* * * This page has been archived (Jan 2019). These are a mix of old school, research, professional, and passion projects that I am no longer working on. * * *
Old Projects
201903
Math Academy Tutorial Videos (2019) Produced 300+ tutorial videos for Math Academy's online learning system. The goal was to produce highquality yet inexpensive videos (at a rate of 23 hours/video) to accompany written tutorials in Math Academy's online learning platform. 
201902
Justin Math Textbook Series (2019) Wrote a textbook series that covers the foundations of high school and college math: Algebra, Calculus, and Linear Algebra (with Differential Equations baked into the latter two). The goal was to provide deep intuition for the core concepts and connections, along with plenty of practice exercises, while remaining as concise as possible. 
201901
CheckMySteps: A Web App to Help Students Fix their Algebraic Mistakes (2019) Developed a web app that automatically detects and explains mistakes when solving and simplifying algebraic equations. Course: CS 6460 (Educational Technology) at Georgia Tech Links: web app, writeup, talk, slides Summary: Many students struggle in mathematics due to technical misconceptions in solving equations and simplifying expressions, such as forgetting to FOIL when multiplying expressions, or forgetting to divide both terms of the numerator in a fraction. $$\begin{align*}\mbox{FOILing error: } (x+2)^2 \rightarrow x^2+2^2 \rightarrow x+4\end{align*}$$ $$\begin{align*}\mbox{Division error: } \frac{x+1}{x} \rightarrow \frac{1+x\hspace{0.3cm}/}{x\hspace{0.3cm}/} \rightarrow 1\end{align*}$$ As a result, mathematics educators spend significant time and effort engaged in a repetitive process of searching student work for these misconceptions, demonstrating that they are indeed incorrect, and explaining how to correct them. This is an inefficient process, because students are sometimes able to correct their own misconceptions when given a generic explanation of their error. An extreme case of student selfcorrection is socalled "silly" mistakes, where the student understands a concept but makes a careless error on a question they would normally answer correctly. Students especially skilled at selfcorrection are sometimes even able to teach themselves new concepts, if given some guidance on what their error might be. To this end, there appears to be a usecase for a web application that automatically assists students in selfcorrecting small errors and minor misconceptions, thus enabling teachers to focus their time on explaining major misconceptions that cannot be selfcorrected by students. A prototype web app, CheckMySteps, has been implemented as a notebook environment where students enter their steps linebyline as they solve equations or simplify expressions. Each line is checked against the previous line for mistakes, and if a mistake is detected, then an example input is chosen to demonstrate the discrepancy, and feedback is generated regarding common misconceptions that may potentially form the basis of the mistake. In particular, this "potential mistakes" feedback classifies the student's mistake as a potential violation of some algebraic rule(s), and informs the student of the correct interpretation of the algebraic rule(s). 
201803
Improving Readmission Prediction by Extracting Relevant Information from Clinical Notes (2018) Developed a model to predict patient readmission using coded features and clinical notes. Course: CSE 6250 (Big Data for Health Informatics) at Georgia Tech Collaborators: Stan Arefjev, Luis FernandezRocha, Devan Stormont (Georgia Tech) Link: writeup Summary: The purpose of this project is to develop a model that will predict patient readmission from the MIMICIII database using coded features and clinical notes. The goal is to predict unplanned patient readmission with a higher ROC AUC score than prior published work [RAJKOMAR]. The approach taken to accomplish this is three fold. First we build a data pipeline to find all readmission events for labeling, as well as processing the coded features from the dataset. Next, the clinical notes are processed using Natural Language Processing (NLP) in order to build additional predictive features. Finally, a Recurrent Neural Network (RNN) is used to train and test the combined processed data in order to make final predictions and calculate the ROC AUC score. 
201802
Intuiting Predictive Algorithms (2018) Explained how various predictive algorithms function and relate to each other, to an audience who is familiar with the algorithms but does not yet intuit their underlying math and see how they fit together. Link: writeup Summary: The goal of this writeup is to connect concepts in machine learning by showing how they relate to each other in a mathematically rigorous yet "storylike" fashion. It is intended for an audience who is familiar with some of the machine learning algorithms but for whom they are not yet intuitive. The story starts out with wanting to model data when we have little knowledge about the process that generates it. We see that the Bayesian optimal model, given some parameter set, is an average over all possible parameters. However, since this average is infeasible to compute, we settle for picking the model that computes most to the average (MAP, MLE). This leads us into an exploration of linear regression, support vector machines, neural networks, and decision trees, over which we gradually transition from using theoretical principles to heuristic techniques. We conclude with ensemble methods as a way to break free from the constraints of a single model and avoid overfitting even when using models that are prone to doing so. This brings us around fullcircle to the Bayesian optimal model, which itself can be interpreted as an ensemble model, and which we can attempt to approximate with strategicallychosen ensembles. 
201801
360Giving Challenge (2018) Visualized which donors funded which themes throughout the years. (This also required classifying grants into highlevel themes based on titles and descriptions.) Links: site Summary: This is a visualization of which donors funded which themes throughout the years. The given dataset consisted of grant records and included donors/recipients, dates/amounts, and titles/descriptions. First, I tagged grants into themes according to keywords in the title and description. Then, for each theme in each year, I computed each donor's average grant amount, total giving, and total giving in that theme as a percent of the donor's total giving in all themes. I visualized the results in an animated dot plot for each theme. 
201705
Predicting Customer Churn with a Random Forest (2017) Built a random forest model to predict customer churn with 80% precision. Advisors: Dave Cieslak & Chirag Mandot (Aunalytics) Summary: The goal of this project was to predict the risk that any given media subscriber would cancel their subscription within the next 3 months. This way, the client media company could prioritize atrisk customers and "pull them back in" by contacting them about their experience, resolving any problems the customer might bring to light, and waiving the next month's subscription charge. The available customer data consisted of singular features such as residence/age/estimated income, as well as timeseries features such as date/type/price of past subscriptions and the dates of complaints/service calls. Each timeseries feature was converted into several singlular variables by aggregating over time windows leading up to the current date, and various models (linear regression, SVM, random forest, neural network) were backtested over roughly a decade of available data. The random forest yielded the best performance  for every 5 predictions that a customer would cancel their subscription, about 4 were correct. The model was implemented into production and runs daily to update the client's risk score dataset. 
201704
The Data Scientist's Guide to Topological Data Analysis (2017) Honors bachelor's thesis  explained the basic theory behind topological data analysis and demonstrated its applications in visualizing highdimensional data. Advisors: Mark Behrens (Notre Dame), Dave Cieslak (Aunalytics) Presented at: Brown Bag Lunch Talk at Aunalytics, Glynn Honors Program at Notre Dame Links: thesis, slides, slides from earlier talk Summary: Topological Data Analysis, abbreviated TDA, is a suite of data analytic methods inspired by the mathematical field of algebraic topology. TDA is attractive yet elusive for most data scientists, since its potential as a data exploration tool is often communicated through esoteric terminology unfamiliar to nonmathematicians. The purpose of this guide is to bridge the communication gap between academia and industry, so that nonmathematician data scientists may add current TDA methods to their analytic toolkits and anticipate new developments in the field of TDA. The guide begins with an overview of Mapper, a TDA algorithm that has recently transitioned from academia to industry with commercial success. We explain the Mapper algorithm, demo opensource software, and present a handful of its commercial usecases (some of which are original). Then, we switch to persistent homology, a TDA method that has not yet broken through to industry but is supported by a growing body of academic work. We explain the intuition behind homotopy, approximation, homology, and persistence, and demo opensource persistent homology software. It is hoped that the data scientist reading this guide will be inspired to give Mapper a try in their future analytic work, and be on the lookout for future developments in persistent homology that push it from academia to industry. 
201703
Connecting Calculus to the Real World (2017) Showed how calculus connects not only to science, technology, and engineering; but also to history, philosophy, business, art, and athletics. Link: packet Summary: Calculus is much more fun to learn when we see how it connects to the real world  and not just STEM subjects, but also business, athletics, and the liberal arts. Even string art has ties to calculus! 
201702
An Intuitive Primer on Calculus (2017) Wrote an introductory lesson to build intuition behind core concepts in calculus. Link: packet Summary: This primer explains the intuition behind the core concepts that tie together all of singlevariable calculus, using many analogies and visual aids. Understanding these core concepts makes it to understand the technical details of calculus later on, because one can then see where they fit in the big picture of calculus. 
201701
Data Science Case Study: Visualizing Reddit Data (2017) Evaluated the potential of topological data analysis for Aunalytics by using it to visualize Reddit data. Advisor: Dave Cieslak (Aunalytics) Presented at: Brown Bag Lunch Talk at Aunalytics Link: slides Summary: The goal of this project was to evaluate the potential of topological data analysis for Aunalytics by demoing it on a toy project, visualizing population segments on Reddit. Applying the Mapper algorithm to a similarity matrix for the 10,000 most popular subreddits yielded an interesting network visualization: Perhaps even more interestingly, applying a continuous transformation to the similarity matrix significantly changed the output visualization  when in theory, continuous transformations should not have any topological effects. To reconcile this finding, I constructed an example demonstrating how said theory can break when there are only finitely many data points. 
201607
AUOpenscoring (2016) Prototyped a method that would allow clients to run new data through models hosted in the cloud. Advisor: Dave Cieslak (Aunalytics) Presented at: Data Science Team and Brown Bag Lunch at Aunalytics Link: not available for public viewing Summary: The goal of this project was to take a step towards selfservice analytics. Nontechnical clients often have trouble deploying models that are built for them, and thus need an easy way to score new data without interacting directly with the model. To this end, I built a Shiny app to demonstrate a method that would allow modelbuilders to upload a model to a server, and modelusers to run the model on new data by posting the data as a request to that server. On the front end, the app allowed the user to create a classification dataset and then play both the role of the modelbuilder and the modeluser, building the model and using it to classify new data. On the back end, the model was converted to PMML and uploaded to the openscoring server, the new data was posted to the openscoring server, and the scored data was returned as the response. 
201606
A Method for Automated Pairwise Relationship Analysis (2016) Prototyped a method for exploring pairwise relationships in columnar datasets. Advisor: Dave Cieslak (Aunalytics) Presented at: Data Science Team at Aunalytics Link: not available for public viewing Summary: The goal of this project was to take a step towards automating the process of hypothesis generation in exploratory data analysis, by introducing a method for exploring pairwise relationships in columnar datasets. The method was based on a quantity I called the "discrepancy fraction," which is given by and which appears in many standard statistical quantities such as chisquared and mutual information. I also built a Shiny app prototype of a tool that would use the discrepancy fraction to help analysts sort through all the relationships between features in a dataset. 
201605
Data Science Gallery (2016) Prototyped a solution for storing and displaying datasets, analytics notebooks, and visualizations. Advisor: Dave Cieslak (Aunalytics) Presented at: Aunalytics meeting Links: not available for public viewing Summary: The goal of this project was to prototype a system for storing and displaying datasets, analytics notebooks, and visualizations. My first iteration used GitHub Pages, and my second iteration made use of GraphDash. I also wrote functions to integrate the system with iPython notebooks, so that one could upload to the GraphDash server directly from an iPython notebook. 
201604
Banking Sales Funnel Analysis (2016) Discovered a sales funnel for a banking client by generating a hierarchical clustering visualization of consumer service usage. Advisor: Dave Cieslak (Aunalytics) Presented at: Data Science Team and Consumer Insights Team at Aunalytics Links: not available for public viewing Summary: This is an exploratory analysis I made for a banking client who had data on its customers' account activities and service usages, and wanted to extract an actionable insight. First, I used the balances, transaction frequencies, and total cash flows of the accounts to cluster the accounts into 4 levels of health: highactivity accounts, mediumactivity accounts, lowactivity accounts, and accounts at risk of churn. Then, for each cluster, I created a heatmap to display the fraction of accounts that used each service. Laid side by side, the heatmaps revealed a hierarchy in transaction types: accounts at risk of closing tended to use only deposits/interest, lowactivity accounts additionally used check/credit/debit, mediumactivity accounts additionally used ATM/pointofsale, and highactivity accounts additionally used fees and transfer credit/debit. This hierarchy could be interpreted as a sales funnel, telling which particular services could be pushed on a customer in attempt to nudge their account toward a level of activity. I also looked for telltale signs in account activity preceding churns. Since I was not able to find any through manual search nor visual inspection, we turned to machine learning for churn prediction. 
201603
Plastic Neural Network Simulations (2016) Found a general principle of network reorganization for random sparse neuronal networks in response to periodic stimulation. Showed that "seizurelike" activity can arise if the refractory period is sufficiently low. Advisor: Dervis Can Vural (Notre Dame) Presented at: ManyBody Physics & Biology Group at Notre Dame's Interdisciplinary Center for Network Science and Applications (iCeNSA) Link: slides Summary: The goal of my project was to simulate and intuit how a neuronal network activates and reorganizes in response to periodic stimulation. My simulation consisted of a couple hundred neurons and displayed the activation patterns and weight changes that resulted from stimulating a subset of neurons with a periodic pulse. Under normal conditions, the network gradually reorganized itself so that only the neurons that were directly stimulated became active. I also observed that when the refractory period was reduced to a fifth of its normal value, the network activity skyrocketed prior to reorganization, somewhat reminiscent of a seizure. 
201602
Shaping STDP Neural Networks with Periodic Stimulation: a Theoretical Analysis for the Case of Tree Networks (2016) Solved a special case of how to periodically stimulate a neural network to obtain a desired connectivity. Advisor: Dervis Can Vural (Notre Dame) Course: ACMS 80770 (Topics in Applied Mathematics) at Notre Dame Link: writeup Summary: The goal of this project was to create a simple neural network model with a biologically realistic learning rule, whose changes in connectivity could be derived analytically. After creating the model, I derived rules for how periodic stimulation of a single neuron would change the connectivity of the network, in the case of a tree network. Then, I used those rules to come up wth twoneuron stimulation patterns to solidify or break connections in the tree as desired. 
201601
Making Indirect Interactions Explicit in Networks (2016) Described a concrete interpretation of weighted categories as explicit representations of indirect interactions within networks. Link: writeup Summary: After reading about Ehresmann & Vanbremeersch's Memory Evolutive Systems and Robert Rosen's Relational Biology, I tried to come up with some concrete takeaways. The main theme seemed to be that category theory provides a language for explicitly describing indirect relationships in graphs  which, while semantically interesting, is ultimately just semantics. 
201509
On the Effectiveness of Social Distancing Advice During Epidemics (2015) Used game theory to show that social distancing advice during epidemics is generally useful, and extremely useful when very few people are immune to the disease. Course: EE 67045 (Static and Dynamic Game Theory), taught by Vijay Gupta at Notre Dame Link: writeup Summary: The goal of this project was to use game theory to evaluate the effectiveness of social distancing advice during epidemics, in which people avoid exposure to disease by avoiding physical proximity with others. Agents choose a number of social connections to keep, and have a payoff function that depends on two competing factors: the number of connections and the probability of remaining healthy. Health officials advise agents to keep a particular number of connections that would maximize everyone's expected payoff if everyone kept that number of connections. In the absence of advice, it is assumed that agents maximize their expected payoff in the worst case, when every neighbor who is not immune becomes infected. I found that following social distancing advice always allowed agents to keep several connections while maintaining a payoff, wherease in the absence of social distancing advice, agents would nearly or fully isolate themselves and even then could expect a payoff only a fraction the size of that under social distancing advice. 
201508
Network MotifInspired Evolution of HodgkinHuxley Neuronal Networks with SpikeTiming Dependent Plasticity (2015) Simulated how cyclic neuronal networks ought to change, under a particular theory of neural plasticity, in response to periodic stimulation. Advisor: Dervis Can Vural (Notre Dame) Presented at: Notre Dame College of Science Joint Annual Meeting (COSJAM) 2015 Link: slides Summary: The goal of this project was to understand how cycles of neurons ought to change connectivity in response to periodic stimulation, under an experimentally observed plasticity rule. I derived theoretical expectations for the case of "sequential spiking," in which exactly one pulse is traveling around the cycle at a given time, and ran simulations with biologically realistic neuron models to verify the results. 
201507
EndofSummer 2015 Report (2015) Implemented spiking neurons in a deep neural network, in attempt to emulate brain waves. Advisor: Garrett Kenyon (Los Alamos National Lab) Link: work summary Summary: The goal of my summer project was to implement spiking neurons and observe "brain oscillations" in an opensource deep learning framework called Petavision. To implement spiking neurons, I had neurons inhibit themselves, so that they would reset whenever they became active. However, I did not observe any oscillations in spike rates, and the network performed poorly on image reconstruction tasks, likely because the training algorithm was tailored to nonspiking neurons. It was beyond the scope and duration of the project to create a new training algorithm tailored to spiking neurons. 
201506
Wixtend: the Free Online Thinktank (2015) Prototyped a wiki site where students could collaborate on academic projects. Videos: Summary: The goal of this project was to create a collaborative project website where users could host their own projects and contribute to projects hosted by other users. (Kind of like Github, but with a focus on the progression of the project and the final project writeup.) I designed the site as a MediaWiki wiki so that individual users' contributions to a project could be tracked precisely: potential collaborators would submit edits to projects, project hosts would decide whether or not to approve the edits, and every submission and approval would be written into the logs. After the initial prototype, the site didn't gain much traction as it was tailored to a population of projectcrazed students (which I eventually realized is incredibly small). So, the project was ended in favor of using GitHub. 
201505
Numerical Investigation of the 3n+1 Problem and its Continuous Extension (2015) Conducted numerical experiments on an open problem in mathematics to reveal both surprising behavior and general underlying principles. Advisor: Jeff Diller (Notre Dame) Appeared in: Scientia Journal of Undergraduate Research 2015 Links: paper, preprint Summary: Start with any positive whole number. If it is even, divide by 2; if it is odd, multiply by 3 and add 1. Do it again, and again, and so on  for example: 3,10,5,16,8,4,2,1. The 3n+1 problem is to prove that no matter what number you start with, you will eventually reach 1. At surfacelevel it seems like there should be a simple solution, but it has remained unsolved for over 70 years and is thought by some mathematicians to require the use of mathematics far beyond that of our present knowledge. In this project, I extended the 3n+1 problem to the set of real numbers using a continuous sinusoidal function that maps every even number to half of itself, and every odd number to one more than three times itself. Repeated application of this function appeared to eventually map every real number to the interval [1,2]  however, and quite interestingly, iteration sequences often differed wildly for input numbers seemingly very close together. I also generalized the 3n+1 problem to the an+b problem and found that the decreasing endbehavior tends to break just above a=3, which is surprising because if the numbers in an iteration sequence have equal chance of being even or odd, then the cutoff should not be until a=4. However, by comparing the increasing vs decreasing area in the continuous version of the an+b problem, I was able to justify the a=3 cutoff. 
201504
A Visual, Inductive Proof of Sharkovsky's Theorem (2015) Presented a friendlier version of a complicated proof in dynamical systems, using extensive visual diagrams. Advisor: Jeff Diller (Notre Dame) Links: post; pdf (rough) Summary: Dynamical systems are objects whose states change over time according to an update function. It is often useful to know about the periodicity of points in the system as they are iterated by the update function  for example, equilibrium states are points with period 1, and other periods can reflect predictable state cycles. In this writeup, I present and visually illustrate a known proof of Sharkovsky's Theorem, which tells us the order of periods of periodic points.
