Undergraduate Complexity Research 2017

In a directed network, we can detect a ranking or hierarchy by assigning `scores' to the vertices based on the connections in the network. These scores can be used to predict the relative importance of different vertices. We are interested in how hierarchy emerges in complex networks, as well as how it evolves over time. In real networks, where the set of edges present in the network may change, we expect that existing hierarchy affects which new edges emerge, with new edges appearing with some probability associated with the ranking of each vertex. At the same time, the ranking of vertices is extracted based on the connections present in the network at a given moment. Using different methods for ranking vertices and rewiring networks according to a given ranking, we explore the dynamics of ranking/hierarchy in directed networks over time. Through computer simulations as well as analytic methods, we investigate limiting degree distributions for different ranking and rewiring algorithms, as well as sudden regime shifts in the emergence of hierarchy in networks.

I will construct a simulation of the Ising model and use it to investigate the thermodynamic properties of computation. An Ising model is a set of discrete elements (representing the spins of atoms) which take a state of “up," or “down," depending on the energy associated with the whole system and the external magnetic field. Above a certain temperature (called the critical temperature), the “spins" of the discrete elements in the Ising model orient themselves in random directions, independent of their neighbors. Below the critical temperature, the spins of the discrete elements in the Ising model preferentially orient themselves along their neighbor's spins. At the critical temperature, the Ising model approximates a mottled surface, with small groups of elements aligning themselves “up" bordered by groups of elements aligning themselves "down". This system can also be changed by an external magnetic field applied to all elements in the model. Our goal is to demonstrate that the work/power/time costs associated with flipping elements for computational tasks are optimized at the critical temperature. To test this hypothesis, we will need to construct a computational Ising model, define work related to the magnetic field, and compile statistics from repeated simulations of this model.

We will examine various measures of morphological computation in the field of embodied intelligence, a field that that emphasizes the role of the body and environment in how an organism thinks. Morphological computation refers to processes which are conducted by the body and environment that would otherwise be carried out by the brain, implying that a well-chosen morphology can substantially reduce the amount of required cognitive control. We will study embodied agents embedded in a “sensorimotor loop,” comparing a variety of measures that aim to quantify an organism's morphological computation by highlighting specific aspects of the behavior. By first testing these measures against an idealized mathematical model, we hope to develop some intuition in formalizing this philosophical concept and perhaps devise new approaches. We will first reconstruct numerical results from prior research on the “binary model,” then extend this model to its completion by including additional constraints, with an ultimate goal of generalizing these results to more complex models with arbitrary constraints. In the process, we hope to draw analogies between measures of morphological computation in embodied agents and measures of complexity in complex systems (defined in terms of information geometry), with possible applications to computer simulations of biological and robotic movements.

As our world becomes more and more urbanized, understanding the intricacies of the human city becomes increasingly important. Much work has been done to understand general urban growth patterns: researchers like Luis Bettencourt and Geoffrey West have identified nearly universal urban scaling laws. However, the underlying structure of that growth is less clear. Do the substructural elements of cities—communities such as neighborhoods or school districts—scale in similar ways? How does the substructure of a city and the interaction between its elements contribute to its overall productivity? Does the mixing of a city's population between neighborhoods inform its over- or underperformance in terms of more general scaling laws? By answering these questions, I hope to nuance my understanding of urban growth and shed light on what it means for a city to be successful and productive.

Scaling relationships have been studied in biological systems widely (West, 1999) and recently extended to social systems, such as cities (Bettencourt, 2007, 2013, 2014) and companies (Metzig & Gordon, 2013). Finding scaling relationships in a system helps reveal the fundamental universality shared by all agents within the system and can determine the fundamental constraints on the growth of the system. However, little research has examined how universities scale—how they differ by size. How do general factors such as resource allocation, bureaucracy or quality of education change in response to the size of universities? Further, how do the changes in these variables regarding size affect the function and potential growth of universities? How are universities different from organisms, companies or cities given their purposes and constraints?  
With these questions in mind, we extend scaling research to the US higher education system, in the hopes of uncovering underlying mechanisms that explain the scaling relationships. We examine institutional data, reported by effectively all universities in the US, seeking scaling relationships between size of university and certain attributes generalizable to all universities: measures of size include total assets, enrollment, and number of faculty/instructors, while attributes of interest include labor share and expenditure dedicated toward instruction, academic support, research, and public service. In particular, exploring how faculty and staff sizes vary, across universities of all scales, may shed light on how all schools crucially balance actual educational activity with organizational maintenance. Likewise, exploring how instructional and research expenditures scale with revenue, or even endowment, may lend new insights on functionality of universities as types of institutions. Throughout, we attempt to distinguish between system-wide stocks and flows of both money, and educational value, in order to understand the duality of universities as financial and educational institutions. 
After investigating the universal trends across universities, we will turn to deviations around these trends, both across universities and in time. This will potentially lead us to explore the role of diversity between universities, and what features at all scales generate or hinder innovation. We will propose theoretical explanations for our findings, drawing on mainstream conceptions of universities, organization theory, network science, and comparison with other complex systems.

Underlying hierarchies govern interaction patterns in many systems. Consequently, observed interactions between members of a system can reveal their positions in the hierarchy. For instance, within a tournament, teams that have similar rankings tend to play against one another more often. The outcomes of these interactions, i.e. which team wins a game, also affect the rankings in the hierarchy. A proposed physics-inspired model formalizes the two aforementioned assumptions to infer hierarchies from network data, and gives real-valued rankings to nodes. We would like to analytically quantify the uncertainty in the inferred ranking from this model. That is, if we were to use the inferred ranking to make a bet on the next game, how confident could we be of our bet? Or is a completely different ranking just as likely to exist?

Popular stories, whether they be fairy tails or non-fiction classics are regularly praised for their ability to be captivating and compelling. One reason why popular stories are popular may be because they consistently illicit high amounts of emotion from numerous individuals. In fact, we suspect when popular stories get retold their emotional structure is often maintained. Here, we construct a linear transmission chain and utilize dictionary-based sentiment analysis to understand these dynamics at the word-level. By extracting sentiment from within a series of chain letters and Dutch Little-Red Riding Hood re-tellings we found words with higher emotional valence are much more likely to be transmitted. We reason this effect is due to words with high emotional valence to be independently encoded, cumulatively recalled, and transmitted and retained with higher fidelity from generation to generation.

Are today's neologisms indicating that we are all a bunch of pessimists? New words are being produced at a rapid rate of about 15 per day and then shared easily online. Some words last only a week in a small circle of friends while others making their more permanent residence in the dictionary. But as with the words that came before them, they are subject to the force of language evolution. Using natural language processing techniques, including sentiment analysis, we track a set of neologisms from their origin to today to see how their semantics and their sentiments may have changed, perhaps steadily becoming more positive, suffering a drastic plummet to negativity, or remaining perfectly constant. We bring into question how closely semantics and sentiments are intertwined in these words, and ultimately if we can predict what types of words are likely to alter their emotional and lexical meanings in their lifetime.

Scaling relationships have been studied in biological systems widely (West, 1999) and recently extended to social systems, such as cities (Bettencourt, 2007, 2013, 2014) and companies (Metzig & Gordon, 2013). Finding scaling relationships in a system helps reveal the fundamental universality shared by all agents within the system and can determine the fundamental constraints on the growth of the system. However, little research has examined how universities scale—how they differ by size. How do general factors such as resource allocation, bureaucracy or quality of education change in response to the size of universities? Further, how do the changes in these variables regarding size affect the function and potential growth of universities? How are universities different from organisms, companies or cities given their purposes and constraints?  
With these questions in mind, we extend scaling research to the US higher education system, in the hopes of uncovering underlying mechanisms that explain the scaling relationships. We examine institutional data, reported by effectively all universities in the US, seeking scaling relationships between size of university and certain attributes generalizable to all universities: measures of size include total assets, enrollment, and number of faculty/instructors, while attributes of interest include labor share and expenditure dedicated toward instruction, academic support, research, and public service. In particular, exploring how faculty and staff sizes vary, across universities of all scales, may shed light on how all schools crucially balance actual educational activity with organizational maintenance. Likewise, exploring how instructional and research expenditures scale with revenue, or even endowment, may lend new insights on functionality of universities as types of institutions. Throughout, we attempt to distinguish between system-wide stocks and flows of both money, and educational value, in order to understand the duality of universities as financial and educational institutions. 
After investigating the universal trends across universities, we will turn to deviations around these trends, both across universities and in time. This will potentially lead us to explore the role of diversity between universities, and what features at all scales generate or hinder innovation. We will propose theoretical explanations for our findings, drawing on mainstream conceptions of universities, organization theory, network science, and comparison with other complex systems.

Theatre plays a crucial role in society, providing a means of critical self-examination. It gives its audience a chance to question societal mores and norms by depicting them within the fiction of a play. This role is perhaps exemplified by Attic Tragedy, developed and perfected in the city-state of Athens between 500 and 400 BCE. Athenians viewed theatrical attendance as a civic duty, mandatory for all citizens. Attic Tragedy is enormously influential. It has not only defined many the conventions of theatre as we know it, but has made an indelible mark on centuries of western thought. Among many features of this highly stylized form of theater is the tragic chorus. Unlike other characters the chorus does not represent a character within the world of the play. Instead the chorus acts as an intermediary between the stage and the audience. Rather than directly participating in the action, the chorus interprets and comments on events in the play. Despite, or perhaps because of, their highly-stylized form, the nature of the chorus can vary greatly depending on the author. For example, Sophoclean choruses act as characters within the story and reinforce the themes of the play. But the choruses of Euripides are far more hands-off, serving as mere bystanders to events, their songs only loosely connected to the themes or events within the play.
Recent work in the quantitative social sciences allows us to study the role of language in social interaction. These techniques are most frequently applied to real-world data, and relatively little work has been done applying these tools to fictional representations of social interactions, such as in drama, film and literature. In this work, we will apply techniques from information theory in and natural language processing to conduct a quantitative analysis of a play’s dialogue to answer two research questions. First, we will investigate whether the role of the chorus is distinct from the role of other, in-world characters. Second, we will study how the chorus’ role evolved over time through the work of the three great tragedians: Aeschylus, Sophocles and Euripides. We hope this will help us to understand how Athenian character and aesthetic sensibilities shifted from its inception with Aeschylus, to ultimate disillusionment during the Peloponnesian War, in the era of Sophocles and Euripides. We hope to provide a new understanding of how both social and cultural changes might have altered the internal aesthetic properties of the text.
Because plays dramatize social interaction, we will focus on the correlations in the semantic and emotional valence of characters in a play. Specifically, we will measure semantic and emotional lag. These quantify the temporal distance between speeches of two characters at which the topic or emotion of speeches is most similar. If the emotional or semantic lag between two characters is small, the corresponding property will appear to be rapidly transmitted from one to the other. Depending on the sign of the lag, the influence will appear to propagate preferentially form one character to the other or vice versa. Using this analysis, we hope to illuminate how the playwrights chose to represent the relationships both between participants within the fiction as well as the commentary provided by the chorus. If the patterns of semantic and emotional lags differ for the chorus compared to other characters, we can conclude that the chorus’ represented social interactions differ from those of the other characters. We will use the same techniques to compare the interactions of the chorus in the works of the three different playwrights. Ultimately, we hope to use our quantitative analysis to help literary theorists better understand the nature of the chorus as well as to aid in the evaluation of the several contrasting scholarly theories concerning it.

Optimizing social structure for arbitrary organization types - A novel application of deep neural-networks for designing social hierarchy models that maximize communication speed, information distribution, redundancy, or fault-tolerance. These models can help demonstrate why different groups exhibit different organizational hierarchies, subject to the availability of resources and the cost of different communications mediums. Among a wide range of potential applications, these models can be used to analyze social organizations such as corporate hierarchies, computer networks, and military command structures.

We address the question of finding topics in a corpus of documents using spectral methods. Our model is similar to probabilistic latent semantic analysis (PLSA). We regard the document as ‘bag of words’ and we care only about the frequency of the unique words in the documents. Using the Poisson factorization with expectation-maximization (EM) algorithm we can detect overlapping communities. By doing the stability analysis of the area around the trivial fixed point of the EM, we gain new insight into what the right linear operator for spectral clustering is. We try to answer the question of finding the number of communities beforehand, by looking at singular values of this new linear operator.

Multicellular organisms can generate complex morphologies. However, there are many multicellular organisms that do not generate such complexity. For example slime molds form very simple shapes such as mobile slug bodies and dispersal structures. In general, it is observed that complex shapes start from single cells or affixed clonal groups. In contrast, when cells aggregate or are not clonal they seem to be limited in the complexity they can produce. To test whether these starting points constrain the organisms morphology or ability generate complex shapes, we use the digital evolutionary software Avida. Avida is an artificial life software platform with self-replicating and evolving computer programs. Through the use of this system, we evolve the shape of an organism. An analysis of the complexity of these structures is given by the speed of replication and the success of the organism. These findings will help us understand how the structure of specific organisms came to be.