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This page contains links to articles written by students (mainly undergraduates and masters students) of ISI Bangalore.

Probability and Group Theory: Computing Commuting Probabilities #

The following article has been author by Snehinh Sen (B. Math, 2022).

  • Title: Probability and Group Theory: Computing Commuting Probabilities
  • Authors: Snehinh Sen
  • Abstract: In this note, we will briefly look into some applications of probability to finite groups, specially in the case of commutativity of elements. We will also look at some further properties and how we can think of bounds of possible probabilities. Finally, we shall briefly see how we can generalise results to rings and infinite groups.
  • Article link: https://drive.google.com/file/d/1idwtEErUXh-ELwLVtKY7wE9UQ8gS6IxY/view

Generalized twisted centralizer codes #

The following article has been co-authored by Shyambhu Mukherjee (B. Math, 2019).

  • Title: On decoding procedures of intertwining codes
  • Authors: Shyambhu Mukherjee, Joydeb Pal, Satya Bagchi
  • Abstract: An important code of length \(n^2\) is obtained by taking centralizer of a square matrix over a finite field \(\mathbb{F}_q\). Twisted centralizer codes, twisted by an element \(a \in \mathbb{F}_q\), are also similar type of codes but different in nature. The main results were embedded on dimension and minimum distance. In this paper, we have defined a new family of twisted centralizer codes namely generalized twisted centralizer (GTC) codes by \(\mathcal C(A,D):= \{ B \in \mathbb{F}_q^{n \times n} \mid AB = BAD \}\) twisted by a matrix \(D\) and investigated results on dimension and minimum distance. Parity-check matrix and syndromes are also investigated. Length of the centralizer codes is \(n^2\) by construction but in this paper, we have constructed centralizer codes of length \((n^2−i)\), where \(i\) is a positive integer. In twisted centralizer codes, minimum distance can be at most n when the field is binary whereas GTC codes can be constructed with minimum distance more than \(n\).
  • Article link: https://arxiv.org/abs/1709.01825

On decoding procedures of intertwining codes #

The following article has been co-authored by Shyambhu Mukherjee (B. Math, 2019).

  • Title: On decoding procedures of intertwining codes
  • Authors: Shyambhu Mukherjee, Joydeb Pal, Satya Bagchi
  • Abstract: One of the main weakness of the family of centralizer codes is that its length is always \(n^2\). Thus we have taken a new matrix equation code called intertwining code. Specialty of this code is the length of it, which is of the form \(nk\). We establish two decoding methods which can be fitted to intertwining codes as well as for any linear codes. We also show an inclusion of linear codes into a special class of intertwining codes.
  • Article link: https://arxiv.org/abs/1801.02010

Stock Price Movement Prediction using Attention-Based Neural Network Framework #

The following article has been co-authored by Soumyabrata Kundu (B. Math, 2020).

  • Title: Stock Price Movement Prediction using Attention-Based Neural Network Framework
  • Authors: Kartik Goyal, Nitin Bansal, Soumyabrata Kundu, Ayan Kundu, Nitish Jain
  • Abstract: There is a lot of scientific work going on NLP trying to predict the impact of news on a stock price, much of this uses basic features (such as bags-of-words, named entities etc.), but fails to capture structured entity-relation, and hence lacks accuracy.
    1. Encoding the information like daily events, meta-stock information and stock’s 50 days moving average using LSTM.
    2. Employing attention mechanism to rate the relevancy of all events for each stock.
    3. Using non-linear neural network on the weighted events to predict the stock movement. The model achieved an accuracy of around 72% on test set.
  • Article link: https://www.ijsr.net/archive/v7i8/ART2019326.pdf

Points at Which Continuous Functions Have the Same Height #

The following article, by Parth Prashant Karnawat (B. Math, 2020) solves an interesting problem which was posed by Prof. B. V. Rajarama Bhat in one of his classes.

  • Title: Points at Which Continuous Functions Have the Same Height
  • Authors: Parth Prashant Karnawat
  • Abstract: As an easy application of the intermediate value theorem, one can show that for any continuous function \(f: [0, 1] \to \mathbb{R}\) with \(f(0) = f(1)\), there are points \(a, a + \frac 12\) both in \([0, 1]\) such that \(f(a) = f(a + \frac 12)\). In this note, we show that this property holds with \(\frac 12\) replaced by any number of the form \(\frac 1n\) for a positive integer \(n\). More interestingly, we show that this is false for every number not of the form \(\frac 1n\).
  • Article link: https://www.ias.ac.in/article/fulltext/reso/023/05/0591-0596