talks on topological data analysis, cheeger's inequality

I did two math/theory CS seminars this semester. One was on Simplicial Algebra, and one was on Spectral Graph Theory. I gave some talks for these seminars and wanted to put them here. Really massive thank you to Ivan, Ekene, and Binghui for leading them! I had a great time. :)

The first talk I gave is about topological data analysis and inference; specifically, about geometric sampling, metric measure spaces, and probability theory in barcode space. It follows sections 3.2–3.3 of Rabadan and Blumberg's Topological Data Analysis for Genomics and Evolution. You can find my notes here.

The second is about Cheeger’s inequality (inequalities are always pretty cool tbh), which is a fundamental result in spectral graph theory connecting the second smallest eigenvalue of the graph Laplacian with the conductance of a graph, both of which help us characterize a special type of graph called an expander. I made a presentation, which you can flip through below. You can also find this presentation, as well as the other talks from the Spectral Graph Theory seminar, on Columbia TCS group’s website here.

The third one is about an application of tools from topological data analysis to viral evolution, specifically viral recombination in HIV. It follows pages 303–324 from Rabadan and Blumberg. It’s pretty cool to see how barcode diagrams and zigzag persistence diagrams might actually be useful. You can find my notes here.

some solutions to øksendal’s stochastic differential equations + my ‘talk’ on the black-scholes formula

This spring, I did the Directed Reading Program (DRP) with the Math department; undergrads get paired with a PhD student to read a math book together. Columbia pays for the book. :)

Richard and I read the book on the right. (Thank you Richard for bearing with me!!)
We also worked through a few exercises, and I typed them up this week along with some notes to understand stuff a bit better. Since Øksendal’s own solutions are quite sparse, I wanted to post them here:

• Chapter 2: Some Mathematical Preliminaries - Probability Spaces, Random Variables, and Stochastic Processes

• Chapter 3: The Itô Integral

• Chapter 4: The Itô Formula and the Martingale Representation Theorem

• Chapter 5: Stochastic Differential Equations

• Chapter 7: Diffusions - Basic Properties

• Chapter 10: Application to Optimal Stopping

• Chapter 12: Application to Mathematical Finance

Also, I prepared a brief talk about the Black-Scholes formula derived in Chapter 12:

The Debut Venture Fund Landscape

The process to raise a new venture fund has largely been shrouded in mystery and guesswork —what kind of people successfully raise new funds from LPs? What experience do they have? How old do they tend to be? And, most importantly: Are any of these factors correlated with how much money they end up raising? Jaclyn and I analyzed data from Pitchbook to shed some light on the debut venture fund landscape. Check the article out here:

medium.com/@zhiroug/bd7a03f51775

Remark: Did these analyses by making simple linear regressions before I learned more cool econometrics stuff, or knew anything about causal inference, really… Recently been wanting to mess with this dataset. Will write an update if it happens!

start-ups innovating on clinical trial design, for columbia venture insights

There’s a drug development bottleneck increasingly faced by pharmaceutical companies, especially at the clinical trial stage. Some start-ups are innovating on this using AI. I had the pleasure of writing an article with other analysts at CVP about this! Check it out ↓

so like what’s quantum computing lol

I think one of the best things about a liberal arts education is the literacy about things: as in, not being completely ignorant about what’s shaping the cultural milieu. One of the liberal arts classes required as a first-year at my school is Frontiers of Science, which aims to equip undergrads with natural science literacy. For our end-of-semester project, we more or less got to explore a related topic and present it in some way to a general audience.

I decided to make a ‘visual exhibit’ on the intersection of quantum mechanics (one of the topics we learned) and data science (something I find really cool and want to learn more about). Also, quantum computing has become somewhat of a buzzword; I wanted to see what this was about, at least in a general sense.

I’m hosting it on my website. Check it out here: http://gaolyra.com/FROSCI.

litigation finance article for the law review

Litigation funding is when a third-party firm helps a plaintiff to finance their civil lawsuit, in exchange for a share of the potential settlement. It’s an emerging sector with a lot of potential, but its activity in New York is restricted. Over the summer, I wrote an article about this for the Columbia Undergraduate Law Review (CULR) and it just got published! Check it out here:

Litigation Funding: The Case for New York to Revise Section 489
culawreview.org/journal/litigation-funding-the-case-for-new-york-to-revise-section-489

The potential of litigation finance and the current restrictions it faces, specifically with regards to New York Judiciary Law Article 15 Section 489.

Update: It’s been 3 days and for some reason, my article is the first search result when you Google “S489 New York Champerty”! This is really cool, so I’m going to put the screenshot here as a commemoration.

AI, Clinical Trials, and Digital Therapeutics for the undergrad science journal

I was recently accepted to Columbia Undergraduate Science Journal (CUSJ)’s Summer Publishing Program, where I researched and wrote two articles. Check them out :)

Beyond Drug Prescriptions: The Promise and Reality of Prescription Digital Therapeutics
journals.library.columbia.edu/index.php/cusj/blog/view/242

A review of the fledgling digital therapeutic market and whether it has the potential to replace traditional medications.

The Future of Clinical Trials
[link coming]

Clinical trials are a major hold-up in the drug development pipeline for pharmaceutical companies, with only ~10% of drugs able to move past it. But only half of all clinical trials fail because the drug itself doesn't work. The other half fails because of errors related to the trial itself—errors that jeopardise investments into not only the trial itself but also the drug development and research that come before it. Digital integration and artificial intelligence can help.

LAUNCHING AN EXPERIMENT INTO SPACE!

See the article I wrote for the Perspectives Blog on our experiment here!

Over the past few months, I’ve been working with a team of dedicated students to launch an experiment up into the International Space Station! It aims to look at how bacteria like E. coli and E. faecalis grow under the microgravity conditions in space. It has potential applications in drug development.

Here are some pictures:

UPDATE: The capsule was launched as of today (April 9 2020) as part of the Soyuz MS–16 mission! It’s going to be in space for 4 months, and then we’ll be able to retrieve the capsule.

My Philosophy Essay Got Published

Questions is a peer-reviewed journal of philosophy sponsored by the American Philosophical Association. For their most recent issue, they invited responses to the theme of “What is your favorite philosophical problem?”

I received a similar prompt in a timed AP Lang. argumentative essay, so I built on what I wrote in class and submitted it as a short article to Questions. I’m excited to say that it’s been accepted and published! Check it out:

Snapshot taken from the Philosophy Documentation Center.

rip socratic.org

Socratic, a website where people can ask and answer academic questions, will close to new questions and answers on August 15. I've been a regular answerer in the Chemistry section (with a brief foray into math until I realized that using KaTeX for actual math angers me even more than for chemistry—maybe someday I’ll learn). You can see my old answers here. As of today, it looks like I've been able to reach 300,000 people in my short stint:

Socratic has a special place in my heart because, there, I felt like I was helping the world understand the things I am so passionate about; the things I am so eager to share. It was a win-win situation: I got to talk about Chemistry and help other people along the way. 

I started contributing sometime in my sophomore year, and it's sneaked its way into my daily routine since.
A daily, repeating task in my mental to-do list has always been "Answer a Socratic question." I do it every weekday after I come home from school; on weekends, it's usually the first thing in the morning.

And, since I feel like I've been ticking that box off every day since the beginning of time, I think a small part of me will die on August 15. 

But I guess the death of Socratic will be the beginning of something beautiful. I'm hesitant but excited to be working with a group of other excited people on a continuation of Socratic. I’ll write an update if we make something.

Happy Birthday, Kant

This beautiful man is 294 years old today

I first met him in my freshman-year World Studies class—we were studying the Enlightenment philosophies that led up to the French Revolution. I wanted to read more about these philosophies, but was a bit reluctant to do so because I was a freshman and I guess freshmen, like all adolescents stuck in the early phase of the Identity vs. Role Confusion crisis, never want to do anything. But I was interested enough nonetheless, so I scanned over some SEP entries. 

Kant's philosophy was one of these articles. This quote piqued my interest:

“I freely admit that it was the remembrance of David Hume which, many years ago, first interrupted my dogmatic slumber and gave my investigations in the field of speculative philosophy a completely different direction.”

I’m not sure why, but before seeing this, I fell into the same set of misconceptions that a lot of people have about philosophy: middle-age; middle-class; meaningless, jargon-filled platitudes written on sheets of scented paper. Not particularly bad—just a bit pompous.

I scanned over it. Then I actually processed it, and paused my steady scrolling to reread what Kant wrote. It struck me as incredibly humble. A thought was born in my head, there: "If philosophy was really just this, just a collection of people applauding themselves for their own ingenuity—how could one philosopher be so frank and humble as to lower themselves and credit another philosopher with so much?"
"How could he so openly acknowledge previous mistakes?" My narrow-minded freshman brain assumed that all philosophers must have thought of themselves as infallible. 

Like most people who are proven wrong, I tried to justify my belief by thinking that the contradiction to my belief was only an exception—obviously, I picked the worst way to think about my theory. I guess it worked for a few days, but gradually, as I learned to understand more about philosophy, I accepted the fact that I was wrong.
I was inspired by these vignettes: Kant’s blatant acknowledgement of his errors; Plato and Xenophon, eager students of Socrates who offered differing interpretations to his daimon but both worked arduously to preserve his thought; Kierkegaard, referring to his teacher, Poul Møller, as the "inspiration of [his] youth". It’s something about the concept of an evolution and acceptance of some non-trivial, ever-growing academic journey that changed my mind about philosophy.

This is all thanks to Kant.

Confession: I still don't fully understand a lot of Kant's ideas. But I think that's what continues to make him, along with other philosophers like him, so intriguing to me—as I evolve on my own intellectual journey, I think I'll begin to understand more and more of his brilliant ideas. I’m 15 and have time to mess with my own head through philosophy, so I’m terribly excited to learn more about him as I grow. 

So, thank you, Immanuel Kant, for sparking my passion for philosophy. I think you've woken me from a dogmatic slumber. Happy birthday or something. :)