1. 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

2. University of Zagreb, Croatia Round of applause use your hands and move your body 31 October 2015S3++ 20121 of 19

3. University of Zagreb, Croatia Group of people same rhythmus 31 October 2015S3++ 20122 of 19

4. University of Zagreb, Croatia Heterogeneous Machine-to-Machine Systems same time 31 October 2015S3++ 20123 of 19

5. University of Zagreb, Croatia Logical questions can we go home? 31 October 2015 1. How hard it is to synchronize different clocks? 2. Why do we need time synchronization? 3. How can we achieve time synchronization? S3++ 20124 of 19

6. University of Zagreb, Croatia Outline try to give logical answers… Research motivation Biologically-inspired computing Firefly-inspired synchronization Results from the laboratory setting Conclusion 31 October 2015S3++ 20125 of 19

7. University of Zagreb, Croatia Computer clock how does it work?  How is this possible? 31 October 2015 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 S3++ 20126 of 19

8. University of Zagreb, Croatia Problem no global notion of time  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) 31 October 2015S3++ 20127 of 19

9. University of Zagreb, Croatia  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) Need for (speed?) time 31 October 2015 Frequency division multiple accessTime division multiple access S3++ 20128 of 19

10. University of Zagreb, Croatia Time synchronization different algorithms  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) 31 October 2015S3++ 20129 of 19

11. University of Zagreb, Croatia Biologically-inspired computing biology applied in distributed systems  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 31 October 2015S3++ 201210 of 19

12. University of Zagreb, Croatia Self-synchronization in nature 31 October 2015S3++ 201211 of 19

13. University of Zagreb, Croatia S3++ 2012 Self-synchronization in humans 31 October 201512 of 19

14. University of Zagreb, Croatia  If oscillators are not coupled, their state variables change following only their own excitations  x i denotes state variable x i (t) = f i (t)  t i * denotes a moment when i-th oscillator flashes R. E. Mirollo and S. H. Strogatz. Synchronization of pulse-coupled biological oscillators. SIAM J. Appl. Math. 50: pp.1645-1662 (1990) Pulse coupled oscillators model one firefly 31 October 2015S3++ 201213 of 19

15. University of Zagreb, Croatia  If oscillators are coupled  state variable x i is adjusted upon the reception of flashes from the others  x i (t) = f i (t) + ϵ ij g ij (t)  ϵ ij is a coupling constant  g ij (t) is a coupling function between i-th and j-th oscillators R. E. Mirollo and S. H. Strogatz. Synchronization of pulse-coupled biological oscillators. SIAM J. Appl. Math. 50: pp.1645-1662 (1990) Pulse coupled oscillators model two fireflies 31 October 2015S3++ 201214 of 19

16. University of Zagreb, Croatia  Pulse coupled oscillators model assumptions faulty  no oscillators with a faulty behavior that desynchronizes the network fully-connected network  oscillators are connected in a fully-connected network mobility  oscillators cannot join or leave the network nor change their positions in the network (i.e. no mobility) same frequencies  oscillators are the same (i.e. have same frequencies) delays  no delays in the message exchange among oscillators Pulse coupled oscillators model limitations 31 October 2015S3++ 201215 of 19

17. University of Zagreb, Croatia  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 Robustness with oscillators with faulty behavior 31 October 2015S3++ 201216 of 19

18. University of Zagreb, Croatia Results robustness 31 October 2015S3++ 201217 of 19

19. University of Zagreb, Croatia Conclusions can we go home? NOW WE CAN!!!!!!!!!!!!!!!!!!! 31 October 2015 1. How hard it is to synchronize different clocks? 2. Why do we need time synchronization? 3. How can we achieve time synchronization? S3++ 201218 of 19

20. University of Zagreb, Croatia Questions? 31 October 2015S3++ 201219 of 19

21. University of Zagreb, Croatia Summation exclusive disjunction InputOutput AB 00 0 01 1 10 1 11 0 31 October 2015S3++ 201220 of 19