# Elena Farahbakhsh TouliPhD

Welcome to my home page! I am a PhD student in the field of Computational Mathematics supervised by Dr. Olha Bodnar. My research interests include but not limited to Algorithm, Optimization and Bioinformatics. For information about my research interests and my papers please look at my google scholar.

My Erdős number is 3.

## Teaching

I am a teacher assistance for the course Numerical Methods and Basic Programming and Numerical Methods (2020-2021) at KTH University.

I am one of the lecturer for the course computer science for mathematitions  (2019) at Stockholm University.

I am a TA for the course algorithm and data structure (2016-2018) at the Ohio State University.

I was a lecturer for the courses discrete mathematics, and enginearing mathematics (2014-2015).

I was a lecturer for the course Mathematica for master students in the field of mathematics in KNT University of Technology (2013).

I also was a TA in KNT University of Technology for the course numerical analysis (2011).

## Research

Clustering Coefficient (Stockholm University) 2021

Relative Clustering Coefficient. At this project we extended the clustering coefficnet to be able to check properties of the networks that are very close to the real life. The idea of this clustering was just to consider the edges in the network that the probability of them were larger than 0.

Distance Between Trees (Stockholm University) 2020

Frechet Like Distance. This project was about finding the distance between two trees to measure the similarity between trees. It was done by defining a new method for finding a distance between two trees. As the idea was based on the Frechet distance between two curves, I called the distance Frechet-Like distance. You can find the paper here.

Interleaving Distance. Interleaving distanceis one of the way for approximating the Gromov-Hausdorff distance. The Gromov-Hausdorff distance is defined between metric spaces and it indicates how far two trees are from being isometric. The aim of this project was approximating the interleaving distance that leads to the approximation algorithm for computing Gromov-Hausdorff distance between trees. The Gromov-Hausdorff distance is NP-Complete even for trees with the length of one. The paper is available here.

Third-Kind Integral Equations (KNTU) 2013-2015

Laguerre Collocation Method. This project was about solving third-kind integral equations. We used Laguerre collocation method for approximating third integral equations. The convergence analysis proves the applicability of the method. Find the paper here.

Birkhoff quadrature formula. Later we defined a new Birkhoff-Type quadrature formula for approximating the Integral part of the integral equation and therefore we could approximate the equations. You can find the result here.