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

Linear time-invariant Systems01:23

Linear time-invariant Systems

209
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...
209
Second Order systems II01:18

Second Order systems II

86
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
86
Second Order systems I01:20

Second Order systems I

131
A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
131
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

94
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence...
94
First Order Systems01:21

First Order Systems

83
First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
83
Introduction to Nonparametric Statistics01:28

Introduction to Nonparametric Statistics

658
Nonparametric statistics offer a powerful alternative to traditional parametric methods, useful when assumptions about the population distribution cannot be made. Unlike parametric tests, which require data to follow a specific distribution with well-defined parameters (such as the mean and standard deviation), nonparametric tests do not require such constraints. This makes them particularly valuable when dealing with small sample sizes, skewed data, or ordinal and categorical variables.
One of...
658

You might also read

Related Articles

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

Sort by
Same author

Assimilative causal inference.

Nature communications·2026
Same author

Trash to treasure: converting plastic waste into a useful graphene foil.

Nanoscale·2017
Same author

Identification of 8 Novel Mutations in Nephrogenesis-Related Genes in Chinese Han Patients with Unilateral Renal Agenesis.

American journal of nephrology·2017
Same author

Real-Time Imaging of Endocytosis and Intracellular Trafficking of Semiconducting Polymer Dots.

ACS applied materials & interfaces·2017
Same author

Associations between <i>Interleukin-31</i> Gene Polymorphisms and Dilated Cardiomyopathy in a Chinese Population.

Disease markers·2017
Same author

Real-time visualization of clustering and intracellular transport of gold nanoparticles by correlative imaging.

Nature communications·2017
Same journal

Research on a Regional Availability Evaluation Model for Road-Area High-Entropy Energy Based on Synergy Factors.

Entropy (Basel, Switzerland)·2026
Same journal

Atmospheric Turbulence Channel Modeling and Performance Analysis of a CO-ZP-OFDM Coherent Optical Communication System for UAV Air-to-Ground Scenarios.

Entropy (Basel, Switzerland)·2026
Same journal

Information Geometry and Asymptotic Theory for SMML Estimators.

Entropy (Basel, Switzerland)·2026
Same journal

Correlation Entropy and Power-Law Kinetics.

Entropy (Basel, Switzerland)·2026
Same journal

Research on the Contagion of Systemic Financial Risk Under the Impact of Climate Risks-From the Perspective of Complex Networks and Machine Learning.

Entropy (Basel, Switzerland)·2026
Same journal

The Statistical-Mechanical Meaning of the Wave Function of Quantum Mechanics.

Entropy (Basel, Switzerland)·2026
See all related articles

Related Experiment Video

Updated: May 31, 2025

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
08:18

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

4.9K

A Martingale-Free Introduction to Conditional Gaussian Nonlinear Systems.

Marios Andreou1, Nan Chen1

  • 1Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706, USA.

Entropy (Basel, Switzerland)
|January 24, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a new martingale-free approach for conditional Gaussian nonlinear systems (CGNS). The method enhances understanding and analysis of nonlinear stochastic dynamical systems, improving the study of extreme events.

Keywords:
Euler–Maruyama schemeconditional Gaussian systemsdata assimilationfilteringnonlinear stochastic dynamical systemsoptimal conditional samplingoptimal posterior state estimationsmoothinguncertainty quantification

More Related Videos

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

8.9K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.5K

Related Experiment Videos

Last Updated: May 31, 2025

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
08:18

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

4.9K
Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

8.9K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.5K

Area of Science:

  • Dynamical Systems and Nonlinear Science
  • Stochastic Processes
  • Computational Physics

Background:

  • Conditional Gaussian nonlinear systems (CGNS) model complex nonlinear stochastic dynamics.
  • CGNS exhibit non-Gaussian characteristics despite their conditionally linear structure.
  • Existing methods lack tractable approaches for analyzing CGNS time evolution and sampling.

Purpose of the Study:

  • To develop a martingale-free methodology for a deeper understanding of CGNS.
  • To derive analytic formulae for conditional statistics and posterior sampling in CGNS.
  • To apply the framework to high-dimensional systems and study extreme events.

Main Methods:

  • Developed a time discretization scheme for proving conditional statistics evolution.
  • Utilized a formal limiting process to obtain the continuous-time regime.
  • Derived analytic formulae for optimal posterior sampling of unobserved variables with correlated noise.

Main Results:

  • Established a tractable, martingale-free approach for CGNS analysis.
  • Provided analytic formulae for time evolution of conditional Gaussian statistics.
  • Demonstrated effectiveness on a climate model with cubic nonlinearity and state-dependent noise.

Conclusions:

  • The new framework offers improved understanding of CGNS, particularly for extreme events and intermittency.
  • The methodology facilitates the study of data assimilation and uncertainty quantification in high-dimensional systems.
  • The approach validates through a complex climate model, showcasing its practical applicability.