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Related Concept Videos

Coordinates and Map Projections01:29

Coordinates and Map Projections

603
Coordinates and map projections are essential tools in accurately representing the Earth's surface for various applications, ranging from navigation to spatial analysis. The latitude and longitude coordinate system is a universally recognized framework for defining locations. Latitude specifies the distance of a point north or south of the equator, measured in degrees from 0° at the equator to 90° at the poles. Longitude indicates a location's position east or west of the prime meridian,...
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Coordination Number and Geometry02:57

Coordination Number and Geometry

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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.
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Coordination Compounds and Nomenclature02:54

Coordination Compounds and Nomenclature

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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...
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Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

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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...
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Equations of Motion: Rectangular Coordinates and Cylindrical Coordinates01:21

Equations of Motion: Rectangular Coordinates and Cylindrical Coordinates

768
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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Spherical Coordinates01:23

Spherical Coordinates

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Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
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Updated: Jan 28, 2026

Brain Mapping Using a Graphene Electrode Array
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Brain Mapping Using a Graphene Electrode Array

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Mapping brains without coordinates.

Rolf Kötter1, Egon Wanke

  • 1C&O Vogt Brain Research Institute, Heinrich Heine University Düsseldorf, Moorenstrasse 5, D-40225 Düsseldorf, Germany. rk@hirn.uni-duesseldorf.de

Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences
|June 24, 2005
PubMed
Summary
This summary is machine-generated.

Coordinate-independent brain mapping offers a flexible alternative to traditional atlases. This approach enhances the integration of diverse neuroscientific data by utilizing parcellation-based techniques and novel mapping concepts.

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Area of Science:

  • Neuroscience
  • Computational Neuroscience
  • Brain Mapping

Background:

  • Brain mapping has historically relied on coordinate-based spatial atlases.
  • Coordinate-independent mapping is crucial for integrating diverse structural and functional neuroimaging data.

Purpose of the Study:

  • To introduce the concepts, techniques, and implications of coordinate-independent brain mapping.
  • To address challenges in constructing and evaluating mapping paths for brain structures.

Main Methods:

  • Introduction of acronym-based mapping (AM).
  • Utilizing a generalized hierarchy (GM ontology).
  • Employing a topographically oriented regional map (RM) for cross-species and inter-individual comparisons.

Main Results:

  • Demonstration of enhanced coordinate-independent mapping using the CoCoMac database of primate brain connectivity.
  • Examples show improved integration of published relational statements.

Conclusions:

  • Coordinate-independent mapping provides a powerful alternative to spatial coordinate-based methods.
  • Highlights perspectives for integrating multi-modal structural, functional, and clinical data using parcellation-based approaches.