_index.org

Gregarious Abstract

Last edited: August 8, 2025

In this experiment, an efficient and accurate network of detecting automatically disseminated (bot) content on social platforms is devised. Through the utilisation of parallel convolutional neural network (CNN) which processes variable n-grams of text 15, 20, and 25 tokens in length encoded by Byte Pair Encoding (BPE), the complexities of linguistic content on social platforms are effectively captured and analysed. With validation on two sets of previously unexposed data, the model was able to achieve an accuracy of around 96.6% and 97.4% respectively — meeting or exceeding the performance of other comparable supervised ML solutions to this problem. Through testing, it is concluded that this method of text processing and analysis proves to be an effective way of classifying potentially artificially synthesized user data — aiding the security and integrity of social platforms.

grid search

Last edited: August 8, 2025

grid search is a hyperparameter tuning technique by trying pairs of all hyperparemeters sequentially

group

Last edited: August 8, 2025

components

requirements for group

  • closed: if \(a,b \in G\), then \(a \cdot b \in G\)
  • existence of identity: there is \(e \in G\) such that \(e\cdot a= a\cdot e = a\), for all \(a \in G\)
  • existence of inverses: there is \(b \in G\) for all \(a \in G\) such that \(a\cdot b = b\cdot a = e\)
  • associative: \((a\cdot b)\cdot c = a\cdot (b\cdot c)\) for all \(a,b,c \in G\)

additional information

identity in group commutates with everything (which is the only commutattion in groups

Group Theory Index

Last edited: August 8, 2025

Notes on MATH 109, group theory.

Lectures

PSets

These links are dead.

Course logistics

  • midterm: November 1st, final: December 14th, 8:30-11:30
  • WIM assignment: December 8th, start of class (no late submissions)
  • PSets: 8 in total, posted on Wednesdays at 8A, due following Tuesday at 8A

grouping

Last edited: August 8, 2025

“Stuffing some stuff into buckets”

How many ways are there to sort \(n\) distinct objects to \(r\) buckets?

\begin{equation} r^{n} \end{equation}

grouping with entirely indistinct objects

You can simply reframe the grouping problem as permutation of the objects with \(r-1\) dividers along with your old \(n\) objects.

i.e.: sort this thing —

So:

\begin{equation} \frac{(n+r-1)!}{n! (r-1)!} \end{equation}