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We were asked to design our own Electrocardiogram. Obviously, recording heart beats without any noise is a real challenge. Seeing the prices of those kinds of devices, we could already imagine that reaching great performances with our means would be difficult. However, the real goal of this project was to be able to analyze the different problems we encountered and to think about possible improvements we could have provided to overcome them.

Principal Components Analysis (PCA) and Canonical Correlation Analysis (CCA) are among the methods used in Multivariate Data Analysis. PCA is concerned with explaining the variance-covariance structure of a set of variables through a few linear combinations of these variables. Its general objectives are data reduction and interpretation. CCA seeks to identify and quantify the associations between two sets of variables i.e Pulp fibres and Paper variables.PCA shows that the first PC already exceeds 90% of the total variability. According to the proportion of variability explained by each canonical variable , the results suggest that the first two canonical correlations seem to be sufficient to explain the structure between Pulp and Paper characteristics with 98.86%. Despite the fact that the first the two canonical variables keep 98% of common variability, 78% was kept in the pulp fiber set and about 94% of the paper set as a whole. In the proportion of opposite canonical variable,there were approximately 64% for the paper set of variables and 78% for the pulp fiber set of variables kept for the two respectively.

The goal of this project is to explore both the theory behind the Extended Kalman Filter and the way it was used to localize a four-wheeled mobile-robot. This can be achieved by estimating in real-time the pose of the robot, while using a pre-acquired map through Laser Range Finder (LRF). The LRF is used to scan the environment, which is represented through line segments. Through a prediction step, the robot simulates its kinematic model to predict his current position. In order to minimize the difference between the matched lines from the global and local maps, a update step is implemented. It should be noted that every measurement has associated uncertainty that needs to be taken into account when performing each step of the Extended Kalman Filter. These uncertainties, or noise, are described by covariance matrices that play a very important role in the algorithm. Since we are dealing with an indoor structured environment, mainly composed by walls and straight-edged objects, the line segment representation of the maps was the chosen method to approach the problem.

Math project.

Template for a report or grant application section, downloaded from the Vanderbilt Biostatistics Wiki.

With the emergence of systems archiving and distribution of PACS medical imaging, also emerged the need to store those images off-site environment, this project aims to study this need, trying to offer a service within an information infrastructure that can integrate the environment site with a remote environment, a transparent and heterogeneous, taking account of the needs of users of teleradiology. Keywords: PACS, teleradiology, Medical Imaging, Archiving.

Benford law states that the occurrence of digits from 0-9 in a large set of data is not uniformly distributed but instead in a decreasing logarithmic distribution with 1 occurring at most. Almost all set of data follows this trend however this law is widely used as a base for various fraud detection and forensic accounting. Benford’s law is an observation that leading digits in data derived from measurements doesn’t follow uniform distribution. Different financial statements such as cash flows, income statement and balance sheet of the 20 tech companies of the Fortune 500 are analyzed in this project. Cash flow is the net amount of cash and cash-equivalents moving into and out of a business. Income statement is a financial statement that measures a company's financial performance over a specific accounting period. Balance sheet is a financial statement that summarizes a company's assets, liabilities and shareholders’ equity at a specific point in time. All of these data of financial statements are extracted from Morning Star database and are analyzed by Python program written by me.I also wrote the Python program to calculate Benford's second digit and third digit probability using the formula. I would like to thank Prof. Erin Wagner and Dr. Courtney Taylor for helping in this research project.