Surreal goings-on at MMU

Surreal numbers are a construction developed by British mathematician John Conway (who also brought us the Game of Life). They are defined recursively: given two surreal numbers xL less than xR, we can define a new number X = (xL|xR) that bisects the two. Starting with the empty set and using this rule, we can generate all the real numbers, and more.

But, of course, those of you from Manchester knew all this already, as their definition may (surreally) be found on Chester Road, at the entrance to the MMU car park.


X = (x_L | x_R) {\rm ~iff~} \nexists x_R \leq x_L


X \geq Y {\rm ~iff~} \nexists x_R \leq Y \& X \leq y_L
X = Y {\rm ~iff~} X \leq Y \& Y \leq X


X+Y=(x_L+Y,X+y_L | x_R+Y,X+y_R)


\emptyset = {\rm void}
(\emptyset,\emptyset) = 0
(0, \emptyset) = 1
(\emptyset, 0) = -1


(0,1) = \frac{1}{2} \rightarrow \infty
{\rm JHWH}

This final panel is my favourite. It seems to say that starting from nothing (∅) we can produce everything (∞),  thus proving the existence a higher power (JHWH, the Tetragrammaton). In fact it is being deliberately ambiguous; “JHWH” is also how American computer scientist Donald Knuth referred to Conway, writing in 1979:

In the beginning, everything was void, and J.H.W.H.Conway began to create numbers. Conway said, “Let there be two rules which bring forth all numbers large and small. This shall be the first rule: Every number corresponds to two sets of previously created numbers, such that no member of the left set is greater than or equal to any member of the right set. And the second rule shall be this: One number is less than or equal to another number if and only if no member of the first number’s left set is greater than or equal to the second number, and no member of the second number’s right set is less than or equal to the first number.” And Conway examined these two rules he had made, and behold! they were very good.

The mystery remains as to how this mathematical memorial found its way to such an unexpected location. Answers on a postcard.

Thanks to my collaborator and lunch-mate Jon Borresen for pointing out the gates.

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In the beginning there was #postaday

The days of heading to your University library to pore over the latest issue of Acta Arithmetica are a thing of the past. It’s a shame, but Generation Z want their research delivered electronically, and they want it delivered immediately. They don’t have the patience for polishing, for peer review, or for paper. For the academic, blogging has a role to play in this new world order, finding a niche in the immediacy:detail spectrum somewhere between twitter (one sentence critiques) and arXiv (unreviewed reports).

I first entered the blogoshpere in 2010. Inspired by gepasi‘s photo-a-day project 365, I embarked on a blogging #postaday challenge. Of course I failed. To write a decent blog post every day, you’d have to be highly imaginative, highly driven, and highly unemployed. I remain none of the above. But I’m back, armed with four years’ material and an 86% less demanding task. Wish me luck!

#postaweek

Enthought and SBML

{First posted 3 January 2012 at u003f.com, saved from oblivion by the internet archive}

A long time ago, I resolved to replace Matlab with python as my programming language of choice. I was recommended the Enthought python distribution (EPD), which has various packages installed around pylab and is free to academics.

I had some issues getting EPD to talk to SBML, until a young man with a weird surname helped me out. The three steps to overcoming your ophidiophobia are:

1. Link EPD’s unusual directory to the normal place …
sudo ln -s /Library/Frameworks/EPD64.framework /Library/Frameworks/Python.framework/

2. … configure libSBML 5.3.0 there …
./configure --with-python=/Library/Frameworks/Python.framework/Versions/Current

3. … and change ~/.bash_profile to
export PATH="/Library/Frameworks/Python.framework/Versions/Current/bin:${PATH}"
export PYTHONPATH=/usr/local/lib/python2.7/site-packages

A python

Wikipubdate

{First posted 13 June 2011 at u003f.com, saved from oblivion by the internet archive}

Some time ago I promised to rewrite the Wikipedia Systems Biology article and I thought I should update you as to how far I’ve got.

Nowhere.

But I’m pleased to announce that other projects are going very well indeed. You see the small, insignificant green plus sign at the top right of the History of Tranmere Rovers F.C. page? I did that. It means Good Article. It’s like getting a B at GCSE Wikipedia authoring. Go me!

The Computational biology wikiproject has really kicked into gear too; a “bunch of geeks” from Hinxton are driving activity, with the backing of the ISCB. Come and get involved!

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MCA revisited [2]

{First posted 8 June 2011 at u003f.com, saved from oblivion by the internet archive}

As a base example, we’ll use the model presented in [1], a 1986 paper describing METAMOD – modelling software for your BBC micro. How I’d love to have a play with METAMOD now.

The model is called SEQFB, a branched pathway with sequential feedbacks. The program is used to find the model’s steady state for metabolite concentrations

Met Conc Copasi
A 2.2099E1 22.0992
B 4.6395E0 4.63950
C 3.3577E-1 0.335772
D 4.3999E-1 0.439992
E 2.7777E-1 0.277773
F 2.6500E-1 0.264999

and reaction rates.

Enz Rate Copasi
1 1.4261E0 1.42613
2 1.4261E0 1.42613
3 6.9765E-1 0.69753
4 6.9765E-1 0.69753
5 6.9765E-1 0.69753
6 7.2847E-1 0.728472
7 7.2847E-1 0.728472
8 7.2847E-1 0.728472

It’s good to see that loading the model [2] into fancy new software [3] gives identical results. Who needs technology eh? OK, so maybe it runs slightly faster today – half a blink of an eye, rather than just under two minutes.

More tomorrow.

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References

  1. Hofmeyr JH, & van der Merwe KJ (1986). METAMOD: software for steady-state modelling and control analysis of metabolic pathways on the BBC microcomputer. Computer applications in the biosciences: CABIOS, 2 (4), 243-9 PMID: 3450367
  2. Model v.1 SBML
  3. Copasi http://www.copasi.org/

MCA revisited [1]

{First posted 7 June 2011 at u003f.com, saved from oblivion by the internet archive}

Quite some time ago I promised to spend some time going over Metabolic Control Analysis (MCA). It’s one of the main reasons I decided to do this silly #postaday business, but have been rather hesitant as I just don’t know if what I hope to do is possible.

He who dares, Rodders.

The landmark paper “The control of flux” was written in 1973 by Henrik Kacser and Jim Burns [1], describing how the rates of metabolic pathways were affected by changes in the amounts or activities of pathway enzymes. Their work was given a sound mathematical basis by Christine Reder in 1988 [2].

Given there are excellent webpages devoted to the topic [3,4] along with countless review articles, you might reasonably ask why on earth I’m rerevisiting old ground.

In the paper, Reder sets out criteria under which her analysis holds. Which means of course that there are situations where it doesn’t hold. These are generally ignored – probably because the paper is so “mathsy” – with software tools typically blindly applying the algorithm. I shall show, by example, where the theory breaks down, and (this is where I’m on shaky ground) how it can be tweaked to encompass these cases.

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References

  1. Kacser H, & Burns JA (1973). The control of flux. Symposia of the Society for Experimental Biology, 27, 65-104 PMID: 4148886
  2. Reder C (1988). Metabolic control theory: a structural approach. Journal of theoretical biology, 135 (2), 175-201 PMID: 3267767
  3. Athel Cornish-Bowden. Metabolic Control Analysis
  4. Pedro Mendes. MCA web

And now for something completely different

{First posted 6 June 2011 at u003f.com, saved from oblivion by the internet archive}

Answers to Friday’s teaser.

Where on the earth where could you travel one mile south, then one mile east, then one mile north and end up in the same spot you started?

To me, this is a Christmas cracker question to which everyone knows the easy Christmas cracker answer. However there’s another, harder and unexpected answer, and another another even harder answer.

Needless to say, @Xpic found this no trouble at all, tweeting all three answers in order. Which leads me to think that classics graduates may be the cleverest people in the world.

Easy answer and harder answer:

[tweet 76666634667950080 hide_thread=’true’ align=’center’]

Even harder answer:

[tweet 76667104476151808 hide_thread=’true’ align=’center’]

Genius.

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