The life sciences are expanding strongly into more quantitative
directions. As a consequence, there is an ever greater need to develop
new mathematical and computational ways of thinking about biological
systems. In this course we will focus on these exciting developments,
taking a quantitative approach to signal processing in biology.
Biological signal processing rarely follows the neat simplifying
assumptions used in standard textbook presentations. Building on
classical results in probability and statistics, stochastic processes,
and information theory, I will present a conceptual framework for
signal processing that is more suitable for the analysis of biological
systems, and in particular for understanding information processing
based on sensory signals. The course integrates presentations about
methods and some of the theory behind them with applications to real
biological systems.    	

Homework will consist of a mix of exercises and analysis of datasets,
usually taken from real measurements. These will therefore involve
computer data processing. For those who need it, the Matlab
interpreter will be introduced in a separate session. A working
knowledge of calculus, complex numbers and some linear algebra will be
required to follow the course. Topics will include:

Methods:
Probability and statistics, random variables
Decision theory, inference, Bayes' rule
Linear systems, Fourier analysis, filtering
Random functions, correlation, power spectra
Shannon entropy and information, encoding and decoding
Time-invariant and time-varying systems
Nonlinearity: adaptive and Wiener-Volterra systems

Applications to biological information processing:
Signals in the lab and signals in the real world
Bacterial chemotaxis: counting molecules
Phototransduction: detection and amplification in a biochemical cascade
Navigation and motion detection: examples of neural computation
Neural coding and information transmission
Adaptive processing as an optimization strategy

Literature: The methods sections will be primarily based on lecture
notes and handouts. In the applications sections we will work with a
combination of notes and papers from the original literature. We will
also treat portions of “Spikes: Exploring the Neural Code” by F.
Rieke, D. Warland, R. de Ruyter van Steveninck, W. Bialek (Bradford
Book - MIT Press, Cambridge MA, 1997), which will be distributed as
notes.