[FRIAM] (no subject)

[jon zingale]

EricS,

Thank you for the kind and thoughtful response. Your 'three levels'
project is interesting to me and reminds me (even if only tangentially)
of an analysis I worked on regarding food webs, n-species Lotka-Volterra,
and ABMs. I wanted to clarify for myself what each level of analysis
offered or bracketed relative to one another. There:

1. Food webs were analyzed as weighted graphs with the obvious Markov
chain interpretation[ρ]. Each edge effectively summarizing the complex
predator-prey interactions found at level 2, but without the plethora
of ODEs to solve.

2. N-species Lotka-Volterra, while being a jumble of equations, offered
dynamics. Here, one could get insight into how the static edge values
of level 1 were in fact fluctuating values in n-dimensional phase
space. But still, one is working with an aggregate model where species
is summarized wholly by population count.

3. ABMs, in theory, ought to be the whole story of individuals located
in space and time. There the agents (a lynx, say) 'decides' what to eat
based, perhaps, on what is most readily available. But as everyone on
the list knows, analysis at such a fine-grained scale is simply a mess.

I never did get as far with the analysis as I would have liked, and I
never got the chance to share my findings, so yeah, thanks for the
tangential opportunity, here and now, to say just this much.

1'. "site-rewrite rules in Walter Fontana’s site-graph abstractions"

Fleshing out some of your references, I found this Fontana paper[σ].
As you suggest, the style is fairly straightforward category theory.
Site-graphs and their morphisms form a well-defined category and a
number of universal constructions (push-outs, pullbacks, cospans,...)
are used to analyze the algebra and to establish its logic.

2'. "There is still an algebra of operation of reactions, but it is
simpler than the algebra of rules, and mostly about counting."

I am not entirely sure that I follow the distinction. Am I far off in
seeing an analogy here to the differences found between my one and two
above? I would love to have a facility with stochastic techniques like
these, but I most likely will need to remain a spectator for the rest
of my days. Occasionally, I meet LANL folk that can talk Feller and
Fokker with ease, and I am always jealous. It would be great to even
have a better understanding of where Lie groups (something I can at
least think about) meet the stochastic world.

3'. "So the state space is just a lattice. The “generator” from Level 2
is the generator of stochastic processes over this state space, and it
is where probability distributions live."

Please write more on this. By 'just a lattice' do you mean integer-valued
on account of the counts being so? Is the state space used to some
extent, like a modulii/classifying space, for characterizing the
species of reactions? I feel the fuzziest on how this level and the
2nd relate.

I am thankful to have had drinks with Artemy on a number of occasions,
though I am embarrassed to have never asked him to blow my mind, as he
could so easily have done.

I am working, slowly, through Valiant's discussion of evolvability
problems regarding monotone disjunction and parity. I will hopefully
have more to say soon. One thing that stands out for me is the idea
that Lamarck could be so right, but about the wrong thing, a concept
in search of a problem. While Lamarckism wasn't right for Darwin, it
was fine for perceptrons.

"""
If that intuition is valid, then the only things Selection could ever
rescue from chaos become those that get canalized into these ur-
developmental “programs”, with defined roles for genes, and merely
allelic variation within each role. I would like to find a formal way to
frame that assertion as a question and then solve it.
"""

Yes, that would be very exciting.

Cheers,
Jon

ps. I wrote Nick and Frank about a dream a day or two before your
post, where I found myself sitting with a figure that kept morphing
between Chris Kempes and Marcus. The figure was attempting to explain
a Turing complete ball game to me. I appreciate the synchronicity.

[ρ] Here, I mostly followed Levine's approach to computing trophic level.
  https://www.sciencedirect.com/science/article/abs/pii/002251938090288X

[σ] https://arxiv.org/pdf/1901.00592.pdf



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