Richard Nixon does not like democratic policies. Therefore, he had 5 operatives break into the DNC. Woodward and Berstein reports on the issue. Nixon rebounds and fires his investigator.

Then, he released the “smoking gun” tape with the middle missing

If we write it in a single set of variables:

\begin{equation} \pdv[2]{u}{t} = \pdv[2]{u}{x} \end{equation}

At a glance, for Dirichlet Conditions:

\begin{equation} u(t,x) = \sum_{k} \qty(a_{k} \sin \qty(\frac{ck\pi}{l} t) + b_{k} \cos \qty(\frac{ck\pi}{l} t)) \sin \qty( \frac{k \pi}{l}x) \end{equation}

this takes two initial condition:

\begin{equation} u(0,x) = \sum b_{k} \sin \qty( \frac{k\pi x}{l}) = f(x) \end{equation}

\begin{equation} \pdv{u}{t}(0,x) = \sum a_{k} \frac{ck \pi}{l} \sin \qty( \frac{k\pi x}{l}) = g(x) \end{equation}

meaning:

let’s consider the web as a directed graph, where…

1. a hyper-link denotes perceived relevance (“quality”)
2. anchor of the hyper-link describe the target page (“textual context”)

anchor text

consider:

• IBM’s mostly graphical homepage
• IBM’s copyright page
• Rival’s span IBM page

Consider, a million picees of anchor text saying “IBM” pointing to ibm.com, suddenly, that legitimizes the home page

<a href="target">[archor text that says IBM]</a>

So, when we index a website, we index not just the website but 1) all links pointing to it and 2) the text of those links.

For instance, in spellcheck, you are more likely to confuse say \(a\) and \(e\) than \(a\) and \(b\). Therefore, sometimes we want to weight our edit distance with DP to account for these “common” paths to make certain corrections more “jarring”.

For two strings, let’s define:

• \(X\) of length \(n\)
• \(Y\) of length \(m\)

we define some \(D(i,j)\) as the edit distance between substring \(X[1:i]\) and \(Y[1:j]\).

Let:

• \(D(i,0) = i, \forall i\)
• \(D(0,j) = j, \forall j\)

for i in range(1,M):
    for j in range(1,N):
        # deletion: ignoring one char of previous string
        d1 = D(i-1,j) + 1 # (cost)
        # insertion: insertion into string before using rest of j
        d2 = D(i,j-1) + 1 # (cost)
        # keep same if char is same or substitute current
        d3 = D(i-1,j-1) + (0 if X[i] == Y[j] else 2)

        # cache
        D(i,j) = min(d1, d2, d3)

Fireside a series of articles that I’m writing to consolidate my learning.

I have always dreamed of blogging. I have even tried once called 20MinuteRants. They worked quite well as a basic format whereby I can write about things in a fairly efficient manner (hence the 20 minutes), and be able to reflect about the things I’m up to.

The problem with the project is that I rarely had the motivation to do one. Once I was too busy, or out of ideas to write about, I stop. If there’s not anything to rant about, why is there a 20MinuteRant?