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

BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

796
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
796
Fast Decoupled and DC Powerflow01:24

Fast Decoupled and DC Powerflow

625
The fast decoupled power flow method addresses contingencies in power system operations, such as generator outages or transmission line failures. This method provides quick power flow solutions, essential for real-time system adjustments. Fast decoupled power flow algorithms simplify the Jacobian matrix by neglecting certain elements, leading to two sets of decoupled equations:
625
The Power Flow Problem and Solution01:26

The Power Flow Problem and Solution

681
Power flow problem analysis is fundamental for determining real and reactive power flows in network components, such as transmission lines, transformers, and loads. The power system's single-line diagram provides data on the bus, transmission line, and transformer. Each bus k in the system is characterized by four key variables: voltage magnitude Vk​, phase angle δk​, real power Pk​, and reactive power Qk​. Two of these four variables are inputs, while the power flow program computes...
681
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

201
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
201
Linear time-invariant Systems01:23

Linear time-invariant Systems

731
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
731
Multimachine Stability01:25

Multimachine Stability

471
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
471

You might also read

Related Articles

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

Sort by
Same author

AE-PocketMiner Uses Attention to Simultaneously Predict Cryptic Pockets and Their Allosteric Coupling.

bioRxiv : the preprint server for biology·2026
Same author

Task-induced topological and geometrical changes in whole-brain dynamics predict cognitive individual differences.

bioRxiv : the preprint server for biology·2026
Same author

Deep mining of the human antibody repertoire identifies frequent and genetically diverse CDRH3 topologies targetable by vaccination.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Comparing Dynamical Models Through Diffeomorphic Vector Field Alignment.

Neural computation·2026
Same author

How Well Can AI and Physics-Based Simulations Predict the Probability a Cryptic Pocket Is Open?

Journal of chemical theory and computation·2026
Same author

On the control of recurrent neural networks using constant inputs.

IEEE transactions on automatic control·2026

Related Experiment Video

Updated: Dec 9, 2025

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

969

Computing and optimizing over all fixed-points of discrete systems on large networks.

James R Riehl1, Maxwell I Zimmerman2, Matthew F Singh1

  • 1Department of Electrical and Systems Engineering, Washington University in St Louis, 1 Brookings Drive, St Louis, MO 63130, USA.

Journal of the Royal Society, Interface
|September 9, 2020
PubMed
Summary

We developed an efficient method to find all equilibrium points in complex discrete dynamical systems on sparse networks. This graph partitioning approach simplifies computation for large-scale systems, enabling analysis in fields like neuroscience and protein folding.

Keywords:
brain networksenergy landscapesfixed pointsgraph partitioningoptimizationprotein folding

More Related Videos

Author Spotlight: An Optimized Automated Method for Investigating Retinoic Acid Receptors in Neuronal Mitochondria
08:33

Author Spotlight: An Optimized Automated Method for Investigating Retinoic Acid Receptors in Neuronal Mitochondria

Published on: July 28, 2023

854
ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data
05:12

ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data

Published on: January 16, 2019

11.8K

Related Experiment Videos

Last Updated: Dec 9, 2025

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

969
Author Spotlight: An Optimized Automated Method for Investigating Retinoic Acid Receptors in Neuronal Mitochondria
08:33

Author Spotlight: An Optimized Automated Method for Investigating Retinoic Acid Receptors in Neuronal Mitochondria

Published on: July 28, 2023

854
ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data
05:12

ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data

Published on: January 16, 2019

11.8K

Area of Science:

  • Dynamical Systems and Network Science
  • Computational Biology
  • Theoretical Neuroscience

Background:

  • Equilibria (fixed points) are fundamental in dynamical systems but computationally intensive to find.
  • Discrete-valued, discrete-time systems on sparse networks present unique challenges for equilibrium computation.

Purpose of the Study:

  • To develop an efficient algorithm for computing all equilibrium points in discrete-valued, discrete-time systems on sparse networks.
  • To demonstrate the applicability of this method to large-scale network problems and specific scientific domains.

Main Methods:

  • Utilized graph partitioning to recursively decompose complex network problems into smaller, manageable subproblems.
  • Combined solutions from subproblems to determine the complete set of equilibria for the original system.

Main Results:

  • Successfully computed all equilibrium points for discrete-valued, discrete-time systems on sparse networks.
  • The method scales to arbitrarily large networks meeting specific criteria.
  • Enabled efficient analysis, including counting equilibria and finding optimal states, without necessarily computing the full equilibrium set.

Conclusions:

  • The graph partitioning approach offers a computationally efficient solution for finding equilibria in large-scale discrete dynamical systems.
  • This method has significant potential applications in areas such as brain network analysis and protein structure prediction.