Archive for August, 2024

What does the deficiency depend on?

August 12, 2024

I have spent a lot of time and energy thinking about chemical reaction networks and, in particular, about the notion of the deficiency of such networks. This is a non-negative number which can be assigned to a network and it gives a certain measure of the complexity of the network. Now I realised something which I should have realised long ago. I am sure that it is widely known and plays a role, at least implicitly, in many papers I have read and talks I have heard. As one recent example of a relevant text I mention a paper of Craciun et al., Math. Biosci. 342, 108720. Given a reaction network describing a system of chemical reactions there is a standard way of obtaining a corresponding system of ODE, assuming mass action kinetics. Given the network we can also compute the deficiency. The point I had not fully understood is that the deficiency cannot be computed from the ODE system. It is a property of the network and more than one network can give rise to the same system of ODE. In particular, two networks with different deficiencies can give rise to the same system of ODE. Thus it makes no sense to talk about the deficiency of the system of differential equations.

A situation in which this can play a role is the following. The ODE corresponding to a reaction network can have linear conserved quantities. In the usual language of chemical reaction network theory (CRNT) the stoichiometric subspace is a proper subspace. It is then often convenient to eliminate some of the variables so as to get an effective system of lower dimension, thus obtaining a simplification of the system. It should however be noted that what is being reduced here is the system of ODE, not the network. Thus I cannot speak about the deficiency of the reduced network. I must first find a network which gives rise to the reduced system and then calculate its deficiency. In general there will be a choice involved in defining the network and the deficiency which comes out may depend on that choice.

Encounter with an anteater

August 5, 2024

In a previous post I wrote about the first time I saw an aardvark live. Here I want to do the same for the anteater. To be clear, when I say anteater without further qualification I mean the giant anteater, Myrmecophaga tridactyla. Many years ago I often used to get home to my flat late on Sunday evenings, after 10 o’ clock. When I got home I would switch on the TV and there was often a programme about a zoo. There an anteater had just been born and so they presented a lot of information on that species. That was the context in which I developed a kind of emotional attachment to anteaters. I would have liked to see one in reality but I learned by experience that even when a zoo has an anteater the chances of seeing it may be small. Once when I was on a business trip to London I had some free time and I used it to go to the London Zoo, knowing that they had an anteater. Of course I saw no trace of it. At least that visit had a bonus. There I saw one very attractive animal which I had not heard of before, the red panda. My next attempt was during a sabbatical where I spent some time at the University of Copenhagen. Again I went to the zoo and again I saw no anteater. There were also red pandas there and some excitement among the staff since one of them could not be found. Another interesting animal which I saw there was the Tasmanian Devil. In Copenhagen they have (or at least had then) a breeding programme for this species which is threatened by a type of cancer. I have known for some time that there is an anteater at the Frankfurt Zoo but although I live not too far from Frankfurt I had never been to that zoo. Yesterday Eva and I finally went there. I knew that the anteater enclosure is very near the entrance. The enclosure where the anteater lives is large and full of lush vegetation. Standing in front of it with Eva I said that I was sure we had no chance of seeing the anteater. Then I looked to my left and there it was, larger than life, only a few meters away from us. It stood there for a couple of minutes and then continued its rounds of its territory. I was quite surprised at how fast it moved and how it went through a stream without hesitating. That was a great start to our visit to the Frankfurt Zoo. Later on we also had good views of tamanduas, the smallest type of anteater.

We also had some other interesting experiences. In the zoo there are rooms where the visitors are together with birds without any partitions. In one of these I was pleased to see a Roller, which flew around and came quite close to us. I did once in my life see Rollers in the wild, in northern Greece. That is a very long time ago and the experience was not repeated. We also saw two Keas. They were separated from us by a fence and that is probably just as well, since I would not trust them. My brother lived in New Zealand for many years. In particular he spent a lot of time in the bush. He told me various stories about Keas. He said that if a car was left out in the bush too long then the windscreen could fall out because Keas had pecked away the rubber which had been holding it. They could also remove the tyres. He also told me about an experience of his own. He was sleeping in a shack in the bush when he was woken by a sound which he thought was that of raindrops on the roof. When he opened his eyes he saw the true explanation, namely a large hole in the roof which Keas had made. The birds were very unpopular with some people, who would throw stones at them. However it was impossible to hit them. The only alternative which might work was if snow was lying. Then it might be possible to hit a Kea with a snowball because it would not see it coming. The Keas we saw were accompanied by a Falkland Caracara. On our trip to Patagonia we had seen caracaras of two species and found them very engaging. Now we had the opportunity to see a third species, although only in captivity. It was interesting to observe the interactions between the Keas, the caracara and the House Sparrows which were also present as non-members of the zoo.


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