1. Increase the number of females in the sample be eight, then perform a t-test on the means
2. Continue collecting more data until the probability of a two-tailed t-test statistic comparing males and females is less tan 0.01.
3. Collect the heights of "all" males and females at UCLA and then calculate the t--statistic to determine if the heights differ at the assigned probability level
4. Collect height data from an age-matched sample in the surrounding community.
5. Add to the sample until there are exactly 100 males and 100 females, and calculate if the heights differ by more than 1%.
6. None of the above.
7. All of the above

[edit] Programming

Formally, students are required to have a background in at least some programming language. The fact of the matter is that Neuroimaging is computationally intensive; programming is a basic skill for this work. I intend to prepare problem sets that will require programming to solve.
This year, all of our programming will be done using MATLAB, purchase of which is a course requirement. The ASUCLA student store has the licenses for students at an incredibly discounted price of $99. You will not regret owning this.

[edit] Mathematics

Can you solve for y or in these equations?

If y = 3x² + 6x + 2, what is ?
If not, please let me know, and we will try to remedy things. In the meantime, there are a number of excellent online math tutorials. For matrices, may I suggest:

• Harvey Mudd mathematics online tutorial
• S.O.S. Mathematics
• MATLAB online tutorial
• Programmed text in Linear Algebra - Hefferon

These are all excellent free sources. Please feel free to suggest more.

[edit] Functional Neuroanatomy

A Functional Neuroanatomy study group exists under the direction of Nanthia Suthana (email). Please contact her with questions about how to get involved. You should know the major structures of the brain, such as the cortical gyri, and have a reasonable grasp of their known functions.

[edit] Class Meetings

Note: there is another room change!

Class will meet from 2 to 4 pm on Mondays and Wednesdays. Our Monday classroom will be 78-215 and our Wednesday classroom will be 37-415, both in the NPI.

[edit] Concepts and Teaching Plan

We will start looking at a few papers that use images of various kinds to address neuroscientific questions. Here, you should be paying especial attention to how the images are used in a theoretical context. Did the investigator pose the question first then collect the data? What is the role of a posteriori interpretation (reverse inference)? What is assumed about the ground truth of the phenomena exposed by neuroimaging?

After this, we will begin to look at the properties of neurons that might make them visible to our neuroimaging tools. We will consider signaling in neurons, its energetic costs, and the changes in the cellular milieu that are associated. We will begin to consider the optical properties of neurons and their size scale, and the chemical changes that are associated with neuroal activity. As best possible, I will try to incorporate neurogenetics here to consider cell identification and labeling.

At the same time, we will start the practical work in MATLAB. If you are already MATLAB proficient, consider your assignment to include bringing the rest of the class up to speed as quickly as possible so that we can move on. As noted above, MATLAB will be used for our quantitative examples, but it is also a strong standard for image and numerical analysis in the sciences and a relatively easy programming language to use, with a pretty quick startup.

We will start also, on developing the mathematical tools we will need to carry forward. In the digital age, we are dealing always with very large numbers of data points and are forced to deal with large sample sizes (at the very least, a large number of pixels) and we need means of quantitative summary. Our initial steps will be in very basic statistical concepts in anticipation of doing more and deeper work later.

This will be followed by work on analytic math, building to transform theory. Depending on what I find out about your skills level in maths, we may start with some calculus review, or we may have to schedule one-on-one meetings to balance everyone’s background. The goal here is to develop a framework with which to understand what happens to the ground truth data we try to observe as it is filtered through our imaging tools. There are very powerful mathematical tools that can be applied here, particularly the field known as linear systems analysis that considers transfer functions and especially convolution. Each device we build or use can be analyzed, at least in part, within this framework. More importantly, for many classes of systems, the filtering they apply can be inverted – in some cases unblurring and recapturing much of the original data. Deconvolution is the general rubrick under which we will try to analyze this process.

Mathematical transforms are, in general, ways to change the representation of equations into forms that are much easier to solve, or that offer additional insight into the underlying properties. We will look at a few transforms, particularly the LaPlace Transform and the Fourier Transform. The latter is simply a means of expressing and quantifying the frequencies contained in a signal. The maths for these includes a little bit of trigonometry and some basic calculus. By the time we start on these topics, you should make yourself responsible for knowing how to integrate sines and cosines, and reviewing properties of the natural logarithm, e. I will introduce, in class, the concepts and algebra of imaginary numbers, which we will need as well.

The essential results of the Fourier transform find their way into literally every means we have of neuroimaging, the statistical processing of images, concepts of noise and a host of other applications in neuroscience. I truly believe, that although you may find this material difficult, you will be happy about knowing it for the rest of your career as a scientist, making it well worth the effort.

Our first direct application of the analytic tools will be in the analysis and then creation of electrical circuits. We do this for several reasons. Unlike many real-world devices, electrical circuit elements: resistors, batteries, capacitors, inductors and operational amplifiers, act very much like their idealized representations, storing and converting energy in very predictable ways. The tools that have grown to analyze such circuit elements are very mature and quite powerful, making prediction of their behavior straightforward. For this reason, many real-world physics and imaging problems are modeled using electrical circuit elements where we can predict their input-output properties.

The second reason for looking at electrical circuits is that they are present in more or less every lab instrument you are likely to use. Towards the end of the first quarter, we will build, in class, an EEG system based on your understanding of these devices. This will also give us an entrée into the important study of noise, which is present in any experiments. We will look at the many sources of noise in neuroimaging and experiments, and consider ways in which modeling the noise can help us to reduce it. Conversely, we will discuss ways in which we can study the characteristics of the noise in order to better understand either our devices, or the actual features of our images.

We will cover principles of optics, emphasizing the issues of resolution, optical spectrum (frequency ranges), distortion and digital imaging. One way to think about the effects of lenses is as convolution filters (see above) that color the signal. Color, as used here, is a rather broad concept. The process of whitening the signal can be considered a deconvolution. Undoing the lens convolution is a way of removing the blur or distortion produced by a lens. As we go on, we will see this theme of convolution blurring and deconvolution sharpening applied to the many modalities used in modern neuroimaging. Similarly, statistical variance or noise can be reduced or at least better understood in this context, sharpening our statistical inferences and improving detection power.

Our next foray will be into electroencephalography (EEG), which is a simply a measure of the differences in electrical voltage from point to point on the scalp or brain. In addition to looking at the biological basis of the EEG, we will build and test an EEG system in class and we will look at some software approaches to interpreting the EEG both as spatially-resolved (i.e., image) data and as cognitive/physiological signals.

[edit] Assignments

[edit] Weekly Reading and Blogging

For our first meeting, we will look at:

• "Can cognitive processes be inferred from neuroimaging data?" Poldrack, 2006
• Making sense of neuroimaging in psychiatry

  [edit] Schedule

  [edit] Week 1: Orientation to Neuroimaging, Organizational, Neurons

  Wednesday 1/7/09

  Readings (for Wednesday and coming Monday)

  • The Active Brain
  • Slides shown in class

  Answers to in-class pop quiz

  The chart below shows the number of people responding correctly to each of the nine questions in the pop quiz. Message: Don't panic

  

  

  Pop quiz results

  MatrixSolutions

  [edit] Week 2

  I suggest very strongly that you start brush up on linear algebra during this week and the next. 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 strongly recommend the Hefferon text noted above.

  This would also be a good time to review your calculus fundamentals:

  Derivatives of Polynomials (based on the quiz results, it looks like most of you know this)

  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 oor other means if this material looks too difficult.

  [edit] Monday 1/12: Neurons (cont'd)

  Today we will continue the discussion of basic cellular energetics. If desired, we can review the pop quiz, for clarification of the answer sheet. We will start on a discussion of the general organization of the human brain, and the regional specialization of cortical areas.

  Suggested readings

  Washington University Programmed text in Neuroanatomy This is an excellent free resource

  These books, by Squire and by Kandel, are intended as full textbooks for neuroscience courses. I find both of them very readable If you want to get into more depth than we can cover in class, of if you feel that you would benefit from a review of neuroscience, I don't think you could do much better.

  Fundamental Neuroscience - Squire

  Principles of Neural Science - Kandel

  [edit] Wednesday 1/14

  Stats 101 We will consider the general problems of statistical inference, with a concentration on developing an intuitive understanding of statistical concepts. 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

  [edit] Problem Set 1

  Problem set using in stats and MATLAB

  More practice with stats and MATLAB

  [edit] Week 3:

  [edit] Statistical Modeling and Inference in Neuroimaging - guest lecturer, Jeanette Mumford

  Dr. Mumford is one of the most talented and clear-thinking statisticians I have ever had the pleasure to work with. My experience is that she likes to make her lectures fully self-contained; The topic she has agreed to is fairly advanced, however, so I recommend strongly that you pay focussed careful attention. The slides posted here develop the key principles of matrix math - if you have not seen this however, you should look the content over in advance and let me know if you don't feel you can get the fundamentals in order before her lecture.

  [edit] Monday 1/19

  Campus Holiday - Martin Luther King Day

  [edit] Wednesday 1/21

  Part I Lecture slides: Statistical Modeling and Inference (pdf)

  [edit] Week 4:

  [edit] Monday 1/26

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

  [edit] Wednesday 1/28

  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.

  [edit] Week 5:

  Monday 2/2

  Signal processing continued

  Example transform derivations

  The Convolution theorem

  Oddness (and Even-ness)

  Please see MATLAB demo of Fourier transforms and convolution

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

  Wednesday 2/4

  Followup: The Fourier shift theorem

  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

  [edit] Week 6:

  Monday 2/9

  TEACHING SLIDES on Circuits: Circuits 1 & 2 <- Revised 2-12-09

  Electrical circuits

  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 (nearly enough to inifinite 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.

  Wednesday 2/11

  Electrical Circuits, cont'd

  We will discuss:

  Gain

  Trasformers

  Rectifiers

  Active Elements

  Amplifiers

  Transistors

  Op Amps

  Op Amp Circuits

  Higher order filters

  [edit] Week 7:

  Monday 2/16 - President's Day UCLA holiday

  Wednesday 2/18

  Active electronics, cont'd Midterm assigned.

  [edit] Week 8:

  Monday 2/23

  Review session

  Wednesday 2/25

  Midterm due in class. Live EEG collection (I hope)

  [edit] Week 9:

  Monday 3/2

  Loose ends: In today's class I want to make sure that we have covered the necessary technical topics to begin the units on MRI and PET next quarter.

  Bandwidth and SNR

  Interpretation of FT space as phase

  Formal discussion of electricity and magnetism

  Line broadening

  Mixing and modulating

  Wednesday 3/4

  Alex Korb, Ian Cook - (slide handout): "Applications of EEG in Psychiatry"

  [edit] Week 10

  Monday 3/9

  Jonathan Wynn - EEG in Schizophrenia Research.

  Dr. Wynn has suggested looking at these two articles:

  Tallon-Baudry, C., & Bertrand, O. (1999). Oscillatory gamma activity in humans and its role in object representation. Trends in Cognitive Sciences, 3, 151- 162.

  Roach, B. J., & Mathalon, D. H. (2008). Event-related EEG time-frequency analysis: An overview of measures and an analysis of early gamma band phase locking in schizophrenia. Schizophrenia Bulletin, 34, 907-926.

  Wednesday 3/11

  Marc Nuwer - Clinical Applications of EEG

  [edit] Week 11:

  Monday 3/15

  Wednesday 3/18 - Final Exam

  Next Step: Principles of Neuroimaging B / functional MRI