Gurobi, CPLEX and XPRESS are the obvious commercial ones. GLPK and Cbc will also do MILP.
For more information, see this page: http://plato.asu.edu/guide.html
5,982 karma · joined April 20, 2018
I no longer have access to this account. If you want to reach me for past comments, you can do so at throwawaymathhn@gmail.com.
For more information, see this page: http://plato.asu.edu/guide.html
We're discussing the hypothetical skills and capabilities of a thing which is fundamentally science fiction. The rules are treated as arbitrary.
I don't see a priori why an AGI would be intrinsically good at hacking, or even why it would be capable of exponentially improving itself.
This is the problem I see with any discussion of AGI. The game's rules don't matter, so we can define whichever properties we'd like for the sake of argument. There's no skin in the game to counteract that, because we have no conception of what AGI will actually be like - nor if it's even possible.
As it stands, in your comment and the rest of this thread I see a variety of leaps and jumps to scenarios which seem completely undefended.
A valid takeaway from the cited list is that being a police officer isn't literally the most dangerous thing you can do for work. An invalid takeaway is that being a police officer isn't dangerous.
You started by saying that the claim that police officers risk their lives is statistically inaccurate, with a citation. I countered that citation with one of my own and a calculation showing they do risk their lives. Now you are talking about garbage collectors and their exposure to risk being greater than that of police officers.
That doesn't really counter my point about police officers' lives being exposed to risk, because I never made a claim that police officers are exposed to more risk than garbage collectors. Likewise I'm not forwarding a normative point about whether or not people should be paid commensurate with the amount of risk they encounter in their professional work. I am making the narrow, positive point which is that, objectively speaking, police officers are exposed to risk (and this is borne out by statistics).
I'm not in a position to make a normative claim about whether or not (or how much, in an absolute sense) we should compensate people more for risking their lives. I'm not sure if you were expecting me to say that garbage collectors shouldn't be paid more than police officers in hazard pay. But if we are assuming a system that pays commensurate with risk, then I'm happy to agree it would be internally consistent to pay garbage collectors more than police officers in hazard pay, sure.
Assuming surviving one year does not impact the likelihood of dying the next year, over a 20 year career a police officer then has a 0.26% chance of dying in the line of duty. We can expect that slightly greater than two out of every 1,000 officers will die prior to retirement.
___________________
In fact, the term "Jewish people" refers principally to an ethnic group with a common cultural heritage and ancestral religion, not to adherents of Judaism. Judaism happens to be the common religion of the Jewish people.
Go/crypto already implements elliptic curve cryptography[1], so I’m curious which specific elliptic curve primitives (or algorithms) they added to their fork.
________
It only seems strange to continue doubting a conjecture like Riemann if your perspective on the subject is experimental. In the scheme of things the relative impact of Riemann on the first trillion cases isn't nearly as important as what it says about all numbers.
You have 16 weeks from the date of registration to complete each course. The courses themselves have weekly homework, two midterms and a final. You must find an eligible proctor to complete the midterms and final in person, but otherwise you need not go anywhere. Each course costs about $1500 - 2000. The lectures for each unit are video recordings of lectures in the corresponding course onsite at UIUC. There is also a certificate you can earn, but it's primarily focused on completion of lower-level courses.[2] Your homeworks are graded (with feedback) by a lecturer or math TA at the university. There are also remote office hours available.
UIUC is probably the highest caliber mathematics program which offers something like this. It's generally difficult to find a top ~20 math university willing to support online, self-paced study for credit. The ones which do offer such a system are usually very expensive[3] or predominantly focus on lower-level courses like a simple calculus sequence.
_____________________________
1. https://netmath.illinois.edu
2. https://netmath.illinois.edu/academics/certificate-program
3. https://cvn.columbia.edu/program/columbia-university-applied...
Climate change is bad because it can end human lives. The lives which it doesn't end may experience significant hardship and unhappiness.
Decreasing the rate of population growth does reduce the number of existing humans, but it doesn't induce that reduction by ending lives. It also doesn't increase the amount of hardship imposed on most humans.
Do you see why climate change and population reduction are not comparable?
If I understand correctly the probabilistic infection rate is "history-less"; in other words, the probability of infecting an adjacent neighbor in the current state is not determined by the state transitions of any previous iterations.
It looks like you could model this naively with a discrete time Markov chain using a 3x3 stochastic matrix and three states: healthy, infected and deceased. I would guess you could do the same thing for the SIS model using states susceptible and infected with a 2x2 stochastic matrix instead.
In either case, modeling the epidemic as a Markov process would let you estimate the probabilities of criticality using the limit of the stochastic matrix. In fact, I think the critical threshold (probability of the epidemic going critical) will be given by left multiplying the initial probability vector by the limit of the stochastic Markov matrix.
I rather like this phrasing because basically everything you'll learn in calculus is a consequence of the completeness property of the reals.
I'll use math as an example since it's what I'm most familiar with. Sheldon Axler, the author of Linear Algebra Done Right, recently released a new textbook on measure theory and integration[1]. He makes the following comment in his preface to the student:
> If you zip through a page in less than an hour, you are probably going too fast.
I loved reading that because it's true, but also because most authors of math textbooks don't spell that out for students. I don't think Guns, Germs and Steel should take an hour per page, but my point is that nonfiction material should be actively engaged with, rather than passively "absorbed." When you passively read a chapter of a math textbook you'll almost certainly fail the exercises. On the other hand if you actively read the material, attempt proofs before reading the author's, investigate how many and which definitions can be removed before a proof fails, come up with your own questions, etc. then you will master the material.
I don't know how you'd do that for a non-technical nonfiction domain, but at it's core I suspect it would dramatically improve the efficiency of learning from books. Likewise, I consider it bad technique to take notes during a lecture. If your professor is implicitly encouraging this by making it so that you have no choice but to do so in order to learn the material (i.e. some material is not in the book or easily found elsewhere, or there is idiosyncratic style), then I also consider that poor form. In my opinion you can significantly improve the efficiency of lectures as a transmission medium by having students lightly read through the relevant sections before the lecture, then actively listen with their entire attention while sitting the lecture.
I also think it would be worthwhile to have lectures recorded and uploaded for a course so students can review material without needing to rely on the book. If you combine these two mediums in the way I've suggested, I really think there is not a whole lot of improvement left to do. There might be a fundamentally novel and strictly superior way of learning, but it's hard for me to see which cognitive bases aren't covered by combining these two methods.
_______________
For those who are unaware: Thomas Pornin is a professional cryptographer. He's a member of the NCC Crypto Services team and one of the authors of the Sosemanuk stream cipher, which was part of the final portfolio for eSTREAM. He's also involved in the development of one of the cryptosystems which has made it to round 2 of the ongoing NIST PQCRYPTO standardization process.
His writing on crypto.stackexchange is prolific and highly informative, and this is a strong rebuttal in particular.
No, it doesn't.
EDIT: To whoever downvoted - developing cryptography is hard. The idea that developing one broken cipher implies mathematical incompetence is laughable. You can't draw any conclusion from it except that it's hard to develop ciphers which aren't broken.
To speak to your example directly: machine learning absolutely has an axiomatic basis. You can conduct legitimate research in implementations and software or hardware optimizations thereof; however, fundamentally every experimental result in machine learning is an application of a variety of theorems in linear algebra, probability theory or calculus.
If you take integration as an example, there is no single approach to solving every integral. More importantly, it's extremely common to encounter integrals for which there exists no closed form antiderivative. In fact it's technically exceptional to find an integral which can be neatly solved in the space of all possible integrals.
As a direct result, solving an integral becomes an (often frustrating) exercise in transforming it into something equivalent integrals up to a negligible constant. Nonlinear optimization problems and differential equations are similar in this regard.
There is something to be said for the depth of analysis, which does provide a deeper meaning and rigor to the "bag of tricks" in calculus. Outside the US it's somewhat common to skip calculus entirely and begin straight away with analysis, and I think there's merit to that. But the profundity and power of analysis doesn't provide you with any fundamentally more complete methods of solving calculus problems except insofar as they become more advanced and rigorous. Ultimately analytic mathematical work (as opposed to algebraic) is characterized by this kind of pattern-matching; this frequently results in seemingly inspired, bizarre looking proofs compared to how neat everything is in algebra.
If they start actively phishing users this way they're solidly in illegal hacking territory on a pretty massive scale. What they're currently doing is "only" a "growth hack" to get more people on their site instead of the competitor's site.
We can quibble about the philosophical role of modern search engines I guess, but the basic idea is just that it should be easy to defensively bid on your own thing.
Not sure you and I are in the same market, friend.
Engineers and doctors are highly commoditized compared to professional athletes and celebrity entertainers. We produce a fundamentally fungible good.
If you can pay the market rate, you can find a replacement engineer to work your software. If Taylor Swift's concert is sold out, you cannot see Taylor Swift. If Aaron Rodgers dies, there are how many quarterbacks in the world capable of replacing him?
These are categorically different things with categorically different market dynamics. Approximately no software engineers (or doctors) have a personal brand, nor an objectively superior skillset.
The reason real analysis is useful is because it's (loosely) a deeper calculus course with proofs. Since probability theory becomes more proof-based (and ventures into measures), real analysis is good preparation for it.