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Related Concept Videos

Entropy and the Second Law of Thermodynamics01:26

Entropy and the Second Law of Thermodynamics

Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
Entropy02:39

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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

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Generating Strictly Controlled Stimuli for Figure Recognition Experiments
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Published on: March 18, 2019

Entropy and distance of random graphs with application to structural pattern recognition.

A K Wong1, M You

  • 1Department of Systems Design Engineering, University of Waterloo, Waterloo, Ont., Canada N2L 3G1.

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
PubMed
Summary
This summary is machine-generated.

This study defines random graphs to analyze relational data probabilistically and structurally. It introduces a novel entropy-based distance measure for synthesizing graph ensembles and classifying patterns using unsupervised learning.

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Area of Science:

  • Graph theory
  • Probability theory
  • Data science

Background:

  • Relational data analysis requires understanding probabilistic and structural properties.
  • Characterizing ensembles of attributed graphs is crucial for data interpretation.
  • Variability in random graphs necessitates robust measurement techniques.

Purpose of the Study:

  • To formally define random graphs and their application to relational data.
  • To propose a method for synthesizing attributed graph ensembles using entropy.
  • To develop an unsupervised learning approach for pattern classification based on random graph distributions.

Main Methods:

  • Formal definition of random graphs.
  • Interpretation of attributed graph ensembles as random graph outcomes.
  • Utilizing Shannon's entropy to measure graph variability.
  • Proposing a distance measure between random graphs based on entropy change.
  • Applying maximum likelihood rule for pattern classification.

Main Results:

  • A formal definition of random graphs is established.
  • A novel distance measure for random graphs is proposed, based on entropy.
  • The synthesis process yields distributions corresponding to different pattern classes.
  • An unsupervised learning framework for pattern classification is demonstrated.

Conclusions:

  • Random graphs provide a framework for analyzing probabilistic and structural aspects of relational data.
  • The proposed entropy-based distance measure effectively synthesizes graph ensembles.
  • The developed method enables unsupervised learning and classification of pattern graphs.