Thema der Dissertation:
Network Propagation with Node Core for Genotype-Phenotype Associations and Module Identification Thema der Disputation:
Random Walks on Graphs
Network Propagation with Node Core for Genotype-Phenotype Associations and Module Identification Thema der Disputation:
Random Walks on Graphs
Abstract: A random walk is a stochastic process where a walker completes a path which is series of random steps in some space. The term random walk was first introduced by Karl Pearson in 1905, and by now it is used as a fundamental model for stochastic processes in many fields.
In the first part of the disputation I will introduce the mathematical foundation of random walks. I will focus on one common variant which is the random walk on a graph. A random walk on a graph is a special case of a Markov chain. I therefore define the random walk using the graph topology and describe the properties corresponding to a Markov chain. The random walk is guaranteed, under certain conditions, to converge by the Perron-Frobenius theorem. I will therefore present the steady-state at the convergence and the equilibrium distribution that is reached.
As an example for the application of the random walk model on a graph I will describe the PageRank algorithm which provides a ranking for the pages of the World Wide Web. Finally I will discuss the random walk with restart variant and its application to protein-protein interaction networks in the aim of addressing biological questions such a protein function prediction or disease association.
The second part of the disputation is dedicated to the content of the dissertation.
In the first part of the disputation I will introduce the mathematical foundation of random walks. I will focus on one common variant which is the random walk on a graph. A random walk on a graph is a special case of a Markov chain. I therefore define the random walk using the graph topology and describe the properties corresponding to a Markov chain. The random walk is guaranteed, under certain conditions, to converge by the Perron-Frobenius theorem. I will therefore present the steady-state at the convergence and the equilibrium distribution that is reached.
As an example for the application of the random walk model on a graph I will describe the PageRank algorithm which provides a ranking for the pages of the World Wide Web. Finally I will discuss the random walk with restart variant and its application to protein-protein interaction networks in the aim of addressing biological questions such a protein function prediction or disease association.
The second part of the disputation is dedicated to the content of the dissertation.
Zeit & Ort
21.01.2021 | 14:00