Complex Systems Summer School 2022

Humans are notoriously bad at objectively assessing their own abilities and skills, sometimes overestimating and sometimes underestimating them. Research has shown that the objective skill level of an individual correlates with the error in skill assessment. This is often referred to as the Dunning-Kruger effect. While this phenomenon has been studied across several diverse domains of knowledge in individual independent settings, relatively few studies have examined how people's abilities and perceived competence may vary over time and with social interactions. Here, we design an agent-based model (ABM) to explore the temporal evolution of agents' objective knowledge and perceived competence in a social setting allowing for knowledge exchange. We express knowledge using strings of numbers representing known knowns, known unknowns, and unknown unknowns. Agents interact randomly with one another and decide to exchange bits of knowledge and assess their perceived rankings and self-improvement based on these interactions. We show that all agents tend to overestimate their social rankings but that the strength of this effect depends on individuals’ objective skills. This relatively simple model captures data patterns that would be expected based on the Dunning-Kruger effect.

Current cutting edge artificial intelligence systems requires large amounts of computing power and correspondingly large amounts of energy. Furthermore, silicon-based systems may not be optimal for tasks where outputs are physical influences on the environment, for example in the form of forces [1]. This motivates the quest for alternative learning systems that may both provide better energy efficiency and more appropriate outputs for a given task. One potential class of candidates, among others, are mass spring systems. Spring systems have already been used in a wide range of artefacts throughout history, from dynamometer and clocks to automaton and vehicles, and they constitute one of the first types of analogue computation mechanism. With current breakthroughs in physical learning algorithms we may now unlock these system’s potential to learn, and be able to effectively optimize them to achieve both better energy efficiency and more appropriate outputs for multiple kinds of tasks. A range of physical learning algorithms exists (see [1] for a recent review), that may be used for this purpose. Here we focus on the so-called Agnostic Equilibrium Propagation (AEqprop) algorithm [2] which previously has been applied to Hopfield networks, and apply it to simulated elastic (mass-spring) networks. We demonstrate that such systems can learn multiple boolean functions.

As the human presence in space grows, collective action and global coordination will be required to ensure that the environment beyond Earth can be sustained and shared for the benefit of all – a “commons.” Already, a plethora of so-called satellite constellations have hampered the work of astronomers and of ordinary people who wish to enjoy the night sky. Human-made debris in space – “space debris” – is threatening the integrity of satellites, the health and safety of crews on board the International Space Station, and the progress of human exploration of space more generally. In the most extreme scenario, the accumulation of debris can lead to Kessler Syndrome, in which the density of objects in low Earth orbit becomes high enough that collisions between objects cause a cascade with each collision generating even more space debris, thereby increasing the likelihood of further collisions. Given these hazards, it is important to study space debris in low Earth orbit through existing human-environment frameworks to ensure long-term sustainability of these global commons. Here, we study the physical and socioeconomic processes affecting the levels of space debris in low Earth orbit. Specifically, we model the proliferation and management of space debris in low Earth orbit as a function of global governance and technological innovations in debris cleanup. We then test the impact of proposed improvements to governance outcomes and cleanup technologies to test whether these methods can adequately prevent a tragedy of the orbital commons. This work will help inform future studies of the sustainability of the human presence in space.

Metabolic scaling theory predicts that several physiological properties of animals scale with body mass. Similarly, the cognitive capacities of animals depend on their physiology and it is known that measures such as brain size and neural connectivity scale with body mass too. Perceived time is a sensation generated via cognitive processes, which are little understood. One of the consequences of metabolic scaling theory is the observation that the number of heart beats per life time of mammals is roughly conserved across body mass. This rises the question, whether the total perceived life time is conserved too. In this preliminary article we propose a simplified model of the brain that provides us with a natural definition of time perception. We explore how perceived time scales as the modelled brain size changes, according to known cognitive scaling laws. Based on our literature review we identified the return time as an important parameter that could potentially dictate the rate of time perception. Our empirical simulations show that for recurrent neural network architectures used in the past, this parameter does not scale with size. In the future simulations on larger neural networks may therefore be required.

Many real-world systems consist of agents that move through space, interact with one another locally, and have individual objectives. We study a modeling framework to explore these features in conjunction. In particular, we consider dynamic networks of nodes moving on a periodic space and connecting via a sharp threshold on spatial proximity. In addition, nodes each have discrete types, and have individual objectives relating the types of the nodes that they are connected to. Here we particularly focus on the homophily objective where each node tries to acquire a minimum number of neighboring nodes of same type. The level of objective-satisfaction in turn influences the motion of nodes by determining their rate of spatial diffusion. These dynamic spatial network models can be thought of as a continuous analogue of Schelling-type lattice models. We study the system dynamics in terms of convergence properties, homophily measures, and the sizes and type-compositions of connected components. We also compare our geometric model with a baseline non-geometric analogue to study the effect of the spatial interactions. Finally, we discuss potential applications of this model and connect it to the general spatial agent based models.

Following World War II, suburban development became the primary way cities adapted to rapid population growth. Suburban development patterns fundamentally differ from how cities had been built for hundreds of years. This modern and efficient creation of static mono-culture development, that experts coined as the ”suburban experiment”, raises questions of fragility and long term sustainability for cities. Given the large scale adaptation of suburban development across the US, it is not clear what implications these policies will have for cities in the long term. There are few efficient feedback mechanism that quickly identify failures in urban planning and therefore we often experience recency bias in our decision making. It can take decades to see the impacts of the policies implemented today. One way suburban development differs fundamentally from traditional city development patterns is the order in which private and public investments take place. Prior to World War II, public spending for infrastructure had to be justified by already existing private investments and equity that would ensure the cost of building and maintaining said infrastructure would be covered though taxation. The suburban development model encouraged cities to rely on debt in the form of municipal bonds to finance infrastruc-ture projects where no private investments existed with the assumption that the creation of infrastructure would eventually lure enough private investments to cover the costs. Unfortunately, suburban development does not appear to cover even the basic maintenance cost for cities and becomes a sunk cost that cities have to deal with in perpetuity. This can be observed in Fig. 1 that is visualizing the operating expense ratio for Lafayette Louisiana, what is noticeable is that older development prior to WWII generates net positive income for cities while newer suburban developments have a net negative financial impact for cities. This finding brings with it a host of questions both economic and sociopolitical. Currently, our interests are to use the complexity approach in tandem with data science methodologies to conduct a longitudinal study of cities to determine if any trends emerge or to find causal links that will point to the possible financial futures of cities based on their development patterns up to the present.

Under what conditions does a “sustainable” society emerge? We explore sustainability as an emergent phenomenon of a system whereby a sustainable society is one that persists in the face of multiple and variable shocks. We are especially interested in the role that within-community knowledge transfer plays in facilitating different forms of resilience that can yield sustainable systems. The role of knowledge transfer in shaping resilience outcomes is well documented, yet relevant knowledge is likely to facilitate resilience only when communities have sufficient resources (natural or economic capital) to translate that knowledge into practice, especially in the face of multiple and multiple types of shocks. To explore the interaction between resources and transmissible knowledge on resilience and the conditions under which sustainability consequently emerges, we design an agent-based model (ABM) in which agents are endowed with a combination of resources and knowledge. Resources are gathered and consumed during each time step. External shocks of varying intensity deplete agents’ resources and occur probabilistically over the life of the agents. Relevant knowledge derived from experience of previous shocks protects agents from potentially catastrophic effects of future shocks. In addition to accumulating knowledge because of surviving a shock, agents can also gain knowledge by learning from cooperative, more experienced neighbors, though the sharing of knowledge imposes an opportunity cost. We explore the consequent tradeoff between knowledge and resource endowment in a society and the conditions under which variations in these endowments yield societies that persist in spite of varying magnitudes, sequences, and frequencies of shocks. Parameters for experimentation include: shock probability, knowledge gain from cooperative sharing, willingness to cooperate, consumption rate, life expectancy, and resource regeneration rate. We view this as a baseline model for thinking about societal persistence as an emergent property of a system. We propose several extensions to this baseline model. Specifically, we hope to differentiate innovative versus traditional knowledge (which may aid in a potential phase transition), and replace cooperative knowledge sharing with a market (trade) based approach. Additionally, we hope to introduce various forms of shocks, whereby only certain types of knowledge are relevant for protecting agents from shocks.

Multi-level model of eukaryotic and prokaryotic GRN evolution. Over the course of generations, mutations occur in the genome, which in turn change the interactions between transcription factors and binding sites. Mutations that increase the rate of reproduction are selected for. We keep track of (a) the specificity of the TFs and (b) the complexity of GRNs over the course of the evolutionary process and study the relationship between the two. Eukaryotes use more complex gene regulatory mechanisms than prokaryotes. However, the eukaryotic transcription factors (TFs) are less specific with respect to their binding targets than prokaryotic ones. How eukaryotic gene regulatory networks (GRNs) that use less specific TFs manage to function reliably is still not well understood. We propose to fill this knowledge gap using an agent-based model of minimal cells with GRNs resembling those of prokaryotes and eukaryotes. In our multi-level model, each cell has a genome that gives rise to a GRN encoding a cell cycle. We evolve populations of these two types of cells to accomplish various regulatory tasks, and track the specificity of the evolving TFs as well as the complexity of the evolving GRNs. Our goal is to study the relationship between the complexity of GRNs and the specificity of their TFs. For this purpose, we will employ known methods for measuring TF specificity and devise measures of GRN complexity. This project will enable us to explore mechanisms employed by eukaryotic cells to accomplish complex behavior and to compare it to the regulatory logic used by prokaryotes.

This project explores Games on a Network, specifically focused on competitions among organized criminal networks. We identified and investigated different norms and incentives of organized crime rings, and propose a network generation procedure based on the findings.  In our model, organized criminal networks (“gangs”) can create periodic value from the controlled territory.  More members operating in a fixed amount of territory leads to a higher value extracted per period.  On the flip side there is a cost to increasing gang size, determined by the gang’s profit distribution policies. Different monetary distribution policies within the gang results in a variety of network structures. Using the generated network structures, we created an agent-based model to simulate the competition between two gangs. Early exploration reveals that even a simple combat model over two networks can produce rich, sensitive and hard-to-predict dynamics, which may have implications for network resilience and group competition dynamics in general. Our code can be found here.

Over the past few decades, it has become increasingly evident that a period of stagnation has overcome the U.S. Congress to the point of being ineffectual. Interestingly, this stagnation extends even to policies that, according to polling data, are highly supported by the American public with the most prominent ex-ample being a lack of firearm-regulating legislation (e.g., federal background checks) which has majority support among the American electorate [12]. This raises the larger question of what influences, or incen-tivizes, voting behavior in the U.S. Congress? Prior political research on this issue suggests several theories on lawmaker behavior that may explain voting outcomes, yet we still do not have a clear understanding of incentive dynamics that might drive voting behavior among voting agents themselves. In short, we seek to address this gap by arguing that given the increasingly competitive and complex incentive structure that politicians, both on the left and the right, must navigate, a complexity perspective might be useful in uncovering some of these mechanics. To do this, we are interested in building an ABM to simulate the voting of representatives in the U.S. Congress based on a list of dynamic incentives.

Biodiversity is important to the functioning of ecosystems. Correlated with both the productivity of an area and the amount of ecosystem functions that can be supported, high biodiversity increases the resilience of an ecosystem to changing environmental conditions. Typically ecosystem complexity is mea-sured as a function of the network structure of the interactions between species within the ecosystem. However, all these approaches require a lot of granular data and are hard to calculate for many ecosystems and of limited use to compare between ecosystems. Here we present a data-driven, top-down approach to quantify ecosystem complexity based on global species abundance data. Drawing from methods in devel-opment economics, we define the Fitness Complexity Index (FCI) and the Genus Complexity index (GCI). We calculate the FCI and GCI on two different datasets, for the continental US and Europe. We compare our measure with species abundance data, a widely used proxy for ecosystem complexity. Ecological mod-els have identified several key drivers for species diversity within ecosystems, notably habitat complexity and temperature. We show that temperature has a positive effect on he FCI, and population density a weakly negative effect. Further, we construct the “genus-space” that quantifies and visualizes the relat-edness of species. The genus-space is a network where the nodes represent genera and the links between them represent the similarity of these genera in terms of the ecosystem conditions they require. We rep-resent an ecosystem as the group of nodes that represent the genera present in it. We hypothesize that under changing environmental conditions, such as rising temperatures due to climate change, the chang-ing species-composition of ecosystems can be modelled as directed diffusion in the genus-space. Our method is inspired by the theory of Economic Complexity that has been developed to quantify the ability of national economies to manufacture sophisticated goods. It is able to predict the economic development of countries, as well as the development of the export basket countries, i.e. the products the countries pro-duce competitively. On a similar note we hope that our method offers a way to predict the ways in which genus compositions of ecosystems will develop, especially in the light of changing temperatures due to climate change.

Despite decades of origin of life research, we still do not know how prominent features of life - complexity, self-organization, and open-ended evolution - emerged in a prebiotic environment. Previous computa-tional studies simulating how these features emerge have often neglected the role of the environment in how chemical systems complexify, develop structure, and continuously adapt to new situations. A chang-ing environment would allow for new opportunities for adaptation, even in a pre-Darwinian chemical evolutionary scheme. Dynamic environments, such as dry-wet cycles and day-night cycles, were likely relevant during the origin life because they affect the formation of new chemical species and also increase the complexity of the existing reaction network. We propose a model where starting from a seed set of molecules; we generate a growing directed hypergraph representing an open prebiotic chemical reaction network by implementing realistic chemical reaction rules while systematically varying reaction rates to simulate a dynamic environment. We start with a fixed concentration of the seed molecules and explore how reaction rules and propagation of concentration apply feedback to the growth of the hypergraph of the prebiotic reaction network. Currently, we have implemented static but randomized reaction rates, which are to be turned into time-dependent quantities to capture the dynamic environment in future work. We present a study of the structural properties of the reaction network obtained through our simulations. We hypothesize that a changing environment will expand the space of possible reactions and can potentially lead to the emergence of life-like properties such as autocatalytic cycles, regulatory feedback, persistent complex molecules, modularity, compartmentalization, and memory. Finding evidence of many of these features would indicate that dynamic environments played an important role in the origin of life.

Aging is a complex process that can arise from multiple attributing mechanisms, yet there are no theories that can unite these mechanisms. While aging is generally viewed as failure or deterioration of various processes both at cellular and organismal level, at times these processes seem disconnected. However, in reality there may be a general theory connecting these age-affected processes together. Life history theory (LHT) is typically applied to organismal-level physiology and describes all traits as either involved in growth, reproduction, or maintenance. We theorize that the same principles can be applied to cell biology to predict and unify age-affected processes. Furthermore, we hypothesize that the majority of age-affected processes belong to cellular signaling pathways which sense the environment and are responsible for cellular maintenance. We will construct a network of pathways most affected by aging. The components of this network are identified by performing ingenuity pathway analysis (IPA) on differentially expressed genes in multiple tissues of young vs old mouse tissues. We will analyze the structure and features of this network. Particularly, we are interested to see if there are any overlaps with pathways identified as maintenance-associated pathways. To identify the maintenance-associated pathways, we perform IPA on the differentially expressed genes in multiple tissues of hibernating squirrels since according to LHT, hibernating animals primarily utilize their resources for maintenance. Our goal is to identify the most important and susceptible nodes in the aging-pathways network and identify its relationship with maintenance pathways.

The emergence of paid online pornography in the 1990s has had an everlasting impact on a whole industry. This business model was later supplanted by a myriad of online tube sites providing instant and free access to millions of adult videos. This shift in how online pornography is consumed has led to the rise of major players, concentrating most of the traffic. This development allows for a transdisciplinary analysis of the content made available on these platforms spanning many domains: sociology, history, legal studies, feminist studies, psychology, etc. While sociological studies on pornography are on the rise, to our knowledge, few papers so far provide a quantitative approach to adult content online. Despite the democratization of online pornography, this subject remains taboo for most consumers. Moreover, this shift to free and massively available online content has drastically changed how pornography is produced. Producers need to come up with new ways of generating money, and actors are subjected to degrading working conditions. The uberization of society is also observed in the pornographic industry, where many creators produce and publish their content independently on paid platforms such as Onlyfans. For all these reasons, a quantitative study of online pornography raises a multitude of potential research questions for future work, for example: What is the demographic profile of content creators? What makes a video popular? What are the trends in online pornography, and is there a shift toward more violent content? To better understand the bigger picture of online pornography, we base our study on data provided by tube sites to embed videos and generate incoming traffic. This project uses data analysis and network science methods to get a first overview of the data collected.

Flocking in birds is a well-known example of collective behaviour that emerges from simple individual-level rules. Mixed-species flocks are particularly interesting since these involve multiple bird species foraging on insects. These flocks exhibit highly complex flocking behaviour, in part owing to the interspecific heterogeneity in strategies and interactions. The constituent species can also be classified in terms of their roles in leading the flock or warning other species against predators. Many field studies have analysed the structure of these flocks as well as the behaviour of different individuals within them. A range of mechanisms have been put forward to explain the observed structure of such flocks, which could vary considerably depending on the flock size as well as the environmental context. This leaves enough room for testing variation in flock composition and individual-level rules that allegedly affect flock formation. This report explores the space of bird and insect behaviours to inform agent-based models of these flocks. Our preliminary agent-based model demonstrates flocking dynamics based on simple rules that take into account bird and insect densities around individual birds (See Figure). We propose ways of building more realistic agent-based models that use rules for avian vocal signalling as well as insects’ life history, with particular examples from ant-following flocks. We conclude with aspects of such flocks that are not easily amenable to modelling, and suggest approaches that combine results from recent studies as well as related systems.

As society aims to mitigate climate change and biodiversity loss, ecologists are seeking mechanistic descriptions of how climate warming is expected to alter communities and ecosystems. The Metabolic Theory of Ecology (MTE) offers a first-principles explanation of how temperature drives a suite of ecological processes via temperature's universal constraints on organismal metabolism. Interestingly, the temperature dependence of photosynthesis is weaker than the temperature dependence of respiration, such that the consequence is that under warming, heterotrophs need to consume more biomass to meet their metabolic demands than autotrophs can produce. This threatens the very structure of food webs. However, it is unclear how spatial dynamics interact with temperature's effect on trophic structure. Island communities offer an intriguing system for studying this dynamic. Here, we combine MTE with elements of Island Biogeography Theory (IBT) two of the most fundamental ideas ecology, to mechanistically describe how warming is expected to influence food web stability in island communities via metabolic changes. Going forward, we will investigate how two important parameters in IBT - distance from mainland and island size - mediate temperature's effect on food web dynamics. We will then demonstrate how, under climate warming scenarios, varying levels of island area and insularity have the ability to dampen warming's effect on trophic stability. Our work bridges the knowledge gap between laboratory experiments and more complex ecosystems, hence providing insights towards more realistic predictions of community dynamics in a warming world. 

The concept of self-sustaining closed ecosystems has long been of research interest due to their potential insight into fundamental underlying ecological processes and as a means of supporting future space travel. This working paper provides the review of such case studies of closed ecosystems. Some were successful at maintaining functioning ecosystems while others collapsed quickly. We explore these examples to identify how they differ in their designs and scales, identifying what aspects are better at sustaining persisting communities. Further, we consider the simplest model for a closed ecosystem, exploring ways to incorporate underlying ecological processes. We thus propose future directions for this area of study. Notably, we conclude that whilst a deterministic approach (aiming to recreate ‘perfect’ conditions to support a defined selection of organisms and processes from the onset), is important for achieving necessary recycling systems, this is alone not enough to allow for long-time scales. Ecological concepts of biodiversity and redundancy may also be necessary to protect against local extinctions or population decreases that may result in a network breakdown in ecosystems.

The transmission and evolution of pathogens is mediated by the spatial distribution and immunological diversity of the host population. Among others, these factors influence the risk as well as the size of potential outbreaks. Understanding the epidemiology of contagions in spatially resolved settings with heterogeneous immunological landscapes is therefore of great im-portance for effective pathogen management. However, the combined impact of immunological diversity, spatial heterogeneity, evolution, and transmission is poorly understood and requires a complex modelling approach. Here we offer a principled, flexible framework to explore evolu-tionary epidemiological dynamics in spatially heterogeneous settings. Heterogeneity is modelled by initializing a diverse host environment on a 2D grid (Figure 1). We devised two complemen-tary models that respectively capture the fine-grained, path-dependent nature of transmission chains, and the average epidemiological behavior. Our preliminary results suggest that, under diffusive epidemic dynamics, vaccine-resistant mutants are more likely to emerge and establish when immune types are well mixed rather than spatially clustered.

Microbial ecology has traditionally used taxonomic diversity markers as a proxy to study community assembly, diversity-functionality relationships, and structural properties such as robustness and resilience. However, recent advances in  the genomics characterization of these communities have evidenced the fracture that exists between inferred taxonomic diversity and actual functional diversity. Additionally, evidence in experimental ecology point to a broader view of the concept of community, where taxa and the chemicals they can produce and consume are intertwined. We hypothesize that these two facets (microorganisms and their metabolic products) feedback on each other non-linearly and that this interaction determines the overall properties and functionality of the community. Multilayer networks have been proposed as a tool to uncover interdependence between the multiple facets of the complexity of ecological communities. Here, we propose a multilayer network-based approach that combines microorganisms and their metabolic products. Initially focusing on the interactions that determine how perturbations spread in the system, we aim to uncover the role that both functional and taxonomic diversity plays in determining the community structure, as well as their non-linear feedback relationship.

Collectives take many forms across many disciplines, ranging from ant colonies, to swarms of robots, to neurons, to human social movements, displaying a multitude of ‘intelligent,’ adaptive behavior. The measurement tools available to make observations about collectives dictate the kinds of questions that can be answered about this adaptation. Across a plurality of disciplines concerning themselves with collective behavior, affordances and information theoretic approaches have arisen as questions and metrics of significant interest. We suggest that a budding multi-disciplinary science of collective adaptation might take the quantification of affordances with information theoretic measures as a preliminary empirical step toward a robustly interdisciplinary endeavor. 

Nations implement different policies aimed at influencing the behavior and socio-economic situations of their residents. Some of these policies may be more or less functional in creating the intended incentives and effects. The question of what kind of policy features are favorable and unfavourable is however difficult to answer. Here, we propose the use of methods and perspectives shared between dynamical systems, evolutionary computing and artificial intelligence to interpret features of a set of policies. We produce "incentive landscapes" akin to dynamical, fitness and loss landscapes, based on specific policies and explore the structure of said landscapes. More specifically, we generate these incentive landscapes through a function that jointly maps the policy and the socio-economic state space a person may inhabit to some economic outcome and we aim to automate the detection of features that may be functional or dysfunctional. On such landscapes, agents are incentivised to move according to their desires for features like income, cost and freetime. We here assume that agents are motivated to improve their economic situation and disincentivised to worsen it and suggest an agent based network model to explore their movements on incentive landscapes. 

This is a cautionary tale about a model gone wrong. To be more precise, it accounts for how the Schelling model, a simplistic agent-based model from the 1960s, rose to fame with the support of countless complexity scientists and spawned a research line that relies on an implicit assumption that racial prefer-ences of the residents drive racial residential segregation. The reception history of the Schelling model is rich with examples of how simplification, in itself a necessary feature of human survival, can lead us astray rather than guide us – if we start off from false premises.

This work is not a comprehensive literature review; rather, it showcases, with the Schelling model as an illustrative example, how getting distracted by the beauty of simplicity and failing to account for the messiness of reality can bring significant damage to humankind – and even more so when the system that is being modeled manifests intersectionally interwoven inequalities. This work is, therefore, not a manifesto against modeling – it is a call to approach modeling with thought and care and to adopt models with full consideration of their assumptions.

We argue, first, that the Schelling model is inherently an actively obfuscating one, and second, that the scientific community has so far failed to adequately shed light on the obfuscating nature of the Schelling model. To paint a comprehensive picture, we first frame modeling as abstractive process with real-life consequences. We then examine the status quo of debates on racial segregation in cities, as well as the historical context in which the Schelling model was conceived. We then take a close look at the reception history of the model up until today, with a particular focus on complexity science teaching. We conclude by giving some recommendations to help make future engagement with the model enlightening rather than obscuring.