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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...

Short-distance Transport of Resources

Short-distance Transport of Resources

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Reinforcement

Reinforcement

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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: Jan 22, 2026

Quantifying Learning in Young Infants: Tracking Leg Actions During a Discovery-learning Task

Quantifying Learning in Young Infants: Tracking Leg Actions During a Discovery-learning Task

Published on: June 1, 2015

Optimal coordination of resource: A solution from reinforcement learning.

Guozhong Zheng¹, Weiran Cai², Guanxiao Qi³

¹Shaanxi Normal University, School of Physics and Information Technology, Xi'an 710062, People's Republic of China.

Physical Review. E

|January 21, 2026

Summary

Optimal resource allocation is achieved when individuals balance learning from experience with exploring new strategies. Breaking this balance leads to poor coordination, even worse than random behavior.

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Novel Apparatus and Method for Drug Reinforcement

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Area of Science:

Computational economics
Game theory
Behavioral economics

Background:

Efficient resource allocation is crucial in natural and social systems facing competition.
The Minority Game (MG) models resource competition, but prior solutions lack adaptive strategies.

Purpose of the Study:

To apply reinforcement learning to the Minority Game, capturing adaptive strategy evolution.
To investigate how balancing exploration and exploitation influences collective behavior and resource allocation.

Main Methods:

Utilized a reinforcement learning framework for adaptive decision-making in the MG.
Analyzed the impact of the exploration-exploitation balance on coordination and resource utilization.
Examined the underlying mechanisms of optimal coordination and its destabilization.

Main Results:

Optimal resource allocation occurs when individuals balance experience-based exploitation with random exploration.
Deviations from this balance result in partial coordination or even anticoordination.
Symmetry-breaking in action preferences underlies optimal coordination and maximum resource utilization.

Conclusions:

Reinforcement learning offers a novel approach to the Minority Game, accounting for adaptive strategies.
The findings provide insights into achieving efficient resource allocation through balanced individual decision-making.
The study highlights the importance of exploration in preventing suboptimal collective outcomes.