Bipolar feedback and biotic patterns in physical, biological and mathematical processes

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• Bios Data Analyzer
• Sugerman, H. Sabelli, L. Kovacevic and L. Kauffman

Chicago Center for Creative Development (CCCD)
And University of Illinois at Chicago
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The Bios Data Analyzer measures the Defining
Characteristics of Bios

• Creativity
• Diversification
• Complexes
• Novelty
• Nonrandom complexity (Arrangement)

• Non-random causation
• Partial autocorrelation
• Consecutive recurrences
• Pattern in series of differences between
  consecutive terms

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Bios but not chaos shows diversification
Local diversification
Local diversification increase in S.D. with
embedding Global diversification increase in
S.D. with N.
(from 2 to 200
embeddings)
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Diversification has physiological significance
Less diversification in patients with Coronary
Artery Disease. (RRI heartbeat intervals)
Embedding
Global diversification S.D. grows with duration
of series (number of RRIs)
Local diversification S.D. grows with embedding
(length of vectors of M consecutive RRIs)
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The Bios Data Analyzer measures two types of
recurrence isometry and similarity, at multiple
embeddings (1-200 or more).
Isometry 2 vectors are isometric when their
Euclidean norms are equal (within a margin of
tolerance)
Similarity 2 vectors are similar when the
Euclidean norm of the differences between their
elements is smaller than a certain cutoff ratio
Novelty and arrangement are detected only by
isometry. Both types of recurrence portray
complexes and causation.
Recurrence plots portray complexes (Bios and
Brownian) or uniformity (chaos or random).
Embedding plots portray changes in recurrence
(or statistical) measures with embedding.
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Embedding plots
To portray both the simple and complex components
of a process requires one to measure properties
at low and high embedding dimensions. Contrary
to much literature (embedology), there is no
appropriate or ideal embedding at which a time
series must be measured.
A sine wave shows recurrence peaks when the
embedding is an integer multiple of the period. A
wide range of embeddings is necessary to
demonstrate periodic order.
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RECURRENCE PLOTS mathematical or natural biotic
series show episodic patterns as clusters of
isometries (complexes). Periodic and chaotic
series show uniform patterns with numerous
densely packed isometries. Complexes are the
hallmark of complexity.
time
Complex
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Bios
Chaos, process
Random
Chaos, logistic
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Novelty less isometry recurrence than shuffled
copies
RRI
Bios and noise are novel
Shuffed
Chaotic and periodic series are recurrent
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Causation in all series
NO high D Arrangement
Novelty
Arrangement at multiple embeddings
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Bios in empirical processes less isometry than
shuffled (novelty), more consecutive isometry
than shuffled at low and high embeddings (simple
and complex causation), significant arrangement
(non-random complexity)
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Periodic periodic recurrence, small arrangement
DNA series
Chaotic recurrence, low dimension consecutive
recurrence arrangement

Biotic novelty, low and high dimension
consecutive recurrence arrangement
Bios
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CAUSATION DISTINGUISHES CARDIAC BIOS FROM 1/F
NOISE
CONSECUTIVE ISOMETRY
PARTIAL AUTO-CORRELATION
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PARTIAL AUTOCORRELATION evidence for CAUSATION
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Arrangement consecutive isometry / total
isometry
Empirical observations suggest that arrangement
measures non-random complexity. Arrangement is
the product of causation (consecutive isometry)
and novelty (1/isometry).
(heartbeats)
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SUMMARY

• BIOS DATA ANALYZER
• Measures diversification and other changes in
  statistical parameters
• Quantifies isometry recurrences
• Detects causation by partial autocorrelation and
  consecutive recurrence
• Examines simple and complex components of
  variation by embedding the time series 1, 2, 3 N
  times.

• .Sugerman et al, CD ROM in Sabelli, Bios, A
  Study of Creation. 2005