Kalanand's August 2015 Log

July 2015

September 2015

August 5th

Linear scoring formula

This is a simple scoring model where the score begins with an initial value then increases at a constant rate with time.

Assume the score is a linear function of some observable 'x': \begin{equation} y = m \cdot x + c \label{eq:01} \end{equation} Given two data points: (x₁, y₁), (x₂, y₂). Therefore, $$y_1 = m \cdot x_1 + c $$ \begin{equation} \Rightarrow c = y_1 - m \cdot x_1 \label{eq:02} \end{equation} Also, $$ y_2 - y_1 = m \cdot (x_2 - x_1) $$ \begin{equation} \Rightarrow m = \frac{y_2 - y_1}{x_2 - x_1} \label{eq:03} \end{equation} Substituting \eqref{eq:02} and \eqref{eq:03} into\eqref{eq:01}, we get the following general formula

\begin{equation} y = \bigg (\frac{y_2 - y_1}{x_2 - x_1} \bigg ) \cdot \big (x - x_1 \big ) + y_1 \label{eq:04} \end{equation}

Logarithmic scoring formula

The logarithmic scoring has a period of rapid increase followed by a period where the growth slows down but continues to increase without bound. The main difference between this model and the exponential model is that the exponential begins slowly and then increases very rapidly with time.

Assume the score is a logarithmic function of observable 'x': \begin{equation} y = m \log(x + b) + c \label{eq:11} \end{equation} Given two data points: (x₁, y₁), (x₂, y₂). Therefore, $$y_1 = m \log(x_1 + b) + c $$ \begin{equation} \Rightarrow c = y_1 - m \log(x_1 + b) \label{eq:12} \end{equation} Also, $$ y_2 - y_1 = m \log \bigg (\frac{x_2+b}{x_1+b} \bigg ) $$ \begin{equation} \Rightarrow m = \frac{y_2 - y_1}{\log \big ( \frac{x_2+b}{x_1+b}\big)} \label{eq:13} \end{equation} Substituting \eqref{eq:12} and \eqref{eq:13} into \eqref{eq:11}, we get the following general formula \begin{equation} y = \frac{y_2 - y_1}{\log \big ( \frac{x_2+b}{x_1+b}\big)} \cdot \log \bigg (\frac{x+b}{x_1+b} \bigg ) + y_1 \label{eq:4} \end{equation} Let's choose the constant term b such that \begin{equation} \frac{x_2+b}{x_1+b} = 11 \label{eq:5} \end{equation} $$\Rightarrow b = \frac{x_2 - 11 x_1}{10} $$ Then

\begin{equation} y = \frac{y_2 - y_1}{\log (11)} \cdot \log \bigg (\frac{10x}{x_2-x_1} + \frac{x_2-11x_1}{x_2-x_1}\bigg ) + y_1 \label{eq:6} \end{equation}

August 24th

To run a forward DNS lookup on the domain name using the host command


host 216.58.192.47

I get back:

47.192.58.216.in-addr.arpa domain name pointer nuq04s30-in-f15.1e100.net.
47.192.58.216.in-addr.arpa domain name pointer nuq04s30-in-f47.1e100.net.

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Last modified: Mon Aug 24 17:50:01 PDT 2015