- Introduction [2.5m]
- Key concepts of complex systems [15m]
- Entering the world of agent-based models [10m]
- Real-world applications [5m]
- Final remarks [2.5m]
A biological clock is complex, but a mechanical clock is complicated.
A look at the internals of a mechanical clock.
A watchmaker designed it. It has a specific function. It has a goal.
It may be hard to understand, but if you take the time and look at all of its parts, you can understand the whole system.
A look at the internals of a biological clock (a timing system).
A mess! A bunch of coupled oscillators
"[...] involve great numbers of parts undergoing a kaleidoscopic array of simultaneous interactions." [@holland1992b]
If you look just its parts, you can't understand the whole system.
It's an emergent phenomenon.
It can be thought as an "aggregate agent" ― aggregate behavior of component agents generates behavior of the aggregate agent. [@holland2012]
Boundaries and signals [@holland2012]
It's adaptive, robust, produces extreme events, and is self-organized.
The behavior of each part don't explain how they behave collectively.
Levels of description [@nicolis2012].
In mathematical terms, the interactions of interest are non-linear [@holland2014].
Emergence isn't magic [@wilson2004].
You are dealing with an emergence phenomenon when there is no need to look under the hood [@krakauer2023].
(joke) Power Rangers Megazord.
"Esquece o jovem místico".
Illustrative example: Societies; immune cells.
A society is formed by individuals and their interactions. In this case, we are the agents and the society is the aggregate agent. And, as we know, we shape the society, but the society also shapes us.
Seemingly random behavior can emerge from deterministic systems, with no external source of randomness [@mitchell2009].
See: Lorenz system.
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Like deduction, it starts with a set of explicit assumptions. But unlike deduction, it does not prove theorems. Instead, a simulation generates data that can be analyzed inductively.
Unlike typical induction, however, the simulated data comes from a rigorously specified set of rules rather than direct measurement of the real world.
While induction can be used to find patterns in data, and deduction can be used to find consequences of assumptions, simulation modeling can be used as an aid intuition.
The main objective of this section is to introduce the concept of agent-based models (ABMs) and other important concepts related to modeling in general.
We have to force ourselves to simplify as much as we can, or even more. The modeling cycle must be started with the most simple model possible, because we want to develop understanding gradually, while iterating through the cycle. A common mistake of begin- ners is to throw too much into the first model version—usually arguing that all these factors are well known and can’t possibly be ignored. The modeling expert’s answer to this is, yes, you might be right, but—let us focus on the absolute minimum number of factors first. Put all the other elements that you think might need to be in the model on your “wish list” and check their importance later [@railsback2019, p. 8].
If someone designed this here, they weren't doing well. This system wasn't designed by a watchmaker, but by evolution.
This is the result of a juggling act of billions of years of evolution. There are no specific functions. There's no proposed goal.
You would hate have this clock. You would be late for everything. Its always changing. That's because it's not a clock, it's a timing system.
Figure 2.11. Bifurcation diagram for the logistic map, with attractor plotted as a function of R [@mitchell2009].
See also: @muller2020 .
Agent-based modeling is “naive” (DeAngelis et al. 1994) in the sense that we are not trying to aggregate agents and what they are doing in some abstract variables like abundance, biomass, overall wealth, demo- graphic rates, or nutrient fluxes. Instead, we naively and directly represent the agents and their behavior. We create these agents, put them in a virtual environment, and then let the virtual world run and see what we can learn from it [@railsback2019, pp. 7-8]
Microscopic patterns that accumulate over time, similarly to evolutionary patterns.
Emergence shares similarities with evolution. On shorter time scales, we observe the formation of patterns. Over longer time scales, entirely new levels of organization appear, leading to phenomena that seem unrelated to their origins (e.g., a rock and a human).
Fig. 8. Structural levels in the organization of the nervous system, a reflection of the hierarchical systems that may underlie the generation of higher cognitive functions, including consciousness. Courtesy of Patricia Churchland and Terrence Sejnowski.
As commonly used, the term "feedback" denotes that an action or activity initiated by someone or something sets in motion activities or responses by others which then affect the original source of the activity [@puccia1985].
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"Figure 1.1: Visual, organizational map of complex systems science broken into seven topical areas. The three circles on the left (Nonlinear Dynamics, Systems Theory, and Game Theory) are the historical roots of complex systems science, while the other four circles (Pattern Formation, Evolution and Adaptation, Networks, and Collective Behavior) are the more recently studied topical areas." [@sayama2015].
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By my own experience. Use of ABM in the classroom (Camilo, 2012).
You don’t need to invest in infrastructure to run simulations. You can use your own machine or cloud computing services to execute them.
ABMs can also be implemented in continuous time, but most are designed as discrete-time simulations.
Agent-Based Models (Social Science) versus Individual-Based Models (IBMs) (Ecology) versus Multi-Agent Systems (MAS) (Engineering) == Computer-Based Models.
The universe is under no obligation to make sense to you [@tyson2021].
Joke: You can always use other tools, but know that I will judge you for that.
Simple [@sun2016; @rand2007] or abstract [@sun2016] models versus photograph [@parker2003], empirical, complicated [@sun2016], elaborated and realistic (ER) [@rand2007] models.
Simple model example: Schelling's segregation model [@schelling1971].
We call this the ‘Medawar zone’ because Medawar described a similar relation between the difficulty of a scientific problem and its payoff [@grimm2005a].
Understanding local interactions helps identify potential leverage points or types of interactions that can amplify the spread of a phenomenon. For instance, by analyzing contact interactions, one might recommend mask usage or design specific protocols for tracking and isolating infected individuals. A global approach, on its own, would not reveal these crucial details.
See: SIR model; Lotka–Volterra's predator–prey model.
- Logo (Seymour Papert: 1967
- NetLogo (Uri Wilensky): 1999) (Rand, Unit 8).