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Hidden costs in NIH grants

Everyone talks about how the NIH funding system is broken. I rarely see numbers besides falling success rates. No one ever talks about real numbers such as the cost of the current system. How much do grants actually cost?

I have tried for a conservative estimate. The real cost may be anywhere from a third again as large to twice as large.

I have left out airfares for professors to attend study sections, paychecks of the bureaucrats, panels to assign grants to institutes, heads of study sections, time spent in study sections, and a wealth of other costs. Some of these are absorbed in the total award cost NIH reports for grants, since half of most grants disappears into overhead, both for the NIH and the institution which receives it.

How long does writing and reviewing take? How much does it cost? I assume $150/h as the going rate. This is what my mother, a professional science writer, charges. MDs and PhDs on the same projects regularly bill $200-$300 an hour. She estimates producing a document takes 2.5h/page and costs $375/page. Reviewing or editing a document takes 0.2h/page and costs $30/page.

An NIH R01 grant — the backbone of the funding system — is 25 pages long. In 2006, the average success rate (counting all repeat submissions as a single grant) was 0.128 (weighting new and continued grants by the number of each). The average award size with the same weighting was $363,731.08.

Each grant gets four reviewers. 25 pages takes 5h and costs $750. Writing it takes 62.5h and costs $9,375. The total cost for a single grant is 4*$750 + $9375 = $12,375. The time for a single grant is 82.5h. We can assign the reviewing cost without worrying about where in detail it should be counted: the reviewers are grant-seeking scientists as well, and someone must review their grants, so this is a shared cost in the community.

A success rate of 0.128 means we need to submit 7.81 grants in order to get one funded. Each R01 gets three resubmissions (which are still counted as one submission in the NIH statistics). Anecdotally, nothing is getting funded right now on first submission, so we have to multiply the expected number of grants by three, or 23.44 grant equivalents.

The mean cost of a successful grant is $290,039.06. The mean time for a successful grant is 1,933.8h. A full time job of 40h a week, 52 weeks a year is 2080h. Getting a grant is 0.93 of a full time job. It is 0.8 of the first year of the average grant size mentioned above, and remember that most of that money doesn’t make it to the professor at all. A full professor can reasonably ask for $220,000 a year. The first year and a third of the grant is eaten by the costs of getting the grant.

The final summary:
Cost of a grant: $290,039.06
Annual award of a grant: $220,000
Time to get a grant: 1,933.8h
Full time job: 2080h/year

Before we wade in to fix this, let’s set a target for what constitutes “fixed.” I say reduce cost and time to a tenth of their current value. Then we should develop a set of possible systems, and run controlled, randomized experiments to compare them.

madhadron :: Nov.25.2007 :: Uncategorized :: 1 Comment »

Shame, Nature Physics

BioCurious points to a Nature Physics editorial that increases my contempt for the vanity journals. All but one paragraph is hypocrisy — injunctions not to label your work as ‘ultrashort quantum nanobiology,’ when Nature accepts no work not so labeled — but that one is revealing:

‘Story’ is the concept that should underlie the structure of the entire paper. The clearer and simpler, the more engrossing it is. On that basis, think about relegating technical details — essential to the science but not the narrative — to a Methods section or to Supplementary Information (the latter published online). Similarly, figures should be designed to enhance the telling of the story and each accompanied by a caption that is as short as possible; to an expert reader, the information conveyed in a figure should be clear without needing to consult the main text.

Do exactly the opposite and you have begun well.

Shun captions. When layout was hard and expensive, pictures and graphs were excised from their surrounding text and typeset on their own pages. This time is behind us. Restore your figures to their natural environment. Dismiss the captions you set to watch over them.

Leave your scaffolding in place. When you have jailed your technical information in ‘Materials and Methods’ or exiled it entirely, what is left but verbiage, citations, and graphs taken on faith? The details of your analysis are shunted elsewhere. Even the measurement technique is banished from its point of use.

Supplemental information has one use: source code, analogous to plasmids and strains in genetics. We would attach our plasmids, too, if only we knew how.

Most damning of all, science isn’t stories. We reason about the world from hypotheses we have justified by stringent test. A mixing angle in quantum field theory is not a story, nor the Gibbs distribution, nor template directed synthesis of DNA. Their value is independent of any story around them. They have value as they provide traction for testing other hypotheses. Wrapping them in a story merely imposes on your reader to unwrap them.

madhadron :: Nov.13.2007 :: Uncategorized :: Comments Off

Encapsulated experience

I spent a little time this morning looking into source control management systems. Today I watched Linus Torvalds’s talk at Google. I’m going to use Git, for the same reason that C is still a standby in programming.

C is a terrible language. Compared to its contemporaries (ALGOL 68, Lisp 1.5, Smalltalk) it’s primitive. Compared to today’s top languages (Haskell, ML, Scheme) it seems ludicrous. C has something these languages lack. It is the codification of how a couple of smart and experienced programmers liked to write assembly. It provides support where its designers wanted support, and nowhere else. Such a language can never be planned or designed, nor should it, but it provides something to fall back if you can’t find a clean language appropriate for your project.

Git represents Linus implementing a system to support how he wants to do source code control, based on years of a large and particularly chaotic development process. Developing software within a laboratory is chaotic and unstructured. I have trusted Linus for years on the kernel of my operating system. I’ll trust him on version control.

The only other thing of real interest out there is darcs, which is version control based on a theory of patches as noncommuting operations in analogy to Hermitian operators in quantum mechanics. Intellectually, it’s very exciting, but I have become jaded and bitter and I need to finish my PhD, not mess with beautiful computer science.

madhadron :: Nov.07.2007 :: Uncategorized :: 2 Comments »

First impressions of Scala

I don’t want to write raw Java again, but I need to write ImageJ plugins. I’m on the hunt for a new language.

Almost a year ago, I wrote an interface between Kawa and ImageJ, but ImageJ’s design precludes giving Kawa the type annotations it needs to make the interface reasonably fast.

I am no longer appalled by languages like Java. They are muck heaps. The last good language in this family was ALGOL 68. I am appalled by Scala. It tries to be a modern language while still poking its tendrils into the muck heap, but managing the muck has contaminated the language.

Certain things tell me I have been in Haskell too long. I am mildly disturbed by assigning types as values. The case classes, which try to be algebraic data types, miss the point, since you can’t check if functions over them are total.

The primary horrors:

Covariant/contravariant types: Java isn’t strongly typed. You can cast a String to an Object, assign it an integer, and the compiler cannot tell. To escape this, Scala introduces covariant/contravariant types.

Consider the function cons :: a -> [a] -> [a]. The first argument can be any subclass of a. We call it "covariant." The second argument, any superclass of a works in the list. It is "contravariant."

The best solution is to remove inheritance entirely, but the muck monster won’t talk to anyone without inheritance.

Implicit parameters: A library call returns a list. You want to use it as a set, which you have set up as a subclass of list. Write a function which converts lists to sets, annotate it with the implicit keyword, and then you can happily treat the library’s return value as a set.

There are two uses for this. One lets you create typeclasses by defining "traits" (Java interfaces with arbitrary restrictions removed) and then implicitly coercing everything you want into this trait. The other lets you add fields and methods to existing classes and objects.

In the first use, the only claim the creators advance for this approach instead of typeclasses is that implicit parameters are scoped. I learned my lesson about implicit things when I had to maintain a large Perl code base, but this makes the implicit conversions in Perl look like child’s play.

The second use is ludicrous. In Smalltalk, if I want to extend a predefined class C with a method f, I just assign the function body to the field f of C. I can only use the public interface of C, so it isn’t dangerous.

madhadron :: Nov.05.2007 :: computers :: 2 Comments »

Conservation of Energy

Last night it occurred to me that, although I knew Landau’s derivation of conservation of energy in Lagrangian mechanics, I had never seen it done from Newton’s third law. A few minutes of scribbling produced a proof that might be of use to some poor physics student somewhere.

The overarching theme is Noether’s theorem. Consider some problem described by a differential equation (or an action principle, but for now let’s stay with differential equations), which has some continuous symmetry. The rotations that leave a square unchanged are a discrete symmetry. All displacements in time of a system which does not depend on any particular position in time are a continuous symmetry. Essentially, if we can construct a continuous function from the transformations to the real numbers, then it is a continuous symmetry.

Our program: change coordinates in the differential equation until the symmetry transformations we’re interested in are represented by a displacement in a single coordinate. For time displacement, this is simple. For spatial displacement, we use Cartesian coordinates with one axis along the direction of displacement. For rotation, we use polar coordinates.

Shift the coordinate infinitesimally, and Taylor expand to first order. For any solution of the differential equation, the zeroth order expansion cancels. Taylor’s remainder theorem makes the second and higher orders smaller than the first order, so to have invariance, the first order must vanish. The invariance must hold for different infinitesimal displacements, so the first order coefficient must vanish, and we may multiply this by something nonzero to get a cleaner form at the end. The integral of the first order coefficient with respect to the coordinate is a constant, then we integrate everything in sight by parts and occasionally use the original differential equation to substitute for things until we find a convenient form. The last part sounds vague, and it is. I don’t know if there is some algebraic structure that will yield an algorithm for getting clean, useable forms for conservation laws. How did I find this particular set of integrations and multipliers? I played around until it worked.

Conservation of energy comes from invariance under a displacement in time. Begin with Newton’s third law, F(x(t),t) = m D^2 x(t). I use D for the total time derivative. This is not the same as the partials, as DF(x(t),t) = \partial_0 F(x(t),t) \cdot Dx(t) + \partial_1 F(x(t), t) (where \partial_n is the partial derivative with respect to the n^{\textrm{th}} argument). Let t\rightarrow t + \delta t.

mD^2 x(t+\delta t) = F(x(t+\delta t), t+\delta t)
mD^2 x(t) + m\delta t D^3 x(t) = F(x(t), t) + \delta t DF(x(t), t)

The first terms on each side are equal by the original differential equation, and they cancel. Now we multiply by sides by x(t) and rearrange to get

\delta t [ m x(t) \cdot D^3 x(t) - x(t) \cdot DF(x(t), t) ] = 0

This must hold for different, nonzero values of \delta t, so the quantity in brackets must be zero.

Aside: There is a subtlety to note: it is also zero before we threw in the x(t), so it remains zero after we multiply by x(t), so long as the particle isn’t at infinity. If we were not already garunteed this, then we would have to set up the coordinates where x(t) was never zero. This requires symmetry under spatial displacement (which yields conservation of momentum), and the fact that in any finite time interval there are points which are not visited by the path. The whole of the path over infinite time may visit all the points in the space (this is called ergodicity), but we can break the whole of time into connected subsets, each of which have an unvisited point, prove it on each subset, and then stitch them together. Spaces where we can do this slicing and stitching are called manifolds, and we’ll use this trick later.

Now we integrate with respect to time. Integration by parts on the first term yields (everything is multiplied by m, but we’ll just put it back in later):

\int x(t) \cdot D^3 x(t) dt = \int D(x(t) \cdot D^2 x(t)) dt – \int Dx(t) \cdot D^2 x(t) dt
  = x(t) \cdot D^2 x(t) – \int D( \frac{1}{2}(Dx(t) \cdot Dx(t)) )
  = x(t)\cdot D^2 x(t) – \frac{1}{2} Dx(t) \cdot Dx(t)

There’s kinetic energy. The other term will cancel after we analyze the second integral.

\int x(t) \cdot DF(x(t), t) dt = \int D(x(t) \cdot F(x(t),t)) dt – \int Dx(t) \cdot F(x(t), t) dt
  = \int D(x(t) \cdot m D^2 x(t)) dt – \int Dx(t) \cdot F(x(t), t) dt
  = m x(t) \cdot D^2 x(t) – \int Dx(t) \cdot F(x(t), t) dt

where the next to last line follows by replacing the force with the mass times accelleration from Newton’s third law. Now we combine these, putting that m we neglected in the first part back in. The [Unparseable or potentially dangerous latex formula. Error 5 : 573x40]

There’s conservation of energy. Now a few remarks to tie things up:

Remark. The second term looks unfamiliar. Try changing variables so that position is independent and time depends on it. This must be done carefully! If the path x(t) intersects itself, we break the integration into a sum of integrals over intervals of time where the path does not self-intersect, and change variables separately in each one so that t(x) is well defined. On any such interval I, we get a term that looks like \int_I x \cdot F(x, t(x)) dx, which is more familiar.

Remark. If our force has the form F(x, t) = – \partial_0 \mathcal{U}(x,t), then the second integral takes the form -\mathcal{U}(x(t), t) + \int \partial_1 \mathcal{U}(x(t), t) dt. For potentials \mathcal{U} which are independent of time, this is particularly useful as the second integral vanishes. For many oscillating potentials, the integral takes on an average value over long times.

For extra credit, go learn the quantum calculus analog of Taylor expansion (John Baez has a nice description) and do the same thing for discrete symmetries.

madhadron :: Oct.18.2007 :: Uncategorized :: Comments Off

James Watson

There’s been a lot of controversy around James Watson over the last couple of days, to the point where emails have been flying around the Rockefeller University talking about boycotting his receipt of the Lewis Thomas Prize for Writing. I haven’t read his book, I find his statements somewhat ridiculous, and worse, I don’t think he actually made that big a contribution, even aside from stealing data. I think two points are enough:

1. Schrodinger wrote What is life? in 1944, nine years before the Watson and Crick paper, and laid out what was necessary for a molecule that carried hereditary structure. With the discovery of DNA methylation and other modifications, it’s become more and more clear that the pure double helix isn’t the sole carrier of hereditary character. Yes, it was nice to actually know what the molecule was, but it wasn’t one of the most important discoveries of the 20th century. The evolutionary synthesis was. The new quantum mechanics was. The structure of this molecule was not. It was a technical tour de force at the time, but Watson and Crick didn’t even do that.

2. I see far too many descriptions of figuring out the rough structure of DNA as “cracking the secrets of life.” It did no such thing. Before Watson and Crick, we knew that it was a polymer (Levene, 1919); we knew that it carried heritable structure (Avery, 1943); we knew that heritable structure was laid out linearly along the polymer (Morgan, no later than 1915). Crick laid out the “central dogma” of molecular biology in 1957, and everyone dug in and figured out how the encodings worked. The structure of DNA was a pleasant thing to have in your head for doing this, but the classical geneticists had been doing very well without such structures for many years. Unfortunately, having such a structure immediately made lots of people confuse genes (heritable traits, alleles of which are selected in evolution) with ORFs (pieces of DNA transcribed into RNA).

madhadron :: Oct.18.2007 :: Uncategorized :: 4 Comments »

Ezra Pound

I’ve poked at the Cantos for years.
finally, made up my mind.
Ezra Pound:
anti-semite, lunatic;
remarkable literary technician – lousy poet;
a great work by formula.
the result?
the Michelin guide to literature.
perhaps useful to the touring poet.
There’s damnation by faint praise!
The young composer must come to grips
with Pierrot Lunaire and the Rite of Spring.

madhadron :: Oct.14.2007 :: Uncategorized :: Comments Off

Physical intuition in biology

To start, a question: why are the expositions of Landau and Lifshitz compelling? Here are ten volumes, without data. Compare them to any number of disastrous texts with an equal amount of data. Why does Landau & Lifshitz leave us credulous and so many others make us peery?

I think the answer is physical intuition. Chapters one and two of Mechanics set forth are a reference on physical intuition. A physicist believe the world has this shape, or one near to it, no matter what object we embed. For the next four volumes we get physics justified only from this intuition, and then the first chapter of volume 5 – Statistical Physics – hammers in the next piece of intuition: here is how many particles behave. The road forward is probabilistic.

These are the preconceptions a physicist carries with him into biology, where at first they seem to fail him. Some physicists become cynical and jettison this baggage (often at the behest of some biologists). Others refuse and build models that fail, fail, and fail again.

Step back for a moment. Imagine a physicist who has internalized the intuition in Mechanics but not in Statistical Physics. What is his fate? Feynman tells us (Feynman Lectures on Physics, vol.1, p.39-2):

“Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach, these people are the failures of the field; the real successes come to those who start from a physical point of view, people who have a rough idea where they are going and then begin by making the right kind of approximations, knowing what is big and what is small in a given complicated situation.”

In other words, don’t neglect the first chapter of Landau and Lifshitz, vol.5.

What must we bolt onto our intuition to handle biology? The key is in Dobzhansky’s statement “Nothing in biology makes sense except in the light of evolution.”

A biologist tells a physicist, “When you have enough of X, this happens.” The naive physicist takes this literally: there exists a concentration of X at which something physically happens. But the mechanism in question probably exists in several related species, from different environments, all of which rely on similar versions of X. X probably is transcribed at different levels, into a different environment, and yet the system functions roughly the same.

More importantly, the system had to evolve, and the system had to function in all the environments leading up to the present. This is what we must add to our intuition. Exact fixed points and thresholds don’t happen. Now when we hear, “When you have enough of X, this happens,” from a biologist we filter it to, “In a bunch of organisms and places, some level of increase of X causes this to happen.” We do this with (as-is) absurd statements about mechanics and ensembles of particles every day.

This can be made rigorous in the same way as the pieces of Landau and Lifshitz. I suspect that evolutionary game theory of some form may be the proper language to express this.

madhadron :: Sep.27.2007 :: computers, teaching :: Comments Off

What I call myself

What follows is abject navel gazing.

I originally studied physics. I did a lot of mathematics. I dabbled in computer science (and programmed a lot, which is something else). Now I’m immersed in biology. What do I call myself when someone asks?

These days, a mathematician.

This strikes me as odd: I don’t define my occupation by what I work on. But I think I finally understand why.

Here is the best definition I know of a physicist: someone who has been through Jackson’s E&M. If you survived it, you cemented a mindset shared by a community. In physics, everything is about time series. Anything not about time series is a statistical property of a time series.

In biology — not biophysics — trees are the natural unit. The logic of genetics deals in trees. Time series are awkward and dangerous. If we go to behavior and psychology, even the tree is inadequate.

After I settled into biology, I found myself with two deep mental frameworks, one next to the other. I spend a lot of thought trying to mesh them, and I have not yet managed it.

But wait! This is half of mathematics. Gian-Carlo Rota pointed out that axiomatic frameworks in mathematics are a sort of “hardware” for a “software” of mathematical facts. Lisp wizards who think of programs as abstract, nigh Platonic objects will interpret this the way I mean it; I hesitate to throw this analogy to anyone used to a FORTRAN descended language. A new mathematical fact is desirable; a new framework that brings known facts closer to trivial is just as novel. It itself is a mathematical fact. This way lies category theory.

The scientific equivalent of a stateless expatriate is a mathematician.

madhadron :: Sep.25.2007 :: computers, teaching :: Comments Off

How to teach Haskell

The authors of Real World Haskell just posted the first drafts for reviewers, including me. Much of the book is spent trying to explain simple concepts, while addressing the subtleties that result from Haskell’s shorthands and abstracctions. Something occurred to me as I was reading: the easiest way to learn Haskell is to learn some Lisp.

But not traditional Lisp. This Lisp is lazy, has nothing but symbols, lists, and tuples, and enforces the type differences among them. There is a let form but no define, certainly no setq. It’s lambdas are curryable. The whole realm can be explored, its lessons learned, in a couple of days.

It’s a useless language, except for its purpose. It is Limbo to Haskell’s Inferno — not Haskell itself, but sitting on the edge, where the virtuous of the past go who did not survive to the monadic revolution…

After developing the patterns of lists and lambda calculus, and the basic habits of strong typing, in this realm, the first descent into Haskell is fast. In ten minutes, you discuss the slightly changed notation, point out that we have entirely hidden the underlying cons structure of the list, and arrive at the type system.

Now the type system is an obvious extension of a habit to handle this new, more complicated world. The first unexpected structure is the algebraic data type, a transformation of a piece of BNF. I think this is the only place in computer science where the BNF is the clearest way to teach something.

Then there’s a bumpy half an hour about the syntax for defining functions, a period of clarity in general but confusion in detail about type classes, and then you arrive at

MONADS

And I don’t know how to make this one easy. sigfpe has made the beginning clear, but the rest is still obscure.

On the other hand, if a newcomer picked up a book on Haskell and was told that they were going to spend two chapters learning a dialect of Lisp they would never use again, it might not sell well.

madhadron :: Sep.21.2007 :: computers, teaching :: 2 Comments »

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