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Identifying Repeated Patterns of Behavior in Time Magnus S. Magnusson Research Professor Human Behavior Laboratory University of Iceland www.hbl.hi.is.

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Presentation on theme: "Identifying Repeated Patterns of Behavior in Time Magnus S. Magnusson Research Professor Human Behavior Laboratory University of Iceland www.hbl.hi.is."— Presentation transcript:

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2 Identifying Repeated Patterns of Behavior in Time Magnus S. Magnusson Research Professor Human Behavior Laboratory University of Iceland www.hbl.hi.is

3 Life and Repetition of Spatio/Temporal Patterns Francis CRICK: “Another key feature of biology is the existence of many identical examples of complex structures.” (1989, p. 138.) (Crick and Watson discovered the double helix structure of DNA.) Some examples: DNA – Base pairs, genes, chromosomes, genomes Behavior – Words, gestures and patterns of these Clothing – Shoes, hats, coats,.. Urban environments – Houses, streets, cars, shops, books, radios...

4 “Behavior consists of patterns in time. Investigations of behavior deal with sequences that, in contrast to bodily characteristics, are not always visible.” Opening words of Eibl-Eibesfeldt’s Ethology: The Biology of Behavior, 1970, p. 1 Opening words of Eibl-Eibesfeldt’s Ethology: The Biology of Behavior, 1970, p. 1; {Emphasis added.} Behavior is Patterns - often hidden patterns

5 Self-organization – The Emergence of Patterns Bénard cells From Scott Kelso, 1997 Visible or hidden

6 “Emergence” often needs to be assisted “It is rarely, if ever, the case that the appropriate notion of pattern is extracted from the phenomenon itself using minimally biased procedures. Briefly stated, in the realm of pattern formation ‘patterns’ are guessed and then verified.” Crutchfiled, J., 1993. (Here cited from Solé & Goodwin, 2000, p. 20).

7 New Research Directions Much theoretical and methodological thinking within the behavioral sciences (and statistics) stems from the time before cheap powerful computers and advanced software development tools Highly complex search patterns and algorithms can now be developed and applied Behavioral scientists can aim for new kinds of discoveries

8 Basic Viewpoint and Task Behavior is more structured than is perceived directly or through standard data analysis methods To fully disclose its structure new pattern types and detection methods are needed to complement existing ones The discovery of hidden patterns is of considerable importance for theoretical and practical reasons

9 Architechture vs. Structure a simple philosophy Search algorithms should correspond to the structure of the phenomenon being studied Even the most sophisticated and powerful square detection algorithm is not adequate for the detection of planetary orbits An imperfect ellipse detection algorithm would be preferable

10 Some Basic Questions What kinds of hidden significant structure exists in behavior? How to characterize such structure? How to discover such hidden structure? How to discover effects of independent variables on such structure?

11 Sequences and Patterns A sequence: “1. an arrangement of two or more things in successive order” “3. an action or event that follows another or others” “Maths. a. an ordered set of numbers or other mathematical entities in one- to-one correspondence with the integers 1 to n” - Collins. A pattern: “1. an arrangement of repeated or corresponding parts, decorative motives etc...” “Most mathematicians define Mathematics as the science of patterns….” A pattern (shape, form) may not be a sequence but may still include one. Detecting a pattern may thus mean detecting a sequence.

12 Behavior as Repeated Patterns Linguistics: repeated hierarchical/syntactic patterns Ethology: repeated hierarchical/syntactic patterns Behaviorism: repeated real-time contingencies Anthropology, Social Psychology and more: scripts, plans, routines, strategies, rituals, ceremonies, etc. The importance of repeated patterns in behavior is widely accepted The recognition of the “hiddenness” of some such patterns is needed New pattern definitions with corresponding detection algorithms and tools (software) are required

13 Verbal and Nonverbal are One The activity of man constitutes a structural wholein such a way that it cannot be subdivided into neat “parts” or “levels” or “compartments” insulated in character, content, and organization from other behavior.Verbal and nonverbal activity is a unified whole,andtheory and methodology should be organized or created to treat it as such “ The activity of man constitutes a structural whole, in such a way that it cannot be subdivided into neat “parts” or “levels” or “compartments” insulated in character, content, and organization from other behavior. Verbal and nonverbal activity is a unified whole, and theory and methodology should be organized or created to treat it as such.” Pike(1960, p. 2). {Emphasis added.}

14 Repetition versus Uniqueness “.. a conversation, … a complex system of relationships which nonetheless may be understood in terms of general principles which are discoverable and generally applicable, even though the course of any specific encounter is unique (cf. Kendon 1963, Argyle and Kendon 1967).” (Kendon, 1990, p. 4). (Emphasis added.)

15 Towards a General Pattern Type Different Time Scales and Content These patterns of patterns have aspects in common: How do you do? How do you do? Very well, thank you. Pass me the salt, Jack. Jack, passes the salt. If..then..else Dinner: Sit down..take an entrée..take a main course..take dessert..drink coffee..stand up Rituals, ceremonies, routines, genes, poems, hospital operations, conferences, classes, football matches, strikes, and melodies

16 Common Structural Aspects Fixed order and “significantly invariant distances” between components Hierarchical/syntactic structure Self similarity / scale independence

17 Such Patterns are Often Hard to Spot d ek w akb c d k w k d e wkakb ckd w T T 1 2 1 and 2 are identical data sets

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21 The six sub-patterns are separated by relatively freely structured intervals of relatively fixed length. (From Magnusson, 2005.) A Dinner...a Time-Flexible Pattern of Patterns

22 Patterns and Causation Very well, thank you – an earlier word is usually not considered as a cause of any word following it within such intra- individual patterns How do you do? Very well, thank you – an earlier part of some inter-individual patterns may be seen as a likely cause of a later part of the same pattern

23 The T-patterns A t-pattern is a particular set of event-types recurring in the same order (and/or concurrently) with “significantly similar distances” between them on a single dimension. T-patterns have a scale-independent and hierarchical structure (often syntactically constrained -- “grammar”) T-patterns may occur randomly, but they often occur in cycles and even when their elements do not

24 An event-type may be an actor’s (agent’s) beginning or ending of a particular behavior. It may also be a base in a DNA molecule or an amino (recid.) in a protein. Sets of such series form multivariate point series to which all T-pattern definitions refer exclusively. aaaaaa The Data: Series of Points on 1-Dim.

25 Multivariate Point Series The Basic Data Type A.......... B...... C..... D.. E............... F.. G........ _______________________________________ t 1 t 2

26 Recursive T-Pattern Definition The T-pattern is an ordered set of T-patterns (X): X 1 ≈ X 2 ≈.. X i-1 ≈ X i.. ≈ X m X 1 ≈dt 1 X 2 ≈dt 2.. X i-1 ≈dt i-1 X i.. ≈dt m-1 X m ≈dt, that recurs with significantly similar time distances, ≈dt, between its elements relative to the zero hypothesis (fiction) of constant probability per unit time for each X i = N Xi / observation time with the event-type as the simplest T-pattern

27 Towards a Detection Algorithm Searching for Critical Intervals [d 1, d 2 ] Repeatedly, an A is followed by a B within approximately the same distance Comparing Series A and B A B Detected Critical (distance) Interval (window) d1d1 d2d2

28 Critical Intervals and Binary Trees Any T-pattern Q = X 1 X 2..X m can be split into a pair of shorter ones related by a critical interval: Q Left [d 1, d 2 ] Q Right Recursively, Q Left and Q Right can each be split until the whole pattern X 1..X m is expressed as the terminals of a binary-tree

29 Bottom-up Detection Patterns Grow & Compete The bottom-up algorithm detects patterns gradually from event types, as pairs of pairs, i.e., as binary trees It detects critical interval relations between the occurrence series of event types and/or already detected patterns and then connects these to form longer patterns (trees). Many binary-trees may correspond fully or partly to the same pattern so all detected patterns are automatically compared and only the most complete (longest) patterns are kept.

30 Completeness Competition - partial and equivalent trees (( A B) ((C D) (E F))) (( A ((B C) D)) (E F)) (( A B) (D (E F )) (( A C ) F ) (B E) (B D) (A F)

31 Behavior Record - Example Two Children (Blue & Red) Play With One Toy for 13.5 Min; 81 Series Time in 1/15 s Event Type Occurrence Series

32 New Pattern Presentation for Complex Patterns

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35 Nature’s Symmetries are Approximate Different instances of the same t-pattern may have quite different internal intervals Still the relationship is always the same, the Critical Interval Relationship. Should this be called relative translation symmetry?

36 Statistical Validation

37 Statistical Validation Types

38 Standard Statistical Methods Inadequate for T-pattern Detection Multivariate statistical methods: look for clouds of points in n- dimensional space rather than for syntactic structures on one dimension Time series analysis looks for trends or waves rather than hierarchical discontinuities occurring irregularly Sequential analysis may look for a priori unlikely time sequences but involves no concept of complex repeated 1-D shapes or patterns. It may therefore detect a multitude of sequential relations without ever detecting such underlying patterns

39 25 min of Children’s Dyadic Problem Solving Data from published studies by Beaudichon and Magnusson.

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41 Univariate Bursts

42 Doctor-patient facial interaction data coded with FACS

43 Interindividual T-patterns in Doctor- Patient Facial Interactions Data from the Psychiatric Hopitals in Geneva, V. Haynal et al.

44 Wild-type Male vs. wild-type Mated FemaleWild-type Male vs. Mature wild-type Virgin Female Wild-type Male vs. Immature wild-type Female #P = 8 #P = 3#P = 4 Drosophila interactions B. Arthur’s data and patterns

45 The T-System or T-model A System of Mathematically Defined Terms The t-pattern type is the basis of a growing system of terms for the description of temporal structure in complex behavioral processes Corresponding detection algorithms have been developed and implemented in the THEME software See patternvision.com & noldus.compatternvision.comnoldus.com

46 Extending the T-model Building on the Critical Interval and T-pattern Concepts Markers & Indicators Composition +/- Associates; Satellites & taboos Gravity- and repulsion zones Packets Packet markers Drifters T-kappa

47 T-markers A t-marker of a t-pattern occurs almost exclusively as a part of that pattern A t-marker’s occurrence thus indicates that a particular t-pattern is occurring A marker that occurs early in a pattern predicts the rest of the pattern A marker occurring late in the pattern retrodicts the earlier part of the pattern

48 T-associates A positive or negative associate of a T-pattern is: some behavior that is not a part of that pattern, but occurs within or around its occurrences significantly more (or less) often than expected by chance Associates may occur only, always, sometimes or even never within or near their corresponding T-pattern The “only and always” case is called a t-satellite The (almost) never case is called a t-taboo

49 The T-packet Structure A T-pattern with its Associates and Zones An instance of a t-packet showing two t-associate instances The gravity zone, [ t 1, t 2 ], of a t-pattern extends from the earliest to the last positive associate The negative gravity or repulsion zone (not shown) is similarly the interval within which any behaviors tend not to occur T-packets are simultaneously sequential and non-sequential structures

50 Neurones as Interacting and Networking (Social) Organisms

51 Neuronal T-data Including Breathing (from Nicol, Kendrick, Magnusson, 2005)

52 A Breathing Related Neuronal T-pattern N = 15 Len= 12 Dur = 266482 %Dur = 88 Log10( P(Template)) = -2,88 Log10( P(Template Occurrence)) = -43,18

53 T-Paths are T-patterns in Space -- A neuronal T-pattern on an Electrode Grid

54 Origins Greener: higher probability of being the origin (first node)

55 Figure from A.J.F. Griffiths et al. 1999, p. 30. Cycles, base-pairs, codons; DNA->tRNA->Protein->>>Phenotype->.. DNA and its “Ticking” Backbone Cyclical and Combinatorial

56 Genes and Genomes as T-patterns Non-coding or “Free” Segments Between and Within Genes Figure from A.J.F. Griffiths et al. 1999, p. 33.

57 The six sub-patterns are separated by relatively freely structured intervals of relatively fixed length. (From Magnusson, 2005.) A Dinner...a Time-Flexible Pattern of Patterns

58 Thank You


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