University of Zagreb, Croatia
Synchronization inspired by fireflies
Iva Bojić
University of Zagreb, Croatia
Faculty of Electrical Engineering and Computing
Department of Telecommunications
Summer School of Science 2012
August 7, 2012, Višnjan, Croatia
Round of applause
use your hands and move your body 
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Group of people
same rhythmus
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Heterogeneous Machine-to-Machine Systems
same time
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Logical questions
can we go home? 
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1.
How hard it is to synchronize different clocks?
2.
Why do we need time synchronization?
3.
How can we achieve time synchronization?
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Outline
try to give logical answers…
University of Zagreb, Croatia
Research motivation
Biologically-inspired computing
Firefly-inspired synchronization
Results from the laboratory setting
Conclusion
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Computer clock
how does it work?
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
How is this possible?
Quartz crystals are manufactured
for frequencies from a few tens
of kHz to tens of MHz
A clock is an electronic device that
counts oscillations in a crystal at a
particular frequency
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Problem
no global notion of time
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 In distributed systems each
node has its own clock and
its own notion of time
 In practice these clocks
drift apart accumulating
errors over time (1 second
every 11 days)
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Need for (speed?)
time
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 Global notion of time is prerequisite for:
 common
resource sharing (e.g. channel)
 depend events tracking (e.g. consistency
of distributed
databases)
 simultaneous events detection (e.g. data collection)
Frequency division multiple access
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Time division multiple access
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Time synchronization
different algorithms
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 Time
synchronization provides a common time scale for
local clocks of nodes in distributed systems
B. Sundararaman, U. Buy and A. D. Kshemkalyani: Clock synchronization for wireless sensor networks: A Survey, Ad Hoc Networks 3, pp. 281-323 (2005)
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Biologically-inspired computing
biology applied in distributed systems
University of Zagreb, Croatia
 Nature is a enormous and a highly
complex system
 processes
are done without any centralized control
 processes
are self-sustainable and self-organized
 Self-organization
is a process where some form of global
order arises out of the local interactions between the
components of an initially disordered system
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Self-synchronization
in nature
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a) fireflies
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b) neurons
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c) heart cells
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Self-synchronization
in humans
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Pulse coupled oscillators model
one firefly
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

If oscillators are not coupled, their state variables change following
only their own excitations
xi denotes state variable
xi
1
flash
 ti* denotes a moment
i-th oscillator flashes
ex
ci t
at
io
n
xi(t) = fi(t)
flash
threshold
when
0
ti*= T
2T
t
R. E. Mirollo and S. H. Strogatz. Synchronization of pulse-coupled biological oscillators. SIAM J. Appl. Math. 50: pp.1645-1662 (1990)
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Pulse coupled oscillators model
two fireflies
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
If oscillators are coupled

xi
state variable xi is adjusted upon the
1
flash
threshold
εij
ta
tio
ci
t*i T
flash
flash
threshold
0
xj
ϵij is a coupling constant
flash
n
1
t
2T
gij(t) is a coupling function between
i-th and j-th oscillators
ex

ci
ta
tio

xi(t) = fi(t) + ϵij gij(t)
ex

εij
n
reception of flashes from the others
flash
εji
0
t*j
T
εji
t
2T
R. E. Mirollo and S. H. Strogatz. Synchronization of pulse-coupled biological oscillators. SIAM J. Appl. Math. 50: pp.1645-1662 (1990)
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Pulse coupled oscillators model
limitations
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 Pulse coupled oscillators
model assumptions
 no
oscillators with a faulty behavior that desynchronizes the
network
 oscillators are connected in a fully-connected
network
 oscillators
cannot join or leave the network nor change their
positions in the network (i.e. no mobility)
 oscillators are the same
 no delays
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(i.e. have same frequencies)
in the message exchange among oscillators
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Robustness
with oscillators with faulty behavior
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

We embedded a cryptographic mechanism in the pulse coupled
oscillators model to ensure robustness
We used the logical operation exclusive disjunction (i.e. XOR)

provides protection from an attack

does not have a negative effect on the time needed for synchronization
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Results
robustness
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Conclusions
can we go home?  NOW WE CAN!!!!!!!!!!!!!!!!!!!
University of Zagreb, Croatia
1.
How hard it is to synchronize different clocks?
2.
Why do we need time synchronization?
3.
How can we achieve time synchronization?
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Questions?
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Summation
exclusive disjunction
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Input
A
B
0
0
0
1
1
0
1
1
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Output
0
1
1
0
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