February 24, 2008
IPAM Workshops: (1) River Networks and (2) the Internet
IPAM has two workshops coming up that look interesting.
The first is part of the Optimal Transport long program, and focuses on, among other things, resource transportation via network structures. Some of the impetus for this workshop stems from recent theoretical work on river networks (summarized well by Dan Rothman and Peter Dodds in a series of three review articles from 2000: 1, 2, and 3), which suggests that many of their complicated-looking structures are driven directly by properties of turbulent flows. My admittedly shallow dive through this literature a few years ago gives me the impression that the mathematical models being used are pretty cute, and may even by right. On the other hand, I'm not sure how good the empirical data and the statistical analyses are. Anyway... River networks, of course, are only distantly related to the kind of networks that I typically study, since they're basically shaped like trees rather than the complex hair balls I usually contemplate. But, they do make very beautiful, space-filling trees. While I was flying into PHL this afternoon, I couldn't help but notice the beautiful fractal-like structures carved into the wet lands by waterways of all sizes.
The second event at IPAM is a long program on the Internet and so-called "multi-resolution analysis" (MRA). I'm not sure the term MRA is a particularly helpful one, but generally the program seems to be focused on measurement and modeling of Internet structure and traffic, at and across different layers of the internet protocol stack. There are a lot of interesting questions involved here (e.g., check out Allen Downey's research), and in general, the idea behind a lot of this research is to help build a better Internet (i.e., it's ostensibly related to the enormously unfocused GENI project).
May 5-9, 2008 at IPAM (UCLA)
Organizers: Andrea Bertozzi (UCLA), Bjorn Birnir (UC Santa Barbara), Dan Rothman (MIT), and William Zame (UCLA).
Description: In recent years a large number of scaling laws in geomorphology have been found to be equivalent to only two scaling laws. Recent results on river meanders indicate that there may be only one universal scaling law, implying all the others. Moreover, recent theoretical results on turbulent flow in rivers indicate that turbulent flow is the source of the universal scaling of river basins and river networks.
These results provide a key to the understanding of the fundamental structure of the surface of the earth, that layers of complexity such as tectonic uplift, earthquake rifts and the action of glaciers can then be added to. It provides a way of quantifying transport of water, sediments and chemicals over the surface and exchanges of dissolved chemicals between the water and the atmosphere. In particular this seems to provide a method to quantify the transfer of carbon dioxide from rivers to the atmosphere. This workshop will explore why and how this transport due to turbulent flow takes place and is optimal.
Other transport such as transport of magma in volcanoes will also be covered and how similar ideas can be used to identify and quantify transport in social networks and economics.
September 8 - December 12, 2008 at IPAM (UCLA)
Organizers: Paul Barford (UW Madison), John Doyle (CalTech), Anna Gilbert (UMich), Mauro Maggioni (Duke), Craig Patridge (Bolt Beranek and Newman), Matthew Roughan (U. Adelaide), and Walter Willinger (AT&T).
Description: The main focus of this IPAM program will be on innovations and breakthroughs in the theoretical foundations and practical implementations of a network-centric multi-resolution analysis (MRA); that is, a structured approach to representing, analyzing, and visualizing complex measurements from Internet-like systems that is (i) specifically designed to accommodate the vertical (e.g., layers) and horizontal (e.g., domains) decompositions of Internet-like architectural designs, (ii) flexible enough to account for the highly heterogeneous (i.e., ``scale-rich'') nature of these designs and the high semantic content of the available measurements, and (iii) capable of retaining some of the mathematical elegance of more traditional MRA schemes. Critical capabilities of the envisioned Internet MRA, in particular, and network MRA, in general, include support for the exploration of multi-scale representations of very large and diverse network-specific annotated graph structures, novel techniques for the study of the dynamics of as well as the dynamic processes over these structures, and new methodologies and tools for dealing with aggregated spatio-temporal-functional network data representations and their associated analysis and visualization.
By leading the way towards the development of a mathematical foundation for network-centric MRA techniques, this IPAM program will be firmly grounded in a number of key Internet MRA target problems (e.g., cyber-security, traffic/network engineering, network control), with close ties to activities that can be expected to arise in the context of a major NSF-led initiative called Global Environment for Networking Innovations or GENI (www.cise.nsf.gov/geni or www.geni.net). At the same time, this IPAM program will also be strongly influenced by developments in other scientific disciplines where informed multiscale approaches to the study of highly engineered or evolved networked systems have proved to be essential for advancing our understanding of their properties, behaviors, and evolution.
- Workshop I: Multiscale Representation, Analysis and Modeling of Internet Data and Measurements. September 22 - 26, 2008.
- Workshop II: Applications of Internet MRA to Cyber-Security . October 13 - 17, 2008.
- Workshop III: Beyond Internet MRA: Networks of Networks. November 3 - 7, 2008.
- Workshop IV: New Mathematical Frontiers in Network Multi-Resolution Analysis. November 17 - 21, 2008.
February 22, 2008
Returning to the alma mater
Next week I'll be visiting my old stomping ground Haverford College, as well as nearby Swarthmore and Bryn Mawr Colleges. A couple of years ago I went to my 5 year reunion there, but this will be my first time back in an "official" academic capacity. It promises to be an exhausting experience (largely because of how many things I've packed into the 4 day visit), but also a slightly surreal one as I'll be on the other side of the teacher-student divide at a place that was really important in the grand scheme of my intellectual career.
To start, I'll be giving a research talk at Swarthmore on Monday (4:00pm in the Science Center, if any of you are local) on some of my recent work on modeling evolutionary trends in species body size. I'll also be chatting with students over lunch about graduate school and jobs in the industry. The next day, I'm giving a guest lecture in a computational physics course at Haverford (I'll be talking about statistical method for network analysis, including an introduction to MCMC in the context of fitting models to data). Lunch that day will be a chat with students from the CS department. Wednesday, I'm paying an early-morning visit to the Emergence discussion group at Bryn Mawr, followed by lunch with physics students. To wrap things up, I'll be briefly returning to Bryn Mawr on Thursday to chat with CS students, before heading back to New Mexico. Sprinkled throughout these events will be meetings with faculty, some I knew from my time in college like Jerry Gollub and Suzanne Amador, and some who are new to me like Steve Wang.
One of my friends here at SFI mentioned that my schedule for next week sure sounds a lot like I'm interviewing for a position at these schools. Fortunately, it's not. Otherwise, I'd be a little more stressed about it... On the other hand, I remember the last year or so at Haverford and the first few years of graduate school thinking that it would be a great job to be a professor at a small liberal arts college (SLAC) like Haverford, where the students are smart and hard working, and there's both space and support to do interesting research. I still mostly agree, although I've also become completely enamored with doing cool research, and you certainly don't have as much time at a SLAC to do research as you do at a bigger, more research-focused university. At this point, though, it's not clear to me how I'll feel when the time finally does come to get one of those tenure-track jobs.
Update 3 March 2008: I've now posted a pdf scan of my lecture notes. Obviously, these omit the narrative and the bits that I added on the fly to make the lecture more coherent. Also, in my lecture, I didn't have time to explain the last several slides of results from using the HRG model in an MCMC context. If you find any mistakes in them, please do let me know.
February 11, 2008
Food for thought (1)
February 02, 2008
The Importance of Mathematics
W. Timothy Gowers (homepage) won the Fields Medal in 1998 for work in functional analysis and combinatorics. Pleasantly, he also writes regularly at Gowers's Blog, although much of what he writes is over my head (I am probably more to blame for that fact than Gowers, however). But, this very pleasant talk he gave at the Clay Mathematics Institute for their Millennium Meeting back in 2000. His topic is generally the "Importance of Mathematics" (which of course is a familiar notion to long-time readers here), and he gives a highly entertaining intellectual meditation on the subject, and touches briefly on problems like graph coloring, computational complexity (as a way of distinguishing those things practical in theory and those things practical in practice), knot theory, and the Erdos-Kac theorem that the number of factors for a randomly chosen integer is normally distributed (something I hadn't heard before). Along the way, he gives a good explanation about why it's dangerous to cut funding to "useless" parts of mathematics (or, science) in favor of funding only the "useful" bits, and tries to convey the idea that the most important mathematics is also often the most beautiful.