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

Navier–Stokes Equations01:28

Navier–Stokes Equations

2.8K
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
2.8K
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

1.5K
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
1.5K
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

4.3K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
4.3K
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

1.9K
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
1.9K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

501
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
501
Neural Circuits01:25

Neural Circuits

3.0K
Neural circuits and neuronal pools are two of the main structures found in the nervous system. Neural circuits are networks of neurons that work together to carry out a specific task or process. They consist of interconnected neurons and glial cells, which provide structural and metabolic support.
Neuronal pools are collections of nerve cells with similar functions and interact through chemical and electrical signals. These pools include both interneurons (the central neural circuit nodes that...
3.0K

You might also read

Related Articles

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

Sort by
Same author

Standing and travelling waves in a spherical brain model: The Nunez model revisited.

Physica D. Nonlinear phenomena·2017
Same author

Combined endoscopic approach for patients with multiple bladder stones.

Annals of the Royal College of Surgeons of England·2015
Same author

Bifurcation study of a neural field competition model with an application to perceptual switching in motion integration.

Journal of computational neuroscience·2013
Same author

The Benevolent Fund.

Provincial medical journal and retrospect of the medical sciences·2011
Same author

Case of Traumatic Tetanus.

Provincial medical & surgical journal·2010
Same author

On Traumatic Tetanus and Its Treatment, with Some Remarks on the Extract of Cannabis Indica of Commerce.

Provincial medical & surgical journal·2010

Related Experiment Video

Updated: Apr 26, 2026

Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro
06:22

Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro

Published on: August 28, 2019

4.7K

Stochastic neural field equations: a rigorous footing.

O Faugeras1, J Inglis

  • 1NeuroMathComp, INRIA, Sophia Antipolis, France, olivier.faugeras@inria.fr.

Journal of Mathematical Biology
|July 30, 2014
PubMed
Summary

This study introduces a rigorous probabilistic framework for stochastic neural field equations, making advanced mathematical biology concepts accessible to neuroscientists. New conditions ensure the existence of solutions for these complex neural models.

More Related Videos

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

2.3K
External Excitation of Neurons Using Electric and Magnetic Fields in One- and Two-dimensional Cultures
08:32

External Excitation of Neurons Using Electric and Magnetic Fields in One- and Two-dimensional Cultures

Published on: May 7, 2017

12.7K

Related Experiment Videos

Last Updated: Apr 26, 2026

Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro
06:22

Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro

Published on: August 28, 2019

4.7K
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

2.3K
External Excitation of Neurons Using Electric and Magnetic Fields in One- and Two-dimensional Cultures
08:32

External Excitation of Neurons Using Electric and Magnetic Fields in One- and Two-dimensional Cultures

Published on: May 7, 2017

12.7K

Area of Science:

  • Mathematical Neuroscience
  • Stochastic Partial Differential Equations (SPDEs)
  • Probability Theory

Background:

  • Neural field equations are central to mathematical neuroscience.
  • A rigorous probabilistic framework is needed for stochastic neural field models.
  • Existing literature often lacks accessible, consolidated information for neuroscientists.

Purpose of the Study:

  • To present a rigorous probabilistic framework for stochastic neural field equations.
  • To bridge the gap between probability theory and mathematical biology/neuroscience.
  • To serve as a reference for solutions and well-posedness in this field.

Main Methods:

  • Application of established stochastic partial differential equation (SPDE) theory.
  • Development of accessible explanations of probabilistic concepts.
  • Analysis of existence and uniqueness of solutions under specific parameter conditions.

Main Results:

  • A clear probabilistic framework for studying stochastic neural field equations is provided.
  • Rigorous results on notions of solutions and well-posedness are collected and clarified.
  • New conditions are identified that guarantee the existence of solutions for the neural field equation.

Conclusions:

  • The study successfully bridges theoretical probability and applied neuroscience.
  • The provided framework enhances the understanding and analysis of neural field models.
  • This work serves as a valuable resource for researchers in mathematical neuroscience.