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Full-Text Articles in Physical Sciences and Mathematics
Mapping Of Stochastic Matrices Into Polynomial Form In The Complex Plane, Jordan Emile Cates
Mapping Of Stochastic Matrices Into Polynomial Form In The Complex Plane, Jordan Emile Cates
Honors Theses
This thesis originated from a specific problem from biology. Namely we need to study probabilistic models that represent molecular interactions that take place inside living cells, such as the number of molecular heat-shock proteins present in a cell. Because of the intrinsic discrete nature of the number of molecules present in cells, the fundamental mathematical models are based on Markov processes. For such processes a transition probability matrix describes the evolution of the state of the cell, whereas the state itself, i.e. the number of molecules present at a specific time, is described by a vector. The components of this …