I don't know, but what I do know is that in Hungary you can just buy 50 liters max, because there is a shortage already. If this situation has not affected your livelihood yet, that's great. But sh*t will hit the fan real hard come autumn in Central Europe.
Also, just FYI, there are actually two simplex methods. One is an algorithm to solve LPs (by George Dantzig), while the other is a derivative-free optimization algorithm for solving general unconstrained problems.
It’s unfortunate they both share the same name, because they’re completely different algorithms.
Simplex AFAIK isn’t used to solve real world “regular” linear programs as worst-case complexity is exponential, and polynomial algorithms exist.
As it happens, MILP solvers often do use the simplex solver internally, as it can be hot-restarted - you can modify the problem a bit and quickly get an amended solution.
On the contrary the simplex method IS used to solve regular linear programs, despite the existence of polynomial time barrier/interior-point algorithms.
Yes, simplex is worst case exponential and barrier is worst-case polynomial, but depending on the problem, the average case characteristics are very different. Depending on the problem, simplex can beat barrier methods. For many large LP/MILP problems, heuristics and randomness usually dominate solution time rather than simplex vs barrier. That’s why commercial solvers so thoroughly beat open-source solvers —- their heuristics are far superior.
For NP-hard problems, it’s not a good idea to judge algorithms by their worst-case complexity —- which only provides bound — but by their real world performance. Before Karmarkar’s method, there was another polynomial time algorithm by Khachiyan. Despite being polynomial time, it was too slow to be of any practical interest.
I did software engineering for 3 years after graduation. Now I teach mathematics in a high school since '20. Software engineering was very stressful for me and I also wanted to sync holidays with my kids. Parents seem to value my background. Pay is low but I have a reasonable amount of extra time to tinker.
I don't understand, there were over 50k non-covid deaths in the twice vaccinated and around 500 covid deaths. That sounds significant, or is it due to the age distribution of twice vaccinated?
How are the theories incompatible? My basic understanding is that GR describes how the space looks like and Standard Model describes fields defined in this space.
That's a very complicated question really and kind of beyond my specialisation, but it mostly comes down to something called "renormalization", which is a technique used to construct a Quantum Field Theory. Unfortunately it doesn't seem to be possible to construct a renormalizable field theory for gravity, which makes it seem incompatible with the approach for the Standard Model.
In their basic forms, GR and the Standard Model are basically entirely different languages, as you said, one using a model of motion in a curved spacetime, and the other using a formalism of quantum fields. However this brings up a big question: why are the electromagnetic, weak, and strong interactions described by a totally different formalism to gravity?
You can do quantum field theory in a curved spacetime, but that is more of a band-aid approach to the problem than anything and doesn't really help to unify the two approaches.
It could be that the answer is that two different Gods designed gravity and the other forces, they certainly seem that disparate. But as a Physicist is it quite hard to accept that gravity and the other interactions are fundamentally separate, we would like a full theory of all four of the interactions.
EDIT: I should point out that QFT is hardly very nice anyway. We don't have evidence for a specific ontology/interpretation for Quantum Mechanics yet, we don't know what Quantum Mechanics is or means. We may come closer in the years coming though.
Numerical methods can be even more similar: there's several approaches to gravitation on the lattice, for instance, that would be familiar to lattice QCD people.
Programmes to make use of objects used by HEP (Lie algebras, configuration/phase/state spaces) for strong gravity are not accidental.
> You can do quantum field theory in a curved spacetime
Birrell & Davies likes to stress "Curved Space" (as in the textbook's title).
It's not a band-aid at all, it's a first approximation, up to the so-called one-loop level. There are higher-order approximations.
It's not the 1960s any more, and especially after the 1982 Nobel (the same year as Birrell & Davies was published), I think it's not super-controversial to argue that every good physical theory is an effective theory, even if the characteristic scale has not been determined.
> why are the electromagnetic, weak, and strong interactions described by a totally different formalism to gravity?
But to me a variational approach on the Ricci curvature tensor (following Pirani https://journals.aps.org/pr/abstract/10.1103/PhysRev.105.108... ) and on the Faraday electromagnetic tensor (Bondi & Pirani started this in http://www.theory.physics.ubc.ca/530-19/planewave-bondi.pdf ) are very similar, not very disparate. Indeed, you can see how one arrives at the spin-2 gauge boson for the former (symmetric rank-2 tensor) in the same way one arrived at the spin-1 gauge boson for the (totally antisymmetric rank-2) Faraday tensor.
But this is certainly not a successful approach to a "full theory of all four of the interactions", however it led to "just" an effective field theory that is good to shorter lengths than we likely will be able to probe any time soon.
There's a lot of interesting stuff here, but none of it has really been settled on by the wider Physics community. It certainly is a huge area of continuing research and debate.
Who is "the wider Physics community", and what do they have to do with it? Do we expect someone in solid state physics to be driving the directions of research into numerical relativity in vacuum higher dimensional spacetimes? Or a general-relativist deciding on the merits of a doctoral dissertation presented in nonlinear optics?
Every point but one in the comment you replied to is as far as I know found in one or more standard graduate-level textbooks on gravitation (even "Teaching tradition!" is paraphrased from Kaiser's MTW preface). If you like I can direct you to them; they are all much more interesting than my HN comment(s).
(The exception is my point on lattice methods in numerical relativity, for which you will need a specialist graduate textbook like Baumgarte & Shapiro.)
Generally in Physics we eventually reach some kind of consensus on the most accurate theory, however as far as I can tell there are multiple competing theories of Quantum Gravity. Similar to how the interpretation of QM is unsolved because we haven't significantly justified a specific interpretation yet.
By "the wider Physics community" I mean Physicists in general having a general sense that the problem has been solved, for example a solid state physicist has some idea that the Standard Model is our most accurate theory of the three interactions it covers, even if they know nothing about the Standard Model. Eventually a theory of Quantum Gravity will reach that kind of recognition if we have some kind of experimental evidence or strong theoretical arguments regarding it. It is a question of marketing and broadcasting
Quantum theory is about linear reversible evolution based on some Hamiltonian operator. GR is non-linear non-Hamiltonian theory (a naive Hamiltonian is zero); it has strange one-way solutions such as irreversible collapse of stars into black holes.
These two theories have very different mathematics and different concepts of state. Nobody has been able to connect them in a way that would be a "success" - a unified theory that explains both GR and QT in a consistent way.
