Hey! The EML function made the rounds recently on the internet as a “cool trick” that allows for the representation of all elementary functions through composition. As a mathematical curiosity, we prove a universal approximation theorem for EML(-type) trees. Intuitively, one expects that if elementary functions can be presented by compositions of EMLs, then so too can polynomials, and polynomials are dense in other functional spaces (like continuous functions or certain Sobolev spaces), then one expects to be able to approximate (to desired accuracy) any function (in a reasonably general space) through an EML tree (with an upper bound on size and depth). One of the key steps in the proof (detailed in the appendix) is an explicit construction of EML(-type) representation of binary operations, polynomials, hyperbolic tangent, and approximate partitions of unity, and subsequently using them as “LEGO” blocks to get more complex functions. There are some technical difficulties that need to be dealt with in the proof, especially in what relates to the the ill-definedness of the natural logarithm for nonpositive inputs, which prompts us to do some “sign-based decompositions” in Theorem1.Step 5 and a suitable affine map in Corollary 1. Comments are welcome! Paper: https://arxiv.org/pdf/2606.23179 (Note: I use the term “EML(-type)” in the above description because, due to some theoretical and practical reasons detailed in the paper, we generalize the original EML function by adding some learnable parameters.) submitted by /u/JoeGermany [link] [Kommentare]

Hey guys Im 33 tried starting a buisness looks like wont work out the way i wanted few paying customers but meh wont become a millionaire from it What can I do can I place my money on a smaller cyrpto market and make millions from it Im not going back to my normal job I have over 200k saved what can i do to make it millions asap? submitted by /u/Prior_Night_985 [link] [Kommentare]

Hello all. I have to withdraw my assets from Binance since, after July 1st, I won't be able to trade on that platform. I was thinking about putting them on Kraken. BUT. I already have an (empty) account with them from my early crypto days. I seem to have forgotten that password so clicked the link to get a new one. First issue : I can't create a new password, the website keeps telling me "Unable to create a new password. Please try again.". Yes, I've checked and re-checked, the password is the correct length and complexity and has never been used. After a good while of looking around the site for help, I haven't found anything. I then found the KrakenSupport subreddit and WTF IS THAT MESS ? Pages and pages of people locked out of their account ? Is that a think with Kraken ? More so than other Exchanges ? Quick note : if you come here with the intent to preach about the need to have coins out of Exchanges, it's not necessary. I'm well aware and only have what I use for trading on an Exchange, the rest is in a secure wallet. I'm asking about Kraken's reliability as an Exchange, and if somebody has a clue how I could get access to my account. Thanks ! submitted by /u/Nothingto6here [link] [Kommentare]