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

Propagation of Action Potentials01:23

Propagation of Action Potentials

7.5K
The propagation of an action potential refers to the process by which a nerve impulse, or "action potential," travels along a neuron.
Neurons (nerve cells) have a resting membrane potential, with a slightly negative charge inside compared to outside. This is maintained by ion channels, such as sodium (Na+) and potassium (K+) channels, which control the flow of ions. When a stimulus, like a touch or a signal from another neuron, triggers the neuron, sodium channels open, allowing sodium ions to...
7.5K
Neural Circuits01:25

Neural Circuits

1.9K
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...
1.9K
Action Potential01:14

Action Potential

9.1K
Neurons communicate by firing action potentials—the electrochemical signal that is propagated along the axon. The signal results in the release of neurotransmitters at axon terminals, thereby transmitting information to the nervous system. An action potential is a specific "all-or-none" change in membrane potential that results in a rapid spike in voltage.
Membrane potential in neurons
Neurons typically have a resting membrane potential of about -70 millivolts (mV). When they receive...
9.1K
Current Growth And Decay In RL Circuits01:30

Current Growth And Decay In RL Circuits

4.1K
The current growth and decay in RL circuits can be understood by considering a series RL circuit consisting of a resistor, an inductor, a constant source of emf, and two switches. When the first switch is closed, the circuit is equivalent to a single-loop circuit consisting of a resistor and an inductor connected to a source of emf. In this case, the source of emf produces a current in the circuit. If there were no self-inductance in the circuit, the current would rise immediately to a steady...
4.1K
Long-term Potentiation01:25

Long-term Potentiation

3.0K
Long-term potentiation, or LTP, is one of the ways by which synaptic plasticity—changes in the strength of chemical synapses—can occur in the brain. LTP is the process of synaptic strengthening that occurs over time between pre and postsynaptic neuronal connections. The synaptic strengthening of LTP works in opposition to the synaptic weakening of long-term depression (LTD) and together are the main mechanisms that underlie learning and memory.
Hebbian LTP
LTP can occur when...
3.0K
The Role of Ion Channels in Neuronal Computation01:19

The Role of Ion Channels in Neuronal Computation

3.3K
A postsynaptic neuron usually receives numerous impulses from several other presynaptic neurons. The axon hillock of the postsynaptic neuron integrates all these signals and determines the likelihood of firing an action potential.
Sometimes a single EPSP is strong enough to induce an action potential in the postsynaptic neuron. However, multiple presynaptic inputs must often create EPSPs around the same time for the postsynaptic neuron to be sufficiently depolarized to fire an action potential....
3.3K

You might also read

Related Articles

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

Sort by
Same author

Extinction scenarios in evolutionary processes: a multinomial Wright-Fisher approach.

Journal of mathematical biology·2023
Same author

SHIFTING POWERS IN SPIVEY'S BELL NUMBER FORMULA.

Quaestiones mathematicae : journal of the South African Mathematical Society·2022
Same author

Favorite Sites of a Persistent Random Walk.

Journal of mathematical analysis and applications·2021
Same author

Horizontal visibility graph of a random restricted growth sequence.

Advances in applied mathematics·2021
Same author

A Markovian influence graph formed from utility line outage data to mitigate large cascades.

IEEE transactions on power systems : a publication of the Power Engineering Society·2020
Same author

Staircase patterns in words: subsequences, subwords, and separation number.

European journal of combinatorics = Journal europeen de combinatoire = Europaische Zeitschrift fur Kombinatorik·2020
Same journal

MULTITYPE BRANCHING PROCESSES WITH INHOMOGENEOUS POISSON IMMIGRATION.

Advances in applied probability·2025
Same journal

ON CLASSES OF EQUIVALENCE AND IDENTIFIABILITY OF AGE-DEPENDENT BRANCHING PROCESSES.

Advances in applied probability·2015
Same journal

APPROXIMATE SAMPLING FORMULAS FOR GENERAL FINITE-ALLELES MODELS OF MUTATION.

Advances in applied probability·2014
Same journal

CLOSED-FORM ASYMPTOTIC SAMPLING DISTRIBUTIONS UNDER THE COALESCENT WITH RECOMBINATION FOR AN ARBITRARY NUMBER OF LOCI.

Advances in applied probability·2012
Same journal

IMPORTANCE SAMPLING AND THE TWO-LOCUS MODEL WITH SUBDIVIDED POPULATION STRUCTURE.

Advances in applied probability·2009
See all related articles

Related Experiment Video

Updated: Oct 15, 2025

Multi-electrode Array Recordings of Neuronal Avalanches in Organotypic Cultures
16:01

Multi-electrode Array Recordings of Neuronal Avalanches in Organotypic Cultures

Published on: August 1, 2011

26.6K

AVALANCHES IN A SHORT-MEMORY EXCITABLE NETWORK.

Reza Rastegar1, Alexander Roitershtein2

  • 1Occidental Petroleum Corporation and University of Tulsa.

Advances in Applied Probability
|October 28, 2021
PubMed
Summary
This summary is machine-generated.

This study analyzes avalanche propagation in excitable networks, mathematically linked to epidemic models. We rigorously connect avalanche behavior to common approximations, providing convergence rates and bounds.

Keywords:
60J8560K4090B15Primary 60J10Secondary 92D25branching processescascading failurescomplex networkscriticalitydynamic graphs

More Related Videos

Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
08:08

Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond

Published on: June 24, 2015

11.7K
Time-dependent Increase in the Network Response to the Stimulation of Neuronal Cell Cultures on Micro-electrode Arrays
10:45

Time-dependent Increase in the Network Response to the Stimulation of Neuronal Cell Cultures on Micro-electrode Arrays

Published on: May 29, 2017

10.1K

Related Experiment Videos

Last Updated: Oct 15, 2025

Multi-electrode Array Recordings of Neuronal Avalanches in Organotypic Cultures
16:01

Multi-electrode Array Recordings of Neuronal Avalanches in Organotypic Cultures

Published on: August 1, 2011

26.6K
Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
08:08

Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond

Published on: June 24, 2015

11.7K
Time-dependent Increase in the Network Response to the Stimulation of Neuronal Cell Cultures on Micro-electrode Arrays
10:45

Time-dependent Increase in the Network Response to the Stimulation of Neuronal Cell Cultures on Micro-electrode Arrays

Published on: May 29, 2017

10.1K

Area of Science:

  • Complex systems
  • Network science
  • Mathematical modeling

Background:

  • Avalanche propagation in excitable networks is often approximated using branching processes for small sizes and deterministic systems for large sizes.
  • These approximations are widely used in applications but lack rigorous mathematical justification regarding their exact relation to the underlying model.
  • Understanding the precise relationship between the exact model and its approximations is crucial for accurate predictions and analysis.

Purpose of the Study:

  • To rigorously analyze the relationship between an exact avalanche propagation model in excitable networks and its common heuristic approximations.
  • To provide mathematical proofs for the connection between the exact model and the branching process and deterministic system approximations.
  • To establish rates of convergence and rigorous bounds for key characteristics of the avalanche model.

Main Methods:

  • Mathematical analysis of an excitable network model, a specific case of a known model and equivalent to an endemic Reed-Frost epidemic model.
  • Proof-based derivation of the exact relationship between the full avalanche model and its limiting approximations (branching process and deterministic system).
  • Development of rigorous bounds and calculation of convergence rates for model characteristics.

Main Results:

  • Formal mathematical proofs establishing the exact connection between the avalanche model and both branching process and deterministic system approximations.
  • Quantification of the rates at which the approximations converge to the exact model's behavior.
  • Derivation of rigorous bounds for common avalanche characteristics, enhancing the reliability of approximations.

Conclusions:

  • The study provides a rigorous mathematical foundation for using branching process and deterministic system approximations in excitable network avalanche models.
  • The established convergence rates and bounds offer critical insights into the accuracy and applicability of these approximations across different scales.
  • This work bridges the gap between theoretical models and practical applications in network dynamics and epidemic modeling.