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Related Concept Videos

Quantum Numbers02:43

Quantum Numbers

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It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
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The Quantum-Mechanical Model of an Atom02:45

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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When an object's velocity changes over time, the total distance traveled can be determined by summing small displacement intervals over short increments. This approach approximates the true distance through numerical summation and the use of integral calculus. An estimate of the total displacement can be obtained by measuring velocity at regular intervals and multiplying each value by the corresponding time step.If a runner accelerates over the first three seconds of a race, speed measurements...
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In geometry, measuring the direct distance between two points on a plane is essential in various practical and theoretical applications. Whether in navigation, engineering, or computer graphics, determining the shortest path between two locations involves using the distance formula. This formula is derived from the Pythagorean Theorem, which relates the lengths of the sides of a right triangle. On a coordinate plane, the horizontal and vertical distances between two points serve as the legs of...
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To achieve precise distance measurements, especially in surveying and construction, certain corrections must be applied to account for potential sources of error like the standardization errors, temperature variations, and slope adjustments.Standardization error emerges when measurement equipment undergoes changes, such as wear, repairs, or weather impacts. To address this, surveyors compare the equipment’s readings to a standard. This process identifies any deviation that might lead to...
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Short-distance transport refers to transport that occurs over a distance of just 2-3 cells, crossing the plasma membrane in the process. Small uncharged molecules, such as oxygen, carbon dioxide, and water, can diffuse across the plasma membrane on their own. In contrast, ions and larger molecules require the assistance of transport proteins due to their charge or size. Transport across membranes also occurs within individual cells, playing a variety of essential roles for the plant as a whole.
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Related Experiment Video

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Synthesis of In37P20O2CR51 Clusters and Their Conversion to InP Quantum Dots
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Improved quantum clustering analysis based on the weighted distance and its application.

Fan Decheng1, Song Jon1,2, Cholho Pang1,3

  • 1School of Economics and Management, Harbin Engineering University, Harbin 150001, China.

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|February 15, 2019
PubMed
Summary

This study introduces a new weighted distance measure for cluster analysis, improving accuracy with real-world data. The Fuzzy-ANP-Weighted-Distance-QC (FAWQC) method accounts for varying property influences, outperforming existing techniques.

Keywords:
Economics

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Area of Science:

  • Data Science
  • Economics
  • Environmental Science

Background:

  • Cluster analysis relies on distance and correlation measures, often overlooking property weights in high-dimensional, overlapping data.
  • Existing methods struggle with real-world data due to unaddressed variations in the influence of different properties.
  • Accurate data analysis requires incorporating the differential impact of various factors.

Purpose of the Study:

  • To propose a novel distance measure that incorporates property weights for improved cluster analysis.
  • To develop a method that transforms overlapping data into a weighted Euclidean space for better separation.
  • To apply this method to analyze economic and environmental data for evaluating low-carbon development.

Main Methods:

  • Developed a new weighted distance measure to project data into a weighted Euclidean space.
  • Utilized the Fuzzy Analytic Network Process (Fuzzy-ANP) to determine the weight of each factor.
  • Applied the Fuzzy-ANP-Weighted-Distance-QC (FAWQC) method to weighted random data and real-world datasets.

Main Results:

  • The proposed weighted distance measure effectively handles non-spherical and overlapping data.
  • The FAWQC method demonstrated superior accuracy in analyzing weighted random data compared to traditional methods.
  • Application to China's 2015 Economics-Energy-Environment (3E) data provided a more precise classification and evaluation of low-carbon economy development.

Conclusions:

  • The FAWQC method offers a significant advancement in cluster analysis for complex, real-world datasets.
  • Incorporating property weights is crucial for accurate analysis in fields like economics and environmental science.
  • This approach enhances the classification and evaluation of economic systems and development levels.