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Related Concept Videos

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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A nonlinear inequality describes a comparison involving an expression that curves or behaves more complexly than a straight line. These inequalities often appear in forms that include squares, products, or variables in the denominator.To solve such an inequality, one starts by rewriting it so that zero appears on one side. For example, the inequality:  can be factored as: This form makes it easier to identify the values that cause the expression to equal zero. In this case, the key values...
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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...
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Related Experiment Video

Updated: Nov 11, 2025

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
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Application of Optimization Algorithms in Clusters.

Ruby Srivastava1

  • 1Bioinformatics, CSIR-Centre for Cellular and Molecular Biology, Hyderabad, India.

Frontiers in Chemistry
|March 29, 2021
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Theoretical investigations are crucial for understanding nanoparticle structures and properties. This review details optimization algorithms and computational techniques for characterizing atomic clusters and nanoalloys.

Keywords:
clustersempirical potentialsglobal optimizationhomotopspotential energy landscape

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Area of Science:

  • Computational materials science
  • Theoretical chemistry
  • Nanotechnology

Background:

  • Experimental methods alone are insufficient for complete structural characterization of clusters and nanoparticles.
  • Understanding size and composition-dependent properties requires detailed geometric arrangement insights.
  • Theoretical investigations are essential to complement experimental data.

Purpose of the Study:

  • To review and discuss various optimization algorithms and computational techniques for cluster structure determination.
  • To explore methods for identifying global minima (GM) on potential energy surfaces (PES).
  • To evaluate the accuracy of different computational approaches for various cluster types.

Main Methods:

  • Exploration of potential energy surfaces (PES) to locate energy minima.
  • Application of diverse optimization algorithms: genetic algorithm (GA), basin hopping, heuristic algorithm combined with surface and interior operators (HA-SIO), fast annealing evolutionary algorithm (FAEA), random tunneling algorithm (RTA), and dynamic lattice searching (DLS) for elemental clusters.
  • Utilization of various empirical potentials (EPs) like Lennard-Jones (LJ), Born-Mayer, Gupta, Sutton-Chen, and Murrell-Mottram for bonding description.
  • Specific algorithms for nanoalloys include GA, basin hopping, modified adaptive immune optimization algorithm (AIOA), evolutionary algorithm (EA), kick method, and Knowledge Led Master Code (KLMC).

Main Results:

  • Development and application of numerous optimization algorithms to solve geometrical isomer problems in elemental clusters.
  • Successful application of various empirical potentials to model interatomic interactions in different cluster types.
  • Adaptation of algorithms to handle the complexity of nanoalloys with numerous possible configurations (homotops).

Conclusions:

  • Theoretical computational methods, particularly optimization algorithms, are indispensable for detailed structural characterization of atomic clusters and nanoparticles.
  • The choice of algorithm and potential energy function significantly impacts the accuracy and efficiency of structure prediction.
  • This review provides a comprehensive overview of the computational landscape for understanding cluster structures and properties.