Posts

The language of life is written in DNA, a four-letter code that orchestrates everything from bacterial metabolism to human cognition. For decades, scientists have sought to decode this language, but its complexity – spanning billions of years of evolution and trillions of nucleotides – has defied simple interpretation.

In my previous blog post, I covered the first three panels of the inaugural Sedona WG13. If you haven’t read it yet, you can do so here! Measurement, Defensibility, and Compliance: Vetting, Validation, and Monitoring of AI Tools and Uses The afternoon of WG13’s first day kicked off with a panel discussing validation and monitoring of AI tools.

Introduction Last week, I had the unique opportunity to attend the inaugural meeting of The Sedona Conference Working Group 13 on Artificial Intelligence and the Law. For those who are unfamiliar with it, The Sedona Conference (Sedona) is a 501(c)(3) research and educational nonprofit dedicated to advancing the law in new and burgeoning areas.

In my opinion, one of the reasons that differential forms are so confusing to new students is that the pedagogy in introductory calculus classes is often insufficiently rigorous. For example, in a first course in calculus, students are taught to integrate single variable functions and are instructed to think of this operation as computing the area under a curve.

Interested in getting your feet wet with machine learning? These are my recommendations for the best books to get you started. I will do my best to keep this list updated as I come across new resources.

The Euler-Lagrange Equation In the previous post, we introduced the variational calculus and took the first steps towards deriving necessary and sufficient conditions for establishing local extrema of functionals. In this post, we will build on our previous work and derive the Euler-Lagrange equation, then subsequently apply it to some physics problems.

In introductory calculus, we learn to take derivatives of functions of a single variable. In vector calculus, we learn to do the same for vector-valued functions, although here the analysis becomes more complex as there is no longer a single, canonical notion of a derivative.

An explanation using Sard’s Theorem.

If you’ve read my article about the REINFORCE algorithm, you should be familiar with the update that’s typically used in policy gradient methods. $$\nabla_{\theta} J(\theta) = \mathbb{E}_{\tau \sim \pi_{\theta}(\tau)} \left[ \left( \sum_{t} \nabla_\theta \log{\pi_\theta}(a_t \mid s_t)\right) \left(\sum_t r(s_t, a_t)\right)\right]$$

Identifying variants in genomic sequences and an introduction to Google’s DeepVariant model.