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Cluster Sampling Method

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
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Graphs of Two-Variable Functions

A weather map provides a practical example of a function of two variables. Across a wide region such as the United States, temperatures vary from one location to another. Each location can be identified by two geographic coordinates: longitude and latitude. Since a single temperature value is assigned to each coordinate pair, the situation can be represented mathematically as a function with two inputs and one output.In mathematical notation, longitude and latitude can be labeled as x and y,...

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Graphs of functions provide a visual representation of how output values change in response to varying inputs. Each point on the graph corresponds to an ordered pair, where the x-coordinate (independent variable) determines the horizontal position and the y-coordinate (dependent variable) determines the vertical position. Linear functions like y = x give a straight line, indicating a constant rate of change.Nonlinear functions display more complex behaviors. Even power functions generate...

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Sampling Plans

Sampling Plans

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Related Experiment Video

Updated: Jun 19, 2026

ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data

ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data

Published on: January 16, 2019

Random graphs with clustering.

¹Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109, USA.

Physical Review Letters

|October 2, 2009

Summary

This summary is machine-generated.

This study introduces a solvable network model that incorporates clustering, a common network property. The generalized random-graph model provides exact solutions for network characteristics and phase transitions.

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Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations

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Published on: February 15, 2017

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Last Updated: Jun 19, 2026

ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data

ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data

Published on: January 16, 2019

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations

Published on: February 15, 2017

Area of Science:

Network Theory
Graph Theory
Statistical Physics

Background:

Standard random-graph models lack the ability to accurately represent clustered networks.
Clustering, or transitivity, is a prevalent feature in real-world networks where neighbors of a node tend to be connected.

Purpose of the Study:

To develop a plausible and mathematically tractable model for networks exhibiting clustering.
To generalize existing random-graph models to include clustering.
To provide exact analytical solutions for key network properties within these clustered models.

Main Methods:

Generalization of standard random-graph models to incorporate a clustering parameter.
Derivation of exact solutions for network properties using the generalized model.
Analysis of phase transitions related to component formation and network percolation.

Main Results:

The proposed generalized random-graph model successfully incorporates clustering.
Exact solutions were obtained for network component sizes, including the giant component.
The positions of critical phase transitions for giant component formation and percolation were precisely determined.

Conclusions:

The developed model offers a significant advancement in network theory by providing a solvable framework for clustered networks.
This work enables more accurate analysis of real-world networks with inherent clustering.
The findings facilitate a deeper understanding of network structure and emergent properties.