It's not processor op-codes, but sure it's part of the software. You wouldn't say that a set of precomputed weights in a numerical integrator aren't part of the software, would you? Or say that the graphics in a game aren't part of the software?
It depends which side you are doing the multiplication on? Most linear algebra textbooks work matrix-vector, where the vector is a column vector. In that arrangement, the resulting vector is formed by dot products of the rows of the matrix with the vector.
On the other hand, you see vector-matrix multiplication a lot in other places, for example, the Markov chain literature. There, the vector is a row vector and the resulting vector is formed by dot products of the columns of the matrix with the original vector.
I'm a mathematician. It's kind of a strange statement since, if we are talking about a matrix, it has two indices not one. Even if we do flatten the matrix to a vector, rows then columns are an almost universal ordering of those two indices and the natural lexicographic ordering would stride down the rows.
"Yet the average indirect cost rate reported by NIH has averaged between 27% and 28% over time."
and a lot of that is simply because nobody wants to do the detailed accounting for things like: lab electricity usage, janitorial services, misc supplies.
> The result? 90%+ of academic science is fraud.
This is dramatic nonsense; a simple made up number.
You could definitely replace "Tuesday" with something like that and part of the pedagogical purpose of the problem is for people to question this. The actual effect comes from not distinguishing the boys. That increases the likelihood that at least one of them will be born on any particular day, upweighing the likelihood that there are larger numbers of boys. i.e. You just get, on average, better coverage of boys-born-on-Tuesday when there are more boys.
But correctly formatting references is pretty much a solved task through reference managers, possibly plus bibtex. It's a well-defined task, after all, and well suited to traditional software techniques. [1] If someone used an LLM to format the references, you would still have to go back through them.
If there is any use for LLMs in paper writing, I would think that it is for tedious but not well-defined tasks. For example, asking if an already written paper conforms to a journal's guidelines and style. I don't know about you, but I spend a meaningful amount of time [2] getting my papers into journal page limits. That involves rephrasing to trim overhangs, etc. "Rephrase the following paragraph to reduce the number of words by at least 2" is the kind of thing that LLMs really do seem to be able to do reliably.
1: As usual, the input data can be wrong, but that would be a problem for LLMs too.
2: I don't actually know how much time. It probably isn't all that long, but it's tedious and sure does feel like a long time while I'm doing it.
That's not what was being said. They are saying that when your body does something different, in this case producing fever, it is (often) because of a change in the level of some number of proteins. You get new copies of proteins through gene transcription, and these changes (both increase and decrease) can be detected through changes in the levels of the transfer RNA corresponding to those proteins. Look up differential transcription analysis for more information.
I feel like the main thing that this will accomplish is to show that the quality of peer review is quite spotty. Usually 1 of 3 truly read and understood the paper enough to critique from a place of knowledge. Entirely miscategorizing a paper is not uncommon.
Having lived within a block or so of the place being described, 125th is a pretty accurate placement of the Harlem's southern border west of Broadway. (Maybe a bit more south at St Clair place.) Further east is different. I can't speak to the situation in the 80s.
Mathematician here (trained as pure, working as applied). Non-elegant proofs are useful, if the result is important. e.g. People would still be excited by an ugly proof of the Riemann hypothesis.^1 It's important too a lot of other theorems if this is true or not. However, if the result is less central you won't get a lot of interest.
Part of it is, I think, that "elegance" is flowery language that hides what mathematicians really want: not so much new proofs as new proof techniques and frameworks. An "elegant" proof can, with some modification, prove a lot more than its literal statement. That way, even if you don't care much about the specific result, you may still be interested because it can be altered to solve a problem you _were_ interested in.
1: It doesn't have to be as big of a deal as this.
On the 3 points bit: One and two points are special. In each of these cases, there is, up to translations and uniform scaling, only one configuration. When you have three points, though, there are as many configurations as there are similar triangles. You could probably get a number for each similarity class of triangle, but you shouldn't expect to get a constant across all classes.