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

Ordinal Level of Measurement00:55

Ordinal Level of Measurement

35.1K
The way a set of data is measured is called its level of measurement. Correct statistical procedures depend on a researcher being familiar with levels of measurement. For analysis, data are classified into four levels of measurement—nominal, ordinal, interval, and ratio.
Data measured using an ordinal scale are similar to nominal scale data, but there is one major difference. The ordinal scale data can be ordered. An example of ordinal scale data is a list of the top five national parks...
35.1K
Periodic Classification of the Elements04:00

Periodic Classification of the Elements

61.8K
The periodic table arranges atoms based on increasing atomic number so that elements with the same chemical properties recur periodically. When their electron configurations are added to the table, a periodic recurrence of similar electron configurations in the outer shells of these elements is observed. Because they are in the outer shells of an atom, valence electrons play the most important role in chemical reactions. The outer electrons have the highest energy of the electrons in an atom...
61.8K
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

290
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
290
Population Growth00:57

Population Growth

28.8K
Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.
28.8K
Area Computation by the Alternative Coordinate Method01:24

Area Computation by the Alternative Coordinate Method

685
The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
685
Couples: Scalar and Vector Formulation01:21

Couples: Scalar and Vector Formulation

654
One might wonder how the captain of a large ship can navigate through the ocean with just a turn of the steering wheel. The answer lies in the concept of two parallel forces that are equal in magnitude and opposite sense, creating a couple moment.
A couple moment is a rotational force that tends to rotate the steering wheel. The wheel's rotation can either be in a clockwise or anticlockwise direction. The right-hand rule is a helpful method for determining the direction of a couple moment....
654

You might also read

Related Articles

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

Sort by
Same author

A multi-ring shifter network computes head direction in zebrafish.

Current biology : CB·2026
Same author

The Simons Collaboration on Ecological Neuroscience: Studying how the brain interacts with the world.

Neuron·2026
Same author

The behavior biopsy: Interpreting animal behavior as embodied, situated, and hierarchical.

Current opinion in neurobiology·2026
Same author

Individual identification of brown bears using pose-aware metric learning.

Current biology : CB·2026
Same author

Joint modelling of brain and behaviour dynamics with artificial intelligence.

Nature reviews. Neuroscience·2025
Same author

Mice navigate scent trails using predictive policies.

bioRxiv : the preprint server for biology·2025

Related Experiment Video

Updated: Feb 23, 2026

Using Generative Art to Convey Past and Future Climate Transitions
06:10

Using Generative Art to Convey Past and Future Climate Transitions

Published on: March 31, 2023

1.5K

Periodic population codes: From a single circular variable to higher dimensions, multiple nested scales, and

Andreas Vm Herz1, Alexander Mathis2, Martin Stemmler1

  • 1Bernstein Center for Computational Neuroscience Munich and Faculty of Biology, Ludwig-Maximilians-Universität München, Grosshadernerstrasse 2, 82152 Planegg-Martinsried, Germany.

Current Opinion in Neurobiology
|September 10, 2017
PubMed
Summary

Neurons use von Mises functions to encode circular stimuli. This leads to population vector readouts and hexagonal grid cell activity, representing flat geometry on a torus for efficient spatial navigation.

More Related Videos

Measuring the Structure, Composition, and Change of Underwater Environments with Large-area Imaging
09:19

Measuring the Structure, Composition, and Change of Underwater Environments with Large-area Imaging

Published on: April 18, 2025

1.6K
Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon
09:44

Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon

Published on: October 16, 2018

10.8K

Related Experiment Videos

Last Updated: Feb 23, 2026

Using Generative Art to Convey Past and Future Climate Transitions
06:10

Using Generative Art to Convey Past and Future Climate Transitions

Published on: March 31, 2023

1.5K
Measuring the Structure, Composition, and Change of Underwater Environments with Large-area Imaging
09:19

Measuring the Structure, Composition, and Change of Underwater Environments with Large-area Imaging

Published on: April 18, 2025

1.6K
Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon
09:44

Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon

Published on: October 16, 2018

10.8K

Area of Science:

  • Neuroscience
  • Computational Neuroscience
  • Mathematical Biology

Background:

  • Neurons commonly encode circular variables using von Mises tuning curves, a class of periodic functions.
  • Population vector readouts are optimal for decoding stimuli from such neural populations.

Purpose of the Study:

  • To propose a framework where the neural representation of Euclidean geometry is transformed into a toroidal (circular) manifold.
  • To explain the emergence of hexagonal activity patterns in mammalian grid cells as a consequence of this representation.

Main Methods:

  • Theoretical analysis of neural population coding using von Mises functions.
  • Modeling the transformation of flat Euclidean geometry into a circular (toroidal) representation.
  • Review of experimental evidence supporting the proposed framework.

Main Results:

  • Population vector readouts are optimal for decoding circular variables encoded by von Mises tuning curves.
  • The framework explains how flat geometry can be represented on a torus, leading to grid cell-like hexagonal patterns.
  • Multiple scales and gain fields can resolve ambiguities in periodic representations of linear variables.

Conclusions:

  • The neural representation of space may involve curling flat geometry into a torus, facilitating efficient spatial coding via grid cells.
  • This framework provides a unified explanation for canonical neural representations and grid cell function.
  • The model offers testable predictions and generalizations for understanding abstract grid-like neural representations.