every major settlement between Pylos in Greece and Gaza in the Levant was destroyed and abandoned. Forty-seven were credibly identified as having been destroyed during this period [of 100 years], and the number is probably much higher in actuality.
This is really cool. A great example of constraining the problem which then allows you do to the impossible. I’ve been working on an implementation of this idea myself.
- It's undecidable whether two arbitrary reals are equal
- But, it's decidable when limited to:
- (1) the four basic arithmetic operations, and square roots
- (2) the sin, cos and tan trigonometric functions and their inverses
- and (3) exponential and (natural) logarithm functions.
- "500 million install of the Android calculator app with no bug reports relating to floating point behaviour"Dynamical systems---by which we mean machines that take time-varying input, change their state, and produce output---can be wired together to form more complex systems. Previous work has shown how to allow collections of machines to reconfigure their wiring diagram dynamically, based on their collective state. This notion was called “mode dependence”, and while the framework was compositional (forming an operad of re-wiring diagrams and algebra of mode-dependent dynamical systems on it), the formulation itself was more “creative” than it was natural.
In this paper we show that the theory of mode-dependent dynamical systems can be more naturally recast within the category Poly of polynomial functors. This category is almost superlatively abundant in its structure: for example, it has \emph{four} interacting monoidal structures (+,×,⊗,∘), two of which (×,⊗) are monoidal closed, and the comonoids for ∘ are precisely categories in the usual sense. We discuss how the various structures in Poly show up in the theory of dynamical systems. We also show that the usual coalgebraic formalism for dynamical systems takes place within Poly. Indeed one can see coalgebras as special dynamical systems---ones that do not record their history---formally analogous to contractible groupoids as special categories.
To better understand immigration paths of the AI workforce, CSET surveyed recent PhD graduates from top-ranking AI programs at U.S. universities. This data brief offers takeaways — namely, that AI PhDs find the United States an appealing destination for study and work, and those working in the country plan to stay.
I tried some examples from the paper and found that they worked okay, not great. I’m really curious about the limitations of techniques like this: What size expressions work? Can this be used for other things besides logic gates? Is it possible there’s a much more suggestive version of this?
As @patio11 likes to say, incentives rule everything around me.
Most excellent tweet (thread) of the year.