PHY2108H 0.25 FCE
Special Topics in Physics I  Stochastic processes in biology
Official description
This course will cover conceptual foundations and practical applications of a number of common statistical learning methods – from classical tools to their modern incarnations, with the emphasis on the connection among the different tools and their relation to a number of models of mathematical physics.
Specific topics will include: maximum likelihood estimation, Bayesean methods, clustering and dimensionality reduction, neural networks and Boltzmann machines, supervised and unsupervised learning, feature extraction and learning.
The mathematical methods will be illustrated by examples from nonequilibrium statistical mechanics, physical chemistry, population dynamics and epidemiology, quantum optics, solid state physics, chemical reactions and gene regulation.
Stochastic/random processes arise in various areas of physics, chemistry, biology and social sciences. The course will cover the theoretical foundations and practical solution methods of various stochastic processes with the goal of preparing the students to deal with a broad range of probabilistic problems arising in modern research.
The course will cover the following mathematical topics: review of probability and probabilistic processes, discrete random processes (random walks, birthdeath and branching processes, master equations), continuous random processes (diffusion type processes, FokkerPlanck equation, Smoluchowski and Einstein theories), stochastic differential equations (Langevin, Ito, Smoluchowski), stochastic simulations methods (Gillespie, Kinetic Monte Carlo), fluctuations and first passage problems.
This course will cover conceptual foundations and practical applications of a number of common statistical learning methods – from classical tools to their modern incarnations, with the emphasis on the connection among the different tools and their relation to a number of models of mathematical physics.
Specific topics will include: maximum likelihood estimation, Bayesean methods, clustering and dimensionality reduction, neural networks and Boltzmann machines, supervised and unsupervised learning, feature extraction and learning.
The mathematical methods will be illustrated by examples from nonequilibrium statistical mechanics, physical chemistry, population dynamics and epidemiology, quantum optics, solid state physics, chemical reactions and gene regulation.
 Prerequisite
 Basic probability theory and statistical mechanics
 course title
 PHY2108H 0.25 FCE
 session
 fall
 group
 quarter course (0.25 FCE credit)
 time and location

Wednesdays 4  6 pm, Sep 14  Oct 19, MP 606
 instructor