Approved CNS Classes
Bioengineering:
| Course Title | Description |
|---|---|
| Neurodynamics (BGGN 260) | Introduction to the nonlinear dynamics of neurons and neural systems using bifurcation theory and chaotic motions, at different levels of abstraction, e.g., biophysical and “reduced” models for analysis of regularly spiking and bursting cells. |
| Magnetic resonance imaging (BENG 278) | This laboratory course provides hands-on experience with MR physics, data acquisition, image formation, and data analysis, using a human MRI scanner. It will cover basic principles of MRI and key applications, including scanner hardware, spin echoes, gradient echoes, echo-planar imaging, MR angiography, fMRI, and perfusion imaging. |
| Principles of biomedical imaging (BENG 280A) | Fundamentals of Fourier transform and linear systems theory including convolution, sampling, noise, filtering, image reconstruction and visualization with an emphasis on applications to biomedical imaging. Examples from optical imaging, CT, MR, ultrasound, nuclear, PET, and radiography. |
| Advanced biophotonics (BENG 247) | Basic physics and chemistry of interaction of photons with matter; photonic radiation pressure; advanced optoelectronic detection systems, devices, methods, time-resolved fluorescent, chemiluminescent methods, fluorescent energy transfer techniques, quantum dots, near-field optical techniques, mechanisms of light sensitive biological systems including chloroplasts for photosynthetic energy conversion and basis of vision processes. |
Data Science
| Course Title | Description |
|---|---|
| Probability and statistics for data science (DSC 212) | Probability, random variables, distributions, central limit theorem, maximum likelihood estimation, method of moments, confidence intervals, hypothesis testing, Bayesian estimation, introduction to simulation and the bootstrap. |
| Topological data analysis (DSC 214) | Topology provides a powerful way to describe essential features of functions and spaces. In recent years topological methods have attracted much attention for analyzing complex data in many fields, e.g., graphics, visualization, neuroscience, and material science. This course introduces basic concepts and topological structures behind these developments, algorithms for them, and examples of applications. |
| Machine learning (DSC 240) | A graduate level course in machine learning algorithms: decision trees, principal component analysis, k-means, clustering, logistic regression, random forests, boosting, neural networks, kernel methods, deep learning. |
| Statistical models (DSC 241) | Linear/nonlinear models, generalized linear models, model fitting and model selection (cross-validation, knockoffs, etc.), regularization and penalization (ridge regression, lasso, etc.), robust methods, nonparametric regression, conformal prediction, causal inference. |
| Geometry of data (DSC 205) | This course will cover graph-based data modeling, analysis, and representation. Topics include spectral graph theory, spectral clustering, kernel-based manifold learning, dimensionality reduction and visualization, multiway data analysis, graph signal processing, graph neural networks. |
Electrical and Computer Engineering
| Course Title | Description |
|---|---|
| Linear systems (ECE 101) | Complex variables. Singularities and residues. Signal and system analysis in continuous and discrete time. Fourier series and transforms. Laplace and z-transforms. Linear Time Invariant Systems. Impulse response, frequency response, and transfer functions. Poles and zeros. Stability. Convolution. Sampling. Aliasing. |
| Digital signal processing (ECE 161B) | Sampling and quantization of baseband signals; A/D and D/A conversion, quantization noise, oversampling and noise shaping. Sampling of bandpass signals, undersampling downconversion, and Hilbert transforms. Coefficient quantization, roundoff noise, limit cycles and overflow oscillations. Insensitive filter structures, lattice and wave digital filters. |
| Parameter estimation I (ECE 275A) | Linear least Squares (batch, recursive, total, sparse, pseudoinverse, QR, SVD); Statistical figures of merit (bias, consistency, Cramer-Rao lower-bound, efficiency); Maximum likelihood estimation (MLE); Sufficient statistics; Algorithms for computing the MLE including the Expectation Maximization (EM) algorithm. The problem of missing information; the problem of outliers. |
| Parameter estimation II (ECE 275B) | The Bayesian statistical framework; Parameter and state estimation of Hidden Markov Models, including Kalman Filtering and the Viterbi and Baum-Welsh algorithms. A solid foundation is provided for follow-up courses in Bayesian machine learning theory. |
Physics
| Course Title | Description |
|---|---|
| Neurophysics of brain circuits and networks (PHYS 278) | Information processing in the brain through physical reasoning and mathematical modeling. Topics include simplified models of neuronal circuits, dynamics of recurrent and oscillatory networks, attractor states, and network computations underlying memory, perception, and motor control. Emphasis on analytical tools, including linear analysis, statistical mechanics, and information theory, with strong connections to ongoing experimental efforts in connectomics and large-scale recording. |
| Nonequilibrium statistical mechanics (PHYS 210B) | Transport phenomena; kinetic theory and the Chapman-Enskog method; hydrodynamic theory; nonlinear effects and the mode coupling method. Stochastic processes; Langevin and Fokker-Planck equation; fluctuation-dissipation relation; multiplicative processes; dynamic field theory; Martin-Siggia-Rose formalism; dynamical scaling theory. |
| Information Theory and Pattern Formation in Biological Systems (PHYS 273) | This course discusses how living systems acquire information on their environment and exploit it to generate structures and perform functions. Biological sensing of concentrations, reaction-diffusion equations, the Turing mechanism, and applications of information theory to cellular transduction pathways and animal behavior will be presented. |