In this paper, we study approximation properties of single hidden layer neural networks with weights varying on finitely many directions and thresholds from an open interval. We obtain a necessary and at the same time sufficient measure theoretic condition for density of such networks in the space of continuous functions. Further, we prove a density result for neural networks with a specifically constructed activation function and a fixed number of neurons.

Functional programming in pure form implies no state and no side effects when called (since there is no state). Azure Functions (much like AWS Lambda and Google Cloud Functions) is a neat concept where you don't need any explicit infra, you just deploy a function and reference it via an endpoint (URI). During my search for the ultimate (aka, ultimately cheap/free) deployment for my ML models, I thought I would try this out since the pricing docs state a high free # of executions. Setup is easy, go to Azure Portal and run thru the usual "Create" and search for "Functions" Not well documented is that you have to install both the node package (npm install -g azure-functions-core-tools) and the python package via pip (pip install azure-functions) if you are coding in Python on Visual Studio Code. Some languages have an online editor within Azure Portal which is kind of nice (though kind of dangerous).

Here's where to search for 7 floating Lightning Bolts in'Fortnite: Battle Royale.'Credit: Fortnite: Battle Royale's Season 5 just kicked off. With it comes another week of challenges, though this Season the first 3 challenges are for everyone, while the final 4 are for Battle Pass owners exclusively, a change from previous seasons. One of the new challenges this week is to search 7 Floating Lightning Bolts across the map---which has seen some big changes in Season 5 including a new desert biome and two new Named Locations: Lazy Links, a golf course replacing Anarchy Acres; and Paradise Palms, a new urban location where Moisty Mires used to be, smack-dab in the middle of the desert. See all of Week 1's challenges here.