Why can't I just download a premade color profile from the internet for my monitor?

Question: Shouldn't the manufacturer of my monitor already know how it differs from the standard?
Comment: Every environment is different. The manufacturer has *no idea* what the lighting in your workspace looks like.
Comment: So it should be possible for something like the Oculus Rift but not for monitors in general?
Answer: Any monitor worth the buying price will have a basic ICC color profile which should be downloadable from the manufacturer's website. (True of any device that produces visual output, including printers.) Usually the profile comes on a CD, which seldom escapes from its sleeve, so that the profile never makes it onto the computer. Worse, an ICC profile for the original monitor that came bundled with a computer may still be in place three monitors later, with horrible results. That's one reason on-screen colors in most offices are so ridiculously variable.
The ICC profile acts as an intermediary, to adapt the standard output from the OS, applications, or videos to the specific characteristics of that display, so that it will achieve some subset of the sRGB gamut (or something the manufacturer fondly believes is "pleasing"). Professional-grade monitors are often pre-calibrated for 100% sRGB and >99% of Adobe RGB. Less expensive graphics monitors and all office-grade monitors are not, and usually aren't capable of more than about 90% of sRGB.
TFT Central maintains a database of ICC profiles and OSD (on-screen display) settings for current and past models from most manufacturers. The ICC profile isn't the whole story, by a long way. You can wreck the color rendering by altering the brightness and contrast settings, for example, but the ICC profile will at least remove any hardware-specific peculiarities from the color rendering.
Simply installing an ICC profile doesn't mean you're getting a calibrated display, only that the monitor, when new, will give you something close to the manufacturer's intent. Color drifts over time for various reasons, so that recalibration is essential if you want to maintain accurate output.
Calibration, whether done with a full-on calibration tool or crudely by adjusting the GPU driver's output, creates a custom ICC profile that overrides the default. Color-critical work also requires taking into account ambient light in the workspace, and necessitates neutral colors in the area surrounding the display.
Comment: Ahh, very good made my answer obsolete.
Answer: The perception of color is determined by range of variable factors that a device manufacturer has no way of controlling (or even determining). This includes the lighting in the room where the display is being used, if there's any natural lighting the date and time will impact color perception, the actual power being delivered to the display, the rods and cones in the eyes looking at the display, and even down to the neural receptors interpreting visual input. A color profile is really just a way of stating that in an ideal world, under ideal conditions, a device should show/interpret colors in a particular way. For most consumer displays, this would be the sRGB color profile or something quite close to it.
Answer: Environment, panel differences and panel decay. The environment affects the profile this can not be accounted for. The monitor panels themselves are different. Mainly because they change over time and they were slightly different to begin with. User settings may also be different, as you may be using different adjustments.
So the downloaded profile is some ideal average, that does not reflect what your monitor looks like. But rather what a new monitor of your make on the average looks like, in standard conditions.
Since the result decays and changes, you need to measure your settings regulary. Even continiously would be an option. Its not enough to make the profile once. So you see you really need an idividualized profile.
However, the downloaded profile may be better than nothing. But on the whole this subject is extremely convolved.


Confession in Buddhism

Question: Growing up in the Roman Catholic tradition, we were encouraged to go to confession (penance) on a regular basis for reconciliation and to be absolved of sins. In Buddhism, the only mention of confession I've seen is in regard to a practice for monks prior to the reciting of the patimokkha. I understand there is no idea of absolving sins in Buddhism, but why is it considered benefical or useful for monks to confess but not for lay people to do the same? I'm assuming there is some sense of unburdening in the confession process and wondering what serves that function for lay people? Thank you.
Answer: This is a good question; if the monks can confess their "sins", why can't lay people?
On the one hand, monastic confession is a product of the rigidity of monastic practice, which requires some formal means of realignment. But on the other hand, reaffirming one's determination to keep precepts is a great practice for all Buddhists.
The standard practice for lay people in Theravada Buddhism to correct a broken precept is to simply retake the entire set of precepts (five or eight). There are standard religious formulae for this, so that might be a similar concept to a confession.
Beyond that, though, I think there is less need for Catholic confession since there is less sense of "sin" in evil deeds; since our concept of morality is utilitarian in the sense of "it's evil because it brings suffering", there isn't the sense of intrinsic "sinfulness" of a deed, and hence there seems to be less of the shame and guilt associated with evil in Catholicism.
So, the practical equivalent to confession in our tradition is probably just talking with a teacher about your problems; e.g., rather than confessing you drank alcohol, you would discuss your alcohol addiction or your view that alcohol brings happiness.
Comment: Part of Catholic "sin" is the idea that you've offended against God and need to become reconciled with Him. However, "bringing suffering" might include bringing suffering to other people. If you hurt other people (I'm not saying *you* do, but other people might), you might feel ashamed and guilty about that, and want a way to become reconciled with the people you hurt.
Answer: The experience I have of confession within Buddhism is mostly within the context of a ritual. I practice with the Triratna Buddhist and in one of our more lengthy rituals we have a section on  confession of faults part of which goes

The evil that I have heaped up
Through my ignorance and foolishness –
Evil in the world of everyday experience,
As well as evil in understanding and intelligence
All that I acknowledge to the Protectors.

The ritual is based on the Bodhicaryavatara an 8th century Mahayana text by Santideva. The Bodhicaryavatara  has a section on the confession of faults. This goes on at greater length on the same themes for example

Overwhelmed by ignorant delusion,
I celebrated the harm that was done.
But now I see it all was done in error,
And before the buddhas, sincerely I confess.

So the notion of recognising on and confessing faults does exists within Buddhism. I'm not an expert on comparative religion but I know that the concept of sin doesn't really exist in Buddhism. Actions are skillful (kusala) or unskillful (akusala) rather than sinful or not. Also it's less clear who you would be confessing to. So any notion of confession would be necessarily different in Buddhism.
On a personal note, it has been suggested to me that the proper course of action when one has done something unskillful is go sit at your shrine, light a stick of incense and try not to be so thoughtless in future. Maybe that's the nearest equivalent in my own experience.
Comment: Just an FYI... The Christian term for sin is from the Greek work hamartia, which literally means missing the target.  Like when an archer misses the bull's eye.  So hamartia or sin in the Greek implies the misdirecting of mind's and body's energies.  Repentance is based on the Greek work metanoia means the changing of mind, redirecting the mind's energies.  So there are ontological similarities between Buddhism and Christianity regarding sin and repentance.  However, some things were lost in translation over the centuries for some folks. :-\
Answer: In the Vajrayana, confession is a specific part of the so-called "preliminary practices" (ngöndro). It is one of the "inner" or "extraordinary" preliminaries, and consists in removing negative actions or "obscurations", namely karmic obscurations; the obscurations of negative emotions; conceptual obscurations; and the obscurations of habitual tendencies.
The removal of obscuration is done through the practice of meditating on the Teacher as Vajrasattva and reciting his mantra (in the context of ngöndro, this is supposed to be done 100,000 times). In what is widely considered the most important commentary on the preliminary practices, Patrul Rinpoche's The Words of My Perfect Teacher (Altamira Press, 1998), one reads:

There is no harmful act that cannot be purified through confession.
  (...) However, purification only takes place when you confess
  sincerely in the right way, using the four powers as antidotes. (1998,
  p. 264)

The four powers are the essential elements in the practice of confession: the power of support "is provided by taking refuge in Vajrasattva and cultivating the intention and application aspects of bodhicitta" (1998, p. 265); the power of regretting having done wrong "comes from a feeling of remorse for all the negative actions you have done in the past" (ibid.); the power of resolution "means to remember the faults you have commited and to resolve never to commit them again" (1998, p. 266); and the power of action as an antidote "involves accomplishing as many positive actions as you can, as an antidote to your past negative actions" (ibid.).
For further reading on the subject, I recommend Khenpo Ngawang Pelzang's A Guide to The Words of My Perfect Teacher (Shambhala Publications, 2004), part 2, chapter 3.
Comment: Hmmm, I never labelled Vajrasattva practice as a confession - I would always call it a purification practice. I was brought up as a Christian and confession for me is saying aloud a list of bad deeds, a some sort of cruel reenactment of shameful moments in front of some authority. Mantra repetitions luckily don't have this feature which I found very comforting.
Comment: I agree with you that "purification" sounds better. The Padmakara translation of _The Words of My Perfect Teacher_ uses "confession" interchangeably with "purification", and both translate the Tibetan _sojong_ (Wyl. gso sbyong; Skt. poṣadha). The confessional aspect has to do mainly with the power of regret, as one reads in _Words_: "in his presence call to mind all the negative actions you can think of that you have accumulated until now... Feel that you are confessing them all in the teacher Vajrasattva's presence, your whole body breaking out in gooseflesh with shame, fear and remorse."
Answer: Confessing faults is very importand for oneself and in cases of relations and communities.
Putting any effort into a community where such is not used, or assossiate is not for ones benefit but for long time pain.
For more, feel given here: [Q&A] Confession in (Buddhism) tradition of the Noble Ones

[Note: This is a gift of Dhamma and not meant for commercial purpose or other low wordily gains by means of trade and exchange.]

Confession in Buddhism


Should the volume of a solute be factored into the volume of a solvent when preparing a substance of a certain molarity?

Question: Upon being asked to prepare a solution of a given molarity from a solution with high concentration I was confused whether or not I should factor in the volume taken from the high concentration substance into the volume of the solvent. I think that an example could illustrate what I am asking more appropriately. Lets say I have to prepare a 5 M substance in 50 ml of water. The substance is in a container that is 10 M so I must calculate the number of moles and then the amount of solute to extract from the 10 M container.  $$M = {m\over{L}} $$ $$5 M = {m\over{.05}} $$ $$moles = .25$$ given that the solution's concentration is 10 M $$10M={.25\over{L}}$$ $$L = .025$$ Now in order to achieve the 5 M in the 50 ml of water, do I pour 25 ml of water and then the 25 ml, which then adds to 50 ml? or do I pour the 50 ml of water and then the 25ml resulting in a total volume of 75 ml?
Answer: The only volume that is important in the denominator of your equation is the total volume of solution; neither the volume of solute or solvent are explicitly relevant.
Pragmatically, there is not likely to be much of a volume change when taking a concentrated solution and diluting it.
So with reference to your question, you should add enough solvent to get the proper final volume.  Explicitly, add the 25 mL of stock solution and 'dilute to mark'-- that is add enough solvent so the total solution is 50 mL.  The added solvent might not be exactly 25 mL to make this final volume.
Answer: You only add the $\ce{25 mL}$ water. After all you want to dilute to a certain molarity. You start from a 10 M solution and want to go to a 5M solution. Neglecting the volume of the dissolved compound you simply add another equivalent of solvent to dilute by a factor 2, i.e. $\ce{25 mL}$ water in this case.
Comment: This answer is explicitly untrue, but may be pragmatically true.  The volume of solute may be negligible, but if it isn't this approach will lead to improper concentration.
Comment: If you want the final concentration to be any more precise than "about 5M," this method is definitely incorrect. This is why you fill to volume using a volumetric flask (as @Lighthart wrote in their answer). The *total volume* is all that matters here, not the volume of solvent. Never assume the volume of solute is negligible.


Nginx proxy forward and preserve original links?

Question: Here is my current config:
server {
    location ~ ^/bugsbunny/?(.*)$ {
        proxy_set_header Host $host;
        proxy_pass       http://127.0.0.2:8080/cartoon/network/$1;
    }
}

I've been trying to figure out how to reverse-proxy requests and preserve the original host. For example let's say I have http://127.0.0.1/bugsbunny as my front-end and I want to reverse-proxy the requests to http://127.0.0.2:8080/cartoon/network. How to preserve the original url so that http://127.0.0.2:8080/cartoon/network/something/other would become http://127.0.0.1/bugsbunny/something/other on the front-end ?
P.S. I tried using proxy_set_header Host $host; but this preserves only the original host.
Answer: Actually I found it myself.
You have to rewrite the links yourself via HttpSubModule. Be sure to set sub_filter_once off so that it replaces all the links on the page, not just the first one it finds.


Why do protein solutions have to be alkalised in biuret test?

Question: I've read that CuSO4 solution reacts with peptide bonds that connect amino acids to create a violet colour, but the instructions always tell me to add NaOH solution to the protein solution before I add CuSO4. How is alkalising the protein solution before adding CuSO4 solution an aid to this process?
Comment: The directions explicitly state to add the sodium hydroxide before the copper sulfate? I've never done the biuret test myself, but I can't imagine it would make a difference. Commercially available biuret reagents are sold as premixed solutions.
Comment: Can you link the recipe you are talking about?
Answer: This is probably to prevent precipitation of copper hydroxide (see Itzhaki & Gill, 1964 - they suggest adding dilute copper sulfate slowly to the NaOH solution to avoid this). If you have the protein already alkalized and ready to react you'll get the color reaction before precipitate forms.
Commercial premixed solutions, like @canadianer mentioned in a comment, have tartrate present to prevent this (Geiger & Bessman, 1972 mention this).
It doesn't seem like it's strictly necessary to add NaOH first, but that's probably the most reliable way to do the assay without using an additional stabilizing agent.

Itzhaki, R. F., & Gill, D. M. (1964). A micro-biuret method for estimating proteins. Analytical biochemistry, 9(4), 401-410.
Geiger, P. J., & Bessman, S. P. (1972). Protein determination by Lowry's method in the presence of sulfhydryl reagents. Analytical biochemistry, 49(2), 467-473.
Comment: Wouldn't adding sodium hydroxide solution to copper sulfate solution encourage the formation of copper hydroxide? https://en.m.wikipedia.org/wiki/Copper(II)_hydroxide
Comment: @UbaidHassan Yes exactly, which is why the OPs recipe tells them to add the hydroxide solution to the protein sample first. Might be confusing since my first reference also suggested adding copper sulfate slowly to sodium hydroxide, but that's only because the worst approach would be to add copper sulfate *quickly* or adding hydroxide to a concentrated copper solution. You use the same procedure with, for example calcium containing solutions that tend to form precipitate: precipitate is minimized when you keep the metal concentration low.
Answer: You mix those two chemicals to get a Cu(OH) 2 colloid, if you mixed them earlier it would settle down and not form a colorful complex (as efficiently). Base is added first because (i presume) it denaturates the protein which partly unfolds it, allowing copper ions to form complexes along a greater surface, giving clearer results.


Besides pantone colors, is there any refrence database for equally distributed fashion colors?

Question: I'm trying to divide color space into 150-200 colors. I'm looking for Hex code/ RGB values and corresponding color name that is simple, well known & understandable by normal people. Is there any reference database I can use ?
Comment: Apart from artists and graphic designers (who are not normal humans) I doubt people can name 150 colors.
Comment: @SZCZERZOKŁY even they can not pair them with colors in a blind test. Color names are just marketting names so they are easier to talk about but yes every color vendor haves their own names like say [copic](https://imaginationinternationalinc.com/media/cms_media/copic/inspire/2014/copic_color_system_root/358_color_family_chart-2.jpg)
Comment: Yeah, and it's usually cultural specific. Like in USA you have fire engine red while in Poland we have "Maryish blue".
Answer: No, best you can get is like 10–20 colors that people will agree a name on (some sources I've seen put this as low as 7). Even so, the variation is huge. But if you must bash your head at this then the XKCD color survey might be of interest to you.
150–200 recognizable color names is not going to happen. I mean you can name them but lo and behold even the most experienced people will have a hard time to distinguish the colors on their own. Best you can do is ask them to place colors in a relative order to each other.
In fact humans see color relative to other colors. So the same color next to a totally different color looks different! A classical example of this is the checkerboard shadow illusion. Under these condition its very hard to agree on a name.

Image 1: Checkerboard shadow illusion, the squares A and B have same color! (source)
Is the square A-B's color in image 1 dark gray or light gray? So for this reason any system you device is very artificial, humans will not really agree on it. So you must remind them.
The second reason is that variation of hex code across uncalibrated devices is quite a bit. Most users and devices fall into this category (>90%). Even so they would need to be watching in standard viewing conditions which is not going to happen. So even if you do name them by 200 different colors the color ranges might overlap on different monitors. So it's also not technically feasible to be accurate here. So if you want to be pedantic then you also need to define in what RGB space those hex values are defined in!
Answer: There are a few colour 'systems' that use names to identify the colours. The most obvious one being the Crayola Crayon Colours. Some of these are obvious like 'Lavender' while others are a bit more obscure, such as 'Tickle Me Pink'. Another example is the colour picker in MacOS which uses Crayons as a quick and easy away to select from a small range of colours. Some of these also have less obvious names like 'Ocean' and 'Bubblegum'.
You would not be able to use either of these systems as a whole because of copyright issues, but they might give you some inspiration to develop your own set of colour names. Also, you would be fine to use the obvious colours like 'Lavender', 'Violet' or 'Sepia' as these are established in common use.
There is also a nice (long!) list of colours on Wikipedia which are available under the Creative Commons License so you should be fine to use a subset of those colours if you wanted to.
I don't think you're going to find an 'off the shelf' solution to this problem, but building your own set of reference colours with names that invoke the correct colour to the average user shouldn't be too big a task.
Comment: Well, Crayola's colours was not a color reference i would ever think of, so is not that obvious. n_n but it is nice to know.
Comment: @Rafael: Maybe I'm just more into Crayons than most people. ;-)
Comment: There are lots of market names for color series like copic markers, bit other vendors like nailpolish makers and most wallpaint companies have a list like this.
Answer: Another color reference* is the color table of web colors (CSS color names that can be used instead of Hexadecimal values) http://www.w3schools.com/cssref/css_colors.asp The oficial w3 color table has less colors: https://www.w3.org/TR/css3-iccprof#x11-color
Some other color systems are Toyo and Munsell. You can even try painter's colour charts like winsor and newton: http://www.winsornewton.com/na/discover/resources/colour-charts/artists-oil-colour
But one note... *The fact that I am referencing another color reference is the crude reality that people do not agree on how the hell a color should be named.
So I totally agree on joojaa. You can not name more than a dozen colors, but even there people can not agree on that.
But an aditional problem is: An RGB color or an Hex value is not a color. It is an instruction to  display a signal. But as you can see on any TV shop, some reds are redder on the neibourg's TV  and the grass is always greener on the other side of the fence.
But for me, the best option in your case is stick to the CSS color chart and do not re-invent the wheel.
(An aditional note... I will never, ever learn thoose names and the exact hex values. But a name is a good starting point to have a rough idea on what the color is.)


Which close price should we use for machine learning?

Question: I am building a machine learning model using historical prices and I am using data from yahoo finance. Currently yahoo finance data have two close prices one normal close price(close) and other adjusted close price(Adj close). My question is which close price should I take for teaching my ML model. Is there any (dis)advantage of using adjusted close price instead of close price?
Answer: You should use Adj close price
Using Adj close price gives you the adjusted values of close price, hence the fair picture in case of off-beat events like splits and dividends. Using close price instead of adj close price provides unrealistic and false values of metrics like returns, which could generate false signals in your ML model.
Answer: Hmm I don't know if I agree that the adjusted price should be used. On the one hand the adjusted prices do help to avoid the impact of corporate actions like stock splits.
On the other hand using the adjusted price incorporates dividends into the price and that will cause a unpredictable shock to price. Lets take an example: you are making a prediction on each days move. On the 4th day a dividend is payed and there are capital gains. Your model wont be able to account for the dividend.
I think the best thing to do is to take the raw data, adjusted it for corporate actions, and not include dividend payments in the price.


What's the difference between "Jew", "Israelite" and "Judaizer"?

Question: What's the difference between "Jew", "Israelite" and "Judaizer"? Can these three terms be used interchangeably? Can only one or only two of these terms be applied to one person?
Comment: where is judaizer from...?
Comment: @Yaakov - I don't know. I just heard this term, but don't remember where.
Comment: @YaakovKuperman - Anti-Hellenizer, i.e., Jews who actively learned torah and fulfilled the commandments during the Hellenistic era, which was considered to be directly in conflict with the Greek doctrine of Hellenism.
Comment: Similar: http://judaism.stackexchange.com/q/68238
Answer: There are several, sometimes overlapping families of terms in play:
Israel
This name was given to Abraham's grandson, Jacob, by God and means "God prevails" or "God fights".  There's some disagreement over which meaning is accurate, but the source is from this passage in the Torah:

And he said unto him: 'What is thy name?' And he said: 'Jacob.'  And he said: 'Thy name shall be called no more Jacob, but Israel; for thou hast striven with God and with men, and hast prevailed.' Genesis 32:28-29 (JPS)

Since Jacob fathered the twelve men who are the founders of the 12 tribes, his name was often used as shorthand for the entire community.  We see the same phenomena with Moab, Edom, etc.  Sometimes the nation was called Jacob, but Israel is more common.  There are several variations:

Israelite—Usually reserved for the descendants of Jacob in the ancient world.  While it can be applied to anyone from his own sons on, it's most common for it to mean the nation that formed during the Exodus.  When the kingdom divided, the northern portion retained the name until they were defeated by the Assyrians.  After that point, the people living in that region were called Samaritans and there is some dispute over the exact relationship with Israel.  The "-ite" suffix comes from Greek, which suggests the Septuagint coined the term.
Israeli—The modern designation for citizens of the nation of Israel.  Since nationhood is no longer strictly tied to genealogy, Israelis do not all trace their ancestry to Jacob.

Judah
Judah was one of Jacob's sons and the ancestor of David.  As such, the tribe of Judah acquired significant political and cultural importance.  When the kingdom of Israel split, the southern portion was called Judah even though it included Benjamin and portions of other tribes as well.  Like Israel, there are several variations of this name as well:

Jew—Perhaps because of lessons learned from the destruction of the Northern Kingdom, the people of Judah maintained their communal identity while in exile.  When the Persian empire conquered the Babylonian empire, the decedents of the kings of Judah where allowed to return to what was now called the province of Yehud.  When Alexander conquered Persia, the name became Ιουδαία and under the Romans it became Judea.  After a few language jumps, the word arrived in English as Jew.  This is the proper term for people who practice the religion described in the Tanakh or have ancestral relationship to Jacob.
Judaizer—This is fairly technical term that comes from one early Christian text which describes the first division of Christianity.  Most of the early figures of the Christianity were Jewish.  Some hoped to spread the religion to all types of people and others hoped to retain Jewish religious practice.  Paul, writing on behalf of the first group, argued that gentiles should not be compelled to adopt Jewish praxis, or "live as do the Jews".  The Septuagint used the same verb when translating Esther 8:17:

And in every province, and in every city, whithersoever the king's commandment and his decree came, the Jews had gladness and joy, a feast and a good day. And many from among the peoples of the land became Jews; for the fear of the Jews was fallen upon them.—Esther 8:17 (JPS)

Christian commentators turned the Greek verb into a noun: judaizer.  Needless to say, outside of this fairly narrow context, the term is not helpful.  It should be avoided, if not because of the possibility of offense, then because it's unlikely to be recognized.

Hebrew
Although not mentioned in the question, "Hebrews" is a commonly used term for the ancestors of Jacob while they were living in Egypt.  The name may have derived from Abraham's ancestor, Eber.  Other etymologies have been proposed.  The word generally signifies the language of the same name, but at various points in history it has been identified with its speakers.  The term emphasizes the text, language, and culture of the people rather than their nation or religion.
Shem
One of Noah's sons, who is identified by Genesis as an ancestor of Abraham.  Many people groups fall under the banner of Semitic, but because the term antisemitism refers to an attitude of hostility to Jews, the word Semite is sometimes mistakenly used for Jews alone.
Conclusion
While there is significant overlap between the term Israelite and Jew, these terms are not always interchangeable.  "Judaizer" probably should not be used at all outside of specific domains.
Comment: @Monica Cellio: [You are correct.](http://en.wikipedia.org/wiki/Judaizers#References_over_time)  Yet another sad moment in history that I wish did not occur, but can't allow myself to forget.
Comment: Jon, thank you for this thorough answer.  I believe "judaizer" was also used by the Inquisition to refer to Jews who only pretended to convert to Christianity.  As you note, it's not a word we would use to describe ourselves.
Answer: As stated, Israelite is a anglicized version of a word meaning "of the nation of Israel" which referred to people in biblical and post-biblical times. Once the kingdom split after the reign of Solomon, that term which would have applied to the Northern Kingdom of Israel, would not apply to the Southern Kingdom of Judah. The name "Judah" (transliterated better as "Yehudah") is what became "Yehudi"= which we got (through the German I would guess) as "Jew." Of the three it is the only one in use now.
A Judaizer is one who gets others to convert to Judaism or, separately, someone who adopts practices to live in a state which conforms to certain Jewish norms without being a Jew. It is not a term used for Jews or generally, by Jews.
Answer: The first two can be used interchangeably, although the use "Israelite" is slightly antiquated now, and is used mostly to refer to the Children of Israel in biblical times. Nowadays, the only term of those three that are used to refer to Jews is, "Jew"
As far as Judaizer, I have come across the term before, but I had to look it up, because it's so uncommon.
The Wikipedia entry on "Judaizer" defines several different uses for the term, none of which would be synonymous with "Jew".
Answer: Judaizer is a pejorative term used by Christians to describe those they claim are attempting to change their religion to conform to the laws of Moses. As an example, the Inquisition killed many people who were accused of attempting to "Judaize" the religionas well as being conversos who were accused of trying to (secretly) return to or remain Jewish.

Judaizers is a term for Christians who insist that their
  co-religionists should follow the Law of Moses. This term is most
  widely known from its single use in the Greek New Testament (Galatians
  2:14)[1] where Paul publicly challenges Peter for compelling gentile
  converts to Early Christianity to "judaize",[2] also known as the
  Incident at Antioch.
This term includes groups who claim the necessity of continued
  obedience to the Law of Moses found in the first five books of the
  Christian Old Testament.[3] Members of such groups, notably the
  Seventh-day Adventist Church, dispute the use of the term because
  "Judaizers" is typically used as a pejorative.

Israelite is the term used up to the end of the second Temple as everyone was a member of the nation which grew fro the descendants of Avraham Yitzchak and Ya'akov (Yisrael or Israel).
Jew After the destruction of the first temple, the term "Jew" became used from the kingdom of Judah, as can be see from the reference in Megillas Esther of "Mordechai Hayehudi (the Jew) who was from the tribe of Benjamin.
Answer: Israelite is the term for the nation of Israel in ancient times as depicted in the Bible. Jew is the modern term for practitioners of Judaism. It would be anachronistic to describe the ancients as 'Jews' or modern members of Judaism 'Israelites'. I have never heard the phrase 'judaizer' before.
Comment: I see. Thank you. Is "Israeli" a modern term?
Comment: Israeli refers to someone living in the modern state of Israel, while Israelite is anyone descended from Jacob (who was also called Israel) - in other words, anyone who would be considered Jewish today


Does Islam allow critically analysing the lives of the Prophets?

Question: Is it allowed in Islam to critically analyze the lives (events and happenings etc, discussed in the Quran, hadiths or accepted as historical facts) of Prophets, specially Muhammad (Peace be upon him)? If it is allowed are there any recommended approach, cares and precautions specified in Islam?
Comment: @ashes999 I never thought about exact definition of critical analysis. So, on top of my head an Unbiased researching, questioning, reasoning, to provide/understand logical, rational and scientific explanation of an event.
Answer: According to Shia Islam yes. There is no limit about asking any question about God, any prophet, any wife of prophet, any Caliph, any war or any of 12 Imams of Shia.
Only if contains insult it has problem and it is recommended the asker first increase his knowledge about their life.

Reference:
Asked from online answering service of Official website of Grand Ayatollah Makarem Shirazi
Answer: In a sense, your question doesn't make sense. Allah says:

Translation: Indeed in the Messenger of Allah (Muhammad SAW) you have a good example to follow [...] (Surah Al-Ahzab, verse 21)
And in Surah Yusuf:

Translation: There was certainly in their stories a lesson for those of understanding. [...] (Surah Yusuf, verse 111)
These verses make it pretty clear that the lives of the prophets (all of them) are here for us to learn and benefit from. And there is no way that we can accomplish that without critically analyzing their lives an extracting lessons from them.
This would include things in the Qur'an, as well as books of ahadith.
However, there is one caveat; rasulullah said:

[...] Do not prefer me over other prophets (like Moses) [...] (Saheeh Bukhari)

That is to say, we do not say that any prophet is better or worse than any other. This is despite rasulullah also saying:

[...] I will be the leader of the children of Adam on the day of
  resurrection [...] (Saheeh Bukhari)

Also, prophets need to be treated respectfully, because they are divinely sent by Allah -- even if we don't always understand everything about their lives.
Wallahu a'lam.
Comment: @ " your question doesn't make sense ... "  So, This might make question very specific and narrow but just to give you a more concrete idea, this thing came to my mind when a friend presented this question that why Hazrat Muhammad (PBUH) married Hazrat Ayesha (My Allah be pleased with Her when she was under age. Being a Muslim we know that He (PBUH) was a perfect man and everything He(PBUH) did was an order from God. So, is it OK to raise Question about him like this or should we consider each and every act by him right and perfect by default.
Comment: This is why I asked you what you meant by "critically analyze." As Muslims, we are encouraged to ask and understand everything, although understanding is not required -- submitting to Allah is. Of course, it's okay to raise questions like this (in appropriate gatherings of knowledge) and seek knowledge!


How can I remotely wipe an iPhone owned by our company?

Question: We have a number of user's in our company who are using iPhones that have been provided by our company.
How can I remotely wipe out all data on an iPhone owned by our company?
Answer: Update:
For iOS 5 Apple now provide the Find My iPhone app that allows you to (amongst other things) remotely lock and wipe your idevice.
Exchange in brief:
Log into your exchange webmail, go to options -> mobile devices.
Select your device and then check Wipe All Data from Device and cofirm.
The next time your device connects to exchange it will be wiped.
If you're using exchange look here.
Answer: Do you use a Microsoft Exchange Server? Iphones connected to such a server can be remotly disabled or wiped.
You could also search the App-Store for an Anti-Theft software like F-Secure Anti-Theft


Why screenshot is 截圖, not 屏幕 圖?

Question:
Why wasn't screenshot translated as 屏幕 圖?

Isn't 截 inaccurate? I screen shot (coincidence!) 截 on CUHK. Here I 截 the Web page to screen shot just the English meanings, but screenshots can be NOT 截. I can screen shot whole screen.
Answer: 截 in 截图 (noun) means something similar to 'that is taken', so 截图 in a word means 'the screenshot that is taken'
This becomes clearer if I use 截 as a verb in this context 请(please)你(you)截(take)一张(a)图(screenshot)
The idea of intercept in this case can be explained as that a screenshot is a static image, so you are intercepting something that is running in a moment of stasis.
But 截图 is always used in the context of screenshot, it is assumed that 图 in this case already means (screen)shot. Much like how the word 'image' can change what it refers to in specific context. You can't use 截图 in the context of taking a photo.
Answer: Video is a stream of moving images on your screen. A video screenshot is a point you cut into the stream and take one single image from it.
Your computer screen is a video screen. Taking a screenshot on your computer is just like capturing a still frame from a video
截圖 = 'cut image' (from moving image stream)
Answer: 截圖 could have 2 meanings.

the action of screenshot.
the screenshot file.

e.g.
請你把螢幕的畫面截圖(1)後,再把截圖(2)傳到我的電子信箱就可以了。
Answer: 截 in this case means "to extract" or "to section". In the action of taking a screenshot, we extract or create a section of the screen to be recorded as an image. 截圖 (or 截图 in simplified Chinese) is more of a fixed phrased for both taking a screenshot and the screenshot itself. In China, we do not say 屏幕圖, but we do say 屏幕截圖 (for the image produced by a screenshot) and 截屏 (for taking the screenshot of the whole screen).

Why screenshot is 截圖, not 屏幕 圖?


Should one who follows the Dhamma give drugs to the dying to ease thier suffering?

Question: My Christian wife is dying and the doctor has prescribed morphine and tranquilizers. She is losing her mind and the drugs may be contributing to that. I don't want her to suffer but I also don't want her mind to be in a bad state for rebirth. Is there any Buddhist scripture or comentary that could give guidance in this situation?
Comment: The First Noble Truth seems applicable and it leads to the Second.
Answer: This is not exactly "Buddhist scripture or commentary" but it's related -- What nurses need to know about Buddhist perspectives of end-of-life care -- here's an extract but you might read it all:

Taking into consideration overall well-being
(including the mental state of the patient), nurses
must balance the level of pain relief needed against
the need for alertness in the dying Buddhist. Proper
pain management can be achieved with minimal disruption of alertness by the use of the WHO analgesic
ladder. The choice of non-opioid analgesics (nonsteroidal anti-inflammatory drugs) and weak opioids
should be preferred over strong opioids and neurolytic
block therapy whenever possible, with the aim of reducing adverse side effects (i.e. sedation and cognitive
impairment), thus maintaining alertness of the individual so that effective spiritual practices may continue. However, if severe uncontrolled pain develops,
cognitive impairment (e.g. delirium) may result that
may require the use of strong opiods for effective
relief to achieve the best cognitive function possible
that would support meditative spiritual practices. In
concordance with good practice and recognizing that
the individual needs of each patient will differ,
nurses should continue to monitor the need for pain
relief, and should clearly document the preferences
of such patients with regard to pain relief, particularly
during initial patient assessment regardless of the
setting (patient's own home, hospice, hospital).

I believe the "analgesic ladder" means, not prescribing more than needed, and, increasing the prescription over time (when the need/illness increases, and as the tolerance to the drug increases, tolerance making it less effective) -- additional details here: WHO Analgesic Ladder

For some patients I think that unmanaged pain and suffering itself, may cause a "mind to be in a bad state" -- for example delirious or suicidal.

This article -- Ministering to the Sick and the Terminally Ill -- includes a lot of sutta references.
One of these is AN 5.124 which identifies qualities of a competent carer -- they include being able to prepare medicine and knowing what's suitable and unsuitable.
Answer:
A patient with five qualities is easy to care for. What five? They do
what is suitable. They know moderation in what is suitable. They take
their medicine. Because their carer wants what's best for them, they
accurately report their symptoms by saying when they're getting worse,
getting better, or staying the same. And they can endure physical
pain—sharp, severe, acute, unpleasant, disagreeable, and
life-threatening. A patient with these five qualities is easy to care
for."
AN 5.123
Comment: In my humble opinion, this answer does not seem to address the specific question posed by the OP about the caregiver's responsibility in administering drugs to a dying patient. Perhaps amendment of the above could more directly assist the OP? Best, Jim
Comment: I think it points to the need for moderation in medicine but as u said it doesn't address the q directly. It would imo best complement Chrisw's answer
Comment: I would agree & I up-voted that answer.
Answer: If they have bad side effects, then not. If they are helpful or beneficial, then go ahead and give them such medications.
Comment: All prescription drugs have bad side-effects, almost by definition -- i.e. that's why they are "by prescription only". A doctor is trained to assess whether the benefit is greater than the harm, when and how much to prescribe, what the alternatives are (and what the consequences are of each alternative), etc.


Is a judge paid by the state allowed to hear criminal cases?

Question: In my case the other party is the state. The judge also receives local judicial benefits from the state which is a party appearing before him. Like in my case it's my name verse state of Washington. And state of Washington has paid my judge $795,000. And I feel like that could be a little conflict of interest since the judge is supposed to be impartial. The code of judicial ethics in Washington state also says that both parties must be aware of any economic interest the judge has and I was never notified.
Comment: The question in your title sounds pretty interesting, but I'm guessing you'll get some close votes based on the "fairness" part.
Comment: In what manner was the Judge paid? Could you explain?
Comment: Assuming you are talking about the judge's regular salary, it's an interesting theoretical question of ethics, but in practice I cannot imagine that it has any practical significance.  I would have to guess that any appeal filed on these grounds would be laughed out of court.
Comment: So what are your thoughts on victimless crimes?
Answer: Salaries are public: http://www.salaries.wa.gov/salary.htm
Judges are understood to be following the rules outlined here
That includes:

The duties of judicial office, as prescribed by law, shall take precedence over all of a judge's personal and
  extrajudicial activities.
A judge shall uphold and apply the law, and shall perform all duties of judicial office fairly and impartially.

, among many other rules that prohibit bias, partiality, prejudice, and influences external to the law.
The judge is paid by the state to do that job, not to decide any individual case in a particular way.
Even if you don't believe justices can be truely impartial, it's the legislature that sets the salaries, and the people that vote in judicial elections to keep or remove judges.
Comment: The state is in charge of all prosecutions, not just prosecutions for victimless crimes. Your plea decisions are your own. No court or statute has ever deemed judge salaries to be bribery.
Comment: You call it salaries but some might see that as bribery. When I go to court for a victimless crime the state picks it up. And the public defender tells me to take the deal it's a good offer even though I told him I was innocent.
Answer: Wait a minute, what are you actually referring to? Do you mean "salaries" in the word "Money"? The one who do the prosecution is the Department of Justice, while the judge is from the Judiciary. So, judge receives salaries from the Judiciary but not the Department of Justice.
We maintain the judge is making verdicts fairly by making judges a Permanent position, means that unless the judge has committed a crime or other offences, he can not be fired. So, simply by the state paying him salaries will not affect the fairness of the verdict. Also, when doing verdicts, the judge need to give reasons when deciding facts and laws, if you find them misleading, you can appeal. I don't see such act of paying salaries affects the fairness. :)
Recommendation: make your question more concise to make sure we know what you are asking.
Comment: In many states, judges are selected by election and can be voted out.
Comment: Elected by the other judges? Or by whom? I am sorry that I am not from US......
Comment: By the people in the state. A popular election, sometimes even with judges listing their party affiliations.
Answer: (US Centric answer)
You are absolutely right about there being the potential for a conflict of interest. This is why trials are public, defendants are guaranteed counsel / representation, and the defendant has a right to a trial by a jury of his peers. As others have pointed out, there are appeals that further reduce the likelihood of falling through the cracks.
Answer: In most modern democratic countries, the government is divided into three independent branches: the legislature, the executive and the judiciary and each is independent of the other.
When someone is prosecuted for a crime (or in a civil suit by the government) it is the executive branch (usually through the office of the Attorney General) that acts as prosecutor and the judicial branch that supplies the judge. Both the prosecutor and the judge are paid by the taxpayer but they are not connected to each other otherwise.
The important point here is that the judge is paid his salary no matter who wins the case. If you win: he gets paid. If the state wins: he gets paid. Since his remuneration is the same there is no conflict of interest, per se.
Comment: @SteveMelnikoff sure, how this is done varies: in some they are fully independent (US) in others the executive is drawn from the legislature (Westminster system)
Comment: Is the first sentence really true in a parliamentary system? (This doesn't affect the rest of your answer, though.)
Comment: Even though the "organization charts" show the prosecutors working for the executive branch, I wouldn't say the prosecutors are independent of the judiciary: All prosecutors are "officers of the court," and maintain constant working relationships with the judges (who themselves are often former prosecutors).
Comment: @feetwet the same can be said of defence council
Comment: But Justice must satisfy the appearance of Justice. Well if I could give the Judge a bigger salary maybe he would side with me will never know but that definitely doesn't give the appearance of Justice.
Comment: @user5249 as side from begging the question - the courts are an organ of the state, just like the executive and the judiciary therefore the state must pay them. There is no conflict of interest here; the judge doesn't care if you get convicted or not.
Answer: There have been plenty of cases where I judge has said "Sorry, guys; I own ten shares of company XYZ so I can't hear a case where XYZ is involved". Even when in practice it's obvious that the share price of XYZ isn't going to move if the judge decides that XYZ has to repair your fridge under warranty or not.
But a judge gets a salary, and that salary is paid no matter how he or she decides in a case where the state paying the salary is one of the parties. So the judge has no financial interest in the outcome of the case.
Answer: You have hit upon a MAJOR problem in justice systems.
In many countries judges are professional bureaucrats employed by the state and whose advancement is controlled by the state.
The U.S. does not have such a system. However, in the federal system, many judges advance through the ranks of the Justice department before becoming judges. Although in theory they are independent, the judiciary is protective of "Mama Government" to a degree that most of the public is not aware of nor would approve of.


If I donate at some place is it considered as good karma (Punya)?

Question: Yesterday I was thinking about donating some money to charity who help people. But at the same time a thought come that if that money will be used for things other than help, say in bad things, then am I responsible for that bad karma done by the charity? And if the money is used in good way, then again upto which level am I responsible for that good karma?
Comment: It is important to donate only to deserving people.  ApAtra dAnam (donation to the un-deserving) is a sin. So make an effort to discern the integrity of the receiver before you give.
Comment: there is no sin. it is just action and reaction. what one does comes back to him. Do good and good comes back. Donate your money and will get that money back. Intention matters more than the action. Did you donate knowing that it will be misused, I doubt it. Then why fear?  It all depends on one's intention. Finally perform actions as Sri Krishna prescribes in the Gita. That is donate, but do not expect anything as a reward, neither good nor bad. Surrender the action and the reward to God. Then where is the question of karma? Karma cannot touch the One who seeks refuge in Lord All the best!!
Comment: Possible duplicate of [Giving Alms (Donation/charity) with the intention of getting merit will give me merit?](https://hinduism.stackexchange.com/questions/20789/giving-alms-donation-charity-with-the-intention-of-getting-merit-will-give-me)
Comment: @Sai: its obvious that if i found that money will be misused, then i never give it to that charity. But if i don't know and money used for say such a bad activity like kidnapping, then if one who get hurt is also indirectly by me. For that reason i am fearing.
Comment: @Kiran yes so intention matters. Use your best discrimination when donating and leave the rest to Bhagavan. So long as one has good intentions, the negative karma (if at all) is not much. The bad karma is only to the one who has cheated the other by misusing the money given for good purposes. Not the other way round. finally it is prescribed to leave all results and surrender to Sri Krishna as He says in Gita. Do not expect neither good nor bad from actions and simply perform tasks. Then no karma good or bad can touch Thee - says the Bhagavan Sri Krishna in His Glorious Gita. All the best sir.
Comment: @Kiran if you have some serious doubts that a charity is misusing the money, then simply avoid that charity and give it to another. Having donated to a particular charity, now leave the rest (the results -good/bad) to the Lord and that's it. :) He will guide you and guard you. After all, God frees and liberates the one who has surrendered to Him
Answer: Donation is a very good thing, in fact a man should donate 1/3 of his earnings. According to Gurus, charity is not only good karma but it brings a lot of peace inside. A person donating to get good karma will not get the fruits of his deed.
But,if you do it selflessly or unconditionally i,e. not expecting a return out of it, then, the good karma is stored.
Intention is key here. If your intention is good, then good karma will come, but if your intention is bad or conditional, then your good karma will not become active.
Comment: @Kiran What Abhishekstudent is trying to say is that no matter what the intention of the charity is, you will gather good karma if your intentions are good. But, selfless service is needed to get Punya. When you donate just to get good karma, it doesn't fall under the selfless service category IMO.
Comment: You are right, But here i am thinking about the intention of Charity. and intention about myself then, I want to donate because "just want" not for any return gift from god.
Comment: EXACTLY! @Dharmaputhiran
Answer: Yes, donation is a good karma. In fact donation or charity is the primary virtue of this age of kali:

tapaḥ paraṃ kṛtayuge tretāyāṃ jñānaṃ ucyate
  dvāpare yajñaṃ evāhurdānaṃ ekaṃ kalau yuge [Manu - 1.86]
Meaning
  Austerity is the supreme virtue in the age of Satya and jnana (knowledge) is said to be supreme in Tretaya. Yajna is supreme in the age of Dwapara and dana alone  in the Kali age.

But even if donation by default is a good karma and awards punya, the result of donation actually depends upon the cause for which the money is donated. For example, someone may donate money without expecting anything in return to support a party or organisation which does bad works or harms others with that money. Then by the law of karma one will get the corresponding negative effects instead of acquiring merit. So it is the responsibility of the donor to see whether he is donating to the right person or organisation and whether his intentions for donating are also good. Hence, depending upon these dana becomes of three kinds which Shri Krishna explains as below in the Gita:

Satvic Dana (when done to right person without expecting anything, gives no results)

Charity given out of duty, without expectation of return, at the proper time and place, and to a worthy person is considered to be in the mode of goodness. [BG - 17.20]

Rajasic Dana (when done to right person with expectations of return, punya, etc. )

But charity performed with the expectation of some return, or with a desire for fruitive results, or in a grudging mood is said to be charity in the mode of passion. [BG - 17.21]

Tamasic Dana (when done to wrong person in wrong way, can give negative results)

And charity performed at an impure place, at an improper time, to unworthy persons, or without proper attention and respect is said to be in the mode of ignorance. [BG - 17.22]

In Kali Yuga however people are very much greedy and don't donate or donate very little. So even if donation is done to a wrong person unknowingly, this act of donation certainly does something good for the donor and at the least makes him a little free from greediness. Hence, saint Tulsidas writes in the Ramcharit Manas:

प्रगट चारि पद धर्म के कलि महुँ एक प्रधान।
  जेन केन बिधि दीन्हें दान करइ कल्यान।। [RCM - 7.103]
Meaning
  There are four legs of dharma (satya, daya, tapa, dana), and in Kali one is the chief. Donation done in whatever way and in whatever form always causes benefit.

Update
Satvic Dana is that which is done from a sense of duty (dātavyam iti yad dānaṁ) without expectations hence it becomes karma yoga and doesn't bind the person with papa or punya.
Comment: Are you saying that sattvic actions, done without expectations of reward or punya, do not generate punya?
Comment: @KeshavSrinivasan You are only generalizing it unnecessarily to start an argument or something when I have clearly written *Svatic Dana* in the post. No where in my post or in the Gita actions has been divided as *svatic*, *rajasic*, or *tamasic*. Only certain actions like *dana*, *yajna*, etc. have been defined as such and for *svatic dana*, as it has been mentioned, it produces no results that bind the *jiva*.
Comment: But where does it say that Sattvic Dana produces no punya?  It just says that it's done without expectation of punya, not that it doesn't produce such punya anyway.
Comment: @KeshavSrinivasan And where does it say that *svatic dana* produces *punya*? So to again remind you, not everything is explicitly mentioned in the scriptures. This is what creates difference in opinions depending upon how statements are reconciled by people of different nature and intellect. Regarding *svatic dana* the presence of the clause *dātavyam iti yad dānaṁ* renders the action motiveless expressing karma yoga where as there is no such clause present while describing other types of *danas*. Ask a saint, sadhu or guru, He will explain it to you. I am not interested in disclosing more.
Comment: If i do dana so as to store good karma.. I know my dana is going to be utilized at good reason, then do i get punnya out of it??? Or does it considered as a good karma?
Comment: http://hinduism.stackexchange.com/questions/8394/donation-at-good-place-with-certain-mentioned-intention-accumulates-good-karma @BeHappy
Comment: @KeshavSrinivasan please help me out with above question


What does it mean to "firewall" an aircraft engine?

Question: I (think) I understand what a firewall is (at least, in a single engine aircraft where the engine is at the front of the fuselage), but what does it mean "to firewall" an aircraft's engines, as described in this incident report: is it just applying full thrust? What is the connection with the physical firewall?
Comment: A firewall is simpy a fire-proof wall.
Answer: "To firewall" is a phrase meaning to go to full power. Most aircraft throttle controls provide full power when moved to their furthest forward position - the direction towards the firewall separating the nose mounted engine from the cockpit in aircraft in the past. The phrase is still used, just as we "dial" a telephone even though the telephone dial is no longer used, either. A similar one for automobile driving is "pedal to the metal".
Comment: Another automotive expression I've heard is having one's "foot in the carburetor", the humorous imaging being that someone pushed the gas pedal so far their foot followed the linkage all the way to the carburetor.
Comment: Foot to the floor will do. Full bore does not get fuller. The floor being a de facto firewall where the pedal hits it in any case.
Comment: Likewise, "hammer down" comes from long-haul truck drivers, when they would put the truck on sustained maximum speed while giving their foot a rest by literally laying a sledge hammer on the gas pedal.  The invention of cruise control made the hammer obsolete, but the phrase remains in use.
Comment: @MasonWheeler that sounds like a bogus etymology to me - got a reference? Most sources indicate that it's related to the firing hammer of a pistol or rifle.
Comment: I've long known it from cars, where firewall means to put your foot (on the gas) to the firewall (the wall between the passenger compartment and the engine.)
Answer: It's just an expression. It means to push the throttle as far forward as it will go (all the way to the firewall, if you can), or full power.
Comment: Like AC-DC says, push the balls to the wall man. From era before engine control quadrants, ends of the controls were balls. Throttle in full, Mixture full rich, Prop control to flattest pitch for max RPM.
Comment: Streetcars typically had controllers that rotated around an axis, there's a stop molded into the top of the control stand, which was made of brass.  Hence, "on the brass" indicated full power.  However, you didn't want to spend any time in a resistor point, you would cruise at full series or full parallel.  So "on the brass" was a normal running point, not near as dramatic as "firewalled".


Accurate Wheeled Robot Odometry

Question: I'm looking for a "good" algorithm/model for wheeled odometry estimation. We have encoders on the two back wheels of the tricycle robot, and IMU on the controller board. Currently we use MEMS gyro for angular velocity estimation and encoders for linear velocity, then we integrate them to get the pose. But it's hard to calibrate gyro properly and it drifts (due to temperature or just imperfect initial calibration). How can we improve the pose estimation? Should we consider model that incorporates both encoders and gyro for heading estimation? Model slippage, sensor noise? Is there some nice standard model? Or should we just use more/better gyro? Not considering the visual odometry.
Answer: First, you can try adding encoders - you don't need to buy anything to do this. Only remember to perform UMBmark procedure first. It will allow you to get much more reliable odometry from encoders alone.
If adding encoders is not enough, try to add magnetometer. It will get you absolute heading relative to magnetic north. Unfortunately, these devices are very sensitive to interference from running motors, so try to keep them away.
As a last step I would go for a better gyro.
Comment: Magnetometer measurement are too bad for indoor environments, we've encoders as you might have seen in a question.

Accurate Wheeled Robot Odometry


What software should I use for converting fisheye photos to normal rectilinear photos?

Question: Can you recommand me a software for doing this job? I shoot using Sigma 8mm lens and I would like to be able to obtain a normal image out of that. The camera is canon 550D.
Answer: Try Panorama Tools - free and very effective: http://panotools.sourceforge.net/
Useful thread here: http://photo.net/digital-darkroom-forum/00CBe8
There is a friendly interface to it called PTGUI.
Answer: For defish the photos you can also use Hugin (it's free). Have a look to this and/or this link.
Answer: Use a Lens Profile
If you're post-processing with Adobe software or software that understands Adobe's lens profiles, the easiest way to correct for the Sigma 8mm circular fisheye is to simply use a lens profile.  According to the Sigma website, both Sigma's 4.5 and 8mm circular fisheye lenses have profiles in Adobe's databases.  Simply enable lens profile correction in Adobe Camera RAW (ACR) or Lightroom's Develop module, and the image will be defished.
Use Panorama Tools via PTLens
The Panorama Tools open source suite of command line tools includes the capability of lens correction--basically building a profile on the fly.  However, since not everyone is a command-line jockey, there are also a number of Panorama Tools GUI front-ends to consider that can do the same thing, such as Hugin or PTGui. But there is one PT frontend that is dedicated solely to the task of lens correction, which is PTLens.  This may be easier to use and suss than going into the overkill of using Hugin or PTGui off-label, as both those apps are centered around panorama stitching.
Fisheye Hemi
Another popular tool for defishing is the commercial Fisheye-Hemi Photoshop plug-in. It's using a proprietary remapping that is not simple rectilinear defishing, which gives results some find more pleasing.
Answer: I use GIMP 2.8 to correct pictures with lens distortion (Fisheye) effect.
This is a free and very extensive software, easy to use.
Click in file on open and add the photo that you want to correct.
In Filters, click on distortion and choose lens distortion.
In "General" you can set the degree of correction with the slider and check in "example" click "OK" in file "Export as" Here I choose as jpeg. Done
Available for the following OS:
GNU / Linux / OS X / Microsoft Windows all.
GIMP - The GNU Image Manipulation Program
www.gimp.org/
Answer: Ken Rockwell wrote a review of DxO Optics that illustrates converting fisheye to rectilinear photos. The most impressive examples are the kitchen ones about 3/4 of the way down the page. I've used DxO and it's pretty good at this as long as you have a body/lens combination DxO has profiled.
Not a cheap solution, but certainly worth considering if you need the ultra-wide angle, but don't care for the distortion.
There are many other less comprehensive posts and of course DxO's own site. Google "DxO +architecture +fisheye".


Central extension and direct sum

Question: Let $R$ be an associative ring with 1 and suppose that $Q$ is a central extension of $R.$ I'd like to know how the ring structure of $Q$ and $R$ are related. For example, it's easy to see that if $Q$ is a prime ring, then $R$ is prime too.
Now, suppose that $Q = I \oplus J$ for some ideals $I, J$ of $Q$ where $I$ is a central prime ideal of $Q.$ Would this imply $R=(R \cap I) \oplus (R \cap J)$? What if I also add this condition that $Q$ is the classical (left) quotient ring of $R$?
Thanks.
Comment: At least without the extra assumption that $Q$ is the quotient ring, the answer is "no". Consider $Q=\mathbb{Z}/p\mathbb{Z}\oplus\mathbb{Z}/p\mathbb{Z}$ with $R=\mathbb{Z}/p\mathbb{Z}$ diagonally embedded into $Q$, so that both intersections are trivial.
Answer: In general, the answer is No. Certainly Alex's example above shows that the condition that $Q$ is the classical left quotient ring of $R$ is necessary for your property to hold. Here is a (commutative) example which shows that it is not sufficient.
Let $k$ be any field, let $R = k[x,y] / \langle xy\rangle$, and let $k(a)$ be the field of rational functions in one variable. Let $Q = k(a) \oplus k(a)$ be the direct sum of two copies of these, and consider the map $\varphi$ $: R \to Q$ which sends $x$ to $(a,0)$ and $y$ to $(0,a)$.
Now $Q = I \oplus J$ where $I = k(a) \oplus 0 = Q\varphi(x)$ and $J = 0 \oplus k(b) = Q\varphi(y)$. This shows that $xR \subseteq \varphi^{-1}(I)$. Since $R$ is spanned over $k$ by powers of $x$ and powers of $y$, $R = xR \oplus k[y]$ as a $k$-vector space. If $\varphi( f(y) ) = (0, f(a)) \in I$ for some polynomial $f[t] \in k[t]$, then $f = 0$ because $k[a] \hookrightarrow k(a)$. This shows that $\varphi^{-1}(I) = xR$. Similarly $\varphi^{-1}(J) = yR$.
Next, $\ker \varphi = \varphi^{-1}(I \cap J) = xR \cap yR = 0$, so we can view $\varphi$ as an embedding of $R$ into $Q$. If we identify $R$ with its image in $Q$ using $\varphi$, then $I \cap R = xR$ and $J \cap R = yR$ by the above paragraph, but $xR + yR$ is not the whole of $R$ (since the ideal $\langle x,y \rangle$ of $k[x,y]$ is proper). Thus $R$ properly contains the direct sum $(I \cap R) \oplus (J \cap R)$.
Let $S$ be the set of regular elements of $R$, that is, the set of non-zero-divisors. We will show that $Q$ is the classical (left and right) quotient ring of $R$. To do this, we have to prove that (a) $\varphi(S)$ consists of units in $Q$, and (b) every element of $Q$ has the form $\varphi(r) \varphi(s)^{-1}$ for some $r \in R$, $s \in S$.
For (a), note that $S$ is precisely $R \backslash (xR \cup yR)$; so if $s \in S$ then $\varphi(s) = (v,w)$ for some non-zero $v,w \in k(a)$. But then $(1/v,1/w) \in Q$ is an inverse for $\varphi(s)$.
For (b), let $(v,w) \in Q$ and write $v = f(a)/h(a), w = g(a)/h(a)$ for some polynomials $f,g,h \in k[t]$ with $h \neq 0$ (you can choose the same denominator $h$ by passing to a common denominator). Then
$(v,w) = \frac{ \varphi(xf(x) + yg(y)) }{ \varphi((x+y) h(x+y))} = \varphi(r) \varphi(s)^{-1}$
with $r = xf(x) + yg(y) \in R$ and $s = (x+y) h(x+y) \in S$.
What's happened here is that the classical ring of quotients $Q$ of $R$ (also known in the commutative literature as the "total ring of quotients") has orthogonal idempotents $\frac{x}{x+y}$ and $\frac{y}{x+y}$ which don't lie in $R$; this stops $R$ from breaking up into a direct sum of two ideals.
Geometrically, $Spec(Q) = \{xQ, yQ\}$ is disconnected, but $Spec(R)$ is not (it's the union of two intersecting lines in $\mathbb{A}^2_k$). This is a fairly common phenomenon.
There are more complicated, but similar, non-commutative examples, too.
Chapter 2 of the book "Noncommutative Noetherian Rings" by McConnell and Robson has information that you may find useful. See in particular Proposition 2.1.16.
Comment: Nice! Welcome to MO, Костя!

Central extension and direct sum


What is the difference between negative rights and positive rights?

Question:
What's the difference between negative rights and positive rights?
Can negative rights co-exist?
Can positive rights co-exist?
Can negative rights co-exist with positive rights?
Comment: How is this unclear what it's asking (It is too broad as worded, but clear)
Comment: This is 4 questions
Comment: It may be you would get better responses at philosophy.se
Comment: positive rights are based on coercion, negative rights are based on the freedom from coercion.
Comment: Well it just seems like a complete answer will address all of them. I can break it up if you want but then the questions would be a little sparse and might fall under some contrived character limit.
Answer: According to Prof. Aeon Skoble
A positive right requires others to provide you with either a good or service.
A negative right only requires others to abstain from interfering with your actions.
They can co-exist in this way : If we believe in negative rights, we can have positive rights as long as it is grounded in a consensual arrangement.
Comment: Perhaps you could include some his support for the 3rd assertion, it seems non-obvious and videos and links may become unusable.
Comment: Your third point doesn't adequately cover how positive and negative rights interact.  What happens in the case where we assume the existence of a positive right? Does it mean anything for the existence of a negative right?
Comment: The 3rd point is self evident. A consensual agreement = a contract. Legally a person can only be held to a contract if they enter into it knowingly, willingly and voluntarily. Once an individual does so he agrees to give up a negative right(s) in exchange for a positive right(s). This is the only way positive and negative rights can coexist without "violence".
Answer: The general idea is that negative rights are protections of your life, liberty, and property from harm by others. All others have to do is not act upon you or your property to ensure your negative rights. Positive rights are rights to some good thing that others are obligated to give you. For example, property rights are negative rights, you have the right to do what you want with your property and others are restricted from stealing your property or destroying it. Other rights generally seen as negative include the right to not be hurt by others, and the right to say or write whatever you want. Here's one definition from a Santa Clara University article:

Negative rights, such as the right to privacy, the right not to be killed, or the right to do what one wants with one's property, are rights that protect some form of human freedom or liberty, . These rights are called negative rights because such rights are a claim by one person that imposes a "negative" duty on all others—the duty not to interfere with a person's activities in a certain area. The right to privacy, for example, imposes on us the duty not to intrude into the private activities of a person.

Meanwhile, the article describes positive rights:

Where negative rights are "negative" in the sense that they claim for each person a zone of non-interference from others, positive rights are "positive" in the sense that they claim for each person the positive assistance of others in fulfilling basic constituents of human well-being like health and education.

An example of a positive right is the right to have healthcare. By this right, others, or more likely the government, have an obligation to provide you with some sort of basic health care. Other positive rights include the right to internet access, the right to basic nutrition, or the right to publicly funded education. Many people who love the idea of negative rights get upset about positive rights. They think protection of one's life and property is all well and good, but are skeptical that such essentials of civilized society as negative rights should be classified in the same category as the idea that government should provide an ever expanding number of "necessities" to its citizenry. For example this libertarian leaning article describes positive rights in a rather negative light

"Positive rights" trump freedom. According to this doctrine, human beings by nature owe, as a matter of enforceable obligation, part or even all of their lives to other persons. Generosity and charity thus cannot be left to individual conscience. If people have such positive rights, no one can be justified in refusing service to others; one may be conscripted to serve regardless of one's own choices and goals.

There are critiques of this negative/positive dichotomy. One goes like this:
As a philosophical or ethical idea, the negative/positive distinction makes sense. Things get fuzzy when we take a step back and look how negative rights are actually guaranteed by government. The most basic negative right is the right to your life. This is your freedom from other people killing you. However, government has to enforce this right. They have to hire police officers to arrest those who would harm you and jailers or executioners to protect you from people who ignore the threat those officers pose. Salaries, equipment, law enforcement facilities, let alone the entire judicial system are all expensive and almost every state in history has found them indispensable for guaranteeing this negative right. Suddenly what looked like a simple right to one's life actually requires a whole bunch of other people's property to fund. If providing for one's right to life is expensive and requires funding from an external source, how is it fundamentally different from providing for someone the right to internet access? They're both nice things that take a bunch of tax dollars to provide. Maybe then, there's no fundamental difference between positive an negative rights.
Comment: This assumes that property is somehow more fundamental than rights. Before society can leave you alone to enjoy your property it must first decide what that property is. You think you own a car. I disagree; I think I own it. It is society that decides which of us is correct, if either. The award of that ownership is therefore a positive right which everyone else is required to give to that person.
Answer: A  positive right is a right to something, a claim. This may be a social (right to education) or political (right to vote) right. A negative right is a right against interference, a defense. An example is the first amendment's prohibition to restrict free speech.
In general, and regardless if negative or positive, rights can conflict with each other and should be seen as a system that has to be brought into balance or even into an optimum. Moreover, a negative right can usually be expressed as a positive right (right to free expression as prohibition to restrict free speech), but not vice versa.
Answer: Positive rights are based on coercion, negative rights are based on the freedom from coercion.
An example of negative rights is freedom of speech, you have the freedom to speak and express your opinion free from coercion or violence.
An example of a positive right is of an entitlement paid to you by the government to guarantee you a certain living standard. however coercion must be used on your behalf to collect the resources in order to pay this entitlement.
Positive rights cannot co-exist with negative rights without some degree of compromise of the negative rights.
IMO there are no such things as positive rights and they are based on the left's fundamental confusion of the difference between power and freedom. Freedom is for everyone, even the poorest person is free to live like a king, they just don't have the power to do so. Positive rights are nothing more than the political redistribution of power and as such are obviously incompatible with freedom.
Comment: How do we enforce the right to not be murdered? Well, we coerce a bunch of people to give up part of their money to pay people to enforce the right... Which is no different from positive rights. See lazarusL's and vicky_molokh's answers.
Answer: Deceptive Simplicity
At their most basic, negative rights are described as 'do not do bad things to me', while positive rights are described as 'please do good things for me'. That simplicity breaks down once we notice the ambiguity of the word 'rights' in these comparisons . . .
Elephant in the Room: Rights-as-Ideals vs. Rights-as-Implemented
Of the many ways in which people differ in their views on rights, perhaps one of the most influential one is about whether or not Natural Rights (Rights-as-Ideals) are a real thing, or whether all rights are merely things we decide to make up and only their implementations matter. This is very much related to the difference between moral realist views and moral nihilist views.
If one doesn't believe in natural rights, one needs to only consider implementation of whatever rights one deems desirable. If one does believe in natural rights, sooner or later one still will have to answer the question, 'So if this is the Right Way For Things to Be, then what do we actually do to achieve the right state of affairs?' and hopefully put one's effort where one's mouth is.
So You Wanna Implement Rights
Here we get to the issue that protecting even negative rights doesn't happen all by itself. If one has a right to property, one is still unlikely to be able to protect one's property against a sufficiently bigger group of robbers. So protecting such rights still requires collective effort, and collective actions often benefit significantly from specialisation, which in turn raises the question of financing such protective work. There are incentives to, after reaching some scale of a community, treat the implementation of the protection of such a negative right as a positive right ('you are granted community protection').
Communities tend to have dim views of inefficiencies of patchwork jurisdictions, and of the losses to freebooters, so financing of such positive rights tends to stop being opt-in, and becomes mandatory for anyone who directly or indirectly benefits by being in a given community's turf. This of course may interfere with certain negative rights (depending on one's views of what negative rights exist and are currently applicable).
The above is just one, and rather simplified, example. Hopefully it does demonstrate how negative and positive rights interact 'in the wild' and become intertwined in societies, and how different views on which (if any) rights are real as a thing in itself can influence the interaction.
Answer: Negative rights = Natural Rights
Positive rights require the violation of one group's Natural Rights in order to accomplish.
Therefore, they cannot co-exist
Easy example:
Marxists say everyone has a universal right to healthcare. In order to provide 1 individual with "free" healthcare, the government has to violate someone else's property rights in order to provide it.
The idea that government can give anyone anything is a fallacy. Government has to steal from one group before it can give it to another group. It doesn't have anything of it's own to give.
Comment: This is also true for negative rights. See lazarusL's and vicky_molokh's answers. I have money "stolen" from me, to fund the police force, to stop people from murdering each other, so that I can have the right to not be murdered.
Comment: So which right doesn't exist - the right to not be murdered, or the right to have the police stop people from murdering you?
Comment: @user253751 this logic is circular. You have the right to defend yourself or own the means to do so. This is a negative right and is just because it doesn't require violence on anyone else to accomplish. Hiring jack booted thugs with the seized fruits of other's labors is not a right. Nobody has a right to employ a mafia to force others to pay 'protection money' so they can feel safe. Positive rights = slavery and cannot coexist with negative rights. Positive rights require that people's negative rights be assaulted to accomplish.
Comment: @user253751 When was the last time you ever heard of anyone not being murdered because the police saved them? In fact there's multiple court rulings that have said that the police are not obligated to protect people. Individuals have the right to protect their own life, liberty and property. Nobody has the right to have someone else do the same. If any of your real(Natural) rights are assaulted you have access to legal remedy and recourse depending on the circumstances of the "assault".
Comment: Catching murderers after the fact stops future murders.
Comment: Who decides what you own? If I decide I own the car you are driving, who is to say I am wrong? I am as entitled to use force to protect what I believe is my property as you are.  So after I've killed you my view is the only one left.


Ultrafilters in $\omega$

Question: Let $U$ be a non-principal ultrafilter in $\beta \mathbb{N}$. Can it have a countable character as a point in this topological space? Is there decreasing chain of clopen subsets of $\beta\mathbb{N}$ $(K_i)_{i\in I}$ such that $$\{U\}=\bigcap_{i\in I}K_i?$$
Answer: No, there are no non-trivial (i.e. not eventually constant) convergent sequences in $\beta\mathbb{N}$, and a point of countable character that is not isolated (as such a U would be) allows one to define a convergent sequence to it.
Answer: For $A\subseteq\Bbb N$ let $\widehat A=\{\mathscr{U}\in\beta\Bbb N:A\in\mathscr{U}\}$.

Let $\mathscr{U}\in\beta\Bbb N\setminus\Bbb N$, and let $\{V_n:n\in\Bbb N\}$ be any countable family of open sets containing $\mathscr{U}$; then $\bigcap_{n\in\Bbb N}V_n\ne\{\mathscr{U}\}$.

To see this, note that for each $n\in\Bbb N$ there must be a $U_n\in\mathscr{U}$ such that $\widehat{U_n}\subseteq V_n$, and we may further assume that $U_{n+1}\subseteq U_n$ for each $n\in\Bbb N$. Now recursively choose distinct $n_k,m_k\in\Bbb N$ for $k\in\Bbb N$ so that $$n_k,m_k\in U_k\setminus\Big(\{n_i:i<k\}\cup\{m_i:i<k\}\Big)\in\mathscr{U}\;;$$ this is possible because $\mathscr{U}$ is non-principal. Let $A=\{n_k:k\in\Bbb N\}$ and $B=\{m_k:k\in\Bbb N\}$, and note that $A\setminus U_n$ and $B\setminus U_n$ are finite for each $n\in\Bbb N$. There are therefore ultrafilters $\mathscr{V}$ and $\mathscr{W}$ on $\Bbb N$ extending the families $\{A\cap U_n:n\in\Bbb N\}$ and $\{B\cap U_n:n\in\Bbb N\}$, respectively. Clearly $U_n\in\mathscr{V}\cap\mathscr{W}$ for each $n\in\Bbb N$, so $\mathscr{V},\mathscr{W}\in\widehat{U_n}$ for each $n\in\Bbb N$, and therefore $\mathscr{V},\mathscr{W}\in\bigcap_{n\in\Bbb N}V_n$. But $A\cap B=\varnothing$, so $\mathscr{V}\ne\mathscr{W}$, and therefore $\bigcap_{n\in\Bbb N}V_n$ is not a singleton.

Ultrafilters in $\omega$


Is there an older name for Cecaelia?

Question: Cecaelia is a modern term for a mermaid with an octopus lower body, instead of a fish. I have read that such legends come from ancient Native American and Japanese culture. Does anyone know their original names for these creatures?
Comment: Welcome to M&F StackExchange!  Not good enough for an answer, but wanted to mention you will also find these referred to as "sea witches."  Of course, a Google search will eventually bring up the Disney character Ursula, which they say is something called an "octopin," but I can't find anything else on what octopins are supposed to be.
Answer:
In Japanse, these are called 人魚 (lit. human + fish) Ningyo
Several Native American tribes have words and stories regarding mermaids:

Halfway People (Mi'kmaq)
Lumpeguin (Maliseet)
Ne Hwas (Passamaquoddy)
Nibiinaabe (Ojibway)
Water-Babies (Western tribes)
Answer: I think I've come across the same references to the legends being from Native American and Japanese culture. As far as Japanese origins, all I've come across are a few online posts referencing to the artist Katsushika Hokusai (1760-1849), who painted some sexually explicit images of women with octopi, such as the 1814 "Dream of the Fisherman's Wife."'
The yokai known as the Jorōgumo is a spider-woman, which is kind of similar at least in the sense of being a hybrid of a human and an eight-limbed creature.
As far as Native American myths, there is a Nuu-chah-nulth (Nootka) tale from the Pacific Northwest titled "Octopus and Raven." In this tale, both are depicted as humans. Octopus appears as a human woman with her hair arranged in eight long braids, which become powerful arms when she is angered.

Keepers of the Animals: Native American Stories and Wildlife Activities for Children, Michael J. Caduto and Joseph Bruchac, pp. 73-74.

I have not been able to find out for sure what the characters' names are in the original language, but according to firstvoices.com, the Nuu-chah-nulth word for Octopus is tiiłuup. Raven is quʔušin.
There also is a Kwakiutl octopus deity named Xa'niyus.
Other than that, however, the site native-languages.org (which I have found very useful) says:

"Octopi do not play a major role in most Native American mythology--
most coastal tribes consider the octopus to be just another type of
shellfish. In some Northwest Coast tribes of British Columbia and
Alaska, the octopus plays a more prominent role as a medicine animal,
considered to have formidable powers over the weather or over sickness
and health."

The cecaelia is a newly created word dating from 2007, inspired by modern depictions of octopus mermaids like Ursula from the Little Mermaid. The word is a distortion of a similar comic book character named Cilia. So technically, there are no legends or original names.
Comment: I found this very useful. I am following up on several of your suggestions.
Answer: In short, not that im aware of at this time. But, there are a lot of various creators in Greek myths that are similar, or usually depicted in a similar way.
https://en.m.wikipedia.org/wiki/Ichthyocentaurs
https://en.m.wikipedia.org/wiki/Cetus_(mythology)
https://en.m.wikipedia.org/wiki/Scylla
Greek/ Roman myth had a lot of these, sort of. The old frescos and statues of mermaids usually had sea serpent tails, not the pretty fish tail we usually imagine. So I think the old myths of mermaids were something in between modern mermaid and cecaelia. They had long serpent tails that resemble tentacles, and occasionally would have multiple tails. There also were apparently 3000/infinite sea nymphs, and they often have all kinds of different forms: mermaid, human, or a mix of human and animal parts, or even sea monsters or forces of nature like a whirlpool, and can often change form too. So I would conclude that a cecaelia could probably fall under the category of sea nymph, as one of any infinite forms they could take.

Is there an older name for Cecaelia?


What affects the order of applications in Lauchpad?

Question: When opening Launchpad I've noticed that every page has different amount of applications laid out. Also, they doesn't seem to be ordered by any criteria (name, usage frequency or size). What are the sorting parameters for applications in Launchpad?
Answer: On a clean install, the core Mac OS X apps are originally ordered alphabetically. Newly installed apps will be appended at the back on an empty spot starting with page 2 (they will never be appended on page 1, even if there is room available, but you can ofcourse drag them there).
Apps can then be arranged manually, and they should remain in the order you sort them. However, I have noticed quite some buggy behaviors, mainly apps changing position after a reboot, and MAS updates pushing apps of the page.
I hope these will get ironed out in a coming update.
Comment: +1 for "Apps can be arranged manually." I did not realize this.
Answer: I'm not sure there is a fixed order.  When I first started LP, they were in alphabetical order.  I moved some around, combined some together, moved some to page 2 and vice versa.  That new order has stuck over many shutdown and startups, even through the SU.
When I add a new app, it shows up on page 2.  I move it to page 1 and it stays there.  It can be tricky to get them exactly where you want, as each time you move one, another moves as well.  It's kind of like trying to solve 2 Rubik's Cubes at once.
Hope this helps, even though it is just my experience and not a hard fast rule.


Why can a wallet not compute the private-key from a public-key?

Question: my goal of questions this is why any wallet not able to compute private key created with public key generate?
Comment: This seems to be about seven different questions, and I'm finding them all pretty hard to understand.  Can you try to edit your post to focus on a more specific question, and to explain more clearly what you are asking?
Comment: I'm sorry, my goal of questions this is why any wallet not able to compute private key created with public key generate?
Comment: I edited your "question" to replace the large number of broad questions with the one in your comment - I think this is more answerable. If you dislike my changes, please use the **"[edited](https://bitcoin.stackexchange.com/posts/80181/revisions)"** link above and then **"rollback"** version 1.
Answer: Your post is a series of questions, each of which I'm having trouble understanding specifically, but in general it seems that you are confused about the role of private and public keys in bitcoin. So, as a high level answer:
Bitcoin uses public key cryptography to verify that users are allowed to spend some bitcoin. A user will create a private/public keypair, and then create a bitcoin address from the public key. Any bitcoin sent to that address is only spendable if the private key signs a transaction spending it (the transaction includes the public key, so that the network can verify the signature).
The way public key cryptography works, it is computationally infeasible to work backwards from the public key, in order to find a private key. So a wallet cannot 'find' the private key for a given public key.
A bitcoin wallet can be thought of as a keychain app, because it stores the user's keypairs. So the wallet will manage your keypairs, create and sign transactions, etc. A private key is not used to sign into the wallet, for that you would use a secure login system (PIN, username, password, 2FA, etc, depending on the type of wallet).
To keep bitcoin safe, it is best to keep your private keys 100% offline, using hardware that never connects to the internet to generate (and potentially store) the keys.
With this setup, there is no reason to specify an 'owner' of an account or wallet, the network only cares about whether or not a signature is valid.
Any good wallet software will generate keys using a proper random number generator, and the keyspace is so large that the chance of ever generating the same private key twice is pretty much zero. The only way to create the same keys in two wallets is to either create the key in one wallet, and then import it to the second wallet, or use an HD wallet architecture and then use the same mnemonic seed phrase to create multiple wallet instances.
Comment: I edited the original question pretty drastically, If you feel I have undermined your (as usual excellent) answer, please rollback my edits.