Atomic Units

Atomic_Units.ipynb

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      "# Atomic Units\n",
      "\n",
      "The basic structural component of AHNs is the atom. The AHN-algorithm defines two different atomic units. Inspired on chemical hydrocarbon compounds, these two atomic units are the hydrogen atom and the carbon atom.\n",
      "\n",
      "Let:\n",
      "\n",
      "* $A^{(\\alpha)}$ be a set of elements $a_i$.\n",
      "* $\\alpha$ be a positive integer related to $A$.\n",
      "* $e_i$ be a positive integer (valence electrons).\n",
      "\n",
      "An element $a_i$ is said to be an atom if it has a fixed value $e_i$ denoting the number of valence electrons satisfying $\\forall i$, $e_i \\leq \\frac{\\alpha}{2}$, where $\\alpha$ stands for the full number of valence electrons. then $A^{(\\alpha)}$ is said to be a ser of atom units.\n",
      "\n",
      "Let also:\n",
      "\n",
      "* $a_i, a_j \\in A^{(\\alpha)}$ be two atomic units.\n",
      "* $e_i, e_j$ be the valence electrons of those. \n",
      "\n",
      "If $e_i = e_j$ the $a_i$ and $a_j$ are called similar atoms denoted by $a_i = a_j$, If $e_i \\ne e_j$ then $a_i$ and $a_j$ are called different atoms denoted by $a_i \\ne a_j$.\n",
      "\n",
      "Where:\n",
      "\n",
      "* $e_i$ is the actual number of electons that an atom $a_i$ has in its outer shell.\n",
      "* $\\alpha$ stands for the total number of electrons shared in $a_i$, so that the $\\alpha$-rule nolds.\n",
      "* The maximum number of pairs of electrons shared in the outer shel of $a_i$ is equal to $\\alpha / 2$.\n",
      "\n",
      "Moreover let:\n",
      "\n",
      "* $H$ and $C$ be two different atomic units with valence electrons $e_H$ and $e_C$, respectively, in the set of atomic units $A^{(8)}$.\n",
      "* $v_H$ and $v_C$ be two complex numbers $v_H, v_C \u2265 C$ which are the atomic values of hydrogen and carbon atoms, respectively.\n",
      "\n",
      "Then:\n",
      "\n",
      "* $H$ is called hydrogen atom with $e_H = 1$ and $C$ is called carbon atom with $e_C = 4$.\n",
      "* $A^{(8)}$ is called the set of atom units of artificial hydrocarbon networks.\n",
      "\n",
      "Notice that the set of atom units of artificial hydrocarbon networks claims for the\n",
      "octet rule as defining \u03b1 = 8.\n",
      "\n",
      "## Implementation\n",
      "\n",
      "* https://github.com/Ismael-VC/AHN.jl/blob/master/src/atomic_units.jl\n",
      "\n",
      "### Bibliography\n",
      "\n",
      "* Ponce, H., Ponce, P., & Molina, A. (2014). [Artificial Organic Networks][1]: Artificial intelligence based on carbon networks. (1st ed., Vol. 521). Springer International Publishing.\n",
      "\n",
      "\n",
      "[1]: http://www.springer.com/gp/book/9783319024714"
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