Full Course Descriptions

UNIVERSITY OF TORONTO

2007F ECE1500H – Stochastic processes

Dept. of Electrical and Computer Engineering, University of Toronto

Instructor: Dr. Ben Liang

This course provides an introduction to stochastic processes and probabilistic modeling, with emphasis on communication system applications.  Topics include probability definitions, random variables, sequences of random variables, stochastic convergence, stationarity, ergodicity, power spectra, systems with stochastic inputs, Fourier and K-L expansions, mean-square estimation, Wiener filtering, branching processes, Markov chains and processes.

2007F PSL1052H – Fundamentals of Ion Channels

Dept. of Physiology, University of Toronto

Instructor: Dr. Zhong-Ping Feng

This course is designed for students who are interested in understanding the essential elements and fundamental mechanisms underlying membrane excitability of cells such as neurons, myocytes, and endocrine cells. It highlights the biophysical properties and molecular structure of voltage-gated and ligand-gated ion channels. It covers major classes of ion channels and their integrative role in controlling membrane excitability and cell physiology. It provides advanced information of regulation of ion channel properties and membrane expression, mechanisms of ion channel block, and ion channel related diseases. It also discusses the past and current perspectives of ion channel research. Reading material will be provided prior to lectures.

2007F ECE1460H – Special Topics in Photonics

Dept. of Electrical and Computer Engineering, University of Toronto

Instructor: Dr. Nazir Kherani

Research course. Performed micro-photoluminescence, micro-Raman spectroscopy, and SEM analysis for optoelectronics research project. Culminated in research paper “SEM-mapped micro-photoluminescence studies of highly luminescent micro-clusters in erbium-doped silicon-rich silicon oxide” (Stanley et al 2010).

2008S JEB1444H – Neural Engineering

Institute of Biomaterials and Biomedical Engineering

Instructor: Dr. Berj Bardakjian

General perspective of neural engineering and neurobiology; biological neural networks; parametric neural models using rate processes; nonparametric neural models, using the Volterra-Wiener approach; artificial neural networks as nonparametric neural models.

2008S ECE516H1 – Intelligent Image Processing

Dept. of Electrical and Computer Engineering, University of Toronto

Instructor: Dr. Steve Mann

This course provides the student with the fundamental knowledge needed in the rapidly growing field of Personal Cybernetics, including “Wearable Computing”, “Personal Technologies”, “Mobile Multimedia”, and the merging of communications devices such as portable telephones with computational and imaging devices. The focus is on fundamental aspects of computer vision associated with computationally mediated reality. Topics to be covered include: mediated reality, the Eye Tap principle, collinearity criterion, vitrionic displays, comparametric equations, photoquantigraphic imaging, comparagraphics lightvector spaces, anti-homomorphic imaging, application of personal imaging to the visual arts, and algebraic projective geometry.

2006F ECE445H1 / JEB1451 – Cellular Bioelectricity (cross-listed)

Dept. of Electrical and Computer Engineering, University of Toronto

Instructor: Dr. Berj Bardakjian

This course deals with generation, transmission and significance of bioelectricity in neural networks. Topics covered include: (i) Basic features of neural and cardiovascular systems. (ii) Ionic transport mechanisms in cellular membranes. (iii) Nonlinear circuit models of neuronal membranes. (iv) Propagation of electricity in neural cables. (v) Extracellular electric fields of cellular moving current sources. (vi) Biological neural networks. (vii) Artificial neural networks. (viii) Learning and memory in artificial neural networks. Laboratory topics include: (a) Measurement of surface potentials on human torsos. (b) Generation of cellular electricity in computer models of nonlinear circuits. (c) Propagation of bioelectricity in computer models of nonlinear neural cables. (d) Design of feed-forward artificial neural networks to investigate learning of digits.

Note: This is a cross-listed graduate course that was taken for credit during my undergraduate studies. I list it here because the course content was highly relevant for my future studies.

2008F CSC2600 – Convex Optimization (audited)

Dept. of Computer Science, University of Toronto

Instructor: Dr. Anthony Bonner

Convex optimization is a form of non-linear optimization that includes linear programming and least squares as special cases. Like linear programming and least squares, convex optimization has a fairly complete theory, very efficient algorithms, and a wide range of applications. Application areas include computer science, engineering, statistics, finance, economics and operations research. This course is an introduction to the theory, algorithms and applications of convex optimization. The goal is to give students a working knowledge of the subject, i.e., the ability to recognize, formulate, and solve convex optimization problems. Topics covered will be selected from the following: convex sets and functions, linear and quadratic optimization, geometric and semidefinite programming, strong and weak duality, algorithms for constrained and unconstrained problems, interior point methods, and applications. Prerequisites: Good knowledge of linear algebra and vector calculus, and a willingness to program in Matlab.  Prior exposure to linear programming and basic probability would be helpful, but is not necessary.  Mathematical maturity will be assumed.

Text: Boyd and Vandenberghe, "Convex Optimization".

2009S PSL1071 – Computational Neuroscience (audited)

Dept. of Physiology, University of Toronto

Instructor: Dr. Frances Skinner

Computational neuroscience seeks to understand how the brain and nervous system compute. This highly interdisciplinary field requires both experiment and theory and encompasses several disciplines including physiology and mathematics. This course will focus on selected computational neuroscience aspects including: types of neuron and network models (detailed and simple representations, phase models), and techniques from dynamical systems theory that are used to analyze different models. The emphasis in this course will be on understanding the neurophysiological basis and assumptions in models and possible insights and understanding that can be achieved from the models and analyses.

 


ARIZONA STATE UNIVERSITY

2009F Modeling for molecular and cellular engineering

Department of Bioengineering, Arizona State University

Instructor: Dr. Michael Caplan

Bioengineering includes the application of math and physics to biology and medicine.  Bioengineering includes biology either as part of the inspiration for the technology or by applying a technology to biological or medical applications.  In this course, modeling approaches will be applied to research problems in biology and medicine. Students will:

  • Be able to make simplifying assumptions, derive accurate equations, estimate parameters, solve, interpret, and validate models based on mass transport and chemical kinetics.
  • Be able to apply mass transport and chemical kinetic models to various topics in molecular and cellular biology including but not limited to metabolic processes, cellular signaling, cell surface receptors and their ligands, the components of gene regulatory networks, and the components of the cytoskeleton.
  • Understand the theory underlying modeling of cell adhesion/motility, metabolic pathway analysis, and Bayesian network analysis.
  • Write a research proposal to develop or use a bioengineering model
  • Write an original research article based on their completed model

2009F Modeling and Simulation of Physiological Systems

Department of Bioengineering, Arizona State University

Instructor: Dr. Jit Muthuswamy

This course is designed to give graduate and upper division bioengineering students the ability to understand qualitatively and quantitatively the complex structure-function physiological relationships that exist in living systems.  The laboratory exercises are integral to the course and provide an opportunity to apply and investigate physiological principles that are first introduced in the lectures.

2010S Computational Neuroscience

Department of Bioengineering, Arizona State University

Instructor: Dr. Leonidas Iasemidis

MICRO: Resting potential, the action potential, axonal propagation, the learning neuron, presynaptic correlations and the firing of a neuron - simulations with Poisson processes, field potentials

MESO: Networks of spiking neurons, applications of information theory to spike generation and neural networks, machine learning and data mining

MACRO: Deterministic signal processing, Convolution (e.g., time shift, windowing, Nyquist sampling), correlation, Fourier transform (power density and phase, filtering, leakage, aliasing), coherence, Laplace transform, Z transform (stability and controllability), state space domain (nonlinear systems dynamics, steady states, stability). Statistical signal processing, stochastic signals and systems, white and colored noise-corrupted deterministic signals, Wiener-Hopf equations, Wiener filter, Autoregressive (AR) parametric modeling, principal component analysis (PCA), KL Transform, entropy, information, conditional entropy, joint entropy, mutual information as a nonlinear extension to Cross-Correlation between signals.