# Recent Advances in Packing

The weekend before last, I overcame my reluctance to travel and went to a mathematics conference, the American Mathematical Society’s Spring Central Sectional Meeting. I gave a talk in the “Recent Advances in Packing” session, spreading the word about SICs. My talk followed those by Steve Flammia and Marcus Appleby, who spoke about the main family of known SIC solutions while I covered the rest (the sporadic SICs). The co-organizer of that session, Dustin Mixon, has posted an overall summary and the speakers’ slides over at his blog.

# ICCS: Emergence in Particle Systems 1

I typed the following notes during Hiroki Sayama‘s presentation on “Phase separation and dynamic pattern formation in heterogeneous self-propelled particle systems.” Unfortunately, I couldn’t get a WiFi signal in the room where Sayama gave his talk, so I’m falling short of the gonzo science ideal, posting about the talk after it was given instead of as it occurs.

Sayama is speaking about particle swarm systems, and the phase-separation and dynamic pattern formation behaviors they exhibit. He adds the novel feature of heterogeneity to the particle system. Research on self-propelled particles goes back to Reynolds (1987), Vicsek et al. (1995), Aldana et al. (2003), Chuang et al. (2006), etc. Reynolds was a computer scientist who created a method for simulating bird flocking, which developed into the simulation which created the bats in the otherwise unremarkable Batman Begins. Vicsek and Aldana were physicists.

These systems show collective behaviors such as random clustering, coherent motions and milling. The same system can exhibit all of these behaviors, depending upon the input parameters. Cranking up the noise can induce phase transitions. Almost all of this work focused on homogeneous particle systems, in which all particles share the same kinetic particles. What, then, would happen if two or more types of self-propelled particles were mixed together?

Sayama works in a framework he calls Swarm Chemistry, which is implemented as a Java applet that can be run online.
Continue reading ICCS: Emergence in Particle Systems 1

# ICCS: Monday Evening

The parts between talks are the best parts of conferences. Sure, it’s great to hear Greg Chaitin deliver his sermon about the ideal realm of pure mathematics being an infinite ocean of complexity, out of which we can only seize finite buckets — but Chaitin writes about that kind of thing, and you can read it for free online. It’s an altogether different experience to discuss during the coffee break Mike Stay and Cristian Calude’s paper, “From Heisenberg to GÃ¶del via Chaitin,” with one of the three men in the title.

Question-and-answer sessions after the presentations can also be quite good. Last night, for example, Barbara Jasny of Science Magazine explained how that publication is adapting to the whizbang modern world. It’s reassuring to hear that at least one person in the publishing community has a common-sense understanding of what cheap, open digital access means: journals can only justify charging prices if those prices reflect the actual value which those journals add. More interesting than that, however, was Jasny’s reaction to the question from Frannie Leautier, former Vice-President of the World Bank and currently head of the World Bank Institute. Leautier asked if Science would publish articles which used cartoons as illustrations (instantly endearing herself to all the Larry Gonick and Sid Harris fans in the audience).
Continue reading ICCS: Monday Evening

# ICCS: Sunday Morning

The following is my first attempt to liveblog ICCS 2007. I arrived at the Quincy Marriott shortly before 8:30 this morning, having driven south on I-93 from Boston. Unlike the first time I drove out here, I didn’t get lost in Braintree, since I took the left fork at the “Braintree split,” where I-93 undergoes mitosis. These things are important to know.

The morning’s plenary talks began with Diana Dabby (Franklin W. Olin College of Engineering), who spoke about chaotic transformations one can apply to music in order to generate musical variations, as in “Variations on a Theme of Beethoven.” Her scheme begins by breaking the musical performance into a sequence of pitches, denoted $$p_i$$, and then mapping each $$p_i$$ to a section of a dynamical trajectory on a chaotic attractor like the Lorentz owl/butterfly mask.
Continue reading ICCS: Sunday Morning

# Quantum Mechanics Homework #1

Well, in the past two days I’ve linked to an Internet quiz and some anime videos, so in order to retain my street cred in the Faculty Lounge, it’s time to post a homework assignment. Don’t worry: if you haven’t met me in person, there’s no way I can grade you on it (unless our quantum states are somehow entangled). This problem set covers everything in our first two seminar sessions on QM, except for the kaon physics which we did as a lead-up to our next topic, Bell’s Inequality. I’ve chosen six problems, arranged in roughly increasing order of difficulty. The first two are on commutator relations, the third involves position- and momentum-space wavefunctions, the fourth brings on the harmonic oscillator (with some statistical mechanics), the fifth tests your knowledge about the Heisenberg picture, and the sixth gets into the time evolution of two-state systems.

Without extra ado, then, I give you Quantum Mechanics Homework #1.
Continue reading Quantum Mechanics Homework #1

# Friday Quantum Mechanics

“So, Blake,” I sez to myself. “You’ve been selected for multiple editions of the Skeptic’s Circle. You’ve been linked, twice, from Pharyngula. Clearly, you’re rising to astonishing heights of science-blogebrity. What worlds are left to conquer?”

“Well,” I replied. “There’s going out for a milkshake with Rebecca Watson.”

I shook my head. “Not gonna happen — she’s just too picky counting tentacles. Anything else?”

“Well, you could do what Revere warned you not to do.”

“Ah, yes, write a sixteen-part series on mathematical modeling! But the modeling of antiviral resistance isn’t really my field.”

“True, but didn’t you spend your spring break in Amsterdam a few years ago, writing that paper which was the first article Prof. Rajagopal ever graded with an A-double-plus?”

“Hey, yeah, on supersymmetric quantum mechanics and the Dirac Equation!”

“So,” I suggested to me, “why don’t you break that paper down into several blag posts, interleave it with some Bill Hicks videos so not all your readers wander away, and have yourself a continuing physics series?”

“Could work, I suppose. But that paper was written for third-term quantum mechanics students, so I’d probably have to build up to it, even just a little.”

“Bah,” I said. “At least you’ll have a purpose in life. And you can start by expounding on the canonical commutation relation for position and momentum. That’ll be your warm-up, after which you can do angular momentum and central potentials —”

“Which I do have written up somewhere,” I interposed, “since I discovered I could type LaTeX as fast as my professors could lecture.”

“Weirdo,” I said.
Continue reading Friday Quantum Mechanics

# Group Theory Homework

One reason I call this site a “blag” and not a “blog” is that I’m always late.

For example, I’m finally typing up the group-theory homework assignment which Ben gave last Monday (and which will be due next Monday). During our seminar over in BU territory, we discussed the relations among the Lie groups SU(2) and SO(3) and the manifolds S3 and RP3. Problems will be given below the fold.

Also, Eric will be discussing statistical physics this afternoon at NECSI.
Continue reading Group Theory Homework

# Info Theory and DNA/Evolution

We’re reviewing the IEEE papers.

After reviewing the first batch of papers, we came up with some questions to answer in the future, in order of difficulty/open-ness:

1. Given the robustness of a code (e.g. due to a many-to-one codon->AA mapping), can we calculate bounds on the channel capacity of such a code? How does the empirical R (info transmission rate) of the codon->AA code compare with the empirical C (channel capacity, e.g. from mutation rates)?

2. How does the length/entropy/complexity of code-bits (e.g. parity bits, non-message bits used for error correcting) relate to the complexity of the error-correcting task, and e.g. the entropy and length of the data-bit sections (e.g. the actual message you’re sending) to satisfy Râ‰¤C?

– Is the von Neumann entropy,
$$H = {\rm Tr\,} \rho\log\rho = \sum\lambda_i\log\lambda_i$$
where {Î»} are the eigenvalues of the matrix, useful for discussing network robustness? (There’s a paper where they use Kolmogorov-Sinai/Shannon entropy to do this, which Blake has somewhere…) If so, then can we apply this to a genetic-regulatory network, and tie in the error-correcting or homeostatic abilities of such a network with VNE or other network metrics?

Next week:

We meet Monday at BU for group theory. Ben will be discussing SU(2) and SO(3) from Artin. Friday, Blake will present on the symmetry-breaking-in-genetics paper, and possibly on the information-theoretic considerations for BLAST.

BLAKE SEZ: I believe the paper which caught my eye was L. Demetrius and T. Manke (15 February 2005) “Robustness and network evolution â€” an entropic principlePhysica A 346 (3â€“4): 682â€“96.

# CRE paper

Friday 4/6/07 we reviewed Rao et al. (2004) IEEE Trans Info Theor, V 50 (6) “Cumulative Residual Information […]”, here.

We decided that while the motivation for the paper was valid, that it was undesirable for a number of reasons — mostly that the CRE of many well-behaved distributions (power laws notably) diverged. We’re all currently working on better generalizations.

# First Session on Group Theory

Yesterday evening, we had our first seminar session on the group theory track, led by Ben Allen. We covered the definition of groups, semigroups and monoids, and we developed several examples by transforming a pentagon. After a brief interlude on discrete topology and â€” no snickers, please â€” pointless topology, Ben introduced the concept of generators and posed several homework questions intended to lead us into the study of Lie groups and Lie algebras.

Notes are available in PDF format, or as a gzipped tarball for those who wish to play with the original LaTeX source. Likewise, the current notes for the entropy and information-theory seminar track (the Friday sessions) are available in both PDF and tarball flavors.

Our next session will be Friday afternoon at NECSI, where we will continue discussing Claude Shannon’s classic paper, A/The Mathematical Theory of Communication (1948). The following Monday, Eric will treat us to the grand canonical ensemble.