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Many different multidimensional and multivariate data-sets are studied currently in almost all research areas. Usually, the aim of such studies is to reveal meaningful patterns and to gain an insights about special characteristics of the particular data-set. It is usually done by scanning over the elements of the data-set at large and bringing up groups or clusters of these elements that exhibit correlations across the variables or dimensions. In this thesis I use different techniques to address two problems: protein folding and the dynamics of the tropical atmosphere. Biological research has generated vast quantities of protein sequences. One of the most important characteristics of the certain protein is its function. It is crucial to understand it in order to use protein for pharmaceutical, engineering or research purposes. Protein folding problems, which predict the spatial structure and the corresponding function of a protein from its amino acid sequence alone, are then critical in biological studies. In this work I study several proteins: start with a penta-alanine molecule, which consists of an acetyl cap group, a methylamide cap group and five residual alanine groups, I then study three polyalanine peptides. Using pairwise correlation, clustering techniques, minimal spanning tree and other techniques, I was able to identify the moments of folding and precursors of the folding event for some of the mentioned molecules. In the Tropics seasonal variations are mainly governed by precipitation, since temperature and day length remain relatively constant throughout the year. The Madden-Julian oscillation (MJO) is the major tropical intraseasonal variability with extensive meteorological impacts, that keeps on puzzling the climate research community on both theoretical and modeling fronts. Together with monsoons, known as dominant water distributors, MJO is an important contributor to the rainfall cycle. In this work, I study dynamics of the MaddenJulian oscillation and its interaction with monsoons. I use satellite data collected by the Tropical Rainfall Measurement Mission (TRMM). Using clustering techniques I managed to identify MJO events, measure its parameters, show relation between magnitudes of MJO and monsoon.

Clustering approach to protein folding problem and dynamics of the tropical atmosphere