02.06.10
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S520, January 22

Here’s another edition of my notes from my S520 class.  (Sorry, I’m a little behind.) This time, I wrote all the notes in LaTeX, both for the challenge and for the practice.  Therefore, today’s entry is a PDF file, not a real blog post.  (Sorry.)  Here are the notes.  Let me know if you find any major errors.

Notes for January 22, 2010

By the way, I am still working on the RAMMCAP post I promised last time–it’s just turning out to be a lot longer than I’d originally intended.  I’ll probably break it up into multiple posts next week.

02.01.10
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I’m back! (Part 2)

One other thing I’m going to try to use this blog for is to help me keep track of some of the tools I’m using for an RA project this year.  (“RA” in the “Research Assistant” sense, not the “Resident Advisor” sense.)  I’m studying metagenomics under Yuzhen Ye, specifically the automated functional prediction based on phylogenetic profiling (which is a fancy way of saying I want to figure out what the various pieces I’m working with do by comparing them with related genes in other organisms for which we know the function).

Needless to say, this new responsibility requires me to use a lot of tools that I’ve never heard of before, and I’ll feature some of them here, mainly so I can summarize the way they work and the way one uses them without having to refer back to the documention (which often is unclear, confusing, incomplete, or over-complicated).  Hopefully other people who come along after me can use these little tutorials and save themselves some time figuring things out.  I’m going to start out with a tool called RAMMCAP.

01.22.10
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S520, January 20

Brief introduction into the class:  S520 is an introductory course in statistics for graduate students taught by Professor Michael Trosset.  It aims for depth in each of the subjects we talk about, explaining the why’s and wherefore’s of each topic instead of trying to cram as many topics in as possible (which is a major perk, in my opinion).  It’s actually taught in conjunction with S320, the undergraduate version of the same course, so I think most of the other students in the course are undergrads (not a bad thing, just an observation).  You can read more about it on the pages linked above.  Ok, on with the notes.

Chapter 3, Probability

Section 3.2

  • Basics of modern probability devised by Kolmogorov as discussed last time.
  • Kolmogorov’s probability space has three major components
    1. S, the sample space – the universe of possible experimental outcomes
    2. C, the collection of subsets of S called “events”- events have well-defined probabilities
    3. P, the probability measure-a function that assigns real numbers (called “probabilities”) to events-in proper notation, that looks like:P : C rightarrow R
      1. There are several criteria the probability measure has to satisfy, though many of the are by convention only.
        1. Convention – we require 0 leq P(E) leq 1, where P(E) is the probability of any given event.
          • If P(E) = 0 Rightarrow not going to happen, generally speaking.  (Apparently there are exceptions I don’t know about.)
          • If P(E) = 1 Rightarrow definitely going to happen.
        2. Convention – P(S) = 1 Rightarrow S has to be an event in S
        3. Crucial property: If A and B are disjoint (A cap B = emptyset ) events, then the probablility of their union is:P(Acup B) = P(A) + P(B)
          • Example: Drawing a cardS = mbox{deck of 52 cards }
            P(mbox{A = card is ace}) = frac{4}{52} = frac{1}{13}
            P(B = mbox{card is king}) = frac{4}{52} = frac{1}{13}
            P(A cup B) = frac{1}{13} + frac{1}{13} = frac{2}{13}
      2. Because of those conventions, we can learn these things:
        1. P(E^C) = 1 - P(E)
          E, E^C are disjoint, then by “crucial property”:

          P(S) = P(E) + P(E^C) ;;; since , E + E^C = S
          1 = P(E) + P(E^C) ;;; mbox{by convention 2 above}
          P(E^C) = 1 - P(E)

        2. If A subset B , then P(A) leq P(B)
        3. P(A cup B) = P(A) + P(B) - P(Acap B)
          P(mbox{Overlapping sets}) = Sigma P(mbox{each set}) - P(mbox{intersection of sets})

Section 3.3 Finite Sample Space

  • S has a finite number N of outcomes, represented byS = {s_1, s_2, dots, s_N}
  • For example:
    • E = {s_2, s_3, s_7, s_9} = {s_2} cup {s_3} cup {s_7} cup {s_9}
    • So, P(E) = ?
    • P(E) = P({s_2}) + P({s_3}) + P({s_7}) + P({s_9})
    • If we know the probability of the individual outcomes, we can compute the probability of any event by adding the probabilities of the relevant outcomes.
    • Core assumption:  individual events in the collection are separate by convention.
  • Important special case (limit of most high school probability): Suppose that each of the N outcomes is “equally likely” (recurring phrase we’ll hear a lot).  In this case, each outcome has probability:P({s_i}) = frac{1}{N} mbox{for } i = 1, 2, dots, N

    This means that with equally likely outcomes, figuring probabilities is basically just counting.

    • Example:

      E = { s_1, s_2, dots, s_k} for k outcomes in E, then
      P(E) = P({s_1}) + P({s_2}) + dots + P({s_k})
      P(E) = frac{1}{N} + frac{1}{N} + dots + frac{1}{N}
      P(E) = frac{displaystyle k}{displaystyle N}= frac{displaystyle #(mbox{outcomes in E})}{ displaystyle#(mbox{outcomes in S})}

    • 3 of a kind example:  Draw 5 cards from a standard deck of cards.  What is P(mbox{3 of a kind})?

      A: frac{displaystyle #(mbox{3 of a kind})}{displaystyle #(mbox{5 cards})} = frac{displaystyle formula , derived , previously}{displaystyle {52 choose 5}}

    • Counting example (Exercise 3.7.2 in book):  Assume the probabilities of throwing an astragalus are:

      P(1) = 0.1, P(3) = 0.4, P(4) = 0.4, P(6) = 0.1

      • So we have:

        p_1 = P({s_1}) = 0.1
        p_2 = P({s_3}) = 0.4
        p_3 = P({s_4}) = 0.4
        p_4 = P({s_6}) = 0.1

      • Make an urn model with equally likely outcomes that mimics an astragalus.
        • First (wrong) idea:
          • 4 slips of paper with one of the four outcomes on it
          • Why wrong?  Doesn’t have the right probability.
        • Second (right) model:
          • 10 slips of paper with the values {1, 3, 3, 3, 3, 4, 4, 4, 4, 6} on them
          • P(1) = 0.1, P(3) = 0.4, P(4) = 0.4, P(6) = 0.1

Friday – Conditional  probabilities

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01.21.10
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I’m back!

Well, I’ve let this go way too long, so I’ve come up with a method to keep me working on this blog periodically.  I’m going to blog my notes from my various classes, or at least what I’m getting out of them, which should put me at about 7 posts a week for the next several weeks.  Time to get started!

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10.03.09
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College geekery

So, I haven’t updated this blog in a while–sorry about that.  School’s been keeping me really busy the past couple of weeks, but I realized that I needed to rectify this problem with something, at least, so I just wanted to mention a couple things I’ve been doing lately.

  1. First off, I’ve been delving deeper into Python lately.  We’re using it for one of my classes, and I’ve gotten to know (and like) it much better than I did before.  Most of my stuff is fairly uninteresting stuff, but here’s a list, anyway.  (Code available on request, though I might post it later.)  I’ve got a couple more things under development, but I’ll add them when they’re finished.
    1. A short file full of biological constants that I’m extending as I find new things to add to it.
    2. A sequence simulator that generates random DNA sequences based on a given base proportions.
    3. A bio-translator that takes in a file with a list of DNA bases and calculates the amino acids that map to each codon, even when you take frameshifting into account.
    4. A CoinChanger, which takes in a domain of coins (say the US coin system of pennies, nickels, dimes, quarters, half-dollars, and dollars) and returns the minimum number of coins you need to make change from that.  Since some domains of coins break the standard greedy algorithm for making change, this CoinChanger also implements a recursive algorithm and a bottom-up algorithm for making change.
    5. A Sequencer which reads in a FASTA formatted file and outputs various statistics about it.
    6. A file which uses the Sequencer code to answer some questions.
    7. A timer file which takes in a list of execution times and a list of run time functions, then computes the largest n that can be computed in those given execution times, where n is the size of the input element.  (My favorite result:  If you have a run time function that grows factorially, you could only have an input of 17 elements before your algorithm takes more than a century of microseconds to compute.  That’s bad.)
  2. I’ve been learning Matlab, which is another programming language with syntax similar to Pascal and Ada.  It’s got a lot of cool features, like built-in matrix operations, and some pretty annoying stuff (like how basically everything is a matrix, which is almost as bad as Java’s treating everything like an object).  It’s growing on me, but slowly–I still think it should work very differently than it does.  The things I’ve written in Matlab include:
    1. An implementation of Insertion Sort.
    2. An implementation of Merge Sort.
    3. A program that uses and compares the two of them, then creates a couple charts based on that data.
    4. An implementation of a Stack.  (Though it’s a global stack because of the requirements of the assignment.  It should be local as far as I’m concerned.)
    5. A partial implementation of a singly Linked List.  (Though again it’s a global list, which is annoying.)  Search seems to work, insert works (mostly), but my delete function has issues, part of which stem from a bug in my insert function that I haven’t had time to track down.
  3. I’ve also worked with a program called Alice in my AI work.  Alice is a 3D graphics program used to help teach programming.  It has most of the basic programming constructs (loops, conditionals, functions, methods), but it does some weird stuff, and I’m still a little skeptical it will help people really understand those programming constructs.  We’ll see next week when we drop to a real programming language (Python, ironically).
  4. I’ve used Audacity to put up a teeny-tiny podcast, but I’m probably not going to keep that one going–too much work, and not really any benefit for me right now.  Maybe someday, but not today.

I think that’s all the major stuff I’ve done over the past couple of weeks.  I’ll try to let you know if anything changes.

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Alright, so I want your head to be on the floor. Taking both legs up, lower your left leg down halfway. Undrafted WR Paul Turner led the Eagles with 80 receiving yards on 6 catches. Yes, the majority of the catches and yards were against a prevent defense, but Turner looked to be open constantly, just like he was during the preseason. All Kuechly did as a rookie was lead the league in total tackles, with 164. He also added a sack, two interceptions, eight passes defensed and three fumble recoveries. In 2005, the Cheap Jordans police received a letter saying that someone knew where the body was buried and who did it. The letter said that he was buried under what currently is the New York Aquarium and named several cops and mobsters as the killers. With our fair value of Dick’s at $31 per share, and the stock above $40, we aren’t very interested in the company at this time. It trades at only about 18x our 2012 forecast; however, we do not see the same years of explosive growth ahead. Prayer Wholesale China Jerseys is also an important component of Eid al Adha.A. Hanukkah is a Jewish holiday that’s also known as the festival of lights. “God gave me a million dollar voice, and I just hope I can do right by him.”Cavaliers spokesman Tad Carper said exact details of the team’s offer and their plans to help Williams with housing were still being worked out.The Cavaliers did not know much about him, but were touched by Williams’ ordeal.”When you know something’s right, you just have to launch,” said Tracy Marek, the team’s senior vice president of marketing. “One of the big things that we talk about here, with our organization, is how important urgency is when you see something that feels good and seems right. Hi, my name is Janet. I’m a personal trainer with Metamorphosis, Cheap Jerseys From China and today I’m going to show you an exercise to replace the diamond push up. Football is the national sport of Italy. This is just one of the reasons the Italians are crazy about football. In order to characterize the onset time of the observed IOSs, the OCT frame speed was increased to 500 Hz, with a reduced frame size (40 pixels 200 pixels) for the experiment represented in Fig. 4. ET Oct. 21, 2016FILE At left, in an Aug. The triumph over the Bengals gives the Steelers the early edge in the AFC North. This game lacked the nastiness of other recent Steelers Bengals matchups oakley sunglasses outlet but was, as always, highly competitive. He has played in big games and made big time throws. But cheap nba jerseys there are questions about his game, including inconsistent accuracy and command of the football, as well as his personality, maturity and leadership. Carlo Ancelotti and his coaching staff had delivered in one season what the club had been waiting 12 years for La Decima, a 10th European Cup. As well as his medal, Clement has a match ball from the final at home on the sideboard; the shirt he wore on the night; and the highlights reel for whenever he wants to relive Sergio Ramos’s injury time equaliser and those three extra time goals..
08.31.09
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About Me

I’m a second-year Masters student at Indiana University, where I’m studying bioinformatics (basically using computers to analyze biological data).  I’m working as a Research Assistant under Yuzhen Ye and working on using environmental profiling for functional prediction in metagenomics.

I emerged from Indiana Wesleyan University with a BS in Computer Science in 2005, and I’ve worked in web application development for the past several years, so you’ll probably find posts here about both subjects along with anything else I find interesting.

You can email me at c.burrus(a)computer.org.  (Email altered to prevent spam.  You can figure the real one out.)  You’re also welcome to look me up on LinkedIn or Twitter.

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08.31.09
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Hello world!

Hi!  This is a new blog specifically for the I101 class I’m AI’ing for this semester.  (An AI is an “associate instructor,” also known as a TA or “teaching assistant.”)  What do you think of it?

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