Theory

Astro search engine

2008-11-04T13:35:18-05:00

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PlotPick program

2008-10-01T19:55:03-05:00

While calibrating my photodiodes, some of my surface bumps went out of the linear-response range. Since I'm not confident in my ability to set boundaries programmatically at the moment, I thought I'd write up a little utility to record clicks on key data points, so I could pick out the “good data”.

Enter plotpick.py, the raw-data version of clicklock.tk. Hope you like it :).

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Good introduction to protein folding simulations

2008-09-10T14:32:09-05:00

Grosberg's chapter of Computational Soft Matter: From Synthetic Polymers to Proteins (available online) seems to be quite a nice intro to basic methods in protein folding simulations. It cleared up the difference between lattice and off-lattice models for me again, hopefully I'll remember this time ;).

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Getting numbers from journal figures

2008-09-05T20:20:30-05:00

This morning I wrote up this quick and easy way to get actual numbers out of graphs and whatnot that show up in journal articles.

$ pdfimages article.pdf fig
$ clickloc.tk fig-000.ppm > fig-000.pixels
$ scale_click.sh 0 10 5 20 fig-000.pixels > fig-000.data

Just use your first four clicks in clickloc.tk to mark out the x and y minimum and maximum values. Then use scale_click.sh to convert the pixel values to the units listed in the figure. In my example, the x axis ran from 0 to 10 units, and the y axis ran from 5 to 20 units. Supports log-scaled axes too.

Having gotten some numbers, my sawtooth simulator matches up fairly well to Schlierf & Rief's results on both models. Hooray! ;).

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Giving up on Gompertz theory

2008-06-30T17:22:51-05:00

I think I've spent enough time trying to find a nice analytic way to guess parameters for a Gompertz model fit to my unfolding probability densities. I now have a heuristic which seems to work :p, and I suppose I'll be satisfied with that for the time being.

On to find out about analytic solutions to Kramers' unfolding rates.

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Data censoring

2008-06-30T15:52:36-05:00

This is a nice paper with pretty pictures explaining the different types of data censoring. I don't have to worry about that, since our data are uncensored (proteins being cheaper and living shorter lives than humans), but I was getting a bit nervous about what failure-censored sampling meant.

In other jargon news, the first order statistic, just means the sample minimum.

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Gompertz' paper

2008-06-30T15:05:40-05:00

The natural logarithm (log base e) used to be called the hyperbolic logarithm (see here). Other than the understandably old fasioned notation, Gompertz article is wonderfully written, so much so that I can follow all his math, even with the strange notation (although obviously I had to look hyperbolic logs up). He makes a number of brief excursions to set up the problem, including a reference to "the great age of the patriarchs of scripture". He even takes a break to clarify his exponent notation. I love this guy.

All the non-symbolic math was starting to confuse me, so I went back and Googled a bit more, turning up this paper which claims to help fit the Gompertz distribution, and even (gasp) uses the same Gompertz distribution that Gompertz does :p. It even talks about probability density functions. I dunno if I'm ready for another relationship yet though, I've been hurt so many times before ;).

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Gompertz/Gumbel distributions

2008-06-30T13:39:51-05:00

This paper by Peter Pflaumer gives a bit more technical detail to the whole Gompertz/Gumbel lifespan thing. I need to remember that my model works, I just need a stable way of estimating the model parameters from which to start optimizing a fit. Pflaumer derives a formula for the mode, but it is still trancendental in the force scaling parameter.

Hmm, I should see what Garrett thinks of the economics of this distribution, since that's what it was originally developed for. He probably already knows all about it, why didn't I think to ask last weekend? Ah, because I started this on Sunday and saw him on Saturday :p.

I though this aught to do it for me, but it seems their rate has an extra -ln(P) in it. Rats.

Desperate times call for going back to Gompertz' original paper.

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Gumbel/Fisher-Tippett distributions

2008-06-29T14:10:54-05:00

Aha, the probability of Bell-model unfolding under constant force-loading has a name! It is a Fisher-Tippett distribution, of which the Gumbel distribution is a particular type. However, NIST refers to it as a minimum Gumbel distribution.

Hmm, hopefully I'm not just confusing myself looking at the standardized form, let me go double check... What is a cumulative distribution function anyway? Ah, CDF(x) is just the probability that the variable will be <= x, so the probability distribution function is given by PDF(x) = -d(CDF)/dx.

Alright, looks like my distribution is a bit different than the Fisher-Tippett because I need a non-unity a factor a in PDF(x) = exp(-ax/b)*exp[-exp(x/b)] with z := exp(-x/b). Basically, I have a Fisher-Tippett distribution with a poorly scaled x, but I don't know how to rescale x until I've fit my distribution. So the search continues...

The Gompertz-Makeham Law law for exponentially increasing failure rate is what I want. But Wikipedia says this is the same as Fisher-Tippett with time inversion.

There is a nice discussion of aging in general, but not much math here.

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