Synchronization
Synchronization
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Synchronization is the coordination of events to operate a
system in unison
Greek: συγ (“same”)-χρον (“time”)-ισ (“sametimeness”)
Latin: uni (“same”)-son (“sound”)-us (“samesoundness”)
Does not always require a leader!
Greek is the language
of early science!
...and Latin is another
one!
Birds Flocking
All birds are born
equal!
There must bea
Master Bird...
“Flocking”
Birds fly at constant speed and follow four rules:
• “Alignment”: turn to move in the same direction
that nearby birds are moving.
• “Separation”: turn to avoid another bird which gets
too close.
• “Cohesion”: move towards other nearby birds
(unless another bird is too close).
• “Inertia”: birds cannot change their velocity too fast
”Flocking”(II)
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Speed vs velocity
Master bird?
Direct interaction
Birds vision: limited by V patches. Realistic?
Change course based on local information
Variables
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Independent variables:
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Population
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Vision v: How far can a bird see?
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Minimum separation s: At least how many patches must
separate two birds?
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Three max-turn variables: The maximum angles a bird can
turn as a result of each rule.
Dependent variables:
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None (use “vox populi”?)
Control variables:
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None
Flocks
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How do we define a“flock”?
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Same way as we defined a “pile”!
Aflock
Not a flock
Research Questions
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How does flocking speed depend on vision?
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For s=1 patch and v=1, 1.5, 2, and 5 patches, measure the
flocking speeds
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Divergence!
What kinds of flocks are possible?
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Look at the flocking patterns for s=1, v=5; s=1, v=10; and
s=0.25, v=5. If the patterns differ, give them “names.”
Explain your observations!
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Which pattern is the most natural?
Phase Transition
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Flocking is an example of a phase transition: abrupt
change of the state of a system (“free-flying birds”) to
another state (“a flock”)
Other examples of phase transitions:
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ice  water  vapor
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solid matter  fluid  gas
???
Phase transition: change between different states of
organization of a complex system
Model Works for Schools of Fish
Go to Boston Aquarium
to verify!
Abstract Model
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An abstract model can be created that describes the
formation of X:
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turn to move in the same direction that nearby Zs are
moving.
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turn to avoid another Z which gets too close.
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move towards other nearby Zs (unless another Z is too
close).
Concrete models:
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Z—bird, X—flock
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Z—fish, X—school
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Z—man, X—crowd...
Fireflies Blinking
Fireflies Pteroptyx cribellata, Luciola pupilla,and Pteroptyx malaccae
that have been observed to synchronize flashing in certain
settings.
This one islovely!
Oh no, bugs again?
“Fireflies”
Each firefly constantly cycles through its own clock,
flashing at the beginning of each cycle.
●At the start of each simulation all fireflies flash erratically
through the population—but at the same cycle length.
●As fireflies perceive other flashes around them they reset
their own clocks to synchronize with the other fireflies in
their vicinity*.
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*Within the radiusof 1.
Periodic Process
Flash length
Time
Period (cycle length)
Periodic process(II)
• Repetitive process – repeated sequences of events: days,
traffic signals
• Periodic process – repetitive process with same delay
between repetitions : days, but traffic signals?
• Aperiodic process: traffic in/out Somerset
• Cycle – periodic repetition
• Pseudo periodic – cycles of different lengths
• Fireflies: simple periodic process with one event
• Cycle length
• Event length
Simple periodic processes and
synchronization
• Events of two simple periodic processes: synchronized?
• 24 hours simple periodic processes: noons, midnights,
sunsets
• Reference simple periodic process: event at the beginning
• Phase of a process – position with respect to the reference
periodic process
• Two simple periodic processes with same cycle lengths,
event lengths and phases are synchronized
Variables
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Independent variables:
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Number (population)
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Strategy: delay or advance? (Ignore this variable)
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Flashes to reset R: how many simultaneous flashes shall a
firefly see to reset its clock?
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Flash length F: how long is a single flash?
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Cycle length C: how long is a cycle?
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Show dark fireflies? (Boolean: “yes” or “no”!)
Dependent variables:
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How many fireflies flash at the same time? (Transient chart.)
Synchronization mechanism
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Each firefly flashes wrt its own clock -- also is mobile
Clocks are not synchronized
Fireflies -- sync with neighborhood based on threshold
Immediate or next cycle reset
Many groups of synced fireflies
Intergroup synchronization ?
”Waves” of synchronization
Fight club?
Sync’ing --- process phase alignment
Experimental aspects
• Global synchronization time(GST) - (almost) all fireflies
start flashing simultaneously
• Determine GST
• Perception
• Inspect flashing fireflies plots -- export plots, check
spreadsheets for flashing cycles
Research Questions
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Does the global synchronization time depend on the flash
cycle parameters, F, C, and R? If so, how?
“Almost successful” synchronization attempts sometimes
are followed by periodic “desynchronization rollbacks.”
Does the period of these rollbacks depend on the flash
cycle parameters, F, C, and R? If so, how?
Abstract Model
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An abstract model can be constructed for Zs, involved in
X'ing:
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Each Z constantly cycles through its own clock, X'ing at the
beginning of each cycle.
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At the start of each simulation all Zs X erratically through
the population—but at the same cycle length.
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As Zs perceive other Xs around them they reset their own
clocks to synchronize with the other Zs in their vicinity.
Concrete models:
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Z—fireflies, X—flashing
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?????