Knowledge network

digraph G {

  subgraph cluster_0 {
    style=filled;
    color=lightgrey;
    node [style=filled,color=white];
    FFT;
    Gauss_Green_Stokes_formula;
    Riemann_function;

    label = "mathematic analysis";
  }

  subgraph cluster_1 {
    node [style=filled];
    特征函数;
    label = "probability";
    color=blue
  }
  subgraph cluster_2 {
    node [style=filled];
    信号_频率分离;
    error_correction;
    Shannon_Theorem;
    label = "computer network";
    color=blue
  }

  subgraph cluster_4 {
    node [style=filled];
    Shannon_entropy;
    label = "information theory";
    color=blue
  }
  subgraph cluster_5 {
    node [style=filled];
    KL_divergence;
    label = "deep learning";
    color=blue
  }
  subgraph cluster_6 {
    node [style=filled];
    polynomial;
    orthogonal_matrix;
    self_adjoint_matrix;
    label = "linear algebra";
    color=blue
  }


  subgraph cluster_7 {
    node [style=filled];
    maxwell_equations;
    geometric_optics -> Fermat_principle;
    quantum_mechanics;
    label = "general physics";
    color=blue
  }
  subgraph cluster_8 {
    node [style=filled];
    BPTree -> IFI;
    Fibonacci_heap;
    label = "algorithms and data structure";
    color=blue
  }
  subgraph cluster_9 {
    node [style=filled];
    index;
    label = "database";
    color=blue
  }

  subgraph cluster_10 {
    node [style=filled];
    variations -> Euler_Lagrange_equations;
    Hilbert_space;
    label = "functional analysis";
    color=blue
  }
  subgraph cluster_11 {
    node [style=filled];
    QFT -> Shor_algorithm;
    Hilbert_space_quantum;
    Hermitian_matrix;
    Unitary_matrix;
    label = "quantum computations";
    color=blue
  }
  subgraph cluster_12 {
    node [style=filled];
    ordinary_generating_function;
    expotential_generating_function;
    Dirichlet_series_generating_function;
    formal_power_series;
    label = "generating funcitons";
    color=blue
  }
  subgraph cluster_13 {
    node [style=filled];
    fast_polynomial_multiplication;
    linear_sieve;
    label = "computer science";
    color=blue
  }

  subgraph cluster_14 {
    node [style=filled];

    Mobius_function -> Mobius_inversion_formula;
    Euler_function -> Euler_inversion_formula;
    Fibonacci_number;
    Catalan_number;
    Stirling_number -> Bell_number;
    label = "number theory";
    color=blue
  }
  subgraph cluster_15 {
    node [style=filled];
    RSA;
    AES;
    ECC;
    label = "cryptography";
    color=blue
  }
  subgraph cluster_16 {
    node [style=filled];
    ring -> Dirichlet_ring -> Dirichlet_convolution;
    ring -> quotient_ring -> Galois_Field;
    ring -> formal_power_series_ring;
    label = "abstract algebra";
    color=blue
  }


  FFT -> 特征函数;
  FFT -> 信号_频率分离;
  Galois_Field -> error_correction;
  Shannon_entropy -> Shannon_Theorem;
  Shannon_entropy -> KL_divergence;
  KL_divergence -> Shannon_Theorem;
  FFT -> fast_polynomial_multiplication;
  Gauss_Green_Stokes_formula -> maxwell_equations;
  BPTree -> index;
  Euler_Lagrange_equations -> Fermat_principle;
  FFT -> QFT;
  quantum_mechanics -> QFT;
  Dirichlet_series_generating_function -> Mobius_function;
  Dirichlet_series_generating_function -> Riemann_function;
  linear_sieve -> Mobius_function;
  linear_sieve -> Euler_function;
  Euler_function -> RSA;
  Shor_algorithm -> RSA;
  Dirichlet_convolution -> Dirichlet_series_generating_function;
  Galois_Field -> AES;      
  Galois_Field -> ECC;
  Fibonacci_number -> Fibonacci_heap;
  ordinary_generating_function -> Fibonacci_number;
  ordinary_generating_function -> Stirling_number;
  expotential_generating_function -> Bell_number;
  fast_polynomial_multiplication -> Stirling_number;
  expotential_generating_function -> Catalan_number;
  formal_power_series_ring -> formal_power_series;
  Hilbert_space -> FFT;
  Hilbert_space -> Hilbert_space_quantum;

  self_adjoint_matrix -> Hermitian_matrix;
  orthogonal_matrix -> Unitary_matrix;
//   start [shape=Mdiamond];
//   end [shape=Msquare];
}