1/f, Fractal, Chaos, and Small world in the brain

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1/f, Fractal, Chaos, and Small worldin the brain

• Jaeseung Jeong, Ph.D
• Department of Bio and Brain Engineering,
• KAIST

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The Length of Coastline of Britain
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Fractal Self-similarity
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Fractal
As a non-fractal object is magnified, no new
features are revealed. As a fractal object is
magnified, ever finer features are revealed. A
fractal object has features over a broad range of
sizes.
Self-similarity The magnified piece of an object
is an exact copy of the whole object.
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Complex dynamics of heart rate variability
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Breakdown of a fractal physiological control
mechanism can lead ultimately either to a highly
periodic output dominated by a single scale or to
uncorrelated randomness.
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Zipfs Law
George Zipf's 1949 observation that the frequency
of words used in the English language followed a
powerlaw distribution is a profound thing. It not
only defined Zipf's Law, which gives a simple
rule to explain why some words (e.g. the, of,
and) are far more commonly used than others.
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The origin of Fractal Music
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Self-Organized Criticality The origin of 1/f in
the Brain
1. Introduction Self-Organization
- A process of attraction and repulsion in which
the internal organization of a system, normally
an open system, increases in complexity without
being guided or managed by an outside source
(From Wikipedia) - Typically displays Emergent
Properties
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Sandpile criticality

• Like a child's sand castle, seeds rain down onto
  a mound that grows until it can't grow any more.
  A complex balancing act keeps the mound stable
  until it reaches the "point of criticality"-the
  point at which the system "fails," creating
  avalanches that change the mound's shape.
• Each avalanche relieves pressure on the pile,
  allowing it to begin growing again. Similar
  patterns of alternating growth and failure show
  up in many complex systems.

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Criticality or critical points

• Criticality indicates the behavior of extended
  systems at a phase transition where scale
  invariance prevails.
• The many constituent microscopic parts bringing
  about macroscopic phenomena that cannot be
  understood by considering a single part alone.

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1. Introduction Self-Organization
bird flocks, ant colonies, highway traffic,
market economies, immune systems in all of
these systems patterns are determined not by some
centralized authority but by local interactions
among decentralized components Resnic, 1995
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Getting on top of self-organized criticality

• Take a sand pile built up by dropping grains
  onto it at a steady rate. The angle of the slope
  will be controlled by the frictional strength of
  the material. This was well known to Coulomb in
  the eighteenth century.

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Brain and complex network (graph) theory

• Node (vertex) Brain region or voxel, channel
  of EEG/MEG
• Link (edge) Functional or anatomical
  connection between nodes
• Network analysis can reveal structural and
  functional organization
• of the brain (Liu, 2008)

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Small-world and scale-free organization of
voxel-based resting state functional connectivity
in the human brain van den Heuvel et al.,
Neuroimage, 2008
normal, resting-state, voxel-based(N10,000), zero
-lag temporal correlation, bandpass-filtered(0.01-
0.1Hz), unweighted, small-world and scale-free
optimal network organization balance between
maximum communication efficiency and minimum
wiring
AD, damage modeling, weighted graph, efficiency
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Constructing Brain Networks
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Brain is a small-world network
high C high C low
C high L low L low L

• high clustering coefficient (C) high
  resilience to damage in local structures
• low average path length (L) high level of
  global communication efficiency
• Brain functional network has small-world
  structure,
• while this property may be disrupted in damaged
  brain such as AD
• (vulnerability to damages, decreased
  communication efficiency between distant brain
  regions )

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Previous study 2
A resilient, low-frequency, small-world human
brain functional network with highly
connected association cortical hubs

Achard et al., The Journal of
Neuroscience, 2006
MODWT (Maximal Overlap Discrete Wavelet
Transform) at 6 frequency scales
healthy young subjects, resting-state, parcellatio
n(90 region-based), unweighted, small-world, NOT
scale-free resilient to targeted attack than SF
network
AD, voxel-based, weighted, efficiency, region
attack
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Spontaneous eyeblinking activity

• Time duration in the blink of an eye
• 0.2-0.3 sec
• Frequency of the eye-blinking
• 15-20 times/min
• 14,000 times/day
• 5,250,000 times/year
• 360,000,000 times/lifespan
• Time duration of eyes-closed for blinking
• 75 mins./day

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Functional roles of spontaneous eye-blinking

• On the act of blinking Eric Ponder and WP
  Kennedy, The Quarterly journal of experimental
  physiology (1927)
• Protect eyeballs from injury or maintaining a
  healthy ocular surface by inducing the formation
  of the preocular tear film.
• ?
• Sauna experiments Parkinsonian patients

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Eyeblinking is controlled by the brain

• Women are eye-blinking more frequently than men.
• The blink-rate is highly dependent on attention
  and cognitive states.
• Blink activity is substantially influenced by
  experimental manipulation of dopaminergic
  circuits in the basal ganglia.
• Significantly, altered blink-rates are also
  observed in several neuropsychiatric disorders
  that are known to affect dopaminergic
  neurotransmission.
• Interesting experiment on eye-blinking during
  reading in the library.

Eyeblinking is an epiphenomenon of information
processing of the brain?!
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Anxiety increases eyeblinking
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Why do we study eyeblinking?

• For better understanding of eye-blinking
• Dopaminergic circuits in the basal ganglia can be
  monitored by eye-blink activity.
• Eye-blinking activity can be used to control
  computer/machine.

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Eyeblink is a signal of decision-making

• Despite the emphasis of previous studies on
  defining the changes in EBR under various
  cognitive or behavioral states, the timing or
  temporal patterning of eyeblinks during specific
  cognitive processes has been examined only
  rarely.
• Clue During the reading of written text, a
  large proportion of eyeblinks occur at or near
  the end of a line of text, before gaze returns to
  the beginning of the next line.
• Also, eyeblinks occur when subjects shift their
  gaze, a so-called gaze-evoked blink.
• Our hypothesis is that eyeblinks may signal the
  end of one cognitive process, the beginning of
  another, or the shift of one of these processes
  to the other.

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How is the eyeblinking changed during cognitive
tasks?
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Eyeblinks in the Stroop task

• Participants name the color of the ink (red,
  yellow, blue, green) in which words are written
  or read the words. The words themselves either
  denote colors or objects unrelated to colors, and
  are variously grouped into three stimulus
  conditions
• (1) congruent, in which the word denotes a color
  that matches the ink in which the word is
  written.
• (2) incongruent, in which the word denotes a
  color other than the ink in which the word is
  written.
• (3) neutral, in which the word denotes an object
  unrelated to color.

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Stroop TaskWord reading vs Color naming

• GREEN YELLOW
• BLUE BLUE
• YELLOW GREEN
• SPOT RED

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Stroop facilitation and interference

• Stroop facilitation
• The naming of ink colors for congruent
  stimuli is faster, and therefore produces shorter
  Reaction Times (RTs), than the naming of colors
  for neutral stimuli.
• Stroop interference
• The naming of ink colors for conflict stimuli
  is slowed, and therefore produces longer RTs,
  than the naming of colors for neutral or
  congruent stimuli,
• This interference is attributed by many to
  the greater automaticity of word reading than
  color naming, requiring greater cognitive control
  and a greater allocation of attentional
  resources, and therefore slowing responses to
  avoid error on the task.

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• Dalrymple-Alford Budayr (1966) First to
  encourage presentation timing of stimuli
  individually. This method now dominates

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The possible role of eyeblinks

• We found the statistically highly significant
  temporal proximity of blinks to the vocal
  response stage of information processing, rather
  than during stimulus presentation or during gaze
  fixation between stimuli.
• This suggests that the cognitive process that the
  blinks accompany is either the termination of
  stimulus processing, the beginning or end of the
  motor response, or the change in set from one of
  these to the other.

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Tourettes syndrome

• Tourette Syndrome (TS) is a complex
  neurobehavioral disorder characterized by a
  changing pattern of motor and vocal tics which
  begins in childhood. To be considered TS, the
  symptoms should last more than a year.

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TS disease progress
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Neural substrates of TS

• Frontal-subcortical cuircuit
• Basal ganglia collection of large subcortical
  nuclear mass
• neostriatum, striatum Caudate nucleus putamen
  
• Corpus striatum caudate, putamen, globus
  pallidus
• Lentiform nucleus putamen and glubus pallidus
• Ventral striatum ventromedial part of th
  putamen and caudate nucleus, nucleus accumbens,

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Complex tic dynamics

• To investigate whether tic dynamics is
  deterministic or stochastic.
• To quantify the severity and progress of the
  disease.
• Early detection of TS and transient tics using
  inter-tic interval (ITI) dynamics.

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The temporal dynamics of tics in Tourette Syndrome
BS Peterson et al. The temporal dynamics of tics
in Gilles de la Tourette Syndrome, Biological
Psychiatry (1998)
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Tic patterns of Tourettes syndrome
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Fractal
As a non-fractal object is magnified, no new
features are revealed. As a fractal object is
magnified, ever finer features are revealed. A
fractal object has features over a broad range of
sizes.
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Physics(Dynamics) ?? Neuroscience

• Theory driven
• first principles
• Reductionism
• simplify the world
• Qualitative understanding
• mathematics

• Empirical and descriptive
• phenomena
• Systems level
• details of the system
• Quantitative understanding
• measurements

• Paradigm Shift
• Complex real systems
• Synthesis whole-istic
• Systems neuroscience using mathematical models
• Universality among the diversity Brain