• High Dimensional Probability

  • • Reading "High dimensional probability. An introduction with applications in Data Science." by Roman Vershynin

The Gapped k-Deck Problem

Publication: J. Golm, M. Nahvi, R. Gabrys and O. Milenkovic, "The Gapped k-Deck Problem," 2022 IEEE International Symposium on Information Theory (ISIT), Espoo, Finland, 2022, pp. 49-54, doi: 10.1109/ISIT50566.2022.9834537

Abstract: The k-deck problem is concerned with finding the smallest positive integer S(k) such that there exist at least two strings of length S(k) that share the same k-deck, i.e., the multiset of subsequences of length k. We introduce the new problem of gapped k-deck reconstruction: For a given gap parameter s, we seek the smallest positive integer Gs(k) such that there exist at least two distinct strings of length Gs(k) that cannot be distinguished based on a “gapped” set of k-subsequences. The gap constraint requires the elements in the subsequences to be at least s positions apart within the original string. Our results are as follows. First, we show how to construct sequences sharing the same 2-gapped k-deck using a nontrivial modification of the recursive Morse-Thue string construction procedure. This establishes the first known constructive upper bound on G2(k). Second, we further improve this bound using the approach by Dudik and Schulman.

Other Projects: Quantum Error Correction, COVID-19 Group Testing

Modeling the dynamics of SARS-Cov-2 to Find Optimal Treatment Strategies (MATLAB)
PI: Dr. Wade Trappe, Location: Rutgers University, Program: James J. Slade Scholars Program, Duration: Sept. 2020 – May 2021

• Compared two COVID-19 viral dynamics models using the MATLAB ODE toolbox by analyzing the rate of change of peak viral load, time of peak viral load, and time till recovery with respect to different parameter

• Learned about different problems in mathematical modeling of drug treatments for cancer and viral infections

Simultaneous trimodal PET-MR-EEG imaging
PI: Mr. Ravichandran Rajkumar, Location: Institute for Neuroscience and Medicine, Forschungszentrum Juelich, Germany, Program: DAAD Rise
Duration: Cancelled due to the COVID-19 pandemic

Brainstorm Plugin for EEG Analysis Algorithms (MATLAB)
PI: Dr. Laleh Najafizadeh, Lab: Integrated Systems & NeuroImaging Lab, Location: Rutgers University, Duration: September 2019-May 2020

• Developed a plugin in MATLAB for Brainstorm EEG to assist analysis of EEG data

• Learned about different machine learning algorithms and their applications to classification tasks in neuroimaging

Automating the Detection of PHI in Clinical Notes Using BERT (Python)
PI: Dr. Jorge Ortiz, Lab: Cyber Physical Intelligence Lab, Location: Rutgers University, New Brunswick, NJ, Duration: January 2019 – September 2019
Funded by: Douglass Project Super

• Modified the BERT NLP model to identify protected health information in Clinical Notes using training data from the i2b2 dataset

• Trained on an AWS EC2 instance and adjusted hyperparameters to improve model performance

Posture Alert System (Senior Design Project)
Where: Senior Design Expo, When: May 2021
Description: Developed a pressure sensor matrix cushion to detect if the user is sitting with correct posture using machine learning

Analysis of COVID-19 Models To Determine Key Factors in Treatment
Where: J.J. Slade Symposium, When: April 13, 2021
Description: Used MATLAB ODE Toolbox to perform a sensitivity analysis on two different viral dynamic models

Computer Assisted Card Game Mat
Where:  Honors Design and Development Symposium, When: May 2020
Description: Created a tool to assist visually impaired people in playing board and card games

Automating the Detection of PHI in Clinical Notes Using BERT
Where: Project Super Poster Symposium, When: October 11, 2019
Description: Improve detection of PHI in clinical notes using BERT

Natural Language Processing with Clinical Notes
Where: Introduction to Scientific Research Poster Symposium, When: April 24, 2019
Description: Using NLP on clinical notes to improve named entity recognition of Protected Health Information using the i2b2 database