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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Cayley Graphs Of Groups And Their Applications, Anna Tripi
Cayley Graphs Of Groups And Their Applications, Anna Tripi
MSU Graduate Theses
Cayley graphs are graphs associated to a group and a set of generators for that group (there is also an associated directed graph). The purpose of this study was to examine multiple examples of Cayley graphs through group theory, graph theory, and applications. We gave background material on groups and graphs and gave numerous examples of Cayley graphs and digraphs. This helped investigate the conjecture that the Cayley graph of any group (except Z_2) is hamiltonian. We found the conjecture to still be open. We found Cayley graphs and hamiltonian cycles could be applied to campanology (in particular, to the …
Residues, Bernoulli Numbers And Finding Sums, Mohammed Saif Alotaibi
Residues, Bernoulli Numbers And Finding Sums, Mohammed Saif Alotaibi
MSU Graduate Theses
A large number of infinite sums, such as , cannot be found by the methods of real analysis. However, many of them can be evaluated using the theory of residues. In this thesis we characterize several methods of summations using residues, including methods integrating residues and the Bernoulli numbers. In fact, with this technique we derive some summation formulas for particular Finite Sums and Infinite Series that are difficult or impossible to solve by the methods of real analysis.
Support Vector Machine And Its Application To Regression And Classification, Xiaotong Hu
Support Vector Machine And Its Application To Regression And Classification, Xiaotong Hu
MSU Graduate Theses
Support Vector machine is currently a hot topic in the statistical learning area and is now widely used in data classification and regression modeling. In this thesis, we introduce the basic idea for support vector machine, its application in the classification area including both linear and nonlinear parts, and the idea of support vector regression contains the comparison of loss functions and the usage of kernel function. Two real life examples, which are taken from R package, are also provided for both classification and regression part respectively, talking about classification of glass type and prediction for Ozone pollution.