I have always felt that a rise in global temperatures was the least of our worries about increasing CO2 in the atmosphere.  I’m much more concerned about how it could perturb the delicate balance that allows mammals to live, i.e. us.  One of the things that could be trouble is that CO2 dissolved in water can make the oceans more acidic by forming more carbonic acid, which could make it harder for marine creatures to make shells through calcification, which  in turn could have a large impact on the coral reefs and the ocean food chain.

Another thing I worry about is that our oxygen supply could decrease.  Although the direct effect of converting oxygen to water and CO2 through increased combustion of fossil fuels is small, the effect on photosynthetic organisms that make our oxygen is largely unknown.  I’ve actually been somewhat optimistic on this account thinking that since we are introducing more nutrients into the oceans and CO2 is increasing then perhaps phytoplankton, which make much of our oxygen and is a blanket term for photosynthetic microscopic sea organisms like cyanobacteria and dynoflagellates, might increase.  However, a paper in Nature this week, says otherwise.

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Summary of SIAM talk

Last Monday I gave a plenary talk at the joint Life Sciences and Annual SIAM meeting.  My slides can be downloaded from a previous post. The talk summarized the work I’ve been doing on obesity and human body weight change for the past six years.  The main idea is that at the most basic level, the body can be modeled as a fuel tank.  You put food into the tank by eating and you use up energy to maintain bodily functions and do physical work.  The difference between food intake rate and energy expenditure rate is the rate of change of your body weight.  In calculating body weight you need to convert energy (e.g. Calories consumed) into mass (e.g. kilograms).  However, the difficulty in doing this is that your body is not homogeneous.  You are comprised of water, bones, minerals, fat, protein and carbohydrates in the form of glycogen.  Each of these quantities has its own energy density (e.g. Calories/kg).  So in order to figure out how much you’ll weigh you need to figure out how the body partitions energy into these different components.

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Slides for second SIAM talk

Here are the slides for my SIAM talk on generalizing the Wilson-Cowan equations to include correlations.  This talk was mostly on the paper with Michael Buice and Jack Cowan that I summarized  here.  However, I also contrasted our work with the recent work of Paul Bressloff who uses a system size expansion of the Markov process that Michael and Jack proposed as a microscopic model for Wilson-Cowan in their 2007 paper.  The difference between the two approaches stems from  the interpretation of what the Wilson-Cowan equation describes.  In our interpretation, the Wilson-Cowan equation describes the firing rate or stochastic intensity of a Poisson process.  A Poisson distribution is notable because all cumulants are equal to the mean.  Our expansion is  in terms of factorial cumulants (we called them normal ordered cumulants in the paper because we didn’t know there was a name for them), which are deviations from Poisson statistics.  Bressloff, on the other hand, considers the Wilson -Cowan equation to be the average population firing rate of  a large population of neurons.  In the infinite size limit, there are no fluctuations.  His expansion is in terms of regular cumulants and the inverse system size is the small parameter.  In our formulation, the expansion parameter  is related to the distance to a critical point where the expansion would break down.   In essence, we use a Bogoliubov  hierarchy of time scales expansion where the higher order  factorial cumulants decay to steady state much faster than the lower order ones.

Word is not Word

I am often forced to write papers in Microsoft Word.  I once wrote a paper in LaTeX and it was perfectly fine with the journal all the way through the submission process.  However, after it was accepted the journal asked for the Doc or RTF file for the paper.  The paper had quite a few equations and there was no way that we could find that would convert a LaTeX file into a Word file so we typed it all out again in Word.  Since that time I always find out ahead of time what format a journal wants and more often than not it is Word.  The one benefit is that it really forces me to minimize the number of equations in a paper.  I managed to cope with this system up through MS Office 2004 on the Mac.

However, things started to fall apart completely with Office 2007.  The first issue is that they switched to an XML format suffixed by .docx, which is completely incompatible with the previous .doc format.  There exist conversion tools that can turn .docx files into RTF files but equations in .docx cannot be converted.  To make things even worse, equations in Office 2007 for Windows are also completely incompatible with equations in Office 2008 for the Mac.  So in effect,  it is impossible for a person using a Mac to collaborate with a person using Windows if the paper has equations.  As far as I can tell, there is no work around.  If anyone knows of a way to make equations in Word 2007 readable by a Mac please let me know.  This really makes me wonder who makes decisions at Microsoft.

SIAM talk

I am currently in Pittsburgh for the SIAM joint Life Sciences and Annual meetings. SIAM is the Society for Industrial and  Applied Mathematics and has nothing to do with the country currently named Thailand.  I just gave my invited joint plenary talk.  My slides are here.  The talk was on my recent work on human body weight change and obesity.  I have posted on this topic recently here and here.  I would write a summary of the talk but I’m feeling a bit under the weather right now and will leave it for another time.

Metabolism of Mice and Men

In the 1930’s, Swiss-American animal metabolism pioneer Max Kleiber noticed that the metabolic rate of animals scales as the body mass to the three quarters power.  There is still some controversy over whether the exponent is really three quarters or something else.  Many theories have been proposed for why the exponent  should be three quarters (or two thirds) but I won’t go into that here.  The crucial thing is that it is less than one and that implies that a large animal is more efficient than a small one.  This efficiency with size is not restricted to biological examples.  As Steve Strogatz pointed out in a New York Times column last year, the number of gas stations doesn’t grow linearly with the population of a city but rather grows in proportion to the 0.77 power of the population.  This sublinear scaling also goes for other city infrastructure like the total length of roads and electrical cables. Large cities may in fact be more efficient than small ones.

Now a mouse weighs about 20 to 30 grams so it is about a factor of 3500 times less massive than an average human.  Metabolic rate scales as mass to the three quarters so power density ( e.g. Watts/gram) scales as mass to the minus one quarter.  Hence, a mouse is 3500^{(1/4)} or 7 to 8 times less metabolically efficient than a human. A colony of mice weighing as much as a human would have to eat 7 to 8 times as much food.

However, in terms of total energy utilized, first world humans are much less efficient than mice and perhaps all other organisms.  The metabolic rate of an average person is about 10 megajoules per day or 115 watts but according to Wikipedia, the United States uses about 10,000 watts of power per capita.  This is a factor of 90 over the metabolic rate implying that an average American is a factor of ten less efficient than a mouse.  However, a very low energy use nation like Bangladesh only consumes about twice as much energy per capita as the human metabolic rate and thus an average Bangladeshi is more efficient than a mouse.

The Philosopher’s Zone

Last Thursday I had to drive from Baltimore to State College, PA for the 16th Congress of the US National Congress on Theoretical and Applied Mechanics to give a talk in one of the sessions.  I gave a condensed version of the kinetic theory of coupled oscillators talk I gave in Warwick last month.  The theme of the session was on recent advances in nonlinear dynamics so the topics were quite diverse.  I’m not sure my talk resonated with the audience.  The only question I received was how was this related to the NIH!

During the six hours of driving I did going back and forth, I listened to podcasts of the Australian radio show The Philosopher’s Zone.  This is a wonderful program hosted by Alan Saunders, who has a PhD in philosophy and is also a food expert.  Every show consists of Saunders talking to a guest, who is usually a philosopher but not always, about either a book she has recently written or some other philosophical topic.  The topics can range from the philosophy of Buffy the Vampire Slayer to Stoicism and everything in between.  Saunders has a knack for making complex philosophical ideas accessible and interesting.  In addition to The Philosopher’s Zone, I still regularly listen to Quirks and Quarks, The Science Show, Radio Lab, and The Naked Scientists.  I’ll also sneak in All in the Mind from time to time.