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Related Concept Videos

Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
Ladder Diagrams: Complexation Equilibria01:07

Ladder Diagrams: Complexation Equilibria

Ladder diagrams are useful for evaluating equilibria involving metal-ligand complexes. The vertical scale of the ladder diagram represents the concentration of unreacted or free ligand, pL. The horizontal lines on the scale depict the log of stepwise formation constants for metal-ligand complexes and indicate the dominant species in all the regions.
The formation constant, K1, for the formation of Cd(NH3)2+ complex from cadmium and ammonia is 3.55 × 102. Log K1 (i.e. pNH3) is 2.55, and...
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.
To break or to melt a covalent network solid, covalent bonds must be broken. Because covalent bonds are relatively strong, covalent network solids are typically...
Bewley Lattice Diagram01:12

Bewley Lattice Diagram

The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Protein Networks02:26

Protein Networks

An organism can have thousands of different proteins, and these proteins must cooperate to ensure the health of an organism. Proteins bind to other proteins and form complexes to carry out their functions. Many proteins interact with multiple other proteins creating a complex network of protein interactions.
These interactions can be represented through maps depicting protein-protein interaction networks, represented as nodes and edges. Nodes are circles that are representative of a protein,...

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Optimization Method for Robustness of Hypernetwork Communication with Integrated Structural Features.

Entropy (Basel, Switzerland)·2026
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Related Experiment Video

Updated: Jun 27, 2026

Modeling Ligands into Maps Derived from Electron Cryomicroscopy
09:30

Modeling Ligands into Maps Derived from Electron Cryomicroscopy

Published on: July 19, 2024

Coupled Map Lattice Modeling and Robustness Analysis of Simplicial Complex Networks with Higher-Order Interactions.

Luqian Wang1,2, Jun Yin1,2, Xiujuan Ma1,2

  • 1The College of Computer, Qinghai Normal University, Xining 810016, China.

Entropy (Basel, Switzerland)
|June 26, 2026
PubMed
Summary

Higher-order networks using simplicial structures better model group interactions to prevent cascading failures. Increasing simplex dimensions enhances network robustness against collapse, offering insights for resilient network design.

Keywords:
CMLcascading failureshigher-order networksrobustnesssimplicial complexes

Related Experiment Videos

Last Updated: Jun 27, 2026

Modeling Ligands into Maps Derived from Electron Cryomicroscopy
09:30

Modeling Ligands into Maps Derived from Electron Cryomicroscopy

Published on: July 19, 2024

Area of Science:

  • Network Science
  • Complex Systems
  • Mathematical Modeling

Background:

  • Cascading failures in complex networks lead to large-scale collapse.
  • Traditional models fail to capture group coordination and higher-order interactions.
  • Higher-order networks with simplicial structures offer a more accurate framework.

Purpose of the Study:

  • Propose a higher-order coupled map lattice (CML) model for cascading failures in simplicial complex networks.
  • Analyze the influence of higher-order structures on network robustness.
  • Investigate robustness differences in fourth-order simplicial networks.

Main Methods:

  • Developed a higher-order coupled map lattice (CML) model.
  • Conducted experiments on fourth-order simplicial networks with varying topologies and attack strategies.
  • Analyzed theoretical perturbation thresholds for third-order networks.

Main Results:

  • Fourth-order simplicial networks show vulnerability to targeted attacks but robustness against random failures.
  • In single-order networks, higher simplex dimensions correlate with greater robustness.
  • Critical perturbation in third-order networks negatively correlates with coupling parameters.

Conclusions:

  • Higher-order structures significantly influence cascading failure dynamics and network robustness.
  • Results validated through network modifications, destructive experiments, and empirical data.
  • Provides theoretical guidance for designing resilient higher-order networks.