lying in the horizontal plane or about an earth-vertical axis, with either one or both eyes viewing the stimulus. Optokinetic stimulus speed was 2 degrees /s, either continuous or alternating in polarity (triangular stimulus). In addition to the gains of the responses, the orientations of the response axes relative to the stimulus axes were determined. 2. In comparison to the response to constant-speed optokinetic stimulation about the vertical axis, the response to constant-speed optokinetic stimulation about horizontal axes was characterized by the lack of a speed buildup. In many cases, slow phase tracking was good as long as the eye was within the central oculomotor range but deteriorated when eye deviation became more eccentric and fast phases failed to be generated. These features suggest that the optokinetic reflex about horizontal axes functions as a position-control system, rather than as a velocity-control system. 3. Binocular optokinetic stimulation at constant speed (2 degrees/s) about the roll axis (0 degrees azimuth horizontal axis) elicited disconjugate responses. Although the gain of the response was not significantly different in the two eyes (0.38 for downward and 0.44 for upward stimulation), the response axes of the two eyes differed by as much as 51 degrees. 4. Monocular, horizontal axis optokinetic stimulation at constant speed elicited responses that were grossly dissociated between the two eyes. The magnitude of the responses was anisotropic in that it varied with the azimuthal orientation of the stimulus axis; the maximum gain for each eye (0.41 for the seeing and 0.33 for the covered eye) was at 135 degrees azimuth for each eye. The axis orientation and direction (sense of rotation) of the optokinetic stimulus eliciting the maximal response for each eye coincided with the optic flow normally associated with the maximal excitation of the corresponding ipsilateral anterior canal. 5. Binocular, triangular optokinetic stimulation with small excursions (+/- 10 degrees), which avoided the saturation problems of constant-speed stimulation, elicited adequate responses without systematic directional asymmetries. Gain was approximately 0.9 for all stimulus axis orientations in the horizontal plane. 6. During monocular stimulation with triangular stimuli, the response of the seeing eye showed a gain of approximately 0.5 for all orientations of the stimulus axis. In contrast, the covered eye showed anisotropic responses, with a maximum gain of approximately 0.5 during stimulation of the seeing eye about its 45 degree axis.(ABSTRACT TRUNCATED AT 400 WORDS)

Sign in / Sign up

Export Citation Format

Share Document