QCN track requirements within the PNI Ph.D. program
In addition to the core curriculum required of all PNI graduate students (completed during their first two years), QCN trainees will be required to take two additional electives. These electives provide in-depth coverage of mathematical and computational methods for formal theory development and data analysis in neuroscience. At least one elective must be taken from a set of seven Computational Neuroscience electives (see below). The second elective can be drawn from one of the Computational Neuroscience electives, or from a broader set of elective courses that provide advanced training in relevant quantitative methods (e.g., COS 513, Foundations of Probabilistic Modeling, is taught by David Blei, who developed many of the probabilistic models being taught in the class; see below for the full course list).
QCN Journal Club
To keep QCN trainees informed about relevant developments in the field, all predoctoral and postdoctoral trainees are required to attend a biweekly QCN journal club and present once a year. The journal club organizers (trainees in the program) choose a broad theme for each meeting, always with a quantitative focus, and then solicit volunteers to present a background and a focus paper on the subject. The journal club focuses on recent articles in the literature, but occasional informal presentations of recent findings from the trainee’s laboratory will also be encouraged. If possible, when a QCN-relevant outside speaker is scheduled for another seminar series (e.g., the Neuroscience Seminar), the journal club will read a paper by that speaker before their visit.
Computational Neuroscience Courses
Princeton offers an extensive set of courses in the area of computational neuroscience. Courses include: (1) Computational Neuroscience, (2) Introduction to Connectionist Models, (3) Animal Learning and Decision Making, (4) Mathematical Neuroscience, (5) Computation and Coding in Microcircuits: The Retina and Beyond, (6) Biophysics, and (7) fMRI Decoding. Below are short descriptions of each of the key courses:
• MOL 437/537 Computational Neuroscience: has 6 topics, each lasting 2 weeks. Each topic begins with a lecture, then continues to in-class discussion of papers from the literature. Most recently, topics included: (i) synaptic computation, (ii) persistent neural activity and short-term memory; (iii) neural coding and decoding; (iv) reinforcement learning; (v) generation of neural sequences; (vi) synchrony. For each topic, Matlab-based problem sets are assigned. The final project is an independent investigation, where each student identifies an outstanding computational question connected to a recent paper in the literature, and in consultation with the instructor, designs a computational model or data analysis method to answer that question. Students begin to develop their projects halfway through the semester and present their results in lieu of a final exam.
• PSY 330 Introduction to Connectionist Models: Bridging between Brain and Mind. Explores the use of connectionist (neural network) models to understand high-level psychological phenomena. The course first describes properties of feedforward and recurrent neural networks, then covers Hebbian (unsupervised) and error-driven (supervised) learning algorithms, and finally applies the network models to psychological phenomena, including like perception, attention, memory, priming, language, and executive control. The course includes weekly computer labs that involve hands-on construction and exploration of models, as well as a final project that involves constructing a new connectionist model (or modifying an old one) to understand a neuroscientific phenomenon of interest.
• PSY 338 Animal Learning and Decision Making: Psychological, Computational and Neural Perspectives. Provides a modern, integrative view of classic animal learning phenomena from experimental psychology, through the lens of contemporary learning theory, computational models of learning and decision making, and current neuroscientific knowledge. Topics include: classical conditioning, the temporal difference learning model, neurophysiology of the basal ganglia, instrumental conditioning, actor/critic leaning models, Bayesian inference, and connection to psychiatric disease. The emphasis is on formulating computational models to describe each form of learning and on making connections to biological mechanisms.
• APC/MAT 351 Mathematical Neuroscience. Combines modeling techniques with mathematical methods including differential equations and elementary stochastic dynamical systems. Topics include the Hodgkin-Huxley (HH) equations that describing action potentials (spikes) in single neurons, generalizations of HH describing bursting neurons (e.g. in locomotion and other rhythmic patterns), propagation of action potentials and reaction-diffusion equations (traveling waves in PDEs with one space dimension), and modeling small networks of neurons coupled by chemical synapses and electrical gap junctions. The course discusses reduction of more complex equations to phase oscillators and integrate-and-fire models, as well as leaky-accumulator models and drift-diffusion models of decision-making and information-theoretic approaches to analyzing neural spike trains.
• NEU 508 Computation and Coding in Microcircuits: The Retina and Beyond. Lectures will provide a unified approach to fundamental questions in systems neuroscience, based on current knowledge of computations in retinal circuits and analogies with other systems. Topics will be selected that include clear examples in which behavior or circuit-level function can be understood at the level of cellular and synaptic mechanisms as well as topics in which quantitative theory has been applied successfully. Examples include: computation and adaptation in biochemical cascades; signal amplification and noise in microcircuits; motion processing; dynamic pattern prediction; adaptation using synapses and circuits; coding information with multiple channels; coding information with timing and correlation
• PHY 562 Biophysics. Covers topics with a confluence between elegant quantitative theory and fundamental biological processes. Topics include: photon counting in the early visual system, noise due to molecular fluctuations, fine-tuning vs. robustness in ion channels dynamics and neural adaptation, and efficient representation in neural codes. Prof. Bialek is in the process of writing a book based on his experiences teaching this course.
• ELE/NEU/PSY 480: fMRI Decoding: Reading Minds Using Brain Scans. Students are taught about cutting-edge techniques for finding meaningful patterns in large, noisy datasets, and students learn how to use these techniques to decode (based on fMRI data) the information that is represented in the subject’s brain at a particular point in time. At the start of the semester, students are given a brief overview of brain scanning and how it has been used to study cognitive processes. In weekly lectures, students are taught about important aspects of brain decoding analysis, including pattern classification methods, signal processing methods, and methods for dimensionality reduction and feature selection. Each week, students explore these techniques by applying them to fMRI datasets in computer-based lab sessions. For the final project, students are given a complex real-world dataset (brain scans of people watching an Alfred Hitchcock movie) and they are asked to decode what is happening in the movie based on the brain data.
Additional computational courses
Many courses offered in other departments are appropriate for learning mathematics relevant to particular thesis projects. QCN trainees have the option of taking one of the following courses (note: other courses may satisfy the requirement so long as they have sufficient quantitative/computational content and they are pre-approved by the PNI Curriculum Committee).
- ELE 521 Linear Systems Theory
- ELE 488 Image Processing
- MAE 434 Modern Control
- ELE 523 Nonlinear Systems Theory
- MAE 542 Advanced Dynamics
- COS 402 Artificial Intelligence
- COS 424 Interacting with Data
- COS 513 Foundations of Probabilistic Modeling
- COS 597C Advanced Probabilistic Modeling
- COS 598A Boosting: Foundations and Algorithms
- APC 520 Mathematical Analysis of Massive Data Sets
- ELE 525 Random Processes and Information Systems
- ELE 530 Theory of Detection and Estimation
- ORF 526 Stochastic Modeling
- MOL 515 Methods and Logic in Quantitative Biology
- EEB 355 Introduction to Statistics for Biology
- MAE 546 Optimal Control and Estimation
- ORF 523 Advanced Optimization