How can a mute cast spells that require incantation during medieval times?

Question: In order for magic to manifest in this world, one has to recite a specific incantation following a visualization of the anticipated result, and only then will the magic occur. Amazingly, many students from the special school of the disabilities, especially the mutes, seem to be able to perform magic unaided. This appears illogical because, in order for magic to be performed successfully, one must not only speak intelligibly but the pronunciation must also be accurate! Since the invention of  voice synthesizer and electronic recorder didn't happen until much later, how do the mutes cast magic spells which require an incantation?
Comment: "*this appears illogical because only for magic to be performed successfully one must not not only speak intelligibly the pronunciation must also be accurate!*" then logically, this requirement is not actually real.
Comment: As far as I understood, mute people in medieval times were seen as 'unteachable' and 'dumb' in the sense of having no intelligence. So if someone was born without the option to learn to speak, it was very likely that they would never learn enough to need those incantations. Having lost speech as an adult, they would likely face a lot of problems and not being able to do magic would only be a small one.
Comment: I'm voting to close this question because without knowing how the magic system works, we cannot answer this question without brainstorming, and building a magic system for the OP. Normally we try to leave old question alone but when they're referenced as justification for other inappropriate questions they should be closed to give new users a consistent experience with this site.
Comment: If they can use magic without reciting an incantation, that likely means that either reciting the incantation isn't actually necessary to perform the magic or that it is but one of the ways one can cast spells. Given how magic is highly variable in how it works and what it can do, it'd not come as a surprise if there was more than one way to manifest it. Kinda like how there are several different programming languages.
Comment: Why are you asking us to solve the logical inconsistencies between your story and your magic system?
Comment: They basically need the vocalize enchantment from AD&D, the only spell that required no verbal components, but then eliminated the need for verbal components.
Comment: @Willeke post it as an answer.
Comment: Where is it written that "incantation" requires voice, not "merely" thought? I thought it was written by you, so please go back to John's comment… By the way, what did "… following a visualization of the anticipated result, and only then will the magic occur…" add, but length?
Answer: Ravens!
Just as blind people can be given a well-trained guide dog, those who cannot speak can be given a trained talking raven.
In your scenario, this type of raven has been bred over centuries to be the best possible of mimics. They are trained from an early age to recite incantations in response to hand signals.
The requirement of magic is that the voice must come from close proximity to the thought. The raven perches on the mute mage's shoulder and that is just as close as the person's vocal chords are or would be.
Even ordinary ravens are capable of this to some extent. Just imagine how much better they would be after generations of selective breeding and maybe even a little magical enhancement.
Ravens can talk! (video)
Comment: @David Mulder - That's an ordinary, non-bred, non-magical raven.
Comment: Considering how often trained talking birds are barely intelligible it feels like a huge stretch to claim they fulfill the "must not not only speak intelligibly the pronunciation must also be accurate"-requirement.
Comment: So, basically familiars. Better than a cat, not quite as cool as a pseudo-dragon.
Comment: @David Mulder - If you watched the video, the bird spoke its few words extremely accurately and intelligibly. Given that ravens are *physically* capable of making realistic human voices, and given that this is a world of magic, I don't think talking ravens are unlikely.  High-level talking ability can be attained by breeding only the best talkers and by the use of magic to increase their linguistic abilities.
Comment: For a few more syllables, try [here](https://www.youtube.com/watch?v=kf42vpQMJ9o) —  a "raven" at Knaresborough Castle saying "Y'alright love?" and "I'm alright", very convincingly and comprehensibly — at least for listeners used to Yorkshire accents.  (In fact it's not the usual Common Raven, but a [Pied Crow](https://en.wikipedia.org/wiki/Pied_crow), a closely related African corvid species.)
Comment: Allegedly magpies can also learn to mimic voices, so accurately that they can go as far as imitating a particular person's voice and fooling people that it is them.  My only source for this is "My Family and Other Animals", though.
Comment: @chasly-supportsMonica In the video I saw a raven saying 'hi' pretty well and saying 'hello' in a slightly off way. Here is the first video I could find of a raven trying to replicate a couple more syllables: https://youtu.be/Rk0jyySGMck?t=29 Without the subtitles (as is the case in the second half of the video) I am pretty sure I wouldn't be able to guess what the raven tried to replicate.
Comment: She says "hello" and he translates into Raven, and she acts like he did something wrong.  Then he says "Hi" and she acts like he did something wrong.  Humans just can't recognize when two words have the same semantic meaning. :)
Answer: I guess the Pied Piper of Hamelin came out of this school.
The trick is being able to find a translation of the spell which works well when it is casted by playing the appropriate sequence of notes in a musical instrument, be it a piper, a flute, a harp or any other instrument with a sufficient extension.
Once the key is properly played, the spell is activated.
Comment: "In order for magic to be performed successfully, one must not only speak intelligibly but the pronunciation must also be accurate"  As much as this is a great justification for the Magic Music Trope (https://tvtropes.org/pmwiki/pmwiki.php/Main/MagicMusic), it does not actually seem to answer the OP's question.
Comment: @Nosajimiki What about an instrument that works like a talk box (https://en.wikipedia.org/wiki/Talk_box)? This would mean the instrument replaces their vocal folds, leaving them to pronounce the incantations.
Comment: I'm reminded of people who are able to whistle into the phone instead of dialing with buttons. The tone is what's important, and pushing the buttons just creates the tones.
Answer: Words aren't important
It was never about the incantations but the mindset formed saying the words.
In the Marvel Movie Doctor Strange, Strange says to the Ancient One he can't cast due to the injuries to his hands at which the Ancient one shows him a caster missing a hand completely.
Magic is all in the mind. Incantations, mystical ingredients, hand movements, artifacts all do nothing except assist the person to reach the correct state of mind to cast the spell exactly like Dumbo has a "magic" feather that helps him fly.
Comment: This is my favorite, go-to explanation. Any highly skilled magic user should be able to forgo the "teaching tools" that are verbal incantations and somatic gestures and simply freely cast instead. This also neatly explains how magical beasts are able to accomplish basic magic (breathing fire, cloaking in shadows, blink teleporting, or etc) despite not being able to speak or read.
Comment: Or the Dresden files, where the 'spell' is entirely irrelevant; all it does is help focus the mind. No set spells. Each wizard has their own personal incantations.
Comment: @Dragongeek - Sadly though, this is not an answer to the question. It is explicitly stated, *"In order for magic to manifest in this world, one has to recite a specific incantation"*
Answer: Nobody realized it is not the sound that is important, but the magic is gesture based - and specifically, the Magic Recognition System is tuned to very accurate movements of your lips and tongue (who said gestures have to be performed by hands only?). For the speaking folk, the "precise pronunciation" is just a side effect of this precise mouth movement. And as everyone who learns foreign languages knows, phonemes you learn in your childhood influence very much the set of phonemes you are able to reproduce accurately (AKA "having an accent"). Thus assuming you learn the magic in your adulthood, the speaking folk has quite a trouble mastering weird and quickly changing mouth shapes, but the mutes are not hindered by their ingrained language (unless they are mute because of a physical deformity, like missing tongue or equivalent).
Comment: Missing, or *cut out* maybe.  In a world where it's known that a mage's power comes from their ability to speak, one would think that a common punishment for a captured mage would be to cut out their tongue to prevent them from casting spells.  (Imagine said tongue-cutter's surprise when the mage learns they still have power despite having lost their tongue...)
Comment: +1, we could also add that the magic follow the same path than the sound do, even if the vocal cords doesn't works
Answer: Sign language is as legitimate a language as any spoken one.  The same parts of the brain are used in the "recitation", and that's all that's necessary to cast the spell?
And, yes, there's no reason sign languages couldn't have existed in the Middle Ages.  Deaf communities naturally create them ex nihilo if necessary.
Answer:
Since the invention of voice synthesizer and electronic recorder didn't happen until much later

As a general world building rule, in any system where you have magic but lack a technology that would be helpful to your plot, you can usually find ways to replace the technology with a magical equivalent.
Need to fly but don't have planes? Use a flying carpet.
Need long range communication, but don't have phones? Use a palantír.
Need an army of killer robots, but don't have robots? Build constructs.
So, just having a lack of technology does not really preclude your setting from having any modern wonder you want, including voice synthesizers.
To resolve this, have mages who are able to speak use their magic in lue of technology to record their voice performing incantations into magical stones, scrolls, wands, or what ever best fits your setting.  Then when it comes time to cast a spell, the mute mage need only tap the enchanted object, and it will recite the spell while he performs the necessary gestures.
A Possible Frame Challenge:  If your setting has healing or transfiguration spells, you will want to address the elephant in the room about why you would ever have a disabled mage to begin with. If a disabled mage gets to the point where he is casting magic, his first priority will probably be correcting his maledy; so, the very concept of the Special School of the Disabilities may actually be flawed unless you put some very clear limitations on what magic can do in your world.
Answer: Define "mute"
There's a common trope in fiction about someone having their tongue cut out to prevent them being able to talk.  Shakespeare used it, and he got it from Ovid, who probably got it from somewhere else.  Of course you'll find it in Game of Thrones as well.
And it's entirely factually incorrect.  I have personally met a girl who had no tongue, and she could talk intelligibly.  It took a bit of work to "recalibrate", but it was doable.  Her speech was rather similar to that of some people with cerebral palsy, who may not have the necessary control over their tongue for fully "normal" speech.
The sounds we produce in language come from breath control, from the vocal cords, from the tongue, and from the lips.  The loss of any one will certainly be an obstacle to fully "normal" speech, but it need not prevent it.

If you eliminate the tongue, you still have access to all vowels, to the "plosive" letters B, M and P, and to the "fricative" letters F and V (and S and SH by using teeth instead of tongue to restrict airflow).  With a bit of work, CH sounds are OK too, and sharp exhalations (using breath control) can fill in a bit for some other sounds. If your incantations can be limited to those sounds, there's no reason someone without a tongue couldn't still perform perfectly well.

The loss of lips would limit different sounds.  In this case the "plosive" letters are lost, and some "fricative" letters.  Teeth can still substitute to some extent though, and mouth shape is still enough to produce vowels reasonably effectively.  If your incantations are all about vowel sounds, that will still work perfectly well.

The loss of vocal cords will naturally reduce the volume - but whispering is (basically by definition) talking without engaging your vocal cords, and we all know that works.  Some letters require vocal cords to be produced - the difference between "f" and "v", or "s" and "z", is down to your vocal cords.  If your incantations don't need those sounds, or those sounds don't need to be distinct, they will still work.  This would also be a clue that only a low minimum level of volume is necessary for an incantation - Gandalf could whisper "you shall not pass" and it would be just as effective as declaiming it forcefully.

Basically, only the complete inability to consciously control breathing would prevent any speech.  Anything else, people can deal with to some extent; and then it simply depends on whether what's lost in translation is important for your magic system or not.
Finally we also need to consider selective mutism.  People may be unable to talk in some settings, but have no problems in others.  Someone with selective mutism may be unable to talk to other people, but be perfectly able to voice incantations.
Comment: How can you do an S sound without a tongue? Feemf wawew impoffibwe.
Comment: @StianYttervik Close your teeth and blow - that gets you a perfectly good S.  I'll edit the answer to make that clearer.
Answer: Mute people are generally able to whistle. They may use a whistling language such as Silbo Gomero in lieu of a regular spoken language to form the incantation of a spell.
Alternatively, they may use pasgas™ for the incantations.
Finally, it may be that the visualization is what is important. As you visualize, you must also hear the incantations with the "ears of the mind", much like you can recall and "listen" to a song inside your mind. Speaking or singing an incantation is just a surefire way to get the proper incantation in your mind. Mute casters have trained so as not to need to speak, they just hear it inside their heads and thus are able to cast successfully.
Comment: +1 for mentioning Silbo Gomero, which I had never heard of before
Comment: Another whisteling language is  kuş dili (Bird Language) from Turkey https://en.wikipedia.org/wiki/Turkish_bird_language
Comment: Or watch the new DOTA animated series on Netflix for a mute protagonist using a whistling language
Answer:
Wikipedia tells me in the Tibetan Buddhist tradition, spinning wheels with prayers written on them has much the same effect as orally reciting the prayers.
Perhaps mutes have discovered something equivalent to speaking the incantation that doesn't need them to speak.
Perhaps the technique is kept secret by mutes, out of solidarity: All their friends from the school for mutes are keeping themselves employed as spellcasters using the secret technique, and revealing it would leave them all unemployed.
Or maybe the technique is something well known, but only available to mutes - maybe making your vocal chords resonate with the magical aether allows you to subvocalise your incantations, but you've got to go 90 days without speaking to achieve that resonance.

Or you could make mutes' extra ability religious in origin - sure, in our world monastic vows of silence are mostly about quiet contemplation and even the quietest religious orders talk some of the time. But maybe in your world there's a god-like power who just really likes silence, even without worship of contemplation. It could even be a mysterious forgotten god, and mutes have satisfied it by coincidence.
Answer: Language in all it's forms
There are two requirements: incantation and visualisation.
An incantation is a series of words that form a spell. An incantation is thus just as valid on paper as spoken. That means the incantation can be done in any form that represent those words. On paper this can still be difficult, as some of the subtleties have to be described instead of written down ("It's leviosa, not leviosa). Still possible if you devote some more time to the written language, but difficult.
Some forms like sign language could add these subtleties in each movement of the hand for example. So any broadcasting of the incantation of any form of language is valid!
Answer: Frame Challenge: Translators May Be Necessary
If you decide to make magic more mental than physical, Thorne's answer is correct. If music, ravens, or gestures could do the trick, those respective answers will be correct. However, you said one has to recite the incantation but mutes are casting regardless, seemingly without aid.
Well, guess what? The term "mute" today is specifically applied to a person unable to use articulate language due to deafness. And deaf people can speak, it's just very difficult to learn how to make the sounds and know what you're saying when you can't hear. In other words, deaf people should be able to chant and therefore cast just fine, albeit with more effort.
Alternatively, if by "mute" you mean anyone who through a mishap or genetic disorder cannot speak, being mute does not necessarily mean being unable to create sound. Think about it; breathing in and out makes a sound now doesn't it? And whistling doesn't require vocal cords at all! Therefore, mutes can create a language of their own based off those sounds and cast with it.
Breathing could be used in a sort of Morse Code, with short, forceful puffs for dots and longer, drawn-out breaths in between. Whistling could be used to sing a tune, and if the tune corresponded to musical notation for a spell, it could count as an incantation. Or you could have a translator.
Seriously, what's wrong with a translator? In Harry Potter, one of the most popular stories about mages, it's technically possible to cast without a wand, but few people ever do because it's so very difficult. Perhaps most mutes are the same; they need a translator to recite the incantation they're signing, but they also know some mutes, through extensive training and sheer force of will, can cast with only their thoughts.
The fact that the mutes are seemingly unaided could come from a telepathic link; if magic is an expression of who you are (just like your unique way of speaking), then translating for someone could forge a powerful bond between the translator and the speaker. Basically, when the mute wants to cast, the translator senses their intent and speaks for them.
You may not like this idea, but it has so much story potential. Perhaps a mute-translator pair casts stronger spells naturally, because both are contributing their will and/or mana to the casting, or perhaps they share the cost of spellcasting with each other. It could even be both!
This mute-translator pairing could also serve as a check on powerful mages; just as the translator gives voice to a mute's will to enable their casting, a mute can do the reverse (give silence in the place of speech), therefore preventing their translator from casting. All in all, this was a very interesting question and I hope my ideas help you.
Comment: Do some mages look down on translators from a point of superiority and see them as nothing but a tool, unworthy servants that are not welcome amidst magic users? On the other hand this might be the only way for people to rise to the privileged life of the mage caste, if they are not born with the gift (if magic can't just be learned by anybody). Siblings teaming up (one mage, one speaker) could proof the most effective because they know each other so well.
Comment: On the other hand this could lead to an ancient heredetary ritual or artifact allowing a non-mage to act as a parasitic "translator" for the force of an enslaved, unconscious mage (a bit like the blood magic in game of thrones).
Comment: The telepathic aspect could also lead to the role of translator being a punishment (similar to the spouse of a Confessor in the Sword of Truth series), basically getting used and possesed. This could even vary between cultures or only be done by "dark" wizards. One especially powerful mage might even speak through whoever is near, resulting in random people in the room or a whole crowd answering. Not being able to perform magic just by himself, he would need one enchanted item allowing the telepathy and from then on just speak through foreign tongues.
Comment: This also allows for a more ***separation of powers* approach of magic** - both parties (the translator and the mage) have to agree on an adequate action, none of both is able to just lash out because of their emotions. This could either lead to an order or socienty of mute magicans (maybe a neighbor country) or to a punishment for evil wizards, being silenced (by a magic ritual or by cutting their tongue out), allowing them to do amends by using their rare magic gift for good, while reducing the danger of them committing more crimes on their own (basically magical community work).
Answer: Magical compulsion.
Some people lack the ability to speak due to paralysis of the larynx.  They cannot send nerve signals to make themselves speak.
However, a magical spell can be cast on them to force them to speak, whether they like it or not, operating their muscles according to that caster's dictate.  That spell can even be cast in advance, to force them to speak the incantation when they make a specified gesture.
The dark practitioners of that grim school of thaumaturgy are more than eager to demonstrate that they can transform the lives of the disabled, just as designers of brain-computer interfaces wax enthusiastically of their plans to improve the lives of paralyzed veterans.
Answer: Not sure if you find this applicable, but in Dungeons & Dragons, there's a metamagic feat called "Subtle Spell" which allows the caster to disguise material, verbal or somatic component of the casting (or was it all three at once?), so technically a mute character could cast the spells non-verbally with this feat.
Answer: I also include and work on the base of other answers, giving credit to their original authors and linking them.

What Is Your Magic Based On?

Do you have to be born with a gift (like the wizards in Harry Potter)?
Can everybody learn magic? (Maybe with a little natural
talent involved, like music or complicated mathematics or any craft; a simple fire spell might be as common as matches!)
Maybe there are different kinds of magic in different parts of the world, either forgotten, banned, not yet detected or rejected by other societies.
In Harry Potter house elves use a different kind of magic to which different rules apply, in The Last Airbender the different elements are controlled in different ways.

This might affect, if the spell just helps the magic user to focus and channel his own magic or if some sort of articulation is needed.

Visualizing Magic
Another big question is, if you need to simply visualize / articulate the content of the spell somehow, or if you need actual actual words/language.
Non-verbal
As L.Dutch already mentioned, there are more forms to express yourself in detail, without language...
Music lets you feel the emotions and images the artist wants to convey.
In Asia and the arabic world calligraphy is an eminently respected craft. At first glance you might want to distinguish the spoken / performed magic from the magic texts. On the other hand there is a long cultural tradition of belief that writing holds magical powers, from ancient Egypt to the Great Plague of London in the 17th century when the spell ABRACADABRA was used as a safety measure. And (written) magic symbols, sigils and summoning circles are commonly used in fantasy.
Different articulations to perform magic might be distinct to different cultures, with native tribes using ritual dances (e. g. rain dance), while master craftsmen are able to incorporate simple blessings or defense magic into temple guardian statues  and lucky charms.
Developing that concept further, every art form and every means of communication holds the potential to envoke magic, however, over time rituals and spells have been passed through by famous teachers, setting the foundations for the different magic traditions in your world, as manyfold as those in our very own.
Actual Languages
If the precise recitation through actual language is needed, this could also include whistling (mentioned by The Square-Cube Law) and sign language (mentioned by Trioxidane and Robert Larkins).
Aside from the mutism aspect it makes a huge difference in general,

if it is only important to understand what you are saying
(every mage casts in their mother tongue),
if there is only one magic language (like in Eragon)
incantations work, even if you don't understand the language you use
(like the Sectumsempra spell in Harry Potter VII).

Another question is, how intricate spells are: Just controlling/summoning something by one word ("fire!") and the thoughts on how you want to use it shape its form (a wall or peak or blade of fire) or does the magic effect have to be described more detailled or with stipulated hexes ("giant wall of flames!").
Magic users could invent their own languages, making it impossible for enemies to foresee what attack to parry. They even might develop a language that use the same words of an existing language but with switched meanings (saying "fire" and creating a blizzard). Or simply thinking outside the box and repurposing magic spells in a way an observer can't predict the outcome (casting "water" to stop the bloodflow of the enemy's body).
At this point I would like to reference a concept of my own from another question, the spellsword, comparing curses to new commands in a computer program:
Instead of always having to cast "a flaming sword of three feet length should appear in my left hand right now" during battle, you could (depending on your magic system) cast a curse like "a flaming sword of three feet length should appear whenever I say the codeword abracadabra or make this special hand gesture".
A curse being placed over something beforehand and being activated, when something is done (stealing the cursed Aztec gold, Sleeping beauty touching the spindle etc.)

Mute Mages vs. Spell Casters
Verbal magic might be easier and safer but also limits the user to the spells he has learned and especially how he learned to apply them, making it harder to think out of the box, while nonverbal magic is much harder to master but allows a more intuitive and free approach. A spell caster casts fire to burn an enemy, while a mute magican just disintegrates the enemy (Thanos style). A spell caster either uses the spells for "rock" or "fire" to reshape a boulder while a mute mage just reimagines the outcome. Therefore maybe mute people might be less likely to master magic but those who do are outstanding.
It could be possible, that verbal and nonverbal magic have different weaknesses and strenghts, e. g. non-verbal magic being better suited for creating, while verbal magic allows quicker fighting.
Also possible: Not being able to speak generally elevates the magical senses (a disabilitiy leading to other heightened abilities).

A Question of Society
There can be reasons why non-verbal magic is not accepted in society although not being much different in effect. No world is perfect and each has its own forms of exclusion, injustice and thoughts of surpremacy, cf. the historic role of women or white surpremacy.

Words stand for control, order and tradition.
The first known grammar was an attempt to preserve the original language of holy texts. A quasi-religious, quasi-military magic order could be interested in maintaining the sacred order of yore. Compare, as an example, the various religious secessions, reformations and counter movements that have been bloodily put down by the major religions throughout history.
It is also a question of teaching methods and educational understanding:
Either seeing unfit children who keep their fellow students back or children who need special support to unlock their potential.
And, as Willeke mentions below, historically mute people were taken for stupid.
(Btw. I didn't think of that argument myself but didn't want to omit a good point after I read it)
Magic that solely relies on focus and willpower is more dangerous (imagine thinking a death curse while suddenly being distracted by your hot spouse).
The use of magic could just be deemed unthinkable for mute people in a society centerd around magic spells, just think of the role of women in religion, society and war over the last couple thousand years. There might even have been some famous exceptions without changing the overall view of the people (cf. historic exceptions of female leaders and warriors).
Here, mutism might be seen as a large humiliation.
There was the thinking, that the appearance of a person matches their
character - someone hidious must have a terrible character, deseases and desasters are a punishment by God and humans are not allowed to interfere with
divine will and fate. Maybe (in your world) lore has it, that if a child with magic
abilities is born mute, this is divine intervention to prevent the
world from a powerful evil wizard or to punish you for your past life (cf. the Indian tradition of rebirth and social castes or the positions one was born into in medieval Europe).
Verbal magic could be part of an honor code: The performer is revealing themself and enabling the opponent to react, similar to the regulation of concealed weapons or the Geneva Conventions or the difference between a honorable duel an a dastard murder. This also proves a magic action to be a willing performance, not just a lack of control over one's magic powers (cf. obscurus in Harry Potter).  In Eragon a magic duel consists of an attacker and a defender reading the attacker's mind to be able to defend themself from the anticipated strike.
Verbal magic might be considered more civilized in comparison to the "wild" tribes performing intuitive magic (cf. colonial Europe).
There might be a rivaling empire, approaching things very differently (some being evil, some bad, some just different) E. g. commonly accepting non-verbal magic (more inclusive than your kingdom) while also commiting  human sacrifices (evil). Therefore non-verbal magic is connected to the evil and wrong practices of the enemy.

To sum up:
Mute children require more effort (a personal tutor, ideally with the same handicap, as the academy refuses mute acolytes) by the parents who are ashamed and disappointed by their offspring and underestimate them. Furthermore it is a sacrilege, according to society, religion and tradition. So how often do children actually find their way into the special school for unusual circumstances? How widespread is the word of that institution at all? Even if mutism doesn't make that much of a difference on a magical level.
This might change, if e. g. a war or a loss of mages boosts the need for more, through a social revolution or a mute hero or royal successor. However there is no guarantee.
Answer: Its not the sound that actually matters, but instead the mouth movements.
In your case the magic is drawn out of the body when you breath. This magic is without an purpose so just "sits" near the breather who then breaths it back in in the next breath. However, if you make the right mouth movements (which in a normal person just so happens to also be recognizable speech) the expelled magic now knows what to do and goes and does something useful.
Comment: I like the flavor of the magic being associated with breathing in this one. I guess for this to make sense, you need to move your lips, tongue, and [subvocalize](https://en.wikipedia.org/wiki/Subvocalization), but no actual sound is required.
Answer: A common concept in Magic is the use of familiars - an animal with which the caster has an extra-sensory connection.  Using the Raven example from chasly's answer, if a mute person has the aptitude for magic, they are paired with a familiar capable of speech.  They then use their extrasensory (psychic) link to speak through the familiar.  This provides the full combination of framing the thoughts in their minds, exercising the power of their will,  and voicing them aloud (through the familiar), and leaves their hands free for any gestures that may also be required.
Answer: A friendly wizard visited the school for children with special needs, and cast spells to make their lives easier. The boy with no feet was blessed with the power to levitate, the boy with no eyes was given an ugly and slightly mischievous imp that whispers in his ear what it sees, and the girl with no voice was inflicted with a curse that makes her innermost thoughts echo audibly around the room.
The teachers were annoyed by these disruptive gifts and did not invite the wizard back the next year.
Answer: To answer this question you must first define how the voice act in the casting of the spell. What part of the "saying a spell out loud" enable the spell to be cast?
Is it the vibration that get created in the air? If so, is it possible to reproduce the spell by achieving similar vibrations with instruments or props?
Or maybe the sound must be produced by the caster himself, because it need to be "imprinted by his personality/spirit/whatever". If so, does the sound has to come from the vocal cords of a person, or can be generated by whistling/clapping/whatever?
Or is not the sound the important part, but the fact that by pronouncing it you are less prone to mistaking your intention with something else (If you have read Eragon this may sound familiar)? In this case with adequate training you may be able to do it.
You mentioned voice recorders. If someone is able to cast a spell by using a voice recorder, how is he able to do that? Is the sound (vibration?), is the "intention" to cast the spell being recorded with the voice?
Answering this questions may help you come up with an answer.
Answer: Posted as a comment but I am asked to post it as an answer:
As far as I understood, mute people in medieval times were seen as 'unteachable' and 'dumb' in the sense of having no intelligence.
So if someone was born without the option to learn to speak, it was very likely that they would never learn enough to need those incantations.
Having lost speech as an adult, they would likely face a lot of problems and not being able to do magic would only be a small one.
Added to fill out the answer:
In our current western world people with handicaps are seen as fully able people who have some restrictions. But in big parts of the world today the situation is not as good. And if you go back in our history, even 100 years ago people with handicaps had it a lot worse. Not being seen as fully human is one thing, seen as valueless as a mongrel dog that has lost it usefulness was more likely in many cases.
Go back 3 or more centuries, forget special education. In fact, most people did not get any education and those who were not fully able to keep up with the brightest would not get any education if they were not the children of the very rich.
And even the rich would often not admit that they had a child less than perfect.
Of course as a writer you set your own world, you may be able to make a setting in which a person without speech can function as a full human, but it will not be as it was in our history.
Comment: Your answer came up in the voting to close as a low-quality post. I don't think it is an answer to the question (but it is a legitimate frame-shift answer) so I'm not voting to close since I think it's a fair statement to make.
Answer: This is not my area of expertise, but I believe that Deaf linguist William Stokoe hypothesised that humans might have developed sign language before spoken language. I don't know how widely this is accepted, but you could simply decide that this is true in your world.
In such a world one could imagine that magic preceded speech and that the incantations are in fact transcriptions from earlier sign language based gestures.
This has all sorts of potentially interesting ramifications.
In our own world "oralism" is known to the educational movement which sought to suppress sign language use amongst the Deaf and teach them to 'speak'. This was hugely damaging to Deaf communities, leaving many Deaf people with only a limited ability to communicate.
In your world, one could imagine a parallel to oralism which sought to suppress sign language because it gave people access to magical powers which authorities feared.
(Although as I write this I realise the risk of slipping into the Disability Superpower trope.)


Display (Sort by, compare product block) to the left?

Question: I use magento 1.7 and I wish to change the position of my "sort by" block and "compare" block to left. What should I do to accomplish that?
Comment: Can you please be more specific on what you mean by 'sort by' block? is that in the list view?
Answer: Layout moves involve unsetting from original parent & inserting in new parent.
In local.xml in your custom theme's layout folder (create if you don't have it), you should add the following:
<default>

    <action method="unsetChild" block="right"><child>catalog.compare.sidebar</child></action>
    <action method="insert" block="left"><child>catalog.compare.sidebar</child></action>
</default>

Regarding the "Sort By" block - that is a part of the so-called toolbar block which contains all of the other controls, and there are additional factors which make this kind of messy to move. The same pattern as above holds true - the block's name in layout is product_list_toolbar, the parent block is product_list, and you will need to execute these directives in the following handles:

catalog_category_default
catalog_category_layered
catalogsearch_result_index
catalogsearch_advanced_result

Ideally this would involve an update layout update directive, but it might not work in this context, as update-based directives are processed before all other directives in the particular handle in which they've been included, meaning that you would be operating on blocks which haven't been created. You could reduce the number of times that you need to call your directives by using the customer_logged_out and customer_logged_in handles which tend to execute at the end of layout processing, but this feels like a bit of a kludge.
At least you have some options.
Comment: yes you can add local.xml in your theme layout
Comment: I am using magento 1.7 and is not using theme's local.xml. I should add my local.xml in 'app/design/frontend/default/default/layout/' ?
Comment: To be clear, yes, local.xml should go into your "highest priority" theme.
Comment: Thanks. I used the catalog.xml of my template and it's work.
Comment: Just be aware that you will need to merge changes from the new catalog.xml into the custom one when you upgrade (within the 1.x branch - so you should be safe, as it is terminating after 1.8)
Answer: <reference name="left">
    <block type="catalog/product_compare_sidebar" name="catalog.compare.sidebar" template="catalog/product/compare/sidebar.phtml"/>
</reference>

write this code app\design\frontend\default\YOUR_THEME\layout\catalog.xml instead of
<reference name="right">
    <block type="catalog/product_compare_sidebar" name="catalog.compare.sidebar" template="catalog/product/compare/sidebar.phtml"/>
</reference>

Comment: Better to use *`local.xml`*
Comment: ya thats right ...you can also use local.xml
Comment: When i edit the name in catalog.xml my block is  disappeared
Comment: your layout is 3 columns or 2-columns-right?
Answer: Thanks All for yours ideas.
I moved many block that i whish to display them in the left like  product_list_related,product_list_related,product_viewed,cart_sidebar
Thats help and it is the solution who i addopted :
I changed the template used in catalog.xml.
Before it is 2columns-right.phtml

    page/2columns-right.phtml
and now 2columns-left.phtml

    page/2columns-left.phtml
i change the position of product_compare_sidebar and product_list_related to left
I changed in reports.xml product_viewed from right to left
I changed in chekout.xml cart_sidebar from right to left
Thanks :)


I had a dream with a jin

Question: First off I have to say that I am not a muslim. I'm an orthodox Christian.
Some time ago I dreamt that I was in my bedroom and there was something like a ghost that I could sense, I was feeling comfortable and protected like i had some kind of relationship with it. Then I saw he was writing things that i cannot remember now in walls and in small pieces of paper. Then I saw him in front of me as a big smoky shadow; then I woke up.
A muslim friend has told me kayer after I saw this dream that it probably was a jinn. I knew nothing about jinns before he mentioned them. Never heard of them. Since then I have dreamt of many random things every night. Also I often hear noises at night such as knocking from a closet in my room etc. Since I was younger I could feel the presence of someone invisible.
Some facts are about me ar : I am a loner. I have some kind of social anxiety and when I'm in a crowd out with friends etc I feel I want to run away to go home. I took almost 2 years to get into a relationship. Since young I had a luck with money or things I wanted. Whenever I ask for something for a help etc I always get it. It's kind of creepy. It's like I have everything but alone. Well I don't have a particular question but I don't know much about jinns and islam so if anyone is interested in telling me about my case please do so.
Also ı want to add that since the age of 5 I was having nightmares like I'm getting killed. I have seen them many times. Like shooting me and waking up thinking I was shot in soul and I need yo get in the hospital or train would run over me or watching my self dead.
Comment: In Quran you will get to see a whole Chapter named on Jinn (Surat Al-Jinn) http://quran.com/72 and its existence is truth ,they can see us and they have families like us ,, we are not able to see them but some of us have special qualities who could see them but its not easy thing to do ,,some of my realtive is dealing with it and they could reallly feel its presence could hear noises and also in dreams but like humans they have some good jinns and some bads but its not good to make some realtions with them not everyone could easily bear this.
Answer: This is sleep paralysis. I've had many of these dreams where i would feel this presence that you're speaking about and wouldn't be able to move or wake up for as long as a minute. Basically it has to do with hallucinations and REM cycles during sleep. Nothing to do with jinns.
Research into it and you'll see that many of your hallucinations are explained.
Comment: Mm i could move. I rememebr also wondering around the bed. I woke up fine .
Comment: Also i added about some dreams i had.

I had a dream with a jin


How to configure fail2ban for constant refreshes

Question: I have a page that shows election results. Some people who want to see these election results will keep clicking refresh as election night goes on. I don't want to block this traffic -- but I do want to block simple ping floods etc. on my server. How should I configure fail2ban to accommodate these different specs?
Comment: Fail2ban checks various log files for repeated login failures and bans the source IP addresses involved. That is the source of it's name - after a given number of failures move to banning. It can be extended to look for other events in logs but that is outside it's original intent.
Comment: Expanding on @Brian's comment, there's no reason why e.g. ping (ICMP echo request) floods would show up in your web server's logs, so you'd just configure fail2ban to look for (at) one but not the other. There's really nothing more to it than that.
Answer: It'd be both easier and more efficient to rate limit ICMP with the firewall:
Linux:
iptables -I INPUT -p icmp --icmp-type echo-request -m recent --set
iptables -I INPUT -p icmp --icmp-type echo-request -m recent --update --seconds 10 --hitcount 5 -j DROP

FreeBSD:
sysctl net.inet.icmp.icmplim=5

Windows:
Windows doesn't support rate limiting, only block/allow.


How do I get rid of stale water smell in my new dishwasher

Question: I have a foul stale smell in my new dishwasher, in spite of the the things they tell you to do.  I have also had the engineer out and they say nothing wrong. I am sure it is to do with the filter.  My old dishwasher filter always had lots to clean out, this one always, every time I check, has none.  Comments please
Comment: Did you try to clean it using any of  [dishwasher cleaning liquids](https://www.google.pl/search?q=dishwasher+cleaning+liquid&client=opera&hs=0FR&tbm=isch&tbo=u&source=univ&sa=X&ved=0ahUKEwju3Li_z6nVAhWhBZoKHba_AMYQsAQIPg&biw=1093&bih=651)?
Answer: I am not an expert.  But, dealing with things that smell stale (mold?, bacteria?, other?) there's a short laundry list of things I'd try.

CLR (Calcium, lime, rust removal)  Does wonders for a lot of things.
Vinegar and salt -  The vinegar is acidic in nature and kills lots of things.  The salt is also violently brutal to other things that are unbothered by acid.

I did say it was a short list.
As an aside, most laundromats will keep the doors to the machines open. This is done, even if only cracked open a bit, so the machine can "breathe" the water out, thus helping to prohibit growth.  If there is a way to chalk the door open, just a bit, to help the machine breathe, I think it might help regardless of the others.
Comment: I have done all of these. The dishwasher is new. I am convinced it is a filter problem.


When do you place the +1/+1 counter for Anafenza?

Question: If I attack with Anafenza, the Foremost and one other creature do I get to place a +1/+1 counter on the other creature or does it have to be tapped before combat?
Answer: Yes, you can put the +1/+1 counter on any creature that is tapped, including a creature that tapped to attack. The situation plays out like this:

You declare which of your creatures are attacking, including Anafenza and another creatures. You tap those creatures.
Anafenza's triggered ability goes on the stack, and you choose the target. At this point, you can choose any other tapped creature, including one that just tapped to attack.
The triggered ability resolves, and the creature gets a +1/+1 counter.
Answer: During the declare attacker step you chose with creatures attack. Then after you chose all creatures who attack this turn, you put Anafenza's trigger on the stack.
While putting the ability on the stack, you have to chose a legal target, which is another tapped creature. This can be a creature tapped prior to attacking or a creature that you just declared as an attacker. If no target can be chosen, the ability cannot be put onto the stack.


Why is it quicker to switch between threads than to switch between processes and share data between them?

Question: Why is it quicker to switch between threads than to switch between processes and share data between them? For example, in the apache web server running on ubuntu can use either the Prefork MPM (spawning multiple child processes) or Worker MPM (creating multiple threads for a single process).
Comment: Context switches between threads are faster than between processes. That is, it's quicker for the OS to stop one thread and start running another than do the same with two processes.

A context switch between processes is heavy. It means storing all processor state (registers, etc) to RAM (at a magic memory location in the user process space actually, guess where!), in practice dirtying all cached memory in the cpu, and reading back the process state for the new process.
Comment: @JohnMerlino, http://stackoverflow.com/questions/7439608/steps-in-context-switching
Answer: Quickie, incomplete explanation:
In a thread switch, there's a lot less context you need to save/load. Specifically, memory is shared. The kernel doesn't have to do any page outs of dirty pages, and VM tricks to pull in all the memory for a new process (though some specific pages may need to be pulled in). There are other process specific data structures in the kernel (say, the open file descriptor table) that don't need to be swapped out.
As a side effect, you're also much more likely to be able to use what's in the processor's caches at that point. a new process probably needs to start a cold cache.
Yes, there are tools to share memory (IPC shared memory, pipes) between processes, but none are as clean/easy as the common memory in a process. You can't grow a shared memory block like you can with realloc() and such. Anything besides shared memory means you need multiple copies of data structures, one in each process, with tricks to copy changes as needed.
Specifically, apache has multiple models for different OSes. The original model was pre-fork, giving process isolation in exchange for some heavyweight process switching. This worked fine with the UNIXes that were common at the time of it's first writing, where some didn't have threads at all.  Windows was so bad with multi-process that apache had to do threading - processes on Windows (at least at the time of apache 1.2/2.0) were too heavyweight. Linux has very light processes, where switching is close to thread switching time, so it stayed pre-Fork usually. Solaris has a complex thread "LWP" model, and does best in a hybrid thread/fork model.
Answer: I think if you read this StackOverflow link here you will understand why it is faster to switch between threads than to switch between processes.


How are Metamask web wallets traceable to owner identity?

Question: When creating a Metamask wallet as a Chrome browser extension, what are all the different identifiers that match the wallet to its owner? Since it takes a password to log into the Metamask wallet, does this mean there is an e-mail associated with the account? Are there logs kept of the IP address where the Metamask was created? What are other identifying features are there?
Answer: To connect to Metamask and recover the wallet an user needs respectively a password and a seed :

seed (also called mnemonic) : 12 secret words generated from the private key. You should never share these words, as they enable to access your funds. The seed is the only thing one need to recover his wallet.
The password : it encrypts the account locally, that means it allows the user to access his account only from the browser where the Metamask extension is installed.

To summarize, when you create a Metamask account, you are given a seed derived from your private key. This seed is encrypted locally in your browser by the password you chose, used to unlock your account. To recover your wallet on another browser/computer you will need your seed that you will encrypt with a new password.
So there is no such thing as mail registration.
What about Metamask and Ip addresses ?
In a previous release, the user account address was automatically shared with visited websites enabling them to link the Ethereum address to the Ip address (more info here : https://github.com/MetaMask/metamask-extension/issues/6325). Since the v7, a privacy mode is enabled by default and Metamask asks the user before sharing the account address with the visited website (more info here : https://medium.com/metamask/privacy-mode-is-now-enabled-by-default-1c1c957f4d57).
Comment: seed and password give no identifying information regarding the owner or their geo-location. unless there are other properties that web wallets possess, there really is nothing connecting a wallet to a human being
Comment: @user610620 I updated my answer.
Comment: Metamask just came out last month saying that they now, and apparently always did, log users' IP addresses, despite their privacy policy saying they didn't. Yikes


A UI over Windows Workflow

Question: Are there any build in UI capabilities when using Windows Workflow..
Lets say I have a workflow that takes an hour to run where different activities are happening all the time. While it's running I want to see what activity is currently active, what activities have already ran etc..
Do I have to code this UI myself or does WF have built in features that graphically show the status etc of the workflow?
Answer: To find out which state a workflow is in, I subscribe to the WorkflowIdled event and do something like this:
<code>           private delegate void UpdateDelegate();
   void workflowRuntime_WorkflowIdled(object sender, WorkflowEventArgs e)
        {
            StateMachineWorkflowInstance stateMachineInstance = new StateMachineWorkflowInstance(MyManager.WorkflowRuntime, MyInstance.Id);
            UpdateDelegate LclUpdateDelgate = delegate()
            {
                // Update the workflow state on the form thread
                if (stateMachineInstance.CurrentState != null)
                    LabelWorkflowState.Text = stateMachineInstance.CurrentStateName;
                else
                    LabelWorkflowState.Text = "";

            };
            this.Invoke(LclUpdateDelgate);
        }
</code>
Answer: Check out the this code sample over at MSDN:
http://msdn.microsoft.com/en-us/library/ms741706.aspx
Answer: There is no built in UI.
But you can create one, either by subscribing to events on the WorflowInstance (see other answer), or by using the Tracking Service.
The former is simple to set up for a quick solution but the latter will work with multiple host processes and long running (unloaded) workflow instances.

A UI over Windows Workflow


ElementaryOS compatible with my system?

Question: I have a i7 7700k
GTX 980 Gigabyte
Asus z170i pro gaming
16 GB DDR4 G.Skill Ram
Will my parts be compatible ? I know some Linux flavours dont offer support for new pc parts.
Answer: https://www.linux.com/news/my-hardware-linux-compatible-find-out-here
It looks as if Nvida supports GTX 980 on linux: http://www.nvidia.com/Download/driverResults.aspx/77844/en-us
I found someone citing wifi issues with the onboard 22 months ago, hopefully, they have patched it by now:
https://ubuntuforums.org/showthread.php?t=2311298
same time frame, citing the same issue plus audio chip complications:
https://forums.linuxmint.com/viewtopic.php?t=212999
Some more digging (Google "linux + chip in question") or the resources in the first link, may complete the rest of your question. I know the people behind linux are constantly working to make it as robust as possible, it is likely this has been patched since these posts almost 2 years ago.
Answer: Using ElementaryOS is sure to work with your setup. I have a I5-7500 which uses the same chipset as the I7-7700K, GTX 1060 Asrock something something that again uses same chipset as the Z170i which is the z170 chipset. Talking about ddr4 ram, it doesn't really matter which company you chose, DDR4 is more or less the same no matter what company you buy from.
To install the latest Nvidia driver do this:
<code>sudo add-apt-repository ppa:graphics-drivers
sudo apt update
sudo apt install nvidia-387
</code>
after that reboot and it should work, if it doesn't work and you get a black screen if you try to login, press Ctrl+Alt+F2 at the login screen, and write
apt purge Nvidia
it will remove the driver and take you back to the original noveau linux driver.

ElementaryOS compatible with my system?


What is the difference between $0$ and $-0$?

Question: Why is there a $0$ and a $-0$? I thought zero meant nothing, so how can we have negative nothing?
Comment: The idea of $0$ being positive or negative might have to do with the confusion between $0$ and $-0$. The first answer and others state that typically $0$ is unsigned, and thus would give another reason that $0 = -0$. Since that's not the answer I was going to post, I just thought it might provide another perspective on "$0$" vs. "$-0$."
Comment: @Stahl how is this relevant?
Comment: http://math.stackexchange.com/questions/26705/is-zero-positive-or-negative
Answer: People often have an unspoken assumption, that, basically
$$\text{If it looks different, it is different}$$
until they learn otherwise, and this is just one of many cases where that isn't true. $0=-0$. And $1=1.0$. And $1/2=2/4=3/6$. And $0.999...=1$. There are plenty of cases where there are multiple ways of writing the same thing down. Writing the negative in $-0$ is perfectly possible, but redundant, because it's just $0$ anyway. So in a sense you can have "negative nothing", but it's just the same as good old regular "nothing".
N.B. In some computer systems this isn't technically the case. If you represent negative numbers with one's complement then you do in fact have two zeroes, and it is sensible to call one of them $-0$. Mathematically we still have $0=-0$ (i.e. they still behave the same way under various operations), but they're stored as two distinct numbers. This is kind of inconvenient, and so we normally use two's complement instead, where there's only one zero.
Comment: Floating point numbers also have multiple representations for zero, since in the encoding there is one bit that represents the sign of the number. Interestingly, the two different representations for zero in floating-point arithmetic actually behave differently in many implementations: `1/0` will return `Infinity`, whereas `1/-0` will return `-Infinity`.
Comment: @PeterOlson I seem to believe that this is required by IEEE 754.
Comment: @Kaz Yes, I think it is. I said "many implementations" just because there are probably some non-conformant languages, as well as some languages that always throw an exception on division by zero.
Answer: For a number $x$, $-x$ denotes the unique $y$ such that $x+y=0$. In the case for $x=0$ we have that $-x=0$ as well.
Answer: Normally, given a number $a$, the number $-a$ is the additive inverse of $a$: i.e., $-a$ is the number that satisfies $a + (-a) = e$, where $e$ is the additive identity. Since $e + e = e$ by definition of an additive identity, we see that $e = -e$. In the case of $\Bbb{Z}$, $\Bbb{Q}$, $\Bbb{R}$, $\Bbb{C}$, and related objects, $0$ is the additive identity, so $0 = -0$.
Answer: Aha, computer science question!
This shows that a sign-magnitude (or one's complement) representation is being used, leading to two zeros with a different sign bit.
(I'm ducking under the desk now to avoid being struck by projectile office supplies).
Answer: In floating point arithmetic $0$ and $-0$ are different.
If you take a positive number $x$ you will get $x/0=\infty$ and $x/(-0)=-\infty$.
Answer: To take the question (possibly a little too) literally, the difference between two numbers, $x$ and $y$ is given by $|x-y|$. Letting $x=0, y=-0$:
$$\begin{align*}
|x-y| &= |0-(-0)| \\
      &= |0+0| \\
      &= |0| \\
      &= 0
\end{align*}$$
So there's no difference between them at all :)


Xcode 4.5 - OS X Cocoa Application - Basic Web View: Load Google when opened

Question: I'm trying to create an extremely basic OS X Cocoa Application that when opens loads http://www.google.com. As basic as possible (no back or forward buttons, etc.).
I have little experience with Xcode 4.5 and I can't find any tutorials regarding a web view for OS X Cocoa Application AND Xcode 4.5. I was able to find a tutorial and create a web view for an iOS web view. I took what I learned but didn't get very far.
Here's what I did so far:

Created New OS X Cocoa Application in Xcode 4.5.2
Added a WebView object to the Window object

Based on the iOS web view tutorial I assume all I need to do is add a couple lines of code and it should work?
This is the code I used in the iOS web view (ViewController.m):
NSURL *myURL = [NSURL URLWithString:@"http://www.google.com"];

NSURLRequest *myRequest = [NSURLRequest requestWithURL:myURL];

[myWebView loadRequest:myRequest];

Any help would be much appreciated. I've been stuck on this all night.
Answer: After adding the WebView to your main window, you'll want to make sure you've added the WebKit.framework to the Linked Frameworks and Libraries for your project otherwise you'll get a linking error.
.h:
@class WebView;

@interface MDAppDelegate : NSObject <NSApplicationDelegate>

@property (weak) IBOutlet WebView *webView;
@property (assign) IBOutlet NSWindow *window;

@end

Assuming you've created an IBOutlet for the WebView named webView like in the code above, you can load a URL using the code below:
.m:
@implementation MDAppDelegate

- (void)applicationDidFinishLaunching:(NSNotification *)aNotification {
    NSURLRequest *request = [NSURLRequest requestWithURL:
                 [NSURL URLWithString:@"https://www.google.com/"]];
    [self.webView.mainFrame loadRequest:request];
}

@end

Sample GitHub project: https://github.com/NSGod/WebViewFinagler
Comment: To have the WewView autosize on the main view do: In Xcode, go to File Inspector window and uncheck checkbox given for "Use Autolayout" and switch to Size inspector you will see the autoresizing window.
Answer: add self keyword to following line
[myWebView loadRequest:myRequest];

like this
[self.myWebView loadRequest:myRequest];

try following code,it work for me,just tested

1) create new project
    2) select ViewController ,goto xcode menu
    Editor->Embed in->Navigation controller
    3)declare myWebView property  in ViewController.h

in ViewController.m write following code
   self.myWebView = [[UIWebView alloc] initWithFrame:self.view.bounds];
   self.myWebView.scalesPageToFit = YES;
   [self.view addSubview:self.myWebView];
   NSURL *myURL = [NSURL URLWithString:@"http://www.google.com"];
   NSURLRequest *myRequest = [NSURLRequest requestWithURL:myURL];
   [self.myWebView loadRequest:myRequest];

Comment: Which file do I add this to?
Comment: @user1822824:in ViewController.m
Comment: I only have AppDelegate.h and AppDelegate.m
Comment: I don't see that. I am doing this for desktop NOT iOS.


Choose function so integral converges

Question: Here we consider the function
$$I(t)=\frac{1}{a\int_{-\infty}^{t}e^{-\int_r^t \lambda (\tau) \ d\tau}dr}$$
And I am trying to find a function $\lambda(\tau)$ such that $I(t)$ converges. Here we take $a$ As constant. I have tried taking $\lambda (\tau)=\frac{1}{\tau}$. I obtained an integral whose solution did not converge. Any help would be greatly appreciated!
Comment: $I(t)$ converges when $t$ goes to a certain limit, or just $I(t)$ is well defined for every $t$?
Comment: $I(t)$ is a function of $t$. It is a variable which changes. So I am trying to evaluate the integral so I can plot the function $I(t)$ against $t$. When evaluated the function should be entirely dependent on $t$
Answer: If you're free to choose $\lambda$ to be whatever, try a simple power law.
$$
\lambda (\tau) = \tau^k\\
I(t)=\frac{1}{a\int_{-\infty}^{t}e^{-\int_r^t \tau^k \ d\tau}dr}\\
I(t)=\frac{1}{a\int_{-\infty}^{t}e^{-\frac{1}{k+1} (t^{k+1}-r^{k+1})}dr}\\
I(t)=\frac{1}{a\int_{-\infty}^{t}e^{-\frac{1}{k+1} t^{k+1}} e^{-\frac{r^{k+1}}{k+1}}dr}\\
I(t)=\frac{1}{a e^{-\frac{1}{k+1} t^{k+1}} \int_{-\infty}^{t} e^{-\frac{r^{k+1}}{k+1}}dr}\\
I(t)=\frac{e^{\frac{1}{k+1} t^{k+1}} }{a \int_{-\infty}^{t} e^{-\frac{r^{k+1}}{k+1}}dr}\\
$$
We need to make sure this all makes sense for given $k$. Everything converging and all. This is where picking $k$ comes in.
If you use $k=1$, the denominator looks like integrating a Gaussian and the numerator is sign flipped from a Gaussian. It blows up real fast but that might be okay for you.

Choose function so integral converges


Difference between FFNN and NAR

Question: What is the difference between feed forward neural network and non-linear autoregressive neural network. Do they have same structure. What is the difference in their equation
Answer: From what I understand—and please someone correct me if I am wrong—FFNN is less of a strict definition of a network and more a category that multiple networks are part of. In that sense, a NAR is an FFNN, but not necessarily the other way around. This is another "all squares are rectangles, but not are rectangles are squares" sort of thing.
But NAR is also not a single model, but rather a model type. This means that neither FFNNs nor NARs have a single equation that you could compare against one another.
Broadly, FFNNs have one-way data flows. This separates them from RNNs and CNNs that have loops built-in. NARs also consist of one-way data flows and are built on the math of autoregressive methods.

Difference between FFNN and NAR


Are there alternative options to getting an appraisal for a refinance of my home?

Question: I live in New Hampshire, USA. I'm trying to get my home refinanced and it most likely requires an appraisal (not sure the requirements), but anyway... they want $1870 for the appraisal fee! I'm aware there's a high demand for appraisers at the moment, but it comes out to about $10.38/month for the duration of my loan. Are there any alternatives? Temporary PMI? Private appraisers?
Comment: Who is the "they" that want $1870?
Comment: I assume it's one of those home loans where the interest rate is exceptionally low, but they make up for it by adding inflated fees.
Comment: Sage/Quicken(RocketMortgage). I started looking at alternative options and another was $450. I think you're right! :) Thanks!
Answer: I would shop around. The last three refi's I did (in Illinois) didn't require an in person appraisal. When I purchased, I think the appraisal fee was around $400. You may not need an appraisal at all, depending on your equity, and even if you do, $1870 seems exorbitant. It's so high that maybe $1870 is the total fees, part of which is for the appraisal. I can't imagine an appraisal by itself being that much.
Comment: I don't know if you have them, but here lenders will sometimes do a drive-by appraisal.  If their exposure isn't too high (good loan-to-value ratio) and data for the area is good, all they need is a check from the outside to make sure the value is compatible with what everyone is saying.  This seems particularly common with refinancing.
Comment: I only knew because they told me they wouldn't have to charge the full fee or enter the property.  I certainly wouldn't have noticed them
Comment: SO NewAmerican quoted me $450. He told me a story about how one time he needed to charge $2,000 for an appraisal because they had to send him out in a helicopter to the middle of nowhere in Alaska.
Comment: @ChrisH that makes sense. I suppose if they did that I wouldn't even know. If they aren't setting foot on our property they wouldn't need permission.
Answer: In almost all cases the lender will require an appraiser. And in almost all cases they want one from their network.
In some cases if the equity in the house is large they might waive it, because they perceive their risk is low. But in most cases their standard procedure requires it.
If you are refinancing with the same lender they might drop the requirement because they already have a good idea of the value of the property.
That being said a cash out refinance will depend on a fresh appraisal because they need a solid number to understand the additional risk.
If you will be counting on a loan-to-value ration of 80% to avoid PMI and you are close, then they will want a fresh appraisal.

Are there any alternatives? Temporary PMI? Private appraisers?

Getting rid of PMI is a process. You will have to wait until you have reached 80% to drop it. Dropping it may require a new appraisal any way.
There is danger regarding a private appraisal, unless the lender agrees in advance. You don't want to pay for two appraisals.
Comment: "But in most cases their standard procedure requires it." the joke from my appraiser when I did my refi was they were mostly just making sure that I didn't turn the garage into a meth lab or something. One of those jokes that are funny because there is that little hint of truth in it based on the area where I live.


How would one extract the list of public keys from Electrum wallet?

Question: I am looking for a way to extract all of the public keys associated with my electrum wallet. I am aware that listaddresses() does this for public addresses, such as 1CWX7o1Ppe4JpEpSLmuovU4HFY3D6Ay24C  - however, I am looking to extract the public keys, such as 02b96c2739e9543bdc17bbe58b73a3a9a16aedf2ed554faca9e5acf0b279f5d0e1.
Answer: You cannot get all of them in one go. You can call getpubkeys("address") for each address (or do it via the GUI by going to the Addresses tab, right clicking on an address, and selecting "Public Keys")
Alternatively, you can get your master public keys (xpub) and derive from those.
Comment: Thank you for the input!
Would I be better off generating them directly from the xPub using something that generates addresses in the same fashion?
Comment: If you're doing it often enough, having the xpub will likely help/save time. Electrum's client is open source, so you should be able to find the xpub->address code in there, and plenty of implementations exist in other languages
Answer: The following code worked for me in the Electrum console and was able to give me all of the addresses in a single command.
for i in listaddresses(): print(i + " = " + getpubkeys(i)[0])


Topological counterexample: compact, Hausdorff, separable space which is not first-countable

Question: I need an example for a compact, Hausdorff, separable space which is not first-countable.
I tried to look for it for some time without success...
Comment: Check [this site](http://www.austinmohr.com/spacebook) out.
Comment: $\beta \omega$ satisfies the first three properties clearly. It takes a little work to show it is not first countable though.
Comment: @David Mitra: This is a fantastic site. You should write this as an answer so that more people know about it.
Answer: The space $I^I$ (i.e., product of $\mathfrak c$-many copies of the unit interval $I=[0,1]$ is a compact Hausdorff space.
It is not first-countable, see here: Uncountable Cartesian product of closed interval
It is separable by Hewitt-Marczewski-Pondiczery theorem,
see here: On the product of $\mathfrak c$-many separable spaces
As pointed out in a comment, we could also prove separability by directly showing that polynomials with rational coefficients form a countable dense subset. See also this answer for a similar approach in a slightly different space.
Comment: No big theorem is needed to show this space is separable. For example, polyomial functions with rational coefficients do the job. Given $\epsilon > 0$ and finitely many points $a_i,b_i$ in $I$, there exists a rational polynomial $p$ with $p(a_i) \approx_\epsilon b_i$.


How can I use Overwatch with no internet connection?

Question: This question has probably been asked before: how can I play Overwatch without WiFi? When I do have WiFi, I can play against AI, but that's kinda pointless if I can just play online; with friends. So, is there a hack or game-code change I can use to play with AI with no  WiFi?
Comment: We're not going to help you hack the game.
Comment: Overwatch is an online game. Online games require internet. Period. There are no hacks, workarounds, or exploits that will allow you to download the server code and play locally without internet. This is true for nearly every single online-only game in existence.
Answer: When playing against AI, you're still playing on a Blizzard server. There is no way to play against AI locally.
Comment: There's no way to download the AI code locally?
Comment: @pagie_ No, there isn't.
Answer: When you launch overwatch, there's a brief period before you hit the main menu when you're connecting to a server. You literally cannot get to the main menu without connecting to a server.
You're also mentioning hacking or game-code changes in relation to a blizzard game, which they have mentioned ammounts to cheating in any capacity


focus() in Edge browser

Question: I am using popup.focus() to focus a popup window after a button is clicked. The focus() is working fine for all the browsers except for ****EDGE**** browser. The issue I am facing is intermittent. At times I am able to view the popup window (child popup dialog box) on the browser and at times behind the browser i.e. on the desktop and I am able to identify that the popup is open by the flashing on the task bar.
Any suggestion would be really appreciated.
var popup = new PopupWind(url,'config')
popup.setFeature('height', height)
popup.setFeature('resizable', 'no')
popup.setFeature('scrollbars', 'no')
popup.setFeature('left', xLoc) // IE
popup.setFeature('top', yLoc)
popup.setFeature('screenx', xLoc) // NS
popup.setFeature('screeny', yLoc)
popup.open()
popup.focus();

I tried using this to make focus() work in EDGE but it did not
popup.blur();
setTimeout( popup.focus,0);

Comment: @KalebAnderson waiting for update from EDGE. this might solve the problem.
Comment: you might need to post a jsfiddle to help debug your issue.
Comment: Did you ever figure this out?
Comment: This is still an issue, I can't get it to work even now! [Link](https://developer.microsoft.com/en-us/microsoft-edge/platform/issues/6274497/)
Answer: I have a solution/Hack
Please open link with the solution in your Edge browser
https://codepen.io/PocketNinjaDesign/pen/OgbQXO
The window wasn't focusing intermittently!
The issue is that you need to mess with the focus of the page.  if you open a popup and then focus on the parent page, then move the parent page even just 1 pixel.  Clicking the button will focus on the popup again.
So for a crippled web browser where window methods don't seem to work what can you do other than wait for a few years for them to fix their focus() bug.
Well, the hack is to remove the focus from the parent window by generating a temp empty popup window.  Then focusing on the main popup and closing the temp popup.  All wrapped by a setTimeout @ 300ms, any lower and it didn't seem to work for me.
HTML

Open Popup

Focus on Popup

JAVASCRIPT
// This is the main guts of this page!
var isMSEdge = function() {
  return window.navigator.userAgent.toLowerCase().indexOf('edge') > -1;
};

$(function() {
  var $bttn = $('#button');
  var $focusBttn = $('#focus');
  var tempWin;
  var testWindow;

  $bttn.on('click', function() {
    testWindow = window.open('', "pocketninja", "width=300, height=300");
    $focusBttn.show();
    $(this).hide();
  });

  $focusBttn.on('click', function() {
    if(testWindow && isMSEdge()) {
        tempWin = window.open('', 'temp', 'width=1, height=1');

        setTimeout(function() {
          testWindow.focus();
          tempWin.close();
        }, 300);
    }
    else {
      testWindow.focus();
    }
  });
});

Comment: still unable to focus on the child window in case of Edge browser. Any other fix ?

focus() in Edge browser


In MS Project :the resource calendar did not show up in the gantt chart but it shows at the resource usage sheet

Question: the resource calendar did not show up in the gantt chart but it shows at the resource usage sheet:
i mean that, i assigned the Friday and Saturday as days off in some resources (i am using the resource calendar ) but at the gantt chart it shows that this days are a working days and calculated the total duration according to that.
Comment: Just a suspicion: Are you using more than 1 calendar?
Answer:
the resource calendar did not show up in the gantt chart but it shows
  at the resource usage sheet

The green shading on the Gantt chart is based only on the Project Calendar* and is for display only. However, Microsoft Project does take into account the Resources' base calendars and Task calendars (if used) when scheduling tasks (e.g. determining the start and finish dates).
See Work with calendars in Project and Understanding the Power of Calendars in Microsoft Project for more information.
Note: the Gantt Chart Nonworking time can be formatted to show shading for a different calendar; the default is to shade based on the Project Calendar.


When to use RxJava in Android and when to use LiveData from Android Architectural Components?

Question: I am not getting the reason to use RxJava in Android and LiveData from Android Architectural Components.It would be really helpful if the usecases and differences between the both are explained along with sample example in the form of code which explains the differences between the both.
Answer: Regarding the original question, both RxJava and LiveData complement each other really well.
LiveData shines on ViewModel layer, with its tight integration with Android lifecycles and ViewModel. RxJava provides more capabilities in transformations (as mentioned by @Bob Dalgleish).
Currently, we're using RxJava in data source and repository layers, and it's transformed into LiveData (using LiveDataReactiveStreams) in ViewModels (before exposing data to activities/fragments) - quite happy with this approach.
Comment: If we understood you correctly, then LiveData is only useful for Android UI-specific implementations.  If we are just building a generic app with Clean Architecture, and sharing this architecture with other platforms, then RxJava is a better fit than LiveData?
Comment: can you suggest any working example of LiveDataReactiveStreams in your answer?
Comment: @kzotin you don't need that `observeOn`, `LiveDataReactiveStreams` does that anyway by calling `LiveData.postValue()`. And there's no guarantee your `subscribeOn` will have any effect in general.
Comment: I found this great article on big nerd ranch [Where RxJava meets LiveData](https://www.bignerdranch.com/blog/livedatareactivestreams-where-rxjava-meets-livedata/)
Comment: @IgorGanapolsky what language/frameworks do you use for generic app?
Comment: Android-independent APIs and Clean Arch written in Java/Kotlin.
Comment: e.g. following extension function converts Flowable into LiveData:

`LiveDataReactiveStreams.fromPublisher(this.subscribeOn(Schedulers.io()).observeOn(AndroidSchedulers.mainThread()))`
Comment: The LiveData also can be used with Room and repository too, not only with viewmodel layer, see the doc : https://developer.android.com/topic/libraries/architecture/livedata#use_livedata_with_room . There are many codelabs that show how to uses the LiveData with this components. See this codelab: https://codelabs.developers.google.com/codelabs/advanced-kotlin-coroutines/index.html#0
Comment: I posted a complete solution interfacing LiveData with RxJava and Retrofit using a slightly modified version of LiveDataReactiveStreams in this thread: https://stackoverflow.com/a/62057939
Comment: You can use coroutines and get rid of the hustle the RX creates.
Answer: Android LiveData is a variant of the original observer pattern, with the addition of active/inactive transitions. As such, it is very restrictive in its scope.
Using the example described in Android LiveData, a class is created to monitor location data, and register and unregister based on application state.
RxJava provides operators that are much more generalized. Let's assume that this observable will provide location data:
Observable<LocationData> locationObservable;

The implementation of the observable can be built up using Observable.create() to map the call back operations. When the observable is subscribed, the call back is registered, and when it is unsubscribed, the call back is unregistered. The implementation looks very similar to the code provided in the example.
Let's also assume that you have an observable that emits true when the application is active:
Observable<Boolean> isActive;

Then you can provide all the functionality of LiveData by the following
Observable<LocationData> liveLocation =
  isActive
    .switchMap( active -> active ? locationObservable : Observable.never() );

The switchMap() operator will either provide the current location as a stream, or nothing if the application is not active. Once you have the liveLocation observable, there a lot of things you can do with it using RxJava operators. My favorite example is:
liveLocation.distinctUntilChanged()
  .filter( location -> isLocationInAreaOfInterest( location ) )
  .subscribe( location -> doSomethingWithNewLocation( location ) );

That will only perform the action when the location changed, and the location is interesting. You can create similar operations that
combine time operators to determine speed. More importantly, you can provide detailed control of whether operations happen in the main thread, or a background thread, or a multiple threads, using RxJava operators.
The point of RxJava is that it combines control and timing into a single universe, using operations provided from the library, or even custom operations that you provide.
LiveData addresses only one small part of that universe, the equivalent of building the liveLocation.
Comment: @DanielWilson the link is not available anymore.
Comment: `The point of RxJava is that it combines control and timing into a single universe, using operations provided from the library, or even custom operations that you provide.`

But isn't LiveData lifecycle aware. If we were to use Rx, wouldn't we have to handle the lifecycle changes?
Comment: Thanks, the LiveData docs don't seem to reference a location sample anymore. There are more interesting points (with a location sample) here: http://androidkt.com/livedata/
Comment: Dude I can't remember wtf was on that link :D I like Mark Allison's sample code for a live data: https://blog.stylingandroid.com/architecture-components-livedata/
Comment: @Sparker0i got point here. RxJava is not lifecycle aware. we have to handle manually. where as in LiveData it is already taken care of lifecycle.
Comment: We can pass LiveData to another thread for example network call and then that thread can postValue in the livedata which subscriber can listen to. It also take care of Lifecycle. I believe RxJava should be used only if you have more complex cases.
Comment: You can achieve everything you mentioned above by mixing it up with Kotlin features. Admit that RX is now irrelevant for most use cases.
Comment: Kotlin's implementation of RxJava is quite good, I understand. However, co-routines and streams are not a replacement for RxJava, as it cannot handle the space-time-space multiplexing inherent in reactive extensions.
Answer: There are many differences between LiveData and RxJava:

LiveData is not a STREAM while in RxJava everything (literally everything) is a STREAM.
LiveData is an observable data holder class. Unlike a regular observable, LiveData is lifecycle-aware, meaning it respects the lifecycle of other app components, such as activities, fragments, or services. This awareness ensures LiveData only updates app component observers that are in an active lifecycle state.
LiveData is synchronous, So you can't execute a chunk of code (network call, database manipulation etc.) asynchronously using just LiveData as you do with RxJava.
What best you can do to exploit the most of this duo is to use RxJava for your business logic (network call, data manipulation etc, anything that happens in and beyond Repository) and use LiveData for your presentation layer. By this, you get transformation and stream capabilities for your business logic and lifecycle-aware operation for your UI.
LiveData and RxJava compliment each other if used together. What I mean is, do everything with RxJava and at the end when you want to update UI, do something like the code given below to change your Observable into LiveData. So, your View (UI) observes to the LiveData in ViewModel where your LiveData is nothing but non-mutable MutableLiveData (or MutableLiveData is mutable LiveData).
So the question here is, why should you even use LiveData at the first place?
As you can see below in the code, you store your response from RxJava to MutableLiveData (or LiveData) and your LiveData is lifecycle-aware, so in a way, your data is lifecycle-aware. Now, just imagine the possibility when your data itself know when and when-not-to update the UI.
LiveData doesn't have a history (just the current state). Hence, you shouldn't use LiveData for a chat application.
When you use LiveData with RxJava you don't need stuff like MediatorLiveData, SwitchMap etc. They are stream control tools and RxJava is better at that by many times.
See LiveData as a data holder thing and nothing else. We can also say LiveData is lifecycle-aware consumer.

    public class RegistrationViewModel extends ViewModel {
        Disposable disposable;

        private RegistrationRepo registrationRepo;
        private MutableLiveData<RegistrationResponse> modelMutableLiveData =
                new MutableLiveData<>();

        public RegistrationViewModel() {
        }

        public RegistrationViewModel(RegistrationRepo registrationRepo) {
            this.registrationRepo = registrationRepo;
        }

        public void init(RegistrationModel registrationModel) {
            disposable = registrationRepo.loginForUser(registrationModel)
                    .subscribeOn(Schedulers.io())
                    .observeOn(AndroidSchedulers.mainThread())
                    .subscribe(new Consumer<Response<RegistrationResponse>>() {
                        @Override
                        public void accept(Response<RegistrationResponse>
                                                   registrationModelResponse) throws Exception {

                            modelMutableLiveData.setValue(registrationModelResponse.body());
                        }
                    });
        }

        public LiveData<RegistrationResponse> getModelLiveData() {
            return modelMutableLiveData;
        }

       @Override
       protected void onCleared() {
                super.onCleared();
            disposable.dispose();
         }
    }

Comment: See LiveData as a data holder thing and nothing else. ==> YES
Comment: Nice example. You forgot to declare the disposable and it would be nice to clear them in `onCleared`.
Comment: I consider using Rx for network calls an anti-pattern. Most things aren't streams. I know. It's a shocker. But they aren't. People who build their life around Rx say they are, but they really aren't. Unless you're using a subscription, a network call has a single result. And a stream with a single result is just dumb. It's like treating everything like a nail because you have a hammer.
Comment: Could you please explain how livedata is synchronous? As far as I know we can send Livedata object to another thread and then that thread can postvalue which observer can listen to in the MainThread.
Comment: If you again read what I wrote it means you can't work on another thread just ( YES, I used "just" even there ) using LiveData as you can do using RxJava
Comment: Isn't lifecycle a big differentiator for LiveData? You 1. describe what your pipeline needs to do and what are your end results, 2. subscribe to the outcome in "observe" clauses, AND then 3. the pipeline is only being operated if your lifecycle state allows it.
Comment: There is some nice extension functions - `Publisher::toLiveData` and `LiveData::toPublisher` (depending on the V - VM data flow) - `androidx.lifecycle:lifecycle-reactivestreams-ktx:$lifecycleVersion` mitating the `Subscriber` in Rx chains and disposing in most casas.
Comment: @funct7 Most things aren't streams -> TRUE. Though I understand that Network calls are mostly Single and not streams, but we can still use Rx for that sake of easy operators and easy handling of threads. Anyway you don't encounter streams in android that easy unless you work with real-touch events, search queries etc.
Answer: In fact, LiveData  is not an essentially different tool to RxJava , so why was it introduced as an architecture component when RxJava could have easily managed the lifecycle by storing all the subscriptions to observables in a  CompositeDispoable  object and then disposing them in onDestroy()  of the Activity  or onDestroyView()  of the Fragment  using only one line of code?
I have answered to this question fully by building a movie search app once using RxJava and then using LiveData here.
But in short, yes, it could, but that would need first overriding the relevant lifecycle methods besides having the basic lifecycle knowledge. This still might not make sense for some, but the fact is that according to one of the Jetpack sessions in Google I/O 2018 many developers find lifecycle management complex. The crash errors arising from not handling lifecycle dependence might be another sign that some developers, even if knowledgable of lifecycle, forget to take care of that in every Activity / Fragment  they use in their app. In large apps this could become an issue, notwithstanding the negative effect it could have on productivity.
The bottom line is that by introducing LiveData , larger number of developers are expected to adopt MVVM without even having to understand the lifecycle management, memory leak and crash. Even though I have no doubt that LiveData is not comparable with RxJava in terms of capabilities and the power it gives to developers, reactive programming and RxJava is a hard-to-understand concept and tool for many. On the other side, I do not think LiveData is meant to be a replacement for RxJava–it simply cannot–but a very simple tool for handling a controversial widespread issue experienced by many developers.
** UPDATE **
I have added a new article here where I have explained how misusing LiveData can lead to unexpected results. RxJava can come to rescue in these situations
Comment: "why was it introduced when RxJava could have easily managed the lifecycle by storing all the subscriptions in a  CompositeDispoable and then disposing them in onDestroy() of the Activity" - `LiveData` would dispose in `onStop` actually
Comment: @arekolek from my understand: even to handle the CompositeDispoablewe have overwrite the life-cycle methods. But in Live data all will include in single line of code. So we are saving minimum 20 lines of code.
Comment: We can define a baseFragment and define Disposable[] subscriptions() method to be overriden by all the derived fragments , call this method in onCreateView and add the return value in a CompositeDisposable, dispose that in onDestroyView, no more forgetting.
Comment: It's not only about disposing. Using RxJava, you have to dispose at onStop, then subscribe again in onStart/onResume, handle configuration changes, and do a bunch of other stuff. That's why there's so many crashes using RxJava. LiveData handles all that, but is not as flexible as RxJava.
Answer: As you may know in the reactive ecosystem we have an Observable that emits data and an Observer that subscribes( get notified) of this Observable emission, nothing strange is how works the so called Observer Pattern. An Observable "shouts"something, the Observer get notified that Observable shout something in a given moment.
Think to LiveData as an Observable that allows you to manage the Observers that are in an active state. In other terms LiveData is a simple Observable but also takes care of the life cycle.
But let's see the two code cases you request:
A) Live Data
B) RXJava
A)This is a basic implementation of LiveData
1) you usually instantiate LiveData in the ViewModel to maintain orientation change (you can have LiveData that is read only, or MutableLiveData that is writable, so you usually expose outside from the class LiveData)
2) in the OnCreate method of the Main Activity(not the ViewModel)
you "subscribe" an Observer object (usually an a onChanged method)
3) you launch the method observe to establish the link
First the ViewModel (owns the business logic)
class ViewModel : ViewModel() { //Point 1

    var liveData: MutableLiveData<Int> = MutableLiveData()

}

And this is the MainActivity( as dumb as possible)
class MainActivity : AppCompatActivity() {

    override fun onCreate(savedInstanceState: Bundle?) {
        super.onCreate(savedInstanceState)
        setContentView(R.layout.activity_main)

        val ViewModelProvider= ViewModelProviders.of(this).get(ViewModel::class.java)

        ViewModelProvider.observe(this, Observer {//Points 2 and 3
            //what you want to observe
        })

        }
    }
}

B)This is the basic implementation of RXJava
1) you declare an Observable
2) you declare an Observer
3) you subscribe the Observable with the Observer
Observable.just(1, 2, 3, 4, 5, 6) // Point 1

   .subscribe(new Subscriber() {    //Points 2 & 3
       @Override
       public void onCompleted() {
           System.out.println("Complete!");
       }

       @Override
       public void onError(Throwable e) {
       }

       @Override
       public void onNext(Double value) {
           System.out.println("onNext: " + value);
       }
    });

In particular LiveData is used with Lifecycle and often with ViewModel(as we have seen) architecture components. In fact when LiveData is combined  with a ViewModel allows you to keep updated in real time every change in the Observer, so that the events are managed in real time where is needed. To use LiveData is strongly recommended to know the concept of lifecycle and the relative objects LifeCycleOwner/LifeCycle, also I would suggest you to have a look at Transformations, if you want to implement LiveData in real life scenarios. Here you can find some use cases from the great commonsware.
To wrap up basically LiveData is a simplified RXJava, an elegant way to observe changes  across multiple components without creating explicit so called dependency rules between the components, so that you can test much easier the code and make it  much more readable.
RXJava, allows you to do the things of LiveData and much more. Because of the extended functionalities of RXJava, you can both use LiveData for simple cases or exploit all the power of RXJava keep using Android Architecture components as the ViewModel, of course this means that RXJava can be far more complex, just think has hundreds of operators instead of SwitchMap and Map of LiveData(at the moment).
RXJava version 2 is a library that revolutionized the Object Oriented paradigm, adding a so called functional way to manage the flow of the program.
Answer: LiveData is a subset of the android architecture components which is developed by the android team.
With the live data and other architecture components, memory leaks and other similar issues are handled by architecture components. Since it is developed by android team, it is the best for android. They also provide updates that handle new versions of Android.
If you only want to use in Android app development, go for the Android architecture components. Otherwise, if you want to use other Java app, like web app, desktop apps, etc., use RxJava
Comment: I've attempted to clarify your answer. If I've in any way conflicted with your original intent, feel free to edit. If you do though, please try to make it clearer than the initial revision. The last part of your answer honestly didn't make sense.
Answer: LiveData as a data holder thing and nothing else. We can also say LiveData is Lifecycle aware consumer. LiveData is strongly recommended to know the concept of lifecycle and the relative objects LifeCycleOwner/LifeCycle, you get transformation and stream capabilities for your business logic and lifecycle aware operation for your UI.
Rx is powerful tool that enables to solve of problem in an elegant declarative style. It handles business side options or Service Api operations
Answer:
LiveData partially equals to Rx Subject or SharedRxObservable
LiveData manages lifecycle of subscription but Rx Subject
subscription should be created and disposed manually
LiveData doesn't have termination state but Rx Subject has OnError
and OnCompleted
Answer: Comparing LiveData to RxJava is comparing apples with fruit salads.
Compare LiveData to ContentObserver and you are comparing apples with apples. LiveData effectively being a lifecycle-aware replacement for ContentObserver.
Comparing RxJava to AsyncTask or any other threading tool is comparing fruit salads to oranges, because RxJava helps with more than just threading.
Answer: My simple answer is don't use RxJava. It is way overly complicated and abused. For all the projects using RxJava, they are hard to maintain and hard to debug. RxJava does things asynchronously, using threads within it to dispatch the requests, in general this is totally unnecessary, and if it is needed, Kotlin coroutine does a better job in perhaps 99% of the time.


How to return back to the default view of pages in Pages?

Question: I've screwed something up with a settings and I cannot go back to the defaults. How to return back to the default view of displaying pages (page under page) instead of having them diagonally or page next to another page ? That's how it looks like rn
Answer: Welcome to Ask Different!
1) Untick the "Facing Pages" option on the right sidebar in the "Document" tab (the open tab in the picture you have shared). This should remove the diagonals.
2) Click on the "Zoom" pull-down menu on the left on the toolbar at the top and select "One Page". This should bring a next page below the previous one.
I highlighted these in red boxes in the screenshot below.
Hope these help.
Answer: This could be result of using "Facing Pages". Turn it off in the sidebar, in Document tab.
https://support.apple.com/en-us/HT206184#pagesformac

Use facing pages
You can set your document up as a two-page spread. Documents set up as two-page spreads can have different headers, footers, and master objects on left- and right-facing pages. Use facing pages for layouts for printed books, or for double-sided documents that you intend to print.


How can i use Files Connect to upload an attachment with apex, to Google Drive?

Question: I'm new to this salesforce world and i recently discovered i can synchronize my salesforce instance with a Google Drive. I already have a connection established using Files Connect to my Google Drive, and now i need to upload attachments to my drive for the user to download later from a folder with all of the attachments that he/she needs using apex. How can i do this? Do i have to use Chatter REST Api? And if yes how? Thank you for your time!
Answer: File connect let you use google drive as local drive for attachments only.
To upload files from salesforce to google drives, you have to use Rest API.