2,124 karma · joined April 27, 2017
The (discrete) Fourier transform is also a linear transformation, which is why the initial effort of thinking abstractly in terms of vector spaces and transformations between them pays lots of dividends when it's time to understand more advanced topics such as the DFT, which is "just" a change of basis.
My appreciation for the subject grew considerably after working through the book "Linear Algebra done right" by Axler https://linear.axler.net
> The Global Anti-Aging Products Market size is [worth] USD 47.4 Billion in 2023
> Women Dominate Anti-Aging Products Market with Over 80% Share in 2022
Depending on how the supervision chain is arranged, a PhD can a journey of discovery, of new science but first and foremost of yourself and your interests. It can be very self-directed and the only mandate is to discover something new. For this reason it is common for people to dip their toes in a few distinct but related subfields during those years until they find something that sticks (if at all), and the person that comes out of a PhD can be very different from the person who started it.
Less popular techniques like normalizing flows do need that but instead of SVD they directly design transformations that are easier to invert.
https://math.mit.edu/~gs/learningfromdata/
Although if your goal is to learn ML you should probably focus on that first and foremost, then after a while you will see which concepts from linear algebra keep appearing (for example, singular value decomposition, positive definite matrices, etc) and work your way back from there
Innovation is hard, most ideas do not pan out, and most people aren't made for it. It really is a number's game: to stay competitive and innovative as a country you need enough people pushing against the frontier, including taking bets that are too risky for the private sector.
I wonder (pure speculation) if this is because many in the non-vaccinated groups die because of COVID and so don't get a cancer diagnosis?
For example, consider computational research in a domain like healthcare: the job is to find new insights about patients or diseases that allow you to develop better treatments. Most of the time is spent on coding data analysis pipelines, but the truly vauable professional also knows enough about the domain that they are able to interpret the results, conduct follow up analyses and talk at eye level with medical doctors and biologists. The skill ceiling for this kind of position is thus quite high since you need to be proficient in three distinct domains (coding, biology, statistics).
> Would you like me to also connect this to user risks (e.g., extra roaming charges, privacy breaches, spoofed SMS trust issues), so the section feels more practical and less purely technical?
Of boomer propaganda. But don't worry, as voters evolve, so does propaganda.
That is well within the confidence intervals published along with the numbers and entirely unsurprising to anybody who is really paying attention.
> reduction of approximately 52% from their data
And of 0.04% of the actual number of employed people. Seems to me way too thin of a margin to get so worked up.
Is this because atoms don't exist, or because we are looking in the wrong way due to partial (mis)understanding?
The "new truth" that you talk about is just a different understanding of the concept of atom, but the actual thing that we call atom and that exists in the real world (whether as matter or in some other form) has not changed.
Either atoms exist or they dont. Our idea of atom has evolved over time, but the thing that we call "atom" has always been there (at least on the time scale of human civilization).
The probabilistic nature of quantum objects isn't really a problem either. Electrons may be particles, waves, both or neither, but the "thing" is a real phenomenon of this world regardless of how we talk about it.
Similarly, the truth value of alien existence is well defined: either they exist at this time or they do not. We don't know it for sure, but this doesn't change whether they are actually there or not.
> You shouldn’t have to choose between open and secure
"... and that's why we chose for you." So kind!
The question is whether and how much these policies are supported, and the popular vote is obviously relevant in this regard.
> 36% of voters said: I support every outcome of the election, no matter what
That's not really true, for all you know those voters didn't support either outcome. You would expect a "loud and clear" victory not to leave one third of people unconvinced enough to avoid voting altogether.
> but not one single person seriously opposing him and his politics
Almost four hundred lawsuits have been filed against his administration, thousands of public protest events are happening, and the tariffs themselves were just ruled illegal. What does "serious" opposition look like to you? In any case, this is certainly not what "full support" looks like.
https://www.lawfaremedia.org/projects-series/trials-of-the-t...
https://time.com/7312601/anti-trump-administration-protests-...
https://www.bbc.com/news/articles/ckgj7jxkq58o
> If the things he does were really that unpopular, he would not be able to do them.
What is the logic behind this?
https://journalism.university/media-and-communication-theori...