Category Archives: human genetics and system modelling

Addressing COVID19 gaps between data, models and decision brings us back to hierarchical PID control, folks!

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I’d like to comment about the way how careful we should be when we use data (even if it’s accurate at the source and at its processing steps!), when we build models to extract some dependencies between elements of the data, and ultimately when we make decisions.

Long time ago (approx. 40 years), when my father took over as head of control engineering department in St. Petersburg electrical engineering institute (LETI) from the previous head, Professor Alexander Vavilov, at their school they were excited by exploring the idea of evolutionary synthesis of control systems. One crucial part of this study was the development of theory of structural synthesis, where models of the system at each level of granularity had to be adequate to the criteria of optimal control. (By the way, graphs were essential in those models)

The basic idea was that depending on the level of granularity (or hierarchy) considered by the modeller, the system can have completely different criteria of correctness and/or optimality, hence certain aspects that are significant at small scale may not be important at a larger scale.
A bit like the criteria of control in the national level is not the same as criteria for control at the municipal level, and not the same at the level of local community, and not the same at the level of family units and individual households.
So, because of these differences and clashes of interest between different levels there is a lot of anxiety and misunderstanding in societies.

So, what the relationship with COVID-19?

Well the relationship is direct.

Let’s take the data on Mortality 2017 from the UK National Statistics: https://www.ons.gov.uk/visualisations/dvc509/chart1/index.html

This data shows that the number of deaths across the country in one year is significant – hundreds of thousands – not far from 1M. The relative number of deaths, that we witness now as a result of COVID-19 even if it will hit 10K-20K would be quite small though.

So, we clearly have different perspectives here, one is national (spatial) that stretches across the whole year (temporal), while the other could be local (e.g. an area of population in London) and taken during these 2-3 weeks of March-April. The relative increase in the number of deaths at the national scale is a small bump on the curve. I.e., integrating the number of deaths, caused by respiratory problems thanks to COVID-19, at the national scale will not give much effect to the game of the totals.

However, if we look spatiotemporally at the small scale we may see a significant rise in terms of differential and even proportional response. So, if we are particularly sensitive to these two aspects, differential and proportional, we may actually decide to react with a powerful action.

What we are facing here is exactly what I started with in my blog. We are facing with the different levels of granularity (or hierarchy, whatever we call it). Consider the coarse granularity. From this point of view our Mother Nature in us may say, well, why bother, the integral response (let’s denote it by letter I) is very small, and we look at time intervals of decades, so there is no need for any great change in decision-making. The problems of environmental nature are much more serious.

But let’s go down to the level of individuals, especially those living in the most affected areas of COVID-19. Again, our Mother Nature in us would tell us, that the rise in deaths due to coronavirus is an alarm, it may trigger a disaster, we may lose the loved ones, lose a job and income. What’s happening here? It’s actually that at the lower granularity level, the criteria for decision-making are based on differential and proportional responses (let’s denote them D and P). So, in mathematical terms at different levels of granularity we apply different coefficients, or what engineers call gains, to these aspects P, I and D, and form our decisions according to those gains or criteria of importance.

So, ultimately it is vital that the data we use, and the models which characterise this data in time and in space, where we calculate partial or full derivatives and integrate in space and time, or proportionalise in space and time, must be adequate to the criteria of significance we apply, and lead to corresponding decision-making at the appropriate level.

No doubt, the nations that are harmoniously hierarchical and fractally uniform, may have less problems in matching criteria of optimality with the P, I and D responses brought be the models from the actual data.

Yet, again we face that PID-control seems to rule the world we live in!

The answer to why women are more robust to COVID-19 than men may lie in the dynamics of women’s gene pool

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Today, people are asking why women are less affected by COVID-19 and have significantly lower death rate than men (in Italy, for example: more than 60% of infected are males and more than 70% of death cases are of male).

While there are hypotheses that this is caused by various societal and life style factors and norms, such as ‘because more men are smokers’ etc., I would like to examine potential genetic causes of that.

Men carry both X and Y chromosomes. Women carry only X chromosomes.

As I wrote a couple of years ago on my blog about the differences of dynamics between X and Y chromosomes (see links to my two articles below), I made a hypothesis that women’s chromosome pool is significantly more dynamic and mutable than men’s. The Y part of men’s genes don’t mutate. They carry Y-DNA through generations unchanged. Thus women naturally bring greater adaptability and robustness to environmental conditions than men. Contrary to that men bring certain long-term elements and inertiality, which is also important for stable societies.

Importantly, perhaps, I also showed an analogy between the combined process of gene evolution in humans and other species, thanks to the presence of both males and females) and PID (Proportional-Integral-Differential) control that is proven to be the most successful type of control in engineering systems.

So, the nature’s own PID control (where the role of P and D is greater than that of I for the purposes of quick response to effects such as viruses) makes sure that only a relatively smaller number of males compared to the number of females are needed to maintain the human kind.

So, as usual, Mother Nature and genetics are the winners in this almost game-theoretic scenario of our battle against coronavirus.

On Relationship between X and Y chromosome evolution and PID control
On the dynamics of evolution of Y and X chromosomes

Potential rise of interest in STEM subjects in society

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I predict that during and following this period of COVID pandemics, we will witness a significant rise in of interest and some kind of renaissance of mathematics and other STEM subjects. You might ask, why?

Well, let’s look back into history. The development of many mathematical ideas and forms such as mathematical series like geometric series, Fibonacci series, theory of probability etc. were the result of people observing various processes in time or frequency domains during those epidemics like plague, cholera and so on, that took place in the past centuries.

Now, you can see how many smart people are doing home schooling and teach their kids to look at the geometric series and exponential and power laws of the proliferation of virus. A 7-8 year ol kid can have a good grasp of the series based models because he or she could witness its manifestation (sadly, but) in vivo.

So, being an academic in Engineering and curious in anything natural, I hope there will be more students doing Maths, Sciences and Engineering after that ….

On “Свой – Чужой” (Friend – Foe) paradigm and can we do as good as Nature?

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I recently discovered that there is no accurate linguistic translation of the words “Свой” and “Чужой” from Russian to English. A purely semantical translation of “Свой” as “Friend” and  “Чужой” as “Foe” will only be correct in this particular paired context of “Свой – Чужой” as “Friend – Foe”, which sometimes delivers the same idea as “Us – Them”. I am sure there are many idioms that are also translated as the “whole dish” rather than by ingredients.

Anyway, I am not going to discuss here linguistic deficiencies of languages.

I’d rather talk about the concept or paradigm of “Свой – Чужой”, or equally “Friend – Foe”, that we can observe in Nature as a way of enabling living organisms to survive as species through many generations. WHY, for example, one particular species does not produce off-spring as a result of mating with another species? I am sure geneticists would have some “unquestionable’’ answers to this question. But, probably those answers will either be too trivial that they wouldn’t trigger any further interesting technological ideas, or too involved that they’d require studying this subject at length before seeing any connections with non-genetic engineering.  Can we hypothesize about this “Big WHY” by looking at the analogies in technology?

Of course another question crops up as why that particular WHY is interesting and maybe of some use to us engineers.

Well, one particular form of usefulness can be in trying to imitate this “Friend – Foe” paradigm in information processing systems to make them more secure. Basically, what we want to achieve is that if a particular activity has a certain “unique stamp of a kind’’ it can only interact safely and produce meaningful results with another activity of the same kind. As activities or their products lead to other activities we can think of some form of inheritance of the kind, as well as evolution in the form of creating a new kind with another “unique stamp of that kind”.

Look at this process as the physical process driven by energy. Energy enables the production of the offspring actions/data from the actions/data of the similar kind (Friends leading to Friends) or of the new kind, which is again protected from intrusion by the actions/data of others or Foes.

My conjecture is that the DNA mechanisms in Nature underpin this “Friend – Foe” paradigm by applying unique identifiers or DNA keys. In the world of information systems we generate keys (by prime generators and filters to separate them from the already used primes) and use encryption mechanisms. I guess that the future of electronic trading, if we want it to be survivable, is in making available energy flows generate masses of such unique keys and stamp our actions/data in their propagation.

Blockchains are probably already using this “Свой – Чужой” paradigm, do they? I am curious how mother Nature manages to generate these new DNA keys and not run out of energy. Probably there is a hidden reuse there? There should be balance between complexity and productivity somewhere.

On Relationship between X and Y chromosome evolution and PID control

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First of all, I would like you to read my previous post on the graphical interpretation of the mechanisms of evolution of X and Y chromosomes.

These mechanisms clearly demonstrate the greater changeability of the X pool (in females) than the Y pool  (present only in males) – simply due to the fact that X chromosomes in females merge and branch (called fan in and fan out).

The next, in my opinion, interesting observation is drawn from the notions of mathematical analysis and dynamical systems theory. Here we have ideas of proportionality, integration, differentiation, on one hand, and notions of combinationality and sequentiality on the other.

If we look at the way how X-chromosomes evolve with fan-in mergers, we clearly see the features akin to proportionality and differentiality. The outgoing X pools are sensitive to the incoming X pools and their combinations. Any mixing node in this graph shows high sensitivity to inputs.

Contrary to that, the way of evolution of Y-chromosomes with NO fan-in contributions, clearly shows the elements of integration and sequentiality, or inertia, i.e. the preservation of the long term features.

So, the conclusions that can be drawn from this analysis are:

  1. Males tend to bring the integral or sequential (cf. sequential circuits in digital systems – with longer term memory) aspect to the overall process of evolution
  2. Females tend to bring the proportional/differential or combinatorial (cf. combinational circuits – with shorter term memory)
  3. The presence of both male and female genetics are essential for stability of the evolution and survival of the kind, much like the PID feedback control helps stability of dynamical systems, and much like the combination of combination and sequential circuits allow computer systems to operate according to their programs.

Again, I would be grateful for any comments and observations!

PS. By looking at the way how our society is now governed (cf. female or male presidents and prime ministers), you might think whether we are subject to differentiality/combinatorics or integrality/sequentiality and hence whether we are stable as a dynamical system or systems (in different countries).

Happy Days!

 

 

 

 

 

On the dynamics of evolution of Y and X chromosomes

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It is a known fact that men inherit both Y and X chromosomes while women only X chromosomes.

As a corollary of that fact we also know that Y-chromosomes, sometimes synonymized with Y-DNA, are only inherited by the male part of the human race. This means that Y-chromosome inheritance mechanism is only forward-branching, i.e. Y-DNA is passed from one generation to the next generation “nearly” unchanged. As I am not an expert in genetics I cannot state precisely, in quantitative terms, what this “nearly” is worth. Suppose this “nearly” is close to 100% for simplicity.

Below is a diagram which illustrates my understanding of the mechanism of inheritance of Y-chromosomes.

This diagram is basically a branching tree, showing the pathways of the Y-DNA from one generation to the future generations of males. The characteristic feature of this inheritance mechanism is that it is Fan-out only. Namely, there is no way that the Y-DNA can be obtained by merging different Y-DNAs because we have no Fan-in mechanism.

Let’s now consider the mechanism of inheritance and evolution of X-chromosomes.The way how I see this mechanism is shown in the following diagram.

X-chromosomes are inherited by both males and females. But, as I understand, this happens in two different ways.

Each female takes a portion of X chromosomes from her father (let’s denote it as X1) and a portion of X chromosomes from her mother (denoted by X2), thereby producing its own set of chromosomes X2’ which is a function of X1 and X2. Similar inheritance is in the next generation where X2’’=f(X1’,X2’).

Each male, however, only inherits X chromosomes from his mother, as shown above, where X1’’=f(X2’).

At each generation, when the offspring produced has a female, there is a merge of X chromosomes from both parents. This means that the pool of X chromosomes as we go down the generations is constantly changed and renewed with new DNA from different incoming branches.

This mechanism is therefore both Fan-in and Fan-out. And this is not a tree but a directed acyclic graph.

What sort of conclusion can we draw from this analysis? Well, I draw many interesting (to me at least) conclusions associated with the dynamics of evolution of the genetic pool of males and females. One can clearly see that the dynamics of genesis of females is much higher than that of males. Basically, one half of a male’s genesis remains “nearly” (please note my earlier remark about “nearly”) unchanged, and only the other half is subject to mutation, whereas in females both halves are changed.

I can only guess that Y-chromosomes are probably affected by various factors such as geographical movements, difference in environment, deceases etc., but these mutations are nowhere near as powerful as the mergers in the X-pool.

In my next memo I will write about the relationship between the above mechanisms of evolution and PID (proportional-integrative-differential) control in dynamical systems, which will lead to some conjectures about the feedback control mechanisms in evolution of species.

I would be grateful if those whose knowledge of human genetics is credible enough could report to me of any errors in my interpretation of these mechanisms.