knappa

Unfertilized bird eggs are single cells, fertilized eggs should be multicellular by the time they are laid.

Fencepost errors aren't errors if you are actually trying to count fenceposts.

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?

Nope. 31% German, 27% Autistic.

They said that they were going to be blunt, not terse.

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 don't know, but I've never had trouble with mud daubers.

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.

Institutional administrators confiscate 50, 60, 70% of every research grant.

Not even the Trump admin is alleging levels of indirect costs that high. See e.g.

https://grants.nih.gov/grants/guide/notice-files/NOT-OD-25-0...

"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.

This is why, Prof. Wildberger says he "doesn't believe in irrational numbers."

Oh boy, I hope that they missed a joke or misquoted.

As I recall, most of the complaints about big pharma were about price-gauging. This is entirely different.

So, by "men", they mean 15 or older. Median age of first marriage is ~30 for US men.

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.

Not a question of merits, but of how to make sure the journal really had acquired the rights to publish the article.

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.

Pretty sure this person meant singular as in singularity, not singular as in one.

Instead of trying to fit a sine wave this way, one can also take the Fourier transform and read off the largest value and its location.

A lot is lost here by using notation that looks like it is rigorous math, but is actually pretty vague. For example, are X and Y indicators for the same flip? If so, they are mutually exclusive, X=Y is contradictory, and hence P(X=Y)=0. If they are samples from different flips (and your coin is the usual idealized one) then X and Y are independent random variables and P(X=Y)=0.25.

It's just like if X~N(0,1), Y~N(0,1) and you want to know the distribution of X-Y. You need to know what the PDF of (X,Y) looks like. Well, you don't know. X and Y could be correlated or they might not be. e.g. if could be that (X,Y)~N( (0,0), [(1,0),(0,1)] ) or maybe (X,Y)~N( (0,0), [(1,1/2),(1/2,1)] ). The distribution of X-Y cares how correlated X and Y are.

Looks like he figured out the problem by at least 2007: http://www.melbochner.net/exhibitions/gabbiano-rome-2007/

As others have noted, exponential smoothing has a different problem, that it asymptotically approaches but never quite reaches its destination. The obvious fix is to stop animating when the step gets below some threshold, but that's inelegant.

This is off the cuff, but you might be able to fix this as follows: Interpret exponential smoothing as a ODE on the distance to the target. Call that distance D. Then exponential smoothing is the Euler update for dD/dt=-C*D. (the constant C>0 being a speed parameter) The issue you bring up is basically the fact that the solutions to the ODE are D(t)=A*exp(-C*t), which is asymptotic to zero as t->oo, but never reaches zero. Now, the fix is to replace the ODE with one that goes to zero in finite time. e.g. dD/dt=-C*sqrt(D). (Solutions are half-quadratic. i.e. they are quadratic for a bit then stay zero once you hit zero.) The Euler update for this is stateless like you wanted.

The rest are different, but in the several US localities I've lived in, water and sewer are paid as separate metered services. (Only the water is metered, the sewer is billed proportionally to the water usage.)

I would read all more formally as: for each element in this list, the element is true. Then you get a vacuous truth. (Think about the negation: there is an element in the list which is false. That's obviously false.)

Any would be more formally: there is an element of the list which is true. But the list doesn't have any elements, so that's false.

Looks logical to me. Plus you get that `not any( map(lambda x: not x, l) )` is the same as `all(l)` for any list `l`.

Professional engineer. That is, a official state licensed engineer.

No, there is nothing all that specific about vector spaces. This is true about general algebraic structures.

What you want to care about here is preserving structures: How would you define addition on a disjoint union? e.g. If you have V⊔W you can add two things in V and you can add two things in W, but what about something in V with something in W? Which zero vector is "the" zero vector?

If you don't have all those properties that make a vector space, then it's just a set. Then, yes, if for some reason you want to do the sum of vector spaces V and W as sets, you will get the disjoint union of these sets. That would be a pretty odd thing to do though; in that case, why are they vector spaces?

There are different sum- and product-like operations for different types of things: For sets (and topological spaces), the sum operation is the disjoint union and the product is the Cartesian product. For vector spaces, the sum operation is the Cartesian product and the product operation is the tensor product.

If you think of finite dimensional vector spaces as functions on finite sets, then these all match up. i.e. if V (vector space) is the functions on S (set) and W (vector space) is the functions on T (set), then the functions on S⊔T are V⊕W because you just list the values of the functions on S and then on T. Further, you can see that functions on S×T are V⊗W since the natural basis for V⊗W consists of vectors e_s⊗e_t that pick out elements (s,t) ∈ S×T.