## Search

Now showing items 1-5 of 5

#### Complex Multiplication on Elliptic Curves

(2014-12-24)

We describe the theory of complex multiplication on elliptic curves as it pertains
to constructing abelian extensions of imaginary quadratic fields. We also briefly
explore how one may construct abelian extensions of real ...

#### Evolutionary Dynamics in an Individual Spatial and a Mean Field Differential Equation Host-Pathogen Model

(2014-01-29)

We examine a host-pathogen model in which three types of species exist: empty sites,
healthy hosts, and infected hosts. In this model six different transitions can occur:
empty sites can be colonized by healthy hosts, healthy ...

#### Coalescing random walks on n-block Markov chains

(2014-01-11)

Fix a discrete-time Markov chain $(V,P)$ with finite state space $V$ and transition
matrix $P$. Let $(V_n,P_n)$ be the Markov chain on n-blocks induced by $(V,P)$, which
we call the n-block process associated with the base ...

#### Merge Times and Hitting Times of Time-inhomogeneous Markov Chains

(2014-06-28)

Concepts of Markov chains mixing, the study of the convergence to stationarity, emerged
three decades ago. Studying times to convergence of Markov chains is crucial as it
ties to many other mathematical areas, such as Markov ...

#### A Stochastic Spatial Model for Tumor Growth

(2014-04-29)

Evolutionary game theory can be used to study the interactions of different cell phenotypes
and describe tumor population dynamics. Instead of killing tumor cells, clinical treatment
could aim to change the nature of the ...