## Archive for the ‘life’ Category

### SMB conference in Utah

July 21, 2017

Now Subgroups are being set up within the Society to concentrate on particular subjects. One of these, the Immunobiology and Infection Subgroup had its inaugural meeting this week and of course I went. There I and a number of other people learned a basic immunological fact which we found very surprising. It is well known that the thymus decreases in size with age so that presumably our capacity to produce new T cells is constantly decreasing. The obvious assumption, which I had made, is that this is a fairly passive process related to the fact that many systems in our bodies run down with age. We learned from Johnna Barnaby that the situation may be very different. It may be that the decrease in the size of the thymus is due to active repression by sexual hormones. She is involved in work on therapy for prostate cancer and said that it has been found that in men with prostate cancer who are getting drugs to reduce their testosterone levels it is seen that their thymus increases in size.

There were some recurrent themes at the conference. One was oncolytic viruses. These are genetically engineered viruses intended to destroy cancer cells. In modelling these it is common to use extensions of the fundamental model of virus dynamics which is very familiar to me. For instance Dominik Wodarz talked about some ODE models for oncolytic viruses in vitro where the inclusion of interferon production in the model leads to bistability. (In reponse to a question from me he said that it is a theorem that without the interferon bistability is impossible.) I was pleased to see how, more generally, a lot of people were using small ODE models making real contact to applications. Another recurrent theme was that there are two broad classes of macrophages which may be favourable or unfavourable to tumour growth. I should find out more about that. Naveen Vaidya talked about the idea that macrophages in the brain may be a refuge for HIV. Actually, even after talking to him I am not sure if it should not rather be microglia than macrophages. James Moore talked about the question of how T cells are eliminated in the thymus or become Tregs. His talk was more mathematical than biological but it has underlined once again that I want to understand more about positive and negative selection in the thymus and the related production of Tregs.

On a quite different subject there were two plenary talks related to coral reefs. A theme which is common in the media is that of the damage to coral due to climate change. Of course this is dominated by politics and usually not accompanied by any scientific information on what is going on. The talk of Marissa Blaskett was an excellent antidote to this kind of thing and now I have really understood something about the subject. The other talk, by Mimi Koehl, was less about the reefs themselves but about the way in which the larvae of snails which graze on the coral colonize the reef. I found the presentation very impressive because it started with a subject which seemed impossibly complicated and showed how scientific investigation, in particular mathematical modelling, can lead to understanding. The subject was the interaction of microscopic swimming organisms with the highly turbulent flow of sea water around the reefs. Investigating this involved among other things the following. Measuring the turbulent flow around the reef using Doppler velocimetry. Reconstructing this flow in a wave tunnel containing an artificial reef in order to study the small-scale structure of the transport of chemical substances by the flow. Going out and checking the results by following dye put into the actual reef. And many other things. Last but not least there was the mathematical modelling. The speaker is a biologist and she framed her talk by slides showing how many (most?) biologists hate mathematical modelling and how she loves it.

### Conference on mathematical analysis of biological interaction networks at BIRS

June 9, 2017

I have previously written a post concerning a meeting at the Banff International Research Station (BIRS). This week I am at BIRS again. Among the topics of the talks were stochastic chemical reaction networks, using reaction networks in cells as computers and the area of most direct relevance to me, multiple steady states and their stability in deterministic CRN. Among the most popular examples occurring in the talks in the latter area were the multiple futile cycle, the MAPK cascade and the EnvZ/OmpR system. In addition to the talks there was a type of event which I had never experienced before called breakout sessions. There the participants split into groups to discuss different topics. The group I joined was concerned with oscillations in phosphorylation cycles.

In the standard dual futile cycle we have a substrate which can be phosphorylated up to two times by a kinase and dephosphorylated again by a phosphatase. It is assumed that the (de-)phosphorylation is distributive (the number of phosphate groups changes by one each time a substrate binds to an enzyme) and sequential (the phosphate groups are added in one order and removed in the reverse order). A well-known alternative to this is processive (de-)phosphorylation where the number of phosphate groups changes by two in one encounter between a substrate and an enzyme. It is known that the double phosphorylation system with distributive and sequential phosphorylation admits reaction constants for which there are three steady states, two of which are stable. (From now on I only consider sequential phosphorylation here.) By contrast the corresponding system with processive phophorylation always has a unique steady state. Through the talk of Anne Shiu here I became aware of the following facts. In a paper by Suwanmajo and Krishnan (J. R. Soc. Interface 12:20141405) it is stated that in a mixed model with distributive phosphorylation and processive dephosphorylation periodic solutions occur as a result of a Hopf bifurcation. The paper does not present an analytical proof of this assertion.

It is a well-known open question, whether there are periodic solutions in the case that the modificiations are all distributive. It has been claimed in a paper of Errami et. al. (J. Comp. Phys. 291, 279) that a Hopf bifurcation had been discovered in this system but the claim seems to be unjustified. In our breakout sessions we looked at whether oscillations might be exported from the mixed model to the purely distributive model. We did not get any definitive results yet. There were also discussions on effective ways of detecting Hopf bifurcations, for instance by using Hurwitz determinants. It is well-known that oscillations in the purely distributive model, if they exist, do not persist in the Michaelis-Menten limit. I learned from Anne Shiu that it is similarly the case that the oscillations in the mixed model are absent from the Michaelis-Menten system. This result came out of some undergraduate research she supervised. Apart from these specific things I learned a lot just from being in the environment of these CRN people.

Yesterday was a free afternoon and I went out to look for some birds. I saw a few things which were of interest to me, one of which was a singing Tennessee warbler. This species has a special significance for me for the following reason. Many years ago when I still lived in Orkney I got an early-morning phone call from Eric Meek, the RSPB representative. He regularly checked a walled garden at Graemeshall for migrants. On that day he believed he had found a rarity and wanted my help in identifying it and, if possible, catching it. We did catch it and it turned out to be a Tennessee warbler, the third ever recorded in Britain. That was big excitement for us. I had not seen Eric for many years and I was sad to learn now that he died a few months ago at a relatively young age. The name of this bird misled me into thinking that it was at home in the southern US. In fact the name just came from the fact that the first one to be described was found in Tennessee, a migrant. The breeding range is much further north, especially in Canada. Thus it is quite appropriate that I should meet it here.

### Becoming a German citizen

May 24, 2017

I first moved to Germany in 1987 and I have spent most of the time since then here. The total time I have spent elsewhere since my first arrival in Germany does not add up to more than two years. There is every reason to expect I will spend the rest of my life here. I am married to a German, I have a job here I like and a house. I could have applied for German citizenship a long time ago but I never bothered. Being an EU citizen living in Germany I had almost almost all privileges of a native. The only exception is that I could not vote except in local elections but since I am not a very political person that was not a big issue for me. It was also the case that for a long time I might have moved to another country. For instance I applied for a job in Vienna a few years ago and I might well have taken it if it had been offered to me. Now the chances of my moving are very small and so there is no strong argument left against becoming a German citizen.

What is more important is that there are now arguments in favour of doing so. With the EU showing signs of a possible disintegration the chance that I could lose the privileges I have here as an EU citizen is not so small that it should be neglected. The referendum in which the Scots voted on the possibility of leaving the UK was the concrete motivation for my decision to start the application process. Scotland stayed in the UK but then the Brexit confirmed that I had made the right decision. At the moment there is no problem with keeping British citizenship when obtaining German citizenship and I am doing so. This may change sometime, meaning that I will have to give up my British citizenship to keep the German one, but I see this as of minor importance.

As prerequisites for my application I had to do a number of things. Of course it was necessary to submit a number of documents but I have the feeling that the amount of effort was less than when obtaining the documents needed to get married here. I had to take an examination concerning my knowledge of the German language, spoken and written. It was far below my actual level of German and so from that point of view it was a triviality. It was just a case of investing a bit of time and money. I also had to do a kind of general knowledge test on Germany and on the state where I live. This was also easy in the sense that the questions were not only rather simple for anyone who has lived in the country for some time but they are also taken from a list which can be seen in advance. Again it just meant an investment of time and money. At least I did learn a few facts about Germany which I did not know before. In my case these things were just formalities but I think it does make sense that they exist. It is important to ensure that other applicants with a background quite different from mine have at least a minimal knowledge of the language and the country before they are accepted.

After all these things had been completed and I had submitted everything it took about a year before I heard that the application had been successful. This time is typical here in Mainz – I do not know how it is elsewhere in Germany – and it results from the huge backlog of files. People are queueing up to become German citizens, attracted by the prospect of a strong economy and a stable political system. Yesterday I was invited to an event where the citizenship of the latest group of candidates was bestowed in a ceremony presided over by the mayor. There were about 60 new citizens there from a wide variety of countries. The most frequent nationality by a small margin was Turkish, followed by people from other middle eastern countries such as Iraq and Iran. There were also other people from the EU with the most frequent nationality in that case being British. My general feeling was one of being slightly uneasy that I was engaged in a futile game of changing horses. It is sad that the most civilised countries in the world are so much affected by divisive tendencies instead of uniting to meet the threats confronting them from outside.

### Herbal medicine and its dangers

December 18, 2016

I recently heard a talk by Thomas Efferth of the Institute for Pharmacology of the University of Mainz on herbal medicine. There is a common point of view that substances derived from plants are harmless and good while the chemical drugs of standard medicine are evil. The speaker emphasized that plants have good reasons for not being good to those who eat them. They do not have immune systems of the type we do and they cannot run away and so it is natural that they use poisons to defend themselves. Herbal medicines are effective in some cases but they need to be subject to controls as much as do substances obtained by artificial chemical means. In the talk a number of examples of the dangers of ‘natural’ medicines were presented and I will write about some of them here.

The first example is that of Aristolochia. This a large genus of plants, some of which are poisonous. One of these, Aristolochia clematitis, has been extensively used in herbal medicine. It was used extensively in the west in ancient times and is used in traditional Chinese medicine until today. In the talk the story was told of an incident which happened in Belgium. There was a product sold as a means of losing weight which contained a Chinese plant. It sold so well that the manufacturer’s supplies of the plant were running out. When more was ordered a fateful mistake took place. There are two plants which have the same name in China. The one is that which was originally contained in the weight-loss product. The other is the poisonous Aristolochia fangchi and it was the one which was delivered. This led to more than 100 cases of kidney failure in the people using the product. Another way in which plants can be dangerous is as weeds in crop fields. In the Balkans contamination of grain with Aristolochia clematitis led to a kidney disease called Balkan nephropathy, with 35000 recorded cases. The substance, aristolochic acid, which is responsible for the kidney toxicity is also known to be a strong carcinogen. Interestingly, this substance is not poisonous for everyone and its bad effects depend a lot on the variability in liver enzymes among individuals.

A class of substances used by many plants to protect themselves against insects are the pyrrolizidine alkaloids. These substances are hepatotoxic and carcinogenic. They may move through the food chain being found, for instance, in honey. It has been noted that there may be risks associated to the amount of these substances contained in medicinal herbs used both in the West and in China. It was mentioned in the talk that drinking too much of certain types of herbal tea may be damaging to health. The problem is usually not the plants that are the main components of the teas but other plants which may be harvested with them in small quantities. There is at least one exception to this, namely coltsfoot (Tussilago farfara). In one case the death of an infant due to liver disease is believed to be due to the mother drinking this type of tea during pregnancy. After that the sale of coltsfoot was banned in Germany.

There were some remarks in the talk on heavy metals which I found quite suprising. One concerned ayurvedic medicine which has an aura of being gentle and harmless. In fact in many of these substances certain heavy metals are added delibrately (lead, mercury and arsenic). According to Wikipedia more than 80 cases of lead poisoning due to ayurvedic ‘medicines’ have been recorded. Another remark was that there can be significant concentrations of heavy metals in tobacco smoke. The negative health effects of smoking are sufficiently well known but this aspect was new to me.

Another theme in the talk was interactions between herbal medicines and normal drugs. Apparently it is often the case that patients who use herbal remedies are afraid to mention this to their doctors since they think this may spoil the relationship to their practitioner. Then it can happen that a doctor is suprised by the fact that a drug he prescribes is not working as expected. Little does he know that the patient is secretly taking a ‘natural’ drug in parallel. An example is St. John’s wort which is sometimes taken as a remedy for depression. It may work and it has no direct negative effects but it can be problematic because it reduces the effects of other drugs taken at the same time, e.g. the contraceptive pill. It changes the activity of liver enzymes and causes them to eliminate other drugs from the body faster than would normally happen, thus causing an effective reduction of the dose.

We are surrounded by poisonous plants. I was always sceptical of the positive effects of ‘natural’, plant-derived medicines. Now I have realised how seriously the dangers of these substances should be taken.

### Honesty is the best policy

December 10, 2016

Yesterday I did the following thought experiment. I imagined a situation where someone asked me two questions, saying that I should answer spontaneously without thinking too long. The first question was ‘Are you happy with your life?’ and the second ‘Are you happy with the society around you?’ My answer to the first question was ‘yes’ and to the second ‘no’. I then started thinking about the cause of the discrepancy between these two answers. I came to the conclusion that it has a lot to do with the concept of ‘honesty’. I believe in and live according to the phrase in the title of this post, ‘honesty is the best policy’ while I feel that in the society around me lies have a huge influence. It is also worth remarking that lies are not the only kind of dishonesty.

If I am honest what is the reason? One important influence is my upbringing. I grew up in a family which was very attached to telling the truth. Here the influence of my mother was particularly strong. What influenced me was not so much what she said on the subject as the example of how she behaved. My mother’s attachment to honesty had a lot to do with her attachment to religion. I did not inherit her religion, becoming an atheist in my teens. I also did not inherit her moral convictions but I did inherit certain patterns of moral behaviour. One thing that stops me telling lies is simply that I find it very unpleasant due to childhood conditioning. Since truth plays a central role in mathematics it is perhaps natural that mathematicians should tend to be truthful, also in everyday life. It might also conversely be the case that among people who go into academia those with a specially strong attachment to truth might tend to go in the direction of mathematics.

Probably the main motivation for lying is the hope to gain some advantage by doing so. This may be short-sighted if despite a short-term profit the net long-term payment is negative. The idea that this is often the case is one motivation for me not to lie. Another is the fact that lies require management in order to profit from them. It is necessary to remember the lies you told so as not to betray yourself and it is also necessary to remember the corresponding true version. A lot of profitable lies require a lot of management and this is stress which I like to avoid. More thoughts in similar directions can be found on this web page
http://www.becomingminimalist.com/why-honesty-is-the-best-policy-for-simplicity/

What types of dishonesty in society bother me? One is political correctness. It means sanctions againt telling the truth, or just speaking plainly rather than in euphemisms, in many situations. There are some cases where there may be good reasons for measures like this but I think that in the majority of cases there are no good reasons. They are based on arbitrary conventions or at best on misguided ideas of well-meaning people. I prefer to speak openly but I often avoid doing so and simply keep quiet in order to avoid problems. I would prefer if this was not so often necessary. A related topic is that of reference letters. When I write references for people applying for academic jobs I generally feel free to tell the truth. For jobs outside academia things are very different. There telling the truth might easily lead to disaster since open criticism is often effectively forbidden. Instead it is necessary to write in code and even then the information which might be helpful for the employer, or for the applicant, might not get through. In other situations it is necessary to be careful when criticising people but it is wrong not to criticise. Constructive criticism can be good. I am happy when I receive constructive criticism although it may be unpleasant at the moment it arrives. I believe that it is also important to make statements in certain situations like ‘in my opinion person X is better than person Y at doing task Z’. This is not a comparison of the value of the two people in general but just in the context of a particular ability.

One other theme I want to mention is marriage, because my marriage is one of the things in my life which contributes most to my happiness. When I use the word ‘marriage’ here I mean it to denote a long-term romantic relationship, not only one which is recognised legally by a piece of paper. I have been married in the latter sense for eight years but the underlying relationship goes back sixteen years. I would not dare to write here about individual marriages (apart from my own) but I will say something about averages. It seems that with time marriages in our society become less and less stable and last for shorter times. I believe in marriage in the old-fashioned sense of ’till death do us part’ and I think it is very unfortunate for many people that they have replaced this by a sequence of shorter-term relationships accompanied by difficult separations. The relation of this topic to that of honesty is as follows. I think that separations often result from the fact that the people involved are pursuing short term gains at the expense of the partner. Then the short-term gains turn into long-term losses. In a talk I heard recently the speaker voiced the opinion that the kind of degradation of marriage (or of love) I have been talking about is due to the fact that many people going into relationships have not had the experience of good marriages in their childhood. I had the advantage of growing up in surroundings where this type of relationship was widespread and I had very direct experience of how it was in the case of my own parents.

### A visit to Iceland

September 4, 2016

I just returned from 10 days as a tourist in Iceland. It was not my first time there. Years ago I went on a cruise which included two stops in Iceland, one in Reykjavik and one in Akureyri. In each case there was a short bus tour to see some typical sights – a waterfall, a geysir and a volcanic region with bubbling mud and hot springs. This time I had a chance to see a lot more. I enjoyed the cruise a lot but I had the impression that the majority of the people on the ship were very bored. The main antidote to the boredom offered was lots of food. One day I got up from the dinner table and went on deck. There had been no indication that there might be something interesting to see. When I opened the door I was confronted with a beautifully conical volcano covered with ice, Snaefellsjökull. (I will come back to the interesting issue of Icelandic pronuciation later.) This was one of my strongest impressions from the whole cruise. The volcano is at the end of a long peninsula to the north of Reykjavik. This time I learned that this volcano is the esoteric centre of Iceland and that it was the starting point of Jules Verne’s Journey to the Centre of the Earth. This was not really a point on the programme of the tour this time but it was clearly visible with binoculars from the hotel in Rekjavik where we spent the last two nights. I had one view of it which was monochrome due to the light conditions but where the sharp edges of the crater stood our clearly.

One attraction of Iceland for me was the bird life. It seems that the country has claimed exclusive rights on the puffin. The numerous tourist shops in Reykjavik are called ‘puffin shops’ due to the number of representations of that bird they sell. I also saw puffin offered as one of the constituents of a special menu also including whale and horse meat. We spent one night in Vik and I discovered two stranded fulmars on a grass area not far from the hotel. These birds can only take off from an elevated starting point like a cliff or from water. If one lands on a flat area some distance from the sea then it is doomed unless it gets help. I rescued two of them by carrying them (ten minutes walk including crossing a road with significant traffic) to the sea. Since there had not been a big storm I suppose they had come down during their first flight after leaving the nest. (There were fulmars nesting on inland cliffs on the other side of the hotel from the sea.) Fortunately I still knew how to catch them and pick them up without hurting them or being the victim of their defence mechanism of spitting foul-smelling oil when feeling threatened. I enjoyed seeing a few glaucous gulls in the harbour in Reykjavik on the last day. Probably the last time I saw any was on the cruise I already mentioned. It was also nice to see and hear many whimbrels. The first one already welcomed me at the airport when I arrived.

I felt at home in the natural surroundings in Iceland and after a few days I thought of one explanation. There are very few trees in Iceland and this is just as it is in Orkney where I grew up. The first time I was on the mainland of Scotland when I was four years old I said ‘I don’t like this place – you can’t see anything for trees’. There are many areas in Iceland where there is only sand, rocks, water and ice. I had the impression of seeing what the Earth is really like, without the veil of green which we usually see. I also got an impression of what it is really like to live next to a volcano. I was in a museum close to (and devoted to) Eyafjallajökull, the infamous producer of ash with the complicated name. I learned that one US journalist just called it E15, due to the number of letters. There was a film showing in the museum explaining what people living near the volcano experienced at the time of the last eruption. Coming back to the name, the pronunciation of Icelandic does seems to be a difficult question but also an interesting one. I would like to spend some time understanding it better. There are nice videos on the pronuciation of Eyafjallajökull here and here. The final double l is the really tricky point. There are points of similarity between the Icelandic language and the dialect I grew up with. This is due to the influence of an extinct language called Norn which was spoken on Orkney and Shetland in past centuries and which is related to (Old) Icelandic. For instance the oystercatcher is called tjaldur in Icelandic and chaldro in our dialect.

I also had some culinary experiences. At breakfast in the hotels there was always a bottle of cod liver oil on the table. I remember this liquid from my childhood as a threat used on young children. ‘If you do not behave yourself I will give you a spoonfull of cod liver oil.’ Due to persistent encouragement from Eva I tried a little and found it not as bad as I expected. Our guide also gave us some pieces of Greenland shark to try. He gave  us a warning about the taste and some of the alcholic drink called the black death to wash it down with. It tastes of nothing at first but chewing leads to a strong taste reminiscent of urine. In fact the flesh of the shark is poisonous due to its content of trimethylamine N-oxide. In Iceland it is treated by first burying it for several weeks and then drying it to get rid of the poison. The result is considered a delicacy. The Greenland shark is interesting because of the fact that it was recently discovered that it can live to be four hundred years old, only becoming sexually mature when it is 150. I want to read more about it.

As a final comment on Iceland: the weather was much better than we expected!

### An eternal pedestrian

June 13, 2016

I am presently visiting Japan. My host is Atsushi Mochizuki who leads the Theoretical Biology Laboratory at RIKEN in Wako near Tokyo. RIKEN is a research organisation which was founded in 1917 using the Kaiser-Wilhelm-Gesellschaft as a model. Thus it is a kind of Japanese analogue of the Max Planck Society which is the direct descendant of the Kaiser-Wilhelm-Gesellschaft. I had only been in Japan once before and looking at my records I see that that was in August 2005. At that time I attended a conference in Sendai, a place which I had never heard of before I went there. Since then it has become sadly famous in connection with the damage it suffered from the tsunami which also caused the Fukushima nuclear disaster. At least I had even then previously heard of Tohoku University which is located in the city.

Yesterday, sitting by the river in Wako, I was feeling quite meditative. I was in an area where motor vehicles are not permitted. There were not many people around but most of those who were there were on bikes. I started thinking of how this is typical of what I have experienced in many places I have been. On a walk along the Rhine in Mainz or in the surrounding countryside most of the people you see are on bikes. Copenhagen is completely dominated by bikes. In the US cars dominate. For instance when I was in Miami for a conference and was staying at the Biltmore Hotel I had to walk quite a distance to get dinner for an affordable price. In general the only people I met walking on the streets there were other conference participants. When I visited the University of California at Santa Barbara bikes were not the thing on the campus but it was typical to see students with skateboards. Summing up, I have frequently had the experience that as a pedestrian I was an exception. It seems that for normal people just putting one foot in front of the other is not the thing to do. They need some device such as a car, a bike or a skateboard to accompany them. I, on the other hand, am an eternal pedestrian. I like to walk places whenever I can. I walk twenty minutes to work each day and twenty minutes back. I find that a good way of framing the day. When I lived in Berlin there was a long period when I had a one-way travelling time of 90 minutes by train. I am glad to have that behind me. I did not consciously plan being so near to work in Mainz but I am glad it happened. Of course being a pedestrian has its limits – I could not have come to Japan on foot.

My pedestrian nature is not limited to the literal interpretation of the term. I am also an intellectual pedestrian. An example of this is described in my post on low throughput biology. Interestingly this post has got a lot of hits, more than twice as many as any other post on my blog. This is related to the theme of simple and complex models in biology. Through the talks I have given recently in Copenhagen, Berlin and here in Japan and resulting discussions with different people I have become of conscious of how this is a recurring theme in those parts of mathematical biology which I find interesting. The pedestrian may not get as far as others but he often sees more in the places he does reach. He may also get to places that others do not. Travelling fast along the road may cause you to overlook a valuable shortcut. Or you may go a long way in the wrong direction and need a lot of time to come back. Within mathematics one aspect of being a pedestrian is calculating things by hand as far as possible and using computers as a last resort. This reminds me of a story about the physicist John Wheeler who had a picture of a computer on the wall in his office which he called ‘the big computer’. When he wanted to solve a difficult problem he would think about how he would programme it on the computer and when he had done that thoroughly he had understood the problem so well that he no longer needed the computer. Thus the fact that the computer did not exist except on paper was not a disadvantage.

This is the direction I want to (continue to) go. The challenges along the road are to achieve something essential and to make clear to others, who may be sceptical, that I have done so.

### Flying to Copenhagen without a carpet

May 11, 2016

This semester I have a sabbatical and I am profiting from it by travelling more than I usually do. At the moment I am visiting the group of Carsten Wiuf and Elisenda Feliu at the University of Copenhagen for two weeks. The visit here also gives me the opportunity to discuss with people at the Niels Bohr Institute. Note that the authors of the paper I quoted in the post on NF$\kappa$B were at the NBI when they wrote it and in particular Mogens Jensen is still there now. I gave a talk on some of my work on the Calvin cycle at NBI today. Afterwards I talked to Mogens and one of his collaborators and found out that he is still very active in modelling this system.

I was thinking about my previous visits to Copenhagen and, in particular, that the first one was on a flying carpet. The background to this is that when I was seven years old I wrote a story in school with the title ‘The Magic Carpet’. I do not have the text any more but I know it appeared in the School Magazine that year. In my own version there was also a picture which I will say more about later. But first something about the story, of which I was the hero. I bought the carpet in Peshawar and used it to visit places in the world I was interested in. For some reason I no longer know I had a great wish at that time to visit Copenhagen. Perhaps it was due to coming into contact with stories of Hans Christian Andersen. In any case it is clear that having the chance this was one of the first places I visited using the magic carpet. The picture which I drew showed something closer to home. There I can be seen sitting on the carpet, wearing the blue jersey which was my favourite at that time, while the carpet bent upwards so as to just pass over the tip of the spire of St. Magnus Cathedral in Kirkwall. In the story it was also related that one of the effects of my journey was a newspaper article reporting a case of ‘mass hallucination’. I think my teachers were impressed at my using this phrase at my age. They might have been less impressed if they had known my source for this, which was a Bugs Bunny cartoon.

During my next visit to Copenhagen in 2008 (here I am not counting changing planes there on the way to Stockholm, which I did a few times) I was at a conference at the Niels Bohr Institute in my old research field of mathematical relativity and I gave a talk in that area. Little did I think I would return there years later and talk about something completely different. I remember that there was a photo in the main lecture room where many of the founders of quantum mechanics are sitting in the first row. From my own point of view I am happy that another person who can be seen there is Max Delbrück, a shining example of a switch from physics to biology. My next visit to Copenhagen was for the conference which I wrote about in a previous post. It was at the University. Since that a lot has happened with chemical reaction network theory and with my understanding of it. The lecture course I gave means that some of the points I mentioned in my post at that time are things I have since come to understand in some depth. I look forward to working on projects in that area with people here in the coming days.

### Trip to the US

October 5, 2015

Last week I visited a few places in the US. My first stop was Morgantown, West Virginia where my host was Casian Pantea. There I had a lot of discussions with Casian and Carsten Conradi on chemical reaction network theory. This synergized well with the work I have recently been doing preparing a lecture course on that subject which I will be giving in the next semester. I gave a talk on MAPK and got some feedback on that. It rained a lot and there was not much opportunity to do anything except work. One day on the way to dinner while it was relatively dry I saw a Cardinal and I fortunately did have my binoculars with me. On Wednesday afternoon I travelled to New Brunswick and spent most of Thursday talking to Eduardo Sontag at Rutgers. It was a great pleasure to talk to an excellent mathematician who also knows a lot about immunology. He and I have a lot of common interests which is in part due to the fact that I was inspired by several of his papers during the time I was getting into mathematical biology. I also had the opportunity to meet Evgeni Nikolaev who told me a variety of interesting things. They concerned bifurcation theory in general, its applications to the kinds of biological models I am interested in and his successes in applying mathematical models to understanding concrete problems in biomedical research such as the processes taking place in tuberculosis. My personal dream is to see a real coming together of mathematics and immunology and that I have the chance to make a contribution to that process.

On Friday I flew to Chicago in order to attend an AMS sectional meeting. I had been in Chicago once before but that is many years ago now. I do remember being impressed by how much Lake Michigan looks like the sea, I suppose due to the structure of the waves. This impression was even stronger this time since there were strong winds whipping up the waves. Loyola University, the site of the meeting, is right beside the lake and it felt like home for me due to the combination of wind, waves and gulls. The majority of those were Ring-Billed Gulls which made it clear which side of the Atlantic I was on. There were also some Herring Gulls and although they might have been split from those on the other side of the Atlantic by the taxonomists I did not notice any difference. It was the first time I had been at an AMS sectional meeting and my impression was that the parallel sessions were very parallel, in other words in no danger of meeting. Most of the people in our session were people I knew from the conferences I attended in Charlotte and in Copenhagen although I did make a couple of new acquaintances, improving my coverage of the reaction network community.

In a previous post I mentioned Gheorghe Craciun’s ideas about giving the deficiency of a reaction network a geometric interpretation, following a talk of his in Copenhagen. Although I asked him questions about this on that occasion I did not completely understand the idea. Correspondingly my discussion of the point here in my blog was quite incomplete. Now I talked to him again and I believe I have finally got the point. Consider first a network with a single linkage class. The complexes of the network define points in the species space whose coordinates are the stoichiometric coefficients. The reactions define oriented segments joining the educt complex to the product complex of each reaction. The stoichiometric subspace is the vector space spanned by the differences of the complexes. It can also be considered as a translate of the affine subspace spanned by the complexes themselves. This makes it clear that its dimension $s$ is at most $n-1$, where $n$ is the number of complexes. The number $s$ is the rank of the stoichiometric matrix. The deficiency is $n-1-s$. At the same time $s\le m$. If there are several linkage classes then the whole space has dimension at most $n-l$, where $l$ is the number of linkage classes. The deficiency is $n-l-s$. If the spaces corresponding to the individual linkage classes have the maximal dimension allowed by the number of complexes in that class and these spaces are linearly independent then the deficiency is zero. Thus we see that the deficiency is the extent to which the complexes fail to be in general position. If the species and the number of complexes have been fixed then deficiency zero is seen to be a generic condition. On the other hand fixing the species and adding more complexes will destroy the deficiency zero condition since then we are in the case $n-l>m$ so that the possibility of general position is excluded. The advantage of having this geometric picture is that it can often be used to read off the deficiency directly from the network. It might also be used to aid in constructing networks with a desired deficiency.