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Coordination Number and Geometry

Coordination Number and Geometry

For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.

Coordination Compounds and Nomenclature

Coordination Compounds and Nomenclature

In most main group element compounds, the valence electrons of the isolated atoms combine to form chemical bonds that satisfy the octet rule. For instance, the four valence electrons of carbon overlap with electrons from four hydrogen atoms to form CH4. The one valence electron leaves sodium and adds to the seven valence electrons of chlorine to form the ionic formula unit NaCl (Figure 1a). Transition metals do not normally bond in this fashion. They primarily form coordinate covalent bonds, a...

Lattice Centering and Coordination Number

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...

Parallel Resonance

Parallel Resonance

The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:

Parallel Processing

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The brain processes sensory information rapidly due to parallel processing, which involves sending data across multiple neural pathways at the same time. This method allows the brain to manage various sensory qualities, such as shapes, colors, movements, and locations, all concurrently. For instance, when observing a forest landscape, the brain simultaneously processes the movement of leaves, the shapes of trees, the depth between them, and the various shades of green. This enables a quick and...

Equations of Motion: Rectangular Coordinates and Cylindrical Coordinates

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Understanding the motion of particles is a fundamental aspect of classical mechanics, and the choice of the coordinate system plays a pivotal role in unraveling the complexities of their dynamics.
When a particle moves relative to an inertial frame, the equations of motion can be expressed using rectangular components. If the motion is confined to the x-y plane, the equations having the x and y coordinates only can be used to simplify the mathematical representation.
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Related Experiment Video

Updated: Feb 8, 2026

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Smart Brushing for Parallel Coordinates.

Richard C Roberts, Robert S Laramee, Gary A Smith

IEEE Transactions on Visualization and Computer Graphics

|July 12, 2018

Summary

This study introduces novel smart brushing techniques for parallel coordinates plots to overcome data visualization challenges. These methods improve high-dimensional data analysis by offering flexible pattern searches and data-driven guidance.

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Published on: May 29, 2013

Area of Science:

Data Visualization
Information Visualization
Human-Computer Interaction

Background:

Parallel Coordinates (PC) plots are essential for high-dimensional data visualization.
Occlusion and overplotting are significant challenges in PC plots with large datasets.
Existing brushing techniques offer limited improvements in visual design and interaction.

Purpose of the Study:

To introduce novel, smart brushing techniques for enhancing parallel coordinates plots.
To address limitations in standard interactive brushing for large, high-dimensional datasets.
To improve user exploration and analytical capabilities in data visualization.

Main Methods:

Development of Higher-order, sketch-based brushing for flexible n-dimensional pattern searches.
Implementation of smart, data-driven brushing for real-time user guidance.
Integration of novel enhancements and user options to complement brushing techniques.

Main Results:

Demonstrated utility of new brushing techniques through a case study with a large telecommunication dataset.
Evaluation of enhanced exploration and analytical abilities.
Positive domain expert feedback from data suppliers on the effectiveness of the methods.

Conclusions:

Novel smart brushing techniques significantly enhance parallel coordinates plot usability for high-dimensional data.
Higher-order and data-driven brushing offer powerful new interaction paradigms.
The developed methods improve the analysis of complex, large-scale datasets.