DNA Of Plague

"Ancient DNA is rewriting the history of plague"

AI Won't Replace Software Engineers

"Why AI hasn't replaced software engineers, and won't"

Romeo And Juliet And Kitty

That time a cat interrupted a stage performance of "Romeo and Juliet" during the pivotal death scene. (Click through to see video.)

Intelligent Bandages

"Scientists Create 'Intelligent' Bandage That Targets Harmful Bacteria". (Via H.R.)

Tao On AI

"How Terry Tao Became an Evangelist for AI in Math"

Wolfram On Rules And Games

"Games between Programs: The Ruliology of Competition"

Apple Device Charging

Lots of good info here: "The Apple Charging Situation". 

Of note, the 80% charging limit really does make a difference in battery life: "This is the math behind Optimized Battery Charging. Every 10% Apple holds back roughly doubles battery lifespan."

Functional Analysis Primer

An introduction to functional analysis for science and engineering"

This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of continuous functions. It resolves important issues, such as whether, why and how we can practically reduce such problems to finite matrix approximations. It is, however, difficult to find a readable introduction that is efficient and comprehensible for scientists and engineers. Here, I have selected only the topics necessary for the most important results, but the argument is mathematically complete and self-contained. 

The article starts from sets and sequences of real numbers. It then develops spaces of vectors or functions, introducing the concepts of norms and metrics that allow us to consider how these can converge. Adding the inner product, it introduces Hilbert spaces, and the key forms of operators that map within or between such spaces. This leads to the concept of compact operators, which allows us to resolve many difficulties of working with infinite sets of vectors or functions. We then introduce Hilbert-Schmidt operators, which are compact operators encountered extensively in physical problems, such as those involving waves. 

Finally, it introduces the eigenfunctions for major classes of operators, and their powerful properties, and ends with singular-value decomposition of operators. This article is written in a style that is complementary to that of standard mathematical treatments; by relegating longer proofs to a separate section, 

I have attempted to retain a clear narrative flow and motivation in developing the mathematical structure. Hopefully, the result is useful to a broader readership who need to understand this mathematics, especially in physical science and engineering.

AI Bootstrapping

"SoftBank's Masayoshi Son says AI is already designing OpenAI's next model"

New Octopus

"A Tiny Bright-Blue Octopus Found in the Galápagos Is Completely New to Science". (Via H.R.)