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Related Concept Videos

Sampling Plans01:23

Sampling Plans

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Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
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Cluster Sampling Method01:20

Cluster Sampling Method

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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.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
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Sampling Theorem01:15

Sampling Theorem

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In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
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Sampling Distribution01:12

Sampling Distribution

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Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
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Random Sampling Method01:09

Random Sampling Method

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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures 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. Among the various sampling methods used by...
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Sampling Methods: Overview01:06

Sampling Methods: Overview

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A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
In analytical chemistry, the choice of...
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Efficient sampling of spreading processes on complex networks using a composition and rejection algorithm.

Guillaume St-Onge1,2, Jean-Gabriel Young1,2, Laurent Hébert-Dufresne1,3

  • 1Département de Physique, de Génie Physique, et d'Optique, Université Laval, Québec (Québec), Canada, G1V 0A6.

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|November 12, 2019
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Efficient simulation algorithms for complex networks are crucial. New methods improve computational efficiency for studying spreading phenomena, reducing time for large-scale network simulations.

Keywords:
Complex networkSpreading processStochastic simulation algorithm

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Area of Science:

  • Network science
  • Computational modeling
  • Stochastic processes

Background:

  • Efficient stochastic simulation algorithms are vital for studying spreading phenomena on complex networks.
  • Current algorithms' efficiency is significantly impacted by network structure.

Purpose of the Study:

  • To analyze how network structure affects the efficiency of existing simulation algorithms.
  • To develop a more efficient algorithm for simulating dynamics on complex networks.

Main Methods:

  • Analysis of algorithm scaling based on network properties (density, heterogeneity).
  • Development and application of a node-based method with composition and rejection sampling.
  • Adaptation of the method for both Markovian and non-Markovian dynamics.

Main Results:

  • Algorithms thought to be efficient exhibit polynomial scaling on dense or sparse heterogeneous networks.
  • The proposed node-based method achieves an average-case complexity of O(1) per update for general networks.
  • The new approach significantly reduces computation time for large network simulations.

Conclusions:

  • Network structure critically influences simulation algorithm efficiency.
  • The proposed O(1) average-case complexity algorithm offers a substantial improvement for simulating dynamics on complex networks.
  • This enhanced approach broadens the scope for studying diverse network dynamics.