NIMBioS Workshop: Information Theory and Entropy in Biological Systems

Over the next few days, I’ll be maintaining a Storify story covering information related to and coming out of the Information Theory and Entropy Workshop being sponsored by NIMBios at the Unviersity of Tennessee, Knoxville.

For those in attendance or participating by watching the live streaming video (or even watching the video after-the-fact), please feel free to use the official hashtag #entropyWS, and I’ll do my best to include your tweets, posts, and material into the story stream for future reference.

For journal articles and papers mentioned in/at the workshop, I encourage everyone to join the Mendeley.com group ITBio: Information Theory, Microbiology, Evolution, and Complexity and add them to the group’s list of papers. Think of it as a collaborative online journal club of sorts.

Those participating in the workshop are also encouraged to take a look at a growing collection of researchers and materials I maintain here. If you have materials or resources you’d like to contribute to the list, please send me an email or include them via the suggestions/submission form or include them in the comments section below.

Resources for Information Theory and Biology

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Machiavelli in Hollywood | Gavin Polone’s ‘Textbook’ on the Entertainment Industry

Dearth of (Great) Textbooks on The Entertainment Business

In having previously taught several classes on the business of the entertainment industry, I was never quite able to pick out even a mediocre textbook for such a class. There are a handful that will give one an overview of the nuts and bolts and one or two that will provide some generally useful numbers (see the syllabi from those classes), but none comes close to providing the philosophy of how the business works in a short period of time.

A Short Term Solution

To remedy this problem, I was always a fan of producer and ex-agent Gavin Polone, who had a series of articles in New York Magazine/Vulture.  I’ve recently gone through and linked to all of the forty-four articles, in chronological order, he produced in that series from 9/21/11 to 5/7/14.

I’ve aggregated the series via Readlists.com, so one can click on each of the articles individually.  Better yet, for students and teachers alike, one can click on the “export” link and very easily download them all in most ebook formats (including Kindle, iPad, etc.) for your reading/studying convenience.

My hope is that for others, they may create an excellent starter textbook on how the entertainment business works and, more importantly: how successful people in the business think. For those who need more, Gavin is also an occasional contributor to the Hollywood Reporter.  (And, as a note for those not trained in the classics and prone to modern-day stereotypes, I’ll make the caveat that I use the title “Machiavelli” above with the utmost reverence and honor.)

I’m still slowly, but surely making progress on my own all-encompassing textbook, but, until then, I hope others find this series of articles as interesting and useful as I have.

 

Gavin Polone is an agent turned manager turned producer. His production company, Pariah, has brought you such movies and TV shows as Panic Room, Zombieland, Gilmore Girls, and Curb Your Enthusiasm. Follow him on Twitter @gavinpolone

Nothing Would be More Devastating than Reduced Access to a Technical Library

Nassim Nicholas Taleb, flâneur
in the Financial Times in response to the question:
“If you lost everything tomorrow, what would you do?”

 


 

Why Aren’t Math Textbooks More Straightforward?

Some General Advice for Math Students of All Ages

I recently saw the question “Why aren’t math textbooks more straightforward?” on Quora.

In fact, I would argue that most math textbooks are very straightforward!

The real issue most students are experiencing is one of relativity and experience.  Mathematics is an increasingly sophisticated, cumulative, and more complicated topic the longer you study it. Fortunately, over time, it also becomes easier, more interesting, and intriguingly more beautiful.

As an example of what we’re looking at and what most students are up against, let’s take the topic of algebra. Typically in the United States one might take introductory algebra in eighth grade before taking algebra II in ninth or tenth grade. (For our immediate purposes, here I’m discounting the potential existence of a common pre-algebra course that some middle schools, high schools, and even colleges offer.)  Later on in college, one will exercise one’s algebra muscles in calculus and may eventually get to a course called abstract algebra as an upper-level undergraduate (in their junior or senior years).  Most standard undergraduate abstract algebra textbooks will cover ALL of the material that was in your basic algebra I and algebra II texts in about four pages and simply assume you just know the rest! Naturally, if you started out with the abstract algebra textbook in eighth grade, you’d very likely be COMPLETELY lost. This is because the abstract algebra textbook is assuming that you’ve got some significant prior background in mathematics (what is often referred to in the introduction to far more than one mathematics textbook as “mathematical sophistication”, though this phrase also implicitly assumes knowledge of what a proof is, what it entails, how it works, and how to actually write one).

Following the undergraduate abstract algebra textbook there’s even an additional graduate level course (or four) on abstract algebra (or advanced subtopics like group theory, ring theory, field theory, and Galois theory) that goes into even more depth and subtlety than the undergraduate course; the book for this presumes you’ve mastered the undergraduate text and goes on faster and further.

A Weightlifting Analogy

To analogize things to something more common, suppose you wanted to become an Olympic level weightlifter.  You’re not going to go into the gym on day one and snatch and then clean & jerk 473kg! You’re going to start out with a tiny fraction of that weight and practice repeatedly for years slowly building up your ability to lift bigger and bigger weights. More likely than not, you’ll also very likely do some cross-training by running, swimming, and even lifting other weights to strengthen your legs, shoulder, stomach, and back.  All of this work may eventually lead you to to win the gold medal in the Olympics, but sooner or later someone will come along and break your world record.

Mathematics is certainly no different: one starts out small and with lots of work and practice over time, one slowly but surely ascends the rigors of problems put before them to become better mathematicians. Often one takes other courses like physics, biology, and even engineering courses that provide “cross-training.”  Usually when one is having issues in a math class it’s because they’re either somehow missing something that should have come before or because they didn’t practice enough in their prior classwork to really understand all the concepts and their subtleties.  As an example, the new material in common calculus textbooks is actually very minimal – the first step in most problems is the only actual calculus and the following 10 steps are just practicing one’s algebra skills. It’s usually in carrying out the algebra that one makes more mistakes than in the actual calculus.

Often at the lower levels of grade-school mathematics, some students can manage to just read a few examples and just seem to “get” the answers without really doing a real “work out.” Eventually they’ll come to a point at which they hit a wall or begin having trouble, and usually it comes as the result of not actually practicing their craft.  One couldn’t become an Olympic weightlifter by reading books about weightlifting, they need to actually get in the gym and workout/practice. (Of course, one of the places this analogy breaks down is that weightlifting training is very linear and doesn’t allow one to “skip around” the way one could potentially in a mathematics curriculum.)

I’m reminded of a quote by mathematician Pierre Anton Grillet: “…algebra is like French pastry: wonderful, but cannot be learned without putting one’s hands to the dough.” It is one of the most beautiful expressions of the recurring sentiment written by almost every author into the preface of nearly every mathematics text at or above the level of calculus. They all exhort their students to actually put pencil to paper and work through the logic of their arguments and the exercises to learn the material and gain some valuable experience.  I’m sure that most mathematics professors will assure you that in the end, only a tiny fraction of their students actually do so. Some of the issue is that these exhortations only come in textbooks traditionally read at the advanced undergraduate level, when they should begin in the second grade.

Patissiere puts their hands to a pie crust in a rustic kitchen
“Algebra is like French Pastry: wonderful, but cannot be learned without putting one’s hands to the dough.” -Pierre Anton Grillet

“It’s Easy to See”

A common phrase in almost every advanced math textbook on the planet is the justification, “It’s easy to see.” The phrase, and those like it, should be a watchword for students to immediately be on their guard!  The phrase is commonly used in proofs, discussions, conversations, and lectures in which an author or teacher may skip one or more steps which she feels should be obvious to her audience, but which, in fact, are far more commonly not obvious.

It’s become so cliche that some authors actually mention specifically in their prefaces that they vow not to use the phrase, but if they do so, they usually let slip some other euphemism that is its equivalent.

The problem with the phrase is that everyone, by force of their own circumstances and history, will view it completely differently.  A step that is easy for someone with a Ph.D. who specialized in field theory to “see” may be totally incomprehensible for a beginning student of algebra I in the same way that steps that were easy for Girgory Perelman to see in his proof of the Poincaré conjecture were likewise completely incomprehensible for teams of multiple tenured research professors of mathematics to see. (cross reference: The Poincaré Conjecture: In Search of the Shape of the Universe by Donal O’Shea (Walker & Co., 2007))

How to Actively Read a Math Text

The Problem

So how are students to proceed? It will certainly help to see a broader road map of what lies ahead and what the expected changes in terrain will look like. It will also help greatly if students have a better idea how to approach mathematics for themselves and even by themselves in many cases.

In my opinion, the most common disconnect occurs somewhere between high school mathematics and early college mathematics (usually a calculus sequence, linear algebra) and then again between linear algebra/differential equations (areas which usually have discussion followed by examples and then crank-out problems) and higher abstract mathematical areas like analysis, abstract algebra, topology (areas in which the definition-theorem-proof cycle of writing is more common and seemingly more incomprehensible to many).

The first big issue in early college mathematics is the increased speed at which college courses move. Students used to a slower high school pace where the teachers are usually teaching to the middle or lower end of the class get caught unaware as their college professors teach to the higher ability students and aren’t as afraid to leave the lower end of the spectrum behind. Just like high school athletes are expected to step up their game when they make the transition to college and similarly college athletes who go pro, mathematics students should realize they’re expected to step up their game at the appropriate times.

Often math students (and really any student of any subject) relies on the teacher assigning readings or problems from their book rather than excersizing their curiosity to more avidly and broadly explore the material on their own.  If they can take the guidance of their teacher as well as that of the individual authors of books, they may make it much further on their own.  High school teachers often skip sections of textbooks for time, but students should realize that there is profitable and interesting material that they’re skipping.  Why not go and read it on their own?

Earlier I mentioned that an average undergraduate abstract algebra textbook might cover the totality of a high school algebra textbook in about three pages.  What does this mean for upper level mathematics students?  It almost always means that the density of material in these books is far greater than that of their earlier textbooks.  How is this density arrived at?  Authors of advanced textbooks leave out far more than they’re able to put in, otherwise their 300 page textbooks, if written at the same basic level as those that came before would be much more ponderous 1000+ page textbooks.  What are they leaving out?  Often they’re leaving out lots of what might be useful discussion, but more often, they’re leaving out lots of worked out examples. For example, a high school text will present a definition or concept and then give three or more illustrations or examples of problems relating to the concept.  The exercises will then give dozens of additional drill problems to beat the concept to death.  This type of presentation usually continues up to the level of calculus where one often sees massive tomes in the 800+ page length. Math texts after this point generally don’t go much over 300 pages as a rule, and it’s primarily because they’re leaving the examples out of the proverbial equation.

The Solution

How does one combat this issue?  Students need to more actively think back to the math they’ve taken previously and come up with their own simple examples of problems, and work though them on their own.  Just because the book doesn’t give lots of examples doesn’t mean that they don’t exist.

In fact, many textbooks are actually presenting examples, they’re just hiding them with very subtle textual hints. Often in the presentation of a concept, the author will leave out one or more steps in a proof or example and hint to the student that they should work through the steps themselves. (Phrases like: “we leave it to the reader to verify” or “see example 2.”) Sometimes this hint comes in the form of that dreaded phrase, “It’s easy to see.” When presented with these hints, it is incumbent (or some students may prefer the word encumbering) on the student to think through the missing steps or provide the missing material themselves.

While reading mathematics, students should not only be reading the words and following the steps, but they should actively be working their way through all of the steps (missing or not) in each of the examples or proofs provided. They must read their math books with pencil and paper in hand instead of the usual format of reading their math book and then picking up paper and pencil to work out problems afterwards.  Most advanced math texts suggest half a dozen or more problems to work out within the text itself before presenting a dozen or more additional problems usually in a formal section entitled “Exercises”. Students have to train themselves to be thinking about and working out the “hidden” problems within the actual textual discussion sections.

Additionally, students need to consider themselves “researchers” or think of their work as discovery or play.  Can they come up with their own questions or exercises that relate the concepts they’ve read about to things they’ve done in the past? Often asking the open ended question, “What happens if I…” can be very useful.  One has to imagine that this is the type of “play” that early mathematicians like Euclid, Gauss, and Euler did, and I have to say, this is also the reason that they discovered so many interesting properties within mathematics.  (I always like to think that they were the beneficiaries of “picking the lowest hanging fruit” within mathematics – though certainly they discovered some things that took some time to puzzle out; we take some of our knowledge for granted as sitting on the shoulders of giants does allow us to see much further than we could before.)

As a result of this newly discovered rule, students will readily find that while they could read a dozen pages of their high school textbooks in just a few minutes, it may take them between a half an hour to two hours to properly read even a single page of an advanced math text. Without putting in this extra time and effort they’re going to quickly find themselves within the tall grass (or, more appropriately weeds).

Another trick of advanced textbooks is that, because they don’t have enough time or space within the primary text itself, authors often “hide” important concepts, definitions, and theorems within the “exercises” sections of their books.  Just because a concept doesn’t appear in the primary text doesn’t mean it isn’t generally important.  As a result, students should always go out of their way to at least read through all of the exercises in the text even if they don’t spend the time to work through them all.

One of the difficult things about advanced abstract mathematics is that it is most often very cumulative and even intertwined, so when one doesn’t understand the initial or early portions of a textbook, it doesn’t bode well for the later sections which require one to have mastered the previous work.  This is even worse when some courses build upon the work of earlier courses, so for example, doing well in calculus III requires that one completely mastered calculus I. At some of the highest levels like courses in Lie groups and Lie algebras requires that one mastered the material in multiple other prior courses like analysis, linear algebra, topology, and abstract algebra. Authors of textbooks like these will often state at the outset what material they expect students to have mastered to do well, and even then, they’ll often spend some time giving overviews of relevant material and even notation of these areas in appendices of their books.

As a result of this, we can take it as a general rule: “Don’t ever skip anything in a math textbook that you don’t understand.” Keep working on the concepts and examples until they become second nature to you.

Finally, more students should think of mathematics as a new language.  I’ve referenced the following Galileo quote before, but it bears repeating (emphasis is mine):

Philosophy is written in this grand book, the universe which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth.

Galileo Galilee (1564–1642) in Il saggiatore (The assayer)

Though mathematical notation has changed drastically (for the better, in my opinion) since Galileo’s time, it certainly has its own jargon, definitions, and special notations.  Students should be sure to spend some time familiarizing themselves with current modern notation, and especially the notation in the book that they choose.  Often math textbooks will have a list of symbols and their meanings somewhere in the end-papers or the appendices. Authors usually go out of their way to introduce notation somewhere in either the introduction, preface, appendices, or often even in an introductory review chapter in which they assume most of their students are very familiar with, but they write it anyway to acclimate students to the particular notation they use in their text.  This notation can often seem excessive or even obtuse, but generally it’s very consistent across disciplines within mathematics, but it’s incredibly useful and necessary in making often complex concepts simple to think about and communicate to others. For those who are lost, or who want help delving into areas of math seemingly above their heads, I highly recommend the text Mathematical Notation: A Guide for Engineers and Scientists by my friend Edward R. Scheinerman as a useful guide.

A high school student may pick up a textbook on Lie Groups and be astounded at the incomprehensibility of the subject, but most of the disconnect is in knowing and understanding the actual language in which the text is written.  A neophyte student of Latin would no sooner pick up a copy of Cicero and expect to be able to revel in the beauty and joy of the words or their meaning without first spending some time studying the vocabulary, grammar, and syntax of the language.  Fortunately, like Latin, once one has learned a good bit of math, the notations and definitions are all very similar, so once you can read one text, you’ll be able to appreciate a broad variety of others.

Actively Reading a Mathematics Text Review:

  • Work through the steps of everything within the text
  • Come up with your own examples
  • Work through the exercises
  • Read through all the exercises, especially the ones that you don’t do
  • Don’t ever skip anything you don’t fully understand
  • Math is a language: spend some time learning (memorizing) notation

Exceptions

Naturally there are exceptions to the rule. Not all mathematics textbooks are great, good, or even passable.  There is certainly a spectrum of textbooks out there, and there are even more options at the simpler (more elementary) end, in part because of there is more demand.  For the most part, however, most textbooks are at least functional.  Still one can occasionally come across a very bad apple of a textbook.

Because of the economics of textbook publishing, it is often very difficult for a textbook to even get published if it doesn’t at least meet a minimum threshold of quality. The track record of a publisher can be a good indicator of reasonable texts. Authors of well-vetted texts will often thank professors who have taught their books at other universities or even provide a list of universities and colleges that have adopted their texts. Naturally, just because 50 colleges have adopted a particular text doesn’t necessarily mean that that it is necessarily of high quality.

One of the major issues to watch out for is using the textbook written by one’s own professor.  While this may not be an issue if your professor is someone like Serge Lang, Gilbert Strang, James Munkres, Michael Spivak, or the late Walter Rudin, if your particular professor isn’t supremely well known in his or her field, is an adjunct or associate faculty member, or is a professor at a community college, then: caveat emptor.

Since mathematics is a subject about clear thinking, analysis, and application of knowledge, I recommend that students who feel they’re being sold a bill of goods in their required/recommended textbook(s), take the time to look at alternate textbooks and choose one that is right for themselves.  For those interested in more on this particular sub-topic I’ve written about it before: On Choosing Your own Textbooks.

Parting Advice

Often, even with the best intentions, some authors can get ahead of themselves or the area at hand is so advanced that it is difficult to find a way into it. As an example, we might consider Lie groups and algebras, which is a fascinating area to delve into. Unfortunately it can take several years of advanced work to get to a sufficient level to even make a small dent into any of the textbooks in the area, though some research will uncover a handful of four textbooks that will get one quite a way into the subject with a reasonable background in just analysis and linear algebra.

When one feels like they’ve hit a wall, but still want to struggle to succeed, I’m reminded of the advice of revered mathematical communicator Paul Halmos, whose book Measure Theory needed so much additional background material, that instead of beginning with the traditional Chapter 1, he felt it necessary to include a Chapter 0 (he actually called his chapters “sections” in the book) and even then it had enough issueshewas cornered into writing the statement:

…[the reader] should not be discouraged, if on first reading of section 0, he finds that he does not have the prerequisites for reading the prerequisites.

Paul Halmos in Measure Theory(1950)

This is essentially the mathematician’s equivalent of the colloquialism “Fake it ’til you make it.”

When all else fails, use this adage, and don’t become discouraged. You’ll get there eventually!

 

Algebra is Like Pastry: Wonderful!

Pierre Anton Grillet (1941 – ), algebraist
in preface to Abstract Algebra, Second Edition (Springer, 2007)

 

2015 Viterbi Lecture: H. Vincent Poor on “Fundamental Limits on Information Security and Privacy”

USC’s Ming Hsieh Department of Electrical Engineeing has announced that H. Vincent Poor will deliver the 2015 Viterbi Lecture

“Fundamental Limits on Information Security and Privacy”

H. Vincent Poor
H. Vincent Poor

H. Vincent Poor, Ph.D.  
Dean of the School of Engineering and Applied Science
Michael Henry Strater University Professor
Princeton University

Education

  • Ph.D., Princeton University, 1977
  • M.A., in Electrical Engineering, Princeton University, 1976
  • M.S., in Electrical Engineering, Auburn University, 1974
  • B.E.E., with Highest Honor, Auburn University, 1972

Lecture Information

Tuesday, March 24, 2015
Hughes Electrical Engineering Center (EEB) 132
Reception 3:00pm
Lecture 4:00pm

Abstract

As has become quite clear from recent headlines, the ubiquity of technologies such as wireless communications and on-line data repositories has created new challenges in information security and privacy. Information theory provides fundamental limits that can guide the development of methods for addressing these challenges. After a brief historical account of the use of information theory to characterize secrecy, this talk will review two areas to which these ideas have been applied successfully: wireless physical layer security, which examines the ability of the physical properties of the radio channel to provide confidentiality in data transmission; and utility-privacy tradeoffs of data sources, which quantify the balance between the protection of private information contained in such sources and the provision of measurable benefits to legitimate users of them. Several potential applications of these ideas will also be discussed.

Biography

H. Vincent Poor (Ph.D., Princeton 1977) is Dean of the School of Engineering and Applied Science at Princeton University, where he is also the Michael Henry Strater University Professor. From 1977 until he joined the Princeton faculty in 1990, he was a faculty member at the University of Illinois at Urbana-Champaign. He has also held visiting appointments at a number of other universities, including most recently at Stanford and Imperial College. His research interests are primarily in the areas of information theory and signal processing, with applications in wireless networks and related fields. Among his publications in these areas is the recent book Principles of Cognitive Radio (Cambridge University Press, 2013). At Princeton he has developed and taught several courses designed to bring technological subject matter to general audiences, including “The Wireless Revolution” (in which Andrew Viterbi was one of the first guest speakers) and “Six Degrees of Separation: Small World Networks in Science, Technology and Society.”

Dr. Poor is a member of the National Academy of Engineering and the National Academy of Sciences, and is a foreign member of the Royal Society. He is a former President of the IEEE Information Theory Society, and a former Editor-in-Chief of the IEEE Transactions on Information Theory. He currently serves as a director of the Corporation for National Research Initiatives and of the IEEE Foundation, and as a member of the Council of the National Academy of Engineering. Recent recognition of his work includes the 2014 URSI Booker Gold Medal, and honorary doctorates from several universities in Asia and Europe.

Texts

  

Introduction to Lie Groups and Lie Algebras (Part 2) | UCLA Extension

Dr. Mike Miller, who had previously announced a two quarter sequence of classes on Lie Groups at UCLA, has just opened up registration for the second course in the series. His courses are always clear, entertaining, and invigorating, and I highly recommend them to anyone who is interested in math, science, or engineering.

Philosophy is written in this grand book, the universe which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth.

Galileo Galilee (1564–1642) in Il saggiatore (The assayer)

Prior to the first part of the course, I’d written some thoughts about the timbre and tempo of his lecture style and philosophy and commend those interested to take a peek. I also mentioned some additional resources for the course there as well.  For those who missed the first portion, I’m happy to help fill you in and share some of my notes if necessary. The recommended minimum prerequisites for this class are linear algebra and some calculus.


Introduction to Lie Groups and Lie Algebras (Part 2)

Math X 450.7 / 3.00 units / Reg. # 251580W
Professor: Michael Miller, Ph.D.
Start Date: January 13, 2015
Location: UCLA, 5137 Math Sciences Building
Tuesday, 7-10pm
January 13 – March 24
11 meetings total
Class will not meet on one Tuesday to be annouced.

Register here: https://www.uclaextension.edu/Pages/Course.aspx?reg=251580

Course Description

A Lie group is a differentiable manifold that is also a group for which the product and inverse maps are differentiable. A Lie algebra is a vector space endowed with a binary operation that is bilinear, alternating, and satisfies the so-called Jacobi identity. This course is the second in a 2-quarter sequence that offers an introductory survey of Lie groups, their associated Lie algebras, and their representations. Its focus is split between continuing last quarter’s study of matrix Lie groups and their representations and reconciling this theory with that for the more general manifold setting. Topics to be discussed include the Weyl group, complete reducibility, semisimple Lie algebras, root systems, and Cartan subalgebras. This is an advanced course, requiring a solid understanding of linear algebra, basic analysis, and, ideally, the material from the previous quarter.Internet access required to retrieve course materials.

Recommended Textbook

Hall, Brian. Lie Groups, Lie Algebras, & Representations (Springer, 2004) ISBN: 9781441923134

 

A photograph of Sophus Lie's very full and bushy beard.
“I wouldn’t lie to you. This is Sophus’s beard.”

 

BIRS Workshop on Biological and Bio-Inspired Information Theory | Storify Stream

Over the span of the coming week, I’ll be updating (and archiving) the stream of information coming out of the BIRS Workshop on Biological and Bio-Inspired Information Theory.

Editor’s note: On 12/12/17 Storify announced they would be shutting down. As a result, I’m changing the embedded version of the original data served by Storify for an HTML copy which can be found below:

BIRS: Biological and Bio-Inspired Information Theory

A 5 Day workshop on Biology and Information Theory hosted by the Banff International Research Station

  1. Wishing I was at the Gene Regulation and Information Theory meeting starting tomorrow  http://bit.ly/XnHRZs  #ITBio
  2. Mathematical and Statistical Models for Genetic Coding starts today.  http://www.am.hs-mannheim.de/genetic_code_2013.php?id=1  @andreweckford might borrow attendees for BIRS
  3. Mathematical Foundations for Information Theory in Diffusion-Based Molecular Communications  http://bit.ly/1aTVR2c  #ITBio
  4. Bill Bialek giving plenary talk “Information flow & order in real biological networks” at Feb 2014 workshop  http://mnd.ly/19LQH8f  #ITBio
  5. #ITBio http://t.co/Ty8dEIXQUT"/>

    CECAM Workshop: “Entropy in Biomolecular Systems” starts May 14 in Vienna.  http://jhu.md/1faLR8t  #ITBio pic.twitter.com/Ty8dEIXQUT
  6. Last RT: wonder what the weather is going to be like at the end of October for my @BIRS_Math workshop
  7. @JoVanEvery I’m organizing a workshop in Banff in October … hopefully this isn’t a sign of weather to come!
  8. Banff takes its name from the town of Banff, Scotland, not to be confused with Bamff, also Scotland.
  9. Good morning from beautiful Banff. How can you not love the mountains? http://t.co/mxYBNz7yzl

    Good morning from beautiful Banff. How can you not love the mountains? pic.twitter.com/mxYBNz7yzl
  10. “Not an obvious connection between utility and information, just as there is no obvious connection between energy and entropy” @BIRS_Math
  11. Last RT: a lot of discussion of my signal transduction work with Peter Thomas.
  12. Live now: Nicolo Michelusi of @USCViterbi on Stochastic Model for Electron Transfer in Bacterial Cables  http://www.birs.ca/live  #ITBio
  13. Nicolo Michelusi (University of Southern California), A Stochastic Model for Electron Transfer in Bacterial Cables  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410271450-Michelusi.mp4 
  14. Listening to the always awesome @cnmirose talk about the ultimate limits of molecular communication.
  15. “Timing is fundamental … subsumes time-varying concentration channel” @cnmirose @BIRS_Math
  16. Standard opening quote of these talks: “I’m not a biologist, but …” @BIRS_Math
  17. Stefan Moser (ETH Zurich), Capacity Bounds of the Memoryless AIGN Channel – a Toy-Model for Molecular Communicat…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410271610-Moser.mp4 
  18. Weisi Guo (University of Warwick), Communication Envelopes for Molecular Diffusion and Electromagnetic Wave Propag…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410271643-Guo.mp4 
  19. .@ChrisAldrich @andreweckford @Storify @BIRS_Math Sounds like a fascinating workshop on bioinformation theory in Banff.
  20. Toby Berger, winner of the 2002 Shannon award, speaking right now. @BIRS_Math
  21. Naftali Tishby (Hebrew University of Jerusalem), Sensing and acting under information constraints – a principled a…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281032-Tishby.mp4 
  22. “…places such as BIRS and the Banff Centre exist to facilitate the exchange and pursuit of knowledge.” S. Sundaram  http://www.birs.ca/testimonials/#testimonial-1454 
  23. We’re going for a hike tomorrow. Many thanks to Lukas at the @ParksCanada info centre in Banff for helpful advice! @BIRS_Math
  24. Alexander Dimitrov (Washington State University), Invariant signal processing in auditory biological systems  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281416-Dimitrov.mp4 
  25. Joel Zylberberg (University of Washington), Communicating with noisy signals: lessons learned from the mammalian v…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281450-Zylberberg.mp4 
  26. Robert Schober (Universitat Erlangen-Nurnberg), Intersymbol interference mitigation in diffusive molecular communi…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281549-Schober.mp4 
  27. Rudolf Rabenstein (Friedrich-Alexander-Universitat Erlangen-Nurnberg (FAU)), Modelling Molecular Communication Cha…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281627-Rabenstein.mp4 
  28. THis week @BIRS_Math ” Biological and Bio-Inspired Information Theory ” @thebanffcentre #biology #math @NSF
  29. “Your theory might match the data, but the data might be wrong” – Crick @BIRS_Math
  30. So information theory seems to be a big deal in ecology. @BIRS_Math
  31. Tom Schneider (National Institutes of Health), Three Principles of Biological States: Ecology and Cancer  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410290904-Schneider.mp4 
  32. “In biodiversity, the entropy of an ecosystem is the expected … information we gain about an organism by learning its species” @BIRS_Math
  33. Seriously, I’m blown away by this work in information theory in ecology. Huge body of work; I had no idea. @BIRS_Math
  34. I encourage @BIRS_Math attendees at Biological & Bio-Inspired Information Theory to contribute references here:  http://bit.ly/1jQwObk 
  35. Christoph Adami (Michigan State University), Some Information-Theoretic Musings Concerning the Origin and Evolutio…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410291114-Adami.mp4 
  36. #ITBio http://t.co/VA8komuuSW"/>

    .@ChristophAdami talk Some Information-Theoretic Musings Concerning the Origin of Life @BIRS_Math this morning #ITBio pic.twitter.com/VA8komuuSW
  37. ICYMI @ChristophAdami had great paper: Information-theoretic Considerations on Origin of Life on arXiv  http://bit.ly/1yIhK2Q  @BIRS_Math
  38. Baez has a post on Tishby's talk "Sensing &  Acting Under Information Constraints" http://t.co/t1nPVI1pxa @BIRS_Math http://t.co/dFuiVLFSGC

    Baez has a post on Tishby’s talk “Sensing & Acting Under Information Constraints”  http://bit.ly/1yIDonR  @BIRS_Math pic.twitter.com/dFuiVLFSGC
  39. INFORMATION THEORY is the new central ...

    INFORMATION THEORY is the new central …
  40. I’m listening to a talk on the origin of life at a workshop on Biological and Bio-Inspired Information Theory. …  https://plus.google.com/117562920675666983007/posts/gqFL7XY3quF 
  41. Now accepting applications for the #Research Collaboration Workshop for Women in #MathBio at NIMBioS  http://ow.ly/DzeZ7 
  42. We removed a faulty microphone from our lecture room this morning. We’re now fixing the audio buzz in this week’s videos, and reposting.
  43. Didn’t get enough information theory & biology this week @BIRS_Math? Apply for NIMBioS workshop in April 2015  http://bit.ly/1yIeiWe  #ITBio
  44. Amin Emad (University of Illinois at Urbana-Champaign), Applications of Discrete Mathematics in Bioinformatics  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410301329-Emad.mp4 
  45. Paul Bogdan (University of Southern California), Multiscale Analysis Reveals Complex Behavior in Bacteria Populati…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410301401-Bogdan.mp4 
  46. Lubomir Kostal (Institute of Physiology, Academy of Sciences of the Czech Republic), Efficient information transmi…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410301534-Kostal.mp4 
  47. Banff ☀️❄️🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲❤️
  48. @conservativelez I’m a big fan of your dad’s research & was reminded of much of it via a workshop on Biological Information Theory
  49. @conservativelez Though he may not have been able to attend, he can catch most of the talks online if he’d like  https://www.birs.ca/events/2014/5-day-workshops/14w5170 
  50. Depressed that @BIRS_Math Workshop on Biological & Bio-Inspired Information Theory is over? Relive it here:  http://bit.ly/1rF3G4B  #ITBio
  51. A few thoughts about that workshop while I wait for my flight back to Toronto.
  52. 1/ Everyone I talked to said it was the best workshop they’d ever been to, and they’d like to do a follow-up workshop @BIRS_Math
  53. 2/ There is an amazing diversity of work under the umbrella of “information theory”. @BIRS_Math
  54. 3/ Much of this work is outside the IT mainstream, and an issue is that people use different terms for related concepts. @BIRS_Math
  55. 4/ Some community building is in order. I think this workshop was a good first step. @BIRS_Math
  56. 5/ Many many thanks to @BIRS_Math and huge kudos to @NGhoussoub for excellent service to the Canadian scientific community. BIRS is a gem.
  57. 6/ Also many thanks to the participants for their excellent talks, and to @ChrisAldrich for maintaining a Storify.


Inquire in the Margine

John Selden (1584-1654), English jurist and a scholar
in Illustrations (1612), a commentary on Poly-Olbion, a poem by Michael Drayton
in the margin next to ‘A table to the chiefest passages, in the Illustrations, which, worthiest of observation, are not directed unto by the course of the volume.’

 

Photo courtesy of Sjoerd Levelt
Photo courtesy of Sjoerd Levelt

 

Announcement: Special issue of Entropy: “Information Theoretic Incentives for Cognitive Systems”

Editor’s Note: Dr. Christoph Salge asked me to cross-post the following notice from the Entropy site here. I’m sure many of the readers of the blog will find the topic to be of interest.


 

Logo for the journal Entropy

 

Dear Colleagues,

In recent years, ideas such as “life is information processing” or “information holds the key to understanding life” have become more common. However, how can information, or more formally Information Theory, increase our understanding of life, or life-like systems?

Information Theory not only has a profound mathematical basis, but also typically provides an intuitive understanding of processes, such as learning, behavior and evolution terms of information processing.

In this special issue, we are interested in both:

  1. the information-theoretic formalization and quantification of different aspects of life, such as driving forces of learning and behavior generation, information flows between neurons, swarm members and social agents, and information theoretic aspects of evolution and adaptation, and
  2. the simulation and creation of life-like systems with previously identified principles and incentives.

Topics with relation to artificial and natural systems:

  • information theoretic intrinsic motivations
  • information theoretic quantification of behavior
  • information theoretic guidance of artificial evolution
  • information theoretic guidance of self-organization
  • information theoretic driving forces behind learning
  • information theoretic driving forces behind behavior
  • information theory in swarms
  • information theory in social behavior
  • information theory in evolution
  • information theory in the brain
  • information theory in system-environment distinction
  • information theory in the perception action loop
  • information theoretic definitions of life

Submission

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are refereed through a peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed Open Access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs).

Deadline for manuscript submissions: 28 February 2015

Special Issue Editors

Guest Editor
Dr. Christoph Salge
Adaptive Systems Research Group,University of Hertfordshire, College Lane, AL10 9AB Hatfield, UK
Website: http://homepages.stca.herts.ac.uk/~cs08abi
E-Mail: c.salge@herts.ac.uk
Phone: +44 1707 28 4490
Interests: Intrinsic Motivation (Empowerment); Self-Organization; Guided Self-Organization; Information-Theoretic Incentives for Social Interaction; Information-Theoretic Incentives for Swarms; Information Theory and Computer Game AI

Guest Editor
Dr. Georg Martius
Cognition and Neurosciences, Max Planck Institute for Mathematics in the Sciences Inselstrasse 22, 04103 Leipzig, Germany
Website: http://www.mis.mpg.de/jjost/members/georg-martius.html
E-Mail: martius@mis.mpg.de
Phone: +49 341 9959 545
Interests: Autonomous Robots; Self-Organization; Guided Self-Organization; Information Theory; Dynamical Systems; Machine Learning; Neuroscience of Learning; Optimal Control

Guest Editor
Dr. Keyan Ghazi-Zahedi
Information Theory of Cognitive Systems, Max Planck Institute for Mathematics in the Sciences Inselstrasse 22, 04103 Leipzig, Germany
Website: http://personal-homepages.mis.mpg.de/zahedi
E-Mail: zahedi@mis.mpg.de
Phone: +49 341 9959 535
Interests: Embodied Artificial Intelligence; Information Theory of the Sensorimotor Loop; Dynamical Systems; Cybernetics; Self-organisation; Synaptic plasticity; Evolutionary Robotics

Guest Editor
Dr. Daniel Polani
Department of Computer Science, University of Hertfordshire, Hatfield AL10 9AB, UK
Website: http://homepages.feis.herts.ac.uk/~comqdp1/
E-Mail: d.polani@herts.ac.uk
Interests: artificial intelligence; artificial life; information theory for intelligent information processing; sensor Evolution; collective and multiagent systems

Git and Version Control for Novelists, Screenwriters, Academics, and the General Public

Marginalia and Revision Control

At the end of April, I read an article entitled “In the Margins” in the Johns Hopkins University Arts & Sciences magazine.  I was particularly struck by the comments of eminent scholar Jacques Neefs on page thirteen (or paragraph 20) about computers making marginalia a thing of the past:

Neefs believes contemporary literature is losing a valuable component in an age when technology often precludes and trumps the need to save manuscripts or rough drafts. But it is not something that keeps him up at night. ‘The modern technique of computers and everything makes [marginalia] a thing of the past,’ he says. ‘There’s a new way of creation. Some would say it’s tragic, but something new has been invented. I don’t consider it tragic. There are still great writers who write and continue to have a way to keep the process.’

Photo looking over the shoulder of Jacques Neefs onto the paper he's been studing on the table in front of him.
Jacques Neefs (Image courtesy of Johns Hopkins University)

I actually think that he may be completely wrong and that current technology actually allows us to keep far more marginalia! (Has anyone heard of digital exhaust?) The bigger issue may be that many writers just don’t know how to keep a better running log of their work to maintain all the relevant marginalia they’re actually producing. (Of course there’s also the subsequent broader librarian’s “digital dilemma” of maintaining formats for the future. As an example, thing about how easy or hard it might be for you to read that ubiquitous 3.5 inch floppy disk you used in 1995.)

A a technologist who has spent many years in the entertainment industry, I feel compelled to point everyone towards the concept of revision control (or version control) within the realm of computer science.  Though it’s primarily used in tracking changes in computer programs and is often a tool used by large teams of programmers, it can very easily be used for tracking changes in almost any type of writing from novels, short stories, screenplays, legal contracts, or any type of textual documentation of nearly any sort.

Example Use Cases for Revision Control

Publishing

As a direct example, I’m using what is known as a Git repository to track every change I make in a textbook I’m currently writing.  I can literally go back and view every change I’ve made since beginning the project, so though I’m directly revising one (or more) text files, all of my “marginalia” and revisions are saved and available.  Currently I’m only doing it for my own reference and for additional backup not supposing that anyone other than myself or an editor possibly may want to ever peruse it.  If I was working in conjunction with otheres, there are ways for me to track the changes, edits, or notes that others (perhaps an editor or collaborator) might make.

In addition to the general back-up of the project (in case of catastrophic computer failure), I also have the ability to go back and find that paragraph (or multiple pages) I deleted last week in haste, but realize that I desperately want them back now instead of having to recreate them de n0vo.

Because it’s all digital, future scholars also won’t have problems parsing my handwriting issues as has occasionally come up in differentiating Mary Shelley’s writing from that of her husband in digital projects like the Shelley Godwin Archive. The fact that all changes are tracked and placed in a tree-like structure will indicate who wrote what and when and will indicate which changes were ultimately accepted and merged into the final version.

Screenplays in Hollywood

One particular use case I can easily see for such technology is tracking changes in screenplays over time.  I’m honestly shocked that every production company or even more likely studios don’t use such technology to follow changes in drafts over time. In the end, doing such tracking will certainly make Writers Guild of America (WGA) arbitrations much easier as literally every contribution to a script can be tracked to give screenwriters appropriate credit. The end results with the easy ability to time-machine one’s way back into older drafts is truly lovely, and the outputs give so much more information about changes in the script compared to the traditional and all-too-simple (*) which screenwriters use to indicate that something/anything changed on a specific line or the different colored pages which are used on scripts during production.

I can also picture future screenwriters using services like GitHub as platforms for storing and distributing their screenplays to potential agents, managers, and producers.

Redlining Legal Documents

Having seen thousands of legal agreements go back and forth over the years, revision control is a natural tool for tracking the redlining and changes of legal documents as they change over time before they are finally (or even never) executed. I have to imagine that being able to abstract out the appropriate metadata in the long run may actually help attorneys, agents, etc. to become better negotiators, but something like this is a project for another day.

Academia

In addition to direct research for projects being undertaken by academics like Neefs, academics should look into using revision control in their own daily work and writings.  While writing a book, paper, journal article, essay, monograph, etc. (or graduate students writing theses) one could use their own Git repository to not only save but to back up all of their own work not only for themselves primarily, but also future scholars who come later who would not otherwise have access to the “marginalia” one creates while manufacturing their written thoughts in digital form.

I can easily picture Git as a very simple “next step” in furthering the concept of the digital humanities as well as in helping to bridge the gap between C.P. Snow’s “two cultures.” (I’d also suggest that revision control is a relatively simple step one could take before learning a particular programming language, which I think should be a mandatory tool in everyone’s daily toolbox regardless of their field(s) of interest.)

Git Logo

Start Using Revision Control

“But how do I get started?” you ask.

Know going in that it may take parts of a day to get things set up and running, but once you’ve started with the basics, things are actually pretty easy and you can continue to learn the more advanced subtleties as you progress.  Once things are working smoothly, the additional overhead you’ll be expending won’t be too much more than the old method of hitting Alt-S to save one of your old Word documents in the time before auto-save became ubiquitous.

First one should start by choosing one of the myriad revision control systems that exist.  For the sake of brevity in this short introductory post, I’ll simply suggest that users take a very close look at Git because of its ubiquity and popularity in the computer science world and the fact that it includes a tremendously large amount of free information and support from a variety of sites on the internet. Git also has the benefit of having versions for all major operating systems (Windows, MacOS, and Linux). Git also has the benefit of a relatively long and robust life within the computer science community meaning that it’s very stable and has many more resources for the uninitiated to draw upon.

Once one has Git installed on their computer and has begun using it, I’d then recommending linking one’s local copy of the repository to a cloud storage solution like either GitHub or BitBucket.  While GitHub is certainly one of the most popular Git-related services out there (because it acts, in part, as the hub for a large portion of the open internet and thus promotes sharing), I often recommend using BitBucket as it allows free unlimited private but still share-able repositories while GitHub requires a small subscription fee for keeping one’s work private. Having a repository in the cloud will help tremendously in that your work will be available and downloadable from almost anywhere and because it also serves as a de-facto back-up solution for your work.

I’ve recently been playing around with version control to help streamline the writing/editing process for a book I’ve been writing. Though Git and it’s variants probably seem more daunting than they should to the everyday user, they really represent a very powerful tool. I’ve spent less than two days learning the basics of both Git and hosted repositories (GitHub and Bitbucket), and it has been more than well worth the minor effort.

There is a huge wealth of information on revision control in general and on installing and using Git available on the internet, including full textbooks. For the complete beginners, I’d recommend starting with The Chronicle’s “A Gentle Introduction to Version Control.” Keep in mind that though some of these resources look highly technical, it’s because many are trying to enumerate every function one could potentially desire, when even just the basic core functionality is more than enough to begin with. (I could analogize it to learning to drive a car versus actually reading the full manual so that you know how to take the engine apart and put it back together from scratch. To start with revision control, you only need to learn to “drive.”) Professors might also avail themselves of the use of their local institutional libraries which may host small sessions on learning such tools, or they might avail themselves of the help of their colleagues or students in the computer science department. For others, I’d recommend taking a look at Git’s primary website. BitBucket has an excellent step-by-step tutorial (and troubleshooting) for setting up the requisite software and using it.

What do you use for revision control?

I’ll welcome any thoughts, experiences, or additional resources one might want to share with others in the comments.

A Mathematical Symphony

Robert B. Ash, mathematician
in A Primer of Abstract Mathematics (The Mathematical Association of America, 1998)

 

A Primer of Abstract Mathematics by Robert B. Ash
A Primer of Abstract Mathematics by Robert B. Ash

 

Introduction to Lie Groups and Lie Algebras | UCLA Extension

Exercise Your Brain

As many may know or have already heard, Dr. Mike Miller, a retired mathematician from RAND and long-time math professor at UCLA, is offering a course on Introduction to Lie Groups and Lie Algebras this fall through UCLA Extension.  Whether you’re a professional mathematician, engineer, physicist, physician, or even a hobbyist interested in mathematics you’ll be sure to get something interesting out of this course, not to mention the camaraderie of 20-30 other “regulars” with widely varying backgrounds (actors to surgeons and evolutionary theorists to engineers) who’ve been taking almost everything Mike has offered over the years (and yes, he’s THAT good — we’re sure you’ll be addicted too.)

“Beginners” Welcome!

Even if it’s been years since you last took Calculus or Linear Algebra, Mike (and the rest of the class) will help you get quickly back up to speed to delve into what is often otherwise a very deep subject.  If you’re interested in advanced physics, quantum mechanics, quantum information or string theory, this is one of the topics that is de rigueur for delving in deeply and being able to understand them better. The topic is also one near and dear to the hearts of those in robotics, graphics, 3-D modelling, gaming, and areas utilizing multi-dimensional rotations. And naturally, it’s simply a beautiful and elegant subject for those who have no need to apply it to anything, but who just want to meander their way through higher mathematics for the fun of it (this will comprise the largest majority of the class by the way.)

Whether you’ve been away from serious math for decades or use it every day or even if you’ve never gone past Calculus or Linear Algebra, this is bound to be the most entertaining thing you can do with your Tuesday nights in the fall.  If you’re not sure what you’re getting into (or are scared a bit by the course description), I highly encourage to come and join us for at least the first class before you pass up on the opportunity.  I’ll mention that the greater majority of new students to Mike’s classes join the ever-growing group of regulars who take almost everything he teaches subsequently. (For the reticent, I’ll mention that one of the first courses I took from Mike was Algebraic Topology which generally requires a few semesters of Abstract Algebra and a semester of Topology as prerequisites.  I’d taken neither of these prerequisites, but due to Mike’s excellent lecture style and desire to make everything comprehensible, I was able to do exceedingly well in the course.) I’m happy to chat with those who may be reticent. Also keep in mind that you can register to take the class for a grade, pass/fail, or even no grade at all to suit your needs/lifestyle.

My classes have the full spectrum of students from the most serious to the hobbyist to those who are in it for the entertainment and  ‘just enjoy watching it all go by.’

Mike Miller, Ph.D.

As a group, some of us have a collection of a few dozen texts in the area which we’re happy to loan out as well.  In addition to the one recommended text (Mike always gives such comprehensive notes that any text for his classes is purely supplemental at best), several of us have also found some good similar texts:

Given the breadth and diversity of the backgrounds of students in the class, I’m sure Mike will spend some reasonable time at the beginning [or later in the class, as necessary] doing a quick overview of some linear algebra and calculus related topics that will be needed later in the quarter(s).

Further information on the class and a link to register can be found below. If you know of others who might be interested in this, please feel free to forward it along – the more the merrier.

I hope to see you all soon.


Introduction to Lie Groups and Lie Algebras

MATH X 450.6  /  3.00 units /  Reg. # 249254W
Professor: Michael Miller, Ph.D.
Start Date: 9/30/2014
Location UCLA: 5137 Math Sciences Building
Tuesday, 7-10pm
September 30 – December 16, 2014
11 meetings total (no mtg 11/11)
Register here: https://www.uclaextension.edu/Pages/Course.aspx?reg=249254

Course Description

Lie group is a differentiable manifold that is also a group for which the product and inverse maps are differentiable. A Lie algebra is a vector space endowed with a binary operation that is bilinear, alternating, and satisfies the so-called Jacobi identity. This course, the first in a 2-quarter sequence, is an introductory survey of Lie groups, their associated Lie algebras, and their representations. This first quarter will focus on the special case of matrix Lie groups–including general linear, special linear, orthogonal, unitary, and symplectic. The second quarter will generalize the theory developed to the case of arbitrary Lie groups. Topics to be discussed include compactness and connectedness, homomorphisms and isomorphisms, exponential mappings, the Baker-Campbell-Hausdorff formula, covering groups, and the Weyl group. This is an advanced course, requiring a solid understanding of linear algebra and basic analysis.

Recommended Textbook

Hall, Brian. Lie Groups, Lie Algebras, & Representations (Springer, 2004) ISBN: 9781441923134

 

Portrait of Sophus Lie (1842-1899)
Sophus Lie (1842-1899)

If I had a dollar for every time someone invited me to a Lie Algebra class, I’d be a…

 

2014 Fields Medal and Nevanlinna Prize Winners Announced

The 2014 Fields Medal and Nevanlinna Prize winners were announced yesterday.

General announcement

Nature: “Iranian is first woman to nab highest prize in maths”
Also includes coverage of the Gauss Prize for research that has had an impact outside mathematics, which was awarded to Stanley Osher of the University of California at Los Angeles.)

Great personal profiles with short videos via Quanta Magazine

Artur AvilaA Brazilian Wunderkind Who Calms Chaos

Manjul BhargavaThe Musical, Magical Number Theorist

Martin HairerIn Noisy Equations, One Who Heard Music

Maryam MirzakhaniA Tenacious Explorer of Abstract Surfaces

Subhash KhotA Grand Vision for the Impossible

Technical explanation of their work

Terry Tao (previous Fields Medal Winner): Avila, Bhargava, Hairer, Mirzakhani

 

 

Bucket List: Write A Joke for Robin Williams

In all the sadness of the passing of Robin Williams, I nearly forgot I’d “written” a short joke for him just after I’d first moved to Hollywood.

Killing some time just before I started work at Creative Artists Agency, I finagled my way into a rough-cut screening of Robin William’s iconoclastic role in PATCH ADAMS on the Universal Lot. Following the screening, I had the pleasure of chatting with [read: bum-rushed like a crazy fan] Tom Shadyac for a few minutes on the way out. I told him as a recent grad of Johns Hopkins University and having spent a LOT of time in hospitals, that they were missing their obligatory hospital gown joke. But to give it a karate chop (and because I’d just graduated relatively recently), they should put it into the graduation at the “end” and close on a high note.

I didn’t see or hear anything about it until many months later when I went to Mann’s Chinese Theater for the premiere and saw the final cut of the ending of the film, which I’ve clipped below. Just for today, I’m wearing the same red foam clown nose that I wore to the premiere that night.

Thanks for the laughs Robin.

Bucket List:
#1. Write a joke for Robin Williams.

http://youtu.be/kx2FhY_akDY