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Information regarding scientific research projects.

# Linear minimum area enclosing triangle implementation

### Problem

Given an arbitrary set of points in the 2D Euclidean plane compute the enclosing triangle having the minimum area. Figure 1: An example of a set of points in the 2D Euclidean plane (highlighted in green) and the corresponding minimal area enclosing triangle (highlighted in red).

### Theoretical solution

Based on an elegant geometric characterization provided by Klee and Laskowski O’Rourke developed a linear algorithm for addressing the above problem; see the An optimal algorithm for finding minimal enclosing triangles paper for more details.

### Implementation

A detailed description of all required algorithms is provided in the Implementation of linear minimum area enclosing triangle algorithm paper and a C++ implementation of these algorithms is made freely available at https://github.com/ovidiuparvu/minimal-area-triangle.

# Behaviour driven model construction in Matlab

Using the Hornberg 2005 MAPK signal transduction pathway model a Genetic Algorithm was implemented in Matlab for moving the peak (i.e. global maximum) of the ERK-PP time series as late as possible i.e. as further away in time as possible. The algorithm starts with a population of randomly initialized individuals and runs for a given number of iterations. In the end, all the individuals for which the peak of the time series of ERK-PP is reached later than a given threshold value are printed in a file “output.txt”. The source code is open source and can be adapted for other projects. You can access it from the github repository behaviour-driver. Thank you to Qian Gao for providing the set of ODEs already implemented in Matlab. They are the result of her own work and only a modified version of the model was used here. For more details regarding the original model, please contact the author.

# Guide for obtaining ordinary differential equations from chemical reactions or a Petri net

During the process of familiarizing myself with the concepts of Petri nets and continuous simulations of bio-chemical networks, I wanted to discover the mechanism of deriving the set of ordinary differential equations (ODEs) corresponding to a given set of chemical reactions or the graphical representation of a Petri net. I have summarized my findings in the following guide and published it here such that other people facing the same question can get a quicker answer. Therefore, this guide is intended to be read by “beginners” and not professionals or experts.