 Okay, hi everyone. I'm Shannon and I'm going to speak today about my PhD research that I've been doing at the University of Western Australia and What you're looking at right now are called murmurations. They're starlings and This is a flock But in collective motion These are also flocks This is a flock of Ecoli That's not moving and this is a flock of people and Given that we see similar sorts of behavior in Something as simple as a bacteria as we do in ourselves and we like to think of us as being somehow superior to Ecoli We'd like to explain this So the thing is is it's not The complexity of the entity that's creating this macroscopic phenomena. It's the complexity of the interactions and Vickshack was the first to look at modeling these as self-propelled particles and he and his team kind of spurred an entire industry of Trying to find new regimes of behavior and understand the Changes in these behavior depending on certain parameters. So he uncovered similar behavior Falling when his particles followed a really simple rule. So all these particles were meant to do is Align with their neighbors. So they adopt the average directional heading of everyone around them within some radius and That was enough to produce dynamics like this Cousin Comes from a more biological background So they took this model and they added some attraction and some repulsion and a blind zone to make it a little more realistic Both of these models uncovered stable regimes of behavior vortexing and Polarization and as first order Langevin equations once these states have been reached they persist So they don't help me in explaining Yeah, it might take a while They don't help me in explaining this sort of behavior This is a bait ball. These are mackerel and they're being attacked by a tuner from below and Seagulls from above and these are reindeer below being hurted by people and this is Budgerigar's and there's falcons in the background there and these predators are driving the dynamics. It's the self-preservation that Is really decide defining how these particles move and so this makes us think that Yes, self-preservation is is more what's going on here than cooperation and In light of similar observations So in light of similar observations Hamilton proposed the notion of a selfish herd and to illustrate this idea he Used a one-dimensional toy model of frogs sitting on a lily pond's edge And there was a snake in the middle of the pond and the snake would emerge randomly and in the life of whoever was nearest so these frogs would start jumping around and trying to improve their odds of survival by reducing The area that is inherently theirs The two-dimensional analog of this is the Voronoi space that was explained by our first speaker So I won't go into too much detail. Just say that so this shaded region is the area In which if the snake were to pop up here, this guy would die Around the edge these particles on the convex hull here have an infinite area and that's not great computationally for us and it's also not particularly biologically Reasonable so we're gonna bound each particle by some sort of you can think of it as a vision radius of the prey or an attack radius of the predator and Voronoi spaces pop up everywhere in nature where things are competing for space or growing from some sort of seed so following on from Hamilton people have Proposed a variety of different selfish movements and mechanisms for their part of their self-propelled particles to move In general we require three things of our selfish model. We would like them to be biologically plausible We would like them to be statistically beneficial to anyone that follows the rule and We'd like for them to result in a compact aggregation So a lot of what Hamilton's work was trying to show was a reason for People being species being gregarious in the first place. Why would things bother to live with each other? When you're depleting resources So they're trying to explain why these gregarious species evolved in the first place and Here I'm just a couple of these so Really simple single nearest neighbor and K nearest neighbor in general so particle moving towards just simply moving towards the average of then K neighbors That uses a topological Network of interactions the Vixek in the Cousin model that I mentioned previously both use metric zonal neighborhoods of interaction the Hamiltonian model Asks that the particles instead move into the space created by their nearest neighbor and their neighbor's nearest neighbor so it's those frogs that are jumping into the space and The local crowded horizon maps all particles onto a circle centered at the individual of interest and the size that those particles occupy on The circle is a function of their distance to that individual that they move towards the densest region So both of these to use a visibility network where some particles are just occluded from vision But otherwise all are visible I'm going to use a Voronoi Jewel for my interaction network. It's the De Launay triangulation or the mesh that was mentioned previously To me and to us it makes sense that if the Voronoi Space and the very Voronoi polygon is what you're defining as your domain of danger, and it's the thing that you're interested in then it also defines what you care about in terms of Who you interact with the problem with these models is None of them explicitly look to minimize that space So moving towards your single nearest neighbor does not necessarily Reduce that domain of danger In fact, it can make it a lot worse. So we want to improve on that our movement rule Takes the current Voronoi polygon and samples around the particle Recalculates the hypothetical area that you would have should you move in that direction and then we build a landscape with these hypothetical areas It's a potential and so just as a ball would roll in the steepest direction down a hill Our particles are going to experience a force in the direction that best improves their domain So two qualitatively different particles here One on the periphery. So it's got an infinite, but we've bounded it still. It's got a very large area And it's got a really simple goal. So it's got a really simple landscape It's sloped and it would like to move inside that flock This guy has a more complex landscape He's sitting pretty with a really small domain and he'd like to maintain that certainly doesn't want to make it worse So he's got a really high potential in areas where he's going to open that triangle up and expose himself In this direction in this direction So what this is is it's an an intuitive understanding of space Which I think is a biologically reasonable assumption that we have an understanding of the space that belongs to us We know when we're invading someone else's personal space It's also an understanding of the consequences of motion. So I know what will happen if I move here I understand that I'm reducing or improving my space Okay So we take this force and we incorporate it into really simple Newtonian update mechanism with an Euler-Marriama Integrator we also have some dissipation and some stochasticity Okay, so Let's see how we go. These are the typical Metrics that are used to assess Selfish networks and the behavior of selfish models Essentially we would like two things we want the majority of our flock to benefit and we would like those that do benefit to Benefit well certainly more than random motion and preferably more than everyone else's model so In the first metric we do More of our flock benefits from following this rule our PDF is shifted to the right good the relative Predation risk which is essentially a measure of how much an individual stands to gain is also improved. So if you can't say this best-case scenario of previous models was about 37 Analysis almost double that so we're doing good in there. We've got Biologically plausible and we've got statistically beneficial for the flock. All right, so let's see how this goes Loading so this is a simulation that I've run. I've initialized my particles randomly in a space this Circle gray circle that you can see here is just an indicative vision range for one particular particle and What we say in the simulation you might have to believe me on that We'll see if it loads is definite aggregation. We see it in the Danger domain of each individual reducing we see nearest neighbors. Here we go. Thank you And Neighbors are reducing we can also look at global measures such as the area of the convex flock It's shrinking. So this is a Before and an after and we've aggregated up here. This is just a zoom in of this and these two do eventually come together So that's good. I've got a good selfish herd model. Yay. What I now want to look at is Once they've aggregated once we've got that reason for being gregarious in the first place. What's going on now? so Continued being selfish once you've kind of exhausted those benefits All right, so what I'm going to do now is zoom in on This motion and we're going to look at what it looks like in here this bit that you've just been watching So we look like a swarm swarm of midges show a fish not much order Correlation certainly but no much order and This is polarization an order parameter in red Rotational order parameter dilational order parameter and this is comparison to data. It's qualitatively similar We look like a swarm of midges. Okay, but I wanted a flock. I really wanted order I wanted an excuse to look at those YouTube videos all day So the problem with these is that they're not particularly bright They will allow their momentum to move them from a good position into a really bad position and they'll keep going And I'd like for them to be a little smarter than that have a little more foresight and Understand the future a little bit better So we're gonna do everything we've done. We're gonna do it again. Okay, so We're gonna take a higher order model. We're now instead of just positions We have an understanding of the velocity of our neighbors as well and we can track that our neighbors forward and understand How our Voronoi network evolves and how the force that we're going to experience Changes as we look further and further in time. So for this particle that's on the boundary He has still his really simple Sloaked landscape to begin with move inside that flock It's becomes really steep gradient when there's a great deal to gain and he actually has that opportunity in the next time Step to get inside the flock and then this landscape Starts shifting and transforming it wants to keep him. It's saying don't go too far Start turning now and fight for good position within the flock and we wait these forces so that Current things are more important And the future is not as important but still present We also include some repulsion as Cousin did for the biological plausibility and This sorry is my flock It's It's ordered there is local order there's rotation so we can see improvements in polarization and in the rotation this is counter and clockwise motion Definite aggregation definite benefits statistically by following this rule, but now we get order We can look at how that forward foresight changes the polarization and the rotational order This is how far we look into the future on the x-axis there and as we look further We see a definite transition into a higher ordered state We've moved from a swarm or a shawl into a school into something That's a bit more biologically plausible and is a bit more similar to something that we'd see in nature So increases in both rotation and polarization So I guess viewing viewing the ability to foresee future configurations as some sort of pseudo intelligence It makes sense that perhaps the small brains of midges are not capable Of this and so are restricted to just aggregating and swarming and maybe flocks slightly more intelligent birds Can be a little more ordered and can flock so Hopefully, I've convinced you of two things that If you're gonna use a Voronoi Network or a Voronoi as a metric for your danger domain Then you need to actively try and minimize that to get a good selfish model or at least a better selfish model And also that looking to the future can transform a swarm into a flock Yes 2d so A swarm of midges certainly Hovers in 3d, but the starlings tend to flock in sheets. So At the moment, that's my justification for 2d, but we're gonna look to move it to 3d The area the sample area No, these are point particles and there's all sort of catastrophes happening in the air with collisions and Passing through each other. Yeah. So at the moment, these are just particles Well, when I introduced the flock like motion, I had a repulsion in that. So But it it wasn't It wasn't rigid. It was just a one-on-R potential for the repulsion. I don't I don't Yes. Yes, I'm sure I could but To be honest, there's other things that I think I'll end up doing like the extension to 3d I'd also like to maybe look at some game theory and Really look at the the selfish Component more so than the the medium or yeah Yeah, but I'm I'm I'm sure it plays a big part in reality, especially for something like a midgie Getting blown around. Yeah Previous models. Yes, mine's inertial Yes. Yeah Mine is a force that that they experience that changes their velocity in that way. Yes Yeah, but yes previous models were purely dissipative and they would just Immediately Exactly. Yeah. Yeah, sorry We build a potential based on Areas hypothetical areas So so yes, yeah, and that's the minimum. So and it's not always It's not a global minimum. It's a local minimum. So Yeah, they'll continue to update in small time steps