Brown v. Board of Education
Last edited: August 8, 2025Brown v. Board of Education is a landmark case in the US. This lead for schools to be integrated, and many children were taken out of school out of protest due to the subsequent integration movement between schools.
Brownian Motion
Last edited: August 8, 2025Brownian Motion is the pattern for measuring the convergence of random walk through continuous timing.
discrete random walk
discrete random walk is a tool used to construct Brownian Motion. It is a random walk which only takes on two discrete values at any given time: \(\Delta\) and its additive inverse \(-\Delta\). These two cases take place at probabilities \(\pi\) and \(1-\pi\).
Therefore, the expected return over each time \(k\) is:
\begin{equation} \epsilon_{k} = \begin{cases} \Delta, p(\pi) \\ -\Delta, p(1-\pi) \end{cases} \end{equation}
Broyden-Fletcher-Goldfarb-SHanno (BFGS)
Last edited: August 8, 2025Broyden's Method
Last edited: August 8, 2025Broyden’s method is an approximate method to estimate the Jacobian. We give the root-finding variant here (i.e. the search direction is for finding \(F\qty(x) = 0\) instead of \(\min F\)).
For function \(F\), let: \(J^{(0)} = I\). For every step
- compute \(\Delta c^{(q)}\) from \(J^{(q)}\Delta c^{(q)} = -F\qty(c^{(q)})\)
- compute \(\arg\min_{\alpha} F\qty(c^{(q)} + \alpha \Delta c^{(q)})^{T}F\qty(c^{(q)} + \alpha \Delta c^{(q)})\) for root finding
- compute \(c^{(q+1)} = c^{(q)} + \alpha \Delta c^{(q)}\)
- set \(\Delta c^{(q)} = c^{(q+1)} - c^{(q)}\)
- finally, we can update \(J\) such that…
\begin{equation} J^{(q+1)} = J^{(q)} + \frac{1}{\qty(\Delta c^{(q)})^{T} \Delta c^{(q)}} \qty(F\qty(c^{(q+1)}) - F\qty(c^{(q)}) - J^{(q)}\Delta c^{(q)}) \qty(\Delta c^{(q)})^{T} \end{equation}
buffer overflow
Last edited: August 8, 2025buffer overflow happens when operations like stcpy runs beyond the edge of the allocated buffer. We need to find and fix buffer overflows, which causes people who use o
buffer overflow horror stories
- AOL messanger
identifying buffer overflows
Think about whether or not what you are going to do will cause buffer overflows. There are stuff which you shouldn’t do:
https://www.acm.org/code-of-ethics “Design and implement systems that are robustly and usably secure.”