Read about the research of the 2021 participants in our Undergraduate Complexity Research (UCR) program.
Minerva Schools at KGI (USA)
Mentors: Albert Kao, Chris Kempes, Mingzhen Lu
2-Dimensional Interactions in the Nutritional State-Structured Model of Foraging Behavior
In order to determine the likely impacts of climate change on biodiversity, there is a need for population dynamics models that can more accurately predict the extinction risks to identify vulnerable species. A better understanding of the ecological interactions driving population dynamics will allow us to build better predictive models and shape conservation policies. The existing models used to determine climate change impact in terrestrial species are simplistic and lack integration of complex interactions within the ecosystems. To better incorporate the complexity of spatial ecological interactions, this project utilizes individual-based modeling to build on the nutritional state-structured model by simulating 2D spatial interactions to model foraging behavior and introducing resource heterogeneity to introduce a climate change impact. Here we show variation in the steady-state populations over time for species of different body masses and how this is impacted through the introduction of resource heterogeneity. It takes around 500 times longer for large body mass species (elephants) to reach a steady state than for smaller species. This 2D model can be expanded upon to incorporate different species coexisting within the same ecosystems, varying resource growth patterns, and incorporating weather differences - to improve further the applicability and prediction of this model for specific species and ecosystems.
New York University (USA)
Mentors: David Kinney
If Philosophers could Draw
Claims about “human nature” have functioned as the logical basis and the cohering principle of most political philosophies since at least the enlightenment. Moreover, they have done so by serving as the rationale for claims of moral equality among humans that were the generative core of enlightenment political thought. Even today, the sediment of those claims is recognizable in the structures of Western democracies. As some developments in modern biology, evolutionary genetics, and neuroscience have threatened these claims by questioning the existence of a coherent “human nature”, they have revealed a foundational precarcity in the philosophical structure of Western states. This project aims both to investigate the extent of the structural damage the demise of these claims about “human nature” has done to liberal democracies and to imagine the composition and consequences of a concept of moral equality not based on claims about “human nature.” Uncovering the signature of “human nature” in Western states involves asking historically grounded questions about the well-covered genealogy of liberal democratic ideas; but it also involves more philosophically accessible questions about ontological priority: to what extent can notions about “human nature” structure political beliefs versus the opposite? While imagining a foundational equality free of the fiat of “human nature” claims is a more obviously philosophical project, it also has an irreducible evolutionary-biology component in that it must furnish the understanding of “humans” necessary to any potential organization of them. As Samuel Moyn points out in his landmark The Last Utopia, the last half century has been characterized by the moralization of politics epitomized by the human rights movement—replacing the old political utopias with a “legalized morality” based on concern for individual human bodies. This project aims to imagine how such a “legalized morality” can be synthesized from an understanding of human bodies that doesn’t succumb to the pitfalls of enlightenment claims about “human nature.”
University of California Santa Cruz (USA)
Mentors: Sid Redner, Andres Ortiz-Munoz, George Cantwell
Waiting in Line
Here we present and analyze a model for supermarket lines. In this model the queue is composed of the items each customer wishes to buy, rather than the customers themselves. While traditional queue models have customers arriving and leaving one at a time, we focus on the arrival of shopping carts full of items. Items arrive in bunches of size n and leave the queue one at a time. We solved for the probability distribution of items in the queue and the expected value when in a steady state. These predictions were validated by event-driven simulations.
University of Michigan (USA)
Mentors: Chris Kempes and Mingzhen Lu
The Dynamics of Company Waste with Analysis on Environmental Impact Scaling
The modern linear economy has been built on the foundation of continuous material production and significant quantities of waste. This waste is often presented through environmental degradation such as carbon emissions, plastic pollution, and a variety of other industry specific byproducts leading to negative environmental, social, and governance impacts.
Historically, corporations have not acted or published environmental reports and the availability of waste statistics has been extremely sparse. However recently, an increasing number of companies have laid out roadmaps to reduce waste and transition to net zero operations while implementing the ethos of the circular economy, a concept which aims to eliminate waste and pollution, reduce material usage, and regenerate natural ecosystems. The following project first builds a conceptual Individual Based Model (IBM) to identify information-based drivers in company decisions to initiate circular mechanisms. Subsequently, to ground our conceptual analysis into real world data for future model development, we also analyze the environmental impact of companies to observe if there are underlying scaling patterns dependent on company size. The developed IBM model shows multiple strategies that companies can take to reach a certain threshold in recycling and waste resources, revealing the dynamic path dependence to obtain environmental objectives. Our scaling results show industry specific environmental scaling patterns, from sub to super linear growth with respect to environmental waste, and an inverse relationship between initial environmental impacts and respective scaling growth.
Our analysis provides deeper insights into industries that should be directly targeted with growth prevention to limit their super linear environmental costs. Ultimately, this work can serve as the foundation for future endeavors to explore inter industry collaboration to reduce environmental waste and explore the changing landscape through scaling laws of humanity’s impact on our natural environment.
University of Maryland College Park (USA)
Mentors: David Wolpert
Stochastic Thermodynamics of Genotype-Phenotype Evolution
The dynamics of genotype-phenotype evolution are explored using methods from statistical mechanics. Following the ground-breaking work of Sakata and Kaneko , we adopt the Ising spin model to represent the evolutionary process. As they did, we identify genotypes with the interaction matrix J of the Ising spin’s Hamiltonian and phenotypes as the global spin conﬁgurations S. The (equilibrium) Gibbs distribution over S speciﬁed by a given J is identiﬁed as the distribution over phenotypes for that genotype, and the ﬁtness is identiﬁed with the magnetization of a pre-ﬁxed subset of the spins. Evolution then proceeds by evolving J to increase the associated equilibrium expected ﬁtness. Previous work only considered the resultant system in equilibrium, both over phenotypes and over genotypes. This research will instead use the recent tools of stochastic thermodynamics to study the non-equilibrium dynamics of the evolutionary process, e.g., to record the distribution of trajectory values of entropy production, and to apply the "speed limit theorems" and "thermodynamic uncertainty relations" to bound the possible evolutionary dynamics.
Jin Hong Kuan
University of Minnesota, Twin Cities (USA)
Mentors: David Wolpert and Hajime Shimao
Inferring Stochastic Diﬀerential Equation from Social Science Time-series
There are numerous challenges in analyzing the rich longitudinal datasets that social scientists have gathered, due to the prevalence of noise, missing data,and presence of artifacts pertaining to how the data was collected. One way to address both problems at once is to exploit the recent major advances in inferring non-parametric stochastic diﬀerential equations (SDE) by using Gaussian process regression. To this end, we propose adapting these new SDE methodologies to suit the unique needs of social science research, including SDE inference for incomplete datasets, SDE-based imputation, perturbation detection, irreversibility measure, and time-series ﬁtting. We also present the results from applying our proposed methodologies on the Seshat dataset, and discuss the novel insights obtained. Through demonstrating the utility of these methods, we hope to provide a preliminary step towards the adoption of stochastic time-series analyses in a broader range of disciplines.
Princeton University (USA)
Mentors: Albert Kao, Chris Kempes, Mingzhen Lu
Spatial Plant Root Modeling: Root Behavior, Structure, and Resource Acquisition
Plants are vital members of their communities and ecosystems which provide an
important connection between the above and below-ground portions of the system via their roots and shoots. Understanding plant structure is thus a very salient question. While above-ground plant dynamics have been studied in amazing depth and breadth, comparatively little is known about below ground dynamics. Existing studies of root structure typically focus narrowly on just one or a few species, and the links between root foraging behavior and root spatial structure are poorly understood. Thus, more general models are needed to understand root structure and the plant behaviors that underlie it, as they navigate several simultaneous constraints, including structural stability, search for water and nutrients, extraction and transport of these materials, and interaction with other organisms. This project created a spatially explicit model of root structure and addressed the following questions. How well do plant roots uptake resources under different foraging behaviors and different resource input regimes? Are there structural factors that play a role in this outcome?
The project found that for the short timescale—while the modeled roots were actively growing—the strategies that led to the greatest efficiency of uptake per root were gradient seeking and sometimes the “greedy” (always chooses to grow into the highest resource concentration) strategies .On the other hand, on the long timescale—after the roots reached maximum size—the modeled roots with the highest efficiency of uptake (described as resources uptaken per root pixel per timestep) were those that had grown randomly or in a biased random strategy (more likely to grow towards high resource concentrations). This result may depend on the boundary conditions of the model (which were non-absorbing). The result may also change if the modeled plants could kill off roots.
In the short timescale, greater resource uptake efficiency was associated with spatial measures that described roots that spread widely through space—greater rooting depth, lower proportion of roots branching, lower root ball density, greater area covered (pixels with at least one neighboring root). In contrast, in the long timescale, greater resource uptake efficiency was associated with smaller, denser root balls with shallower root depth, greater proportion of roots branching, higher density and lower area covered.
Frank Palma Gomez
City University Of New York Queens College (USA)
Mentors: Tyler Millhouse (Melanie Mitchell)
This project is still in progress with a goal of publication. Information will be provided at a later date.
University of New Mexico (USA)
Mentors: Marco Buongiorno Nardelli & Tyler Marghetis
Understanding Jazz Through Networks
Understanding the musical frameworks that characterize the compositional process across genres involves a deep knowledge of many rules and exceptions deﬁned in music theory. We propose a data-driven method that converts musical pieces into networks. We re-conceptualize attributes from the modal and tonal frameworks as network properties and analyze whether these network properties appear in the networks corresponding to twenty-eight diﬀerent jazz/classical modal/tonal pieces. We ﬁnd that scale-free degree distributions and progressions between nodes give a quantitative, intuitive representation of certain musical attributes characteristic of these frameworks. This work demonstrates the power of a network science approach to explore a variety of questions ranging from music generation to appreciation.
Harvey Mudd College (USA)
Mentors: George Cantwell and Melanie Mitchell
How does the brain compute? Building upon Assembly Calculus.
How does neural activity give way to the thoughts and actions? Elucidating the process through which the brain transforms the interaction of neurons into cognitive thought is an important question in neuroscience. Recently, a formal system called Assembly Calculus has been proposed to mathematically characterize these interactions via operations on assemblies, which are populations of neurons that imprint cognitive information. In this paper, we modify an assumption of Assembly Calculus by changing its base graph model, propose how interactions of assemblies may evolve over varying time scales, include language experiments that serve as a useful jumping board to extend Assembly Calculus, and suggest what learning via assemblies may involve.
Grinnell College (USA)
Mentors: Mike Price + Tyler Millhouse
Correlating Science with Science Fiction
Often, we consider science to happen within a bubble of scientists. We don’t think about where ideas come from especially if they aren’t directly related to what we are working on as individuals. Science is fundamentally linked to how the scientific community interacts with society at large. One cannot function without the other. Literary work has been done to collect themes and do some analysis of science
fiction as a genre and some work has been done looking at the span of astrobiology to classify it as a field. The goal of this project is to compare themes in science fiction to the topics in astrobiology from its initial rise as a distinct field to the present to establish a correlation between the two. First, I will create a topic model to understand what kinds of topics astrobiology encompasses. I will then use the same topic model to make a timeline of topics in science fiction novels. Finally, I will align this timeline with the rise of astrobiology and see if there is a correlation (if not causation) between the topics. Whether there is a spike in sci-fi about life on other worlds before astrobiology emerged or if astrobiology gaining status led to a shift in sci-fi topics.
Understanding the way that scientific fields and the more general society interact, and pass information can give us insight into how the larger system of science functions within society. Using this same technique for other areas of scientific research such as artificial intelligence or communication systems could produce a clear model of how scientific interests are reflected in society. This in turn can lead to better communication between scientists and nonscientists (and possibly within science itself) and could be extended to look at how ideas come about, and which ones are of the most interest to people in general.