Was it more of his idea, and he handed it off to you? How did that relationship work? MIKE BURROWS: What happened was that he never bothered writing it up. I learned about it from him as a graduate student.
And the years ticked by after that. And he never wrote it up. At the time when I was a student, I thought that it was just one of those things that grad students learn.
And then eventually, I realized, no, this was really special, and the world ought to know about it. When he did it, he did not think of it as a practical algorithm. He thought of it as an algorithm to use to calibrate other algorithms. It wasn't practical for him, because he didn't have a really fast implementation.
And computers at the time were significantly slower. And so it didn't really go fast enough. So I decided that what I should do is write it up myself. And in order to do that, I had to do something. And so I worked with him to make it go fast Casinoslots New Zealand.
And we came up with ways to implement it efficiently. COLT MCANLIS: So I've got to ask you, in the 20 years since this algorithm's invention, what has been the most amazing thing you've seen it applied for? I mean, it's been everywhere, from the Linux operating system to a protocol on the internet.
What's impressed you so much about its use so far? MIKE BURROWS: Well, I suppose the most unexpected thing has been its use in DNA sequencing. It puts together the fragments of DNA that have been sequenced independently very efficiently into a combined whole. But there have been many other advances around it, particularly in ways to do the sorting efficiently, also variance of the transform, one that sorts only limited-length contexts. It turns out that Michael Schindler of the Technical University of Vienna discovered that if you sort the context up to any finite length k, it's still invertible as a transform.
Unfortunately, the inversion takes twice as long, so it's not popular. But it still works. David Scott and Yossi [? Azah ?] managed to find a bijective variant of the transform, where the size of the transform string is exactly the same as the size of the input string. COLT MCANLIS: So you don't need the row index at the end?
MIKE BURROWS: Yes, that's correct. It's a bit more involved and a bit slower to do the compression, but it still works. And that was another surprise for me.
COLT MCANLIS: Give me a little bit of background here. Where did you actually publish the paper originally for this? MIKE BURROWS: There's a funny story about that.
We first of all sent the paper to the Annual Data Compression Conference. But they rejected it. And there were no comments about why they rejected it.
So I wrote to them and asked why they had rejected it. And they told me that it was their policy not to explain why they rejected papers. So we just published it as a technical report. The next year, people at the same conference actually asked me to submit the paper again so that they could publish it. And I said, no.
All right, all right, all right. Calm down. Why don't you hit the showers, and I'll walk the people through the rest of the algorithm, all right? Good job today. Good job. I don't think he's got a shot at that one.
Anyhow, thanks to Magnus, we've got a recreated permutation table alongside a nifty row index that we output during the encoding phase. Since this matrix over there is identical to the post-sorted one from the encoder, the fourth row actually contains the original input string, "BANANA." See?
Pretty easy stuff. Oh, and to be clear, kids, training to be a world champion at sorting requires a lot of practice and dedication. So eat your vegetables and listen to your parents.
MALE SPEAKER: Take one. COLT MCANLIS: How do you make your hair do that? MALE SPEAKER: Lots and lots of gel. COLT MCANLIS: Really? I'm gel-ous, and not just because it's a pun. Nice.
It'll take him a second. In 1994, Mike Burrows and David Wheeler were set up to be the title fight at the second annual UFC championship in Las Vegas, Nevada. But before the fight, while playing a few rounds of pai gow, the two ended up creating the Burrows-Wheeler Transform algorithm.
MIKE BURROWS: That isn't really true. COLT MCANLIS: No, no. No, it is not.
Um-- ha. You know, one of the problems about working at Google is you can't really throw a stone around here without hitting the inventor of some amazing algorithm. Ladies and gentlemen, I want to introduce you to the co-inventor of the Burrows-Wheeler Transform, Mr. Mike Burrows. Mike, it's fantastic to see you. Maybe if you have a second, can you sit down and talk to us a little bit about your algorithm?
MIKE BURROWS: Certainly. I'd like to put you straight about that title fight. COLT MCANLIS: OK. So I guess at the beginning, let's start there. MIKE BURROWS: Well, it really started with David Wheeler.
He was on the faculty of the University of Cambridge, but on sabbatical at Bell Labs, and working on compression. And he came up with the algorithm there. I only learned about it some years later when I became his graduate student.
COLT MCANLIS: In the world of data compression, Burrows-Wheeler Transform just stands alone against everything else. There's nothing really like it. How did you all come up with it? MIKE BURROWS: Well, I asked David what was going through his mind when he came up with it originally.
And he didn't know. He could not explain to me how he came up with that particular algorithm. I got the impression that he was playing around with sorting the contexts of characters that were to be encoded and using that as a good predictor. And then he must have realized that it was possible to invert that sort under certain conditions. COLT MCANLIS: Did you and Mike kind of co-create the article together?
Great form, nice. Remember, clench those abs. Yeah, good, stay with it. Fantastic. MAGNUS HYTTSTEN: All right! Ha ha.
COLT MCANLIS: This kid's good. All right. Now that we've got a sorted table, the next step is to prepend the input string again. So Magnus, another N-N-B-A-A-A, please.
MAGNUS HYTTSTEN: Over there? COLT MCANLIS: Right there. MAGNUS HYTTSTEN: Great, man. COLT MCANLIS: This guy kind gets it, right? Good.
Nice. Nice. MAGNUS HYTTSTEN: Ah! COLT MCANLIS: Now-- all right. Now that it's there, we've got to do another sort. MAGNUS HYTTSTEN: A sort?
COLT MCANLIS: Another sort. MAGNUS HYTTSTEN: OK. COLT MCANLIS: All right. Now, I'm going to time this one. MAGNUS HYTTSTEN: OK. COLT MCANLIS: This is going to be a good warm up round? MAGNUS HYTTSTEN: Yeah.
COLT MCANLIS: All right. Ready? When you're ready, three, two, one, go. MAGNUS HYTTSTEN: OK. Let's go. COLT MCANLIS: Now, remember, you've got to tighten your abs during the sort. You're going to be judged on speed and accuracy here.
MAGNUS HYTTSTEN: Boom! COLT MCANLIS: Fantastic. Look at that. 11 seconds. MAGNUS HYTTSTEN: Yeah!
COLT MCANLIS: That's a personal best for this guy. MAGNUS HYTTSTEN: Wow! COLT MCANLIS: You're already sorting faster than Michael Phelps. MAGNUS HYTTSTEN: That's great to know. COLT MCANLIS: I agree. So this is how the BWT decode works.
We append our input string across the rows of our input table, then sort, and then continue on until we've recovered our original matrix. So Magnus, ready for the big one? MAGNUS HYTTSTEN: Yeah. Yeah, yeah! COLT MCANLIS: All right. So here's what we're going to do.
OK? We're going to do this four more times-- MAGNUS HYTTSTEN: Four? COLT MCANLIS: --so we've got six letters in each row. MAGNUS HYTTSTEN: Wow! COLT MCANLIS: You think you can do it? MAGNUS HYTTSTEN: Yeah!
COLT MCANLIS: Are you ready to do it? MAGNUS HYTTSTEN: I'm ready, ready, ready! COLT MCANLIS: This is for the World Championship! MAGNUS HYTTSTEN: Yeah, man!
Let's do it! COLT MCANLIS: Ready? MAGNUS HYTTSTEN: Yeah! COLT MCANLIS: Set, go! All right.
Good. Great. Good job. Good job. N-N-B-A-A-A. We're going to get you so many endorsements.
You're almost there, Magnus. Finish strong! Finish strong! Ah!
Oh-oh-oh. Man. Great job, kid.
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I have another thing. I think that the big takeaway mystery INS Mark Walberg basically still looks like more all work. I C minus even coverage for the gambler. A lot unzipped photos come online.
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This point, I'm not feeling it. What do you think really thats Tamil? Thank you.
Some of the letters helped bridge the distance between friends and family or helped to heal a hurt. These are real letters people wrote at a time in their lives when hurt, anger or misunderstanding left them feeling as if they were stuck on opposite sides of a tightly closed door.
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So if you want to connect with the people you care most about, "From Me to You" will show you how to share your memories, thank people who have helped you in life, apologize to those you may have hurt, inspire friends and invite people to think of you with love and a smile.
Book Review: Very highly recommended
Rating: 5 stars
Words provide continuity from generation to generation that surpasses our limited life spans to enrich the shared love of friends and family, to bind generations, and to offer hope to the future. Despite the power of words, many people are reluctant writers, uncertain of what to say or how to say it. To that end, authors JacLynn Morris and Paul L. Fair, Ph.D. bring their own writing skills, teaching experience, and research to bear, offering aid to the reluctant writer in FROM ME TO YOU.
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This recently came up on a forum I sometimes visit. What is it about lay and lie that is so difficult?
There are two basic issues:
What’s the difference between look (at), watch and see?
All these verbs are related to sight and vision
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