P' Fraundorf

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Measures of useful information in layered networks
P. Fraundorf UM-StL Physics Astronomy Center
for Nano Science MIST Lab Washington U.
Physics email pfraundorf_at_umsl.edu web
http//www.umsl.edu/fraundorfp
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Grad student project Progress on quantifying
correlations
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Outline

• Applications for KL divergence
• ecology, IT and statmech
• useful information
• Layered niche-networks
• multiscale thought
• excitations codes
• boundary-directed correlations
• Combinations of the two
• measures of health
• simplex model for communities

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Part 1

• Applications of KL divergence
• ecology correlating ideas with the world
• information theory mutual information
• e.g. in communications, data compression,
• clade analysis, and quantum computing
• stat mech available work wrt/ambient
• all useful information with 2nd law chops

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A few standard definitions
For k 1/ln2,1,kBoltzmann, surprisals are in
bits, nats, J/K.
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How many know that

• In ecology and related fields the KL divergence
  of "model from reality" is useful in ranking
  models against experimental data, according to
  the residuals they don't account for (cf. Burnham
  and Anderson).
• In communications theory, in clade analysis, and
  in quantum computing the KL divergence of
  "uncorrelated from correlated" measures the
  mutual information associated with fidelity,
  inheritance, and entanglement.
• In thermodynamics, the KL divergence of "ambient
  from actual" measures a distance to equilibrium
  and (multiplied by ambient temperature) available
  work.

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Sample PV map of KL-divergence
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Useful information

• Thus KL divergence of reference state from
  reality is a robust measure of correlation that
  obeys the 2nd law of thermodynamics.
• It can be used to measure the information content
  of assertions about the world around, as well as
  thermodynamic availability, in both cases with an
  upper limit of available work/kTambient.
• Applications by and large have so far focused on
  one layer of organization at a time.

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Part 2

• Layered niche networks
• excitations and codes
• evolution of steady-state correlations seems to
  be aided by data storage in replicable codes
• multiscale thought
• cells do amazing things with molecule codes, but
  can metazoans work similar magic with idea codes?
• boundary-directed correlations
• it may help to scope niches as structures that
  have direction wrt/a small set of physcial
  boundaries

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Why inform our ideas to multiple scales of space,
time, and organization?
On the level of cells, only eukaryotes can
assemble a bobcat from one cell, thanks to the
fact that code expression is informed to multiple
scales of space, time, organization. What if
metazoans did that for idea codes?
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These figures illuminate multiple scales of
space, time, and organization
Background

• I) Subsystem correlations require thermodynamic
  availability, just like the ordered energy we get
  from solar photons.

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Single strand curls of a DNA molecule, like those
wrapped around nanotubes here, go through many
levels of folding to create chromosomes visible
in the light microscope during cell division.
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The many scales of organization in natural bone.
(credit J. Liu) Collagen triple helices
spontaneously form nanoscale bundles of protein,
which act as a template for the crystallization
of hydroxyapatite nanocrystals. The collagen
matrix is also recognized by undifferentiated
bone-marrow stem cells, which become bone-forming
osteoblasts after signals from bone-specific
proteins in the matrix.
then the leg bone connects to the hip bone
Background II) Cosmic evolution, discussed e.g.
by astrophysicist Eric Chaisson and biologist
Ursula Goodenough, generally involves powered
formation of a series of subsystem correlations
with respect to a hierarchical set of physical
gradients and boundaries.
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Background III) Molecule surfaces and cell
membranes define the in/out correlations that
comprise microbial life, as do organ surfaces and
skins for metazoan individuals. Molecular and
memetic code-pool boundaries predicate four more
correlation layers in metazoan communities.
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Part 3

• Combining the two correlation measures and
  multiscale thought
• measures of health metazoan niche networks with
  layers directed in/out from self, family and
  culture
• simplex models of community counts of level
  multiplicity only, from 6 pi values

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physical boundary-directed niche networks

• The right figure takes a clue from the way our
  species (e.g. Schaik in Sci Am 4/2006)
  conceptualizes its own networks.
• The left column lists three geometically complex
  physical boundaries metazoan skin, gene pool,
  and meme pool.
• At right, find six niche layers that each
  individual can concurrently occupy.

M is harmonic avg of Mi
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The Attention-Slice Simplex
A one simplex in 2-space, a two simplex in
3-space, and an un-embedded three simplex
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Attention-space tracking might help e.g. us get a
handle on the interaction between electronic
media and human communities today.
Attention-slice models and the 5-simplex
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Spatial vs attention-slice modeling
Spatial correlation models (left) are applied in
population ecology, e.g. plants predator/prey
modeling. That recent NECSI Science paper looks
at spatial correlations of violence. Fractional
resource/ attention models could extend this
beyond skin to all niche layers.
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Layered network spiders, for visualizing your
connections to the world around. The color of
the numbers in these figures reflects ones
emphasis on inward-looking (blue) versus
outward-looking (red) objectives. In the
modern world, we might like for everyone to be
able to connect well in all six ways.
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Monitoring modeling requires data. Help! How
can we quantify the correlation-focus of
individuals in communities? Possibilities
include (i) population surveys at right, (ii)
behavioral observation,(iii) data on
communication focus
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Refined methods for monitoring these correlations
might help us ask

• Should the survival perspective of ideas, not
  just individuals, be considered in balancing
  ones options?
• Can extremism be linked to perspectives that do
  not respect care of observation, belief,
  consensus, family, friends, and self all at once?
  
• How long have six distinct layers been evident
  with humans?
• Might measures of correlation standing crop be
  less monochromatic than e.g. GDP, longevity, or
  census?
• Eric Chaisson has argued that complexity
  correlates with free energy rate density. Will a
  lower per capita free energy rate mean we cant
  maintain all six layers?
• Can a theory of correlations in physical systems
  inspire dialog on scientific, cultural and
  political grounds among ALL who dont yield to
  that innate tendency to ignore one layer or
  another?

arXiv physics/0603068
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How can we further work together on this big
picture?