Words from a past few days of thinking.

This is a cloud of what I have written in the past few days for a possible project I may be involved in. It’s interesting to somewhat statistically understand what my brain spews on paper. It can show if I am interested in something or I am just forcing myself to think about things. The latter can suggest I better not work on the thing. It becomes clear somehow when you see a word that is massive and that may just not be something you like to think about, but you have written. Hmmm…

Imagine a blob of plasticine of some colour. Mould it into whatever shape you like and it still is a blob of plasticine of the same colour, just a different shape. Put this plasticine on a plate and play with it. With a leap of imagination, consider this plasticine blob as a protein! Some proteins can be very flexible, and they are a literal chain of chemicals folded into a blob, thus the analogy with a plasticine blob.

Some of the proteins I am playing with these days are distributed in the kinds of shapes they can take as shown in the figure below. Proteins are very small, so instead of the naked eye observing the shape, as can indeed be done with a plasticine blob, some tricks become necessary. One of these tricks is understanding the shapes by shining X rays in a certain way on these tiny blobs. When X rays pass through them (let’s imagine the plasticine blob to be translucent for this purpose), they scatter, and we let them scatter on a plate, and then observe the scattered light. The nature of this scattering of light (more intense at some parts on the plate and less at others), tells us something about the shape of the tiny blob.

In the figure below are shown such observations. The shapes can be distinguished more in the middle region of the figure, which can be considered as the area on the plate where the X rays scatter at a certain angle, as denoted in the figure. This angle at the left extreme is zero. This left extreme in the graph is associated with the scattered light being observed at the centre of the plate – imagine a ray of light passing through the blob of  plasticine, going straight through and hitting a place on the other side of the blob at the centre of a plate. As we go right on the graph along the scattering angle axis, it simply suggests the observation being made further away from the centre of the plate.

Shape distribution detail.

These are shape shifting proteins. The same protein can take many different shapes, which in this case is 1000. For the left extreme, the figure shows a ribbon like thing that connects the 1000 shapes. This is just to show how the observed light varies with the protein when observed at that angle on the plate. Not a lot I would say, as compared to ribbons as we go right. As an analogy, we can see this as how jittered the ribbon would look if placed on top of 1000 plasticine blobs on, say, the left extreme side of these blobs, when the blobs are put one next to the other in a straight line. Since the blobs are different, they may have weird protrusions and intrusions and what not that an imaginative mind can mould them into. Apparently, the left most side has little imagination going for it. However, there is a lot of imagination going on as we go right and place another ribbon on top of all the blobs (see how ruffled up it is!). These ribbons continue to be ruffled up until, at some point along the blobs, the imagination runs out again!

In the next few weeks, I am not going to be more imaginative with moulding the blobs, but will surely do something with them.

November 7, 2010:

Just to go a little deeper into the manner in which the blobs vary when X rays pass through them and the intensities observed at various distance from the centre of the plate, we get the following figure:

Distribution at various scattering angles.

The right most bell shaped curve corresponds to the distribution of light at the centre of the plate (0.0 scattering angle) as it passes through all the 1000 blobs. The bars that the curve tries to approximately cover or fit, correspond to the number of blobs resulting in an intensity of the passed light to be in the region specified by the width of each bar. The bars in the middle are higher than the bars on the ends of the bell shape, suggesting that more blobs let X rays pass through and hit the plate with intensities within the regions specified by the width of the bars (an idea of this region can be had by looking at the bottom axis). Similarly, other bell shaped curves correspond to the distribution of light passing through the 1000 blobs at various distances from the centre of the plate (left most curve – 0.09 scattering angle – being the farthest).

The bells corresponding to the scattering angles 0.02 and 0.03 are much wider than the others. These correspond to the ribbons in the middle of the earlier figure for these scattering angles. The ribbons are more ruffled up accordingly.

November 22, 2010:

Of all the shapes above, let us take a subset of shapes together, assuming it to be a subset of shapes our protein can be in, and that it cannot be in any other shape outside of this subset. This means our actual protein may not actually be able to take up all the shapes described above, but instead shift into only the shapes within the subset. In reality, this is what a shapeshifting protein does. It can only shift into certain shapes out of the many shapes possible. This is the ensemble of shapes that characterise a shapeshifting protein. But there is yet another game that this shapeshifting protein plays. It does not tell us which exactly which shapes it can shift into. How deceptive eih? Well, it does what it does in accordance with nature. But, it is important for medicine research to understand what shapes it can take it seems. We thus need to discover these shapes. How?

The following figure depicts an ensemble of shapes with a few more details which I will talk about soon. For now, the size of the ensemble is N. K is the number of scattering angles at which the measurement of the scattered light was carried out. Each bar in the figure is just a pictorial representation of these K measurements for each shape in the ensemble. The horizontal bar is a pictorial representation of the fact that we need to do something with the values that it hides behind it i.e. it shows the values of all the shapes in the ensemble for one of the K scattering angle measurements. We are eventually going to take an average of these values and do something with this average.

Ensemble of shapes.

November 23, 2010:

What is it that we want to do with shapeshifting proteins?

As mentioned above, we want to discover the ensemble of shapes a shapeshifting protein can mould itself into.

Today I have had the first encouraging experiment with this identification process, or so it seems right now.

Following figures show what I want, and what I achieve. If the red bars in both the figures were to match perfectly, that would mean the discovery of the shapes to be perfect! Of course, there is work to be done as this is not the case. But, the red bars in the two figures are not that far apart, hence it is all encouraging.

Target to achieve.

Discovered ensemble of shapes.

I always view a motorist as being on some sort of a pareto frontier, as compared to other motorists, when the competition is sequential i.e. points accumulate over time with every race. What can decide the optimal point assignment mechanism e.g. who receives how many points given their rank in a particular race? How will this relate to the ranking in the next race and thus the points given then? These are interesting questions to ask, but very hard to answer.

The aforementioned paper is very interesting as it tries to frame the question and answer it using the idea of ‘the race being a voting mechanism’ that ranks motorists. What is the optimal voting scheme then?

What does this say to you?

I happen to have bumped into this topic, by accident or by luck, as it happens, and have a very unstable relationship with it. The notion is the most plausible explanation of goal seeking behaviour of humans that I can relate to. This does not mean however, that I can use the ideas expressed in the economics and psychology literature, which are boundedly mature, to serve my current needs as an explorer of computational methods. Well, it actually does, because, for some reason, I cannot be asked to be more informed from those two disciplines. The reason, for some reason, is possibly a form of cost in terms of energy that I somehow already feel to be reducing my normal functioning as this accidental explorer, thus helping me sustain or give a feeling thereof.

So, for now, I am quantifying bounded rationality the simplest way I can and understand the evolutionary alchemy it results in, in simulation.

So, let’s carry on with this energy alchemy, and I will let you know what I find out, as I find out…

(1) It gives me a high. Why wouldn’t it? I solve a problem when I pick a route to move up on. And, after all, we are all curious problem solvers.

(2) It makes me live in the moment, thus encouraging me to DO stuff as opposed to THINK more than I can afford to.

(3) Every climb involves two essential ingredients of being human: beating an opponent while at the same time realising that the opponent helped beat them in the process by providing you with the holds to move up. Essentially, the opponent is not so much of an opponent, but more of a teacher. You are not a brutal killing machine, but a learner. Every grade beyond your level teaches you something whereas everything below has learnt to be what it is and so was there to teach you when you were below it. Eat your cake and have it too!

(4) It makes me be part of a team. Without being in a team, neither I, nor you, can do much! Just practicing this is rewarding!

In general, people feel worthless all the time in India (truth). Diamonds for some brought hope for happiness of the sort that we should not aim for (buying help). Given the only recourse to it however (why?), people do not have the choice, or so it seems!

They run after the diamonds, they cut them, and they give them to traders (and the traders pass it on to the niche) for money. They feel valued. They do not do it because they like it. They do it out of necessity. However, the sad part is that their necessities are valued in terms of money, and money alone. In other words, they find a way to be helped by someone else, accumulating this help over time so that they can use it when they are helpless, which is always (why?). In general however, help that is of value ‘now’ may or may not be of value ‘later’. People somehow forget about other issues that are important to create value and concentrate on one: money. They find a way to make money, not a way to solve a problem. 

Let’s kill the niche now. 

There are diamonds and there are people feeling worthless. They run after the diamonds, they cut them, and they give them to traders (and the traders pass it on to the niche) for money. Oh, there is no niche. Oh, there is no money. Oh, people are still feeling worthless. They lose value/energy and kill themselves. Why?

Conclusion: Niche dead, people dead.

Conclusion from conclusion: Change the niche (and not like this) or change the way people think.

Questions:

1. Why do people feel worthless and find it ok for money to solve it?

2. Why do people don’t still get the diamonds to cut?

In other words,

1. Why are people made to feel worthy when they have money?

2. Why are people not made to feel worthy when they work to do the stuff which leads to the trade?

Main conclusion/questions:

1. Why is there a focus on ‘goals’ and not the ‘effort’?

2. How can this be switched/transformed?

I call this post ‘distracted dreamcatcher’ because I got distracted by this news, while I was trying to catch a dream (literally) i.e. an idea I had while asleep and which felt worthy of experimenting with/thinking about, but woke up from it somewhere near the end. Bet the only thing these people which are killing themselves dream about is money. Why don’t they dream of other stuff? Why?

Yesterday, I happened to have the pleasure of sitting through a seminar which essentially deals with the question ‘How do roots (plant roots) deal with cooperative and cheating (free riding i.e. taking in the nutrients from the roots without giving anything in return) organisms that surround them?’. Toby Kiers, was the speaker, and she had a few answers, albiet, incomplete.

The way she tries to answer the question is by forcing organisms to cheat and see how the roots react. Do the roots have a punishment mechanism in place which the cheaters cannot dodge. If so, why are there cheaters in the first place? Is the punishment mechanism not good enough? She shows that the roots do indeed have a mechanism whereby they cut off supply (sanction) of neutrients, if they discover they are being cheated upon. She does not tell why roots cannot distinguish between cheaters and cooperators perfectly. On the other hand, there seems to be an evolutionary stable state with the host, cooperators and cheaters, all co-existing.

This kind of raises a question in my head. Are cheaters necessary for the mutualism or co-existence within this root subsystem to survive? Are cheaters necessary for the host to ‘not forget’ what cheating is? Possibly.

The stuff that worried me at a later point during the talk was they she is planning on applying her cheating/cooperation enforcement technique in agriculture by making cooperators bountiful near roots, in the special case of soyabean farming (read, big soyabean business in order). Will this disturb the evolutionary stability of the mutualism, thus changing the actors (roots, cooperators, cheaters, and other unknown variables) in time, making cheaters harder to deal with on the fields? Or, end of soyabeans in a few thousand (or more, but who cares right?) years? I suppose the mechanism that roots use to punish should be further studied for its ‘malleability with respect to time’?

NB: I may have misunderstood the work, so apologies to the speaker if that is the case. Someone correct me if I am wrong.

What interacts with what and how the interaction changes the effective magnetic fields, affecting the way one should behave so as to achieve a ‘certain goal’ of standing up straight on the magnet, given every other piece of iron wanting to do it as well, are obvious situations that one comes across and will think about. Does not matter how you do it, as long as you keep all the pieces erect.

Couldn’t this be a little method of teaching kids what cooperation and conflict is all about and where knowledge nicely fits in to make cooperation (and simulated conflict as an instance of cooperation) the key to standing up straight and doing what one wants. Possibly, IMHO!

I so want to work on it too, if only…