#P vs NP

[glassedplanets]

🤍🤎 🩶💛

[straightlightyagami]

i'd honestly bet on the riemann hypothesis being proven before p vs np and the collatz conjecture. collatz seems like something you'd need to make a new area of mathematics to even approach, whatever it is most likely we simply do not have the tools to approach it at this point in time i think, and we probably won't for a while

[tofu-bento-box]

why is picking a new name a fucking NP problem

[owain-glyndwr-dot-html]

All this talk of cook and Karp reductions… making me hungry

[max1461]

It's always "P vs. NP". Why do we have to fight? Why cant we all just love each other?

[clumsyghosts]

Numb3rs: I want The 5th Man, Angels and Devils, and Hangman meta.

I want to read about how Charlie shut down when Don was shot at in the first episode and retreated to P vs NP just as he did when his mother was dying; when Don is stabbed he becomes obsessed with uncovering a serial killer.

His solace is in his math work.

When Amita is kidnapped, Charlie can't focus. He can't work, he can't pull the algorithms or concentrate on the data, so he retreats - not into his work, but to his other safe space: Don. He seeks comfort from his brother physically when he's prevented from seeing what he believes is Amita's body. Emotionally, he can't stay in the conference room where all the math takes place, so he goes to the bullpen, in Don's cubicle, Don's space, until Don comes to talk to him.

Until Don saves him from himself, like he has his entire life.

I wish more GIFs were made of these episodes. There are so many good moments.

[covid-safer-hotties]

Correlation of patient symptoms with SARS-CoV-2 Omicron variant viral loads in nasopharyngeal and saliva samples and their influence on the performance of rapid antigen testing - Published Oct 9, 2024

Study showing 1. The one-and-done method of rapid testing used by many is not good enough to prove covid negativity because rapid test were desined for serial testing 2. saliva swabs increase the accuracy of Rapid Antigen Tests.

ABSTRACT Evaluating SARS-CoV-2 viral loads in nasopharyngeal (NP) and saliva samples, factors affecting viral loads, and the performance of rapid antigen testing (RAT) have not been comprehensively conducted during SARS-CoV-2 Omicron epidemic. This prospective study included outpatients enrolled during Omicron variant period in Japan. Paired NP swab and saliva samples were collected to measure viral loads by reverse transcription-quantitative polymerase chain reaction (RT-qPCR). The correlation between viral loads and clinical symptoms was examined. The performance of an immunochromatography-based RAT kit was also assessed. A total of 153 patients tested within 3 days of symptom onset were included. The mean viral load was 5.60 log10 copies/test and 3.65 log10 copies/test in NP and saliva samples, respectively, resulting in a significant difference (P < 0.0001). Fever over 37°C (axillary temperature) and total number of symptoms other than fever were identified as independent factors positively correlated with the viral loads in both NP and saliva samples. RAT sensitivity using NP and saliva samples was 92% and 68%, respectively, using positive RT-qPCR results as the reference. The sensitivity of RAT using NP and saliva samples was significantly higher in patients with fever ≥37°C and/or at least one symptom than in those with fever <37°C and/or no symptoms (97% vs 83% in NP swabs; 80% vs 50% in saliva). Distinct symptoms, including fever ≥37°C, may reflect high Omicron variant viral loads. Rapid antigen testing, not only using nasopharyngeal swabs but also using saliva, would be useful for COVID-19 diagnosis as point-of-care testing, particularly for symptomatic patients.

IMPORTANCE We examined nasopharyngeal and salivary viral loads using samples collected from outpatients with SARS-CoV-2 infection during the Omicron epidemic in Japan and explored the outpatient factors correlated with viral loads. In addition, we evaluated the performance of an authorized rapid antigen testing (RAT) kit using nasopharyngeal and saliva samples with RT-PCR testing as the reference. Intriguingly, a correlation between fever and other symptoms and SARS-CoV-2 viral loads in nasopharyngeal and saliva samples was observed based on one COVID-19 outpatient visit. RAT sensitivity was influenced by viral loads. Nevertheless, nasopharyngeal RAT is considered useful for SARS-CoV-2 point-of-care diagnosis. In patients with distinct symptoms, including high-grade fever, salivary RAT could be a practical diagnostic tool because of the higher estimated viral loads. After the Omicron epidemic, outpatients with mild COVID-19 have become the main focus of diagnosis and treatment. Our study provides valuable information regarding the point-of-care diagnosis of these patients.

[koipalm]

mainwash from @glassedplanets's P vs NP au

[wozziebear]

In the early days of computing, scientists were busy grouping problems by their scaling difficulty. Some problems, like multiplication, seemed to have algorithms (like the ones you learn in school) that we’ve discovered to solve for them in a relatively short amount of time. As the number of digits grows and the problem gets harder, our algorithms seem to keep up. Other problems, like factorization, seem to elude us. In spite of our best efforts, we can’t figure out good algorithms for solving them quickly.

So, in order to formalise these observations and get a better handle on the situation, computer scientists and mathematicians created classes (buckets) of problems. When we encounter a computational problem, we look at how difficult it is to solve at scale, and based on that difficulty we place it into one of the classes/buckets

Verifiability, the act of being able to prove the correctness of an answer, turned out to be just as important as being able to generate the answer itself. If I were to ask you what the product of 111 x 133 is, you could compute that in a short period of time [...] The test administrator verified your answer by doing that same multiplication and compared the results in order to check for mistakes. That’s exactly what all teachers do for their students;  They compute and compare in order to verify. The fact that the multiplication problem is so easily solvable is what also made it possible for the test administrator to check your solution for mistakes.

In the #4th problem however (factoring 201863), it took you a long time and you still did not manage to produce a solution. Yet, if I were to tell you that 201863 has the factors 337 and 599, you could easily check my work by multiplying the two factors to see if they actually produce the right number. In other words, for the factorization problem, checking an answer for errors is easier than finding the two numbers. This is the difference between P and NP.

P is a class of problems that are easy to solve and easy to verify. For the sake of simplicity we can define “easiness” as: being solvable in a reasonable amount of time.

NP, on the other hand, is a class of problems that are hard to solve yet easy to verify.

EXP is a class of problems that are hard to solve and hard to verify. A classic example of an EXP problem would be a generic chess game. Think of a randomly generated chess board configuration with pieces all over the place, what’s the best move to make there? What algorithm do you even use to find out what the best move is? How can you even verify the correctness of any given suggestion?

It all boils down to scale. As you scale things up [...], certain problems grow much faster in difficulty than others and quickly become out of reach. And while we’re currently discussing algorithms and math questions, the same actually applies for any given problem we might face. Cooking dinner for two people is not the same as running a restaurant – even though the act of cooking might be the same. Scale is, and will always be, the fundamental challenge we have to overcome when solving important generalised problems of any kind.

Every decade or so we come across an algorithm that takes a problem from the NP domain to the P domain. This happens because some clever person makes a breakthrough that solves that problem much faster than we previously thought was possible. So the question now remains: is every NP-problem a P-problem in hiding? or are these classes fundamentally different and NP problems will forever be hard to solve?

Introduction to P vs. NP

https://wesammikhail.com/2023/03/22/the-complexity-series-p1-p-vs-np/ Comments

[glassedplanets]

FUCK IT WE BALL

[maxwellshimbo]

I made a thing ✨

[keatxu]

sorry i lied about being able to solve p vs np i was trying to flirt

[pv1isalsoimportant]

9 and 49 for the ask game

I would ask about P vs NP but I think I already know your stance on that lol

Thank you for the questions!

9. Do you have any favorite theorems?

I like Herbrand-type witnessing theorems, in fact I'm writing my thesis about them right now. My favourite is probably the KPT-theorem:

"Assume T is an universal theory such that T proves \forall x \exists y \forall z \varphi(x,y,z), \varphi(x,y,z) open. Then there exists a number k≥1 and terms t_1(x), t_2(x,z_1),..., t_k(x,z_1,...,z_{k-1}) such that T already proves \varphi(x,t_1(x),z_1) \vee \varphi(x,t_2(x,z_1),z_2) \vee ... \vee \varphi(x,t_k(x,z_1,...,z_{k-1}),z_k).

49. What’s your favorite number system? Integers? Reals? Rationals? Hyper-reals? Surreals? Complex? Natural numbers?

I'm dealing with a lot of theories of arithmetic so I would say natural numbers. Integers are also pretty cool (I'm looking at you \Z-modules!).

Real's math ask meme

[librarycomic]

The Phantom Scientist by Robin Cousin. Translated by Edward Gauvin. MIT Press, 2023. 9780262047869. 125pp.

This graphic novel opens with the arrival of Sorokin at the 4th Institute for the Study of Complex and Dynamic Systems. The armed clean-up crew that has just finished with the 3rd Institute is leaving the site, and one of the masked men hands things over to him. Sorokin watches a video from the previous director who explains the Institute a bit, from the type of researchers it includes to the fact that the system tends toward entropy and chaos in its last year, when results are expected. Sorokin's role is to slow the spread of chaos at the end of the 4th Institute during its final year.

Then on the next page, the book jumps forward six years, to the arrival of the final researcher, Stéphane, whose field is morphogenesis. He is offered a lab plus whatever resources he needs. On the way to his lab he meets two others who live in his building, Louise (linguistics) and Vilhelm (he seems to be modeling the Institute itself). As Louise gives him a tour, a lone scientist in the woods observes them. He's the so-called Phantom Scientist of the title, a man supposedly living in their building (though he's never been seen), a researcher looking into the mathematical problem of P vs. NP.

It all makes for a decent mystery full of drawings that I loved, and it had me searching and reading scientific terms. After finishing the book I was able to send a cryptic (to me anyway) text to the smartest math person I know, which will (I hope) lead me to a deeper understanding of P vs. NP next time we talk. If not, at least I'll have a better sense of how much my brain has petrified in recent years.

Worth noting: There's some cool stuff on plants and origami and much more in here.