If you're tiling a circular room with square tiles, how many do you need? What if your tiles are parallelograms? As the circle gets larger, is there a pattern? Mathematically, this can be framed as counting integer points in a large circle. We're interested in how this count changes as you change the shape of the tiles, and to understand this better, we started by counting the number of integer vector pairs within a ball of radius R so that the parallelogram they make has a fixed area (determinant). We created a Python program that would generate all of the primitive points out to radius R, which we then extended to count the number of vector pairs with a certain determinant k. We were able to compute the limiting density of this count, extending known results for the case of determinant 1. We are now studying other discrete sets, such as ones generated by objects from hyperbolic geometry, known as Hecke triangle groups. In the future, we plan to use our research for counting pairs of vectors in different spaces and generalize it for counts of k-tuple vectors. Come for floor tilings, stay for beautiful pictures!

First-passage and last-passage algorithms are two diffusion Monte Carlo methods that we can use to obtain the charge density distribution on a conducting surface. Usually, we use first-passage algorithms to obtain the capacitance and the overall charge distribution of the arbitrary-shaped conductor. On the other hand, the last-passage algorithms calculate the charge density at a point on a conducting surface by initiating the random walk at that point. The last-passage algorithm utilizes the dipole Green’s function to expedite the diffusion process which starts from the point. Past results determine the initial sitting using the largest hemisphere around that point with a radius that is contained in the surface, which inefficiently starts the random walk if the point is near the edge of the surface. Here, we derive the dipole Green’s function to start the diffusion process from a point on the hemisphere off-centered from the original point using weighted sampling to further expedite the computing process.

Measurement in Psychology usually assumes continuous dimensions. Correspondingly, theoretical constructs are typically conceptualized as dimensions, meaning that observations differ in degree. However, theoretical constructs may also be categorical, i.e., rather than differing by degree, differing qualitatively. Different construct operationalization’s may lead to different scientific conclusions. Self esteem has long been of interest in Psychology. It has been conceptualized in various different ways, but always dimensional. Some self-esteem measures (for example, the The Rosenberg Self Esteem scale) seek to measure globally how much one values themselves as a person, without focusing on specific domains. On the other hand, other self-esteem measures (for example, the State self esteem scale) focus on perceived capabilities in specific domains, such as performance, social, and appearance. In the National Survey of Youth, participants rated themselves in specific areas, and then again as they would like to be. Using these data, we examined how different operationalization’s of self-esteem are associated with a few psychologically interesting outcomes such as drug use and crime. Specifically, we compared continuous and categorical representations of self-esteem. By examining the assumption of continuous latent variables, we shed light on how scientific conclusions differ based on construct operationalization.
 

The nematode C. elegans is a common model organism for investigating cellular aging mechanisms and there is an extensive database of known genes which influence their lifespan. Protein kinases are regulatory enzymes which function in the cell as molecular switches. Here we use RNA interference to disrupt 11 classes of protein kinases to determine their role in 10 different C. elegans mutant backgrounds known to affect aging. With the included controls this involved over 120 individual lifespan experiments. In order to perform this many experiments we used a custom robotics platform called the Wormbot, a novel, high-throughput technique for measuring worm lifespans that our laboratory developed. We present here the results from 120 combinations of longevity mutants and inhibited protein kinases. The findings of this study may identify biochemical pathways or interactions which may play a role in the regulation of human aging or development of age related disease.

The goal of this project is to encode peptides, i.e., short amino acid sequences, in terms of smaller molecular components such as their VSEPR (Valence Shell Electron Pair Repulsion) features for training interpretable models with reasonable predictability of functionality. This enables us to go beyond the limitations imposed by treating peptides as sequences of letters, thereby enabling a generalized encoding that works for lipids and other biomolecules that are of interest in a comparable scenario. Biological processes are rarely disjoint and often complicated which lends justification to our approach. Current methods for binding affinity prediction, such as one-hot encoding, where letter-based sequences are converted to a binary representation, do not take into account molecular level features. Combined with a neural network, such a simple encoding is better at predicting affinities of short peptides, e.g., 5-9 Amino acids long, but with an increase in length from 9 to 10, the predictability suffers an exponential drop. Several alternatives have been employed in literature, but they also suffer from the negative impact of distal effects. In the VSEPR approach, encoding peptides in terms of their component functional-group geometries enables us to encode the actual physical length, rather than the number of amino acids. This leads to an overlap between peptides of different length, thereby reducing the fall in predictability. In this encoding, we create 5 channeled matrices with each channel corresponding to ‘central-atom connectivity’, ‘bond-types’, ‘bond-lengths’, ‘bond-angles’ and ‘lone-pairs’ that is then fed through a Deep Residual-Neural-Network. The metrics used to evaluate the models are Pearson-Correlation, Spearman-Rank-Correlation-Coefficient, and Area-under-Receiver-Operating-Curve. With this technique, we were able to consistently predict binding affinities of peptides without an appreciable loss between 9 or 10 length peptides. This method would allow one to create length invariant encodings, not limited to just peptides, significantly improving the practicality of using such a model. The research is supported by NSF/DMR-DMREF program under Materials Genome Initiative.

Mapping is a powerful tool to visualize space and data. However, working with historical data and maps is problematic as spaces change across time. Given this, the scope of this research is to create visual maps using GIS software that accurately represents the Baghdad-Basrah region of the Ottoman Empire in the late nineteenth century. Our key research question is: how can cholera data from primary sources in the nineteenth century be visualized through mapping? We gathered the data for this research from the diaries of Joseph Svoboda, a resident of the region who traveled frequently up and down the river system and recorded information about numbers of deaths and quarantines from cholera in the cities he passed. The method we used for mapping the data includes a comprehensive reading of the diaries currently being transcribed to assess which information is important for mapping purposes, including the location and time period of the event in question. We mapped the data using Geographic Information Systems (GIS), a software that is used to analyze and represent data through maps, to geocode locations and include cities and other features as they appeared in the nineteenth century. Anticipated results include an interactive choropleth and dot maps that are accurate to the specific time period and show deaths from cholera in specific locations over time. One key implication for further work would be a standardized way to map disease data from primary sources and to increase the number of individuals who use data visualization with historical data. Additionally, our mapped data can be used for other types of GIS analysis that may be of interest to those studying the history of cholera or historic epidemics.

Our research group performs one of the highest-precision tests of Einstein’s equivalence principle, perhaps the most fundamental property of gravitation, using a sensitive rotating torsion balance. Among the leading experimental challenges are temporal and spatial temperature variation. Notably, horizontal temperature gradients across the apparatus, if not properly characterized, can emulate an equivalence-principle violating signal. We have implemented thermal shielding and run tests to measure the thermal effects on our measurement. Past tests have shown a need for both absolute and differential temperature sensors with higher sensitivity. Hence, my research project focuses on investigating the effect of temperature gradient on our experiments by constructing a thermal monitoring system. I have designed, laid out, constructed, and tested sensitive bridge thermistor circuits that can function as both absolute and differential temperature sensors. Current tests of our prototypes have shown that temperature sensitivities reaching 10 micro-Kelvin in one second (10^-5K/Hz^0.5). We are scaling-up these sensors and plan to deploy them in this academic year. Successful completion of this project will yield improved understanding of the temperature gradients within our experimental apparatus, allowing us to test the equivalence principle with yet higher precision.

It has shown that there are higher death rates with individuals with darker skin types due to lack of diagnosis based on wording of skin sensitivity surveys. In the realm of research and dermatology, the Fitzpatrick Skin Type (FST) scale has been the gold standard of measurement to classify sun sensitivity for human’s skin. More research of the subject is necessary but it is important not to underestimate the impact of UV exposure and exclude a portion of society. It is the scope of Study 3 to reword part of the survey for cultural awareness as well as introduce an objective source of measurement using photospectroscopy. It is important to include these groups that have been discounted in prior studies. Some of the language has been utilized in prior research and it was an attempt of this study to improve on the language used. Participants were asked to complete a brief self-report skin type survey prior to measurement of skin melanin using a reflectance photospectroscopy device. The areas measured were dorsal and ventral wrist area and ventral upper arm area. The results correlate well with the subjective and objective components. Improvement will be paramount to future research in this project as we aim to bring this group to understanding what might be necessary in the future design of this project and how a statistically significant correlation can bring us closer to asking the pertinent questions that help people determine their skin types. We hope to design a replicable and accurate way to categorize skin type which will be able to deliver the most accurate sun exposure behaviors.

Augmented reality (AR) for the consumer market is gaining momentum and public attention. Besides smartphone platforms, early-stage head-mounted displays such as the Microsoft HoloLens are now publicly available. Many compelling uses of these AR technologies are multi-user: for instance, in-person collaborative tools, multiplayer gaming, and telepresence. Although multi-user AR technologies enable new forms of interaction, they also raise new security and privacy challenges, not only from untrusted applications but also from other users’ malicious or unthinking behavior. It is imperative that these challenges be addressed while the technology is still new and highly malleable. In this work, I explore emerging challenges in securing multi-user AR content sharing from user-to-user threats. I argue that supporting secure and private AR content sharing when users can augment each other’s reality requires careful consideration of AR’s tight integration with the physical world. I systematize design goals for security and functionality that an AR content sharing module should support, and I design and prototype an application-level module for the HoloLens that meets these goals. By evaluating my module against representative application case studies, I show that it meets desired security and functionality goals flexibly across a range of use cases. I further demonstrate that applications’ content sharing needs can be achieved in relatively few lines of code and with low performance overhead. I am currently converting my research prototype into an open-source toolkit so that developers can address these challenges in practice. This work opens up directions for future research on supporting developers in effectively addressing these issues in practice, including making recommendations on how these underlying paradigms should manifest in user interface design. By building foundations for secure multi-user AR content sharing, my work takes steps toward allowing AR to securely reach its full potential.

Neural networks are machine learning instruments capable of solving a vast array of problems ranging from image classification to decision making. Developers of neural networks algorithms have many consequential decisions they must make in order to adapt a model to a particular task. Recurrent neural networks (RNNs) are an important instance among these algorithms — they are popular and powerful due to their ability to integrate information over time. A structured understanding of how RNNs are affected by the decisions made during model adaptation will improve RNN performance. Unlike conventional feed-forward neural networks, RNNs are allowed to evolve over time. The study of time-dependent systems is known mathematically as dynamical systems analysis. Hence, we can build upon existing machine learning literature by incorporating a dynamical systems perspective to describe an RNNs regime. Through this lens we investigate how an RNN which operates in different dynamical regimes (chaotic or stable) displays optimal temporal integration abilities. We establish a relationship between a mathematical metric for the dynamical regime and the qualitative solution for the network. Our preliminary results further suggest improved performance when the RNN is encouraged to operate in a chaotic dynamical regime.

Immanuel Kant, in the Critique of the Power of Judgement, describes how we come to find objects beautiful through an aesthetic judgement. In particular, he claims that an object is beautiful in virtue of its property that we cannot find a concept to match it with. This explains our contemplation when looking at art whereas an object such as a hammer does not motivate us to contemplate it. He also notes that beauty does not rely on the idea of perfection, which is to have the most of certain qualities. In contrast to beauty, Kant puts forth the idea of purposiveness, which is a consideration towards an object's existence being a part of the causation of some end. This means for an object to have a purposiveness would be for it to fit as a means to an end goal. Kant then puts forth the idea of there being two types of beauty, being adherent and pure. Pure beauty follows Kant's general agreement that beauty should be free from concepts. However, Kant experiences certain tensions in terms of adherent beauty, in which an object is beautiful because of its utility. This appears contradictory to Kant's previous commitments to a lack of concepts. I explore these tensions and consider possible Kantian explanations for this. I’ve begun study on Robert Clewis’ “The Origins of Adherent Beauty” to inform this topic as well. Clewis elaborates on the different approaches during that time to reconcile utility and beauty, noting several position Kant takes before assuming his current ideas. If we are able to resolve answers relating to adherent beauty, we will be able to design possible criteria for secondary adherent beauty. Doing so will also allow us to possibly add a purpose to different types of art depending on what concept they are the perfection of.

Despite the high growth rate of minority-owned business in the US, economics literature suggests that minority business owners have a harder time getting loans for their businesses compared to their white counterparts. If minority-owned businesses are doing well in the U.S., it is expected that loans to minority owners have high returns (or low defaults). It is paradoxical that banks would discriminate against minority loan applicants since it's against their economic interests. My research project hypothesizes that financial institutions' loan approval process is flawed for assuming that the predictors of loan defaults have the same effect on minorities and non-minorities. For example, credit score is often an important factor in predicting default, however, many minority immigrants haven't had a chance to build up their credits to the same degree as their white counterparts. In this case, a low credit score means a high probability of default for white business owners but does not predict a high default rate for non-white owners. To test the hypothesis, the research project examines the heterogeneity in the effects of common determinants of their loan repayment between minority vs. non-minority business owners through an econometric analysis of a dataset collected by the U.S Treasury Department on CDFIs(Community Development Financial Institution Fund). More specifically, my project tests if the differences in the coefficients of predictors for each group are significant. Evidence supporting the hypothesis suggests that banks are losing out on economics gains by overlooking certain factors on their applicants and actions should be taken to prevent further loss for minority business owners.

The environmental and human health damage associated with industrial waste has been an undeniable concern since the late 20th century environmental disaster at Love Canal, which had devastating effects on birth defect and miscarriage rates. Since this event, the Environmental Protection Agency (EPA) has been dedicated to the remediation of toxic waste through the Superfund program. There are Superfund sites across the country, in locations as varied as urban Tacoma, Washington and rural Evansville, Wyoming. Which toxic site should enjoy the advantages of faster cleanup? A range of factors could influence the remediation rate at these sites, yet a striking difference in site characteristics presents itself; These two sites are home to very different population densities. Population density, an emblematic proxy variable, can be used as an effective tool to investigate different aspects of socioeconomic site characteristics. Scholarly models of optimal remediation, however, often focus exclusively on the financial costs and environmental damage of cleanup. This project investigates how Superfund site remediation would change if the EPA were to incorporate specific socioeconomic criteria in its decision to remediate toxic sites. Particularly, it explores various aspects of the Superfund program and focuses on and extends a particular theoretical model for temporal remediation. Population density enters the model through its effects on costs, although other consequences of population density will be investigated. The results of the extension indicate that a higher population density corresponds to a decrease in the optimal toxic waste cleanup rate.

The relationship between fertility and economic development can be modeled in many different ways. To microeconomists, fertility may determine the “quality” of children in one family, where quality is typically interpreted as a child’s level of education. These models of child quality are based on the classical quantity-quality tradeoff model by Becker, in which parents choose to substitute child quality for child quantity under some circumstances. The focus of this paper is to detect whether the quantity-quality tradeoff exists under the two-child policy in China, implemented in 2015. Since 2015, Chinese families have been permitted to have two children, and this change in the quantity of children in a family may affect child quality as well. However, the two-child policy was implemented only three years ago, so data is lacking. Thus, I chose Taiwan as my case study. I use data from Taiwan to find some the effect of fertility and apply those results to circumstances in China. By using linear regression, I find that the results from Taiwan are consistent with the classical model. Once the quantity-quality tradeoff under two-child policy is clear, scholars can further research on the short-term and long-term influence of two-child policy in China.

The Svoboda Diaries Project works with personal diaries written at the turn of the 19th century, capturing over 40 years of the life, politics, and landscape of Ottoman Iraq. Written through the unique lens of a British steamship purser with a rich family history and connections in the area, these texts provide a unique insight into a locale on which there exists minimal literature for this time period. Undergraduate interns transcribe these diaries and develop open-source tools to make the texts available in a variety of formats. We are currently redesigning our website to better serve the needs of its various users, and our main question is: How do we realize the needs of prospective users when creating a digital platform for viewing historical manuscripts? Our current website is not sufficient in meeting the needs of the project’s diverse users: historians/researchers, contributors, and the general public. Therefore we intend to create an engaging and interactive user interface. At its core, the Svoboda Diaries comprise a personal narrative. We also intend to infuse a storytelling approach to present these unique documents in a larger political and historical context, and allow the user to explore them in different ways. We utilize a variety of user-centered research and design methods, such as conducting user interviews with domain experts and other interested individuals, creating prototypes, and conducting pilot usability sessions to refine the website.We anticipate that our website redesign will allow users greater access to explore the diaries. In addition, the redesign will draw attention to the most important aspect of the website: the diaries themselves, and the fascinating and valuable accounts within them.