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

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

53
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...
53
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

89
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....
89
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

12.1K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
12.1K
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

69
Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
69
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

81
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
81
Area Computation by the Alternative Coordinate Method01:24

Area Computation by the Alternative Coordinate Method

52
The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
52

You might also read

Related Articles

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

Sort by
Same journal

Preferred hospitalization of COVID-19 patients using intuitionistic fuzzy set-based matching approach.

Granular computing·2024
Same journal

Solving Pythagorean fuzzy partial fractional diffusion model using the Laplace and Fourier transforms.

Granular computing·2024
Same journal

Multicriteria group decision making for COVID-19 testing facility based on picture cubic fuzzy aggregation information.

Granular computing·2024
Same journal

Multi-attribute decision-making for electronic waste recycling using interval-valued Fermatean fuzzy Hamacher aggregation operators.

Granular computing·2024
Same journal

Correlation coefficients for T-spherical fuzzy sets and their applications in pattern analysis and multi-attribute decision-making.

Granular computing·2024
Same journal

Developing a novel stock index trend predictor model by integrating multiple criteria decision-making with an optimized online sequential extreme learning machine.

Granular computing·2024

Related Experiment Video

Updated: Jun 28, 2025

Modeling the Functional Network for Spatial Navigation in the Human Brain
05:55

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

1.1K

Rough approximation models via graphs based on neighborhood systems.

Abd El Fattah El Atik1, Ashraf Nawar2, Mohammed Atef2

  • 1Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.

Granular Computing
|April 16, 2024
PubMed
Summary

This study introduces novel j-adhesion neighborhoods for graph approximation, extending existing methods. New j-lower and j-upper approximations are developed and their accuracy analyzed for graph subgraphs.

Keywords:
GraphsLower approximationsNeighborhood systemRough setsUpper approximationsj-Accuracy measure

More Related Videos

Topographical Estimation of Visual Population Receptive Fields by fMRI
06:02

Topographical Estimation of Visual Population Receptive Fields by fMRI

Published on: February 3, 2015

9.3K
Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
12:27

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations

Published on: February 15, 2017

7.0K

Related Experiment Videos

Last Updated: Jun 28, 2025

Modeling the Functional Network for Spatial Navigation in the Human Brain
05:55

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

1.1K
Topographical Estimation of Visual Population Receptive Fields by fMRI
06:02

Topographical Estimation of Visual Population Receptive Fields by fMRI

Published on: February 3, 2015

9.3K
Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
12:27

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations

Published on: February 15, 2017

7.0K

Area of Science:

  • Graph Theory
  • Topology
  • Data Analysis

Background:

  • Graphs are approximated as finite topological structures using neighborhood systems.
  • Existing neighborhood notions by Allam et al. and Yao provide foundational concepts.

Purpose of the Study:

  • To introduce and define novel j-adhesion neighborhoods for graph vertices.
  • To extend existing graph approximation techniques using these new neighborhoods.
  • To investigate and analyze new types of j-lower and j-upper approximations for graph subgraphs.

Main Methods:

  • Construction of eight new types of neighborhoods, termed j-adhesion neighborhoods.
  • Extension of Allam et al. and Yao's neighborhood notions.
  • Development of algorithms for generating j-adhesion neighborhoods and rough sets on graphs.
  • Calculation of accuracy measures for the proposed approximations.

Main Results:

  • Introduction of generalized j-adhesion neighborhoods.
  • Formulation of new j-lower and j-upper approximation spaces for graph subgraphs.
  • Quantitative analysis of approximation accuracy and boundary regions.
  • Algorithmic implementations for practical application.

Conclusions:

  • The proposed j-adhesion neighborhoods offer a generalized framework for graph approximation.
  • The new approximation methods provide enhanced accuracy and detailed boundary region analysis.
  • The study includes a chemical example to demonstrate the practical utility of the developed methods.