Shuhong Dai
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Maximal Entropy of the Boltzmann Distribution: A Quantum Perspective

Specifically, in the classical limit (when βEn << 1), the quantum energy levels become very close to each other, and the partition function can be approximated by an integral over continuous energy states rather than a sum over discrete states. In this limit, the quantum Boltzmann distribution approaches the classical result...

18 min read   ·   2024

Is the Transition from Univariate to Multivariate Gaussian Distribution Linear?

Now that we have the foundation in place, let’s shift gears and consider the generalization of the univariate Gaussian to higher dimensions. In the multivariate case, we are no longer dealing with a single random variable, but rather a vector of random variables...

11 min read   ·   2024

Problem Ⅲ: Group Theory

23 min read   ·   2024

Problem Ⅱ: Linear Transformations

22 min read   ·   2024


  • Problem Ⅳ: Dual Spaces and Functional Analysis

    1 min read   ·   June 10, 2024

    2024   ·   Mathematics   ·   A Commentary of the Pre-Practice for Boston University's EC525 Course

  • Sampling Smarter: Unlocking the Power of Latin Hypercube Sampling

    Unlike random sampling, which might leave some regions underrepresented while others get chosen repeatedly...

    26 min read   ·   May 03, 2024

    2024   ·   Statistics   Probability Theory   ·   Bits and Pieces

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  • Problem Ⅲ: Group Theory

    23 min read   ·   March 22, 2024

    2024   ·   Mathematics   ·   A Commentary of the Pre-Practice for Boston University's EC525 Course

  • Problem Ⅱ: Linear Transformations

    22 min read   ·   February 26, 2024

    2024   ·   Mathematics   ·   A Commentary of the Pre-Practice for Boston University's EC525 Course

  • Problem Ⅰ: Vector Spaces

    30 min read   ·   December 09, 2023

    2023   ·   Mathematics   ·   A Commentary of the Pre-Practice for Boston University's EC525 Course

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