# (older syllabus

## Contents

- 1 Principles of Neuroimaging A - Class Schedule and Syllabus
- 1.1 Week 1: Orientation to Neuroimaging, Neurons, Brains
- 1.2 Week 2: Linear Systems
- 1.2.1
*Monday 1/11"***Transforms and the Convolution Theorem** - 1.2.2
*Wednesday 1/13/10***Fourier Transform Properties** - 1.2.3 Problem Set 3 will be a matlab assignment.
- 1.2.4 "Monday 1/18"
**Martin Luther King day observed** - 1.2.5
*Wednesday 1/20***Stats 101**

- 1.2.1
- 1.3 Week 3: Statistics for Neuroimaging
- 1.4 Week 5: Noise, Circuits
- 1.5 Week 6:
- 1.6 Mid-Term
- 1.7 Week 7:
- 1.8 Week 8:
- 1.9 Week 9:
- 1.10 Week 10:
- 1.11 Week 11:
- 1.12 Topics To Be Scheduled

# Principles of Neuroimaging A - Class Schedule and Syllabus

Course main page Principles_of_Neuroimaging_A The course and classes will move quite quickly this year. We have two Monday holidays. If people can agree, I can try to move lectures to a different day of the week (say, 1/19 and 2/16) to get these back.

## Week 1: Orientation to Neuroimaging, Neurons, Brains

### Monday 1/4/2010 **Orientation & Neurons**

Please come to class having read the following papers:

- Readings

- "If Neuroimaging is the Answer, What is the Question?" Kosslyn, 1999
- The Active Brain
- Slides shown in class

In this first class we will review the basics of neurophysiology with an eye towards what signals of brain function might be visible to the neuroimager. We will discuss information coding

*Suggested Further Reading*

- Neuroanatomy Programmed Learning
- Squire, Fundamentals of Neuroscience
- Kandel, et al., "Principles of Neural Science"

- Optional reading

This paper, by Malhi, is a nice orientation in methods of neuroimaging. Making sense of neuroimaging in psychiatry

### "Wednesday 1/6/10" **The Organization of the Human Brain**

Guest Lecturer: Susan Bookheimer We will discuss the general organization of the human brain, and the regional specialization of cortical areas. The emphasis will be on understanding principles of organization:

- Phylogenetic Layering
- Functional Specialization
- Principles Divisions of the Brain
- Brain Systems

- Readings

### Problem Set 1 Neuroanatomy. Due in class 1/11.

We will be studying linear systems next week. This coming week until Monday would be a good time to review your calculus fundamentals:

*Derivatives of Polynomials**Integrals of polynomials**Basic trig + derivatives and integrals of sine and cosine functions*

When we start on the linear systems section, we will be using these fundamentals to develop the LaPlace and Fourier transforms, which involve the use of imaginary numbers. The math content for that section is largely contained in this link: Mathematical Tools.

Please let me know by email or other means if this material looks too difficult.

- Readings

## Week 2: Linear Systems

Why the emphasis on Linear Systems? Because they are actually *easy* (as compared to non-linear systems, which are not.) As we go through this course, we will see many ways in which linear systems theory is applied to:

- Modeling of Neural Systems
- Extraction of Signal from Noise
- Design of Circuits
- Image Enhancement
- Understanding of Image artifacts, and others.

Linear systems analysis is one of the great technologies of the 20th and 21st century. It is now the basis for virtually all electronics design, and its extension into the discrete (digital) domain is the basis for most of modern signal processing.

In our specific case, we will use these few basic principles of linear systems to understand both the instruments we use and the neuroimaging signals we collect. When you have mastered this material, you should be in a much better position to model the systems that you study in order to develop an approach to studying them.

*Monday 1/11" ***Transforms and the Convolution Theorem**

**Transforms and the Convolution Theorem**

- Required Reading - Mathematical Tools

Please see MATLAB linearity demo

If you are the type who sees beauty in mathematics, the Euler identity may be one of the most beautiful pieces of math in the world.

*Wednesday 1/13/10* **Fourier Transform Properties**

- Example transform derivations
- The Convolution theorem
- Oddness (and Even-ness)
- The Fourier Shift Theorem

Please see MATLAB demo of Fourier transforms and convolution

Time Allowing: Laplace transform and linear solutions to differential equations

### Problem Set 3 will be a matlab assignment.

Problem Set 1 is in two parts: Problem Set 1A and Problem Set 3B

---

I suggest very strongly that you brush up on linear algebra during this week in anticipation of Dr. Sugar's lectures in statistics. In particular, I would like you to have an understanding of :

*Matrices as solutions to linear equations - determinants and inverses**Matrix multiplication*

For these, I can recommend the Hefferon text noted above.

### "Monday 1/18" **Martin Luther King day observed**

*Wednesday 1/20* **Stats 101**

We will consider the general problems of statistical inference, with a concentration on developing an intuitive understanding of statistical concepts.

*Review of*:

- Descriptive Statistics: mean, mode, variance, standard deviation
- Statistical Inference. The Binomial and Normal Distribution
- Basic Tests: t-test, linear correlation
- Modeling and non-linear relations
- Bayes rule

The first problem set for the course will be a matlab assignment. If you have not already done so, please make certain that you have the program available.

Suggested reading

- Statsoft online text (
*free*) - The Cartoon Guide to Statistics - Gonick $17.95 new
- The latter teaches stats at what I feel to be the right level - developing intuitions about the kinds of questions that can be answered using stats and about the statistical tests and measures

Slides (with notes) as presented in class

#### Problem Set 3

## Week 3: Statistics for Neuroimaging

Suggested Readings On-line lectures by Jeanette Mumford Statistical Modeling and Inference (pdf)

### Week 4:

**In this "draft" schedule, I have class on ML King Day. I would like to find an alternate day for this missed class.**

*Part II*- Lecture slides: Statistical Modeling and Inference (pdf)

*Monday 1/18/10* **Statistics II** Guest Lecturer: Catherine Sugar

- The General Linear Model
- Linear Algebra applied to Statistical Solutions
- Analysis of Variance

*Wednesday 1/20/10* **Statistics III** Guest Lecturer: Catherine Sugar

- Fixed and Random Effects
- Repeated measures

- Bonferroni and Other Corrections

- Non-Parametric Methods
- Autocorrelation
- Unknown Distributions

#### Problem Set 2

==Week 4

## Week 5: Noise, Circuits

Noise comes in all shapes and colors. It is present in every measurement we make, from an EEG voltage to an estimate of the effects of dopamine on forebrain signal. Our best weapons are an understanding of the statistical properties of noise, the sources of noise and the ways to control it. Noise in the discrete digital domain is special, as it is both *created* by digitization and amplified by sampling.

*Monday 2/1/10* **Noise**

It is what you *don't* want.

- Additive noise
- White Noise
- Boltzmann noise
- Colored Noise
- Gaussian Noise
- Coherent noise
- Sampling Errors
- Aliasing
- Quantization noise
- Spectral filtering

Time allowing: Intro to Laplace

*Wednesday 2/3/10* **Electrical and Electronic Circuits**

Why circuits?

- (Virtually) Every device you use in your research is electronic. You access your primary data only indirectly
- The device you
*really*want in your lab doesn't exist. You very well may have to make it. - There are electronic analogs to most of the linear systems that you have so far studied (and
*vice versa*- the tools you now understand can be used to analyze and predict circuit behavior).

If you have not had any of this background, you might want to have a look at this handout, Electrical Circuits, in advance. There are near infinite numbers of resources on the web that cover similar material (near enough to infinite that by the time you read all of them, there would be a whole new set.) I have recently come across a link to Online Books: All About Circuits *IF* you want practical hands-on knowledge about this material, my all-time favorite text is "Horowitz and Hill: *The Art of Electronics.*" The latest edition, however, is dated 1989 and a new third edition is promised. I have therefore stopped short of recommending a purchase unless your need to make circuits is immediate. In this book, you will find an excellent education on the fundamental principles of electrical circuits and an incredible compendium of practical data, such as how to assemble circuit boards, how to make measurements, etc...)

I found a nice intro lecture on charge, current and voltage.

**TEACHING SLIDES on Circuits**: Circuits 1 & 2

We will discuss:

- Gain
- Trasformers
- Rectifiers
- Active Elements

- -
*Amplifiers* - -
*Transistors* - -
*Op Amps*

- -

- Solutions with Matrices

## Week 6:

*Monday 2/8/10 *Circuits, cont'd

- Laplace transform analysis
- Op Amp Circuits
- Active Filters
- Noise Control

## Mid-Term

- The midterm will be a take home test. Due in class on 2/16/10

*Wednesday 2/10/10* **A Practical Circuit**

- Design Demo of an EEG Circuit

## Week 7:

**In this "draft" schedule, I have class on Presidents Day. I would like to find an alternate day for this missed class.**

*Monday 2/15/10* **Topic**

Review of MidTerm

*Wednesday 2/17/10* **Topic**

## Week 8:

*Monday 2/22/10* **Topic**

*Wednesday 2/24/10* **Topic**

## Week 9:

*Monday 3/1/10* **Topic**

*Wednesday 3/3/10* **Topic**

## Week 10:

*Monday 3/8/10* **Topic**

*Wednesday 3/10/10* **Topic**

## Week 11:

*Monday 3/15/10* **Final Exams**

## Topics To Be Scheduled

- Point Spread Functions

- Principles of Optical Neuroimaging and Microscopy
- Lenses
- Airy Disk
- Blur as convolution
- Image sharpening
- Photons and Photodetection
- Color
- Fluorescence
- Lasers

- Practical uses of EEG

- EEG and fMRI Demo

- Exploratory Data Analysis
- PCA
- ICA
- Blind Source Separation

- Loose ends:
- Bandwidth and SNR
- Interpretation of FT space as phase
- Formal discussion of electricity and magnetism
- Line broadening
- Mixing and modulating

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Jonathan Wynn - EEG in Schizophrenia Research.

Dr. Wynn has suggested looking at these two articles: