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Full-Text Articles in Other Applied Mathematics
Algorithms To Compute Characteristic Classes, Martin Helmer
Algorithms To Compute Characteristic Classes, Martin Helmer
Electronic Thesis and Dissertation Repository
In this thesis we develop several new algorithms to compute characteristics classes in a variety of settings. In addition to algorithms for the computation of the Euler characteristic, a classical topological invariant, we also give algorithms to compute the Segre class and Chern-Schwartz-MacPherson (CSM) class. These invariants can in turn be used to compute other common invariants such as the Chern-Fulton class (or the Chern class in smooth cases).
We begin with subschemes of a projective space over an algebraically closed field of characteristic zero. In this setting we give effective algorithms to compute the CSM class, Segre class and …
Optimizing The Analysis Of Electroencephalographic Data By Dynamic Graphs, Mehrsasadat Golestaneh
Optimizing The Analysis Of Electroencephalographic Data By Dynamic Graphs, Mehrsasadat Golestaneh
Electronic Thesis and Dissertation Repository
The brain’s underlying functional connectivity has been recently studied using tools offered by graph theory and network theory. Although the primary research focus in this area has so far been mostly on static graphs, the complex and dynamic nature of the brain’s underlying mechanism has initiated the usage of dynamic graphs, providing groundwork for time sensi- tive and finer investigations. Studying the topological reconfiguration of these dynamic graphs is done by exploiting a pool of graph metrics, which describe the network’s characteristics at different scales. However, considering the vast amount of data generated by neuroimaging tools, heavy computation load and …