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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. Creativity Diversification Complexes Novelty Nonrandom complexity (Arrangement). Non-random causation : Partial autocorrelation
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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
Creativity Diversification Complexes Novelty Nonrandom complexity (Arrangement) Non-random causation: Partial autocorrelation Consecutive recurrences Pattern in series of differences between consecutive terms The Bios Data Analyzer measures the Defining Characteristics of Bios
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)
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)
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.
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.
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
Bios Chaos, process Random Chaos, logistic
RRI Novelty: less isometry recurrence than shuffled copies Bios and noise are novel Shuffed Chaotic and periodic series are recurrent
Causation in all series NO high D Arrangement Novelty Arrangement at multiple embeddings
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)
Periodic periodic recurrence, small arrangement DNA series Chaotic: recurrence, low dimension consecutive recurrence & arrangement Biotic: novelty, low and high dimension consecutive recurrence & arrangement Bios
CAUSATION DISTINGUISHES CARDIAC BIOS FROM 1/F NOISE CONSECUTIVE ISOMETRY PARTIAL AUTO-CORRELATION
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)
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