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

Applications of Integration to Probability Density Functions01:27

Applications of Integration to Probability Density Functions

178
Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF),...
178
Properties of Continuous Functions01:29

Properties of Continuous Functions

285
Continuous functions exhibit smooth, uninterrupted behavior, and combining them through standard operations retains this continuity. If f and g are continuous at a point a, then the functions f+g, f-g, cf (where c is a constant), fg, and fg (provided g(a)a) are also continuous at a. This allows the construction of complex functions from simpler continuous parts without losing smoothness.Polynomials, which are expressions formed by sums of powers of x with constant coefficients, are continuous...
285
Discrete-time Fourier transform01:26

Discrete-time Fourier transform

1.5K
The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...
1.5K
Continuity of a Function01:23

Continuity of a Function

404
A function is continuous at a point a if three conditions are met: the function is defined at a, the limit of the function as x approaches a exists, and this limit equals the function’s value. Mathematically, this is written asThis definition ensures the graph of the function does not exhibit any breaks, holes, or jumps at that point. Discontinuities occur when any of these conditions fail. A removable discontinuity exists when the two-sided limit exists but the function is either...
404
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

1.3K
In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
1.3K
Improper Integrals: Discontinuous Integrands01:28

Improper Integrals: Discontinuous Integrands

186
Evaluating Areas Under Curves with DiscontinuitiesA definite integral is considered improper when the integrand is discontinuous at one of the limits of integration. This occurs when the function is undefined or becomes infinite at an endpoint, making the corresponding region under the curve unbounded. Such behavior is commonly associated with vertical asymptotes at the boundary of the interval. To properly define and evaluate these integrals, a limiting process is used to determine whether a...
186

You might also read

Related Articles

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

Sort by
Same author

Nanoparticle modulation of immune and vascular microenvironment dynamics following spinal cord injury.

The Journal of neuroscience : the official journal of the Society for Neuroscience·2026
Same author

Nanoparticle and epothilone D combinatorial intervention improves motor performance and regeneration in chronic cervical spinal cord injury.

Neurotherapeutics : the journal of the American Society for Experimental NeuroTherapeutics·2025
Same author

Longitudinal Monitoring of T cell Dynamics in Metastatic Breast Cancer via a Remote Diagnostic Implant.

Immunomedicine·2025
Same author

Early nanoparticle intervention preserves motor function following cervical spinal cord injury.

Bioengineering & translational medicine·2025
Same author

Design Principles of an Engineered Metastatic Niche for Monitoring of Cancer Progression.

Biotechnology and bioengineering·2024
Same author

Allergen-Encapsulating Nanoparticles Reprogram Pathogenic Allergen-Specific Th2 Cells to Suppress Food Allergy.

Advanced healthcare materials·2024
Same journal

Analysis of strength degradation of coal and rock masses and stability of mined areas under long term immersion environment.

PloS one·2026
Same journal

Biogenic Silver-Selenium nanocomposite with anticancer activity and potent efficacy against vancomycin-resistant Staphylococcus aureus.

PloS one·2026
Same journal

Preparation and physicochemical characterization of a biodegradable chitosan/carboxymethyl cellulose hydrogel synthesized in NaOH/urea medium.

PloS one·2026
Same journal

Action-guilt, survivor-guilt, and depression in combat-related PTSD.

PloS one·2026
Same journal

Explainable machine learning for predicting activities of daily living at discharge in stroke patients: A retrospective study using SHAP interpretability.

PloS one·2026
Same journal

Deep learning based two-way feature depiction model for brain tumor detection.

PloS one·2026
See all related articles

Related Experiment Video

Updated: May 2, 2026

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
09:23

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Published on: August 16, 2017

9.4K

Mutual information between discrete and continuous data sets.

Brian C Ross1

  • 1Department of Physics, University of Washington, Seattle, Washington, United States of America.

Plos One
|March 4, 2014
PubMed
Summary
This summary is machine-generated.

We developed a new method to accurately estimate mutual information (MI) between discrete and continuous data. This approach avoids data binning issues and can be extended to calculate Jensen-Shannon divergence.

More Related Videos

Using Informational Connectivity to Measure the Synchronous Emergence of fMRI Multi-voxel Information Across Time
07:12

Using Informational Connectivity to Measure the Synchronous Emergence of fMRI Multi-voxel Information Across Time

Published on: July 1, 2014

12.3K
Dynamic Digital Biomarkers of Motor and Cognitive Function in Parkinson's Disease
10:28

Dynamic Digital Biomarkers of Motor and Cognitive Function in Parkinson's Disease

Published on: July 24, 2019

16.7K

Related Experiment Videos

Last Updated: May 2, 2026

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
09:23

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Published on: August 16, 2017

9.4K
Using Informational Connectivity to Measure the Synchronous Emergence of fMRI Multi-voxel Information Across Time
07:12

Using Informational Connectivity to Measure the Synchronous Emergence of fMRI Multi-voxel Information Across Time

Published on: July 1, 2014

12.3K
Dynamic Digital Biomarkers of Motor and Cognitive Function in Parkinson's Disease
10:28

Dynamic Digital Biomarkers of Motor and Cognitive Function in Parkinson's Disease

Published on: July 24, 2019

16.7K

Area of Science:

  • Biostatistics
  • Bioinformatics
  • Computational Biology

Background:

  • Mutual information (MI) is crucial for analyzing relationships in diverse datasets.
  • Existing MI estimation methods face challenges with 'binning' when data types differ (discrete vs. continuous).
  • Accurate estimation is vital for applications like gene expression analysis and drug efficacy studies.

Purpose of the Study:

  • To introduce a novel, accurate, non-binning mutual information estimator.
  • To address the specific challenge of estimating MI between one discrete and one continuous dataset.
  • To demonstrate the adaptability of the method for calculating Jensen-Shannon divergence.

Main Methods:

  • Developed a non-binning algorithm for mutual information estimation.
  • Applied the estimator to scenarios involving one discrete and one continuous data set.
  • Extended the methodology to compute Jensen-Shannon divergence for multiple datasets.

Main Results:

  • The proposed estimator accurately quantifies relationships without problematic data binning.
  • Successfully applied the method to biological data examples, such as base sequence and gene expression.
  • Demonstrated the utility of the adapted method for Jensen-Shannon divergence calculations.

Conclusions:

  • The novel MI estimator provides an accurate solution for mixed discrete-continuous data analysis.
  • This method enhances the reliability of relationship detection in biological and clinical research.
  • The technique offers a versatile tool for information-theoretic analyses, including divergence measures.