Interpret t-values when not assuming normal distribution of the error term

Question: Assume that you have a regression with a whole set of variables and you know that the residuals are not normal distributed. So you just estimate a regression using OLS to find the best linear fit. For this you disclaim the assumption of normal distributed error terms. After the estimation you have 2 "significant" coefficients. But how can anyone interpret these coefficients? So there is no way to say: "These coefficients are significant", although the Hypothesis $\beta=0$ can be declined with a high t-statistic (because of disclaiming normal error assumption). But what to do in this case? How would you argue?
Answer: If the residuals are not normal (and note that this applies to the theoretical residuals rather than the observed residuals), but not overly skewed or with outliers then the Central Limit Theorem applies and the inference on the slopes (t-tests, confidence intervals) will be approximately correct.  The quality of the approximation depends on the sample size and the degree and type of non-normality in the residuals.
The CLT works fine for the inference on the slopes, but does not apply to prediction intervals for new data.
If your not happy with the CLT argument (small sample sizes, skewness, just not sure, want a second opinion, want to convince a skeptic, etc.) then you can use bootstrap or permutation methods which do not depend on the normality assumption.
Comment: @Gregg You and @mpiktas seem to be saying similar things, so I believe comments about his reply may also pertain to yours.
Answer: If the errors are not normally distributed, asymptotic results can be used. Suppose your model is
$$y_i=x_i'\beta+\varepsilon_i$$
where $(y_i,x_i',\varepsilon_i)$, $i=1,...,n$ is an iid sample. Assume
\begin{align*}
E(\varepsilon_i|x_i)&=0  \\
E(\varepsilon_i^2|x_i)&=\sigma^2
\end{align*}
and
$$rank(Ex_ix_i')=K,$$
where $K$ is the number of coefficients. Then usual OLS estimate $\hat\beta$ is asymptoticaly normal:
$$\sqrt{n}(\hat\beta-\beta)\to N(0,\sigma^2E(x_ix_i'))$$
Practical implications of this result are that the usual t-statistics become z-statistics, i.e. their distribution is normal instead of Student. So you can interpret t-statistics as usual, only p-values should be adjusted for normal distribution.
Note that since this result is asymptotic, it does not hold for small sample sizes. Also the assumptions used can be relaxed.
Comment: I'm not clear about the use of asymptotic arguments in this case.
Comment: I second @Frank's remark and would add that the very first thing one suspects when residuals appear non-normal is that one or both of the first two expectation assumptions is wrong: that is, there may be lack of fit ($E[\varepsilon_i|x_i] \ne 0$ for some $x_i$) or heteroscedasticity ($E[\varepsilon_i^2|x_i]$ varies with $x_i$).
Comment: @Frank, @whuber, clearly I misunderstood the question, but I do not get how, could you clarify? I thought the OP asks how to interpret t-statistics if the residuals are not normal, **but all other usual assumptions hold**. If this is not the case, the question is too broad.
Comment: My comment was related to the extremely high type II error that can result from a failure of the normality assumption to hold, and also about the "how large is large" question about the sample size.  t-tests may perform poorly on the regression parameters even if all other assumptions hold.
Comment: @whuber and @frank, I know I have little experience compared to yours, but this is what I think: Using OLS to estimate the $\beta$s is ok, the only problem comes is while performing inference. (am I correct?). In inference, as @greg and @mpiktas pointed out, if symmetry holds and CLT kicks in, using t-test would not be that bad (or simply using normal distribution would be ok). I would *definitely* perform bootstrap of residuals for inference. I would also check Box-Cox transformation for elimination of possible variations from normality.
Comment: Using OLS to estimate the $\beta$s is not necessarily OK if the residuals are far from normal with equal variance.  You would have efficiency and robustness problems.  And as stated above, the $t$-test can have very low power.


On dativ and akkusativ

Question: "Ich gratuliere dir zum Geburtstag."
"Ich rufe dich an."
In both sentences the other party is "receiving" the action, so why is one dativ and the other akkusativ ?
Thank you!
Comment: In SW Germany and Switzerland you will also hear "Ich rufe *dir* an" - Maybe shows best that there can be no strict rule.
Answer: Thoughts about giving/receiving (dativ) or accusing (accusative) just give a first hint. The actual case is defined by the verb. Some verbs need their object in dative case, some in accusative case, and some even in other cases.

The verb »gratulieren« needs its object in dative case.

Ich gratuliere dir.

The verb »anrufen« needs its object in accusative case.

Ich rufe dich an.

In fact there is no logic behind. Just stubborn verbs that have individual requirements.
Comment: *Ich nenne ihn einen Lügner* - Both objects accusative. That is one of the reasons why you shouldn't use the terms direct and indirect objects in German
Comment: That's ... impractical to say the least. Thank you.
Comment: Verbs are as stubborn with the cases of their objects as nouns are with their genders.
Comment: Oh and does that mean that the indirekt objekt can be non dative too? Maybe with some "dative direkt objekt" verbs?
Comment: Better to leave "accusing" out of this discussion.
Answer: Something like "receiving an action" may give you a first hint, but it is not sufficient to decide the case, you have to learn that together with the verb.
Compare

Ich gratuliere dir.

with

Ich beglückwünsche dich.

or

Ich frage dich.

with

Ich antworte dir.
Comment: It's still unclear putting it like that, for all the sentences I can only see the other party as the direkt objekt.
Comment: @archaic, the answer is: Because this is how "gratulieren" works, which a dictionary will tell you.
Comment: So there's no logic behind it?
Comment: Not the sort of logic you're looking for. You need to learn the ruled case with the verbs.
Comment: @archaic, you can come up with rules, but like all good grammar rules they will have exceptions ;)
Answer: As Wikipedia says "The dative case (...) is a grammatical case used in some languages to indicate, among other uses, the noun to which something is given." This can be helpful in very many (of course not in all) cases. I think it works for 'gratulieren'.
'As time goes by', learners will understand that there are clusters of verbs having correspondant intern and extern structures:

jemanden anrufen like den Fernseher anstellen, jemanden bei der Polizei anzeigen, jemanden ansehen/anschauen, den Drucker anschließen ...

but!

jemandem das Salz = etwas angeben like jemandem etwas zu trinken anbieten, jemandem den Drucker anschließen, jemandem etwas ansehen (z.B. seine Enttäuschung) ... [person = dative, non-person = accusative]

In the same way you say _jemandem etwas bescheinigen.
However, contrary to the general dative rule you say

jemanden beglückwünschen like jemanden beraten, jemanden beurteilen, jemanden beruhigen, jemanden begrüßen, jemanden bewaffnen ...

but!

jemandem bevorstehen like _jemandem in nichts nachstehen, jemandem zur Seite stehen, jemandem gut zu Gesicht stehen, jemandem stehen (Kleidungsstück), jemandem im Weg stehen, einer Sache entgegenstehen ...

It could be very useful to have a catalogue and a hierarchy of those structures and sub-structures, but I don't know if it exists.
Answer: For Akkusativ you are asking "wen oder was": wen oder was rufe ich an?
That works, but this one doesn't: wen oder was gratuliere ich zum Geburtstag?
Correct it would be "wem gratuliere ich zum Geburtstag" and thus it is Dativ.
Hope that helps.
Comment: Diese Antwort hilft niemandem, der aus einer Sprache kommt, in der es weder Dativ noch Akkusativ gibt. Die Wen/Wem-Frage hilft nur Leuten, die bereits ein sicheres Gefühl für diese beiden Fälle haben. Für jemanden, der Probleme mit diesen Fällen hat, sind »wen gratuliere ich« und »wem rufe ich an« genauso plausibel wie die korrekten Fragen.
Comment: This "ask a question" exercise does rarely play well with learners. It only works if you know what to ask.
Comment: And why is it wem not wen? It's still "Who do I congratulate...?"
Comment: In terms of direkt objekt and indirekt objekt I simply can't seem to clearly differentiate them in the "Ich gratuliere dir ..." sentence, because literally translated it's "I congratulate him" so he's the direkt objekt ...
Comment: I should look at it more as gratuliere = "to give" congrats ?

On dativ and akkusativ


Why didn't Odin regrow Thor's arm?

Question: In the recent Thor comics, after losing Mjolnir, he also loses his arm to Malekith.
Odin calls upon a dwarf to forge him a new arm, composed of Uru.
But...why? Odin is a reality warping skyfather who has destroyed galaxies, revived the dead, and created planets from nothing.
Why not simply heal Thor, regrowing his arm. If he wanted Thor to have a magical Uru arm for some reason, he should have been able to create that as well.
So, beyond PIS, is there any reason Odin couldn't simply will Thor to be healed?
Comment: same reason he didn't regrow his own eye?
Comment: Thor saw [Bucky's](http://marvel.wikia.com/James_Buchanan_Barnes_(Earth-616)) arm and begged his dad to get him one for Christmas/Odinmas?
Comment: Given the personalities of Asgardians in general and Odin in particular, having an awesome wound as a reminder of a well-fought battle is likely not a problem in their minds.  Especially when you have a prosthetic arm, so you don't lose any practical functionality.
Comment: Odin is a practitioner of what we parents call "tough love".
Comment: While not refering to the Marvel-Comics: Here's another take - why would Odin have Mjolnir made by Sindri and Brokkr in the first place instead of making it by himself (being near-to-almighty and all)?
Comment: @JasonBaker I'm not sure if [Odin's Day](http://en.wikipedia.org/wiki/Wednesday) is really a special occasion, though.
Answer: The answer is: Because he didn't want to. Yes, Odin is completely capable of growing the Odinson a new arm, if he so desired. He didn't. He preferred to let Thor be without one, as with so many things between those two, as a lesson to be learned.

The relationship between the Odinson and his father has always been a complex one. With Asgard in flux, no longer in its own private dimension, threats to Earth abounding and Asgard not in peak performance, Odin has a lot on his plate. Add to that, a mysterious woman (who granted, to Odin, MAY not be the mystery it is to the rest of us, and woe be unto to anyone if it IS a mystery) suddenly becoming worthy enough to wield one of the mightiest weapons in his kingdom and you have an All-father who is truly peeved.

Currently The Odinson is not in favor with Odin. He has lost access to Mjolnir. In and of itself a statement so great, there is little left to be said between them. He, however need not be without the resource and since he can have a new arm made for Thor, he does. Keeps his craftsmen happy and resolves the issue of his main enforcer and protector of Asgard, being fully armed...so to speak. He all but says so below:

Eventually, as with all things, Odin will either allow the Odinson to correct his own problem or if he should become worthy enough to wield Mjolnir again, grant him access to either magic or technology which will give him a functioning arm, once again.

You have to realize, Odin doesn't like correcting the Odinson's mistakes. Remember, when Thor was banned from dying by Hela, and cursed with brittle bones, his body became a mess held together only by armor? (Thor #373) Odin could have fixed this. He did not. It's not his way to fully correct his son's difficulties unless it suits his purpose to do so.

As a side note: Odin's eye is lost as a sacrifice to the Well, Mimir in exchange for knowledge of previous Asgards and previous attempts to avoid Ragnarok, the Twilight of the Norse gods. As a sacrifice, the eye can never be regrown. It was the price of knowledge.
A second side note: Tyr's hand was also lost as part of a sacrifice to bind the Fenris Wolf. It will also not regrow due to the nature of the sacrifice/betrayal necessary to place an unbreakable chain on the wolf. Odin isn't being cruel to Tyr. It was his destiny to sacrifice his hand for the benefit of Asgard.
Comment: Just one thing: Odin doesn't know who Fem Thor is, and he's reaaaaaaally pissed about it. But the answer makes sense.
Comment: It's amusing that it's later revealed even Odin himself couldn't lift Mjölnir anymore. I wouldn't be surprised if he pinned that on Thor, too.
Comment: Plus, you know, that makes it a bit less of a jerk move that they haven't regrown Tyr's hand all of this time...
Comment: So, given that a thousand dwarves worked to forge Thor's new arm, how much of a jerk does that make Thor when he decides not to use it?

Why didn't Odin regrow Thor's arm?


Is the Manfrotto 190XPROB a good first tripod for a student with an entry-level DSLR?

Question: I have a Canon Digital EOS 400D (XTi) and am looking into purchasing my first tripod. I was wondering whether the Manfrotto 190XPROB would be a good choice as a first tripod and what head I should get to go with it.
Comment: This will probably be closed for being too subjective: one guy might say the 190X is the best tripod ever, another might disagree. Perhaps a rewording to something more general like 'What are the properties of a good tripod'.
Comment: This question http://photo.stackexchange.com/questions/2505/ has some good general advice on selecting a tripod.
Comment: What are you planning on using it for? e.g. nature/city/studio? walking long distances or driving to sites? macro close to the ground? landscapes on windy outcrops? etc...
Comment: possible duplicate of [How good is Manfrotto 190CXPRO3 tripod for a beginner](http://photo.stackexchange.com/questions/24382/how-good-is-manfrotto-190cxpro3-tripod-for-a-beginner)
Answer: I have the Manfrotto 190XPROB and it is very good. Obviously it is quite heavy.
I bought a mini ball head which isn't strong enough, I regret not spending enough on the head.
Comment: Was it the 496RC2? Do you think it would be strong enough for the XTi with a 18-55 mm lens?
Comment: According to Manfrotto, the 496 head will carry a 6Kg load. It should be easily able to cope with the XTi with 18-55 lens. Martin may have been referring to the 494 which is designed for a 4Kg load. That probably can't cope well with large telephoto lenses but the 18-55 would be OK I would have thought.
Comment: @Miriam, I have one with the 496RC2 ball-head. It is a well made and sturdy tripod that has met my needs for portrait, landscape, flower and macro photography. It will support your camera and lens with no problem at all.
Comment: (+1) I'm going to agree with Martin about the head - spend some money on a good one! A bad head on my compact tripod makes it something I just don't want to use.
Comment: ... and a quick release plate makes life a lot easier. Be aware that manufacturers' plates and heads probably aren't compatible with each other.
Comment: I'm looking at the tripod kit on the B&H website and it lists the quick release plate as being included.
Answer: I'm quite happy with mine. I have an 804RC2 head which is good for panning, however a ball-head or trigger-grip head would allow for faster repositioning.
The 190XProb isn't a full-height tripod, though it is tall enough and steady enough for most uses. It is also a very versatile tripod because the legs can be individually adjusted to different angles and the column can be placed horizontally - which is useful for photographing documents or other objects on a table, the floor etc. It is heavier than cheap aluminium tripods I have used, but much more rigid.
Comment: What does "not a full-height tripod" mean? I'm 5'3'' and plan to use it mostly for landscapes and portraits.
Comment: @Miriam: With the centre-column raised, the 190 is 1.46m high, the 055 is 1.77m high. If you are 5' 3" the 190 will be perfect. The height of the head and of the camera added to this will bring the viewfinder up to my eye-height when I am standing fully upright. There are carbon-fibre versions which reduce the weight by about half a kilo (but are more expensive).
Comment: Thank you. I'm not sure I can justify the expense of a carbon fiber tripod at this time.
Answer: Your first comment on RedGrittyBrick's answer fills in some much-needed detail. One of the main features of the 190XPROB is the center column's ability to go horizontal (for shoot-down capability). It is a good set of legs, but you do pay a premium for that one feature. The same legs without the trick center column (the 190XB) is $40-50 dollars cheaper if you don't need the feature. Nobody, though, ever got fired for buying Manfrotto (or Bogen/Avenger, when the American version carried a different brand), and you won't feel like you've settled for something less than you deserve if you get either of those sets of legs.
That being said, don't let your own height dictate your tripod's height. You can make more interesting pictures from unusual points of view than you can from a mechanically-assisted version of "just standing there". Granted, getting down low is often more important than getting up high, but I don't think I'd ever be satisfied again with a tripod that wouldn't let me (1)get up on a step-stool for a look down on things, or (2)let me work on uneven terrain with at least one leg extended far beyond where it would have to be on level ground. Induro (AT213) and Benro (A297EX) (among others) offer tripods at about the same price level as the 190XB that are every bit as sturdy, but nearly a foot taller. Of course, they're heavier as well (as is Manfrotto's 055 model) if that's a concern -- they're not nearly as heavy as a commercial-quality video tripod would be, but they might be just a bit much for a long hike.
(Disclosure: I'm using an Induro AT213 at the moment -- well, not at this moment, obviously, since I'm sitting at the computer typing, but... -- and could only be happier when my Benbo #2 is back in action. The Benbo is an acquired taste, and I've acquired it badly. It'll go to over eight feet tall, and I can put one leg on the floor, one on the ceiling and the third on a wall if I have to. I've also been the happy owner of a number of Manfrotto 'pods over the years -- the only thing I've ever disliked about Manfrotto is that they don't believe in the ArcaSwiss QR plate system, so I either have to use someone else's head or put adapters on all of my favorite accessories. If you've ever used an L-plate, you'll never use the 90-degree tilt feature of a tripod head voluntarily again.)
Comment: I appreciate all your advice and wisdom but I find it a bit overwhelming. Like I said , this will be my first tripod. I have never used a tripod before. I've been hand holding my XTi for years and now that I'm learning more creative approaches to my pictures it seems to be less then adequate.
Comment: I plan to use my tripod for taking pictures of small children and landscapes for the most part. The ability to get low (at least in my opinion) makes for better portraits of children.
Comment: Getting low is indeed important, and not just for the little ones, but most tripods will let you get very low. There's no law that says you have to extend the legs (it'll be even sturdier if you don't), and most good tripods will let you spread the legs out very wide. The XPROB system (any of them) will let you get right down to the ground (or as close as you can get with a tripod head under your camera) as will the Benbo; other tripod types make you shoot with the camera upside-down if you want a worm's-eye view.
Comment: That said, almost any "pro grade" tripod (one that doesn't feel like it's made of recycled '60s lawn chairs) will let you get down to a foot or a foot and a half from ground level (whatever the length of the center column happens to be). The 190XB will go low enough for most purposes; so will the taller models I mentioned. If you have a choice, it's best to go to a real photography store and have somebody demonstrate what the various 'pods can do. If you can save fifty bucks on the legs, you can spend it on the head instead, and a good ball head is worth its weight in gold.
Comment: Oh -- when I said "it'll be even sturdier if you don't", I meant for low-down shooting. Your tripod will always be most stable when the center column is fully collapsed, and the less you have to raise the center column, the better. That's another reason why I like tall tripods -- I rarely have to raise the center column more than an inch or so, and that's only to fine-tune the height.


Where does Voice Actions store my "Note to self" recordings?

Question: I've been messing around with Android's Voice Actions. I tried recording various jibberish notes to test it out. However, I noticed that with each "Note to self" that I send to myself, the attached .amr recording has a suffixed number. For example, RecordedMessage2.amr, RecordedMessage3.amr and so on. It therefore occured to me that the recordings may have been saved on my phone and thus, the reason for the increment. I tried looking for those files via OI File Mnager but failed to locate it. Can anyone help me figure out where it's being stored? I'm not rooted btw.
Answer: When I did the "Note to Self", I was sent an email with the attachment (I assume this is the function, I've never used it before!). The attachment is the *.amr file that you can then download, and it will save it to download/RecordedMessage#.amr.
After some searching, the original file is stored in phone memory, not external, at /data/data/com.google.android.voicesearch/files/RecordedMessage#.amr
Note that you could not find this file because you weren't rooted, I used File X-Plore and did a search in the entire Root section to find them.
Note: If you would like to delete them:

with root: navigate to the aforementioned folder and delete them with your favorite root browser or adb
without root: from the home screen, press Menu, select Settings then choose Applications->Manage Applications and select Voice Search from the list. On the app info page select Clear data. This will delete all data associated with Voice Search, including any recorded "Notes to self", but keep in mind, it may also erase any data recorded to better results on a user-by-user basis.
Comment: Is there a way to delete them though? Surely they couldn't have made it a one-sided approach wherein data only gets written and not deletable.
Comment: @Shedo updated my answer, see **NOTE**


Assuming UAC is enabled, does a non-administrator account offer any security improvements?

Question: I've been wondering: assuming a modern Windows edition (>= 7), and that UAC is enabled, what benefits are there if I additionally use the system as a standard user? From what I understand, the only difference is that instead of just clicking "yes" on the dialog, I'll have to provide an administrator password, but programs will still be prevented from administrative actions without my consent because of UAC.
Comment: Related: https://security.stackexchange.com/q/101725/71460
Answer: The DFIR Blog has a great summary of UAC
In the article, the author recommends the Always Notify approach, especially for administrators and critical servers. Besides social-engineering attacks such as the exploits/windows/local/ask module in the metasploit-framework, there are also tens of UAC bypasses. The author covers the techniques and tools to bypass UAC better than most.
The author does not make mention to, and I do not know of a tool or technique to bypass Always Notify -- however, escalation of privilege -- especially to the SYSTEM account -- may be possible through a privilege-escalation exploit and/or a misconfiguration issue (although any-given privesc exploit must not require administrator privileges, which is not necessarily rare, but a condition that must exist for some exploits to work). Misconfigurations typically include UNC path and/or file/folder/service permission issues. Typically, these privilege escalation techniques require an advanced understanding of the Windows environment that even most NT administrators do not posses, however, again, some are available in the metasploit-framework and other exploitation engines (or bundled with exploit kits) -- thus lowering the barrier to entry to anyone with adversarial intent. Other times, admins or admin tools simply leave password in cleartext (or an easily-reversible format) in files on the operating system, on a sticky note, or other lowered-care OPSEC.
Most end users will revolt against Always Notify, but perhaps not the next-lower setting, the medium-integrity process (which many UAC-bypass techniques work against).
As for local or domain administrator accounts for end user machines, it's very bad practice, as users can simply right click any executable and choose "Run As Administrator" to elevate privileges and destroy the power of UAC (N.B., this can also be done via cmd.exe if a separate admin account password is known by any end user). A lot of malware, especially persistence techniques, rely on administrator access (e.g., for Windows service installation). If UAC must be set to something lower than Always Notify, the best strategy is to also disallow any administrator access (privileged access) and provide additional protections against end-user app installation. My favorite platform for Privileged Identity Management is STEALTHbits and this can be combined with BeyondTrust and other privilege-management solutions.
As an additional protection for non-administrator accounts, the permissions on the user-specific AppData\LocalLow folders also allow malware to activate and persist. Another one to look out for is that some orgs will set the AlwaysInstallElevated registry key to allow non-admins to install applications. However, MSI's elevated privileges can be abused and there is even a metasploit-framework module to do so (i.e., exploits/windows/local/always_install_elevated).
Another distinction to make is for elevation prompts (apps can be written to automatically prompt, but UAC behavior can override/preempt this capability). The book Least Privilege Security for Windows 7, Vista and XP covers this and says:

Microsoft recommends that in corporate environments, system administrators should configure UAC to automatically deny elevation requests using the User Account Control: Behavior of the elevation prompt for standard users local or Group Policy setting. This ensures that malware can't intercept an elevation prompt and harvest the credentials of an admin account.
Comment: +1. My related answer might be of help to someone as well. http://security.stackexchange.com/a/104393/21426
Comment: A new UAC bypass was just published this morning -- http://www.kernelmode.info/forum/viewtopic.php?p=28249
Answer: The existing answers covering most of the important things. I just want to add that in case of ransomware the software doesn't need any elevated privileges. If the malware doesn't has privileges to persist somewhere this wouldn't even a problem. If the user has write access to (some of) their important files which is very likely, the ransomware just encrypts it and leaves a good visible notice with further instructions.
Answer: Microsoft doesn't consider UAC a security barrier, and thus they often don't fix UAC bypasses. These bypasses are common and easy. See for yourself: https://www.google.com/#q=uac+bypass
Answer: The benefit would be that ALL rights would be run as a standard user, not as administrator. Installers that trigger the UAC are far from the scariest things that go bump in the night.

What you are describing is what a standard user would see, not what goes on at the OS level. UAC on its own does not make you secure.


Private key of a specific bitcoin address

Question: I need to find out the private key of a specific bitcoin address '1FVoAyGnHueH1uNR4dAQgRZcsBkAd3Mo3K'. This is the bitcoin address of a scammer who made me lose my last savings in the name of cryptocurrency trading. I recovered the fund with the help of a special intelligence unit but it is still 'Non-spendable'. Please help me recover my funds and save my life.
Answer: You cannot.  If you could, the cryptography on which Bitcoin relies would be worthless.
I don't know who this "special intelligence unit" is, but if all they did was find the address, then that is no help.  (If the "intelligence unit" took money from you to find out this address, and told you that they had recovered your funds, then you've been scammed again.)
You have not recovered your funds and you are not going to.  Your time will be better spent figuring out how to do without them.  Sorry.
Answer: There are a few ways this could (theoretically, with almost 0 probability of success) be done:

Go forward by generating new private keys until you find one that corresponds to this address. There are about 2^256 possible private keys (actually a smaller number, but it's huge).
Go backwards by breaking all the cryptography involved in Bitcoin:

First, that address is the hash 9f03f344848612f1f456b08187706017888a6bb6. This is in form hash160, which is RIPEMD-160 (SHA-256 (Public Key)).
Step 1: Break RIPEMD-160 to get the SHA-256 hash.
Step 2: Break SHA-256 to get the public key.
(You could also get this public key once it's published when that key is used to spend. Of course, at that point it may not help you.)
Step 3: Break secp256k1, Bitcoin's elliptic curve, to get the private key from the public key.
Good luck spending less in research costs than the $4,500 you hope to get back. (Plus if you somehow succeed, consider the greater impact on Bitcoin.)

Determine who owns the address and get the private key from them.


Does the web-based Evernote app have keyboard shortcuts?

Question: If it does? What are they?
The most important shortcuts for me are: search & new
Answer: There is a Chrome extension that offers this functionality;
https://chrome.google.com/extensions/detail/hffokedddmbcngcmkhpbdoeljdglfpna?hl=en

... add gmail like keyboard shortcuts to Evernote ...

Hope this helps
Comment: It has a rating of 1.6 stars out of 5 - so not really a good solution at this time.
Comment: "Not work for me" is the most comments there.:(
Answer: I note that some limited keyboard shortcuts/hotkeys work with the current version (Feb 2017).
The ones I have found are:

bold ctrl-b
italics ctrl-i

I've searched for an official list, but there doesn't appear to be one. This could be because different browsers and platforms may have  conflicting shortcuts.
Eg:
In the list of keyboard shortcuts for Evernote for Windows ctrl-e centres text, but in Chrome browser it will shift focus to the search bar.
Answer: None of the extensions worked for me so I wrote my own called Evercuts. It's really pretty simple but it does most of what I need. (FYI its only available for chrome)
Search
Toggle Fullscreen
Move Note
Delete Note
Copy Note Internal Link
Open note in new tab
Open note in new window
Navigate the notes up/down

The above shortcuts are configurable via chrome://extensions/shortcuts
You can also Alt+Click on a note to open it fullscreen in a new window.
The code is available on my GitHub or you can install directly from the Chrome webstore.
Answer: Here's a good chrome extension Evernote Shortcuts
Few shortcuts which it offers:
General options:
    ?      show the help dialog
    A      Add a note
    /      search notes
    W      goto Workchat
    S      goto Shortcuts
    N      goto Notes
    B      goto noteBooks
    T      goto Tags
    C      goto Contiguration

Dialogs:
    Enter  accept
    Esc    cancel

Nodes list:
    j      next note
    k      previous note
    l      edit note
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Marriage In Jannah with someone else

Question: What happens if a Muslim wife serves her husband and pleases him but doesn't want to be with him in Jannah and marry with someone else, is she given a choice ?
Comment: Does this answer your question? [Wishing husband to be only mine in Jannah](https://islam.stackexchange.com/questions/23446/wishing-husband-to-be-only-mine-in-jannah)
Answer: Our appearances in Jannah will be way more beautiful and amazing and just remember in Jannah we will be satisfied and happy from our Lord and our Lord will be happy from us.
But such thinking about a person who is not your spouse in this world can end up in sins or other troubles in this life, so it is advised to shed off any such thoughts and live with sabar and shukar in this life with the spouse you are given.
Answer: You will have whatever you ask for in Jannah.. It is in the Quran. IN SHAA ALLAH if you still desire that man you like if you reach Jannah you will have him. Don't listen to anyone who says you won't have him. If you are fulfilling your Islamic duties in Dunya and if ALLAH (SWT) grants you Jannah then you will get WHATEVER you want IN SHAA ALLAH

Marriage In Jannah with someone else


Why do we need to use fake k-points when doing HSE band structure in VASP?

Question: I want to know why we need fake k-points in HSE band structure calculation? I mean why we can't take a simple high symmetric path like we do in PBE calculation?
Comment: Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
Comment: +1 and welcome to our new community! Thank you for contributing your question here and we hope to see much more of you in the future !!!
Answer: The reason is that the HSE method are obtaining the band structure with self-consistent calculation rather than non-self-consistent calculation like PBE band structure calculation. For self-consistent calculation, you will sample the k-space with a uniform k mesh. The fake k-points are just the high-symmetry path used in PBE calculations, which are added into the self-consistent calculations to calculate the eigenvalues or energy band you are wanted.
Comment: ok so what if I do the HSE  calculation in the same manner as we do PBE calculation? Is there any specific advantage or motive to do the HSE calculation in a different manner i.e. the fake k-point procedure.
Comment: You can try and see what will happen.
Answer: This question has already been answered in the quantum espresso forum here. To reiterate the Fock operator at a certain k-point needs the wavefunction on a grid that is commensurate with it. Hence we cannot calculate the single k-point non-selfconsistently from the charge density. Therefore, in a hybrid functional we have to  use the entire self consistent calculations.
Comment: Ok I understood what you are trying to say but what if I do a first self consistent calculation(SCF) with HSE tags and I take the WAVECAR of this SCF as you mentioned Fock operator needs the wavefunction on the grid and now with this WAVECAR I do non-SCF calculation with high symmetry K-point path. I know I am adding an extra step but I just want to know will it give the same results?


Why can't I puppet a City-State in Civ V?

Question: I started a game of Civilisation V with God & Kings expansion (GOTY edition, so a bunch of DLC as well). Started as Genghis Khan and warred a bit for prospective expansion areas, gaining an enemy capital, that I happily annexed. Then I turned my eye towards neighbouring city-states aiming to claim their luxury resources by conquering and puppeting them, but to no avail. Game didn't prompt me for choice, as I entered the city with my infantry, it immediately became annexed. Now I cannot raze or puppet the captured city-state. Why? Is this a game bug?
Comment: Is your civ in revolt?
Answer: No, it is not a game bug. The game does not allow you to puppet an enemy capital once you capture it. Since a City State has only one city, that city is considered as their capital. Hence you cannot puppet a city state, in most cases.
Comment: What? I thought it was razing that was prevented. I could've sworn you still had the choice to annex or puppet city states and capitals.
Comment: If a city state has captured another city except their capital, and you conquer that city, then you have the option to puppet that city. If you conquer the city state's capital (their starting city) you don't get that option.


which phrase is more suitable in an official text :"ordinary people" or "normal people

Question: I am confused which phrase is more suitable to put in an official text that is comparing two phrases : 1) successful person 2) Ordinary or normal person.
Comment: Wouldn't "average person" be a better choice here?
Comment: why not just 'people'
Answer: Man in the street TFD

the typical or ordinary person, esp as a hypothetical unit in statistics
  Origin:
  1825–35

Synonyms: Joe Bloggs, Joe Blow, John Doe,
common man, common person, commoner - a person who holds no title,
Personally, I would go for the average man in the street, the phrase is typically used to convey a person without exceptional abilities, talents or defects. A non-offensive term for the average member of the public.

Would you have done these things if you weren't successful, if you
  weren't rich? What if you were the average man in the street, with a
  poorly paid job, a small house, little money, two children, and debts.
Answer: I personally think you shouldn't use any of the two options as they are not the opposite of a "successful person". But if you have to choose between the two, "ordinary people" is a better option. Using "normal person" might suggest that a "successful person" is abnormal.
Answer: Ordinary is (marginally) better than normal, as a normal person may be successful or unsuccessful, while an ordinary person is average, middle of the road, which implies neither very successful nor very unsuccessful. It seems to me, however, that neither of these words fill your need. Either contrast a "highly successful person" with an "ordinary person", or use the direct opposite: "unsuccessful person".


HD Antenna Specs / Distance

Question: Is there a set of specs and / distances to narrow down the choices or to know how to choose an HD antenna that could replace my cable provider for access to local channels?
Comment: Try one. It's very dependent on where your house is, where the transmitter is, and the terrain in-between.
Comment: Pretty much what I was thinking, I was at best buy, perhaps get the $70 and the $30 one and see if the work.
Comment: It's a complicated calculation based on your local topography and the location of your local broadcasters.  You need to use a tool like [http://antennaweb.org/](http://antennaweb.org/Address.aspx).
Comment: Does an HD antenna have to be mounted outside?
Comment: the antenna can be inside but outside will provide better reception, some models are not rated for outdoor use.
Answer: I wondered the same thing when I shopped for an antenna. Unfortunately, I couldn't find a set of specs or a way of comparing antennas from different manufacturers. All I found were reviews but they were all subjective and didn't help me rank one antenna over another, especially when the antennas were from different manufacturers.
That's when I bought various antennas and tested them myself using a Winegard Signal Strength Meter and my Tivo. Using the Winegard (which I have no affiliation with) was a very objective way of comparing them because you select a frequency and it gives you a signal strength.
I test the antennas in two different ways. For the first test I rotate the antenna for each frequency and record the maximum signal strength. For the second test I point the antenna in the same direction and leave it stationary (which is how most people use an antenna). I then run through the frequencies and record the results.
Even though I can only test the frequencies in my area, I figured these results might be useful to others so I put them on my website at: http://byebyecabletvbill.com/tv_antenna_side_by_side_comparisons.php. As time progresses, I'll be testing more antennas and adding the results there.
Answer: you want the highest gain in Db for the antenna. If an amplified model high gain Db with the lowest noise S/N (signal/noise ratio).
Not always are the most expensive the best. The last thing is location, the higher you can mount it the better. When looking at Db a difference of 3 is big 2x the signal.
Comment: Lowest S/N - really? Little signal, lots of noise? Is that your FINAL answer?
Comment: For the signal to noise ratio you want the lowest noise possible. the correct term is signal/noise as I have a degree in this i will leave it this way.
Comment: @edbeal pls edit your answer

HD Antenna Specs / Distance


Should I provide the option to change the language in an app?

Question: Smartphones settings allow you to choose a default language thereby ensuring your application displays in that language. Is it useful to provide an option to change this language within my application itself?
Comment: Do you mean: should I provide the option to change the language in an app? And not listen to the language of the OS.
Comment: Yes indeed, my english is basic, I'm sorry for the confusion
Answer: It could be useful in the following circumstances:

When the user's native language isn't English, but they are more familiar with English labels than the native equivalents.
For users who need to switch keyboards (and auto-complete dictionary) using both their native language and English (or another secondary language).
For users that give their old phones to their kids, and need to set the language back to native language...

So yes, being able to change the language of a single application could be useful.
Edit
Having the option to switch the interface language could be very useful, if you want to let users override the system language. It depends on the type of application you're developing. If you don't provide a setting you could still switch language according to systems language. So if the user switches language from Spanish to English in the system, you're application does the same.
Comment: Point no. 3 is very interesting and cannot be learned from a book :) BUT

for all 3 points, I think phone's native language or the language setting of the dictionary would do the job. When one gives old phone to kids, they probably wouldn't use the apps which their father was using :)
Comment: I assume @Anthony means: should I provide the option to change the language in an app? And not listen to the language of the OS.
Comment: @Pesikar I see - I'll change my answer accordingly. Thanks
Comment: Even though I agree with Benny but the situations which Benny mentioned are not the first or second frequent use scenarios.


How exactly does damage scaling appear to high level characters?

Question: I'm currently leveling all the classes to 100, and i'm using invasions to gain the exp. I know when I see bosses, they usually have between 250k-400k, with the commanders at 1mil+. My spells/abilities hit for 1200-5000 depending on the class(at level 65ish). If a 100 is hitting the same mob-what do they see, and how is our damaged compared? I mean, are they hitting for 4k on my 250k mob, or am I hitting for 100k on their 8million hp mob?
Comment: I dont think this is completely answerable without input from the devs. However from my experience in the Beta from a user point of view both of those statements are true (seen by using recount) while running dungeons at less than max level with other max levels I see their damage output as lower, and as a max level character running with lower level as much higher.
Answer: There's no technical source for this, but the intention of the devs is to go for %.
If you hit a mob at lower level and deduct around 10% hp overall the level 100 mob will lose 10% hp as well (similar to scaling up your damage server side). The same counts for all participants (friend and foe) life* and attacks. They're scaled down to your level, but only for you. Everyone sees everything scaled to their own level. The scaling is not perfect, so some mobs might hit pretty hard, but Blizzards keeps pushing hotfixes for this.
In numbers: You hit a 100k hp mob for 10k damage. The level 100 version of that mob with 1m hp would then lose 100k hp. You just can't see it, because your mob only has 10k hp.
You can see a similar effect in timewalker dungeons and as of next week in all Legion zones.
<code>*</code> Only the life loss and gain infight. The actual hp numbers of players are real.
PS: Mind controlled people don't scale. So a lvl 100 will always slap you to death, if you're a few lvl behind.


Computed property with HTML LightSwitch

Question: I followed the tutorial here:
Computed Properties With the LightSwitch HTML Client (lightswitchhelpwebsite.com)
Here is the tutorial code:
myapp.AddEditFlowerShopOrder.NumberOfDetails_postRender = function (element, contentItem) {
    function updateTotal() {
        // Compute the total for the Order
        contentItem.screen.TotalOfOrders =
            TotalOrders(contentItem.screen.FlowerShopOrderDetail);
    }
    // Set a dataBind to update the value when the collection changes
    contentItem.dataBind("screen.FlowerShopOrderDetail.count", updateTotal)
};
// Function to compute the total for the Order
function TotalOrders(OrderDetails) {
    // Start with 0
    var TotalAmountOfOrders = 0;
    // Get the data for the collection passed
    var OrderDetail = OrderDetails.data;
    // Loop through each row
    OrderDetail.forEach(function (order) {
        // Add each row to TotalAmountOfOrders
        TotalAmountOfOrders = TotalAmountOfOrders +
            (order.Quantity * order.FlowerShopProduct.Price);
    });
    // Return TotalAmountOfOrders
    return TotalAmountOfOrders;
}

Here is MY code:
myapp.AddEditOrder.Order_Subtotal_postRender = function (element, contentItem) {
    //Write code here.
    function subtotalDetails() {
        contentItem.screen.Order.Subtotal =
            TotalOrderDetails(contentItem.screen.OrderDetails);
    }
    subtotalDetails();

    //contentItem.dataBind("screen.OrderDetails.count", subtotalDetails(contentItem));

};

function TotalOrderDetails(details) {
    var subtotal = 0;
    var detail = details.data;
    detail.forEach(function (order) { subtotal = subtotal + order.Total; });
    return subtotal;
}

I could not get the dataBind to bind, it says it can't return the call. So I commented it out and called it just once, when it renders to get the rest of the code working. I have no idea how the .data member works, but if I change the detail.forEach into a for, it's not iterating through a collection of ProductDetails' ProductDetail objects.
Just to clarify, I have these tables: Order >- OrderDetails. My goal is to bind the Order.Subtotal = sum of Order.OrderDetail(all items).Total.
Answer: The differences I see in your code versus the demo is that the demo uses a Screen property to hold the Subtotal(screen.TotalOfOrders), while you're apparently trying to change a Subtotal field in your Order record (screen.Order.Subtotal).  Remember that to access a field in a Parent table from a Child record, you need to use screen.data.fieldnameyouwant instead of screen.ParentTable.fieldname. I know the second way seems like the logical thing to do, but Lightswitch doesn't see it that way.
What I would try is to make a screen property called DetailTotal like the demo does, then wait until the screen's validation event fires and update the parent record subtotal there.  That way, nothing actually gets written to the parent until you're leaving the screen anyway.
myapp.AddEditOrder.beforeApplyChanges = function (screen) {
    // Write code here.
   var targetOrder = screen.findContentItem("Order_Subtotal");
   targetOrder.data.Subtotal = screen.DetailTotal;
};

Computed property with HTML LightSwitch


How many non-decalogue commandments from the Old Testament are still morally binding for Christians?

Question: Many denominations believe that Christians should obey the ten commandments (also known as the decalogue), which can be found in Exodus 20:1-17. However, there are 613 commandments in the Old Testament, not just 10. Moreover, Jesus himself claimed in Matthew 22:36-40 that the two greatest commandments are not part of the decalogue. In other words, Jesus endorsed the observance of two non-decalogue commandments. This makes me wonder: how many of the 603 non-decalogue commandments are still morally binding for Christians today? I know that the two greatest commandments definitely are, but are there others?
Comment: In a certain spiritual sense, all of them, even if their (re)[interpretation](http://judaism.stackexchange.com/questions/37374) is not to be taken literally.
Comment: If the Two are asserted, then the Ten must be also ... and all the others, besides. (***OR*** - one is 'dead to the law by the body of Christ', another thing altogether.) Good question > up-voted +1.
Comment: Questions like this are off-topic if they do not specify a denomination. Christians disagree greatly over what our relationship to the OT law is.
Answer: Jesus affirmed the two greatest commandments because "All the Law and the Prophets hang on these two commandments" (Matthew 22:40). Paul says similarly in Romans 13:8, "Let no debt remain outstanding, except the continuing debt to love one another, for whoever loves others has fulfilled the law".
The Law, especially the Decalogue, was given as an expression of the two greatest commandments - to love God and neighbour.
The other 613 laws are more complicated. It's common to speak of the tripartate division of the law - moral, civil, and ceremonial. As that link shows there are complexities. Some commands are specifically abrogated in the New Testament (e.g. Mark 7:19). Jesus fulfilled the need for sacrifices to be made (Hebrews 7:18-19).
I would suggest a more nuanced approach than seeing it as a binary thing (commands we either do or do not need to obey). I think the commands are there to teach us how to live, but not to be obeyed in the Old Testament sense. This is because in the New Testament we need to walk in step with the Spirit, who alone can give us a deeper obedience to the Law. Galatians 3:24, "So the law was our guardian until Christ came that we might be justified by faith."
Jesus came to fulfill the law (Matthew 5:17). This means that the righteous demands of the law can only be fulfilled in us through him, through his death and resurrection. We cannot obey perfectly, yet through Christ and the Holy Spirit working in us we can begin to love as God wants us to love. Rather than being an external obedience, God writes his law on our hearts (Jeremiah 31:33).
Therefore the law that needs to be obeyed is the law of love - the two greatest commandments. But the rest of the law we need to see through the lens of being fulfilled in Jesus Christ.
Answer: How many non-decalogue commandments from the Old Testament are still morally binding for Christians?
Do not know how many there are, but there still exists a few here and there.

Here are six Bible passages that deal directly with bestiality or zoophilia (sexual contact with animals):

Exodus 22:19  Whosoever lieth with a beast shall surely be put to death.

Leviticus 18:23  Neither shalt thou lie with any beast to defile thyself therewith: neither shall any woman stand before a beast to lie down thereto: it is confusion.

Leviticus 20:15  And if a man lie with a beast, he shall surely be put to death: and ye shall slay the beast.

Leviticus 20:16  And if a woman approach unto any beast, and lie down thereto, thou shalt kill the woman, and the beast: they shall surely be put to death; their blood shall be upon them.

Deuteronomy 27:21  Cursed be he that lieth with any manner of beast. And all the people shall say, Amen.

Jude 1:7  Even as Sodom and Gomorrha, and the cities about them in like manner, giving themselves over to fornication, and going after strange flesh, are set forth for an example, suffering the vengeance of eternal fire.

As we can see, God clearly abhors any type of sexual contact with animals. It goes against God's design for procreation and sexual behavior. As Leviticus 18:23 pointed out, this is nothing more than confusion!
God's Word clearly tells us that sexual immorality of any kind is a vile sin, and unless a person repents of such wickedness, he or she will not inherit the kingdom of God:

Know ye not that the unrighteous shall not inherit the kingdom of God? Be not deceived: neither fornicators, nor idolaters, nor adulterers, nor effeminate, nor abusers of themselves with mankind, nor thieves, nor covetous, nor drunkards, nor revilers, nor extortioners, shall inherit the kingdom of God" (1 Corinthians 6:9-10).

What Does the Bible Say About Bestiality or Zoophilia? The Sin of Sexual Relations with Animals.
Comment: Will continue as time permits.
Answer: What non-decalogue commandments from the Old Testament are still morally binding for Christians?

Leviticus 18:16 in regards to Mark 6:17-18 :

Mark 6:17-18 [NIV]
[17] For Herod himself had given orders to have John arrested, and he had him bound and put in prison. He did this because of Herodias, his brother Philip's wife, whom he had married. [18] For John had been saying to Herod, "It is not lawful for you to have your brother's wife."
Leviticus 18:16 [MT]

You shall not uncover the nakedness of your brother's wife. It is your brother's nakedness. (עֶרְוַ֥ת אֵֽשֶׁת־אָחִ֖יךָ לֹ֣א תְגַלֵּ֑ה עֶרְוַ֥ת אָחִ֖יךָ הִֽוא)

Leviticus 18:22 in regards to Mark 10:6-8.

Mark 10:6-9 [NIV]

[6] "But at the beginning of creation God made them male and female." [7] "For this reason a man will leave his father and mother and be united to his wife," [8] "and the two will become one flesh. So they are no longer two, but one flesh."

Leviticus 18:22 [MT]
You shall not lie down with a male, as with a woman. This is an abomination. (וְאֶ֨ת־זָכָ֔ר לֹ֥א תִשְׁכַּ֖ב מִשְׁכְּבֵ֣י אִשָּׁ֑ה תּֽוֹעֵבָ֖ה הִֽוא)

Leviticus 26:1 in regards to Mark 12:15-17.

Mark 12:15-17 [NIV]
But Jesus knew their hypocrisy. "Why are you trying to trap me?" he asked. "Bring me a denarius and let me look at it." [16] They brought the coin, and he asked them, "Whose image is this? And whose inscription?" - "Caesar's," they replied. [17] Then Jesus said to them, "Give back to Caesar what is Caesar's and to God what is God's."

Leviticus 26:1 [MT]

**You shall not make idols for yourselves, nor shall you set up a statue or a monument for yourselves**. And in your land you shall not place a pavement stone on which to prostrate yourselves, for I am YHVH, your-God.(לֹא־תַֽעֲשׂ֨וּ לָכֶ֜ם אֱלִילִ֗ם וּפֶ֤סֶל וּמַצֵּבָה֙ לֹֽא־תָקִ֣ימוּ לָכֶ֔ם וְאֶ֣בֶן מַשְׂכִּ֗ית לֹ֤א תִתְּנוּ֙ בְּאַרְצְכֶ֔ם לְהִשְׁתַּֽחֲוֹ֖ת עָלֶ֑יהָ כִּ֛י אֲנִ֥י יְהֹוָ֖ה אֱלֹֽהֵיכֶֽם)

--------------

Leviticus 19:17 in regards to Mark 11:25.

Mark 11:25 [NIV]
And when you stand praying, if you hold anything against anyone, forgive them, so that your Father in heaven may forgive you your sins.

Leviticus 19:17 [MT]
You shall not hate your brother in your heart. You shall surely rebuke your fellow, but you shall not bear a sin on his account. (לֹֽא־תִשְׂנָ֥א אֶת־אָחִ֖יךָ בִּלְבָבֶ֑ךָ הוֹכֵ֤חַ תּוֹכִ֨יחַ֙ אֶת־עֲמִיתֶ֔ךָ וְלֹֽא־תִשָּׂ֥א עָלָ֖יו חֵֽטְא)


Why is $\sin(\alpha+\beta)=\sin\alpha\cos\beta+\sin\beta\cos\alpha$

Question: Why is $\sin(\alpha+\beta)=\sin\alpha\cos\beta+\sin\beta\cos\alpha$? How can we find the RHS if we don't know what it is? (instead of proving the identity itself)
I could find a geometric solution in Wikipedia, but is there any solution that doesnt require drawing something?
Edit: I now saw some nice proofs using $e$ and Euler's identity. I would appreciate anything NOT using them too, as a change.
Out of curiosity, Is there a proof that says you actually "can't" prove the identity using only other simple 1-variable identities like $\sin^2\alpha+\cos^2\alpha=1$?
Comment: What are your definitions of sine and cosine? This can be proved in several ways, which do not require appeal to geometric arguments, if your definition is analytic. (In terms of solutions to differential equations, or using power series, for example.) If your definition is geometric, you definitely need a geometric argument and, in that case, the "drawing" is just so you can follow the argument, it is not an essential part of it.
Comment: You will not be able to find a proof involving only the other trig identities.
Comment: Well, the cosine satisfies the same kind of identity that the sine does, after all. **Or:** Let $S(x)=2x/(x^2+1)$ and $C(x)=(x^2-1)/(x^2+1)$. Then $S^2+C^2=1$, I think.
Comment: Here's a [relevant thread](http://math.stackexchange.com/questions/1292/how-can-i-understand-and-prove-the-sum-and-difference-formulas-in-trigonometry/1342#1342).  I think the proof using rotation matrices is a nice non-picture proof.
Comment: In total agreement with @AndresCaicedo, I saya that if your *definition* of sine is geometric, then you ought to look for a geometric proof; if your definition is the $y$-coordinate of the terminal ray's intersection with the unit circle, you should look for a proof on the unit circle — it'll be partly geometric, partly algebraic; if your definition comes out of the exponential function, your proof should be related to that; if your definition comes out of complex numbers, similarly.
Comment: Thank you for the info. Btw, i was looking for some algebra methods using only the identities i already know, like $\sin^2\alpha+cos^2\alpha=1$
Comment: @StevenGubkin Is there a proof that says you actually "can't" do that? (added this question to the question body too"
Comment: @Downvoetrs: Please explain the reason of your downvote. Just downvoting and leaving is just rude.
Answer: I usually like to reduce these to problems involving complex exponents. Note that
$$\sin\alpha\cos\beta + \sin\beta\cos\alpha = \frac{e^{i\alpha} - e^{-i\alpha}}{2i}\frac{e^{i\beta} + e^{-i\beta}}{2} + \frac{e^{i\beta} - e^{-i\beta}}{2i}\frac{e^{i\alpha} + e^{-i\alpha}}{2}$$ and simplify this expression.
Answer: Using the scalar product :
let $A$ and $B$ be the points on the unit circle at arc length $a$ and $b$. Then $A(\cos(a);\sin(a))$ and $B(\cos(b);\sin(b))$, and $\widehat{BOA}=a-b$. Therefore :
\begin{aligned}
\overrightarrow{OB}\cdot\overrightarrow{OA} &= OA\times OB\times \cos(\widehat{\overrightarrow{OB};\overrightarrow{OA}})\\
&= 1\times 1\times \cos(\widehat{BOA})\\
&= \cos(a-b)
\end{aligned}
and as $\overrightarrow{OA}\binom{\cos(a)}{\sin(a)}$, $\overrightarrow{OB}\binom{\cos(b)}{\sin(b)}$ :
$$
\overrightarrow{OB}\cdot\overrightarrow{OA} = \cos(a)\cos(b)+\sin(a)\sin(b)
$$
Therefore $\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)$
Then
\begin{aligned}
\sin(a-b)&=\cos\left(\frac{\pi}{2}+b-a\right)\\
&=\cos\left(\frac{\pi}{2}+b\right)\cos(a)+\sin\left(\frac{\pi}{2}+b\right)\sin(a)\\
&=-\sin(b)\cos(a)+\cos(b)\sin(a)\\
&= \sin(a)\cos(b)-\sin(b)\cos(a)
\end{aligned}
Comment: This is the kind of proof I like best.
Comment: Thanks. That's what i wanted.
Comment: @CODE : that's the proof french students get in high school, as an application of the scalar product. And then we use the result to introduce the exp notation of the complex numbers.
Answer: To find the RHS (assuming that we may forget the result) we write:
$$\sin(\alpha+\beta)=\Im\frac{1}{2}(e^{i(\alpha+\beta)}-e^{-i(\alpha+\beta)})\\=\Im\frac{1}{2}((\cos\alpha+i\sin\alpha)(\cos\beta+i\sin\beta)-(\cos\alpha-i\sin\alpha)(\cos\beta-i\sin\beta))$$
and we develop and we take the imaginary part we find the desired formula.
Comment: كان هذا دليلا لطيفة ومتسقة.
Comment: أين أنت من سامي؟
Comment: شكرا لك أدوب يسرني أن أراك تكتب باللغة العربية
Comment: وذلك بفضل الترجمة من Google. :p
Comment: Nicely done, @Sami! +1
Answer: I like to see it using Euler's formula $e^{i\theta} = \cos{\theta} + i \sin{\theta}$. We have
$$
\begin{eqnarray}
 e^{i(\alpha+\beta)} = \cos(\alpha+\beta) + i \sin(\alpha+\beta)
\end{eqnarray}
$$
but also
$$
\begin{eqnarray}
 e^{i(\alpha+\beta)} &=& e^{i\alpha}\cdot e^{i\beta} \\\\
 &=& [\cos(\alpha) + i \sin(\alpha)]\cdot [\cos(\beta) + i \sin(\beta)]\\\\
 &=& \cos(\alpha)\cos(\beta) - \sin(\alpha)\sin(\beta) + i[\cos(\alpha)\sin(\beta) + \cos(\beta) \sin(\alpha)]
\end{eqnarray}
$$
So you get both
$$ \sin(\alpha+\beta) = \cos(\alpha)\sin(\beta) + \cos(\beta) \sin(\alpha) $$
and
$$ \cos(\alpha+\beta) = \cos(\alpha)\cos(\beta) - \sin(\alpha)\sin(\beta) $$
Answer: The differential equation
$$f''=-f$$
has a unique solution for given initial conditions $f(0)=x_0$, $f'(0)=y_0$. To show uniqueness assume that $g$ is another solution for the same initial values. Then $h:=f-g$ also satisfies $h''=-h$, and $h(0)=h'(0)=0$. But then
$$\frac\partial{\partial t}(h(t)^2+h'(t)^2)=2h(t)h'(t)+2h'(t)h''(t)=2h(t)h'(t)-2h'(t)h(t)=0,
$$
and it follows that $h(t)=0$ must hold for all $x$, so $f=g$.
This unique solution is
$$f(t)=y_0\sin t+x_0\cos t,
$$
as one checks immediately.
Now we can apply this to the function $f(t)=\sin(t+\beta)$. It satisfies
$f''(t)=-f(t)$, $f(0)=\sin\beta$, $f'(0)=\cos\beta$, hence we must have
$$f(t)=\cos\beta\sin t+\sin\beta\cos t
.$$

This may seem to come out of the blue at first, but if one sets $x(t)=f(t)$, $y(t)=f'(t)$, then $f''=-f$ becomes
$$\begin{pmatrix}x\\y\end{pmatrix}'=\begin{pmatrix}y\\-x\end{pmatrix},
$$
which describes a motion on a circle around the origin (the velocity is perpendicular to the vector from the origin to the current point), and of course $\sin$ and $\cos$ are all about circles. The calculation done above for $h$ shows that indeed $x(t)^2+y(t)^2$ is constant.
Answer: If you don't want to use geometry, you can do it with complex powers of $e$:
$$
\sin(x)=\frac{e^{ix}-e^{-ix}}{2i}\\
\cos(x)=\frac{e^{ix}+e^{-ix}}{2}\\
\sin(x+y)=\frac{e^{i(x+y)}-e^{-i(x+y)}}{2i}
$$
You can now also express the right hand side of your equality in terms of powers of $e$, and this wil give the same result.
Answer: Consider the vectors $$\vec{u}=(\sin \alpha,\cos \alpha)= \left(\cos \left(\frac{\pi}{2}-\alpha\right),\sin\left(\frac{\pi}{2}-\alpha\right)\right) $$
and $$\vec{v}=(\cos \beta,\sin \beta) $$
in $\mathbb R^2$. The dot product $\vec{u} \cdot \vec{v}$ can be calculated in two ways:

$\vec{u} \cdot \vec{v}=\|\vec{u}\| \|\vec{v}\| \cos \theta$
, where $\theta=\frac{\pi}{2}-\alpha-\beta$ is the angle between $\vec{u}$ and $\vec{v}$. Since $\vec{u},\vec{v}$ are unit vectors, this representation gives $\vec{u} \cdot \vec{v}=\cos \left( \frac{\pi}{2}-\alpha-\beta \right)=\sin(\alpha+\beta)$.
$\vec{u} \cdot \vec{v}=\sin \alpha \cos \beta +\sin \beta \cos \alpha$.

Compare the two.
Answer: Even though that is just the complex numbers argument in disguise...
You asked specifically how we can find the RHS. Now if you believe that rotations are linear maps and that a rotation by an angle of $\alpha$ followed by a rotation by an angle of $\beta$ is the same as a rotation by an angle of $\alpha+\beta$ then you are lead to
\begin{align}
D_{\alpha+\beta}&=D_\beta D_\alpha,
&
D_\phi&=\begin{pmatrix}
\cos\phi&-\sin\phi\\
\sin\phi&\cos\phi
\end{pmatrix},
\end{align}
which is equivalent to the formula for $\sin(\alpha+\beta)$ and the corresponding one for $\cos(\alpha+\beta)$.


How to deal with classification problem where labels are non uniformly distributed?

Question: I have a data set which has around 1000 samples and are divided in 4 groups - A, B ,C , D. The problem I am facing is that there are very high number of data sample which have B and C s output. They outweigh other two by factor of 3:1. Due to this most of the classification problems are producing very inefficient results with results from other two classes being mapped to A and B quite often . Is there any way to deal with it?
Comment: You have unbalaned-classes. I added that tag so you can see the question there. For more details see http://stats.stackexchange.com/questions/220026/can-a-classifier-trained-with-oversampled-data-be-used-to-classify-unbalanced-da/220116#220116
Answer: Welcome to DataScience.SE! You need to ensure that your training distribution is similar to your test distribution in order to get the best results. This can be done through stratified sampling. It might be that there is no problem, and that the classifier is simply allocating its resources to best classify the majority case, though I'm a bit confused by your description because you say that B and C dominate and the "other two classes" (A and D) are "mapped to A and B quite often". One option is to use more discriminating features, if you can think of any. Another is to partition the large classes into (B becomes the union of $B_i$ and likewise for C) if applicable. This can help if the shape of the class is complex by breaking it up into learnable pieces. It helps to plot your inputs, colored by class, to understand which classes overlap or have complex shapes. Finally, you can modify your loss function if getting certain classes wrong is more important than others.
Comment: I don't get why he need to ensure that the training distribution should be similar to the test distribution. In this case, shouldn't be the test distribution left untouched? In case of unbalanced classes I would down-size the largest classes to the size of smaller class, but only in the training set.
Comment: Because you want your training set to be representative of your test set, assuming your test set is also representative of data you expect to process. We seek the parameter $\arg \min_w \mathbb E_\theta f(X,Y; w)$ under distribution $\theta$ by minimizing $\frac{1}{N} \sum_i f(x_i,y_i; w) + \lambda r(w)$. The approximation only holds if the samples are from $\theta$, no?
Answer: You can try merging the groups A and D which will provide more significant boundaries to the model. Apart from this you can try to sample the given data to form a new data so as to form a uniform distribution of all the groups.


Where should I ask a question about abstract physics/economics/information theory that I invented?

Question: I wrote this and a couple other related papers and I'd like to discuss, where should I go?
Comment: Always the diplomat @JohnRennie. I'm impressed.
Comment: Your paper may be a bit advanced for us. I could not understand a word of it.
Comment: Please explain your notation and provide proofs for your theorems. Also, I would gladly discuss your theory in chat!
Answer: Not here, and probably not anywhere on Stack Exchange. These sites are not for discussion. You should find some place that admits reviews of original research. (Well, actually what you should do is try to get it published, but that's a whole separate issue.)
You could try bringing it up in chat to see if anyone would care to discuss it with you, but no guarantees.
Comment: I can't think of any offhand.
Comment: Any suggestions on sites that will do that, I will bring it up in chat as well.


From where did the concept of Juzu' came?

Question: For example, Juzu' 30 starts with sura Naba and ends with sura Nas. My question is, when, how and why did the idea of juzu' came?
Comment: [Juz](http://en.wikipedia.org/wiki/Juz%27) is the correct Islamic term
Comment: @Ezati - since this is a practical facilitation that Muslims derived after Islam had been canonized, there is no such thing as a "correct Islamic term" for this :) It is the Arabic term, yes, but there is no harm in using "para" or "thirtieth" or any other term
Answer: As I read, the term of juz' was not established in the time of Prophet Mohammad (PBUH). This term and this methodology was introduced by earlier muslims. To be exact, it was introduced by Al-Hajjaj ibn Yusuf when he was the Governor of Iraq in Umayyad caliphate .
My reference is (I'm sorry but it is arabic) :
http://islamqa.info/ar/ref/109885
Update :
I found some facts(in english) about the role of Al-Hajjaj ibn Yusuf in introducing sections in qur'an in the famous tafsir  , Tafsir al-Qurtubi(Sciences of the Qur'an)  :
http://bewley.virtualave.net/ulum3.html
Comment: The link you cited is quite lengthy. Please quote (using the quote feature) some of the relevant sections in your answer.
Comment: Its not that I don't believe you, but as I did not understand your reference (in Arabic), I cannot accept the answer. But of course +1.
Comment: @Mohayemin see the new update of the answer


When does Windows decide to pull out pages from Working Set?

Question: I am looking at the distribution of physical memory using the RAMMap tool by SysInternals. The distribution (see image below) shows

1.7 GB in Free (Zeroed) memory list
1.2 GB in Working Set list
550 MB in Standby list
125 MB in Modified list

I understand that when a process requires memory, Windows searches for memory in the lists in the order Free (Zeroed) -> Standby -> Modified. Hence, as long as we have Free page frames, everything should either be in the Working Set list or Free list.

Is this assumption right?
If so, why do we see 125 MB of pages in the Modified list?
In general, when does Windows decide to pull out pages from Working set list to Modified/Standby list even when there is Free memory left?

I am using Windows 7, with 4.0 GB of installed RAM, 3.5 GB being usable.
Answer:
No. If a page is going to be read from disk, or if it's an allocation from kernel mode,  the free list is checked first, then the zeroed list. If it isn't going to be read from disk, the zeroed list is checked first, then the free list (if allocated from the free list the page will be zeroed in-line before the faulting process gets to see it). In both cases, the standby list comes next. I don't believe the modified list is ever used to satisfy page faults (except soft faults that are resolved TO pages on the modified list)... since the pages have to be written out to disk before they can be assigned to other uses... so, might as well wait for the modified page writer to do its regular thing, whereupon the pages will show up on the standby list.

1a. "As long as we have free page frames, everything should  either be in the working set list or free list." No. The standby list is considered "available" but until someone needs that RAM its pages are used for two different types of caches.
The second question (stupid automatic list formatting keeps starting over at "1" here): That's rather a lot. Did you delete your pagefile?
The third question: First, keep in mind that there is a working set list for every process, not just one. And each has its own "limit". When the limits are being enforced (they aren't if there is plenty of free RAM), the process has to give up a page for every new page it faults in. There is also a working set reclamation process that tries to shrink long-idle processes.
When a process loses a page, it goes on the modified list if it was touched with a "modify"-style operand while it was in the working set, or on the standby list if not. If the process later faults to the page before it is assigned to some other use or process, it can be brought back into the process working set without going to disk for it. (This is a common example of a "soft" page fault.) In this way these lists form a sort of common system-wide extension to all processes' working sets. But everything on the Standby list is still counted as part of "Available" memory, because it can be used by any other process immediately - noting has to be written out to disk.
Starting with Vista, there is a new concept called memory priority. Pages on the standby list that are of low priority can be reassigned for use by the new proactive file cache, SuperFetch. But this doesn't cost any "available" RAM because they're still on the standby list. (The old reactive cache  is still there; it used to be part of the system working set; as of Windows 7 it has its own.)
This is but the tip of the iceberg. The Mm chapter of Windows Internals is 200 pages long, enough for a smallish book all by itself. But if you really want to understand this stuff, there isn't really a substitute.


How can I account for lack of data during an on-boarding process?

Question: My application manages and measures data (like visits, social activity) around a specific type of web page. The data doesn't really get interesting until you have a corpus of 4 or 5 different pages in the tool. For some users this process could take a month.  How can I keep users interested, and not disheartened by flat lines and sparse tables, whilst they on-board?
Answer: Honestly, when there's nothing for them to do, keeping their engagement is going to be an uphill battle. For me, when signing up for these kinds of tools, what helps the most is getting an email when there IS enough data. Odds are, I've forgotten I signed up and wandered off, and getting notification that there's now something worth looking at is often enough to draw me back and cause me to become more engaged with the product.
Answer: When reading your question, I immediately thought about the web app "RescueTime". It track the time you spend on your computer so you can quickly see how productive you are. Even if you recorded only some minutes, the design has been made so you don't feel like it's empty.

If collecting data takes time then let them do something else but keep doing your work and then, depending on how much time you need to give usefull informations, send them an email.


PHP ,MySQL memory DB and memcached

Question: I've a site which is running in a shared host without memcached.
So, how about make a MySQL memory DB as object cache just like memcached?
Answer: I would say that if you operate a website that would need memcached, you shouldn't be running it on a shared host.
That's my flippant answer.  Here's a real answer:
Memcached has some good advantages over the MEMORY storage engine.

Storage is distributed over multiple servers.  MEMORY storage engine is limited to a single host, and constrained by the CPU and memory of that host.
Quick access of individual entries.  MEMORY storage engine has table-level locking only, so concurrency suffers.
Non-relational key/value storage.  MEMORY storage engine is more structured, which isn't as useful for cache-type usage.  Also MEMORY expands varchar to full length, so is less efficient storage.

As a caching solution, I wouldn't choose the MySQL MEMORY storage engine.  Since you're using PHP, you should be using APC or Xcache or something.  These have data cache features that are better for typical usage in PHP.
If you're not using one of these PHP caching technologies, that's a more important area to improve than worrying about memcached versus MEMORY storage engine.
Answer: I agree with Bill and you wouldn't get the same performance boost using MySQL that way.
Hypothetically:
Make sure your host has the memory storage engine enabled.
<code>SHOW ENGINES;
</code>
This will show you a list of and status of all the storage engines installed in your mysql instance.
Memcache allows you to store data of any length. Internally, its checking your data to see how long it is, and placing it in a pre-allocated memory bucket which is closest to the size of the item your storing. That part of the logic, you'll need to implement yourself. MySQL's memory storage engine only accepts fixed length rows. To get a similar effect in mysql, you'd need to create several in memory tables with different lengths of char fields to store the data.
http://dev.mysql.com/doc/refman/5.0/en/memory-storage-engine.html
Selecting the tables with a union between all your 'buckets' would yield the correct value no matter which table the key was actually stored in.
One gotcha with mysql, if you store data in a field that is longer than the field (18 chars in a 16 char field for example), mysql will truncate it without any kind of error.
Here is a better idea: Use Zend_Cache with the 'file' backend.
This will store stuff just like memcache on the webservers local disk.
Connecting to a db in a shared hosting is usually expensive. (1 to 2 seconds for the first connection on my godaddy accounts.) Even a slow disk is faster than that.
http://framework.zend.com/manual/en/zend.cache.html

PHP ,MySQL memory DB and memcached


How fast can serum calcium, magnesium and potassium levels change?

Question: Can serum electrolytes (such as Ca Mg or K) within NORMAL limits rise or drop substantially within 12-24 hours?  Enough to go outside of normal range, even to the point of being symptomatic?
Comment: Hey Yette, I'm sorry to hear that. We can't gibe you a personal medical diagnosis (I.e. tell you what your health problem is), so I have edited out your personal clinical information. The question can stand on itself the way it is now. // If you have already visited 10 doctors, I'd suggest rushing to one of them (or another one) when the symptoms are very strong. That's the last thing that comestibles my mind. If you actually have difficulty breathing and an inability to stand up, you might want to visit an EHR (depending on the setup of your local health system). Hope that you get well soon!
Comment: The answer to your question is yes, in some health conditions and/or medications.  It's impossible to answer this question generally, as there are too many variations to discuss in an answer.  It would have to be individualized, which we can't do here.  Gather all your results and take them to a primary care doctor (or GP or whatever they're called where you're from) along with a list of your symptoms (in chronological order) and questions.  Good luck!
Comment: I don't have sufficient knowledge to answer this question well, but I can tell you from personal experience that serum potassium levels can vary dramatically very quickly.
Answer: Answer:
Blood levels for electrolytes are maintained by homeostasis in most people, primarily in the kidneys.  But they can actually vary quite widely within hours - depending on health conditions and medications.  It can even vary fatally in some (rare) cases.
Why I cannot give a more complete answer:
There are too many possible reasons to discuss adequately in an answer.  Therefore it would have to be individualized, which we can't do here.
Advice:
Gather all your results and take them to a primary care doctor (or GP or whatever they're called where you're from) along with a list of your symptoms (in chronological order) and questions.  They can guide your evaluation.
Answer: Yes, there are conditions that cause this.  One of the most well known is familial periodic paralysis.

Each form of familial periodic paralysis involves a different gene and electrolyte channel. In 70% of affected people, the hypokalemic form is due to a mutation in the alpha-subunit of the voltage-sensitive muscle calcium channel gene on chromosome 1q (HypoPP type I). In some families, the mutation is in the alpha-subunit of the sodium channel gene on chromosome 17 (HypoPP type II).


Question about Equilibrium Price

Question:
To find the equilibrium price I understand you set $$ Q^s = Q^d $$
and then solve for p. But as P is not indpendently labeled in $$Q^d$$ I am slightly confused how you would go about writing this equation? Thanks!
Answer: So you want to find $\partial p / \partial k$
By implicit differentiation what they mean is let $p=p(k)$ so p is a function of k.
Take your equilibrium condition $Q_s-Q_d=0$ and now differentiate with respect to k.
Comment: @BNA You were able to solve it?
Answer: By the implicit function theorem, when we have an equilibrium equation $F$
$$F \equiv   Q^s - Q^d = 0   \implies F\equiv   kp^2-D(p)=0$$
the equilibrium change of, in this case, $p$ when $k$ changes is given by
$$\frac {dp}{dk} = -\frac {\partial F/\partial k}{\partial F/ \partial p}$$
Since $D(p)$ is not given explicitly, you won't get a fully parametric answer of course, but the sign of $D'(p)$ will help you determine the direction of movement.

Question about Equilibrium Price


Waterproof finishing for buffet

Question: I am building a "Buffet" and I would like to know the best method of finishing the top. It needs to be very waterproof. Thanks for the help.
Comment: Laqueur, oil-based varnish, bar-top epoxy layer, or the traditional glass plate cut to fit the top.... That last being most waterproof, of course.
Answer: If you want literally waterproof — any amount of water can be left on the surface without concern — then you probably need to use a solid plastic or resin coating, such as a pour-on finish sold for bartops or an epoxy coating system (often sold as a marine finish). Note that these create a solid, plastic coating on the surface of the wood and some people are very much not fan of how that looks. To give an idea of just how thick these can be only one coat can be equivalent to maybe 20 coats of varnish, so thick, and very glossy*.
If you just need very good water-resistance as on a table or counter that will get a lot of sweaty glasses in the summer, will be wiped down regularly with a wet cloth etc. then varnish can provide sufficient protection. Any decent polyurethane varnish will work for this, both oil-based and waterbased types, although the former usually provide greater protection from water.
See this previous Answer for a little more detail, Protecting against water damage
Long-term durability
Not sure if this is a primary concern but thought it worth mentioning that thick plastic/resin coatings are essentially unrepairable. Being supremely tough, down the road if you get a scorch from a hot pan being put on the surface, a crack from something heavy being dropped on it or discolouration (epoxies and some resins tend to yellow eventually from light exposure) it is extremely difficult to remove the finish and get down to bare wood to prepare for refinishing. It's so difficult in fact that often people will throw the top away and build a new one rather than face the work.
Varnish isn't nearly as tough or durable (it can still take quite a beating, just not in the same league) but it can be removed far more easily. So refinishing in due course is not only possible it's commonplace. Even a very substantial varnish application such as six full-strength coats applied by brush or roller could be taken off a counter in under an hour, less than 10 minutes with the right plane or scraping tool.

*The gloss level can be taken down fairly easily using hand methods after the finish has cured (e.g. rubbing down with steel wool or Scotch-Brite) but it won't reduce the apparent thickness of the coating.

Waterproof finishing for buffet


Earning semichah with just a test

Question: What if someone does know a lot of halachah and wanted to earn semichah and become a posek? Are there any good semichah programs which will award semichah with just a test (as opposed to a additional time requirement for example)?
Comment: Having smicha is a prerequisite to being a posek - but being a posek requires a lot more, e.g., "shimush", apprenticeship
Comment: You might want to clarify what your definitions of "semicha" and "good semicha programs" are.
Comment: [Related](https://judaism.stackexchange.com/q/16375/15571)
Answer: Just knowing a lot of halacha does not make someone capable of being a posek. A posek is someone who is not just familiar with the Psak Halacha in the Shulchan Aruch or the Mishna Brerura, but it is someone who is familiar with the major commentators and the reasoning behind each halacha, and how it applies to new questions.
Taking a test will NOT make you into a posek. It can give you semicha (Rav Zalman Nechemia, Rav Zafrani AFAIK offer semicha tests), but they are not meant to bestow upon someone the ability to pasken shealos. Rav Zalman Nechemia actually goes out of his way to point this out upon receiving his Semicha (at least in my experience).
The Rabanut Semicha test in Israel, which is notorious for its difficulty, also confers Semicha.
Being a posek requires two major factors 1. An intimate knowledge of the sugyos and the meforshim as mentioned previously, and 2. Shimush (apprenticeship) from an authoritative halachic expert. Just taking a test will not give you that.
There are rabbinical programs that usually require at least 2 years in the program (Rav Yitzchak Berkowitz, Rav Yosef Lerner..etc.) and there are currently alumni from those programs currently acting as Poskim.
Other programs that are actively geared towards becoming a leaders and poskim in Israel (there are Chaburos in Lakewood and Baltimore that I know of, but I am not intimately knowledgeable about them) for example are, CKD Center For Kehilla Development, run by Rabbi Leib Keleman, and Toras Chaim in Sanhedria under Rabbi Daniel Yaakov Travis. But these are long programs that require a lot of testing and a time commitment.
The short answer to sum up is that there are test to receive semicha, but there is no test to make you a posek, that requires a tremendous investment of time and Shimush.
Comment: @Orion "But nobody will accept his psak if he doesn't have smicha." I don't think that's entirely true. Note that several 'big rabbis' didn't have any formal 'Semichah'. There's a famous story with the Chafetz Chaim where in his later years when he had to interact with government officials, he asked another Rav to give him a 'Semichah' so that he wouldn't be 'lying' when he was introduced as a Rabbi. And this was long after he published most of his works.
Comment: "is someone who is familiar with the major commentators and the reasoning behind each halacha, and how it applies to new questions" That's what I meant by "Knows a lot of halachah". Halachah is not just what's in shulchan aruch and mishna berurah. As you point out there are many other commentaries. I was wondering about somone who knows enough to be a posek and whether he's have to go through a apprenticeship to get semichah or not. A posek is just somone who paskens. But nobody will accept his psak if he doesn't have smicha. Hence my question.
Comment: True but its probably easier. Additionally the more controversial the posek the more people would question if he was 'qualified'. But your right that you don't NEED semichah.
Comment: Aren't there different types of *semicha*. I gather that only *yadin yadin* allows one to be a posek. And, I think one must first have *yoreh yoreh* beforehand. Correct?

Earning semichah with just a test


Security of decompression tools

Question: How safe is it to decompress untrusted files with unrar-free?  With unzip?    I'm using debian jessie. What steps can be taken to minimize the threat while extracting the file's contents?
Answer:
How safe is it to decompress untrusted files

Just looking at the CVE's for unzip you will find several possible code executions, modifying the permissions of existing files, overwriting arbitrary files outside the current directory....
The CVE list for unrar is shorter but includes also code execution.

What steps can be taken to minimize the threat while extracting the file's contents?

Any kind of privilege separation and sandboxing, i.e. virtual machines, chroot environment or containers, ...  And of course have the latest patches.
There is actually nothing special about unzip and unrar - you should take the same care with any kind of potentially malicious files (which includes at least everything with suspicious origin).
Answer: Malicious payload contained in a file must be run so that it can be used. Merely deposing a file on a filesystem does not present a risk, provided that:

there is no action triggered automatically once a file of a given type is discovered. This is usually done by graphical UIs which want to be smart and, for instance, generate thumbnails
the zip file itself is not crafted in a way which will, for instance, create recursive directories until you run out of inodes (or other resources)

If you have doubts use a throwaway virtual machine without a GUI which you will snapshot after installation and run from that snapshot for sensitive operations.
Comment: However, if the unzip utility is itself flawed, then a sufficiently malicious malformed zip file could trigger that flaw and allow arbitrary code execution during the unzipping process.
Comment: Do zip or unrar formats allow any sort of code execution during extraction?  Or are there likely to be execution vulnerabilities in these tools?
Comment: No, they just extract the files (see http://linux.die.net/man/1/unzip)
Comment: Sorry, what am I supposed to see in the man page?  That it doesn't mention code execution?
Comment: Yes, that there is no mention of parameters for code execution (and there is no such functionality which would run by default)
Answer: I suggest looking at the files size and content. Sometime in June 2015 my place of employment where I work as IT got hit by cryptoware. I was tasked with finding out where it came from and what it effected.
After a few hours I tracked it down to a single zip attachment on an email. It was just under 300 bytes. Double clicking the email cause it to inject code into the built in windows zip program which then downloaded the cryptoware and installed it from the users temp directory. This was a windows XP machine. I removed execution privileges from the temp folders and that fixed the issue. A few days ago we got another present in the mail but this time it errored out since it couldn't execute.
I would have to say that most if not all cryptoware and other little nasties are targeting windows exclusively. If you're using Linux you're probably fine. Just isolate the file first. I agree with Steffen Ullrich on that point.
On a side note, we didn't give in to terrorism. We brought the effected files back from backup. Always keep a good set of backups.

Security of decompression tools