Frequent readers of the blog will already know that I have just completed the first draft of an ambitions paper to define many features of system dynamics: tipping points, robustness, path dependence, and the many, many concepts related to these. One concept related to robustness considerations is sustainability. In my typography ‘sustainability’ refers to a system’s ability to keep its dynamics within a particular set of states (leaving and coming back doesn't count). Sets are collected together into a set because they all share some property (which could be a property of the dynamics or a property within the system’s parameters). The methodology itself is agnostic about what generates the sustainable dynamics, it just measures the sustainability based on revealed behavior. The reason to do that, however, is not because the generating mechanisms aren't important, but to foster the research to isolate exactly those features which do, in fact, generate sustainable operation.

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Many complex systems are homeostatic (aka autopoietic aka self-maintaining). Such systems are, by their nature, resistant to change because they contain mechanisms to return system dynamics to a particular pattern. However it is not the case that such systems only have one possible self-maintaining pattern. If a homeostatic system receives a large enough perturbation then the system may settle to a different pattern. We would expect that as a homeostatic system experiences a series of shocks it would spend a much greater amount of time in each homeostatic pattern compared to the transition time between patterns. That is precisely the phenomena called punctuated equilibria.

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Physicists have been struggling for nearly a century to bend and twist the so-called “standard model” to include room for gravitational force (and presumably a particle to carry it), but so far to no avail. The recent failures of string theory have left another candidate in the ditch. Electric and magnetic forces have been unified, and they in turn were unified with the strong and weak nuclear forces…why is quantum gravity so hard? Perhaps because it is not a force like the others. Perhaps gravitation is only a property of the dynamics of aggregates for which there is no micro-level phenomenon corresponding to it. Perhaps gravitational behavior emerges from the forces acting at the micro-level instead of being one itself.

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In my upcoming paper on how to measure tipping points, robustness, and path dependence I plan to provide examples in the form of illustrations. Since the technique uses Markov modeling to measures these properties of system dynamics my illustrations are (not surprisingly) going to be Markov diagrams that provide examples of the definitions and applications of the algorithms. Eventually I will create software in Java to run these analyses and these will produce a visual output; so one option is to build that software now and use screenshot for my diagrams. The problem is that it is quite hard to get java to output exactly what I want and have it look the way I want it. My answer came in the form of Mathematica 6.

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It occurs to me that since the body has natural mechanisms to deal with cancerous cells, and since we only find cancers (in people) when they are large and intrusive, research into preventative measures for cancer is missing data on the features of those cancers that the body can fight. That information could be very helpful if we could impinge those features of cancers that our body can deal with on those cancers that we can’t yet deal with. That is, it might be easier to trick faulty cells of ours to act like other faulty cells of ours (that can be dealt with by our immune response) than to attack the cancer with external and alien means. The hard question of course is how to find cancerous cells that the body is already successfully battling since they don’t produce symptoms and won’t last long.

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This post represents a small philosophical excursion from the measures of robustness research program I am working on. That research program constructs Markov models of systems from data and analyzes them so find the system’s tipping points and further uses those points (and other features) to measure robustness-related properties (including sustainability, resistance, recoverability, stability, and being static; as well as their counterparts: susceptibility, vulnerability, fragility, and collapsibility. While working on the formal definitions of those concepts I realized that these are all dispositional properties and dispositional properties are philosophically interesting and troublesome. That connection immediately made me wonder if my mathematical formalism might shed some new light on how to differential dispositional properties form categorical ones; some first thoughts on that are below.

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A recent study published in PLoS Biology reveals that so-called "identical" (monozygotic) twins are not completely genetically identical. Visible differences in phenotype (such as height, freckles, etc.) have hinted to differences, so have difference in disease susceptibility, but researchers couldn't eliminate purely environmental factors as the cause. This recent work definitively shows that there are genetic differences, specifically with the number of copies of genes. Because the twins start from the same cell, they must have started genetically identical. So something in the environment during development must explain the deviation in the genes. A person's genes change over time. That's supposed to be a radical idea, but perhaps because I am not deeply steeped in the dogma of this research field for me this is pretty obvious. It's quite easy to hypothesize several plausible mechanisms through which this happens and that's what I'll do here.

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While eating some freeze-dried peas and corn I wondered how the nutritional content had changed compared to raw or boiled peas and corn. That opened the door to the whole gamut of considerations of how different ways to age, cut, process, cook, and mix foods affects their chemistry and thus their nutritional value. Complications are further exacerbated by the dynamics of food digestion, activity levels, body chemistry, and metabolism. Even the order, amount, and time in between eating two foods have a tremendous affect on how the body will absorb nutrients from them. The science of food chemistry and nutritional assessment is clearly a complex system akin to gene regulatory networks and should therefore be analyzed as such.

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One virtue of the differential equation method of system dynamics is that if one wants to know the system state at some point in the future one can often just plug in the appropriate t value and get the system state at that time (given the specified starting conditions). Not always. In some applications (such as for chaos theory) the system must be iterated step by step and there is no way to just “skip ahead” to a particular time. Agent-based models have this property too. One specifies the initial conditions and then to find out what will happen at some arbitrary time in the future one must actually run the simulation through all the intermediate steps. What a pain! The situation is not hopeless, however – there might be some shortcuts we can exploit and I’ve got a few ideas.

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The tipping points technique under development by yours truly (see here then here) is intended to be something akin to a statistical technique the following sense: it uses data from a system (real or modeled), determines which model of a different kind (Markov) would also generate the observed data, and then conveys information about the imputed model not directly ascertainable from the data. And so like descriptions of statistical modeling techniques I need to provide a description of how to generate the Markov model from the original data and the properties/caveats of doing it in different ways.

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