Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Vector Components in the Cartesian Coordinate System01:29

Vector Components in the Cartesian Coordinate System

29.3K
Vectors are usually described in terms of their components in a coordinate system. Even in everyday life, we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if someone gives you directions for a particular location, you will be told to go a few km in a direction like east, west, north, or south, along with the angle in which you are supposed to move. In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is...
29.3K
Cartesian Vector Notation01:28

Cartesian Vector Notation

1.8K
Cartesian vector notation is a valuable tool in mechanical engineering for representing vectors in three-dimensional space, performing vector operations such as determining the gradient, divergence, and curl, and expressing physical quantities such as the displacement, velocity, acceleration, and force. By using Cartesian vector notation, engineers can more easily analyze and solve problems in various areas of mechanical engineering, including dynamics, kinematics, and fluid mechanics. This...
1.8K
Cartesian Form for Vector Formulation01:26

Cartesian Form for Vector Formulation

1.2K
The Cartesian form for vector formulation is a process to calculate  the moment of force using the position and force vectors. The moment of force is defined as the cross-product of these vectors, making it a vector quantity. The Cartesian form of the position and force vectors involves unit vectors, which can be used to express the cross-product in determinant form.
1.2K
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

18.4K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
18.4K
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

20.3K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
20.3K
Vector Transformation in Rotating Coordinate Systems01:16

Vector Transformation in Rotating Coordinate Systems

2.8K
Consider a vector rotating about an axis with an angular velocity, such that its tip sweeps a circular path.
2.8K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Coordination of spike timing among the neurons of the cerebellum.

Research square·2026
Same author

A neural language for the cerebellum: control of behavior via competing populations of Purkinje cells.

Journal of neurophysiology·2026
Same author

Coordination of spike timing among the neurons of the cerebellum.

bioRxiv : the preprint server for biology·2025
Same author

Separating the control of moving and holding in human post-stroke arm paresis.

eLife·2025
Same author

Goal uncertainty attenuates sensorimotor adaptation.

Journal of neurophysiology·2025
Same author

Purkinje cells of the cerebellum control deceleration of tongue movements.

PLoS biology·2025

Related Experiment Video

Updated: Mar 8, 2026

Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches
10:50

Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches

Published on: June 21, 2022

2.2K

A vector calculus for neural computation in the cerebellum.

Mohammad Amin Fakharian1, Alden M Shoup1, Paul Hage1

  • 1Laboratory for Computational Motor Control, Department of Biomedical Engineering, Johns Hopkins School of Medicine, Baltimore, MD, USA.

Science (New York, N.Y.)
|May 22, 2025
PubMed
Summary

Null space theory reveals that neurons prevent unwanted effects by canceling other neurons

More Related Videos

Revealing Neural Circuit Topography in Multi-Color
09:11

Revealing Neural Circuit Topography in Multi-Color

Published on: November 14, 2011

15.5K
Ex Vivo Culture of Chick Cerebellar Slices and Spatially Targeted Electroporation of Granule Cell Precursors
10:02

Ex Vivo Culture of Chick Cerebellar Slices and Spatially Targeted Electroporation of Granule Cell Precursors

Published on: December 14, 2015

9.8K

Related Experiment Videos

Last Updated: Mar 8, 2026

Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches
10:50

Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches

Published on: June 21, 2022

2.2K
Revealing Neural Circuit Topography in Multi-Color
09:11

Revealing Neural Circuit Topography in Multi-Color

Published on: November 14, 2011

15.5K
Ex Vivo Culture of Chick Cerebellar Slices and Spatially Targeted Electroporation of Granule Cell Precursors
10:02

Ex Vivo Culture of Chick Cerebellar Slices and Spatially Targeted Electroporation of Granule Cell Precursors

Published on: December 14, 2015

9.8K

Area of Science:

  • Neuroscience
  • Computational Neuroscience
  • Cerebellar Function

Background:

  • Null space theory posits that neuronal activity serves dual roles: driving behavior and preventing interference from other neurons.
  • Competitive cancellation is a proposed mechanism for neural computation, particularly relevant in complex brain regions like the cerebellum.

Purpose of the Study:

  • To investigate the role of competitive cancellation in cerebellar computation.
  • To elucidate how Purkinje cells contribute to motor control and movement termination.

Main Methods:

  • Identified Purkinje cell (P cell) spike vectors influencing eye displacement in marmosets.
  • Analyzed population activity resulting from superimposed P cell spike vectors.
  • Investigated the role of mossy fibers and molecular layer interneurons in processing motor commands and movement goals.

Main Results:

  • Purkinje cell spikes were found to displace eye movements along specific vectors.
  • Spike contributions perpendicular to the intended movement direction were canceled in population activity.
  • Mossy fibers relayed motor commands and movement goals, while interneurons signaled movement completion.

Conclusions:

  • Competitive cancellation is crucial for understanding cerebellar computation.
  • The cerebellum utilizes competitive cancellation for precise motor control and timely movement cessation.
  • Neural circuits involving Purkinje cells, mossy fibers, and interneurons coordinate movement execution and termination.