scholarly journals A gravity-based three-dimensional compass in the mouse brain

2019 ◽  
Author(s):  
Dora E Angelaki ◽  
J Ng ◽  
AM Abrego ◽  
HX Cham ◽  
JD Dickman ◽  
...  
Keyword(s):  
Horizontal Plane ◽  
Degrees Of Freedom ◽  
Mammalian Species ◽  
Three Dimensional ◽  
Retrosplenial Cortex ◽  
Orientation Tuning ◽  
Head Direction ◽  
Head Direction Cells ◽  
Dimensional Gravity ◽  
Three Degrees Of Freedom

SummaryHead direction cells in the mammalian limbic system are thought to function as an allocentric neuronal compass. Although traditional views hold that the compass of ground-dwelling species is planar, we show that head-direction cells in the rodent thalamus, retrosplenial cortex and cingulum fiber bundle are tuned to conjunctive combinations of azimuth, pitch or roll, similarly to presubicular cells in flying bats. Pitch and roll orientation tuning is ubiquitous, anchored to gravity, and independent of visual landmarks. When head tilts, azimuth tuning is affixed to the head-horizontal plane, but also uses gravity to remain anchored to the terrestrial allocentric world. These findings suggest that gravity defines all three degrees of freedom of the allocentric orientation compass, and only the azimuth component can flexibly remap to local cues in different environments. Collectively, these results demonstrate that a three-dimensional, gravity-based, neural compass is likely a ubiquitous property of mammalian species, including ground-dwelling animals.

Hippocampal Place-Cell Firing During Movement in Three-Dimensional Space

2001 ◽  
Vol 85 (1) ◽  
pp. 105-116 ◽  
Author(s):  
James J. Knierim ◽  
Bruce L. McNaughton
Keyword(s):  
Hippocampal Neurons ◽  
Horizontal Plane ◽  
Three Dimensional ◽  
Place Cell ◽  
Place Cells ◽  
Limbic Cortex ◽  
Head Direction ◽  
Head Direction Cells ◽  
Recording Apparatus ◽  
Place Fields

“Place” cells of the rat hippocampus are coupled to “head direction” cells of the thalamus and limbic cortex. Head direction cells are sensitive to head direction in the horizontal plane only, which leads to the question of whether place cells similarly encode locations in the horizontal plane only, ignoring the z axis, or whether they encode locations in three dimensions. This question was addressed by recording from ensembles of CA1 pyramidal cells while rats traversed a rectangular track that could be tilted and rotated to different three-dimensional orientations. Cells were analyzed to determine whether their firing was bound to the external, three-dimensional cues of the environment, to the two-dimensional rectangular surface, or to some combination of these cues. Tilting the track 45° generally provoked a partial remapping of the rectangular surface in that some cells maintained their place fields, whereas other cells either gained new place fields, lost existing fields, or changed their firing locations arbitrarily. When the tilted track was rotated relative to the distal landmarks, most place fields remapped, but a number of cells maintained the same place field relative to the x-y coordinate frame of the laboratory, ignoring the z axis. No more cells were bound to the local reference frame of the recording apparatus than would be predicted by chance. The partial remapping demonstrated that the place cell system was sensitive to the three-dimensional manipulations of the recording apparatus. Nonetheless the results were not consistent with an explicit three-dimensional tuning of individual hippocampal neurons nor were they consistent with a model in which different sets of cells are tightly coupled to different sets of environmental cues. The results are most consistent with the statement that hippocampal neurons can change their “tuning functions” in arbitrary ways when features of the sensory input or behavioral context are altered. Understanding the rules that govern the remapping phenomenon holds promise for deciphering the neural circuitry underlying hippocampal function.

scholarly journals The brain compass: a perspective on how self-motion updates the head direction cell attractor

2017 ◽  
Author(s):  
Jean Laurens ◽  
Dora E. Angelaki
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Head Tilt ◽  
Head Direction ◽  
Motion Velocity ◽  
Head Direction Cells ◽  
Motion Cues ◽  
Head Direction Cell ◽  
On Line ◽  
Self Motion

ABSTRACTHead Direction cells form an internal compass that signals head azimuth orientation even in the absence of visual landmarks. It is well accepted that head direction properties are generated through a ring attractor that is updated using rotation self-motion cues. The properties and origin of this self-motion velocity drive remain, however, unknown. We propose a unified, quantitative framework whereby the attractor velocity input represents a multisensory self-motion estimate computed through an internal model that uses sensory prediction error based on vestibular, visual, and somatosensory cues to improve on-line motor drive. We show how context-dependent strength of recurrent connections within the attractor itself, rather than the self-motion input, explain differences in head direction cell firing between free foraging and restrained movements. We also summarize recent findings on how head tilt relative to gravity influences the azimuth coding of head direction cells, and explain why and how these effects reflect an updating self-motion velocity drive that is not purely egocentric. Finally, we highlight recent findings that the internal compass may be three-dimensional and hypothesize that the additional vertical degrees of freedom are defined based on global allocentric gravity cues.

scholarly journals A model-based reassessment of the three-dimensional tuning of head direction cells in rats

2019 ◽  
Vol 122 (3) ◽  
pp. 1274-1287 ◽  
Author(s):  
Jean Laurens ◽  
Dora E. Angelaki
Keyword(s):  
Experimental Data ◽  
Model Comparison ◽  
Three Dimensional ◽  
Orientation Tuning ◽  
Head Orientation ◽  
Published Data ◽  
Head Direction ◽  
Head Direction Cells ◽  
Vertical Orientation ◽  
Model Based

In a recent study, Shinder and Taube (Shinder ME, Taube JS. J Neurophysiol 121: 4–37, 2019) concluded that head direction cells in the anterior thalamus of rats are tuned to one-dimensional (1D, yaw-only) motion, in contrast to recent findings in bats, mice, and rats. Here we reinterpret the author’s experimental results using model comparison and demonstrate that, contrary to their conclusions, experimental data actually supports the dual-axis rule (lson JJ, Jeffery KJ. J Neurophysiol 119: 192–208, 2018) and tilted azimuth model (Laurens J, Angelaki DE. Neuron 97: 275–289, 2018), where head direction cells use gravity to integrate 3D rotation signals about all cardinal axes of the head. We further show that the Shinder and Taube study is inconclusive regarding the presence of vertical orientation tuning; i.e., whether head direction cells encode 3D orientation in the horizontal and vertical planes conjunctively. Using model simulations, we demonstrate that, even if 3D tuning existed, the experimental protocol and data analyses used by Shinder and Taube would not have revealed it. We conclude that the actual experimental data of Shinder and Taube are compatible with the 3D properties of head direction cells discovered by other groups, yet incorrect conclusions were reached because of incomplete and qualitative analyses. NEW & NOTEWORTHY We conducted a model-based analysis previously published data where rat head direction cells were recorded during three-dimensional motion (Shinder ME, Taube JS. J Neurophysiol 121: 4–37, 2019). We found that these data corroborate previous models (“dual-axis rule,” Page HJI, Wilson JJ, Jeffery KJ. J Neurophysiol 119: 192–208, 2018; and “tilted azimuth model,” Laurens J, Angelaki DE. Neuron 97: 275–289, 2018) where head direction cells integrate rotations along all three head axes to encode head orientation in a gravity-anchored reference frame.

scholarly journals A re-interpretation of the experimental data of Shinder and Taube “Three-dimensional Tuning of Head Direction Cells in Rats”, Journal of Neurophysiology 121(1), 2019

2019 ◽  
Author(s):  
Jean Laurens ◽  
Dora E. Angelaki
Keyword(s):  
Experimental Data ◽  
Model Comparison ◽  
Three Dimensional ◽  
Orientation Tuning ◽  
Head Direction ◽  
Experimental Protocol ◽  
Head Direction Cells ◽  
Vertical Orientation ◽  
One Dimensional ◽  
Anterior Thalamus

AbstractIn a recent study, Shinder and Taube (2019) concluded that head direction cells in the anterior thalamus of rats are tuned to one-dimensional (1D, yaw-only) motion exclusively, in contrast to recent findings in bats (Finkelstein et al. 2015), mice (Angelaki et al. 2016; Cham et al. 2017; Laurens et al. 2017), and rats (Page et al. 2017). Here we re-interpret the author’s experimental results using model comparison and demonstrate that, contrary to their conclusions, their data actually supports the dual-axis rule (Page et al. 2017) and tilted azimuth model (Laurens and Angelaki 2018), where head direction cells use gravity to integrate 3D rotation signals about all cardinal axes of the head. We further show that this study is inconclusive regarding the presence of vertical orientation tuning; i.e. whether head direction cells encode 3D orientation in the horizontal and vertical planes conjunctively. Using model simulations, we demonstrate that, even if 3D tuning existed, the experimental protocol and data analyses used by Shinder and Taube (2019) would not have revealed it. We conclude that the actual experimental data of Shinder and Taube (2019) are compatible with the 3D properties of head direction cells discovered by other groups, yet incorrect conclusions were reached because of incomplete and qualitative analyses.

The statistical distribution of the length of a rubber molecule

1948 ◽  
Vol 44 (3) ◽  
pp. 342-344 ◽  
Author(s):  
P. A. P. Moran
Keyword(s):  
Normal Distribution ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Statistical Distribution ◽  
Equal Length ◽  
Fixed Angle ◽  
A Chain ◽  
Image Position ◽  
Three Degrees Of Freedom

A rubber molecule containing n + 1 carbon atoms may be represented by a chain of n links of equal length such that successive links are at a fixed angle to each other but are otherwise at random. The statistical distribution of the length of the molecule, that is, the distance between the first and last carbon atoms, has been considered by various authors (Treloar (1) gives references). In particular, if the first atom is kept fixed at the origin of a system of coordinates and the chain is otherwise at random, it has been conjectured that the distribution of the (n + 1)th atom will tend, as n increases, towards a three-dimensional normal distribution of the formwhere σ depends on n. Thus r2 (= x2 + y2 + z2) will be approximately distributed as σ2χ2 with three degrees of freedom.

scholarly journals Carter's constant and superintegrability

2018 ◽  
Vol 27 (07) ◽  
pp. 1850066
Author(s):  
Payel Mukhopadhyay ◽  
K. Rajesh Nayak
Keyword(s):  
Dynamical System ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Integrals Of Motion ◽  
Superintegrable System ◽  
Simple Observation ◽  
Superintegrable Systems ◽  
Axisymmetric Spacetime ◽  
Three Degrees Of Freedom

Carter's constant is a nontrivial conserved quantity of motion of a particle moving in stationary axisymmetric spacetime. In the version of the theorem originally given by Carter, due to the presence of two Killing vectors, the system effectively has two degrees of freedom. We propose an extension to the first version of Carter's theorem to a system having three degrees of freedom to find two functionally independent Carter-like integrals of motion. We further generalize the theorem to a dynamical system with [Formula: see text] degrees of freedom. We further study the implications of Carter's constant to superintegrability and present a different approach to probe a superintegrable system. Our formalism gives another viewpoint to a superintegrable system using the simple observation of separable Hamiltonian according to Carter's criteria. We then give some examples by constructing some two-dimensional superintegrable systems based on this idea and also show that all three-dimensional simple classical superintegrable potentials are also Carter separable.

Thermogasodynamic Analysis of the Segmented Annular Seal

2020 ◽  
Vol 143 (7) ◽  
Author(s):  
Samia Dahite ◽  
Mihai Arghir
Keyword(s):  
Parametric Study ◽  
Thermal Effects ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Leading Edge ◽  
Test Case ◽  
Isothermal Model ◽  
Pocket Depth ◽  
Annular Seal ◽  
Three Degrees Of Freedom

Abstract The present work deals with the thermogasodynamic analysis of the segmented annular seal provided with Rayleigh pockets. The paper is a continuation of the work presented Arghir, M., and Mariot, A. (2017, “Theoretical Analysis of the Static Characteristics of the Carbon Segmented Seal,” ASME J. Tribol., 139(6), p. 062202.) where an isothermal model of the segmented annular seal was first presented. Each segment had three degrees-of-freedom, and its static position was obtained by solving the nonlinear equations of equilibrium. Thermal effects are now introduced by considering a simplified form of the energy equation in the thin gas film coupled with the three dimensional heat transfer in a segment of the seal and in the rotor. An efficient numerical algorithm is developed. A parametric study was performed for a segmented annular seal with pockets taken from the literature and operating with air. First, a test case proved the necessity of considering three degrees-of-freedom for the segment and not only its radial displacement. The parametric study was then performed for two different pocket depths, two pressure differences, and different rotation speeds. The results showed a non-uniform heating with larger temperatures at the leading edge of the segment where the minimal film thickness occurs. Heating is proportional to the pocket depth that lowers the lift force of the segment and to the pressure difference that closes the seal.

scholarly journals Contact Force Control of Three-Dimensional Flexible Manipulator

2020 ◽  
Author(s):  
Minoru Sasaki ◽  
Shunta Ito ◽  
Daiki Maeno ◽  
Waweru Njeri ◽  
Muguro Josephh ◽  
...  
Keyword(s):  
Contact Force ◽  
Force Control ◽  
Degrees Of Freedom ◽  
Force Feedback ◽  
Three Dimensional ◽  
Flexible Manipulator ◽  
Force Tracking ◽  
Feedback Method ◽  
Three Degrees Of Freedom ◽  
Contact Force Control

This paper proposes a contact force controller for a constrained flexible manipulator in three-dimensional motion. This controller used the conversion formula obtained empirically and experimental results showed the effectiveness of the proposed contact force controller. First, the manipulator was operated with the tip of the second link restrained, then, time response of the root strain, joint angles and contact force were used to derive the relational between the three quantities. The effectiveness of the relational expression was verified by conducting a target contact force tracking experiment by inputting the angle from the relational expression. The contact force control using the strain feedback method was proposed with the strain amount estimated from the target contact force as the target value, and its effectiveness was verified by experiments. From the results obtained, controller using the strain feedback method was designed for the purpose of controlling the contact force at the tip of a flexible manipulator with two links and three degrees of freedom that performs three-dimensional spatial motion, and its effectiveness was shown by comparison with the contact force feedback method.

A First Example: The “Particle in a Box“ and Quantized Translational Motion

2020 ◽  
pp. 59-96
Author(s):  
Jochen Autschbach
Keyword(s):  
Degrees Of Freedom ◽  
Separation Of Variables ◽  
Translational Motion ◽  
Three Dimensional ◽  
Potential Wells ◽  
Quantum Tunnelling ◽  
Atomic Force ◽  
Quantum Behavior ◽  
The One ◽  
Three Degrees Of Freedom

The simple ‘particle in a box’ (Piab) is introduced in this chapter so that the reader can get familiar with applying the quantum recipe and atomic units. The PiaB is introduced in its one, two, and three dimensional variants, which demonstrates the use of the separation of variables technique as a strategy to solve the Schrodinger equation for a particle with two or three degrees of freedom. It is shown that the confinement of the particle causes the energy to be quantized. The one-dimensional PiaB is then applied to treat the electronic spectra of cyanine dyes and their absorption colors. The chapter then introduces more general setups with finite potential wells, in order to introduce the phenomenon of quantum tunnelling and to discuss more generally with the unintuitive ‘quantum behavior’ of particles such as electrons. Scanning tunnelling and atomic force microscopes are also discussed briefly.

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.

Sign in / Sign up

Export Citation Format

Share Document