How to migrate lightning nodes?

Question: I am wondering what steps to take to migrate a lighting node to a different server, keeping the pubkey/identity. The safest option is obviously to close the channels first. How is the identitiy pubkey created? From the 24 seed, random, or other means?
In case I want to tranfer the node with opened channels, which files would I have to make sure to backup / transmit?
Comment: which lightning implmentation are you talking about?
Answer: In C-Lightning it is fairly easy. Just shutdown the server and make a full backup of the <code>~/.lightning</code> folder. This folder contains in particular the HSM secret which is used for key derivation of later keys and it also has the sqlite3 database which is used to store all current states. This means that there is no need to close channels or anything.

How to migrate lightning nodes?


When is it appropriate to use what alphabet?

Question: I'm very new to Japanese, and I was wondering when is it appropriate to use what alphabets? I've been practicing entirely in hiragana thus far, and I know that katakana is for foreign words and sounds, but how do you know when to use kanji?
Comment: I personally use kanji whenever I can, it makes the reading more fluid in my opnion, but there are set words that have kanji but people use hiragana instead like 所 - ところ for instance
Comment: Another time you shouldn't use kanji is for words that have rare, non-jouyou kanji that the average reader wouldn't recognize (unless you are able to supply furigana).
Answer: Japanese is written using a combination of all the three sets of characters: hiragana, katakana, and kanji.
You should expect them to come together in an average Japanese text (meant for adults) and not in isolation or in exclusivity. Children start off reading and writing everything in hiragana because it is easy (if you look at children's books, you can confirm that is the case), but as they learn more and more kanji (Chinese characters), they have to use those instead.
Kanji are characters originally from China and are, easily speaking, used to convey ideas. In Japanese, they are used as the basis of each word while hiragana complements it by adding conjugation, etc.

e.g. 食べる(たべる to eat); 旅行する (りょこうする to travel)

Katakana are a set of characters that have a one-to-one correspondence with Hiragana characters. Some of them might look very similar, like hiragana か vs katakana カ. Essentially, Katakana are used for foreign or loan words. Furthermore, they are also used for technical and scientific words. In manga, a character using katakana for its speech bubble might also indicate he is a robot.

e.g. コンピュータ computer; アナウサギ word for a kind of rabbit (demonstrates scientific terms are written in katakana)

So in conclusion, you have to use all of them to read and write "fluent" Japanese. In my opinion, once you learn the Kanji, your reading becomes so much faster and convenient. Talking from experience, after having studied Japanese for more than four years, I feel rather annoyed if I have to read some text that only has hiragana (like children's books). It is much faster to read a single character (e.g 表す) than to read four characters just to speak the same word (表す is read as あらわす).
Answer: Gonna try to summarise what each system represents:
Pure hiragana/kanji words are native Japanese, kanji came from China a long time ago; kanji often marks the start of the word, but not always:
元気 = healthy, lively
ある = to be (inanimate)
行く = to go
Some words have kanji, but are written as pure hiragana instead; some are/aren't based on the context in question:
可愛い -> かわいい = cute
Actually, you can write any word without kanji; it's just that some are more common, and doing it to much will make your writing look kinda cute:
捥ぐ -> もぐ = to pluck
Some words are in the middle, with it being just as common to use kanji, as it is to just drop the kanji and use pure kana:
持つ -> もつ = to hold
Pure katakana words are used for loanwords. Hiragana like る will be used if the loanword is a verb, in which case it's a godan verb:
プロジェクト = project
カー = car
ググる = to google
ウィキ = wiki
ウィキる = to look-up on wikipedia
Some loanwords are unique though, like using English characters:
Tシャツ = T-Shirt
There is an infinite amount of nuance in the Japanese writing system, just like how the English alphabet is just as much of a written/spoken mess; I struggled a lot at first, too; so don't worry, you'll figure it out as you get used to using it; you know, you'll learn to feel it; just need practice.
As for names: katakana is used used to make names like ancient, as katakana was the first Japanese script, with hiragana and kanji coming later. Names are normally all kanji, but if the names kanji is dropped by the Japanese government's list, they gotta use hiragana in it's place instead, at least for legal documents.
Sorry if my answer is messy, if you want me to clean it up a bit; or explain something, just ask!
Comment: I love this answer, but there's still something I'm slightly confused about.  There are some words that have a kanji, but are still written as kana only.  A couple examples would be 為(ため)or 有る(ある)Some of those I get because the kanji are super complicated, but why the kana only in the case for 有る?
Comment: ある is a special verb, one used incredibly often; thus, you write it in kana for sake of grammar. There are no fixed rules for when you use all kana, each case is unique, and filled with nuance, something you just gotta get a feel for.


Are "Hackintosh" questions allowed?

Question: I've seen questions about pirating software down voted and closed. I'm wondering if Hackintosh questions are also disallowed? If so, why?
Comment: @JasonR.Mick: Up Vote the bejesus out of this question.
Comment: You can always put it to a vote.  Post a Hackintosh question and lets see if the Community wants to keep it around.
Comment: @surfasb How do you put things to a vote on these forums?
Comment: Can't we change the policy now? There is a good amount of upvotes for the "accept hackintosh" position.
Comment: Modern revisit: [Revisit the Hackintosh policy](https://meta.superuser.com/q/12050/194458). cc @speeder
Answer: Simple. As discussed in many similar matters on Meta Stack Overflow, there is no such things as worldwide legal agreements. Apple can put into their usage agreements whatever they like, in many countries that would never hold in court. One could use the comments to warn people about it, or when answering mention it as well. But forbidding questions smells like censorship.
So, I'd allow these questions.
Comment: @nhinkle - what US law is being broken by answering a question about "hackingtosh" installations?  (Assume, for the moment, the asker has a legal unopened disc of the Mac OSX, not installed on any machine, and that the asker wants to install a single instance on one PC. (to avoid any "piracy" / torrent / etc distractions))
Comment: as Diago answered quite some time ago, the moderation team has decided to discourage these questions. Furthermore, Stack Exchange is a US company, and is therefore beholden to US law.
Comment: @nhinkle If this is official policy, wouldn't it make sense to delete this answer? The current accepted answer doesn't look "official" in any way, considering that Diago stepped down as a moderator. If I were a visitor of this Q/A here, I'd find it highly confusing.
Comment: @Arjan, @nhinkle, @slhck: there is no applicable SE-wide policy, so this is a community decision. The moderators do not have a binding vote here. Diago spoke here as a community member, just like Arjan. Hackintosh questions became banned because until you (Arjan) posted your answer, the consensus was against them. The policy would change if your answer rose to a significantly higher score that Diago's.
Comment: (For some background on the comments above, see also [Are Hackintosh questions off topic because of community consensus or just moderation policy?](http://meta.superuser.com/questions/4438/are-hackintosh-questions-off-topic-because-of-community-consensus-or-just-modera), and the [deletion history of this very answer](http://meta.superuser.com/posts/2405/revisions).)
Comment: it seems that this community is very divided about this issue. The "allow the hacking/pirating!" comments are gettings as much points as the "don't censor" comments...
Comment: @slhck, agreed. Will delete this soonish.
Comment: @nhinkle, please see the new comments at Diago's answer. Thanks!
Comment: @slhck, I [did delete this](http://meta.superuser.com/posts/2405/revisions), but as I am not sure it's indeed a moderator decision, I've undeleted again. See the new comments at Diago's answer. (And this very answer might be deleted again; that's fine to me, **if** it's indeed an official decision.)
Comment: Is this becoming a new dogma and people that really want to know or ask something will be "burned at the stake"? Seems like the history of Inquisition where if you even "DARED" to think something outside of norm you were imprisoned or tortured. It's like saying: Let's ban physics and chemistry as somebody could develop weapons or poisons.
Answer: Simple. It's a legal grey area. Super User doesn't want to build a reputation for encouraging something that may or may not be illegal, so it was decided to stay safe rather than sorry.
I have actually proposed to have the tag banned here and given some more reasons why.

Sathya ♦: There is no reversal in status. This answer still holds good from a moderation point of view.
Comment: In that case, don't say, "Super User doesn't want to build a reputation for encouraging something that ... may not be illegal;" say, "Super User doesn't want to build a reputation for encouraging any activities contrary to EULAs." These are completely distinct concepts.
Comment: Are you sure SU "doesn't want to build a reputation" for this kind of stuff? I seem to recall an interview with one of the stack exchange founders, where he said, in general, he has no problems at all with "questionable" questions (he was talking about breaking NDA's on stack overflow).
Comment: SU doesn't want to build a reputation for encouraging something that may not be illegal? You want to rule out encouraging legal activities?
Comment: There is no reversal in status. Diago's answer still holds good from a moderation point of view.
Comment: @sampablokuper: We don't want to encourage using different methods than those allowed by the usage agreements, whether or not the user agreement holds in court. As there aren't worldwide guaranteed legal agreements, we can't suppose this is completely legal. We don't want to discuss every single matter that might be illegal in one or another way, it's very clear that if one does a Hackintosh that he is not using what he is supposed to be using. As a comparison, BitTorrent and Tor have their legal uses and merely serve as a medium hence those are allowed...
Comment: @hqt see here http://www.lockergnome.com/osx/2012/02/24/are-hackintosh-computers-legal/ Apple does not allow it. "Use MacOS on Windows" is also wrong btw; unless the topic suddenly changed to virtualising ;)
Comment: No. Use MacOS on Windows is not illegal. Apple just doesn't support this for any error appear !!!
Comment: Good point, @Gilles, especially as when I deleted my answer I flagged Diago's answer to ask the moderators to make Diago's answer more official. Though [that flag was considered helpful](http://i.stack.imgur.com/KNzvr.png), no such change was made. Any moderator: feel free to delete my answer again, **if** the above is indeed the official point of view.
Answer:
All innovation explores the limits of performance and behaviour.

Hacking is just making hardware do something you know it is capable of doing. When the designers don't meet expectations--whether non-tech-related considerations motivate restrictions on permissible usage, or the designers simply fall short in the inspiration department--it is only natural to marshal one's D.I.Y. resources.
Superuser should be one of those resources. The contributors here are both helpful and knowledgeable. It's a powerful combination that should be allowed to foster creativity and encourage innovation. Collaboration isn't forced on anyone who isn't comfortable with the ethical foundations of a question--if you don't want to get involved, just don't answer the question.
No country allows its corporations to single-handedly impose statutory limits on its citizens--even when the corporation is as successful and respected as Apple. It is absurd to imagine that any arbitrary EULA might enjoy the force of law.

There is nothing illegal about asking questions that abjure a EULA--you cannot call it a "grey area" if there is no law to skirt.
There is nothing illegal about offering ideas on how one might subvert a EULA. Speculation isn't contravention--and neither one is
illegal.

Any site that calls itself Superuser has to allow a degree of freedom for forward-thinking.
Comment: While I agree with your opinion; technically an EULA is a form of contract; which again are in principle protected by law
Comment: Any site that calls itself Superuser has to allow a degree of freedom for forward-thinking ==> true that. Else it should be call "normal-user"
Comment: Where I live a legitimate Apple computer cost easily the same as a motorcycle, or even a car (for MacPro stuff).

Also, OSX and iOS coding is the only source of income me, and many other programmers have right now (because no matter how much the economy is sinking, people wanting iOS code always show up willing to pay, even if a tiny amount, but tiny money is better than zero money).

So how worth is it? To me is worth being able to afford food and medicine.
Comment: @speeder Your comment seems to advocate the use of cracked software because it makes technology affordable for poor people. This has been studied in length, and the results have always shown that IT specialists are practically doomed to poverty in countries which allow piracy, and things get better when copyright laws start to be enforced. And BTW, you can easily find a used car in EU or US with a MacBook Pro price tag.
Comment: I wasn't talking about USED vehicles, but new ones. Also, the only reason why I learned to code in first place is because I could use lots of cracked (not necessarily pirated) software. As for the studies, "what" got better when copyrights were more enforced? Wages?
Comment: @DmitryGrigoryev: One could make a good argument that selling software for profit is inherently immoral, because it takes the focus away from making good, long-lasting software in favor of making profitable software that you have to buy again every year or two.
Comment: @Vikki That is an argument against capitalism in general. It will become valid the moment someone invents a better economic system. For now, one is free to use the good long-lasting software from North Korea, provided they find some.
Comment: @DmitryGrigoryev: It is _not_ an argument against capitalism in general, merely against wastage of nonperishable goods.  Houses burn down; food is eaten or rots; well-built software is good forever.
Comment: @Vikki What exactly is "wastage of nonperishable goods"? And BTW, well-built software is only good while you have a computer to run it on, and without maintenance it will become poor or unusable software on the next generation of computers. Average houses last much longer than average software products.
Answer: The existing answers focus on "legal" issues and censorship.  I think that is the wrong way to frame it, and not the basis on which a site scope decision should be made.
Legality
None of this comes under criminal law, so it isn't even a question of legality.  If there is a legal issue, it is whether Apple's EULA is enforceable in a way that would allow Apple to collect damages.  If Apple won a court ruling affirming its claims, or another party won a ruling that told Apple to go suck wind, that would provide a basis for discussing site policy.
Short of a court ruling, there is simply the EULA.  Apple can specify any terms they want; it's their product.  You don't own it, you only pay to use it within Apple's terms.  If you don't like the terms, buy something else.  If you agree to Apple's terms, your voluntary agreement is what binds you to them.
Implications for the site
Let's put aside the business issues, like do we want to expose SE to potential heavy-handed action by Apple; e.g., using deep pockets to win a judgement against SE regardless of merit.
Most questions of scope differentiate technical factors to define what is within SU's bailiwick.  Devices other than computers and their peripherals are off-topic.  Software recommendations go to another site.  The community is expert on those kinds of issues and it's appropriate to decide scope by consensus.
What makes Hackintosh special is the legal and ethical issues people associate with it.  I suggest that those kinds of issues would be more appropriately driven by core, guiding principles.  If we decide, as a matter of policy, to make Hackintosh questions officially off-topic, it should be based on core principles rather than the winds of consensus.
Suggestion
Let me suggest that a guiding principle would be a version of the Hippocratic Oath, "First do no harm."  We don't make IT administrators' lives miserable by advising people on how to circumvent their policies.  We don't use this open forum to instruct people on how to create malware.  We don't help people circumvent the terms of service with their Internet provider.  If they want the ISP's service, they agree to abide by their terms.  How is that really different?
I think the same logic applies to EULAs.  Two other parties have agreed to terms and it's inappropriate for us to inject ourselves into the relationship and facilitate one of those parties violating their agreement.  To Gilles' comment, below,  to not facilitate violating the EULA is not putting us in a role of "enforcing" the EULA.  It's remaining uninvolved.
Comment: I don't understand your answer. You start with saying that we shouldn't base our decision on legal issues, and you conclude by saying that we should enforce the EULA (or rather your interpretation of the EULA).

Are "Hackintosh" questions allowed?


What steps has the Catholic Church taken as a whole to address a shortage of priests?

Question: It seems like the first instinct of the news media when it comes to the Church's response to a shortage of priests is to end the rule enforcing celibacy.   But that is not what the Church has been doing.  So, what has she done (as a whole) to address the fact that an aging population of priests is not being replaced at the rate that the Church is growing?
Comment: Why aren't young people joining the priesthood at rates that match growth? Are they actually and you have bad information? Is there actually a priest shortage while church membership is growing?
Comment: @fredsbend Yes.  It's not so much the current shortage but the demographic lump/graph.
Answer: The comments by Pope Francis about allowing older married men to be ordained and serve in isolated areas is interesting, although I don't think this will happen any time soon, and certainly not in the numbers needed if 25 per cent of churches do not have a resident priest.
What I have observed being reported is that dioceses around the world are addressing the shortage of priests as best they can, by merging parishes. This seems to have been made possible because fewer Catholics are attending mass at the same time as there are fewer priests1. Another thing I have noticed in a limited way is the employment of lay ministers to assist the priests.

1The RCC is growing in sub-Saharan Africa. Gross numbers are steady in US, balancing leavers with Latin immigrants, but with falling attendances at mass, which is what we are talking about. Numbers are falling in Europe because of a move away from religion, and also in South America, where significant numbers are converting to evangelical denominations.
Comment: Peter says the church is growing. You say mass attendance is down. Who's right? Are both of you?
Comment: @fredsbend The RCC is growing in sub-Sahara Africa. Gross numbers are steady in US, balancing leavers with Latin immigrants, but with falling attendances at mass, which is what we are talking about.  Falling in Europe & South America.
Comment: Dick, can you add your points in that comment into the answer?   I think they support your answer. @fredsbend the non marriage of Priests is a "discipline of the church" not dogma ... and in the Eastern Rite, priests may marry (but bishops can't ...)
Answer: One of the things some bishops are doing is increasing the number of permanent deacons in their dioceses. In my diocese, the archbishop has increased the number of permanent deacons in the archdiocese. Many of these permanent deacons will be working in federal institutions of correction (prisons) and thus easing the burden of the workload for priests to work more exclusively in parishes. Nevertheless, priests will visit prisons, but will do it less frequently. Some of the other permanent deacons will be assigned to hospitals or other facilities to ease the workload of priests.
Some diocese are also permitting the Sunday obligation of attending Mass to be transferred to another day of the week in more isolated areas in order to make it possible to have a priest travel to them and say Mass for parishes in more isolated locations.
Eucharistic Ministers have their particular area of aiding the parish priest, such as taking communion to the sick in hospital or at home and informing the pastor if a particular soul desires to go to confession, so that the parish priest may fulfill his parishioner's desire.
It can arise that the number of priests is so few that a diocesan bishop may even have recourse to Rome to have some Pastoral Administrators established in order to fulfill the Sunday obligations for the faithful. This naturally involves reading the gospel during a communion service by lay ministers  (outside of Mass). The Diocese of Whitehorse, Yukon has between 4-8 priests at any one time and has several Pastoral Administrators working in the diocese.
Many dioceses have opted to institute what is now termed as lay ministers at various levels of "lay ministry".
More information may be gleaned in the following post:
How does one become a "lay-ministers" in the Catholic Church?
Comment: Our diocese is doing that, increasing the diaconate.  FWIW, my wife serves in the Homebound Ministry (bringing the Eucharist to those unable to attend) and I serve as an EM (when called on, I assist the priest/deacon in distributing body/precious blood during Mass.
Comment: Why increase the number of permanent deacons rather than the number of priests?
Comment: @curiousdannii priesthood is a calling. Are you aware of the attrition rate from start to finish?  Also, deacons can come from the number of married men in a community.  Priests cannot.
Comment: @Korvin Ah, I wasn't aware deacons could be married. But is being a deacon not also considered a divine calling?
Comment: @curiousdannii Yes, it is, and many who begin the 5 year course do not complete it.
Answer: In my diocese, the bishop has done several things: he merged some (smaller) parishes, he assigned some others to monks from religious orders (which are not part of diocesean clergy, but are priests too) and he made a deal with some other diocese in Africa or India.
Those dioceses send some young priests here to serve in our dioceps for some years, and our diocese allow them to study Italian and theology in or schools.
After some years (usually, when they completed their studies) those priests can return to their homelands (where they will be very educated for their country standard, and maybe receive some important role) or choose to stay in here in Italy


Optimization models for portfolio optimization

Question: What are the mainstream models for portfolio optimization? We have Markowitz mean-variance model and CVaR-based models (e.g., max return subject to a CVaR constraint). What else is out there in terms of risk measures or formulations?
Answer: Here's what is not really mainstream now, but should be.  The mean and especially the covariance matrix of returns is not known. Treating estimates of then as though they are known with certainty can lead to very suboptimal results.
Just to start vectoring yourself in the right direction, you can start by looking at
MEAN–VARIANCE PORTFOLIO OPTIMIZATION WHEN MEANS AND COVARIANCES ARE UNKNOWN, TZE  LEUNG LAI, HAIPENG XING, and ZEHAO CHEN, Annals of Statistics, 2011, Vol. 5, No. 2A, 798–823.
Improving Portfolios Global Performance with Robust Covariance Matrix Estimation:Application to the Maximum Variety Portfolio, Emmanuelle Jay, Eugenie Terreaux, Jean-Philippe Ovarlez, and Frederic Pascal.
You may also find of interest methods to identify financial risk factors using large data sets.
Identifying Financial Risk Factors with a Low-Rank Sparse Decomposition, Lisa Goldberg and Alex Shkolnik.  This  decomposes covariance as a sum of a rank-one factor component and a diagonal security specific return component
Here is a semi-classic paper advising you NOT to use the sample covariance matrix for portfolio optimization. "Shrinking" it toward a better conditioned matrix. even though producing a biased estimator of the covariance matrix, can improve the results of portfolio optimization (note that the condition number of the sample covariance matrix is a very biased estimator of the condition number of the true covariance matrix, and is infinite when the number of vector data points is less than the number of variables).
Honey, I Shrunk the Sample Covariance Matrix, Olivier Ledoit and MichaelWolf, The Journal of Portfolio Management Summer 2004, 30 (4) 110-119 (link is to free version of the paper)
Comment: Thanks for the references. I agree that parameter estimation is often disregarded in this particular problem.
Answer: Another aspect of portfolio optimization which is often important in practise is sparsity, i.e., requiring that the portfolio invests in at most $k$ non-zero stocks to cut down on transaction fees and avoid functioning as an index fund. This can be achieved by imposing a sparsity constraint $\Vert x \Vert_0 \leq k.$
The classical reference on this topic is this 1996 paper by Bienstock.
Comment: You could certainly do that instead. If you did that you would have a fixed cost component for each stock which you invested in, plus a marginal transaction cost which you can model by modifying the expected return vector accordingly, so this approach would lead to adding a $\lambda \Vert x \Vert_0$ term to the objective. You may however want to impose $\Vert x \Vert_0 \leq k$ instead, since MINLPs are solved via decomposition schemes and cardinality constraints restrict the size of the subproblems. I've given some other reasons in section 2.2 of [this](https://arxiv.org/abs/1811.00138) paper.
Comment: Interesting. Why not simply penalize the transactions fees itself in the fitness function, and leave it to the solver to figure out how many to incur?
Answer: I'm no expert on the topic, but I found the textbook Optimization Methonds in Finance really accessible. The authors teach optimization modeling and solving motivated by applications in finance, including portfolio optimization.
In particular they describe a linear model using mean absolute deviation as a linear proxy for variance.
Answer: For what it's worth, here's a video explanation and the source code of my Portfolio Optimization implementation. Run InvestmentApp to try it yourself.
For the sake of having a simple example, we decided to go with expected return (1 year), standard deviation risk and asset correlation. The example xlsx data came from Yahoo Finance IIRC.
Comment: Very nice. So the underlying model is Markowitz 52'?
Comment: I am not sure about the spec version any more (I wrote this 4 years ago in a day or 2), but it was based of [the wikipedia article about Markowitz Portfolio Theory](https://en.wikipedia.org/wiki/Modern_portfolio_theory) and the formula shown in the video, [see also the problem spec in docs section 3.18](https://docs.optaplanner.org/latestFinal/optaplanner-docs/html_single/#investment).


How to create a vector field whose Curl and Divergence are zero at any point?

Question: What is the mathematical procedure to derive a vector field whose curl and divergence are zero at any point at any time?
Edit: Please explain it by solving the differential equations of curl and divergence.
Comment: Set it equal to a constant?
Answer: Take any harmonic function $\phi$, and set your vector field to be $v = \nabla \phi$, the gradient.
Edit On any simply connected domain (if your space is just the entire Euclidean space, for example), any curl free vector field can be written as the gradient of a function. You can see this explicitly by verifying that given a curl free vector field $v$, the function $\phi(x) = \int_{C} v(s)\cdot ds$ where $C$ is a curve starting at the origin and ending at the point $x$ is independent of the choice of the curve $C$, and hence $\phi$ is well-defined. (This is generally treated in any introductory textbook on vector calculus, and is a special instance of Stokes' theorem.) Once you have that, plugging $v = \nabla \phi$ into the divergence equation you automatically get that $\nabla^2\phi = 0$.
Comment: @sree This is the most general solution. See [this Wikipedia article](http://en.wikipedia.org/wiki/Laplacian_vector_field) for more details.
Comment: @Willie: would this be suitable for migration to math.SE? I don't think there's much of any physics in it.
Comment: Thanks, But are there any general solution possible?
Comment: Thanks, If we solve those differential equations, whether we will get this or not?
Comment: @David: Either way is fine with me. Ping me if you do migrate it so I can retag on Math.SE.
Comment: Here you go, it's migrated. (I was busy yesterday and this completely slipped my mind) I'm also flagging just to make sure it gets taken care of.
Answer: There is a theorem  (which apriori has nothing to do with Stokes' theorem) which is called Poincarais' Lemma. The version that applies here states that in $U$ - a sufficiently convex subset of (or whole) $R^3$.
a) for every divergence-free vector field V there exists another field A such that
$\nabla \times A = V$.
b) for every curl-free vector field V there exists scalar field $\phi$ such that
$\nabla \phi = V$.
Consult textbooks if interested in definition of 'sufficiently convex'.
One can use one of those statements to simplify our search - because using this theorem reduces our requirements from two ($\nabla \times V = 0, \nabla \cdot V = 0$)  to one. For example, let us use b). Then, our search reduces to finding a solution to Laplace's equation $\nabla \cdot \nabla \phi = 0$ and the second requirement ($\nabla \times V = 0$) will be automatically satisfied. Furthermore, Poincarais' Lemma makes us certain that this is a way of generating ALL such fields.
Now, how to solve Laplace equation?
It appears that well-posedness (existence and uniqueness of a solution) of this equation requires additional information - the boundary data. More specifically, we have to supply smooth values of field $\phi$ on the boundary $\partial U$ of the set for which Poincarais' Lemma works.
To understand this, let us see some examples:
1) $U = R^3$ (whole space). Laplace's equation reads $$\left(\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2}\right) \phi(x,y,z) = 0$$ boundary values - $\phi = 0$ at all infinities. Then we immediately see, that we can find a solution which satisfies those boundary conditions - namely $\phi = 0$ everywhere! Because solution has to be unique, we conclude that the field found in this case is $\nabla \phi = \vec{0} $ which is of course true - the 0 vector  has no divergence and curl!
2) $U = R^3$ but this time we demand $\phi \to \infty$ as $x \to \infty$ and $\phi \to -\infty$ as $x \to -\infty$. We do not say a thing about other boundary layers so the boundary value problem is singular in this case - fortunately what we lose is just uniqueness. For example, we can take $\phi(x,y,z)=x$ as well as $\phi(x,y,z)=3x + y$.
The corresponding fields will be $(1,0,0)$ and $(3,1,0)$.
To classify solutions we have to analyze all the possible boundary values. Yes, it is a pain.
But for most real-world fields which decay at infinity the answer is simply - there are no such fields unless they are $\vec{0}$ - case 1)
When $U$ is finite, one has to impose boundary conditions (which is easier than on unbounded domain) which most often come directly from the physical problem in hand. Then, one has to adapt coordinates suitable for such boundary structure (spherical for sphere, cartesian for box, etc.) and solve BVP for Laplace equation - which is different every time - no general solution. However, most textbooks on electrodynamics are full of examples.
The most interesting part (and least seen in physics) is when $U$ is so chosen that the assumptions of Poincarais Lemma are not satisfied. But for this, consult mathematical exchange, please :)
Answer: A nice example in physics is the standard expression for a dipole field, either magnetic or electric. With the exception of the origin, where the dipole is located, div and curl are zero, and so must also satisfy the Laplace equation. But, wait! del$^2$$\left(\frac{1}{r}\right)$ is $-4\pi$ (Dirac $\delta(r)$) ...ah grass hopper...
Answer: A differentiable vector field $F=(u,v)$ defined on an open set $\Omega\subset\mathbb{R^2}$ is curl and divergence free if and only if $f=u-iv$ is a holomorphic function (easy consequence of Cauchy-Riemann equations).
Then, if you want to obtain a differentiable curl and divergence free vector field on an open set $\Omega\subset\mathbb{R^2}$, simply take the conjugate of any holomorphic function defined on $\Omega$.
Answer: Cleaning up for us lazy physicists.
1) First solution:
We want: $$\nabla\cdot {\vec{B}}=0$$$$\nabla\times {\vec{B}}=0$$
From the above mentioned theorem of Poincare:
$$\nabla\cdot {\vec{B}}=0 \implies \vec{B}=\nabla \times\vec{A}$$
By the identity:
$$\nabla \times(\nabla \times\vec{A})=\nabla(\nabla \cdot \vec{A})-\nabla^2\vec{A}$$
So the divergence and curl are both zero if we have $\vec{B}=\nabla \times\vec{A}$ and $\nabla(\nabla \cdot \vec{A})-\nabla^2\vec{A}=0$
2) Seconds solution.
Again by Poincare as mentioned above:
$\nabla \times \vec{B}=0 \implies \vec{B}=\nabla \phi$
Then we have $\nabla \cdot \vec{B}=0$ if:  $$\nabla^2 \phi=0$$
This is Laplace's equation. Probably the most important you'd encounter in undergrad physics.
Legendre Polynomials are among the most important solutions to this equation. They represent solutions to Maxwell's Equations for static charges and currents as well as angular momentum in quantum mechanics.


Tips for golfing in Befunge

Question: What general tips do you have for golfing in Befunge? I'm looking for ideas that can be applied to code golf problems in general that are at least somewhat specific to Befunge (e.g. "remove comments" is not an answer). Please post one tip per answer.
Comment: We've had a recent [Befunge 93](http://codegolf.stackexchange.com/questions/49891/tips-for-golfing-in-befunge-93) topic, but I think it'd be better to generalise this topic instead. Would that be okay? (and maybe mark which tips are good for which version/s, in the same way that Python tips say whether or not they're Python 2/Python 3 specific)
Comment: I'm unsure if this should be changed to Befunge in general, but Befunge 93 is much less ideal for golfing than 98.
Answer: When using a multi-line loop, try to use as much of it as possible:
>1234....v
^        <

vs
>1234v
^....<

Answer: Need to drop a value after a conditional (e.g. because the other path depends on the value, but this one doesn't)?  Instead of using >$ or $<, take advatage of the fact that you know the truth value of the variable and use _ instead to both change direction and pop stack.
Example
'* : v           >$ .. @          Prints number in binary followed by the original
                                  decimal number.
     > :2%\2/ :!#^_ \.

gets turned into
'* : v           _  .. @          Since we know that the topmost value on the stack
                                  will be 0, we combine `>$` into `_`.
     > :2%\2/ :!#^_ \.

Answer: Don't forget that 0 is always on the stack. For example, this means that, with an empty stack, g is equivalent to 00g and p is equivalent to 000p.
Answer: If you need to push a number larger than 15, use ' to fetch the ASCII value of the next character:
'*

to push 42 rather than:
4a*2+

Comment: @Doorknob Maybe I should have chosen a prime number to get my point across clearer, but 42 is such a great number.
Comment: Note that this tip only applies to Befunge-96 and later. Befunge-93 did not support the `'` instruction.
Comment: Or, `67*` works too
Answer: Instead of using |, requiring another line (often with many extra spaces), try using j. For example:
01-`j@more code here

would stop if the number on top of the stack was negative and continue onward otherwise. If you need multiple characters, use n*j where n is the number of characters you need when the value passed to j is 0. Example:
01-`4*j01-*more code

which would negate a negative number.
Comment: Note that this tip only applies to Befunge-96 and later. Befunge-93 did not support the `j` instruction.
Comment: Is the 0 at the beginning necessary? 0 is always on the stack.
Answer: In Befunge-93, if the first thing you're pushing onto the stack is a string, you can often get away with dropping the opening quote. For example this:
"!iH",,,@

could be simplified to this:
!iH",,,@

Try it online!
What's happening is the interpreter first tries to execute the characters in the unquoted string. The ! performs a harmless not, and the i and H are not valid instructions, so they're ignored (although on some implementations you may get a warning).
When the " is encountered, that is considered the start of the string, but because there is no closing quote, it wraps all the way around the playfield until the " is encountered a second time. What ends up pushed onto the stack is then this:
,,,@  ···72 spaces···  !iH

Since we only care about the last few characters, though, none of that other stuff matters. So after the quote, we then finally get to execute the three , commands, writing out the message, and the @ command, which exits.
Note that this won't typically work in Befunge-98, since an unrecognised instruction will cause the interpreter to reflect instead of ignoring it.
Comment: In Befunge-98 you can instead put the required string at the *end* of the line, like so; `",,,@!iH`. Note that Pyfunge adds an extra space, while FBBI doesn't.
Comment: @JoKing I didn't want to suggest that, because, as you pointed out, the behaviour differs from one interpreter to the next. And even when it seems to work, it's inconsistent (note the extra space in FBBI in [this case](https://tio.run/##S0pNK81LT9W1tPj/X0lHR8dBMdODi6s8o1IhJT@1WKEkI7NYISczL1UhMS0tNbkEKJCqkJSakViWmV9aZP//PwA)), so it's quite possibly a bug that may end up being fixed at some point.
Comment: Hmm... I think the space might actually be part of the specification. I remember reading somewhere that multiple spaces will be skipped and counted as a single space. [Example](https://tio.run/##S0pNK81LT9W1tNAtqAQz//8vslLWiS9TNlTyz0tVKC5ITE5V4lJQUNBJtCkzVAopz1eACBaDRO1Aah3@/wcA) in both PyFunge and FBBI. FBBI seems to pad [each line to the length of the longest line](https://tio.run/##S0pNK81LT9W1tPj/X0lHR8dBMdODi6s8vyi7WPH/fwA) while PyFunge adds the extra spaces implicitly.
Comment: You're right - the spec does say that multiple spaces in a string should be treated as a single space. In fact that rule was specifically proposed to deal with the problem of wrapping strings in an infinite playfield (so PyFunge is clearly correct AFAIC). But the spec's description of the wrapping algorithm is somewhat open to interpretation, so I can understand why some implementations might do things differently. But the bottom line is this is a fairly complicated issue, and I think it would be better covered as a separate tip specific to Befunge-97/98.
Answer: In Befunge-93, the character input command (~) can often be used as a shortcut for -1, since that is the value it returns on EOF.
As an example, the code below will output -1:
~.@

Try it online!
This is not recommended in production code, since when run in an interactive environment, the program would pause and wait for user input. And obviously if the user were to input something, the result would no longer be -1.
That said, the rule on PPCG is that a program may assume an empty input stream, and that's how it would typically be run on TIO.
Also note that you aren't necessarily precluded from using this trick just because your program needs to read something from the input stream. You just have to make sure you process your inputs up front, after which all future uses of ~ should return -1.
Answer: In Befunge-93, it can often be advantageous to flatten a loop into a single line, with the loop section of code being executed in both directions.
For example, consider the code below, which outputs the letter a eight times:
"a"9>1-:#v_@
    ^\,:\<

This can flatten be flattened into a single line by interspersing the loop sequence with bridge instructions (#):
"a"9>1#\-#,:#:>#\_@

Try it online!
If you're just looking at the non-whitespace characters, you may get the impression that this is longer than the the original. But once you take into account the linefeed and the additional padding required in the two line version, you actually end up saving four bytes.
In this particular case, the code be compressed even further by noting that that sequence :#: can simply be replaced with :.
"a"9>1#\-#,:>#\_@

Try it online!
In fact, any time you have the same instruction repeated on either side of a # command, you can simplify that to just the one instruction, so this is something you should always be looking out for when flattening a loop.
To understand how this works, it can help to write out the loop sequence twice, once with all the characters following the # removed (i.e. what happens when executing left to right), and once with the characters preceding the # removed (i.e. executing right to left).
"a"9>1#\-#,:>#\_@
    >1  -  :>  _      ; executing left to right
    >  \  ,:  \_      ; executing right to left

You can clearly see now how this matches the original two line version of the code.
Answer: Use the direction of the IP when dealing with _ or |, rather than using an extra character for !.
Real example (from this post):
#v~
,>:!#@_

Can be changed to
#v~
:<,_@#

Answer: Don't forget that 0k does not execute the next instruction. This means that instead of doing:
;some boolean test;!jv;code if false;
       ;code if true;<

You can save a character by doing
;some boolean test;kv;code if false;
      ;code if true;<

Comment: Note that this tip only applies to Befunge-98 and later. Earlier versions of Befunge did not support the `k` instruction.
Answer: Output by exit code, where this is an allowed output form. If the challenge asks you to print one number, you can save a byte by ending the program with q instead of .@
Comment: Note that this tip only applies to Befunge-98 and later. In earlier versions of Befunge the `q` instruction had a different function (queue mode) or was not supported.
Answer: Don't forget about the k operator. Instead of "!dlroW olleH",,,,,,,,,,,,@, do "!dlroW olleH"bk,@. Note that k does the operation on the cell that it is at so 9k, would print not 9 times but 10; 9 times with the k, and once with ,.
Comment: Note that this tip only applies to Befunge-98 and later. Earlier versions of Befunge did not support the `k` instruction.
Answer: When pushing small numbers onto the stack, you can probably figure out easily enough that 45* will get you 20, and 67* will get you 42. When it comes to larger numbers, though, you really need a program that can calculate the most efficient representation for you.
The easiest option for this is Mike Schwörer's online interface for BefunRep. You simply type in a number and it'll spit out an equivalent Befunge representation. It's not always the most optimal, but it's close enough, and it's almost certain to be better than anything you could come up with by hand.
The online system is limited to numbers in the range 0 to 16777215, so if you need anything larger than that, you'll want to download the standalone BefunRep utility and run the calculations yourself.
If you're programming in Befunge-98, another option to consider is Fungify. In general it isn't nearly as optimal as BefunRep, but for some of the lower numbers, where hex digits and single quote characters are most effective, it can sometimes produce better results.
Comment: When pushing small numbers in Befunge 98, you'd use `'`. E.g. for `42`: `'*`
Comment: @Justin I mentioned that in the last paragraph, but the whole point of this tip is you don't need to know a whole lot of these tricks for generating numbers if you just use a tool to do it for you.
Answer: Merge branches as soon as possible
If two or more code branches are merging together and they all end with the same sequence of instructions, you can merge them immediately before the instructions they have in common. This is a fairly common circumstance to be on the lookout for.
As an example, I have this subprogram for reading input onto the playing field from my self-interpreter:

Notice that three different branches are coming together at the marked cell, each of which wants to write to the playing field. The one on the top right is 520p to put 5 at (2,0). The top left is 00p to put the computed value at (0,0). And on the right (and below) is 20p to put the computed value at (2,0). Since all of these instructions end with 0p, I save at least 4 bytes by merging the branches first and then doing 0p afterwards.
Answer: Use String Mode to Allow the IP to Pass Through Other Code
If you need the IP to get from here to there and there's a bunch of existing and unmovable code in the way in every direction, just push a 0, go into string mode, pass through the code, come out of string mode, and pop all the garbage before continuing. This trick employed in Wim Rijnder's Wumpus here:

(Yes, it would have been more efficient to put the quotes closer to the actual code there, but this is golf--we don't care about speed!)
This trick requires you to be able to spare at most 2 cells on this side and at least 3 on the other side, but it might end up saving space in the long run if writing yourself into a corner that requires this trick ends up greatly compressing the rest of the program. (In particular it could save you from having to write in a low-code-density "lane" for the IP to travel down.)

Tips for golfing in Befunge


What's the best way to store unused sushi rice?

Question: Let's say, I only want to make 1 sushi roll right now.  Is there a good way to store the rest of the rice for tomorrow's rolls?  And what about storing the nori?
Answer: Storing cooked rice is generally not a good idea.
With the high starch content in rice, it is simply an excellent growing ground for bacteria. Add to this the fact that uncooked rice can contain spores of Bacillus Cereus which when germinated to bacteria can lead to food poisoning causing vomiting and diarrhea.
Bacillus Cereus spores can survive cooking, so when rice is left to cool they can germinate and start multiplying in the rice. It isn't the bacteria itself that is dangerous, but a toxin they produce. This toxin does not disappear from re-heating.
If you do want to store the rice, make sure to cool it really quickly and store it in the fridge for no more than a day. Personally I never do that and only cook as much rice as I need.
Anecdotal: In fact, a friend working at a big sushi chain in London told me recently that over the course of four or five years they had one incident of proven food poisoning in one of their many restaurants. The source of the food poisoning was not the fish, but actually the rice which had been standing too long.
Storing nori I don't know much about, but if you seal it in an airtight bag and keep it dry I see no problems with that.
Answer: I don't agree with Manne on storing rice.  If you refrigerate what you don't use, then long grain rice could be used for a rice salad (similar to pasta salad) or fried rice.  You might be able to use short grain rice in a rice pudding.
But once the vinegar and sugar is added to make sushi rice -- I wouldn't try saving it for sushi -- it's not going to have the same consistency the next day, and I really don't think it would work.  You'd be better off making a vegetable roll or two with the leftovers and chilling that for the next day.
Off hand, I'm not sure where I might re-use leftover sushi rice where the consistency wasn't an issue ... maybe a rice-based casserole?
As for the nori -- I use a zip-top bag, and compress the air out, and haven't had any problems.
Comment: I regularly use previously made sumeshi to make a couple quick nigiri or maki rolls for lunch the next day or later in the same week.  The texture of the rice reheated is not the same as the original, but it is better than the crunchy texture from cold rice in previously made rolls.  The key is to microwave the rice minimally (30-60s), so that it is just above body temperature, then brighten up the flavor with a little splash of vinegar.  As for other re-use ideas... Warm dashi or miso soup can be ladled over cold leftover sumeshi and topped with cooked fish or vegetables.
Answer: For a different take, I've stored seasoned sushi rice (Nishiki) for a few days in the refrigerator, reheated it in the microwave and had acceptable results.  The consistency isn't quite as uniform, fluffy, or cohesive, but it can still make a decent dinner with a couple ounces of fish from your monger.
Regarding food safety, and speaking as a biologist who cultures microorganisms for a living, cooking the rice (boiling) will kill the vast majority of bacteria. Not all, but the only cooking method that really cares about true sterility is canning. Unless you leave your rice in the danger zone (not that danger zone, or this one) for an excessively long time, the amount of bacteria that survived (few), wake up (fewer), and reproduce will be negligible.
Basically, buy a refrigerator thermometer and make sure you're keeping it cool enough (2-4 °C, or 35-39 °F). Not just for this, but for all your food.


Use cases for CMAC vs. HMAC?

Question: Both can be used to verify the integrity of a message. Assuming you have the needed primitives available to you (i.e. the code space of needing both a cipher and a hash function isn't prohibitive), is there any reason to prefer one over an other? In practice HMAC seems to be much more widely used, is that a result of cryptographic, or social reasons?
Answer: HMAC was there first (the RFC 2104 is from 1997, while CMAC is from 2006), which is reason enough to explain its primacy. If you use HMAC, you will more easily find test vectors and implementations against which to test, and with which to interoperate, which again explains continued primacy. Being the de facto standard is a very strong position.
On many embedded systems, one may expect HMAC to be faster than CMAC, because hash functions are usually faster than block ciphers. This is not true if the platform includes some hardware optimization for a specific block cipher (e.g. dedicated AES opcodes), or if the messages are short (HMAC has the same asymptotic cost as hashing, but also a fixed overhead), or if you do something stupid like selecting a slow hash function as a basis for HMAC (e.g. Whirlpool). As with all performance things, actual measures are needed to reach any kind of definitive conclusion.
If you need to both encrypt and MAC, then the smart thing to do is not HMAC or CMAC, but rather to use an authenticated encryption mode which will do both properly, simultaneously, and at a lower cost (or at least so it is hoped). Usual candidates are EAX and GCM. The CAESAR competition was held to find new, better AE (Authenticated Encryption) ciphers.
Comment: Hashes usually faster than block ciphers sounds weird. After all most hashes are built from block ciphers and have stronger requirements than PRPness. Could be a historical accident since hashes are commonly ARX based, which is efficiently implementable in software, but that's no inherent property of hashes.
Comment: Beware: MD hash functions like SHA-1 are built out of a block cipher, but with the data as _key_, which apparently allows for better bandwidth. At least we can empirically notice that the SHA-3 competition yielded algorithms which are quite faster than all AES candidates on the same hardware. Even AES-based SHA-3 candidates (e.g. ECHO) turned out to be quite faster than AES itself on the same machine.

Use cases for CMAC vs. HMAC?


Why is there Turner syndrome if one of the X chrosomes is inactivated anyway?

Question: In females one of the two X chromosomes will condensate and turn into Barr bodies. So chromosome abnormality-free women will only have a single transcriptionally-active chromosome. Then why can abnormalities like Turner's syndrome still occur in the  presence of a single active X chromosome?
Answer: Pseudoautosomal region in mammals
On sexual chromosomes, we have a so-called PseudoAutosomal Region (PAR). The PAR is the region which still recombine with the Y chromosome (in males only) and is though to be important to allow separation of chromosomes during meiosis.
Pseudoautosomal region and dosage compensation
Because the PAR is diploid in males too, there is no need for a mechanism of dosage compensation and hence, in females, the PAR of the inactivated X-chromosome remain active.
Turner Syndrome
Turner syndrome is caused by an issue of dosage of functional elements found in the PAR. In people having Turner syndrome the PAR is haploid, while it remains diploid in both healthy males and healthy females.
Here is a small review paragraph from Sybert and McCauley (2004) that report the evidences suggesting that Down syndrome is caused by haploidy in the PAR. Please see the linked paper directly for further references.

Loss of interstitial or terminal long-arm material of the X chromosome (Xq) can result in short stature and primary or secondary ovarian failure.15 Deletions distal to Xq21 appear to have no effect on stature. In general, loss of the short arm (Xp) results in the full phenotype. Very distal Xp deletions are compatible with, but do not ensure, normal ovarian function. Loss of this region usually confers short stature and the typical skeletal changes, in part as a result of haploinsufficiency of the short stature–homeobox (SHOX) gene, located in the pseudoautosomal region of Y and Xp. The SHOX gene is probably not the only gene responsible for the skeletal features. Aneuploidy itself may contribute to growth failure. Loss of a region at Xp22.3 appears to be associated with the neurocognitive problems in Turner's syndrome. Loss of the testis-determining factor (SRY) gene locus on the short arm of the Y chromosome (e.g., 46,X,del(Yp)) also leads to the phenotype of Turner's syndrome, even without a 45,X cell population. A region on Xp11.4 has been proposed as critical for the development of lymphedema.
Comment: In addition, 35% of the genes in the inactivated X chrosomes are "escapees", which means that they remain active. The rest is mostly repressed by the expression of gene Xist.
Comment: @Jagoe I did not know that +1 Do you happen to know what fraction of these 35% are from the PAR? If you happen to have a reference, I would happily add that to the answer. Thanks
Comment: I've found a reference that tells of a similar figure (12-20% for humans, 3-7% for mice) for genes escaping "XCI" (X-chromosome inactivation) [https://www.cell.com/trends/genetics/pdf/S0168-9525(16)30002-6.pdf]. So yeah, the original percentage I wrote might not be accurate. I heard it from a genetics professor at college. Regarding PAR, well, I just heard it existed.
Comment: @Jagoe Ok. Note that your link is broken
Comment: https://www.cell.com/trends/genetics/pdf/S0168-9525(16)30002-6.pdf


Mima nafshuch?

Question: How do the words "ממה נפשך" mean what they mean, i.e. "either way"?
Comment: Relevant [glossary](https://judaism.meta.stackexchange.com/a/2304/9682).
Answer:
אם יש את נפשכם לקבור את מתי מלפני

I think "nefesh" / "soul" can sometimes mean "will" or "desire."  "From whatever your desire; if you say it's A, then it works, if you say it's B, then it also works."
Answer: My understanding has always been:
"ממה נפשך" literally means "From what your soul/self," which is short for "[You may interpret this] from what[ever approach] your self [prefers]."

The closest entry in The Practical Talmud Dictionary is for "מה נפשך," which R' Frank translates as "What is your desire [to say]?!" or "Which position would you adopt?!" - a rhetorical question that implies that whichever of the two positions about to be offered you choose, you'll end up losing.
It could be that "ממה נפשך" is just a variant form of the same expression, or that the extra 'מ' indicates that your position is about to be attacked "from" (or by) a "מה נפשך" argument.
The Dictionary cross-references its entry on "נפש," one of the senses of which is desire/wish. R' Frank gives the same example of this meaning in Biblical Hebrew that Shalom does.
Comment: We find for instance "malin oso miMa Nafshach" -- we can do circumcision on this baby, FROM a "what is your desire" argument.
Answer: This term is used when there is a kushya i.e. difficulty on the both  צדדים  i.e possible sides. This definition is by Darchei Hatalmud (or Hagemara) by Rabbi Yitzchak Kanpanton. The "instruction" of this term is for you to understand clearly what are the difficulties on both sides. See if it is a chiddush( i.e.new idea) to be able to ask the kushya. Do you have to accept certain premises in order to be able to ask the kushya?

Mima nafshuch?


Why does HSTS not automatically apply to subdomains to enhance security? For what reason would someone not want HSTS on every subdomain?

Question: HSTS restricts the connection to be always HTTPS if deployed by any domain, however for it to be applied to sub-domains the 'includeSubDomain' attribute is needed. Why doesn't the policy itself make it mandatory to include all subdomains? For what reasons/restrictions is the flag asked to be set?
Comment: Wouldn't that require certificates for each sub domain or a wildcard certificate? You cannot use HSTS with self signed certificates. This would lead to significantly higher deployment costs and thus hurt the adoption of HSTS.
Comment: By extension, for what reason would someone not want HSTS everywhere?
Answer: Subdomains can often be used for different purposes, and as a result they can be using different web applications possibly hosted on different equipment.
Not every website on every subdomain needs to follow the policy of the domain, it can even be the case that sites on subdomains do not support HTTPS due to lack of support in the application and/or not having a SSL certificate.
So automatically enforcing a policy on the main domain could possibly break things for subdomains.
Comment: @IsmaelMiguel having images over HTTP in a HTTPS page is a bad idea. I think most browsers would at least give a mixed-content warning.
Comment: +1 - if HSTS was subdomain mandatory, many orgs could not use it if they have an Active Directory domain which is a subdomain off their public domain. Which is exactly what Microsoft publish as best practice.
Comment: @RobertGrant say you own `example.com` and you deploy your AD on `ad.example.com` - now you set up a web service at `service.ad.example.com` - if HSTS was forced on for subdomains, it would be forced on for `service.ad.example.com` which you may not want, or may not even be supported for that application/appliance.
Comment: @MarkHenderson why would that affect AD?
Comment: Something else that comes to my mind is to serve cookie-less static content. This is usually done by having your site `example.com` fetch images on `http://images.example.com/`, instead of `httpS://example.com/images/`, which can improve on speed and parallel download of files.
Comment: @PaŭloEbermann You're right. But, at least, a specific sub-domain may not have a certificate. Or you may not be able to afford a wildcard certificate. Or you can have different certificates, which may be bizarre and may not even influence what I'm saying.
Answer: It's best to let the site owner decide whether subdomains are affected, just as the site owner decides whether to use HSTS at all. The extra flexibility could help improve HSTS adoption by reducing compatibility obstacles.
Some of the subdomain services may not have an HTTPS server installed yet. There are a few cases where it's not important security-wise to have HTTPS on certain subdomains.
That answers why includeSubDomain is not mandatory.
One could still ask why it is not the default:
For this I would like to point out that HSTS cannot be undone except by asking your visitors to clear cache in their own browser. Chances are your visitors will not do this.
So, if you accidentally applied HSTS to more than you intended to, that (sub)domain goes down permanently for those visitors until they switch devices or browsers, clear cache on the browser, or the site owner installs an HTTPS server. (which might be technically difficult on some legacy services)
Comment: "Some of the subdomain services may not have an HTTPS server installed yet." -- An in fact, may not even be under your control.  It's fairly common to add DNS records for subdomains for SaaS apps like a CRM, recruiting software, etc.
Comment: Chances are at that point you have no easy way of contacting the visitors of your site in the first place.
Answer: My best example on why this would be bad, is webhosting.
Imagine a webhost, lets say somecheapwebhostingexample.com has HSTS and even a payment page. And then they don't have wildcard certificates or anything like that.
Then a customer signs up as customer1.somecheapwebhostingexample.com .
Its obvious its a bad example to deploy subdomains per default here.
There are other examples where theres multiple subdomains, but no certificate available for them all.


What would change if we focused more on Political Science?

Question: In this question, I raise the possibility of attempting to attract more academic political scientists to the site. As the site sits now, most of the questions and answers rely upon popular (i.e. non-academic) sources, and contemporary events. A shift towards the academic would necessarily cause certain changes. What changes would have to occur to make that shift, and what effects would that have on non-academic users?
Comment: "what effects would that have on non-academic users" - the answer is "it probably depends on the user". Personally, I would gladly welcome our new Academia overlords... well, at least their contributions. However, it's unlikely that any user of the site would object to heavier inclusion of more academic topics, even if they won't necessarily directly participate.
Comment: What feature are you requesting?  This seems like a pure discussion question.
Comment: @Brythan I included the "feature-request" tag for the issue of "verified users" with automatic reputation. If that is inappropriate I'll delete it.
Comment: @user4012 Actually, at least the "academic overlords" part I want to avoid. I am an academic, and I'm not ashamed of it, but I believe that 1) many academics are insufficiently humble about the limits and sources of their knowledge, and 2) don't do enough interaction with people who are serious, but not in the academic bubble. It is partly for this reason that I'd love to have more academics involved here. It ***would*** help the site, but it would also improve academia as well. SE has been nothing but good for Computer Science, and I think that could be replicated elsewhere.
Comment: Possible duplicate of [Would Focusing more on Political Science improve the site?](http://meta.politics.stackexchange.com/questions/2646/would-focusing-more-on-political-science-improve-the-site)
Answer: How We Can Expand the Site to Include Political Science

Allow meta-Political Science questions (e.g. "What are the 3 dominant structural theories of International Relations?") This is key to both getting political scientists to visit, and to have this site show up in searches.
Favor answers with links to peer-reviewed material and add peer-reviewed links that are supportive, to existing answers. Down-voting non-peer reviewed material may not be necessary, but only time will tell.
Encourage and upvote multiple correct answers to the same question so that people who are familiar with different theoretical traditions to answer, so that someone from the English School of IR can give their answer, and someone who is a Domestic politics expert can give theirs, and both are equally right. Upvoting many answers is super-important to increase the profile of participants on the site, so there are more mods, too.
Allow and encourage "process" questions and answers when there is currently no answer. (e.g. "How could I figure out if SES makes someone more likely to vote for Marxists?" or "In order to know that we would need a sample of 1000 people in Uganda who were ethnic Tutsi with annual responses, and not expelled during the Rwandan civil war, and we would conduct a panel analysis of their answers.")

Something that may or may not exist, but could be helpful would be to immediately give status points to people who are recognized experts outside SE to participate here. For example, if Gary King were to sign up using his Harvard e-mail, he should start out with a sizable status, because we know who he is, and he will likely be able to contribute significantly to the moderation of the board, should he choose to do so.
What This Would Mean for non-Political Science Members and Questions
The core audience of SE are professionals, but the key beneficiaries are the amateurs. If more experts participate in the site, the amateurs both get better answers and will get good feed-back on their answer. Just because someone doesn't have a PhD. (or even a BA) does not mean that they can't answer a question well, but having others who do around might help sharpen that answer, and it will likely lead to better answers in the future. This should not force out any amateur, nor should it discourage them from participation.
That said, some people might no be able to access gated materials. If that becomes a consistent issue, then something should be done about that. This is a problem dealt with on other SEs regularly, so I assume there is some kind of SOP or best practices that can be copied.
Comment: I Would also point you to [this meta discussion](http://meta.politics.stackexchange.com/questions/40/should-we-have-a-back-it-up-rule-for-answers)


Term for someone who has an eye for detail

Question: Is there a term that could describe this sort of person? Like, an eye for detail in arts, an eye for detail as to what is the cause of a conflict (something which other people hadn't seen yet), an eye for detail, which is why a photo was taken from the right angle or perspective.
Answer: You mention two different use cases.

an eye for detail in arts ... an eye for detail, which is why a photo was taken from the right angle or perspective

Like jimsug and ChristopherW, my immediate inclinations are meticulous and keen- or sharp-eyed. I don't know of a single adjective (or even a concise phrase) which has this meaning and also carries a specifically artistic connotation. I can only recommend general terms and suggest that you add modifiers to specify the artistic bent. Other potential choices:

Assiduous
Sedulous
Scrupulous (very often used in a moral or ethical sense)
Fastidious (very often used when speaking about cleanliness)
Detail-oriented

an eye for detail as to what is the cause of a conflict (something which other people hadn't seen yet)

For this case, I'd use astute. 1, 2. It applies specifically to situational assessment, and I would not use it to describe an artist's attention to detail, e.g. when painting or composing a photograph.
Answer: You could call them:

meticulous, though this might have a negative connotation, depending on the context - as has been pointed out, not always:

very precise about details, even trivial ones; painstaking

vigilant, though this has a bit of a supervisory/oversight connotation to it:

keenly alert to or heedful of trouble or danger, as while others are sleeping or unsuspicious

And.. both of those entries have synonyms and links to thesaurus entries:

thorough, detailed, particular, strict, exact, precise, microscopic, fussy, painstaking, perfectionist, scrupulous, fastidious, punctilious, nit-picky
watchful, alert, on the lookout, careful, cautious, attentive, circumspect, wide awake, on the alert, on your toes, wakeful, on your guard, on the watch, on the qui vive, Argus-eyed, keeping your eyes peeled or skinned

I'm intuiting that what you want is closer to meticulous than painstaking, though.
Comment: I'm not sure I'd describe "meticulous" as having a negative connotation. To describe someone as being *negatively* detail-orientated, I'd probably use words like *pedantic*, *nit-picker* or *fussy*
Comment: I was looking for a positive term, mainly. Like, some people's brains might just enable them to have more eye for detail. Some of the terms you mentioned are a bit negative, perhaps? Like, fussy, painstaking and nit-picky e.g.
Comment: @Matt true, this would depend on the co-text/context.
Answer: I usually refer to people like this as observant.

Ted noticed that Kathy and Carol are no longer friend despite always being cordial.
Yea, he's a pretty observant person.

Observant is not typically used with tangible objects though. While it can be, I believe jimsug's first word is a better fit.
Another word that comes to mind is thorough. Thorough simply means that all the details have been examined. You would want a thorough airplane mechanic running quality control to ensure planes are ready for takeoff. You would want an observant manager to realize that a mechanic is thorough enough for the job of quality control.
Answer: The another lesser known term for it is "anal".
This wikipeida link must be able to help you
Answer: I'd go with perceiver or percipient that are defined as:

A person who becomes aware (of things or events) through the senses.
One that perceives.
Comment: @LucianSava Oh!  I'm sorry, I thought *percipient* was (only) an adjective, so I didn't realize you were trying for nouns specifically.  I see now that dictionaries say it's a noun, too!  (I don't see any indication that the question is asking for a noun, but I s'pose someone could ask the OP and find out!)
Comment: -1 because those sound extremely unidiomatic to me. An English speaker would be much more likely to use the adjective *perceptive* than *percipient*.
Comment: @ Matt, thank you, I fairly appreciate that you explained your reasons. If anyone did like you we, learners, would really be helped and the site would function better.
Comment: @LucianSava But if you changed your answer to say *perceptive*, I could upvote it :-)
Comment: @Snailplane, sorry but I'm afraid I can't do that. Perceptive was my first reaction but I couldn't find to be defined as a noun, all dictionaries define it only as adjective, and I think OP asks for a noun.
Comment: @Snailplane, I think you're right and I misread the question. My bad.


Difference between Alexa, Google Analytics, Quantcast and Compete website statistics

Question: I am getting confused by the following traffic metric systems: Google Analytics, Alexa, Quantcast and Compete metrics because they each show different values. ie. unique traffic, visits, pageviews, etc. Which among them would be the most reliable and why does each show different values.
Answer: Google Analytics would be the most reliable.
Edit
I was being a bit lazy for not posting this, earlier, I realize that this comparison might help others (including myself!)
All the services you mentioned offer javascript code based tracking. Alexa also does this in their Pro Plan, so do Quantcast and Compete. However, the data reported by all these services is not accurate.
This has been reported by SEOmoz in an extremely neat fashion, Compete and Alexa have been scoffed at in TechCrunch.
A non-biased version is provided by Avinash Kaushik on the differences between these and other systems. I would highly encourage you to go through this post, because I cannot explain things as clearly and as indepth as this man. He rocks!
In short, if you want to measure metrics about only your site, then Google Analytics is the best tool (I could be biased since I have been using this for the past 3 years on a daily basis and am generally able to find answers about data discrepancies if any).
Do note that GA does not provide competitor data, where as some of the other systems do. You can find such data using Google Trends for Websites. Do read a longer post on KISSMetrics on this.
Comment: From the stats services mentioned this might be correct, but why?
Comment: Because Google Analytics is usually not estimated (to a degree), but the traffic is counted and sent to Google's servers through your own tracking snippet.
Comment: DKOATED that's correct but I'm sure w3d is fully aware of this and indicating that @Prasad should be answering with more detail in why for the sake of people not knowing :P
Comment: I should have answered that in more detail, the way @DKOATED has done, I apologize for that temporary lapse in laziness.

Posting a detailed answer ... turns out that the simple answer can require a fairly lengthy reasoning!
Answer: Google Analytics measures your traffic on your own site through a Javascript snippet integrated into all your website's pages.
Alexa, Compete and Quantcast merely do estimates of your traffic and are generally not very reliable. Not sure about Alexa and Compete, but Quantcase does offer to integrate a javascript snippet of their own, which increases reliability of the measurement.
If you really need to know your traffic as accurate as possible:
Make sure you have Google Analytics integrated and running on all your pages or even better: Install some serverside tracking.


Natural headphone Mean?

Question: What does it mean when people say a headphone is natural sounding ? does it mean the headphones is flat and boring when listening to songs ? does it make your music sound amazing or just normal but with more detail ?
example :sennheiser hd 448
i would like some detailed answers and anyone with the headphone above(the sennehsier hd 448)
can give me their take on it ' thanks!!
Comment: Yes it means flat & boring. The manufacturers go to great lengths to get them to sound that boring :P
Comment: lol you a joker
Answer: This might be of interest:
Would you rather use flat headphones for monitoring?
Answer: i believe it means there is no gain of certain frequencies.  example, the DREs headphones have a gain in low frequencies.
Answer: Yep, read the article above.
You can only assume that it means they have a flat frequencey response, which mean thst no particular frequencies are emphasised or cut. They are specifically meant to provide you with a representation as true as possible, without any colour (ie. distortion) provided by the speakers.
You will generally find that you can hear more detail with a decent pair of monitor speakers/headphones. If music is poorly mixed or produced, it will show up theses flaws.
If you produce and mix, then it is important. If you are just a music listener, then not so much - unless you value sourcing quality music on a decent format and hearing it as intended (ie. not on mp3).
For example - if you have speakers that 'make your music sound amazing' in your studio by say, boosting the bass a bit. When you pass that music onto others, their system will have no such bass boost, so your music might sound thin and crappy.
Look into the concept of MASTERING if you are curious to learn more.
D
PS. I have a pair of HD25s which are comfortable and have good sound exclusion. I use them for music listening, studio, and DJ applications. For actual mixing I prefer speakers - monitors which I know the sound of very well.

Natural headphone Mean?


How do I make sure my stupid edit never sees the light of day?

Question: I was an idiot and edited an answer rather than my question - how do I make sure my stupid edit never sees the light of day?

Question where I screwed up
Answer I accidentally vandalised
Answer: I rejected your edit suggestion (hope it was the one you meant - the comment was a good clue), so the edit won't be applied :)
But in general, you've hit on a small problem - there's no way to retract an edit suggestion as far as I know.
You can click the Edit button again and sort of undo your changes, but this is often tricky, especially if the text has formatting, so I don't recommend it unless the suggestion you made was very minor. Of course, this is the right action if you spotted a mistake in an otherwise good edit suggestion you've made (just not one you didn't actually want to make at all).
Another option is to ask someone to reject the edit - for example you could leave a comment for the post author asking them to reject your suggestion, or come to the Downboat or Ask Ubuntu General Room and ask folks there to reject.
Comment: Thank you. I had a momentary BSoD moment when I saw that I had edited a perfectly fine answer instead of my question.
Comment: To those wondering what the comment was: "*For goodness sake ignore my last edit. i am an idiot.*"
Comment: @BeastOfCaerbannog ahaaa that helps to understand why the edit came to be accidentally suggested - I guess OP wanted to copy and paste that text from the answer into the question to give an update on what happened when they tried to follow the advice. That text in the question should probably be formatted as a quote - I'll do that
Comment: @MatthewBrownakaLordMatt lol @ the BSoD moment... This is nothing - one day I should put together a list of my editing errors, including the one where I somehow made my entire edit with a non-Latin keyboard layout on without even noticing (thus filling some poor person's question with random characters), and the one where I replaced a link to an article about some Ubuntu thing with one to a video clip from *The Labyrinth* due to not checking what was in my clipboard XD
Comment: Why the [revisions](https://askubuntu.com/posts/1361619/revisions) look as if heynnema had "Update #1" (OP's edit) in their answer in the first place?
Comment: "Be careful" kinda works. Practically, one of the advantages of the suggested edit, and psudo-version control of rollback is that its semi trivial to fix - so one or two oops is unlikely to have a lasting effect
Comment: @BeastOfCaerbannog OP's suggestion accidentally removed the update #1 part I think
Comment: @Zanna You're probably right! It seemed to me that *this* was the OP's suggestion that they later wanted to remove, as it exists in both the question and the answer.


What's the exact curve for natural audio fading?

Question: I'm making a DJ type program (it's geared more towards theatre productions) where I need to fade sound. I know that when you fade, doing a direct linear line doesn't sound natural and that a bit of a curve is better. Does anyone know/have an idea of what the exact curve should be. Is there a formula or equation or anything you can use to describe it?
Answer: There's no particular standard - there are lots of ways to fade audio. A straight line is one of them, but in many cases some kind of curve is preferable and it's down to your preference which one is best.
I found this image from this page about potentiometers and their fading properties, which I felt illustrated this well:

Some kind of logarithmic curve, like depicted here, is common, but some audio packages like Reaper let you customize it a bit further, using something like a Bezier curve. I don't know if that's the specific kind of curve that is used, but it or something like it should work just fine.
Although these represent cross-fades, you can get a feel for the wide range of possibilities (or perhaps read it as the lack of a standard).
Comment: Potentiometer curves aren't really relevant here, as even when fading by hand with a physical fader you normally won't use a constant velocity, but a somewhat smoothed motion.
Answer:
doing a direct linear line doesn't sound natural

Hm. First off, fading isn't a "natural" thing to start with, so if anything sounds natural it's mostly what we're used to, rather than some "law" based on mathematics, physics or even psychoacoustics. Traditionally, fades were in fact done by hand, and the engineers usually would have a whole lot of stuff to their mind, so the exact curve was often something of a random process. Indeed many pre-70s records have fades that sound hasty, undecisive or otherwise odd.
There are sure enough some aspects of a fade where you can find objective criteria. Since a fade is something artificial, generally a means rather than an end, it should normally be as subtle as the time permits. This means, at no point change too fast, and also not too fast-changing derivative. Particularly, it is seldom good for a fade to start abruptly, rather it should smoothly get going, i.e. the "upper edge" should smoothly approach the constant "on/loud" level, in a round curve. At the other end, this applies in principle as well: if the curve is too steep there, it will sound almost like a discrete switch at this end. The most natural thing would be an exponential decay, like a guitar string. However, particularly for fades of just one track in a multitrack setting, the faded one will usually be inaudible already at about -30 dB, so the very low-end is hardly relevant. You shouldn't waste too much time here then.
For the middle part, there doesn't remain much choice, just smoothly keep the track.
Going after this, we get pretty much the "S-curve". That is IMO a good default for fades to 0. For crossfades, something constant-power-ish is often better.
Comment: I'm a big fan of the S-curve. It generally reflects the natural decay of sound and, as such, sounds more "natural" to my ear.


Why is neutron star a star?

Question: I am wondering since neutron star is smaller than the average main-sequence stars and it doesn't produce energy via fusion so why do we still call it a star?
Comment: https://en.wikipedia.org/wiki/Compact_star
Answer: It seems Walter Baade and Fritz Zwicky may have coined the term in 1934 (see here) and the name stuck around.
I've known some astronomers to label them 'stellar remnants' for the reason you gave; they are not stars in the sense they do not produce energy via nuclear fusion, and that they are not made entirely of neutrons as the name would suggest.
They seem to be called stars for lack of another layman's term (from our point of view on Earth, not all neutron stars are pulsars), and that they still share some characteristics of stars: they emit their own light, they have masses greater than the Sun and can even have planets orbiting them.
Answer: According to wikipedia:

A star is a luminous sphere of plasma held together by its own gravity

then it goes on to say that

Near the end of its life, a star can also contain degenerate matter

(see also nuetron degeneracy).
http://www.dictionary.com/browse/star has:

Any of the heavenly bodies, except the moon, appearing as fixed luminous points in the sky at night.
Astronomy. any of the large, self-luminous, heavenly bodies, as the sun, Polaris, etc.".

Nothing in those definitions explicitly requires fusion, though the mention of plasma seems to infer it. The quantum mechanical effects in a nuetron star are an analogue to an ideal gas in classical physics. The degeneracy pressure thereof prevents the star from collapsing into a black hole.
Comment: I agree, but they were the only definitions I could find at 5am in the morning.  Let's try to fix that at wikipedia.
Comment: I would argue that those definitions are not great technical definitions because a star is defined as becoming a star once it begins hydrogen fusion. Before that point, it may be called a proto-star, but it isn't a star, despite meeting the requirements in your definition.

Why is neutron star a star?


FogBugz compared to OnTime

Question: Has anyone used both FogBugz and Axosoft's OnTime and care to offer an opinion?  AxoSoft has a big feature comparison chart but I'm also interested in more subjective thoughts on things like ease of use and stability.
Answer: I've used both from a project lead perspective and a team member, to manage parallel projects and teams.
OnTime has a big feature matrix, but that doesn't translate into more value in an organization. For ease of use, OnTime fails. OnTime does NOT have a well designed interface, so for me, it does not stand out in the crowd. FogBugz, on the other hand, is pleasant to use, and I found myself "happier" to login every morning.
For me, the most important "feature" is: How well the tool presents and tracks issues and simplifies  participation by team members. If it does this poorly, most of the other features fade. If it does this well, then some missing features can be forgiven.
On this one point, I find OnTime particularly inadequate and FogBugz particularly superior.
OnTime is loaded with different tabs in which information becomes lost or difficult to track. Teams and individuals often use different tabs for different purposes. I have to click around or I might miss something.
FogBugz tracks the issue with minimal clutter, like a discussion thread. When updates are made to the issue, all parties are notified via email, and no information is visually lost. At a glance, I always know what is going on with FogBugz.
OnTime 2009 also doesn't allow us to assign and track issues with multiple team members in parallel. You simply assign to a single person. No way to CC others. Big deficiency for team work.
Also, when performing a project review, we often take down a lot of fast issues as the customer speaks. With FogBugz I can use the quick mode to punch the issue in as fast as I can type descriptions, and return later to flesh it out. We cannot do this with OnTime, with its various required fields. Besides that, OnTime is just sluggish, taking 5-6 seconds just for the defect window to popup. I need to be able to enter issues during a meeting as fast as I can type it into Excel. The total time & clicks to create an issue in any tool is a key benchmark.
In short, with customers who use OnTime I see people constantly fallback to email for discussions, and I also see degraded communication (someone enters notes that others never see). I do not see this trend with FogBugz.
Feature matrixes look good on paper, but it is difficult enough to keep teams using a tool properly without the tool adding more difficulty. FogBugz makes it as simple as you want, while allowing you to drill down as needed.
OnTime, however, feels like a very detailed tracking database with quick WinForms app thrown on top.
The downside for me with FogBugz is price for upgrades. Yearly maintenance is steep at 50% of the original cost. I could not justify upgrades, in part because we are happy with FogBugz 6, but in part because I could not see what I was getting for my yearly maintenance fees. FogCreek wasn't very flexible on licensing discounts for us, after all they need to make a living, so we just decided to stick with v6 forever.
UPDATE 2014: A year or so after I wrote this, FogCreek sent me a free upgrade to v7 to fix a security bug. Just this year, they did the same thing again. They are the only company I've ever deal with to give me a free upgrade just to fix a bug, even without maintenance. A top-notch company with good people.
I'd still spend my money again on FogBugz without a second thought.
Comment: Never used FogBugz, but I have to echo your comments on OnTime. It's not well-designed, and it makes issue tracking unpleasant. The side-effect of this is that we don't use it very often because of the mental obstacle of having to use the darn thing. Features != quality.
Answer: I actually encouraged the company I work for to begin tracking bugs with software (specifically FogBugz) and have been very pleased with FogBugz.
We blindly let our customers send bug requests into FogBugz through email, which has it's advantages and disadvantages.  But we really haven't had any problems integrating FogBugz into a team that was totally unfamiliar with any bug tracking software.  Overall, I'd rate FogBugz about a 9 on ease of use and stability.
Answer: I've used both extensively in production software development environments.
OnTime isn't bad - once you set it up to handle support tickets sent to an email, it has all the daily activities of software developers pretty well integrated.
I personally prefer FogBugz, because of the predictive estimation stuff that it includes.  Being able to pick a due date, and then getting a likelihood of hitting that date based on your past performance is pretty awesome.  I also think in general FogBugz is faster to use and organize your features/defects, and I like how it tracks time better.
One area where OnTime wins out is that it is much easier to make reports against OnTime.  It stores everything in a SQL server so it is easy to access (granted if you get the non-hosted FogBugz maybe you could do this too).  Also, it includes a report designer so you can get to your data.  FogBugz has the weakness that while you can track and enter the time you spent per item for the purposes of its experienced-based scheduling, it doesn't give you an easy way as a manager to look at how much time a given employee spent on what things that week.  Hopefully they will add that in the near future.
Answer: OnTime is more an ALM tool - it's trying to do everything.
FogBugz just deals with bugs (and feature requests) and at that it's excellent. I'm not sure about some of the newer extensions (like discussions), but for bugs it's really good.
There's lots of stuff that I'd add to it in terms of better reports, searching and the like, but I can definitely recommend FogBugz.
Answer: I've used OnTime for a few years now. It's actually a very easy tool to use and not just a bug tracking tool as was suggested. Where it falls down for me is the slowdown I've experienced as the volumes of Features / Defects/ Tasks have grown. Also, the web client tries too hard to be a parallel of the winform version and can be flaky as a result.
Answer: I have not tested the OnTime thing, but keep in mind that both FogBugz and OnTime have free versions as well, Axosoft for 1 user and FogBugz for 2 Users, although it's the hosted version. (Check my answer here to see how to sign up for the free FogBugz version)
So you can have some real first-hand experience on both systems.
Comment: Axosoft don't offer a free hosted version - Fogbugz do.
Answer:
Are you bug tracking or project planning?

FogBugz has better bug tracking features. FogBugz has better e-mail integration, state tracking and triggers. FogBugz is easier to drill down to an individual task without needing to apply a lot of filters.
For project planning, however, OnTime is the superior tool. The monte carlo estimation feature in FogBugz is cool--don't get me wrong--but honestly, getting the project entered into FogBugz so you can actually use the estimator is such a pain in the rear it can be downright frustrating. The scrum planning board in OnTime is really sexy. If you're used to using whiteboards or sticky notes, it's a breeze to enter and visualize.
OnTime provides better project overview information and custom reporting; this is better for managers.
FogBugz provides better drill-down information; this is better for implementers.
FogBugz has more features; this is better for tech-centric users.
OnTime is more graphical; this is better for non-engineers (project planners, artists and other people who often have to use scheduling tools).
Other factors: Some people have mentioned speed issues. I haven't noticed speed issues with either, but my only experiences have been local installs. OnTime is expensive for mid-sized teams; it's free for a single user and by the time you get to 10+ users the price is average, but for 3-6 man teams it's expensive especially if you want the pivot charts.
Quite honestly if you can afford it, it would not be stupid to consider both. Use OnTime for writing quotes, and FogBugz for tracking defects. They are radically different tools, and neither one excels in all areas but both are very good at select tasks.
Comment: Tried both, FogBugz UI is ugly. OnTime, way too slow for internet app. In the end we went with Countersoft Gemini. It is a 20mb download and does what both of these are doing+.
Answer: I haven't worked with FogBugz, although I recently recommended our company goes with that.
OnTime is what the company decided to use and I personally don't like OnTime because of slowness and badly organized GUI. We opted to host it ourselves, but I don't think the machine is slow. The web app doesn't really look like a web app, more like it copies a windows app, just as Brian Scott said in his answer. And don't try using the windows app over Internet (over VPN). It's awfully slow. I suppose it could be due to our Internet connection latency.
Of course, my experience might be different than other people's, I could be having network issues. Someone else will have to confirm my claims of slowness. :)

FogBugz compared to OnTime


Create a sphere with multiple layers and a chunk cut out showing them

Question: I have a graphic that I plan to use in a video. Right now it's 2D and I plan to animate the layers as we discuss each point. I'm brand new to blender, but was wondering if it's possible to translate this design to a 3D one and animate the model instead. Any help would be appreciated!
Comment: what kind of animation would you like?
Answer: Start with a sphere and delete the faces that you don't want. Then, select the whole object in edit mode, press "E" to extrude, press "S" to scale, press "0", and then press "Enter".

You can duplicate this as many times as you want and then add a normal sphere in the middle.
Answer: Boolean and optionally solidify modifiers.

Starting with the default cube, move it to location (1, -1, 1).  This will be our boolean "cutting" object.
Add a default sphere, optionally give it a solidify modifier and a boolean modifier.  With a solidify modifier will be akin to revealing a tennis ball, without chopping a quadrant out of a solid pool ball. Using solidify will stop any chances of z-fighting with overlapping cuts on inners.
Set the thickness of the "crust" using the thickness of the solidify modifier.
Set the cube as the cutting object of boolean modifier.  (otherwise settings are defaults)

 One I prepared earlier, showing wireframe cube, the modifiers, with without solidify, and forgot to twiddle thickness
For each next inner layer, duplicate the sphere, this ensures it also has same modifiers,  scale it down, if using solidify adjust thickness to suit, .
Finally the inner core has no modifiers.
Notes:
This uses the one cutting cube, having a unique cutting object for each  sphere to reveal layers on each separately.
Answer: Depending on what animation you need, you may be able to keep the model very simple... (which may help with animated cutaways, etc.)

.. and take advantage of the 3D Gradient (spherical) texture, quantizing it with a color ramp..

Which gives this sort of result without explicitly constructing shells.

(For example, any other intact sphere centered on the same place, sharing the same material, could be scaled in and out from the center, and would change color automatically)