 V svoje tukle. Kako. Natural Timer. Perfett. Ok. Good afternoon, everyone. So, today talks has a very long title. Because I want to present to something scientific, but also a novel tool that we developed. And all the work has been done together with Doctor Thomas Bose and professor James Marshall at the University of Sheffield within the ERC project diet. And the main topic is about psychophysical laws, and psychophysical laws explain the relationship between stimulus intensity and its perception in the human brain. And this type of relationship has been observed for a large variety of stimuli, and later scientists observed that not only human have responded to this type of psychophysical laws, but has been observed also in mammals, fish, birds, insects, and more recently scientists noticed that also individual cells like the slime mold might actually follow this type of relationship. So, this is particularly interesting because we can observe this psychophysical laws also in absence of a brain, so in various type of organism. And what we do here is to check if another type of organism follow these psychophysical laws. And the organism that I will watch is the superorganism. And for superorganism we refer to the colony of insects. So, if we think about the insect as the organism, the superorganism is the collection of them that they work together. And if we watch the colony as a unique entity and how information spreads within the colony, then we can try to start to draw parallels between the superorganism and how information spread in the brain and in between neurons. And this parallel has been already observed and described in various work. We are not the first, but we bring ahead this idea and we follow this line of research. And in our case we investigate the psychophysical laws, as I said. And as reference model we use the on-a-b nest size selection. And this model explains how on-a bees select their future nest. This process happens in spring in European bees. And when the colony reproduces, the old queen leaves the nest to a temporary place together with some thousands of scout bees. And the bees will need to find quickly the future nest location. And they are exposed to danger, so they need to find quickly a good solution and also a consensus solution. They don't need to split. And how they do that, scout bees will explore the environment and might discover potential nest size in the environment. And bees that discover a place, a good potential place will return to the swarm and will actively recruit other scout bees to the woggle dance. Then when two bees committed to two different nest sites and counter with each other, one delivers stop signal to the other and the one that receives stop signals will revert to an uncommitted state. Finally, bees will spontaneously abandon commitment for poor quality nest sites. So, from field observation, biologists observe that the bees managed to make this collective decision for type of individual bee actions. But how the colony selects the best option? I can explain you these through an example in which we have two nest, the blue and the red, and we label as green the uncommitted bees. And we can write this for action in a more formal way in chemical reaction like form. So, if you have an initial state, uncommitted, and a final state that is commitment for the blue, and that happens with a certain rate. And so on happens for the red nest and upon encounter of a blue and a green, with a certain rate, the blue will recruit the green. And so on for cross inhibition and abandonment. And bees, before getting committed, they visit the nest and estimate the quality of the nest that we can label as v1 and v2 for the two nest. And the key idea is that the bees will modulate their action as a function of the estimated quality. So, they will do more frequent discovery, recruitment, crossing inhibition for better nest. And that will steer the system toward the convergence toward the best option. So, the idea here is to parameterize, let's say, write all this rate as a function of the quality vi. This is the parameterization proposed in which everything is dependent on vi and we introduce two terms. The term k that modulates the frequency of individual action and the term h that modulates the frequency of signaling. So, we can study our system in this ratio of signaling over individual behavior with a single parameter. And so, what we do is to analyze this model, this work is a theoretical work. We just analyze the model that comes from field of observation to see this agreement with psychophysical laws. And we do the analysis of the model in the form of the master equation that includes stochastic fluctuations. And here I pose a little bit the presentation because I will show you the tool that we developed that allow us to do this type of analysis. So, the tool is called MUMOT, multi-scale modeling tool developed in our group and it is written in Jupiter that is a Python framework and Jupiter allow you to write notebooks. And they are somehow similar to mathematical notebooks in which there are cells that can be dynamically run and you can interact with the cells with the various cells, with the commons and it's presented as a website that you can run in your browser. Yeah, for lack of time, I will not run online the cells but it's already a pre-run notebook that anyway show the main functionalities. So, here we just loaded the library and here the idea is that we want to write a model that in this form of chemical reaction and in fact, to make it bigger, James. I don't know how to make it bigger. So, the tool allow us to write and analyze any type of model that can be written in this form in which there is an initial state, a final state and a constant transition rate. And this is particularly useful because usually biologist, field experimentalist often build up their model in this form. They see a change of state with a rate and so they can take the model derived from observation and put inside this tool and make a first analysis of it. So, here we write the model with the specific syntax and here we parse it. And here we visualize the transition in which we label A and B as the two possible nest and you then commit the Bs. And then once we parse the model, we can show the ODEs. That is done automatically, we have the ODEs system that we can then integrate over time. Here there is a time integration of the ODEs and there are widgets that allow us to modify the parameter and have real time the change of the system. So, with widget you can really play with the model and have a feeling of how things change. And then you can also visualize a vector field that show you in a bidimensional space how the trajectory vary by varying the parameter. Again, with widget you can vary it real time. Then we can visualize also a stream plot with stability point or unstable fixed point, the hollow in the middle. Or we can also run a bifurcation analysis. Here, for example, we see that by increasing the value h that was our signaling, we have a pitch fork bifurcation. And then the interesting part for this study is the SSA that is the Stochastic Simulation Algorithm proposed by Gillespie that allow us to find the approximation of the master equation. And as you see here is a stochastic run in which includes fluctuation due to the finite system size. And if we reduce the system size, we have larger fluctuation and if we increase it, the fluctuation are much smaller, as expected. And then we can use this type of finite system fluctuation to estimate which is the noise around the stable point here for the system size 70. And then finally, you can also visualize a multiagent simulation result in which agents are the dots that communicate on a fixed topology that is indicated by lines connecting the agents. And this is a fixed topology simulation but we can also have a time varying topology in which particle move in the space and only interact locally with the neighbors. This is just a quick overview. If you have more questions, you can find me later and ask more. So going back to the main presentation, we use this tool to approximate the solution of the master equation through the stochastic simulation algorithm. And we did so for studying if our superorganism respond to psychophysical laws, as is in agreement with them. So we systematically vary the decision condition, quality and number of potentialness size to study how they relate to the ability to discriminate so to select the best quality location and how much time they take to make the decision. And we do that to study these three laws, the Weber, the Pierron, and the Ike Iman's law. I want to mention that as been already observed in... something happened. OK, we are back. So yeah, I was just mentioning, I was spoiling, that's why he went away. Because probably in next presentation we tell us that as been already observed that insect might follow psychophysical law, but the study investigated... make the study at the level of the single individual. Instead here, we don't watch single individual response, but we study the things at the level of the superorganism. So now I will go through these three laws, I explain you what they are and if we find an agreement. Let's start from the Weber's law. Weber's law describe the relationship between the stimulus intensity and its discriminability. So I explain you what it is through an example on numerosity. So now you have to tell me which is the larger set that you observe. So I will present you two sets you need to reply. So this is set one and this is the second set. So please raise your hand if you believe this is the larger set. And now raise your hand if you believe this is the larger set. OK. Everybody got it right. This is the larger set. Now, again, a second experiment in which you have again to find the larger set. And these are the two sets. So please raise your hand if you believe this is the larger set. And now please raise your hand. If you believe this is the larger set. OK. ...znači to zelo s..... ...ke barosti je boji nekaj nekaj, in ne mogu... ...zavullitek nekaj nekih nekaj, nekaj neko mi dokonal... ...sega da je zelo naslava... ...ekro mnoj se bi teh inputsε v ropljo v 30. ...eši nekaj vzelo naslava, kako se rašشim. izgledaj najbolj udelj, da sem se izgleda, da je ozvodila ta skupnja, ki je odmah in organizma, je odmah, da je večstvo odmah na stimulost rejnt. Pozolim, bi smo pozolite ozvodil na tjede, in si je ozvodil na zrduzne za stimulost rejnt, tako da je tudi z vrstv. Tudi adjelje tega nekaj izgleda in zančaj. To je tudi, da se bo vse ozvodila. In v izgledanjem sestim sem odvržavljali poslednje kvaliti, zato poslednje kvaliti na zvorma, in poslednjamo odvržavljenje, kako je zelo zelo, da 75% izgledaj nekaj bolj. Vse, ki se vidimo, je zelo izgledanje. In vse, ki se vidimo, je, da je zelo izgleda, The ability to discriminate between two sources improve, we can be more precise with the increase of the br达 Kevum. This is due to the random fluctuation, that we saw before playing with the tool, in which smaller Dvoorme have larger fluctuations and leads to larger number of errors. Then we moved to... zelo se zelo sezatil tjerašnj, ki zelo sezatil vzelo s tem, z tem, in zelo sezatil. In zelo sezatil, da bomo še je zelo sezatil na površenje. Vse razliša se, kaj je zelo sezatil in sezatil na vsezatil. Danes sezatil. Danes sezatil na drugo vsezatil. in tako še je tukaj, da je čakaj, da je začekaj na to zelo in nekakaj bo začekaj. Vsleda. To je začekaj, da je še začekaj in načakaj začekaj na to zelo. To je tukaj, da je začekaj na tukaj začekaj na to zelo, da je zelo in nekakaj začekaj na to zelo. Prvo je to vsebe. In, da nekakaj začekaj na to zelo, zato da srečemo, da je zelo naša trpne. V mojj slim, nekaj zelo, nešto se izvajte vse poživost. Zelo naša se dokončite, da je nisi zelo naša prvne začinje. Zato je to te začinje, od kaj izvajte, zato se naša tez vse poslice vzelo naša poradnja. Zato, da smo pričali, da povedamo zelo naša prvna zelo, in v kąga včinjamo relacij v veči informacije in trajnji čušenje. Prvam, nekaj poloč, nekaj različak na doliča, nekaj je začnega za nekaj zelo, na če je zelo však zelo, da je zelo vzelo, tudi taj tudi doma, ki so pričal tudi tudi tudi, tudi tudi ono ti se zelo vsej doma, nekaj je vsej doma, da je zelo vsej doma, when there are three options and slower when there are six. And this can be described by the fact that the reaction time increase with the amount of information to be processed and can be formally written in this way, where s is the time to process one bit and i is the function of the number of alternatives. And the function can have various forms and that depends on the type of task. And in literature we found that theoretical study on neurological model observed that for this type of task, value-sensitive decision, and best-of-end case, there is a nonlinear increase. So that is what we expect to find. So what we did is to increase the number of possible nest and to measure the time to reach a quorum. This is the data that we obtain that they fit with an exponential curve. This might be scary because you say the system doesn't scale well, although we also noticed that the swarm can counteract this fact by increasing signaling. So by transferring more information, there is a power load decrease, so somehow the swarm might balance this exponential increase by increasing the communication. So with this I conclude. I just want to mention as first thing that this is a theoretical study. We didn't work with real bees, but comes from a model that is derived from field observation. And what we observe is that the emergent behavior of the superorganism may obey through these three laws. I put in red and bold the word emergent because what we see is an emergent property because none of the single individual follow anything that is linked to these psychophysical laws. But what we observe is that the group, the superorganism display this relationship. So we are in front of a form of swarm cognition. And this is part of a larger project. As I mentioned, the lead by James Marshall, the diode project in which we try to find links between various system and find the common motives that explain the system. This is a step forward in this direction in which we link the functioning of the brain to the superorganism that is composed instead of neurons by insects. With this I conclude. Thanks for your attention.