In this paper we discuss how to price American, European and Asian options using a geometric Brownian motion model for stock price. We investigate the analytic solution for Black-Scholes differential equation for European options and consider numerical methods for approximating the price of other types of options. These numerical methods include Monte Carlo, binomial trees, trinomial trees and finite difference methods. We conclude our discussion with an investigation of how these methods perform with respect to the changes in different Greeks. Further analysing how the value of a certain Greeks affect the price of a given option.

Considering the growing impact of ideas nowadays, via quaternary sector, the plagiarism detection has become constant in texts, songs, as well as source codes. This work proposes the creation of the tool \nameOfProgram \ for plagiarism detection in simple texts with GNU GPL license. \nameOfProgram \ was designed to allow your extension for plagiarism detection in source codes. The tool was tested and results are presented in this paper.

We are given spans of the target text which align to concepts in the AMR graph.These alignment do not cover every token in the target sentnce. Typically function words are not aligned to any graph fragment. Next, we obtain word alignments between the target sentence and source sentence. Since we have word alignments between target and source, and phrase alignments between target and AMR graph, we must convert the word alingments into phrase alignments. The phrases on the source side will then be projected to the AMR concepts via the target sentence

By adapting a previously written percolation model in C, the threshold probabilities for square, triangular, and cubic lattice types were confirmed. An algorithm to count the distribution of cluster sizes at a variety of percolation probabilities was developed, and the expected trends towards the so called infinite cluster was achieved. An equivalent bond percolation model was adapted to the original site algorithm, and by treating occupied bonds as springs, a total compression trend for the model was constructed, which implied that structures under the boundary conditions that were imposed does not have behavior that changes the total compression constant significantly at the percolation threshold.\\

This paper implements Simultaneous Localization and Mapping (SLAM) technique to construct a map of a given environment. A Real Time Appearance Based Mapping (RTAB-Map) approach was taken for accomplishing this task. Initially, a 2d occupancy grid and 3d octomap was created from a provided simulated environment. Next, a personal simulated environment was created for mapping as well. In this appearance based method, a process called Loop Closure is used to determine whether a robot has seen a location before or not. In this paper, it is seen that RTAB-Map is optimized for large scale and long term SLAM by using multiple strategies to allow for loop closure to be done in real time and the results depict that it can be an excellent solution for SLAM to develop robots that can map an environment in both 2d and 3d.