Why do we care about the small world properties of atomic clusters?

This summary is to try to keep a bigger picture in mind before getting too specific too quickly: a brief survey of a topic of interest in a text. It is specifically in the context of global optimization. I first wrote this post a few months back. Most of meat is obtained from Wales’s Energy Landscapes and Doye and Massen’s “Characterizing the network topology…atomic clusters”. Finding the global minimum and local minima on an energy landscape (a purely theoretical thing determined from pure quantum-mechanical models or hybrid quantum-classical models) gives us cues as to how a set of molecules will structurally stabalize. Practically, this information is invaluable to molecular structure prediction, which helps us better understand how molecules are actually built.

The issue lies in finding the global minimum. I don’t pretend to deeply know this area or detail it here by any means, but I may soon! Finding the global optimum in general is an NP-hard problem in computational complexity. In other words, “there is no known algorithm that is certain to solve the problem within a time that scales as a power of the system size”. So what do we do? Exploit structural properties of a given atomic cluster to drastically improve the running time of the algorithm. (Wales, “Global optimisation”)

This subfield in itself is very active with many different algorithms suited for all sorts of structures. But as far as small worlds go, it seems a basin hopping global optimization approach that could take advantage of the relatively scale-free properties of the landscape. But as implied (Wales, “Small worlds”), we should take caution in considering the cluster we’re applying these algorithms to, how exactly the global optimization search is improved, and whether the small world results apply generally enough to a broader class of molecules or not:

It is not yet clear how general this result may be for other potential energy surfaces [than Lennard-Jones]. For example, the connectivity of the constrained polymer conformations was found to exhibit a Guassian rather than a power law distribution for a noninteracting lattice polymer. For the Lennard-Jones polymer…Doye has found that the connectivity distribution does not really follow a power law, but the scaling is stronger than exponential…If low energy minima are generally highly connected then they should be easier to locate in global optimisation searches…However, the best way to utilise this information more efficiently is not yet clear.

Though it has been a few years since that was written, it seems to still hold true from my cursory understanding. Most of the work that has been done seems to be applied to Lennard-Jones clusters. Needless to say, I’m motivated to dig a little deeper.

The spirit of this log (and welcome!)

Not so long ago, a friend brought up to me that the Atom feed on my home page that I edited by hand was infrequently updated even though I frequently added thoughts to my home page. My initial intent was to post only very significant changes, but the more thought I gave to the subject, the more I realized that the a web log with user comment capabilities and a significant user base is a good thing to participate in, and the personal home page is better for organizing the chronological information as I see fit. I feel that many bright people have web logs of interest to me and they have benefited me. In the rest of this post, I will try to explain (1) why I appreciate the way web logging has evolved from my perspective, and (2) if I’m fortunate enough to gain a reader or two, what you can expect of the quality of the entries to come. This entry in particular will avoid referencing other material and stay focused on my personal motivation for beginning the log.

A little history

This is not my first attempt at web logging. I used to keep logs in raw HTML on my server followed by spending some time with MovableType. I’ve spent many years learning how Internet news scoops, forums, and logs are truly used and feel that there are certain simple truths when approaching the subject. Trying to keep a system that kept all my thoughts categorized, organized, and consistent in one data store frustrated me at times. I have stubbornly (better now than never) come to accept the roles that certain web services play so I can use them to my advantage. It is OK to have duplicated information not all in one beautiful framework. The world is messy, our thoughts our messy, and the way we present them should aim to be valuable, and just a little less messy, but certainly not perfect or even close to it!

(Warning.) For some quick background so you know what kind of crank you’re dealing with, being actively interested in the sciences as well as computers in high school, I went on to pursue a B.S. in computer science at Northwestern University. During the day, I’m in gov. service and deal with computer-related problems from mundane to very technical. During the evenings, when I get the chance, I like to exercise my drive towards the physical sciences and the statistical laws that govern so many systems not nearly as explored as we would like them to be. Consequently, I have geared myself towards a track of research that tends to relate those two topics.

Some of the content you can expect

Most recently, I’ve been interested in complex networks as they relate to physical structures–more specifically energy landscapes of many kinds. I’m also interested in hash-based data structures and the nature of the transition from discrete to continuous shapes in geometry. Most of the technical articles you will see on this log should relate to that. Though I don’t expect a huge comment-base, if you have relevant thoughts in response to especially the technical subjects, I’d appreciate it. I don’t promise pristine referencing, but I will try my best–especially on technical subjects–to be thorough with references.

While I promise no fleeting 2-sentence blog entries, some entries may be non-technical or avant-garde/controvertial/even stupid in what they suggest. I’d like them to be about something–maybe topics more close-to-home about family and friends will hopefully be of interest to some.

Why web logging makes sense

Let’s knock out some of the stupid criticisms of web logging services that I’ve run into. The first and most foolish responses to them are, “why not just keep an HTML file?” and “why post thoughts like that to everyone anyway?” To answer the latter, in the cases where little is being discussed and too much trolling going on, this is a reasonable criticism. I feel entries with little thought put into them and too much emotion sometimes stir controversy that is often not even worth arguing about and personal forum/comment battles ensue with little to be gained. But if that criticism has to do with posting undeveloped thoughts that aren’t “articles”, per se, I’d have to disagree whole-heartedly. The best learning goes on when simple, obvious questions are answered by people who are more knowledgable and when those knowledgable people are read like human beings with lives, charisma, and flaws, and not as almighty authorities. It is exactly that potential for mutual improvement why I think it’s reasonable to post a thought every-so-often to the world to see if they have anything to say, or just to let something out there.

My response to the first criticism is simple. Web log services provide two things that your HTML file on your server doesn’t help with: (1) a community of people partially networked and (2) technical features that help facilitate bulletin-board discussion amongst that community. Features like comments, trackback, and automatic syndication allow people to keep up with each other’s thoughts and motivate discussion in them, and the interfaces, as ghastly as they can be, certainly make writing them easier than in HTML (and this comes from some time attempting to do the opposite).

Finally, I think web logs have a unique role in discussion on the net in the sense that unlike a forum, most web loggers have their identities revealed. Folklore of anonymous statements and hacking galore can be fun, but sometimes I like to cut the bullshit and see who I’m talking to, what their background is, and why are they honestly interested in responding to my thought.

In the end, a log is just a log…that’s why I often don’t call web logs “blogs” because of the loadedness of the term, but certainly I’ve seen a strong growing community of very bright people beginning to actually have discussions and the communities naturally form from social communties that already exist with the addition of a little help from your friendly search engine. (Better algorithmic methods to derive community structure from existing web logs and the content of their entries is a topic for another article, but they’ve been brewing, so they may find themselves an entry.) This new intensification, most notably in the academic specialties, is what motivates me to become a more frequent web logger myself. For better or worse, my shit is out there, and I’m hoping, for lack of a better system, it may be for the better.