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Related Concept Videos

Column Efficiency: Plate Theory01:10

Column Efficiency: Plate Theory

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Band broadening in a chromatography column is measured by its efficiency. This is determined by the number of theoretical plates (N). Theoretical plate theory states that a separation column consists of a continuous series of imaginary plates where solute equilibration occurs between stationary and mobile phases.
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Column Efficiency: Rate Theory01:12

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The rate theory of chromatography provides quantitative insight into the shapes and widths of elution bands. These bands are based on the random-walk mechanism governing molecular migration within a column. The Gaussian profile of chromatographic bands arises from the cumulative effect of random molecular motions as they progress through the column.
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Area Computation by the Alternative Coordinate Method01:24

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The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
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Valence Bond Theory and Hybridized Orbitals02:38

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According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
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Extraction: Partition and Distribution Coefficients01:14

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The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
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Profile leveling and cross-sections are surveying methods used to determine and document terrain elevations for infrastructure projects such as highways, railroads, canals, and pipelines. These methods provide data for earthwork planning and alignment of proposed routes.  Profile leveling involves measuring elevations along a fixed line to create a vertical terrain profile. A surveyor sets up a leveling instrument at the benchmark (BM) and records a backsight (BS) to determine the...
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Updated: Apr 21, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Vertex collocation profiles: theory, computation, and results.

Ryan N Lichtenwalter1, Nitesh V Chawla1

  • 1Interdisciplinary Center for Network Science and Applications (iCeNSA), The University of Notre Dame, 384 Nieuwland Hall, 46556 Notre Dame, USA ; Department of Computer Science, The University of Notre Dame, 384 Fitzpatrick Hall, 46556 Notre Dame, USA.

Springerplus
|November 14, 2014
PubMed
Summary
This summary is machine-generated.

Vertex Collocation Profiles (VCPs) offer a novel network analysis tool. VCPs enhance understanding of network growth and link formation, excelling in link prediction tasks across diverse network types.

Keywords:
Graph theoryIsomorphismLink predictionNetwork analysis

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Area of Science:

  • Network Science
  • Data Analysis
  • Computational Social Science

Background:

  • Understanding complex network structures is crucial for various scientific domains.
  • Existing methods for analyzing network growth and link formation have limitations.
  • Predicting future links in dynamic networks remains a significant challenge.

Purpose of the Study:

  • Introduce the Vertex Collocation Profile (VCP) concept for detailed local network structure analysis.
  • Develop the theoretical framework, mathematics, and algorithms for VCP computation.
  • Evaluate VCPs for link prediction accuracy and scalability across different network types.

Main Methods:

  • Developed the Vertex Collocation Profile (VCP) concept and underlying algorithms.
  • Implemented VCP analysis for network growth and link formation studies.
  • Applied VCPs to link prediction tasks, including multirelational and longitudinal networks.

Main Results:

  • VCP analysis provides rich information on local network structures.
  • VCP algorithms demonstrate scalability for large networks.
  • VCP methods achieve competitive link prediction performance against existing approaches.
  • VCPs effectively leverage multirelational and temporal data for improved prediction accuracy.

Conclusions:

  • Vertex Collocation Profiles (VCPs) are a powerful new tool for network science.
  • VCPs offer significant advantages in analyzing complex network dynamics and link prediction.
  • The method shows promise for future advancements in network analysis, especially for longitudinal and multirelational data.