0:00:03welcome to all work on guaranteed global synchronisation networks were stochastic interaction
0:00:10synchronization is that it in various view that shared by all the two
0:00:14you think
0:00:15and engineering
0:00:16right on the one inside you might have
0:00:19continuous coupling
0:00:21you might have on the other hand side this continuous part company
0:00:26especially in the field of wireless communication
0:00:29where packets are transmitted
0:00:32and receive
0:00:34quite naturally a discontinuous system
0:00:37so you're interested in parts coupling
0:00:40at the strategy to
0:00:42achieve synchronization
0:00:45with that just to them
0:00:46you might have
0:00:48i which are net the conditions
0:00:50and individual delay and additionally you will have a probability to read the packet
0:01:00this mean
0:01:01that
0:01:02there is a chance
0:01:04then the signal that is transmitted is not going to be written
0:01:08the that's all the to be taken into account
0:01:11if you want to achieve and guarantee think annotation
0:01:15and that's exactly what we do
0:01:17and i'm going to show you now how we going to achieve this goal
0:01:24let us take
0:01:27late the running
0:01:28on a circle
0:01:30here's the all clear
0:01:32entrance counterclockwise on the circle until it passes the threshold
0:01:37whenever tested a threshold
0:01:39it will emitted signal
0:01:41with some probability
0:01:44p ten
0:01:45any oscillator
0:01:47on the circle which receives the signal
0:01:50that's a here's austria that k
0:01:52years austria later j
0:01:55so whenever one of those received signal emitted by oscillator
0:01:59i
0:02:00it will adjust
0:02:02it will adjust according to our update function
0:02:06this means basically that are not later that is in the lower ha
0:02:12will jump
0:02:13for words
0:02:14and then also later that is in the above
0:02:17will jump backwards
0:02:20that the main idea of the update function is to oscillators
0:02:24one the d m at their
0:02:27of the set
0:02:28the i
0:02:30and we will not know that is the i
0:02:33we monotonically decreases
0:02:35for combination of how this applies to bigger is that of oscillators
0:02:39will not be shown in the video
0:02:42on the left we see realization with ten oscillators on the random network
0:02:47if i of an oscillator is indicated by red light
0:02:51on the top right we show the oscillator spaces at the five times
0:02:55note that the y-axis is centered around zero
0:03:01well oscillators between the plot lines are combined in a set s
0:03:05on the bottom right with you did em at their of this and the size
0:03:09of face
0:03:10as soon as well oscillators are you know s then d s equals d i
0:03:15and is monotonically decreasing and synchronization is achieved
0:03:23after all this technical detail
0:03:27we are now able to see the bigger picture
0:03:30we guaranteed synchronisation
0:03:32for arbitrary network conditions
0:03:35for arbitrary individual the late
0:03:38and sarcastic interactions
0:03:42did not give the guarantee
0:03:44and that and out that to better include those things for applications
0:03:49such as they may connect works
0:03:51robert swarming
0:03:54and network protocols for wireless communications
0:03:59thank you