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Related Concept Videos

Network Covalent Solids02:18

Network Covalent Solids

Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

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Cyclic Processes And Isolated Systems01:19

Cyclic Processes And Isolated Systems

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Complexation Equilibria: Overview01:23

Complexation Equilibria: Overview

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Cluster Sampling Method01:20

Cluster Sampling Method

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Related Experiment Video

Updated: May 31, 2026

Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms
08:51

Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms

Published on: November 1, 2019

Heterogeneous k-core versus bootstrap percolation on complex networks.

G J Baxter1, S N Dorogovtsev, A V Goltsev

  • 1Departamento de Física, I3N, Universidade de Aveiro, Campus Universitário de Santiago, Aveiro, Portugal. gjbaxter@ua.pt

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 7, 2011
PubMed
Summary
This summary is machine-generated.

We introduce the heterogeneous k-core, a network pruning process generalizing the k-core. This study reveals two distinct transitions and highlights network structure

Related Experiment Videos

Last Updated: May 31, 2026

Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms
08:51

Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms

Published on: November 1, 2019

Area of Science:

  • Network Science
  • Statistical Physics
  • Graph Theory

Background:

  • The k-core decomposition is a fundamental tool for analyzing network structure.
  • Bootstrap percolation models activation processes on networks.
  • Existing models often assume uniform vertex properties.

Purpose of the Study:

  • Introduce the heterogeneous k-core, a generalized network pruning model.
  • Contrast heterogeneous k-core pruning with bootstrap percolation activation.
  • Investigate the impact of varying vertex thresholds on network transitions.

Main Methods:

  • Define the heterogeneous k-core based on individual vertex thresholds r(i).
  • Analyze the pruning process and remaining subgraph.
  • Compare critical phenomena, clusters, and avalanches with bootstrap percolation.

Main Results:

  • The heterogeneous k-core exhibits two transition types: continuous and discontinuous hybrid.
  • Network structure significantly influences the heterogeneous k-core formation.
  • A giant heterogeneous k-core emerges immediately for power-law distributions (γ<3) and any f>0.

Conclusions:

  • The heterogeneous k-core offers a more flexible framework for network analysis.
  • Understanding vertex heterogeneity is crucial for predicting network behavior.
  • Network topology, particularly power-law distributions, can lead to immediate giant component formation.