Archived Course Catalog for Academic Year 2016 2017

This course aims to provide common mathematical frameworks for adaptation at different scales and to link them with biological reality of control, learning, and evolution. We will look at different classes of adaptation problems using real-world examples of robot control, web searching, gene analysis, imaging, and visual receptive fields.

1. Introduction: variety of learning and adaptation
2. Probability theory: entropy, information, Bayes theorem
3. Pattern classification
4. Function approximation
5. Kernel methods
6. Clustering, Mixture Gaussian, EM algorithm
7. Principal Component Analysis, Self-organizing map
8. Graphical models, Belief propagation
9. Sampling methods, Genetic algorithms
10. Kalman filter, Particle filter
11. Reinforcement learning, Dynamic programming
12. Decision theory, Game theory
13. Multiple agents, Evolutionary stable strategies
14. Communication and cooperation
15. Presentation and discussion

Assumes good knowledge of statistics and ability to look at biological problems in a mathematical way.

OIST courses to complete beforehand: B03 Math 1, B07 Statistical Methods

A102 Mathematical Methods of Natural Sciences

Course Coordinator: Jonathan Miller

Basic course in non-relativistic quantum mechanics. Wave functions and the Schrödinger Equation; Hilbert space; central forces and angular momentum; one-dimensional problems including particle in box, tunneling, and harmonic oscillator; hydrogen atom; Pauli principle; scattering; electron spin; Dirac notation; matrix mechanics; the density matrix; time-independent perturbation theory; Heisenberg picture; time-dependent perturbations; degenerate harmonic oscillators; electrons in a uniform magnetic field; quantized radiation field; absorption and emission of radiation; symmetry principles, entanglement. 

1. Quantum description of a particle, Schrödinger equation, notations
2. The Heisenberg picture and implications
3. Spin ½ particles, magnetic field effects and resonance
4. One-dimensional harmonic oscillators, Hamiltonians
5. Particle in a box; tunneling, coupled oscillators
6. Coherent states; phonons and photons
7. Angular momentum, spherical harmonics
8. Approximation methods
9. Electrons in a uniform field
10. Time-independent perturbation theory
11. Fine and hyperfine structure of the Hydrogen atom
12. Time-dependent perturbation theory
13. Scattering theory
14. Radiation and absorption
15. Entanglement and information transfer

This course introduces students to the fundamental laws that characterize fluids at rest and in motion. The equations for the conservation of mass, for momentum balance, and for conservation of energy are analyzed in control volume and, to some extent, in differential form. Students will learn to select appropriate models and solution procedures for a variety of problems. Flow phenomena that occur in actual flow situations are also illustrated, so that students will learn to assess the strengths and limitations of the models and methods.

1. Introduction (Background, Definitions, general concepts, etc)
2. Fluid Statics (Hydrostatic balance, pressure forces on objects)
3. Fluid Statics (Effects of constant acceleration or rotation)
4. Bernoulli Equation (Use of Newton's second law)
5. Bernoulli Equation (Pressure and its measurement)
6. Fluid Kinematics (Description of velocity field)
7. Fluid Kinematics (Control volume, system representations)
8. Fluid Kinematics (Reynolds transport theorem)
9. Control volume Analysis (Conservation laws)
10. Control volume Analysis (Many applications)
11. Dimensional Analysis (Dynamic similarity)
12. Dimensional Analysis (Pi theorem, Applications)
13. Flow in Pipes, Ducts, Etc. (Laminar and turbulent pipe flow, etc)
14. Flow Around Objects (Boundary layers & potential flow, etc)
15. Compressible Flow (Mach number, sound speed, etc)

Review of geometrical optics; wave properties of light and the wave equation; Helmholtz equation;  wave optics, including Fresnel and Fraunhofer diffraction, transfer functions, coherence, auto and cross-correlation;  Gaussian and non-Gaussian beam profiles; quantum optics and photon statistics; spin squeezing; applications of optics including fiber optics, laser resonators, laser amplifiers, non-linear optics, and optical trapping; quantum properties of light; interaction of photons and atoms.

1. Review of classical optics
2. Ray and wave optics
3. Laser optics and Gaussian beams
4. Non-Gaussian beam optics 
5. Fourier optics 
6. Electromagnetic optics
7. Nonlinear optics
8. Lasers, resonators and cavities
9. Photon optics
10. Photon statistics and squeezed light
11. Interaction of photons with atoms 
12. Experimental applications: Optical trapping 
13. Experimental applications: Laser resonator design
14. Experimental applications: Light propagation in optical fibers and nanofibers
15. Experimental applications: laser cooling of alkali atoms
16. Laboratory Exercises:  Mach-Zehnder & Fabry-Perot Interferometry; Fraunhofer & Fresnel Diffraction; Single-mode and Multimode Fiber Optics; Polarization of Light; Optical Trapping & Optical Tweezers

Advanced course in Quantum Mechanics, based on recent theoretical and experimental advances. Evolution in Hilbert space and quantum bits; conditional quantum dynamics; quantum simulations; quantum Fourier transform and quantum search algorithms; ion-trap and NMR experiments; quantum noise and master equations; Hilbert space distances; Von Neumann entropy; Holevo bound; entanglement as a physical resource; quantum cryptography; lab: quantum eraser, interaction free measurement.

1. Quantum Mechanics: Mathematical Framework
2. Quantum Mechanical Postulates
3. Quantum Measurements
4. Quantum Algorithms
5. Quantum Computing: Physical Realisations
6. Quantum Noise
7. Entropy and Information
8. Quantum Statistical Mechanics
9. Quantum Information Theory

The interface between engineering and miniaturization is among the most intriguing and active areas of inquiry in modern technology. The aim of this course is to illuminate and explore microfluidics as an interdisciplinary research area, with an emphasis on emerging microfluidics disciplines, including molecular assembly to bulk and device level scales, with applications in novel materials synthesis, bio-microtechnology and nanotechnology.

The course will begin by highlighting important fundamental aspects of fluid mechanics, scaling laws and flow transport at small length scales. We will examine the capillary-driven, pressure-driven, and electro-kinetic based microfluidics. We will also cover multi-phase flow, droplet-based microfluidics in microfluidics. This course will also illustrate standard microfabrication techniques, micro-mixing and pumping systems. 

1. Introduction to microfluidics; Scaling analysis
2. Low Reynolds number flows
3. Pressure-driven microfluidics
4. Capillary-driven microfluidics
5. Microfabrication
6. Diffusion in microfluidics
7. Mixing in microfluidics
8. Droplet microfluidics and 2-phase flows
9. Bio-MEMs

In this course, students will learn basic principles of electrochemistry with a particular focus on redox behavior of transition metals including metalloproteins. Modern research in application of transition metal complexes for renewable energy storage and production will be highlighted and discussed in detail, including metal-catalyzed water oxidation, proton reduction and CO2 reduction processes. The course will provide practical training in voltammetric techniques and spectroelectrochemistry, and analysis and simulation of cyclic voltammetry data.

1. Basic aspects of electrochemistry
2. Electrochemical instrumentation
3. Cyclic voltammetry: Reversible, irreversible and quasireversible processes
4. Cyclic voltammetry: Effect of coupled chemical reactions; Digital simulation of cyclic voltammograms
5. Bulk electrolysis and pulsed voltammetric techniques
6. Hydrodynamic techniques: application for studying reaction intermediates and mechanisms.
7. Electrochemical behavior of transition metal complexes.
8. Redox-active metalloproteins
9. Redox-induced structural reorganization of metal complexes
10. Electrocatalysis by transition metals for renewable energy production and storage: water splitting to O2and H2
11. Transition metal-catalyzed electroreduction of CO2 and dehydrogenation of formic acid and alcohols: application for hydrogen storage
12. Immobilization of metal catalysts on electrode surface
13. Photoelectrochemistry
14. Application of electrochemical processes in chemical industry

The course provides an understanding of the neuronal mechanisms that underlie animal behavior. We will study the neuronal mechanisms for specialized animal behaviors such as sensory processing, motor pattern generation, and learning by reading original papers, which also provide an understanding of experimental technique. The course further discusses the evolutionary strategy and the biological ideas of animal behavior and underlying neuronal mechanisms.

1. Introduction (Basic Neurophysiology and neuronal circuits)
2. Sensory information I: Visual and Auditory (map formation, plasticity and critical period, etc.)
3. Sensory information II: Olfactory (Chemical) and other senses
4. Sensory perception and integration I (Echolocation, Sound localization, etc.)
5. Sensory perception and integration II (Sensory navigation, etc.)
6. Motor control I (Stereotyped behavior)
7. Motor control II (Central pattern generator)
8. Sexually dimorphic behavior
9. Learning I (Learning and memory)
10. Learning II (Associative learning)
11. Learning III (Sensory motor learning during development)
12. Learning VI  (Spatial navigation)
13. Behavioral plasticity and the critical period
14. Recent techniques in neuroethology

The course Controversies in Science aims to develop critical thinking and argument, essential skills for effective independent scientists. The course will be flexible in content and presentation. Invited lecturers will present topics of some controversy or recent interest in science and lead debates by the students. We will also look at some historical controversies in different fields such as neuroscience and genetics, in which we will assign students to take sides by reading only one side of a specific argument, and encourage them to discuss the issue and arrive at a resolution in class. 

1. The Scientific Method, Ockham's Razor, Basic Philosophy of Science
2. Boundaries of Science, L’Affaire Sokal, “Crackpots”
3. Science & Racism in 1940s Germany and Japan
4. Science and Capitalism: the pharmaceutical industry & biomedical science
5. Science and Communism: Lysenko
6. Scientific Misconduct I: Piltdown Man
7. Scientific Misconduct II: Recent Cases
8. Insights ahead of their time: Mendel and others
9. Paradigm shifts: the reception of evolutionary biology
10. Science and Religion: opposition to evolution
11. Science and the media: the case of the autism-vaccination link, and others
12. Science and the law: the suppression of psychedelics research
13. Science and war: the making of the nuclear bomb
14. The animal rights movement and science
15. Conclusions: science as a social enterprise

The course is designed as a mix of introductions into selected topics in the theory of transmission electron microscopy followed by practical demonstrations and hands-on exercises, which provide an opportunity to comprehend the concepts by experimenting with commonly-used image processing software. Students will be required to read and digest scientific papers for a subset of lecture topics on their own, which will subsequently be discussed jointly during student presentations with the goal to immerse them into the subject without passive consumption. The lectures cover several important concepts of the physics of image formation and analysis, which require a basic level of mathematics. An emphasis will be given to highlighting common properties between diffraction and image data and how to take advantage of tools from both techniques during the final image processing projects.

1. History of the TEM / Design of a TEM - Lecture
2. Design of a TEM (cont’d) -  Lecture
3. Design of a TEM (cont’d) -  Lecture
4. Demonstration of a TEM - Demo
5. Math refresher / Electron waves - Lecture
6. Fourier transforms - Lecture
7. Intro to image processing software in SBGRID - Practical
8. Image alignment - Practical
9. Contrast formation and transfer -  Lecture
10. Image recording and sampling - Student presentation
11. Applications in biology - Lecture
12. Preparation of biological samples -  Demo
13. Low-dose cryo-EM - Student presentation
14. 2D crystallography - Student presentation
15. Overview of the single particle technique -  Lecture
16. Review of theory - Lecture
17. Electron tomography (guest lecture) - Lecture
18. Physical limits to cryo-EM - Student presentation
19. Particle picking -  Practical
20. Classification techniques -  Student presentation
21. 3D reconstruction - Student presentation
22. Image processing project 1 - Practical
23. Resolution-limiting factors -  Student presentation
24. Refinement and sources of artifacts -  Student presentation
25. Image processing project 2 - Practical
26. A sampling of original literature - Discussion

Ideally combined with A403 Strucutral Biology: Protein Xray Crystallography (Samatey) and A410 Molecular Electron Tomography (Skoglund)

The course will show through theoretical and practical work how the 3D structure of a protein can be determined to about 2nm resolution directly in a buffer solution or in tissue. The students will get a direct hands-on experience of the processes involved in the practical and theoretical aspects of molecular electron tomography (MET). The students will be aware of how to carry out their own MET reconstruction and understand the limitations of the method and how to optimize its use.

1. Learning the computer
2. Learning the computer
3. Practical Aspect of sample preparation for cryo-TEM
4. Sample preparation for cryo-TEM
5. Sample preparation for cryo-TEM; data collection
6. 3D reconstruction
7. 3D reconstruction
8. 3D reconstruction
9. Generating simulation-data
10. 3D reconstruction from simulation-data
11. 3D reconstruction from simulation-data
12. Electron Microscopy: Sample Preparation

This course introduces necessary background and fundamental mathematics for graduate biologists.  The course emphasizes relevant topics in calculus, probability, and numerical methods with their applications in biology.

1. History of mathematics and relation to natural sciences.
2. Geometry: Distance, Euclidean and other spaces.
3. Geometry: Vectors, dot and cross products.
4. Geometry: Computation of angles and distance from a point to a line segment and a plane.
5. Geometry: Volume of a tetrahedron. Application to concept of rank.
6. Probability: Concepts (frequentist and Bayesian), independence, conditional probability, Bayes’ Theorem.
7. Probability: Random walk, Bernoulli processes, Stirling’s formula, normal distribution.
8. Probability: Nearest-neighbour distance distribution for randomly distributed points in a plane.
9. Calculus: Concepts of limit and slope. Application to biology.
10. Calculus: Taylor expansions. Exponential decay.
11. Calculus: Harmonic oscillator. Diffusion.
12. Numerical Methods: Roots of a quadratic polynomial.
13. Numerical Methods: Least squares curve fitting. Bisection.
14. Numerical Methods: Approximation of functions by polynomials.
15. Student presentations.

Principles of physics of central relevance to modern biological analysis and instrumentation are introduced with an emphasis on application in practical research areas such as electrophysiology, optogenetics, electromagnetics, the interaction of light and matter, and brain recording, stimulation, and imaging.

1. Introduction - Physics in Biology: How physics contributes to life sciences.
2. Nature of light
3. Nature of matter
4. Fundamentals on light and matter interaction
5. Fluorescence and its applications
6. Biophotonics
7. Photosynthesis
8. The physics of optogenetics
9. Linear optics
10. Microscopy
11. Non-linear optics, lasers, two-photon microscopy, super resolution microscopy
12. The physics of electron microscopy
13. The physics of DNA, lipid membranes, and proteins
14. Bioelectricity
15. Electronics for electrophysiology
16. Magnetic resonance

This course aims to introduce the function of the brain at the macroscopic level, namely, the control of behaviors and the cognitive and adaptive mechanisms behind it. The topics include the following: Reflex, classical and operant conditioning. Perception, adaptation, and attention. Feedback and predictive control. Procedural and declarative memory. Motivation and emotion. Thinking and reasoning. Communication and language. Psychological disorders. Clinical and experimental neuropsychology.

Research methods (I)

• Ethics
• Hypothesis testing
• Dependent and independent variables
• Reliability and validity
• Bias, blinding

Research methods (II)

• Data collection methods
• Observation
• Surveys
• Experimental and quasi experimental designs
• Data analysis

Learning and behavior (I)

• Classical, Pavlovian, respondent conditioning (elicited responses)
• Operant, instrumental conditioning (instrumental responses)

Learning and behavior (II)

• Reinforcement and punishment
• Operant schedules

Learning and behavior (III)

• Behavior modification
• Applications

Motivation and reward

• Drug addiction
• ADHD

Memory and cognition (I)

Memory and cognition (II)

Perception and attention

Behavioral neuroscience (I)

Behavioral neuroscience (II)

Genes and behaviour

Animal models

Life span

A graduate course in analytical mechanics, covering the essential equations and their applications, to prepare for later courses in electrodynamics and quantum physics.  This course assumes undergraduate level knowledge of mechanics and a firm grasp of calculus and vector mathematics. An understanding of static electromagnetic fields is extended through Maxwell’s equations to a discussion of dynamic vector fields and electromagnetic waves.  Along the way, numerous physical and technical applications of these equations are used to illustrate the concepts, including dielectrics and conductors, wave guides, and microwave engineering.  Special relativity is introduced with discussion of relativistic and non-relativistic motion and radiation, using linear accelerators and synchrotron radiation as illustrative applications.

1. Charge and Gauss's Law
2. Current and Ampere's Law
3. Divergence and Rotation
4. Induction
5. Capacitance and Inductance
6. Maxwell's Equation 1
7. Maxwell's Equation 2
8. Vector and Scalar Potentials
9. Electromagnetic Waves
10. Energy, Dispersion
11. Impedance Concept
12. Reflection and Matching Condition
13. Relativistic Equation of Motion
14. Radiation from a Moving Charge
15. Synchrotron Radiation

Matter can exist in many different phases. The aim of this course is to explain why, and how one phase can transform into another. Starting from the question “what is temperature?”, the ideas of entropy, free energy, and thermal equilibrium are introduced, first in the context of thermodynamics, and then as natural consequences of a statistical description of matter. From this starting point, a simple physical picture of phase transitions is developed, with emphasis on the unifying concept of broken symmetry. The course is designed to be accessible to students from a wide range of educational backgrounds. It will be assessed through weekly problem sets, and a final presentation on a modern example of the application of statistical physics ideas, chosen by the student.

1. General overview of phase transitions - what are they, and where do they happen?

2. Introduction to the basic concepts of thermodynamics - temperature, entropy, thermodynamic variables and free energy - through the example of an ideal gas.
3. Introduction to the basic concepts and techniques of statistical mechanics - phase space, partition functions and free energies. How can we calculate the properties of an ideal gas from a statistical description of atoms?
4. Introduction to the idea of a phase transition. How does an non-ideal gas transform into a liquid?
5. The idea of an order parameter, distinction between continuous and first order phase transitions and critical end points. How do we determine whether a phase transition has taken place?
6. Magnetism as a paradigm for phase transitions in the solid state - the idea of a broken symmetry and the Landau theory of the Ising model.
7. Universality - why do phase transitions in fluids mimic those in magnets? An exploration of phase transitions in other universality classes, including superconductors and liquid crystals.
8. Alternative approaches to understanding phase transitions: Monte Carlo simulation and exact solutions.
9. How does one phase transform into another? Critical opalescence and critical fluctuations. The idea of a correlation function.
10. The modern theory of phase transitions - scaling and renormalization.
11. 11.To be developed through student presentations: modern applications of statistical mechanics, with examples taken from life-sciences, sociology, and stock markets.

In this course, students will learn basic principles of immunology including the cellular and molecular mechanism of innate and adaptive immunity. The course also provides the clinical importance of immunology in various diseases such as HIV/AIDS, autoimmunity and allergy. Then, students will learn how the immune response can be manipulated by vaccination to combat infectious diseases and cancer.

1. Basic concepts in immunology
2. Innate immunity
3. Antigen recognition by B-cell and T-cell receptors
4. The generation of lymphocyte antigen receptors
5. Antigen presentation to T lymphocytes
6. Signaling through immune system receptors
7. The development and survival of lymphocytes
8. T cell-mediated immunity
9. The humoral immune response
10. Dynamics of adaptive immunity
11. The mucosal immune system
12. Failures of host defense mechanism
13. Allergy and Hypersensitivity
14. Autoimmunity and Transplantation
15. Manipulation of the immune response

This course covers biological phenomena at or above the scale of a single organism.  We will broadly cover topics in evolutionary biology and ecology including but not limited to population genetics, animal behavior, adaptation and natural selection, speciation, phylogenetics, population biology, community ecology, ecosystem ecology, and macroecology. 

Course Content: 

1. Introduction, levels of organization in biological systems.
2. Taxonomy, systematics, phylogenetics.
3. Biodiversity
4. Energy flows and transformations in biological systems.
5. Genomics and Genetics of Adaptation
6. Physiological ecology.
7. Population dynamics and regulation
8. Life histories
9. The evolution of sex and the evolution of cooperation
10. Community Ecology
11. Ecosystem Ecology
12. Global Climate system and Climate change
13. Conservation Biology

In this course, students will learn to formulate mathematical models leading to rate equations, transport equations, and variational principles. They will also learn techniques for extracting qualitative and quantitative information from those models. In particular, they will study phase line analysis, phase plane analysis, the method of characteristics, dimensional analysis, and methods for constructing similarity solutions.

Rate equations

1. Particle motion
2. Chemical reaction kinetics
3. Ecological and biological models
4. One-dimensional phase-line analysis
5. Two-dimensional phase-plane analysis

Transport equations

1. Reynold’s transport theorem
2. Deriving conservation laws
3.  Linear advection equation
4.  Systems of linear advection equations
5.  Method of characterisitcs
6.  Quasilinear equations and shocks

Variational principles

1. Functionals
2. Necessary and sufficient conditions for extrema
3. Essential and natural boundary conditions
4. Application to classical mechanics
5. Treatment of constraints

Dimensional scaling analysis

1. Dimensional quantities
2. Dimensional homogeneity
3. Nondimensionalization
4. Applications
5. Buckingham Pi theorem

Self-similar solutions of partial differential equations

1. Scale-invariant symmetries
2. Similarity variables and solutions
3. Application to the heat equation
4. Application to a nonlinear diffusion equation

In this course, students will learn to apply regular and singular perturbation methods to ordinary and partial differential equations. They will also be exposed to boundary-layer theory, long-wave asymptotic methods for partial differential equations, methods for analyzing weakly nonlinear oscillators and systems with multiple time scales, the method of moments, the Turing instability, pattern formation, and Taylor dispersion. 

Perturbation methods

1. Asymptotic expansions
2. Regular expansions
3. Singular perturbation problems
4. Applications of perturbation methods

Boundary-layer theory

1. Inner and outer asymptotic solutions
2. Distinguished limits
3. Matching
4. Applications of boundary-layer theory

Long-wave asymptotic solutions to partial differential equations

1. Separation of variables
2. Dirichlet problem for a slender rectangle
3. Application to wires

Weakly nonlinear oscillators

1. Linear oscillators
2. Poincare–Lindstedt expansions
3. Method of multiple time scales

Fast/slow dynamical systems

1. Strongly nonlinear oscillators
2. Chemical reactions
3. Enzyme kinetics

Reduced models for problems involving partial differential equations

1. Method of moments
2. Turing instability and pattern formation
3. Taylor dispersion and enhanced diffusion

This course will provide an introduction to Evolutionary Biology focusing on the developmental process of multicellular organisms for students with and without an undergraduate background in this field. Two major goals in this course will be to understand evolutionary changes in development and to learn modern creatures and technologies employed for addressing issues in evolutionary developmental biology.This course presents the basic principles and recent findings in evolutionary developmental biology.

1. Animal phylogeny
2. Gain and loss in evolution
3. Gene homology
4. Cell homology
5. Gene expression
6. Basic body plan I: Embryogenesis
7. Basic body plan II: Main body axes
8. Basic body plan III: Main body axes
9. Signaling pathways and gene regulatory networks
10. Body axes in basal metazoans
11. Multicellularity
12. Research tools I: Genome/transcriptome analysis and molecular phylogeny
13. Research tools II: New animal models
14. Research tools III: Gene function analysis

No prior knowledge assumed