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.
I assume they're talking about how when multiplying by a matrix by a vector, it's more natural to think of the matrix as a collection of columns than as a collection of rows, and to think of the vector as a column vector.
That layout is a nearly universal convention in applied practice such as statistics. Readers would be very very confused if you flipped it the other way.
The irony is that "programmers" are much more divided on this than statisticians are.
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.
"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.
> Not even the Trump admin is alleging levels of indirect costs that high.
The 70% "indirect cost" number had latched into my brain. I was willing to concede this point, but it looks like 50, 60, 70% are accurate as of 2025 [0].
While there exist institutions with only 30% indirect cost, every single not-especially-prestigious university in my region are retaining 60% or more.
> As of May 2025, indirect cost reimbursements for [institutions of higher education (IHE)] are typically determined by an indirect cost rate that is pre-negotiated with the federal government and varies by IHE—ranging from 30% to 70%.
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.
Well, "born on a day" would not convey any information unless it means "during daytime". If that has probability 1/2, the answer would be 3/7. With Tuesday (or, indeed, any other weekday, with probability 1/7), it is 13/27.
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.
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