Transcript T-pattern

Proteomics and Bioinformatics Conference
2016, 24-26 October, Rome, Italy
Temporal and Spatial T-patterns in
Behavior and DNA
Is the structure of DNA reflected in the structure of
neuronal and human behavior?
Dr. Magnus S. Magnusson
Research Professor, director
Human Behavior Laboratory hbl.hi.is
University of Iceland english.hi.is
Email: [email protected]
Methodology for the Analysis of Social Interaction” -- MASI.
Formal Inter-University Research Network of 24 Universities formed around TPA
Research published in many papers and in two dedicated edited books, 2005 & 2016
The Hidden Structure of Interaction:
From Neurons to Culture Patterns
Discovering Hidden Patterns in Behavior and Interactions:
T-Pattern Detection and Analysis with THEMETM
2005
2016
See also Comprehensive Review of TPA
by Casarrubea et al published in 2015 in
Journal of Neuroscience Methods.
DNA Structure Came as a Surprise
Seemed like an example of T-Patterns:
Genes
Repeated Structured Hierarchical Flexible Clusters
Light green = introns; dark green = exons; white = intergenic regions
Genes as exons separated by characteristic, mostly “meaningless” but
with possible meaningful elements, while the exons are themselves
made up of smaller patterns (possibly only ≈2000, occurring in various
combinations; Denis Noble, 2006).
Gene: a Repeated Pattern of Patterns….
with Characteristic Separating Intervals in a
Flexible Molecule
• The (black) sub-patterns are separated by relatively freely-filled intervals (white).
• Any parts can be compressed and stretched -- to a limit -- like rubberbands.
Towards Behavioral and Neuronal T-Patterns
Behavior is Patterns in Time
- often Hidden Patterns
“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; {Emphasis added.}
Most Modern Mathematicians define
Mathematics as „the Science of Patterns“*
Thus the concept of „Pattern“ is impossibly broad and nearly the same
goes for „Sequence“. Much further specification is clearly required.
Neither are necessarily hierarchical and fewer self-similar.
Some may involve repetition and translation symmetry in their
definition and detection and be undefined and undetectable
otherwise, which is the case of T-patterns.
*Mathematics: The Science of Patterns: The Search for Order in Life, Mind and the Universe. by Keith Devlin
Behavior as Repeated Hierarchical Patterns
Widely Recognized in Behavioral Science
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.
Towards a General Behavioral Pattern Type
Structured Hierarchical Repeated Clusters in Flexible Time
How do you do? (non causal)
How do you do? Very well, thank you. (causal)
Pass me the salt, Jack. Jack, passes the salt.
If..then..else
(causal)
(non causal)
Dinner: Sit down..take an entrée..take a main course..take
dessert..drink coffee..stand up (non causal)
Other example: Words, common phrases, rituals, ceremonies, routines,
poems, hospital operations, conferences, classes, football matches, and
melodies.
“…” = variously filled intervals of nonrandom/constrained lengths
Common Structural Aspects
Fixed order (incl. concurrence) of the components with “significantly invariant
distances” between them
Variable number and kinds of events may occur between the components
Hierarchical structure (typically with syntactic constraints)
Self-similarity, flexible scale, scale independence
Dinner: Patterns of Patterns of Patterns..
with Characteristic Separating Intervals in Flexible Time
• The (black) sub-patterns are separated by relatively freely-filled intervals (white).
• Any parts can be compressed and stretched -- to a limit -- like rubber bands or melodies.
• Such patterns facilitate various processes within the Human City.
• About the “Dinner-Gene” see Magnusson, in Anolli et al, 2005.
Such Patterns are Often Hard to Spot
Even in the simplest data
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2
d ek w akb c d k w k d e wkakb ckd w
d ek w akb c d k w k d e wkakb ckd w
1 and 2 are identical
T
T
K is here
the only
“noise”
What exacltly are T-Patterns and
What Kind of Data do they Refer To?
The Data: Discrete Point Series 1 to n within [ 1, T ]
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i = occurrence points of Event-Typei (for example, a spike from neuron i)
Randomizations used in Monte Carlo tests: Shuffling, where each series is replaced by an equal number of random
points within [ 1, T ] and Rotation, where each series is randomly shifted by dt = random(T); t = ( t + dt ) mod T
The T-pattern
Self-Similar Ordered and Spaced Recurrent Hierarchical Cluster on One Flexible Dimension
A T-pattern is m ordered components, X1..Xi..Xm, any of which may be
primitives or T-patterns, recurring on a single discrete dimension, such
that, for each occurrence of the pattern and for each value of i, the
distances Xi  Xi+1 vary within a significantly small interval, called a
critical interval (CI): [d1, d2]i
It may vary greatly in size within and between patterns.
The T-Pattern may then be written:
X1 [d1,d2] 1 X2 [d1,d2] 2 .. Xi [d1,d2] i Xi+1 .. Xm-1 [d1,d2] (m-1) Xm
(m = length)
Occurrences of a T-Pattern; Repeated Pseudo-Fractal Objects
with self-Similarity and Translation Symmetry
Any T-pattern Q = X1 X2..Xm can be split into at least one pair of
shorter ones related by a critical interval:
QLeft [ d1 , d2 ] QRight
Recursively, QLeft and QRight can thus each be split until the pattern
X1..Xm is expressed as the terminals of a binary-tree.
-- Detection works in the opposite direction.
T-Pattern Detection Essentials
• Patterns are gradually constructed level-by-level as binary trees of
detected CI’s
• Detected patterns are added to the data
• Patterns are compared and selected and evolve through a
completeness competition as partial and redundant patterns are
removed
• Validation: statistical and external; global and per pattern
Two Toddlers Playing with one Toy for 13.5 min
It Goes Back and Fourth Four Times – Ethological Categories
Series
1/15 s (video frame)
Detected Interactive T-pattern
The four occurrences of this T-pattern cover 100% of the observation
Statistical Validation Shuffling and T-Rotation
STDs from Random Mean Per Length (100 random runs)
Neuronal Interactions in a Living Brain
Data collected from a number of individual neurons with a chip placed on the olfactory lobe of a rat.
Data of A. Nicol, University of Cambridge, UK.
The Brain’s Structure is Hierarchical and Self-similar
“…a nested hierarchy -- smaller elements join together to form larger elements, which,
in turn, form even larger elements, and so forth … many of the integrative aspects of
brain function depend on this multiscale structural arrangement of elements and
connections. “ Discovering the Human Connectome (Olaf Sporns, 2012, p. 41)
From the Human Connectome Project Gallery
Neuronal Data Acquisition – from Chip in Olfactory Bulb
Data of A. Nicol
• Using an MEA, multiple electrode array, of either 48 or 30 sharpened tungsten
electrodes in the OB, action potentials (spikes) were sampled from mitral layer
OB neurons across an area of ~2.2mm2
• Spikes sampled in the mitral cell layer are assumed to be generated by mitral
cells, as the other cell type in this layer, the granule cell, does not have an axon
(Price & Powell, 1969).
• Typically, spikes were sampled from >50% of the electrodes (18.4 ±1.7 sem
electrodes per rat).
• Spikes from individual neurons were discriminated from multineuronal activity
sampled from each electrode. Typically, spikes were sampled simultaneously
from 100 or more neurons across the array (6.4 ± 1.0 sem per electrode).
• Event-types entered into T-pattern analyses were times of occurrence of spikes
from individual neurons, and times of onset of inhalation and exhalation in the
breathing cycle.
Statistical & External Validation
Deteriorating Subject*
A number of subjects were presented with various odor stimuli in a
series of sets of trials separated by a single control trial where only
air was presented.
The subject’s condition was deteriorating and it finally had to be
terminated.
Allowed external validation of the detected patterning.
*See Nicol et al (2015) in J. Neuroscience Methods.
The next slides show the raw spike series at the
first and last control trials
and then the gradual decrease of patterning throughout
all the 12 control trials
Spikes at First (Normal) and Last (Near Terminal) Trial
Minimal Difference – a Few Percent More Spikes in the Latter
First
Trial
Last
Trial
Data = R2control1, by A. U. Nicol
Time Unit 0.03 millisec.
First Trial
Most Complex T-Pattern Including Breathing
Inhales
C80,n3
Last Trial
No Neurons Connect to Breathing
Most Complex Pattern Including Breathing
Difference Between Real and Random Detection
At First vs. Last Trial
First Trial
Last Trial
Standard Deviations Between Real and Random Detection
At First vs. Last Trial
First Trial
Last Trial
Trials 1 to 12: Gradually Fewer and Shorter Patterns
Random vs. Real Differences Decrease
Self-similarity in the Behavior of a Self-Similar Brain
T-Patterns in Intra- and Inter-Brain Interactions
At the cellular interaction level, that is, in interactions within a population of brain neurons
repeated statistical hierarchical self-similar (fractal) patterns have also been found.
Complex spike patterns in olfactory bulb neuronal networks
Journal of Neuroscience Methods, Volume 239, 15 January 2015, Pages 11-17. Alister U. Nicol,
Anne Segonds-Pichon, Magnus S. Magnusson
Human Connectome Project Galery.
See “Discovering the Human Connectome.“ (O. Sporns, 2012)
See same volume: T-pattern analysis for the study of temporal structure of animal and human
behavior: A comprehensive review. Casarrubea et al.
Genes and Behavioral Routines: Patterns of Patterns of Patterns..
with Characteristic Separating Intervals on a
Flexible Scale
• The (black) sub-patterns are separated by relatively freely-filled intervals (white).
• Any parts can be compressed and stretched -- to a limit -- like rubber bands or melodies.
• Such patterns facilitate various processes within Cell City and its descendant: the Human City.
• About the “Dinner-Gene” see Magnusson, in Anolli et al, 2005.
Thank You
[email protected]