Quantum Biological Information Theory by Ivan B. Djordjevic | Springer

Bookmarked Quantum Biological Information Theory (Springer, 2015)

Springer recently announced the publication of the book Quantum Biological Information Theory by Ivan B. Djordjevic, in which I’m sure many readers here will have interest. I hope to have a review of it shortly after I’ve gotten a copy. Until then…

From the publisher’s website:

This book is a self-contained, tutorial-based introduction to quantum information theory and quantum biology. It serves as a single-source reference to the topic for researchers in bioengineering, communications engineering, electrical engineering, applied mathematics, biology, computer science, and physics. The book provides all the essential principles of the quantum biological information theory required to describe the quantum information transfer from DNA to proteins, the sources of genetic noise and genetic errors as well as their effects.

  • Integrates quantum information and quantum biology concepts;
  • Assumes only knowledge of basic concepts of vector algebra at undergraduate level;
  • Provides a thorough introduction to basic concepts of quantum information processing, quantum information theory, and quantum biology;
  • Includes in-depth discussion of the quantum biological channel modelling, quantum biological channel capacity calculation, quantum models of aging, quantum models of evolution, quantum models on tumor and cancer development, quantum modeling of bird navigation compass, quantum aspects of photosynthesis, quantum biological error correction.

Source: Quantum Biological Information Theory | Ivan B. Djordjevic | Springer

9783319228150I’ll note that it looks like it also assumes some reasonable facility with quantum mechanics in addition to the material listed above.

Springer also has a downloadable copy of the preface and a relatively extensive table of contents for those looking for a preview. Dr. Djordjevic has been added to the ever growing list of researchers doing work at the intersection of information theory and biology.

Why math? JHU mathematician on teaching, theory, and the value of math in a modern world | Hub

Bookmarked Why math? JHU mathematician on teaching, theory, and the value of math in a modern world (The Hub)

Great to see this interview with my friend and mathematician Richard Brown from Johns Hopkins Unviersity.  Psst: He’s got an interesting little blog, or you can follow some of his work on Facebook and Twitter.

Click through for the full interview: Q+A with Richard Brown, director of undergraduate studies in Johns Hopkins University’s Department of Mathematics

 

Heaven

A glass of wine and a good book

Heaven

Instagram filter used: Ludwig

Eugenia Cheng, author of How to Bake Pi, on Colbert Tonight

The author of one of the best math (and cooking) books of the year is on Stephen Colbert's show tonight.

Earlier this year, I read Eugenia Cheng’s brilliant book How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics. Tonight she’s appearing (along with Daniel Craig apparently) on the The Late Show with Stephen Colbert. I encourage everyone to watch it and read her book when they get the chance.

How-to-bake-pi

You can also read more about her appearance from Category Theorist John Carlos Baez here: Cakes, Custard, Categories and Colbert | The n-Category Café

My brief review of her book on GoodReads.com:

How to Bake Pi: An Edible Exploration of the Mathematics of MathematicsHow to Bake Pi: An Edible Exploration of the Mathematics of Mathematics by Eugenia Cheng
My rating: 4 of 5 stars

While most of the book is material I’ve known for a long time, it’s very well structured and presented in a clean and clear manner. Though a small portion is about category theory and gives some of the “flavor” of the subject, the majority is about how abstract mathematics works in general.

I’d recommend this to anyone who wants to have a clear picture of what mathematics really is or how it should be properly thought about and practiced (hint: it’s not the pablum you memorized in high school or even in calculus or linear algebra). Many books talk about the beauty of math, while this one actually makes steps towards actually showing the reader how to appreciate that beauty.

Like many popular books about math, this one actually has very little that goes beyond the 5th grade level, but in examples that are very helpfully illuminating given their elementary nature. The extended food metaphors and recipes throughout the book fit in wonderfully with the abstract nature of math – perhaps this is why I love cooking so much myself.

I wish I’d read this book in high school to have a better picture of the forest of mathematics.

More thoughts to come…

What An Actual Handwaving Argument in Mathematics Looks Like

I’m sure we’ve all heard them many times, but this is what an actual handwaving argument looks like in a mathematical setting.

Handwaving during Algebraic Number Theory

Instagram filter used: Normal

Photo taken at: UCLA Math Sciences Building

Handwaving during Algebraic Number Theory

A photo posted by Chris Aldrich (@chrisaldrich) on

Winter Q-BIO Quantitative Biology Meeting February 15-18, 2016

Bookmarked Winter Q-BIO Quantitative Biology Meeting February 15-18, 2016 (w-qbio.org)
The Winter Q-BIO Quantitative Biology Meeting is coming up at the Sheraton Waikiki in Oahu, HI, USA

A predictive understanding of living systems is a prerequisite for designed manipulation in bioengineering and informed intervention in medicine. Such an understanding requires quantitative measurements, mathematical analysis, and theoretical abstraction. The advent of powerful measurement technologies and computing capacity has positioned biology to drive the next scientific revolution. A defining goal of Quantitative Biology (qBIO) is the development of general principles that arise from networks of interacting elements that initially defy conceptual reasoning. The use of model organisms for the discovery of general principles has a rich tradition in biology, and at a fundamental level the philosophy of qBIO resonates with most molecular and cell biologists. New challenges arise from the complexity inherent in networks, which require mathematical modeling and computational simulation to develop conceptual “guideposts” that can be used to generate testable hypotheses, guide analyses, and organize “big data.”

The Winter q-bio meeting welcomes scientists and engineers who are interested in all areas of q-bio. For 2016, the meeting will be hosted at the Sheraton Waikiki, which is located in Honolulu, on the island of Oahu. The resort is known for its breathtaking oceanfront views, a first-of-its-kind recently opened “Superpool” and many award-winning dining venues. Registration and accommodation information can be found via the links at the top of the page.

Source: Winter Q-BIO Quantitative Biology Meeting

Dr. Michael Miller Math Class Hints and Tips | UCLA Extension

An informal orientation for those taking math classes from Dr. Michael Miller through UCLA Extension.

Congratulations on your new math class, and welcome to the “family”!

Beginners Welcome!

Invariably the handful of new students every year eventually figure the logistics of campus out, but it’s easier and more fun to know some of the options available before you’re comfortable halfway through the class. To help get you over the initial hump, I’ll share a few of the common questions and tips to help get you oriented. Others are welcome to add comments and suggestions below. If you have any questions, feel free to ask anyone in the class, we’re all happy to help.

First things first, for those who’ve never visited UCLA before, here’s a map of campus to help you orient yourself. Using the Waze app on your smartphone can also be incredibly helpful in getting to campus more quickly through the tail end of rush hour traffic.

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 Dr. Miller’s math courses, not to mention the camaraderie of 20-30 other “regulars” with widely varying backgrounds (from 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.) 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 Autumn and Winter. 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.

Don’t be intimidated if you feel like everyone in the class knows each other fairly well — most of us do. Dr. Miller and mathematics can be addictive so many of us have been taking classes from him for 5-20+ years, and over time we’ve come to know each other.

Tone of Class

If you’ve never been to one of Dr. Miller’s classes before, they’re fairly informal and he’s very open to questions from those who don’t understand any of the concepts or follow his reasoning. He’s a retired mathematician from RAND and long-time math professor at UCLA. Students run the gamut from the very serious who read multiple textbooks and do every homework problem to hobbyists who enjoy listening to the lectures and don’t take the class for a grade of any sort (and nearly every stripe in between). He’ll often recommend a textbook that he intends to follow, but it’s never been a “requirement” and more often that not, the bookstore doesn’t list or carry his textbook until the week before class. (Class insiders will usually find out about the book months before class and post it to the Google Group – see below).

His class notes are more than sufficient for making it through the class and doing the assigned (optional) homework. He typically hands out homework in handout form, so the textbook is rarely, if ever, required to make it through the class. Many students will often be seen reading various other texts relating to the topic at hand as they desire. Usually he’ll spend an 45-60 minutes at the opening of each class after the first to go over homework problems or questions that anyone has.

For those taking the class for a grade or pass/fail, his usual policy is to assign a take home problem set around week 9 or 10 to be handed in at the penultimate class. [As a caveat, make sure you check his current policy on grading as things may change, but the preceding has been the usual policy for a decade or more.]

Parking Options

Lot 9 – Located at the northern terminus of Westwood Boulevard, one can purchase a parking pass for about $12 a day at the kiosk in the middle of the street just before Westwood Blvd. ends. The kiosk is also conveniently located right next to the parking structure. If there’s a basketball game or some other major event, Lot 8 is just across the street as well, though it’s just a tad further away from the Math Sciences Building. Since more of the class uses this as their parking structure of choice, there is always a fairly large group walking back there after class for the more security conscious.

Lot 2 – Located off of Hilgard Avenue, this is another common option for easy parking as well. While fairly close to class, not as many use it as it’s on the quieter/darker side of campus and can be a bit more of a security issue for the reticent.

Tip: For those opting for on-campus parking, one can usually purchase a quarter-long parking pass for a small discount at the beginning of the term.

Westwood Village and Neighborhood – Those looking for less expensive options street parking is available in the surrounding community, but use care to check signs and parking meters as you assuredly will get a ticket. Most meters in the surrounding neighborhoods end at either 6pm or 8pm making parking virtually free (assuming you’re willing to circle the neighborhood to find one of the few open spots.)

There are a huge variety of lots available in the Village for a range of prices, but the two most common, inexpensive, and closer options seem to be:

  • Broxton Avenue Public Parking at 1036 Broxton Avenue just across from the Fox Village and Bruin Theaters – $3 for entering after 6pm / $9 max for the day
  • Geffen Playhouse Parking at 10928 Le Conte Ave. between Broxton and Westwood – price varies based on the time of day and potential events (screenings/plays in Westwood Village) but is usually $5 in the afternoon and throughout the evening

Dining Options

More often than not a group of between 4 and 15 students will get together every evening before class for a quick bit to eat and to catch up and chat. This has always been an informal group and anyone from class is more than welcome to join. Typically we’ll all meet in the main dining hall of Ackerman Union (Terrace Foodcourt, Ackerman Level 1) between 6 and 6:30 (some with longer commutes will arrive as early as 3-4pm, but this can vary) and dine until about 6:55pm at which time we walk over to class.

The food options on Ackerman Level 1 include Panda Express, Rubio’s Tacos, Sbarro, Wolfgang Puck, and Greenhouse along with some snack options including Wetzel’s Pretzels and a candy store. One level down on Ackerman A-level is a Taco Bell, Carl’s Jr., Jamba Juice, Kikka, Buzz, and Curbside, though one could get takeout and meet the rest of the “gang” upstairs.

There are also a number of other on-campus options as well though many are a reasonable hike from the class location. The second-closest to class is the Court of Sciences Student Center with a Subway, Yoshinoya, Bombshelter Bistro, and Fusion.

Naturally, for those walking up from Westwood Village, there are additional fast food options like In-N-Out, Chick-fil-A, Subway, and many others.

Killing Time

For those who’ve already eaten or aren’t hungry, you’ll often find one or more of us browsing the math and science sections of the campus bookstore on the ground level of Ackerman Union to kill time before class. Otherwise there are usually a handful of us who arrive a half an hour early and camp out in the classroom itself (though this can often be dauntingly quiet as most use the chance to catch up on reading here.) If you arrive really early, there are a number of libraries and study places on campus. Boelter Hall has a nice math/science library on the 8th Floor.

Mid-class Break Options

Usually about halfway through class we’ll take a 10-12 minute coffee break. For those with a caffeine habit or snacking urges, there are a few options:

Kerckhoff Hall Coffee Shop is just a building or two over and is open late as snack stop and study location. They offer coffee and various beverages as well as snacks, bagels, pastries, and ice cream. Usually 5-10 people will wander over as a group to pick up something quick.

The Math Sciences Breezeway, just outside of class, has a variety of soda, coffee, and vending machines with a range of beverages and snacks. Just a short walk around the corner will reveal another bank of vending machines if your vice isn’t covered. The majority of class will congregate in the breezeway to chat informally during the break.

The Court of Sciences Student Center, a four minute walk South, with the restaurant options noted above if you need something quick and more substantial, though few students use this option at the break.

Bathrooms – The closest bathrooms to class are typically on the 5th floor of the Math Sciences Building. The women’s is just inside the breezeway doors and slightly to the left. The men’s rooms are a bit further and are either upstairs on the 6th floor (above the women’s), or a hike down the hall to the left and into Boelter hall. I’m sure the adventurous may find others, but take care not to get lost.

Informal Class Resources

Google Group

Over the years, as an informal resource, members of the class have created and joined a private Google Group (essentially an email list-serv) to share thoughts, ideas, events, and ask questions of each other. There are over 50 people in the group, most of whom are past Miller students, though there are a few other various mathematicians, physicists, engineers, and even professors. You can request to join the private group to see the resources available there. We only ask that you keep things professional and civil and remember that replying to all reaches a fairly large group of friends. Browsing through past messages will give you an idea of the types of posts you can expect. The interface allows you to set your receipt preferences to one email per message posted, daily digest, weekly digest, or no email (you’re responsible for checking the web yourself), so be sure you have the setting you require as some messages are more timely than others. There are usually only 1-2 posts per week, so don’t expect to be inundated.

Study Groups

Depending on students’ moods, time requirements, and interests, we’ve arranged informal study groups for class through the Google Group above. Additionally, since Dr. Miller only teaches during the Fall and Winter quarters, some of us also take the opportunity to set up informal courses during the Spring/Summer depending on interests. In the past, we’ve informally studied Lie Groups, Quantum Mechanics, Algebraic Geometry, and Category Theory in smaller groups on the side.

Dropbox

As a class resource, some of us share a document repository via Dropbox. If you’d like access, please make a post to the Google Group.

Class Notes

Many people within the class use Livescribe.com digital pens to capture not only the written notes but the audio discussion that occurred in class as well (the technology also links the two together to make it easier to jump around within a particular lecture). If it helps to have a copy of these notes, please let one of the users know you’d like them – we’re usually pretty happy to share. If you miss a class (sick, traveling, etc.) please let one of us know as the notes are so unique that it will be almost like you didn’t miss anything at all.

You can typically receive a link to the downloadable version of the notes in Livescribe’s Pencast .pdf format. This is a special .pdf file but it’s a bit larger in size because it has an embedded audio file in it that is playable with the more recent version of Adobe Reader X (or above) installed. (This means to get the most out of the file you have to download the file and open it in Reader X to get the audio portion. You can view the written portion in most clients, you’ll just be missing out on all the real fun and value of the full file.) With the notes, you should be able to toggle the settings in the file to read and listen to the notes almost as if you were attending the class live.

Viewing and Playing a Pencast PDF

Pencast PDF is a new format of notes and audio that can play in Adobe Reader X or above.
You can open a Pencast PDF as you would other PDF files in Adobe Reader X. The main difference is that a Pencast PDF can contain ink that has associated audio—called “active ink”. Click active ink to play its audio. This is just like playing a Pencast from Livescribe Online or in Livescribe Desktop. When you first view a notebook page, active ink appears in green type. When you click active ink, it turns gray and the audio starts playing. As audio playback continues, the gray ink turns green in synchronization with the audio. Non-active ink (ink without audio) is black and does not change appearance.

Audio Control Bar

Pencast PDFs have an audio control bar for playing, pausing, and stopping audio playback. The control bar also has jump controls, bookmarks (stars), and an audio timeline control.

Active Ink View Button

There is also an active ink view button. Click this button to toggle the “unwritten” color of active ink from gray to invisible. In the default (gray) setting, the gray words turn green as the audio plays. In the invisible setting, green words seem to write themselves on blank paper as the audio plays.

History

For those interested in past years’ topics, here’s the list I’ve been able to put together thus far:

Fall 2006: Complex Analysis
Winter 2007: Field Theory
Fall 2007: Algebraic Topology
Winter 2008: Integer Partitions
Fall 2008: Calculus on Manifolds
Winter 2009: Calculus on Manifolds: The Sequel
Fall 2009: Group Theory
Winter 2010: Galois Theory
Fall 2010: Differential Geometry
Winter 2011: Differential Geometry II
Fall 2011: p-Adic Analysis
Winter 2012: Group Representations
Fall 2012: Set Theory
Winter 2013: Functional Analysis
Fall 2013: Number Theory (Skipped)
Winter 2014: Measure Theory
Fall 2014: Introduction to Lie Groups and Lie Algebras Part I
Winter 2015: Introduction to Lie Groups and Lie Algebras Part II
Fall 2015: Algebraic Number Theory
Winter 2016: Algebraic Number Theory: The Sequel
Fall 2016: Introduction to Complex Analysis, Part I
Winter 2017: Introduction to Complex Analysis, Part II
Fall 2017: Introduction to Algebraic Geometry
Winter 2018: Introduction to Algebraic Geometry: The Sequel
Fall 2018: Gems and Astonishments of Mathematics Past and Present 
Winter 2019: Introduction to Category Theory
Fall 2019: TBD
Winter 2020: TBD

The Mathematics Literature Project

Bookmarked The Mathematics Literature Project (tqft.net)

“The Mathematics Literature Project intends to survey the state of the freely accessible mathematics literature. In particular, it will index freely accessible URLs for mathematics articles. These are legitimately hosted copies of the article (i.e. at publishers, the arXiv, institutional repositories, or authors’ homepages), which are freely available in any browser, anywhere in the world.”

Game Theory’s Tit-for-Tat is Just a Mathematically Complete Version of Religion’s Golden Rule

Francis Fukuyama (1952- ), American political scientist, political economist, author
in The Origins of Political Order: From Prehuman Times to the French Revolution (Farrar, Straus and Giroux, 2011)

 

Why Information Grows: The Evolution of Order, from Atoms to Economies

I just ordered a copy of Why Information Grows: The Evolution of Order, from Atoms to Economies by Cesar Hidalgo. Although it seems more focused on economics, the base theory seems to fit right into some similar thoughts I’ve long held about biology.

Why Information Grows: The Evolutiion of Order from Atoms to Economies by Cesar Hidalgo
Why Information Grows: The Evolutiion of Order from Atoms to Economies by Cesar Hidalgo

 

From the book description:

“What is economic growth? And why, historically, has it occurred in only a few places? Previous efforts to answer these questions have focused on institutions, geography, finances, and psychology. But according to MIT’s antidisciplinarian César Hidalgo, understanding the nature of economic growth demands transcending the social sciences and including the natural sciences of information, networks, and complexity. To understand the growth of economies, Hidalgo argues, we first need to understand the growth of order.

At first glance, the universe seems hostile to order. Thermodynamics dictates that over time, order–or information–will disappear. Whispers vanish in the wind just like the beauty of swirling cigarette smoke collapses into disorderly clouds. But thermodynamics also has loopholes that promote the growth of information in pockets. Our cities are pockets where information grows, but they are not all the same. For every Silicon Valley, Tokyo, and Paris, there are dozens of places with economies that accomplish little more than pulling rocks off the ground. So, why does the US economy outstrip Brazil’s, and Brazil’s that of Chad? Why did the technology corridor along Boston’s Route 128 languish while Silicon Valley blossomed? In each case, the key is how people, firms, and the networks they form make use of information.

Seen from Hidalgo’s vantage, economies become distributed computers, made of networks of people, and the problem of economic development becomes the problem of making these computers more powerful. By uncovering the mechanisms that enable the growth of information in nature and society, Why Information Grows lays bear the origins of physical order and economic growth. Situated at the nexus of information theory, physics, sociology, and economics, this book propounds a new theory of how economies can do, not just more, but more interesting things.”

The Category Theory Site Is Now Live

Administrative notes and a new website for the Category Theory Summer Study Group 2015

Platform Choice

I’ve made a few posts here [1] [2] about a summer study group for category theory. In an effort to facilitate the growing number of people from various timezones and differing platforms (many have come to us from Google+, Tumblr, Twitter, GoodReads, and friends from Dr. Miller’s class in a private Google Group), I’ve decided it may be easiest to set up something completely separate from all of these so our notes, resources, and any other group contributions can live on to benefit others in the future. Thus I’ve built Category Theory: Summer Study Group 2015 on WordPress.  It will live as a sub-domain of my personal site until I get around to buying a permanent home for it (any suggestions for permanent domain names are welcome).

Registration

We’ve actually had a few people already find the new site and register before I’ve announced it, but for those who haven’t done so yet, please go to our participant registration page and enter your preferred username and email address.  We’ll email you a temporary password which you can change when you login for the first time. Those who want to use their pre-existing WordPress credentials are welcome to do so.

Once you’ve registered, be sure to update your profile (at least include your name) so that others will know a little bit more about you. If you’d like you can also link your WordPress.com account [or sign up for one and then link it] so that you can add a photo and additional details.  To login later, there’s a link hidden in the main menu under “Participants.”

You can also add your details to the form at the bottom of the Participants page to let others know a bit more about you and where you can be reached. Naturally this is optional as I know some have privacy issues. In the notes, please leave your location/timezone so that we can better coordinate schedules/meetings.

Category Theory Blog

Your username/password will allow you to post content directly to the study group’s blog. This can be contributed notes, questions, resources, code, photos, thoughts, etc. related to category theory and related areas of mathematics we’ll be looking at. Initially your posts will be moderated (primarily only to prevent spam), and over time your status will be elevated to allow immediate posting and editing. If you have any questions or need administrative help, I’m easy to find and happy to help if you get into trouble. Most of the interface will hopefully be easy to understand.

For those with questions, please try to read posts as you’re able and feel free to comment with hints and/or solutions.  I’ve created “categories” with the chapter titles from the text we’re using to facilitate sorting/searching. Depending on the need, we can granularize this further as we proceed. There is also the ability to tag posts with additional metadata or upload photos as well.

As appropriate, I’ll take material out of the blog/posts stream and place it into freestanding pages for easier reference in the future. As an example, I’ve already found some material on YouTube and MIT’s Open Course Ware site (Spivak posted his 2013 class using our same text, though it unfortunately doesn’t include video or audio) that may be relevant to many.

For those interested, WordPress supports most basic LaTeX, though I doubt it supports any of the bigger category theory diagramming packages, so feel free to draw out pictures/diagrams, photograph them, and upload them for others to see if necessary.

As an advocate of the open web and owning one’s own data, I highly recommend everyone publish/post their content here as well as to their favorite site/platform of choice as they see fit.

Textbook

In emails and chatter around the web, I haven’t heard any major objections to the proposed textbook so far, so unless there are, I’m assuming that it should serve most of us well. Hopefully everyone has a copy by now (remember there are free versions available) and has begun reading the introductory material.  Those requiring a bit more mathematical rigor and challenge can supplement with additional texts as I’m sure I and many others will. If you’re posting questions to the site about problems/questions from other texts, please either state them explicitly or tag them with the author’s last name as well as the problem/exercise number. (I’ll try to make them all canonical on the back end as we progress, so don’t worry too much if you’re not sure how or what to tag them with.)

Conference Call Tool

At the moment, most people have been fairly open to the three big platforms, though a few on either Linux or Chromebooks don’t have access to be able to install/operate anything but Google Hangouts, so I’m presently proposing that we adopt it for our group. Nearly everyone in the group already has a gmail account, so I don’t expect it to be an undue burden. If you haven’t used it before, please download/install any plugins you may require for your platform in advance of our first “call.”

Meeting Times

I’ve only heard back from a small handful of people on availability so far, but it doesn’t look like it will be difficult to find an appropriate time.  If you haven’t already done so, please fill out the “survey,” so we can determine a good call time for next week. If necessary, we can do additional times to help serve everyone’s needs. We don’t want to leave out any who sincerely want to participate.

Office Hours

As most of the participants are spread over the United States, Europe, and Asia, I’m suggesting that everyone carve out a standing block of time (we can call them “office hours”) that they can use to be available (via Google Hangouts or otherwise) to help out others having difficulty or who have questions. Since there isn’t a “professor” I’m hoping that we can all serve each other as unofficial teaching assistants to get through the process, and having standing office hours may be the easiest way to catch others for help in addition to the web site itself.

Questions? Comments? Snide Remarks?

If you have any questions, or I’ve managed to miss something, please don’t hesitate to make a comment below.  I’m hoping to get enough responses by Friday/Saturday this week to post our first meeting time for next week.

 

Commutative Diagrams in LaTeX

A meta-review of resources for typesetting commutative diagrams in TeX & LaTeX. Save time in trying to find the right commutative diagram package on CTAN.

Overview

With my studies in category theory trundling along, I thought I’d take  moment to share some general resources for typesetting commutative diagrams in \LaTeX. I’ll outline below some of the better resources and recommendations I’ve found, most by much more dedicated and serious users than I. Following that I’ll list a few resources, articles, and writings on some of the more common packages that I’ve seen mentioned.

Naturally, just reading through some of the 20+ page user guides to some of these packages can be quite daunting, much less wading through the sheer number that exist.  Hopefully this one-stop-shop meta-overview will help others save some time trying to figure out what they’re looking for.

Feruglio Summary

Gabriel Valiente Feruglio has a nice overview article naming all the primary packages with some compare/contrast information. One will notice it was from 1994, however, and misses a few of the more modern packages including TikZ. His list includes: AMS; Barr (diagxy); Borceux; Gurari; Reynolds; Rose (XY-pic); Smith (Arrow); Spivak; Svensson (kuvio); Taylor (diagrams); and Van Zandt (PSTricks). He lists them alphabetically and gives brief overviews of some of the functionality of each.

Feruglio, Gabriel Valiente. Typesetting Commutative Diagrams.  TUGboat, Volume 15 (1994), No. 4

Milne Summary

J.S. Milne has a fantastic one-page quick overview description of several available packages with some very good practical advise to users depending on the level of their needs. He also provides a nice list of eight of the most commonly used packages including: array (LaTeX); amscd (AMS); DCpic (Quaresma); diagrams (Taylor); kuvio (Svensson); tikz (Tantau); xymatrix (Rose); and diagxy (Barr). It’s far less formal than Feruglio, but is also much more modern. I also found it a bit more helpful for trying to narrow down one or more packages with which to play around.

Milne, J.S. Guide to Commutative Diagram Packages.

Spivak Pseudo-recommendations

David Spivak, the author of Category Theory for the Sciences, seems to prefer XY-pic, diagXY, and TikZ based on his website from which he links to guides to each of these.

Resources for some of the “Bigger” Packages

Based on the recommendations given in several of the resources above, I’ve narrowed the field a bit to some of the better sounding packages. I’ve provided links to the packages with some of the literature supporting them.

Diagxy: Michael Barr

XY-pic: Kristoffer Rose & Ross Moore

Diagrams: Paul Taylor

TikZ-CD: Florêncio Neves

Is there a particular package you recommend? Feel free to add your thoughts, comments, and additional resources in the comments below.

Category Theory Summer Study Group 2015

A suggested syllabus for a summer study group on category theory.

Syllabus

Initial details for putting  the group together can be found at http://boffosocko.com/2015/05/21/category-theory-anyone/.

Below is a handful of suggestions and thoughts relating to the study group in terms of platforms to assist us in communicating as well as a general outline for the summer.  I’m only “leading” this in the sense that I put my foot forward first, but I expect and sincerely hope that others will be active leaders and participants as well, so please take the following only as a suggestion, and feel free to add additional thoughts and commentary you feel might help the group.

Primary resources:

General Communication

Since many within the group are already members of the Google Group “Advanced Physics & Math – Los Angeles.” I suggest we use the email list here as a base of communication. I believe the group is still “private” but am happy to invite the handful of participants who aren’t already members. Those actively participating are encouraged to change their settings so that they receive emails from the group either as they’re posted, or in batches once a day.  Those subscribed only once a week or less frequently are likely to miss out on questions, comments, and other matters.

Alternately we might also use the GoodReads.com discussion group within the “Mathematics Students” group. I believe only about three of us so far may already be goodreads members, so this may require more effort for others to join.

If anyone has an alternate platform suggestion for communicating and maintaining resources, I’m happy to entertain it.

I wouldn’t be opposed to setting up a multi-user WordPress site that we could all access and post/cross-post to. Doing this could also allow for use of \LaTeX as well, which may be useful down the line. This would also have the benefit of being open to the public and potentially assisting future students. It also has built-in functionality of notifying everyone of individual posts and updates as they’re entered.

Meetings

I’ll propose a general weekly meeting online via Google Hangouts on a day and time to be determined.  It looks like the majority of respondents are in the Pacific timezone, so perhaps we could shoot for something around 7pm for an hour or so if we do something during weekdays so that East coasters can join without us running too late. If we decide to do something during the weekend, we obviously have a good bit more flexibility.

If we could have everyone start by indicating which days/times absolutely won’t work for them and follow up with their three to four preferred days/times, then we might be able to build a consensus for getting together.

Alternate videoconference options could include Skype, ooVoo, or others, in some part because I know that most participants are already part of the Google ecosystem and know that one or more potential participants is using Google Chromebooks and thus may not be able to use other platforms.  Is anyone not able to use Google Hangouts? If we opt for something else, we want something that is ubiquitous for platform, allows screen sharing, and preferably the ability to record the sessions for those who aren’t present.

Ideally the videoconference meetings will be geared toward an inverted classroom style of work in which it would be supposed that everyone has read the week’s material and made an attempt at a number of problems. We can then bring forward any general or specific conceptual problems people may be having and then work as a group toward solving any problems that anyone in the group may be having difficulty with.

I’ll also suggest that even if we can’t all make a specific date and time, that we might get together in smaller groups to help each other out.  Perhaps everyone could post one or two regular hours during the week as open “office hours” so that smaller groups can discuss problems and help each other out so that we can continue to all make progress as a group.

Primary Textbook

Spivak, David I. Category Theory for the Sciences. (The MIT Press, 2014)

Given the diversity of people in the group and their backgrounds, I’ll suggest Spivak’s text which has a gentle beginning and is geared more toward scientists and non-professional mathematicians, though it seems to come up to speed fairly quickly without requiring a large number of prerequisites.  It also has the benefit of being free as noted below.

The textbook can be purchased directly through most book retailers.  Those looking for cheaper alternatives might find these two versions useful. The HTML version should be exactly in line with the printed one, while the “old version” may not be exactly the same.

Following this, I might suggest we use something like Awody’s text or Leinster’s which are slightly more technical, but still fairly introductory. Those who’d like a more advanced text can certainly supplement by reading portions of those texts as we work our way through the material in Spivak. If all of the group wants a more advanced text, we can certainly do it, but I’d prefer not to scare away any who don’t have a more sophisticated background.

Additional References

Proposed Schedule

The following schedule takes us from now through the end of the summer and covers the entirety of the book.  Hopefully everyone will be able to participate through the end, though some may have additional pressures as the beginning of the Fall  sees the start of other courses. Without much prior experience in the field myself, I’ve generally broken things up to cover about 35 pages a week, though some have slightly more or less.  Many, like me, may feel like the text really doesn’t begin until week three or four as the early chapters provide an introduction and cover basic concepts like sets and functions which I have a feeling most have at least some experience with.  I’ve read through chapter two fairly quickly already myself.  This first easy two week stretch will also give everyone the ability to settle in as well as allow others to continue to join the group before we make significant headway.

If anyone has more experience in the subject and wishes to comment on which sections we may all have more conceptual issues with, please let us know so we can adjust the schedule as necessary.  I suppose we may modify the schedule as needed going forward, though like many of you, I’d like to try to cover as much as we can before the end of the summer.

Week One: May 24 (24 pages)

Administrative tasks

  • Purchase Textbook
  • Decide on best day/time for meeting
  • Decide on platform for meetings: Google Hangouts /Skype /ooVoo /Other
  • 1 A brief history of category theory
  • 1.2 Intention of this book
  • 1.3 What is requested from the student
  • 1.4 Category theory references
  • 2 The Category of Sets 9
  • 2.1 Sets and functions
  • 2.2 Commutative diagrams

Week Two: May 31  (50 pages)

  • 2.3 Ologs
  • 3 Fundamental Considerations in Set 41
  • 3.1 Products and coproducts
  • 3.2 Finite limits in Set

Week Three: June 7 (40 pages)

  • 3.3 Finite colimits in Set
  • 3.4 Other notions in Set

Week Four: June 14 (31 pages)

  • 4 Categories and Functors, Without Admitting It 115
  • 4.1 Monoids
  • 4.2 Groups

Week Five: June 21 (38 pages)

  • 4.3 Graphs
  • 4.4 Orders

Week Six: June 28 (19 pages)

  • 4.5 Databases: schemas and instances

Week Seven: July 5 (36 pages)

  • 5 Basic Category Theory 203
  • 5.1 Categories and functors

Week Eight: July 12 (28 pages)

  • 5.2 Common categories and functors from pure math

Week Nine: July 19 (48 pages)

  • 5.3 Natural transformations
  • 5.4 Categories and schemas are equivalent, Cat » Sch

Week Ten: July 26 (45 pages)

  • 6 Fundamental Considerations of Categories
  • 6.1 Limits and colimits

Week Eleven: August 2 (15 pages)

  • 6.2 Other notions in Cat

Week Twelve: August 9 (26 pages)

  • 7 Categories at Work 375
  • 7.1 Adjoint functors

Week Thirteen: August 16 (32 pages)

  • 7.2 Categories of functors

Week Fourteen: August 23 (19 pages)

  • 7.3 Monads

Week Fifteen: August 30 (23 pages)

  • 7.4 Operads

Additional resources

Requested/Required Responses from participants:

Preferred platform(s) for communications:

Email and/or online discussions

Platform Can use Can’t use Prefer Not to Use
Google Group
WordPress Site
GoodReads Group
Other:

Videoconferences

Platform Can use Can’t use Prefer Not to Use
Google Hangouts
Skype
ooVoo
Other

 

Dates and times you absolutely CAN’T make for meetings (please include your local time zone):

Weekdays:

Weekends:

 

Dates and times you prefer (please include your local time zone):

Weekdays:

Weekends:

 

One or two time periods during the week you could generally/reliably be available for “office hours”:

 

Any other thoughts on the material above:

  • Textbooks
  • Schedule
  • Additional resources for the group
  • Other

If you’d like to join us, please fill out the contact information and details below based on the material above:

Please indicate which videoconference platforms you are able to use by placing a checkmark in the corresponding boxes below. If you’re technically unable to use one or more, please indicate which in the “general comments” box above, and provide the reason why.

The Information Universe Conference

"The Information Universe" Conference in The Netherlands in October hits several of the sweet spots for areas involving information theory, physics, the origin of life, complexity, computer science, and microbiology.

Yesterday, via a notification from Lanyard, I came across a notice for the upcoming conference “The Information Universe” which hits several of the sweet spots for areas involving information theory, physics, the origin of life, complexity, computer science, and microbiology. It is scheduled to occur from October 7-9, 2015 at the Infoversum Theater in Groningen, The Netherlands.

I’ll let their site speak for itself below, but they already have an interesting line up of speakers including:

Keynote speakers

  • Erik Verlinde, Professor Theoretical Physics, University of Amsterdam, Netherlands
  • Alex Szalay, Alumni Centennial Professor of Astronomy, The Johns Hopkins University, USA
  • Gerard ‘t Hooft, Professor Theoretical Physics, University of Utrecht, Netherlands
  • Gregory Chaitin, Professor Mathematics and Computer Science, Federal University of Rio de Janeiro, Brasil
  • Charley Lineweaver, Professor Astronomy and Astrophysics, Australian National University, Australia
  • Lude Franke, Professor System Genetics, University Medical Center Groningen, Netherlands
Infoversum Theater, The Netherlands
Infoversum Theater, The Netherlands

Conference synopsis from their homepage:

The main ambition of this conference is to explore the question “What is the role of information in the physics of our Universe?”. This intellectual pursuit may have a key role in improving our understanding of the Universe at a time when we “build technology to acquire and manage Big Data”, “discover highly organized information systems in nature” and “attempt to solve outstanding issues on the role of information in physics”. The conference intends to address the “in vivo” (role of information in nature) and “in vitro” (theory and models) aspects of the Information Universe.

The discussions about the role of information will include the views and thoughts of several disciplines: astronomy, physics, computer science, mathematics, life sciences, quantum computing, and neuroscience. Different scientific communities hold various and sometimes distinct formulations of the role of information in the Universe indicating we still lack understanding of its intrinsic nature. During this conference we will try to identify the right questions, which may lead us towards an answer.

  • Is the universe one big information processing machine?
  • Is there a deeper layer in quantum mechanics?
  • Is the universe a hologram?
  • Is there a deeper physical description of the world based on information?
  • How close/far are we from solving the black hole information paradox?
  • What is the role of information in highly organized complex life systems?
  • The Big Data Universe and the Universe : are our numerical simulations and Big Data repositories (in vitro) different from real natural system (in vivo)?
  • Is this the road to understanding dark matter, dark energy?

The conference will be held in the new 260 seats planetarium theatre in Groningen, which provides an inspiring immersive 3D full dome display, e.g. numerical simulations of the formation of our Universe, and anything else our presenters wish to bring in. The digital planetarium setting will be used to visualize the theme with modern media.

The Information Universe Website

Additional details about the conference including the participants, program, venue, and registration can also be found at their website.

Category Theory Anyone?

I'm putting together a study group for an introduction to category theory. Who wants to join me?

I’m putting together a study group for an introduction to category theory. Who wants to join me?

Usually in the Fall and Winter, I’m concentrating on studying some semblance of abstract mathematics with a group of 20-30 kamikaze amateurs under the apt tutelage of Dr. Michael Miller through UCLA Extension. Since he doesn’t offer any classes in the Spring or Summer and we haven’t managed to talk Terence Tao into offering something interesting à la Leonard Susskind, we’re all at a loss for what to do with some of our time.

A small cohort of regulars from Miller’s class has recently taken up plowing through Howard Georgi’s Lie Algebras and Particle Physics. Though this seems very diverting to me given our work on Lie groups and algebras in the Fall and Winter, I don’t see any direct or exciting applications to anything more immediate.

Why Not Try Category Theory?

Since the death of Grothendieck I have seen a growing number of references to the area of category theory from a variety of different fronts.

Most notably, for the past year I’ve been more closely following John Baez’s Azimuth Blog which has frequent posts relating to category theory with applications I can directly use in various areas. Unfortunately I couldn’t attend his recent workshop at NIMBioS on Information and Entropy in Biological Systems, which apparently means I missed meeting Tom Leinster who recently released the textbook Basic Category Theory (Cambridge University Press, 2014). [I was already never going to forgive myself after I missed the workshop, but this fact now seems to be additional salt in the wound.]

The straw that broke the proverbial camel’s back was my serendipitously stumbling across Ilyas Khan‘s excellent post “Category Theory – the bedrock of mathematics?” while doing a Google image search for something entirely unrelated to anything remotely similar to mathematics. His discussion and the breadth of links to interesting and intriguing papers and articles within it and several colleagues thanking me for posting about it have finally forced my hand. (I also find myself wishing that he would write on a more formal basis more frequently.)

So over the past week or so, I’ve done some basic subject area searching, and I’ve picked up David I. Spivak’s book Category Theory for the Sciences (The MIT Press, 2014) to begin plowing through it.

Anyone Care to Join Me?

If you’re going to get lost and confused in the high weeds, you may as well have company, right?

Chris Aldrich

 

Category Theory, Anyone?
Category Theory, Anyone?

Since doing abstract math is always more fun with companions, and I know there are several out there who might be interested in some of the areas which category theory touches on, why don’t you join in?  Over the coming months of Summer, let’s plot a course through the subject.  I’ll suggest Spivak’s book first as it seems to be one of the most basic as well as the broadest out there in terms of applications. (There are also free copies of versions available through arXiv and MIT.) It doesn’t have a huge list of prerequisites either, so a broader category of people might be able to join in as well.

We can have occasional weekly or bi-weekly “meetings” via internet using something like Google Hangouts, Skype, or ooVoo to discuss problems and help each other out as necessary.  Ideally those who join will spend at least 3 hours a week, if not more reading the text and working through problems. Following Spivak, we might try dipping into Leinster, Awody, or Mac Lane.

 

 

From the author of Category Theory for the Sciences:

This book is designed to be read by scientists and other people. It has very few mathematical prerequisites; for example, it doesn’t require calculus, linear algebra, or statistics. It starts by reintroducing the basics: What is a set? What is a function between sets?

That said, having a teacher or resident expert will be very helpful. Category theory is a “paradigm shift”—it’s a new way of looking at things. If you progress past the first few chapters, you’ll see that it’s a language for having very big thoughts and making unusually deep analogies.

To make real progress in this book (unless you’re used to reading university-level math books on your own) it will be useful to periodically check your understanding with someone who has some training in the subject. Seek out a math grad student or even a Haskell expert to help you. A growing number of people are learning basic category theory.

In order to really learn this material, a formal teacher or a professor would be best. Encourage your local university math department to offer a course in Category Theory for the Sciences. I can recommend this in good faith, because I went to special efforts to make this book available for free online. An old version of the book exists on the math arXiv, and a new MIT Press-edited version exists in HTML form on their website (see URLs below). That said, the print version, available here on Amazon and elsewhere, is much easier to read, if you want to get serious and you can afford it.

This book contains about 300 exercises and solutions. For those who wish to teach a course in the subject, there are 193 additional exercises and solutions behind a professors-only wall on the MIT Press website (see URL below). You simply have to request access.

To everyone: I hope you enjoy the book, and get a lot out of it!

Old version: arxiv.org/abs/1302.6946
HTML version: mitpress.mit.edu/books/category-theory-sciences

David Spivak, mathematician
in Description of Category Theory for the Sciences on Amazon.com

 

References

Awody, Steve. Category Theory (Oxford Logic Guides, #52). (Oxford University Press, 2nd Edition, 2010)

Lawvere, F. William & Schanuel, Stephen H. Conceptual Mathematics: A First Introduction to Categories. (Cambridge University Press, 2nd Edition, 2009)

Leinster, Tom. Basic Category Theory (Cambridge Studies in Advanced Mathematics, #143). (Cambridge University Press, 2014)

Mac Lane, Saunders. Categories for the Working Mathematician (Graduate Texts in Mathematics, #5). (Springer, 2nd Edition, 1998)

Spivak, David I. Category Theory for the Sciences. (The MIT Press, 2014)

 

Why write a new textbook on Category Theory, when we already have Mac Lane’s ‘Categories for the Working Mathematician’? Simply put, because Mac Lane’s book is for the working (and aspiring) mathematician. What is needed now, after 30 years of spreading into various other disciplines and places in the curriculum, is a book for everyone else.

Steve Awody, mathematician
on page iv of Category Theory (Oxford Logic Guides, #52). (Oxford University Press, 2nd Edition, 2010)

If you’d like to join us, please leave a comment below and be sure to include your email address in the comment form so we can touch base regarding details.