I recently accepted a position as a Fellow at Harvard University.  So, I am in Massachusetts these days.  I spend on the Harvard main campus mostly, although sometimes I’m at the Medical campus in Longwood.   It’s all very new and so it’s much, much too early to claim there is any pattern yet, or that whatever patterns there are will persist.  Although, it’s nice to be able to move around between both Campuses.

I’m currently a member of the Mango Lab, which is a relatively big lab run by Susan Mango. Susan is a MacArthur fellow also known as the ‘Genius Award’. She works primarily on C. elegans, which is the organism that I’ll be working on.

C. elegans is a worm (nematode) than some scientists have decided to understand the heck out of. When biologists really drill down deep in trying to understand an animal, they call it a model organism.  I’ve started to eat and sleep these little guys; their DNA anyway.

Life in Boston

This morning was a delightful morning.  The air was crisp and clean.  I suspect, judging by the lack of people of the streets, many thought it wet and dreary.  However, with the help of my trusty umbrella, the drizzle was held at arms length which left room to appreciate the weather.

Boston has fewer people than New York, but somehow feels more crowded.

I’m getting used to the buses in Boston.  They can be quite crowded, but the places I get on and off are well positioned so that the bus is empty or mostly empty when it gets to me and it’s not too hard to pull out a journal article and start reading.

Life at Harvard

Harvard is fast paced, at least for me.  I’ve worked at all sorts of places (in three different countries) and even telecommuted and I have to say that Harvard is a great working environment.   The support staff at Harvard is fantastic.  It never takes very long to get administrative stuff resolved.  I usually just send off an email and within a day or two it’s done, with very little need for follow up.  I don’t know if this is a Boston trait or a  Harvard thing.  I’m just used to longer lag times for these types of things.

I am spending large chucks of my days sucking down as much information as I can.   As I mentioned, C. elegans is my best friend now.  I feel a lot more energized; the atmosphere is very conducive to study and focus.   I will have more to say about all this as I have more time to get used to everything, but this is it for now.   I have work to do!

Graduate students are notoriously frugal. Although this is sometimes an economic necessity, in some ways I think we are a little too frugal. One of the ways that this frugality manifests, and that I find most prevalent, is risk aversion. This can be hard to detect because we are an adventuresome bunch. Although, perhaps more button-downed than the general college lot, we will try new foods, learn new languages and travel to new spots. However, in things that matter to our subject of interest, we tend to show our conservative side. I believe we ought to be more interested in doing unconventional things like entering contests, starting blogs, writing articles, making friends in other departments or collaborating with friends in other departments.

In matters institutional, social or organizational, we are trained to get creative as a last resort, rather than a first resort. While there is nothing wrong with wanting to pursue approaches that have a high probability of success, I believe that, paradoxically, success is not synonymous with the avoidance of failure. If exploitation is defined as the act of profiting from a known strategy with a known amount of benefit; and exploration is the act of searching for avenues of improvement; then, there is often a trade-off between exploitation and exploration. If we curtail our explorations, we risk missing out on better ways of doing things. If we spend too much time exploring, we risk not accruing much benefit from the knowledge we’ve gathered.

One complicating factor is the cost of experimentation. I make a distinction between expensive and cheap environments. In a cheap environment, one should be a lot more free to try something new. For instance, trying out a new pen or listening to a talk for an hour. In an expensive environment, you might be more reluctant to buy an unfamiliar brand of computer, that you have doubts about, on the off-chance that you might actually turn out to like it.

Rather than having a policy of saying no to unlikely ventures, I try to say no with a large probability and yes with a small probability. That is to say, every now and again, I try something that I don’t expect will work. I avoid doing this with very expensive decisions. However, in a cheap environment, I feel it’s important to try something unlikely every now and then. We make thousands of decisions a day. It’s actually quite easy to find one thing and do in the complete opposite way to the way that you normally do it.

I am even more intrigued by those things that work for others, but never seem to work for me. I am not a fan of broccoli. However, many people are. So every now and then, I try broccoli just in case I was wrong. I still don’t like it, but at least I end up eating more vegetables. In work, I sometimes try to emulate the approach of people who work in a completely opposite way to myself. I often learn a lot of new things things way. Of course, I am most comfortable doing things they way I have trained myself to do things and I get most of my work done that way.

Bring things full circle to where we started with frugality, I find that in academia, we are sometimes let concerns about cost override more important questions like whether the purchase is worth it. We send a lot of time doing things for ourselves. In our minds, it seems like we are saving money. However, the loss in productivity of doing things at which we are unskilled can outweigh the benefits of not spending a few extra dollars.

One way of figuring out if doing something yourself is not necessarily worth it is to consider whether you would find it tempting to do the same task if a friend offered to pay you the going-rate to do it. The famous example is a man who won’t pay someone else to cut his lawn for $5 and so cuts it himself, although he wouldn’t, all things being equal, cut his neighbour’s lawn for $5. In one case, he is saying lawn care is worth $5 and in the other case he’s saying it’s not. So, this is a trick I try often – looking at a cost from the other side of things, to see if I’m being too conservative.

I consider myself a work-in-progress. My sense is that I really ought to take on more risk than I do. I think the rewards to be gained from being more open to new opportunities can be worth it. Besides, it makes things less boring.

Are there some ways in which you consider yourself too risk averse?

It can be hard to keep up with a blog especially when you have a lot of other things going on … for instance, being the Editor-in-chief on a second blog. So, I will try not to neglect this one. I will also, probably, do something cheap on occasion like link to posts on the other blog.

It’s sort of confusing how many possible Pi Days there are.

When searching for papers, one gets this result:

Your query resulted in too many hits, only 1000 hits are being displayed. These are not necessarily the 1000 most recent papers. We recommend that you try a more specific search.

This limitation on the number of results makes it difficult to get more data.  I wrote the arXiv.0rg a few times (I am sure they are quite busy) to request access to more data but I was never able to get a reply.

If anybody has an ideas for other databases, I would be glad to hear about it.

1. AMS Council Meeting – Part 1
2. AMS Council Meeting – Part 2
3. AMS Council Meeting – Part 3

Introduction
Overview of Supervised Learning
Linear Methods of Regression
Linear Methods of Classification
Basis Expansions and Regularization
Kernel Smoothing Methods
Model Assessment and Selection
Model Inference and Averaging
Additive Models, Trees and Related Methods
Boosting and Additive Trees
Neural Networks
Support Vector Machines and Flexible Discriminants
Prototype Methods and Nearest-Neighbors
Unsupervised Learning
Random Forests
Ensemble Learning
Undirected Graphical Methods
High-Dimensional Problems

The last four chapters seem to be new.  They are not in my first edition copy.

[Hat tip: Paper Pools]

Closely neighbouring, immediately adjacent, next, nearest (in space, serial order, quality, etc.); close, intimate

In this article, a proximate value will mean a value which we shall use as a stand-in for an unknown value .  The unknown variable is known to have the property that

Choosing some value as a proximate value for x entails incurring an absolute error of and a relative error 0f .  If we intend to choose a proximate value that minimizes absolute error, we are solving

.

If we are intending to minimize relative error, we are solving

That is to say, we are looking for the proximate value that minimizes the damage of being given the worst possible value of for that proximate value.  The solution to the first problem is the arithmetic mean of the end points of the interval,

and to the second is the harmonic mean of the end points,

.

This is of some practical relevance as I often notice that scientists choose the arithmetic mean by default when choosing a proximate value.  At least in cases where the relative error is of greatest concern, this may be an error.

I try to keep posts relatively short so I will go into the proofs in a second installment.

This article is based on a paper by George Pólya, On the Harmonic Mean of Two Numbers.