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Information Theory/Informatics in Modeling Dynamic Systems - help wanted

  
 
break
21:52 / 15.11.08
I'm currently working on a project for a class that will eventually become a chapter in a masters thesis and later a dissertation wherein I am trying to incorporate differences in the rate of information travel relative to distance from the center of the system within as two different system types encroach one another. For those with a background in ecology, I'm specifically looking at the effect of a larger-scaled r-phase system (high-growth, constrained by internal-ability-to-transform-exergy-into-work/thermodynamics [eg. one that is all about getting more stuff]) on a smaller-scaled k-phase system (externally constrained by lack of resources or ability to move energy [information] around the system, behavior focuses on using what is around more efficiently) in terms of the overcoding of the rule set of the k-system by the r-system.

By scaling the systems differently I'm basically implying connectivity is topographically determined in the smaller one and topologically determined in the larger one. Distance still matters but it ceases to be spatially considered.

If information typically follows an exponential decay curve over distance, what is topographically distant can be topologically proximate. Therefore the quality of information of the larger system is able travel further before the decay sets in. (Think information capabilities over distance of local, isolated, marginal farmers circa 1800 versus 21st century information urbanites. The result of this (I argue) is that the internal codes of the more localized system can become overwritten by the code system of the larger system - particularly if the localized system is unfamiliar with this other rule set so has no internal defense against it.

In the hopes that this is (relatively) clear for people into this sort of thing, I'm trying to establish a set of equations for a dynamic model that would establish the relationship between the two systems in order to show at what difference between the two curves this overcoding is likely to occur. I know the equations will be logistic and I'm currently going through literature on information in ecosystems (see: Robert Ulanowicz). I also know that it's not simply a matter of one curve being above the other - there is an issue of degree here. That said, the last time I took a math class was over 10 years ago, and although I've been relearning maths as I've been fiddling with differential equations over the past few weeks, I would appreciate help from someone with a better handle on all this stuff than I have (I do theory - not equations).

So... any information theorists/theoretical mathematicians in the house? Have any equations up your sleeves? If needed, I can post some diagrams from a power point I'm working on as I try to figure this out if people want some sort of visual cues to what I'm thinking.
 
 
grant
15:15 / 17.11.08
Not I, but it sounds like a way to make some cool maps.
 
 
Closed for Business Time
17:40 / 17.11.08
Can you explain what the difference in meaning between topography and topology in the above is?

Also, if you haven't already, take a look at Kenneth Frank's work, especially his Kliquefinder program. And this paper, which is more theory than equations but nonetheless looks interesting.

###

I sincerely hope I am not talking out of my @$$ here.
 
 
break
00:15 / 18.11.08
By topography I mean physical space on a landscape. Topology is network space, so physical location doesn't necessarily factor in to distance. Latour's simple example is that someone on a phone is topologically closer to the person on the other end of the line than they are to the person in the phone booth next to them.

Significance of one doesn't mean the lack of the looming significance of the other, though. As Deleuze said, every deterritorialization (emergent topology) is followed by a reterritorialization (reintegration on the plane of immanence or something like that).

I'll take a look at the links you posted.
 
 
break
00:46 / 18.11.08
Thanks for the Ken Frank link. I wasn't aware of him (at least not consciously as a name to regularly refer to), but his work looks related. I've now gone through and downloaded a bunch of his articles. I'm not sure at the moment if I've read the other paper before, but Holling looms large in almost everything I do, even if it's not explicit. At some point in my work I'll pull his panarchy concept back in, although right now I'm actively avoiding it. That said, the article does remind me that I'm essentially talking about system resiliency and trying to model it within the context of information and connectivity. I'm taking a class with Carpenter next Spring.

In an effort to pull this away from just me and into a more general theoretical ecology discussion (not that I wouldn't appreciate further feedback on my question), I'll throw out these links to Robert Rosen and James Kay, two hugely significant ecologists for me. While I'm at it, here's Resillience Alliance.
 
 
Saturn's nod
03:14 / 18.11.08
Nice thread, break.

I'm mothering a baby who is under six months at the time of writing so my keyboard time is under severe restriction, and I give the highest priority to completing my own doctoral thesis before the axe falls. Please forgive my limited attention. Send me a pm if you'd like to initiate the kind of sporadic light email contact I'm capable of.

I guess my supervisory question to you would be, is there a specific advantage to doing this in the 'hard sums' fashion?

The only dynamic ecosystems modelling project I've coded, I used a pretty lightweight MCMC modelling approach and the output was a dynamic graph of the relevant dependent variables of each population through a java application, and I did some light descriptive statistics for each 10k summed runs with a particular set of initial conditions. I didn't pursue it to publication because I changed track, but I may be able to excavate the code and open source it if pressed. It might be even more naive than I remember!

That kind of approach is not hard to code, avoids hard sums, and in my opinion needs an exacting theoretical justification, which sounds like it might suit your learning style.

It depends what your intention is for the output - i.e., what publications might you be looking at?
 
 
break
04:24 / 19.11.08
Thanks for the ideas. To a certain extent, I'm not really sure how to parameterize my question to even go on from there. I have in my head graphs of information entropy for my two systems and how I envision they overlap, but I'm trying to figure out 1: how to establish relationships of dominance and 2: what the level of dominance needs to be for one structure to be abandoned or overcoded. I know it can't be a simple issue of one system has a higher connectivity to its center than the other does because there will be an issue of inertia in the system. There will have to be an amount of extra connection to serve as the activation energy for the flip.

For the second issue, I have an analogy in my head that consists of two light sources facing each other that cast shadows of an object between them:

` /` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `\
|(~O ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` O~)|
| \` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/`|
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `_` ` ` ` ` ` ` ` ` `|
|` ` ` ` ` ` ` `__| |__` ` ` ` ` ` ` ` |

(I did this little diagram and thought it was totally awesome and dorky, but when I looked at the preview it was all wonky. I tried to dewonkify it by bringing in the marks in the middle, but it's still pretty wonky.)

I envision that the difference in brightness between the two lights that is needed for there to only be one shadow is a rough equivalent to the extent of the difference in informational connectivity between the two systems at the point of their intersection for the one (in this case r-phase [eg. growth phase]) to overcode the other. I would then get readings with the object at different positions between the light sources to account for diffusion over distance.

The lights make sense to me because brightness and information are both considered logistically and they are in a sense variations on a theme. I just don't know at this point what those differences are in order to set parameters and I don't know at this point if this is an already-established relationship or not.

As far as the first point goes (relationship of dominance), a part of me sees it as an issue of the change in connection to the center multiplied by maximum connection to the center divided by the distance. There will be a log base (???) in there, either on the full expression or else just on the numerator, I'm not really sure. The log should probably be negative, too, since the rate of change will be negative and information entropy has a negative log. If this sounds like crap it very well could be since I last took calculus over 10 years ago and I was 18 and didn't care at all at the time.

As to why the approach I'm taking, in part it's due to the nature of the class and the discourse I'm somewhat trying to engage in. I'm doing all of this on STELLA at the moment, a fairly easy to work with GUI based modeling software. It's all stock and flow stuff, and although I know there are ways to incorporate stochastic parameters and other elements of probability into it, I don't actually know enough about those to have tried them yet. On the other hand, I know that this (or any) modeling approach is not sufficient for the full extent of what I'm looking at. At this point, though, I've developed a model of my two systems for themselves (one is simple exponential growth, the other incorporates resource depletion, increased extraction to make up for depletion, and feedbacks that limit that increase based on changing use and death rates). Now I need to figure out how to integrate them so the one can disturb the other in the hope that I can get a bifuraction or, better yet, get it to go chaotic to symbolize an approaching regime shift.

Ultimately, too, this will become a chapter in my thesis and eventual dissertation, for which I'm planning on writing a really awesome book (doesn't everyone...). The rest of my work will not be much in this direction (it's going to be all poststructural and crap), making for a fairly bipolar piece of work. I don't expect any of my code to be pretty (before this I haven't done any coding since my days playing with BASIC on an Apple IIe, although I recently got the Odum's modeling book and they use BASIC so there might be some life left in that language for me) - I'm just tooling with equations until I get the graph output I want. Justifications come later. My work is principally theory, I'm just using modeling as a means of creating justifications or quantifications for the larger issues I'm talking about. As far as any potential publications, Eco Complexity perhaps. I haven't though about it to that point yet. My thesis is the first target. After that it's just tweaking.

Anyway...

For those still reading this, I thought I should say a few words about the links I posted previously instead of simply posting them. James Kay was a theoretical ecologist that did really cool work incorporating the second law of thermodynamics (entropy) into an explanation of ecosystem development. Key papers are "Life as a Manifestation of the Second Law of Thermodynamics" and "Ecosystems as Self-organizing Holarchic Open Systems," both of which (and many more) are on his posthumous website. Robert Rosen was a theoretical biologist and complex systems theorist whose work might best be approached through his book _Essays on Life Itself_. The website has some of his work, and his daughter says she intends on posting all his work for free at some point. Resilience Alliance is a group of researchers on complex adaptive systems that is the current stomping grounds of CS (Buzz) Holling, an amazing ecologist who is largely responsible for the examination of resilience in systems and moving ecology away from a study of static systems. Lots of cool stuff.
 
 
Saturn's nod
21:46 / 23.11.08
I guess my point was that equations can be the hard way to describe the way a population behaves. The kind of object orientated programming approaches I chose allow the behaviour of populations using a particular set of rules to be simulated on an 'agent-centred' basis, and that's pretty easy. Then whichever descriptive stats are of interest may be extracted from the populations for perusal, after sufficient numbers of trials have been conducted to explore a justifiable section of the probability space.
 
 
Lurid Archive
23:54 / 23.11.08
As a pretty mathsy person (though not of the kind that would be very useful to you) its not clear to me what purpose the model you want to construct would serve. Since you say,

I'm just tooling with equations until I get the graph output I want. Justifications come later.

I can't help feeling that it would be easier to cut out the middle man and just explain what your ideas are without the sums. Fine tuning models until they give you what you always wanted is unconvincing to scientists and overly technical for non-scientists.
 
 
Saturn's nod
10:48 / 24.11.08
Word, Lurid. Yeah. Ptolemaic orbits are a good example, if I'm remembering correctly.

Ptolemy got the planetary orbits by using a load of fixes; once Copernicus pointed out the error in the middle of the model, the solutions were very much simpler, and became powerful *because they were describing motion close to the motion caused by the underlying laws* rather than because the equations were fixed up to match the observation.
 
 
break
21:37 / 24.11.08
Oh, sure. Totally. But to an extent this is a problem of dynamic modeling as a whole. The big atmospheric ones are in their way fundamentally Ptolemic: write, run, correlate, repeat with additional variables, etc. That doesn't mean, though, that inductive processes don't have a role to play. Any model of a system will be wrong, but there is the issue of how well it can predict relevant questions. If I recall, the Ptolemic model is still the one used for launching rockets even if it is less descriptively valid than Copernicus's model. For my part, I'm just trying to figure out a relation that I can use to create disturbances on a different model I've already constructed and which behaves as intended with fairly simple and justifiable mathematical relationships.

But, yeah, hard sums isn't really my bag but I need to include a certain level of quantitative work to buttress my overwhelmingly qualitative work. To a certain extent I know that sums /can't/ be used for all that I'm interested, but I'm trying to manifest behaviors to show how certain types or extents of a disturbance (in this case informational) can be accommodated by the system versus causing a collapse and reconfiguration. The reconfiguration can't be modeled, but the precipitation of collapse versus accommodation can be.

Also, as far as this approach versus oop or something else entirely, part of it is because as a non programmer its what I know more about (to the extent that I do). Plus I'm trying to situate this within an ecological energetics paradigm that doesn't /necessarily/ have to do with populations of things, although that's the example I've been using. I'm rather agnostic about all of this, but that's what I'm in at the moment.
 
 
Lurid Archive
11:39 / 25.11.08
I am certain that Ptolemic models are not used to launch rockets - I think it is mostly Newtonian physics, but there may also be some relativistic calculations for extra precision.

Also, I don't want to be overly critical of what you are doing but when I read this:

I need to include a certain level of quantitative work to buttress my overwhelmingly qualitative work.

I can't help feel that you would do well to question *why* the qualitative works needs buttressing with sums. Surely you don't want to fall into the trap of using technical language solely as a way to impress. And yet your modelling isn't - or doesn't seem to be - for anything but a formal descriptive framework. Qualitative work is often more appropriate than a quantitative analysis - you shouldn't do it down.
 
  
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