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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 non-equilibrium 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, birth-death and branching processes, master equations), continuous random processes (diffusion type processes, Fokker-Planck 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 non-equilibrium 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

Delivery Methods

In Person

A course is considered In Person if it requires attendance at a specific location and time for some or all course activities.*.

* Subject to adjustments imposed by public health requirements for physical distancing.

Online - Synchronous
A course is considered Online Synchronous if online attendance is expected at a specific time for some or all course activities, and attendance at a specific location is not expected for any activities or exams.
Asynchronous
A course is considered Asynchronous if it has no requirement for attendance at a specific time or location for any activities or exams.