Tongan Paʻanga

November 2024. When you start reading diffusion papers, you'll quickly come across an equation like this: $$dx = f(x,t)dt + g(x,t)dw$$ where $w$ is Brownian motion. When I first saw these, I admit that I just thought about the discretized version $$\Delta_x = f(x,t)\Delta_t + g(x,t)\Delta_w$$ and moved on. You can generate approximate samples in code easily enough: dt = 0.001 x_last = 0 t = 0 while t < 1: dw = np.

I sometimes read articles or papers about type systems that use some funny-looking, two-dimensional notation with lots of unfamiliar symbols and Greek letters. The notation seems mathematical, but ...

Below is a collection of interesting articles I've read in 2022. There are two papers in differential privacy: A Better Privacy Analysis of the Exponential Mechanism and Differentially Private Approximate Quantiles. There's an article in the history of mathematical philosophy and a survey introduction to an area of logic: The introduction of topology into analytic philosophy and Incomplete and Utter Introduction to…

[Updated on 2020-11-12: add an example on closed-book factual QA using OpenAI API (beta). A model that can answer any question with regard to factual knowledge can lead to many useful and practical applications, such as working as a chatbot or an AI assistant🤖. In this post, we will review several common approaches for building such an open-domain question answering system. Disclaimers given so many papers in the…

Article URL: https://natejh.com/Voronoi-Relaxation-Under-Different-Distance-Metrics Comments URL: https://news.ycombinator.com/item?id=32038361 Points: 1 # Comments: 0

Article URL: https://douglasorr.github.io/2021-12-echolocation/article.html Comments URL: https://news.ycombinator.com/item?id=29931349 Points: 1 # Comments: 0

Donovan Young looks at the shapes made when two cones collide

This post will be my attempt to explain intuitively what is Quantum Field Theory. This idea came to me after reading two books: "QED: The Strange Theory of Light and Matter" by Richard Feynman, and "Quantum Field Theory in a Nutshell", by A. Zee (that I only started). Both books use path integrals, but in a very different way: Feynman tells us that the particles can move anywhere they want in space and time, while…

What is Ergodic Theory? In this post, I present some wonderful and intuitive proofs for the ergodic theorems and describe an application of ergodic theory.

In this post, I show how can we leverage the extra information we get from knowing that a car has survived a certain amount of time. I formalize the idea mathematically and then build a framework to optimize the total costs.

The idea for what was later called Monte Carlo method occurred to me when I was playing solitaire during my illness. Stanislaw Ulam, Adventures of a Mathematician The Russian Roulette offers a simple way to construct an unbiased estimator for the limit of a sequence. It allows for example to …

Article URL: https://physics.weber.edu/schroeder/r5/ Comments URL: https://news.ycombinator.com/item?id=32660485 Points: 1 # Comments: 1

The many families on the island nation of Tonga who rely solely on the ocean for their food and income, are struggling to recover from last month's volcanic eruption and tsunami.

The 15 January blast sent shock waves around the globe and defied scientific expectations. Researchers are now scrambling to work out why.

If you want to know what cache revalidation is, how it works, and why it can involve rolling a die, read on. This blog post presents a lock-free probabilistic approach to cache revalidation, along with its implementation.

A core feature of complex systems is that the interactions between elements in the present causally constrain their own futures, and the futures of other elements as the system evolves through time. To fully model all of these interactions (between elements, ...

Recently room temperature superconductor was claimed in Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O (also known as LK-99) with $x\in (0.9,1.1)$. Density functional theory (DFT) calculations suggest that the conduction electrons are from the doped Cu atoms with valence close to $d^{9}$. Motivated by this picture, we build a two-orbital Hubbard model on a triangular lattice formed by the $d_{xz}$ and $d_{yz}$ orbitals with total…

On the phenomenon of in-context learning in large language models and what researchers have learned about it so far.

The attention mechanism was introduced to improve the performance of the encoder-decoder model for machine translation. The idea behind the attention mechanism was to permit the decoder to utilize the most relevant parts of the input sequence in a flexible manner, by a weighted combination of all the encoded input vectors, with the most relevant […]

Article URL: https://www.math.columbia.edu/~woit/wordpress/?p=13319 Comments URL: https://news.ycombinator.com/item?id=34828894 Points: 2 # Comments: 0