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The "suggested for you" content is typically Facebook trying to cross-sell you to other parts of the app. It's not an actual ad, but it's not entirely organic content either.

One of the product teams at Facebook mistakenly believes you'd be interested in using marketplace or whatever and has enough clout internally to get their stuff added to your feed.

"It's important to remember that Facebook can precisely measure the impact of news articles like this"

What would that measurement look like? What is the control group for a news cycle? What signal would you expect to see change?

This is silly. It's not going to disrupt Li-ion. Power outputs are way too low. C14 has a half life of 5700 years. This isn't going to output Li-ion levels of power/weight for 5 millennia. It looks like it might give you microwatts/gram, but this is much closer to existing nuclear tech like RTGs or beta voltaics than it is to Li-ion batteries.

Need based scholarships allow universities to have nearly perfect price discrimination. This allows them to charge different prices to different consumers and extract the maximum amount each consumer is willing/able to pay. If they had to charge everyone the same price, that price would be considerably lower than the sticker prices now.

That's a pretty good summary. There are many different sets of approximations and simulation techniques that make different trade-offs of accuracy/scale.

They're essentially using outputs of a higher-fidelity model to tune the free parameters of a lower fidelity model, and using ML to explore the parameter space efficiently.

The higher fidelity model is itself still an approximation, but there's a lot of interest in this approach and quite a few groups doing work like this targeted towards various material properties, since there just isn't nanoscale experimental data to train models that depend on nanoscale material features.