The set of homotopy classes of maps between compact manifolds is countable

Question: I'm reading Ravenel's book Nilpotence and periodicity in stable homotopy theory. In section 1.1, it says the set of homotopy classes of maps of maps between compact manifolds or between algebraic varieties over real or complex numbers is countable. I know that the set of homotopy classes between triangulable spaces is countable. I also know that algebraic varieties over real or complex numbers are triangulable while compact manifolds are not always triangulable. So I want to know how to prove that the set of homotopy classes of maps between compact manifolds is countable.
Comment: Smooth manifolds are triangulable. Topological manifolds are homotopy equivalent to CW complexes. Or a simpler way to treat topological manifolds for this purpose might be to observe that they are ENRs and therefore are retracts of triangulable spaces.
Comment: To expand on Tom Goodwillie's comment, the key point is that functoriality of $[X,Y]$, the set of homotopy classes of maps $X\to Y$, implies that if $X$ is a retract of $X'$ and $Y$ is a retract of $Y'$, then $[X,Y]$ injects into $[X',Y']$. Since compact manifolds are retracts of finite simplicial complexes (as shown in Corollaries A.8 and A.9 of my book for example) this reduces countability of $[X,Y]$ when $X$ and $Y$ are compact manifolds to countability when they are finite simplicial complexes.
Comment: You don't need triangulabilty, but merely that the homotopy class is determined by a finite set in the source and a countable set in the target.
Comment: @AllenHatcher: Thank you for your answer and your book from which I have learned a lot.
Answer: This may be somewhat heavy-handed but it follows from work of Kirby-Siebenmann that any compact manifold is homotopy equivalent to a finite CW-complex (implying what you want because any finite CW-complex is homotopy equivalent to its regular neighborhood in some Euclidean space, which in turn can be triangulated as a finite simplicital complex).
More precisely, let $M$ be a compact manifold, possibly with boundary. If $M$ has dimension $\ge 6$ and empty boundary, then $M$ is homeomorphic to a CW-complex [p.107 of Kirby-Siebenmann's book "Foundations of Topological manifolds"]. In general, fix $k$ such that $W=M\times D^k$ has dimension $\ge 7$. On the same page 107 it is stated that $W$ is homeomorphic to a mapping cylinder of a map $f:\partial W\to X$, where $X$ is a finite CW-complex. As mentioned above $\partial W$ is also a CW complex. The map $f$ can be homotoped to a cellular map, so the mapping cylinder $W$ is homotopy equivalent to a CW-complex as promised.
Comment: @ZheyanWan: How does it answer the question? Note that A.12 does not claim that any compact manifold is homotopy equivalent to a finite CW complex. It just claims homotopy equivalence to some CW complex. (Naively one might think that this CW complex surely can be chosen finite. What is true and easy to show is that any compact manifold is dominated by a finite complex, but the latter property is not the same as being homotopy equivalent to a finite complex because of Wall's finiteness obstruction).
Comment: Thanks a lot. I have already found these results in Hatcher's algebraic topology. Theorem 2C.5 and Corollary A.12 together answer my question.
Comment: Thank you for your answer and comment. This is a good starting point for me to study algebraic K-theory.


Postgresql Insert and Update only replica

Question: Is it possible to create a replica from a database that only inserts and updates replicated and not deletes in PostgreSQL ?
Answer: By default, I would say no, but you have some options:

You can use triggers (with DBLinks if you want to send to another server).
You can also use Change Data Capture (CDC).
Answer: The Postgres logical replication protocol allows you to identify the change type, so you can write a custom decoder that filters out messages that you want to ignore.
Alternatively, you could use an existing third-party CDC solution that allows filtering by message attributes, such as Debezium.
Comment: built-in pgoutput plugin is enough, no need to write a separate decoder. `create publication ... with (publish = 'insert, update')`


Can one use a question mark after "Please"?

Question: I'm imagining someone importuning another person.  For example, if someone asked another person if he or she could come join them on an outing, and when the other person doesn't seem too keen on the idea, the person who asked the question could say, "Please?"
Using an exclamation mark gives the sense that the person is raising his or her voice, and a period just doesn't seem strong enough at all.  Could a question mark work here?
Comment: I'd use it. 'Please!' isn't the politeness-marker usage, but the testy drawn-out vowel (PLEE-eese) version, the 'Oh, come on!' rebuke, as you imply. Punctuation is here to serve us (though we shouldn't use it to please ourselves at the expense of clarity). Sentences which are in the form of questions but are actually polite requests are increasingly considered best left unmarked as questions by question marks: 'Would you just shut the window please John.'.
Answer:
Please?

The question mark at the end of a sentence, when quoting a speaker, causes me to hear them saying it with a rising intonation, as if they are pleading.

Please!

An exclamation mark makes it seem like the speaker is insistant, raising their voice or shouting.
If they are importuning (harassing persistently), I would use "Please!"
Answer: Take "The sky is blue?". "The sky is blue" is an expression of fact, but obviously I am asking if the sky is blue, although gramatically nothing about that is a question except for the presence of a question mark. The presence of a question mark implies I actually want confirmation of this fact.
You can apply the same logic to requests and commands. Take "Give me that pencil". If you add a question mark to make "Give me that pencil?" (strange when written, but fine spoken), it implies that you want confirmation that your request/command has been received. "Please" acts as an expression of politeness that can be added to requests, so we can be more polite by saying "Give me that pencil, please" (the same meaning as "Give me that pencil", but more polite) and "Give me that pencil, please?" (the same meaning as "Give me that pencil?" but more polite, and this time maintaining the request for confirmation).
The final step would be that, if the meaning is clear, you could emit the actual body of the question if the meaning is clear. If you were pointing to the pencil at the time you could just go "Please?" and you will be understood. Of course, without physical context, the use of "Please?" on its own would usually mean "Can you repeat that?". Nevertheless this isn't common in English but is very common in, for example, German, where "Bitte?" would be unambiguous in this meaning. Likely the reason that "Please?" despite being uncommon English, would still be understood, is because of the Germanic roots of English (among other roots).


Why Phasic Policy Gradient (PPG) can update value function in auxiliary phase?

Question: My questions is that how could we train the value network (separated from shared network) by using data from previous policies, which varies a lot since we collect data from different policies with many training phases done to start a auxiliary phase, especially returns are calculated by those policies. Wouldn't it hurt the stability of fitting value function?
Answer: PPG can update the value function in the auxiliary phase because it uses a technique called "reparameterization" which allows for the gradient of the value function to be computed more efficiently. Additionally, PPG can take advantage of the structure of the problem to provide a better estimate of the value function.
I think you can train the value network on data from any policy, but
it will have more variance. If you have access to more data, it could help to smooth out the value function.

One approach would be to update the value network after each training phase of the policy network. This would ensure that the value network is always fitted to the current policy. However, this might not be practical if the training phases are very long.

Another approach would be to fit the value network using a rolling window of data from the previous training phases. This would strike a balance between stability and accuracy.

<code>"Wouldn't it hurt the stability of fitting value function?"</code>$\rightarrow$
$\color{red}{\textbf{No}}$, it should not hurt the stability of fitting the value function. In fact, using data from different policies can actually help to improve the stability of the value function estimate. This is because of "reparameterization" which allows for the gradient of the value function to be computed more efficiently as discussed above.
Comment: Aren't we estimating the value function w.r.t $\pi$? If we fit the value function with returns coming from different policies, we are moving towards different $V^{\pi}$?


Male dog was forcefully removed from female dog

Question: A male dog mounted my female dog for like 2 minutes and my brother forced the male out of the female, will the male release sperm in her?
Answer: It can but of more importance is that fact that you can seriously injure both dogs. Don't ever force separate mating dogs. You can still have the female spayed and head off pregnancy.
You can read more about it at our existing question Why does my dog get stuck to the female after mating?
Comment: Welcome to Pets! If you have a minute, please take the [tour] and have a look at the [help]. I'd like to add that dogs "stick together" for several minutes *after* the male ejaculated, which makes seperating them pointless. Could you please [edit] your question to add in this detail?
Comment: I added a link to our existing question in your answer.  References are always good, and links to existing posts on our site even better.


How to verify if a webpage is completely loaded using JavaScript

Question: I need to disable an image which I am using in  until the page completely loads.
I cannot use document.ready() because I need to disable the the BEFORE the document is ready.
Can someone please help me with this?
Answer: Define it in your HTML as disabled:
<button disabled="disabled">My Button</button>

And then on page load re-enable it.
This has the downside of breaking functionality for users without Javascript. The other way to do it is to add a small line of code directly after the button:
<button id="myButton">My Button</button>

...and then re-enable on document.load()
Edit with new info:
Is it an input with type "image"? If so, the above will still work. If not, and it's an  tag with an image inside it, I wouldn't recommend doing what the accepted answer suggests, sorry. Having an image suddenly appear at the end could get quite frustrating or distracting, considering that the page takes so long to load that you need to disable the link. What I'd suggest instead is this:

and then in your document.ready function, change the definition of the function:
myLinkHandler = function() {
    alert("Yay, page loaded.");
    return true;
};

Alternatively, you could put a check inside the function to see if the page has loaded or not.
var documentReady = false;
function myLinkHandler() {
    alert (documentReady ? "Ready!" : "Not ready!");
    return documentReady;
}

document.onload = function () { // or use jQuery or whatever
    documentReady = true;
};

Comment: I am sorry for not providing the info correct.
i need to disable an image which is acting as a button in my case
Answer: In the case of the image, just set the style to display:none in the  tag and then use the other suggestions to remove the CSS attribute Or change it:

$(document).ready(function(){ $("#myImage").css("display","block"); });
This way, the image won't even appear until the document is ready and then the user can click on it.  If you need to go the extra mile, do as the other suggested and hide/disable the link also in the tag and use jQuery to show/enable it.
Answer: A full code sample using jQuery:
<input type="button" value="My Button" id="mybutton" disabled="disabled" />

Comment: I am sorry for not providing the info correct.
i need to disable an image which is acting as a button in my case


Which way locks? / Which way is locked?

Question: This is in regards to every lock that turns 90-degrees. Meaning, not combination locks and unconventional locks. Let's just restrict it to:

Deadlocks
Door locks
The keyhole on the other side of a door lock
keyholes in general

I guess this is two questions:

Which way is locked? Vertical or horizontal?
Which way locks? Clockwise or counter-clockwise?

I've seen doorknobs have all sorts of configurations of this, so it never feels natural to lock or unlock someone else's door. The best thing for UX would be to have it be consistent across all locks. Are locks mostly consistent in these configurations or not?
Comment: Are you asking what the most intuitive direction is, which is certainly is a UX question? I'll be taking some pictures of my locks at home in a few hours (when I get home) now. :)
Comment: Yeah, I suppose. What I *really* want is to not feel like an idiot when I unlock a door and *try* to open it, only to realize I just locked it. =P
Comment: Well, there is no de facto rule - it could go either way, but I'll assume "the most usable direction." :)  Though, now that I think about it I'm trying to visualize a lock mechanism that would work in correctly going the "wrong" way (short answer: clockwise = lock, counterclockwise = unlock).
Comment: All locks should be adaptable to work the same as dead bolts. Less confusing for my 82 year old mother. Schlage has a lock that suits my application. Wiser has been bought out by another company and I will never buy another one of those silly smart locks. Soon all of my smart locks will be in the land fill. Hello Schlage. best lock on the market.
Comment: I am 64 years old. I always had the lock horizontal to be open and vertical to be locked. We just bought a house where all the locks are vertical for open and horizontal for close. This has caused getting myself locked out of the house a multitude of times. I think a standard was made a long time ago, and then someone had a flash thought that the whole world was doing it wrong. Hence the confusion.
Answer: The first point to make is that there is no standard in the way which locks turn in order to lock or unlock. So what makes the most sense?
Padlocks
Start with the easiest. Turning the key in either direction opens the padlock in each of the locks I tested. Simple!

But what it only one direction works? In this case, what is the most intuitive direction to turn it? I would argue counterclockwise (or anti-clockwise, as some prefer). Why...
Righty Tighty, Lefty Loosy" - The age old phrase to remember which was to rotate a screw to tighten or loosen it. The rationale being that you are "loosening" the bolt and then rotating to the left (the "left" rotation is in relation to the top) -- aka: counterclockwise.
Doors
A simple turn hand turn mechanism is on my front door. When it is in a horizontal position, the door is locked.

The mechanism can be seen as a representation of the position of the bolt. In this case, highlighted by the red line, the bolt follows the horizontal line made by the mechanism -- indicating it is locked.
To unlock the bolt, which way do you turn it? Counterclockwise.

Why? Because you're turning the bolt away from the opening. To lock you turn the bolt mechanism towards the door opening.
A similar door sits in my basement. In this case a keyhole is on the deadbolt, with a turn lock on the knob itself.

The knob's turn mechanism works in the same way as described above. The position tells me what state the lock is in (horizontal = locked and vertical = unlocked, as described above). Turning the mechanism "away" from the opening will unlock the knob.

But what about the keyhole? It always faces straight up. In fact, I can't get the key out of it unless it is straight up so how do I tell what state it is in? Although I can't tell the state, I can follow the same rule of turn "towards" the opening to verify that it is locked.
Both of these doors open to the left. What about doors that open to the right? Thankfully, I have a kitchen door too...

Here we have both a deadbolt and a knob lock. Both in the locked position -- known by their horizontal position.
So which way do we turn them to unlock the door? Counterclockwise would seem logical, because that is the direction all the other locks worked! But no...

Perhaps a little annoying, but they still fall inline with the mental model of what's happening above. Turning the mechanism away from the door opening will unlock them, and turning the toward the opening will lock them.
What's Your Mental Model?
What I've presented here is my "mental model" of how the lock mechanism works. When I encounter a lock that I've not used before this is the model I use to address the operation of that lock.
Others may have a different mental model; perhaps an "always counterclockwise" mental model in which a lock is always turned to the left -- no matter its relation to what is being unlocked. In this case, the user would be very annoyed with my kitchen door.
Because there is simply no standard (and you don't have to follow standards, it's just nice when you do) we can't claim there is a correct mental model to have. But, naturally, I would argue that my mental is the more proper one. Most people would tend to argue their mental model is the more proper, too.
Turning the mechanism away from the point you are locking means you know which is way is which. An arbitrary direction is always open to interpretation and potential confusion, while an action in relation to the object (the door opening) is a constant reference to base off of.
But that's my mental model. Your mental model may say otherwise...
Update: Muscle Memory
Since writing this answer I've naturally paid a little more attention to how I lock and unlock doors around my house. I've discovered a lock that works totally opposite of the rest.
The screen door leading out of kitchen has a lock which turns counterclockwise to unlock and clockwise to lock. If you remember my description of my kitchen door above, you'll remember it is a right opening door and that the locks on it work in the opposite direction. In the case of the screen door turning the lock "away" from the opening locks it, and turning it "towards" the opening locks it.
I can't use my mental model of how doors work on this! But I've realized that my "muscle memory" has kicked in and I instinctively remember how this particular door works (i.e., opposite of how I would normally expect it). As a result I don't have an issue with it... but I wouldn't be surprised if I did in the past.
Comment: +1 regarding "no standard". Simple example: Door keys in my minivan turn the opposite direction from door keys in my girlfriend's. Different manufacturers, different conventions.
Comment: When I put the bathroom locks in our house I used the horizontal = locked model because it's similar to a British "No Entry" road sign - My kids were very into road signs at the time so they knew exactly what it meant straight away!
Comment: Another data point for "no standard": I've seen deadbolts that are locked when in the vertical position and unlocked when horizontal, and [I'm not alone](http://blogs.msdn.com/b/oldnewthing/archive/2005/01/13/352157.aspx).  They always give me a brief moment of panic that I've left the door unlocked all day/night.
Comment: @keshlam I wonder if that has anything to do with country of origin like toilet flush direction and side of the door that the lightswitch is on when entering (although I'm fairly sure both aren't true but are perpetuated).
Answer: First, I would like to say that I install locks for a living. While I do a lot of locksmith work, I do not call myself a locksmith, because I strictly work on locks for buildings. That is, I don't crack safes or open cars. I own a company that specializes in selling and installing residential and commercial door hardware.
I just stumbled upon this question, because with all of my expertise, I was actually wondering the same thing. I know the thread is pretty old, but I feel like I can contribute for posterity. So, here's my take:
There are basically two types of locks on doors: cylinder and mortise. Mortise locks are comprised of a rectangular box that fits inside of a, well... a mortise, which a carpenter cuts into a door. Because of their design, the key is inserted into one side, and the latch attaches to the other. They cannot be reversed, and they can only be installed one way. There are four types: left hand, right hand, left hand reverse bevel, and right hand reverse bevel.
To understand the types, it is easiest to first understand cylinder locks. While mortise locks are still manufactured and used, they have fallen out of favor over the years. This is mostly because they require a skilled carpenter, or a specialized machine (which no one makes anymore), to install. A cylinder lock, which is what you probably have on your home, can easily be installed with a drill and the proper bits. They essentially just fit into a hole.
Cylinder locks can be reversed, because they fit into a round hole instead of a rectangular mortise. So, unless you have a curved lever or latch, they are all the same. The only time they are "handed" is if they have an exposed piece, which is meant to be displayed in a certain way. Even then, they only come in left and right hand. The "bevel" refers to the angle cut on the striker, so that the door closes without you having to turn the knob first. Even if a cylinder lock is handed, you can still rotate the bevel to face the door frame and strike plate when it closes. Thus, there's no reverse bevel.
If you're still with me, there are four types of mortise locks, because the key can only be inserted into one side, and the bevel of the striker cannot be rotated. There are four types of doors. The hinges can be on the left or right, and the door can open into or out of a room.
With mortise locks, the key was always inserted vertically, and the key was turned towards the frame to lock and away from the frame to unlock. Likewise, the thumb latch on the inside operated the same way. So, it makes sense that a cylinder lock should be installed the same way, since locks have worked this way for at least a century.
However, there are some nuances to cylinder locks, which prevent this from being a universal rule. The actual locking mechanism of a cylinder lock has a flat piece of metal that connects the inside and outside of the lock and passes through the latch/bolt, which holds the door closed. This is called the "tailpiece."
If the correct key is inserted into the lock, you can turn the tailpiece left or right, 90 degrees, from the outside. The tailpiece can be freely turned by the latch without a key. If you held just the locking mechanism, you would see that the tailpiece has a total of 180 of free rotation. THAT is why this question exists in the first place. You can install almost any cylinder lock in the unlocked position with the thumb latch in the vertical OR horizontal position.
So, here's what I do know for certain. Some manufactures design their locks to function one way or the other. From what I understand, this is because there is more tension on the lock when it is turned until it stops. If you think about it, and remember that the tailpiece turns 180 degrees, there is tension on the pins of the lock when it is turned left or right, but none when it is in the middle (the vertical position).
I know that this is confusing, but some locks are designed to be under tension in either the locked or unlocked position. It depends on the manufacturer and model. I will say that, when the direction does matter, it is always noted in the instructions. So, check those first and follow them.
Also, to obfuscate things more, some manufacturers make locks where the latch sits at a 45 degree angle. All cylinder locks only have to turn 90 degrees to function. So, these particular locks tilt towards the frame when locked and away when unlocked. But, they never rest in a vertical or horizontal position. Schlage makes many models in this style.
Lastly, I have also seen cylinder locks with labels on the faceplates. Some have an arrow or mark for the locked position. Others actually have the words locked and unlocked etched into the plate. To further complicate things, I have seen these labeled faceplates with the locked position vertical, horizontal, and in between.
TLDR: All locks are different. Follow the manufacturer's instructions. If the direction is not specified, then install the lock so that it is unlocked when the thumb latch is vertical and locked when it is horizontal. The latch or key locks when turned towards the frame (strike plate) and unlocks when turned away. Whether that is clockwise or counterclockwise depends on whether it is a left or right handed door.
Answer: I actually own a car that locks/unlocks differently on each side. On the driver's side, you turn clockwise to unlock. On the passenger side, you turn counterclockwise to unlock. It drives me crazy, since it doesn't even follow the idea of turning away from the direction of the door opening to unlock.
Comment: I've seen that too. It may help to think of it as toward front/back of the car, rather than deasil and widdershins.
Answer: A horizontal bar blocks your passageway, hence should mean closed. Based on the same idea that a 'go straight' sign's arrow points upwards, a horizontal bar will block your way.
Or possibly it's just a remnant from a simpler design where the angle of the lock directly informs you on the status through it's physical nature. And therefore, just a result of how doors work.

The direction of rotation, clockwise / counter clockwise, depends on your location. I've clearly noticed locks in Europe and New Zealand consistently going the other way when locking.
Comment: I'd guess that, yes, it's a remnant from a simple design, and that's why most locks are in horizontal/vertical positions in general. In any case, that picture makes it very clear (on that door) which angle is locked.
Answer: Until a few years ago I can't remember one toilet doorknob (shaped like a bar) that was in a vertical position when closed. The horizontal position always meant that the door is closed. This seemed to me a convention that had to be followed just to avoid you forget to close the door and when looking at the doorknob you believe that you actually closed it. I leave the possible scenarios following that situation up to your imagination.
Recently I noticed that in many places no thought at all is given to this notion and doorknobs with vertical and horizontal closing position are carelessly mixed up even in the very same lavatories.
This is definitely a huge gap in UX. There should be an IEEE RFC for that.
Answer: There are some Schlage mortise locks at my work that vary, some are vertical when unlocked and horizontal when locked, and vice versa. Some of the locks turn away from the frame to lock it, and vice versa.
Answer: Just installed new locks throughout my home, deadbolts and knobs. I set all the deadbolts to vertical when unlocked and a turn of the latch clockwise now locks them with the latch remaining in a horizontal position, the same direction as the deadbolt itself. This was completely contrary to how I initially installed the old ones without any thought whatsoever. I looked up this question because it's taking some getting used to and I wasn't sure if there was a standard. However, for some unknown reason, I chose, if not by default to have all the door knobs lock in the vertical position turning them clockwise to unlock. This seemed natural presumably from many years of locking doors. Just the reasonable man looking for a reasonable answer.
Answer: The simple latch on the door knob will indicate how to install your matching deadbolt.  The door knob on my new sets locks when vertical, therefore I installed all the deadbolts to lock when vertical.

Which way locks? / Which way is locked?


How does Fairy Tail's strongest team get back to Earth Land the second time?

Question: In Fairy Tail: 100 Years Quest, Natsu, Lucy, Erza, Gray, Happy, Carla, and Wendy all go to Edolas again. How do they get back to Earth Land?
Answer: Chapter 67:

They devise a plan to get back to Earth Land with the help of a dimension-travelling Elentearean Exceed (Elentear is another parallel dimension, a magical one, unlike Edolas) and by consuming the last of the X-Balls in Edolas (X-Ball is a medicine that allows denizens of magical dimensions to retain their natural ability to produce magic while in Edolas, see Fairy Tail chapter 180).

Chapter 68:

The plan is disrupted by Dragon Goddess Selene, who decides to teleport them to Elentear for her own amusement.

Chapter 89:

Eventually they'll come back to Earth Land from Elentear with the help of the local mages.


Does this sentence use the word "myriad" correctly?

Question: "Linezolid is an antibiotic with myriad uses worldwide, including treatment of pneumonia and skin infections."
Comment: Whether "correct" or not, it's fairly idiomatic.  (I observed earlier that "myriad" always looks wrong, no matter how it's used.)
Comment: Is it often used in the singular without an indefinite article on the web?
Comment: I agree with @HotLicks. The usage is idiomatic and clear in a non-scholarly context. And I also agree with Robert Simpson's comment below. In a scholarly context, _myriad_ is not appropriate for this statement. For a medical journal or some such publication, it would probably be better stated that the drug is "versatile" and "broadly used" for various infections, etc.
Answer: No, I  think myriad is not correctly used here.  When used as an adjective it describes something of such a great number as to be uncountable; but, a little research into linezolid indicates that its uses can be broadly categorized into a few categories of bacterial infection control.  Should the writer wish to convey that he or she is speaking of the skin infections or pneumonia within such a broad category, it is still not "innumerable" because it is possible to count them.
Comment: It's sometimes used hyperbolically; this entry would seem to endorse this (note the quantifier usage): **myriad** Idiom: quite a few.
[The American Heritage® Roget's Thesaurus](http://www.thefreedictionary.com/myriad) But certainly, hyperbole is inappropriate in a scientific register. Though this could be science-for-the-masses.
Comment: @EdwinAshworth, I don't disagree with your comments.  Hyperbole would be unseemly in the context OP wishes to include the word.  If OP's audience could be expected to understand the broad nature of skin infections, then it becomes unnecessary to say.
Answer: There is an article on the syntax involved in Fowler's Dictionary of Modern English Usage
 By Henry Watson Fowler, Jeremy Butterfield (reformatted):

Rather inexplicably, myriad has become a usage issue for certain
  people. The word is quite legitimately, and with good historical
  precedent, used in three [four?] syntactic patterns (dates of first known use
  [given] in the OED in brackets):
(i)   As a plural noun [+ of]: myriads of stars (1555)
(ii)  As a singular  noun + of: a myriad of stars (1609)
(iii) As a … quantifier: a myriad stars; myriad stars (1735)
… The first usage book to proscribe [the noun usages] dates from as
  recently as 1996.

The usage in the above example would thus be considered not ungrammatical by Fowler.
As regards meaning, Fowler goes on to say:

[T]o use it when the numbers involved are not large cheapens it; [but]
  often it seems to mean little more than 'a large range'.

So Fowler would not recommend the use of myriad here on style grounds (unless there are say thousands of uses of Linezolid).


How to Create a Date Input Field

Question: How can I create an apex input with data type date?
I tried using showDatePicker but it has an error:

value for <apex:inputField> is not a dynamic binding.
Answer: There are several ways in which you can achieve this.
If you want to mimic datepicker which is seen in salesforce UI, the simplest one is as suggested by @Boris in his answer.
The other ways include:

Use HTML input tag with attribute as type="date"
<input type="date" name="bday">
Use HTML input tag and any javascript library like jQuery, ExtJs etc. The below example is for jQuery. You can use jQuery datepicker() function to turn a text box into datepicker.
<input type="text" id="datepicker">

Use salesforce apex:inputText tag and any javascript library like jQuery, ExtJs.
<apex:inputtext id="datePicker" onclick="openDatePicker()"/>

Answer: If I understood the question correctly (input field date), you're referring to VisualForce.
You can create a temporary instance of an sObject which has a date field, for an example Opportunity which has a field CloseDate.
So in your controller add:
public Opportunity oppty {get; set;}
Then inside your constructor or init method create a new instance:
oppty = new Opportunity();
Finally in your VisualForce page you can use it as:
<apex:inputField value="{!oppty.CloseDate}" />
Then whatever you do in your controller, you can always reference the value in oppty.CloseDate.
This is one of the quickest but not cleanest solutions.
Comment: I am not using Opportunity object but have to use it in order to enable  .This seem little dirty but solve the issue instead of waiting this feature to be available by salesforce.

How to Create a Date Input Field


What would happen if, hypothetically, money velocity would reach infinity?

Question: If, hypothetically, money velocity would reach an infinite speed, what would happen to that economy? If it would be infinite then it would mean that there would be infinite transactions and therefore Y would be infinite aswell? But infinite transactions would also be a sign of infinite demand and therefore the price would become infinite? Furthermore, if the money velocity is infinite, then it also would mean that every economic agent of the economy is in possession of the same amount of money and thus no wealth inequality would exist? I am curious to if there is a more solid theoretical answer to this and or what others think about this question.
Answer: No $Y$ would not become infinity. $Y$ represents the real output of an economy. A real output is limited by the economy's production possibility frontier. For example, if we assume simple production function $F(L)=10 \sqrt(L)$ with assuming the economy's stock of labor being $100$ such economy would not be able to produce more than $100$ units of output whether velocity is infinite or not.
In the short run an economy might not be using its resources to the full extent and in that case increase in the velocity could have some effect - although causality would go through prices not directly from velocity (see Blanchard et al. Macroeconomics an European Perspective).  Furthermore, to see the effect of velocity we could use a simplified model for money market equilibrium given by the equation of exchange:
$$MV=PY$$
Where $M$ is money supply, $V$ velocity, $P$ price level and $Y$ output. As explained above $Y$ is limited by the production capability of an economy. Hence $Y$ can be treated as fixed. Next $M$ is under a control of a government through central bank or other institutions. Since in your problem you dont specify any government action regarding $M$ we can also treat it fixed. Then the only other variable that remains is $P$. Hence if $V$ wold increase to infinity $P$ would also increase ceteris paribus.
However, as alluded to above in a short run economy might not be operating at its full potential. In such scenario increase in $P$ in the short run would also stimulate firms to produce more according to standard macro AS-AD model. Hence in short run some of the increase in velocity could also be soaked by $Y$ (through increase in $P$ induced by increase in $V$) but certainly not anywhere near to reach infinity. $Y$ must in the end respect the country's PPF which in a world of scarcity will be finite.

Furthermore, if the money velocity is infinite, then it also would mean that every economic agent of the economy is in possession of the same amount of money and thus no wealth inequality would exist?

No, a velocity of money is defined as: "the frequency at which one unit of currency is used to purchase domestically- produced goods and services within a given time period" (see FRED). High velocity does not imply more equal distribution of money. For example, imagine an economy with two people A and B, with A having one 1 $\\\$1$ banknote and B having 2 $\\\$1$ banknotes - and lets for simplicity assume anytime they spend money they instantly get it back as an income. If A uses his banknote only twice to purchase goods and services (he purchases something - immediately gets it back as an income and purchases something again) but B uses both of his two banknotes 10 times the velocity will be $22/3 \approx 7.33$. If B decides to use his banknotes 50 times the average velocity will be 34 and so on we could go on. Point is that higher or even infinite velocity does not necessary tell us by itself much about distribution of money in economy.
Furthermore, in public economics wealth is usually defined as a value of net assets. The value of net assets a person has does not correspond to the amount of money one has. For example, imagine person with house worth $\\\$ 100,000$ and no debt but absolutely no money. An economist would say that person's wealth is $\\\$ 100,000$. Now imagine person B with $\\\$1,000,000$ in a bank account while having also $\\\$1,000,000$ debt. Such person would be recorded as having $0$ wealth. Different scholars might disagree about whether wealth should include things like social security and on other details but I know of no economist that would equate wealth to money holdings.   Hence there is no simple relationship between distribution of money and wealth distribution.
Comment: Just a comment on a point that is implied by this answer, but not obvious to people new to the field. Not all transactions count for GDP. For example, financial market transactions do not directly add to GDP. Therefore, there can be an extremely high velocity with respect to transactions, but standard definitions of velocity apply to the transactions in goods and services that add up to GDP.
Comment: But isn't it that you cannot have infinite money velocity when resources are limited and therefore the PPF would be limited as well? So if money velocity would be infinite then it would mean that there is an infinite amount of resources and therefore an infinitely large PPF? Or what am I missing here?
Comment: @Kroko well in the end it's physically impossible to use a unit of currency infinite times but it is not equal to the size of GDP. For example, if A sells apple for 10e to B the velocity will be 1 as each unit of currency was used only once while GDP will be 10e. I think it's also possible to construct example where we transact one apple back and forth where a resale won't be counted in but the unit of currency is still used in transactions for final goods and services. Not that any such situation would be realistic. Also, I think that rest of your Q is addressed by Brian's +1 comment.


The soundness of modus ponens (?)

Question: I've been told that a proof can be provided to the effect that modus ponens is a sound logical principle. I know that modus ponens is a valid principle in classical logical but I can't see what it could mean for a logical principle to be sound. As a result, I can't see what a proof of modus ponens' soundness may look like. Can you help me?
Comment: With some more context, like what logic you are studying, we might be able to provide some more direct answers.
Comment: See [Soundness of a proof system](https://en.wikipedia.org/wiki/Soundness#Logical_systems) : "In an axiomatic system, proof of soundness amounts to verifying the validity of the axioms and that the rules of inference preserve validity (or the weaker property, truth). If the system allows Hilbert-style deduction, it requires only verifying the validity of the axioms and one rule of inference, namely *modus ponens*."
Answer: Most likely it means the same as you're use to calling "valid".
The word "sound" is most often applied to entire logics:

A logic is "unsound" (with respect to a particular semantics) iff there exists statements $A, B_1, B_2, \ldots, B_n$ such that the logic can derive $A$ as a consequence of the $B_i$s, and yet the semantics allows a situation where all the $B_i$s hold but $A$ doesn't.
A logic is "sound" if it is not unsound.

The most likely interpretation of "modus ponens is sound" would be that if we take a logic where the only way to conclude anything is by modus ponens (that is, no axioms, no other rules of inference, no nothing), then that logic is sound.
And that is basically the same as what is also commonly expressed as "modus ponens is a valid inference rule".

In philosophy (and the early pages of some textbooks of mathematical logic) one can also call an argument "sound" if it is a valid deduction from premises that happen to be true. But there doesn't seem to be any reasonable way to extend that meaning to apply to a rule of inference in isolation.
Answer: According to Wikipedia " For modus ponens to be a sound argument, the premises must be true for any true instances of the conclusion. An argument can be valid but nonetheless unsound if one or more premises are false; if an argument is valid and all the premises are true, then the argument is sound."
Comment: This meaning of the word "sound" is completely different from its meaning in mathematical logic. The last paragraph of Henning's answer indicates that philosophers may use the word "sound" in this way. But I think this passage on Wikipedia is potentially misleading.

The soundness of modus ponens (?)


Why are two permutations conjugate iff they have the same cycle structure?

Question: I have heard that two permutations are conjugate if they have the same cyclic structure. Is there an intuitive way to understand why this is?
Comment: Have you read a proof of this fact, and found it to be unintuitive?
Comment: @Zaz That's not how conjugates are defined. If $a b = b c \implies b^{-1} a b = c \text{ for } a,b,c \in G$ then $a$ and $c$ are said to be conjugates. You're example just shows that $(12)$ and $(12)$ are conjugates i.e. they lie in the same conjugacy class, which is trivial.
For $(12)$ to be conjugate with $(1)$ you have to show the existence of some $g \in G$ such that $g^{-1} (12) g = (1)$ and no such $g$ exists, hence $(12)$ and $(1)$ are not conjugates.
Comment: The "[theorem that won World War II](https://en.wikipedia.org/wiki/Marian_Rejewski#cite_ref-34:~:text=%22the%20theorem%20that%20won%20World%20War%20II%22)"
Answer: It's much like with linear transformations: conjugating a matrix amounts to a "change of basis", a translation from one basis to another, but similar matrices still represent the same linear transformation.
Conjugating by a permutation amounts to "translating" into new labels for the elements being permuted, so "similar permutations" (conjugate permutations) must represent the same underlying "shuffling" of the elements of the set, just under possibly different names.
Formally: Suppose that $\sigma$ and $\tau$ are permutations.
Claim. Let $\rho = \tau\sigma\tau^{-1}$ (multiplication corresponding to composition of functions). If $\sigma(i)=j$, then $\rho(\tau(i)) = \tau(j)$. In particular, the cycle structure of $\rho$ is the same as the cycle structure of $\sigma$, replacing each entry $a$ with $\tau(a)$.
Proof. $\rho(\tau(i)) = \tau\sigma\tau^{-1}\tau(i) = \tau\sigma(i) = \tau(j)$. QED.
Conversely, suppose that $\sigma$ and $\rho$ have the same cycle structure. List the cycles of $\sigma$ above the cycles of $\rho$, aligning cycles of the same length with one another. Now interpret this as the two-line presentation of a permutation, and call it $\tau$; then $\tau\sigma\tau^{-1}=\rho$ by the claim.
For example, if $\sigma=(1,3,2,4)(5,6)$ and $\rho=(5,2,3,1)(6,4)$, then write
$$\begin{array}{cccccc}
1&3&2&4&5&6\\
5&2&3&1&6&4
\end{array}$$
Then we let $\tau$ be the permutation $1\mapsto 5$, $3\mapsto 2$, $2\mapsto 3$, $4\mapsto 1$, $5\mapsto 6$, and $6\mapsto 4$. Then by the claim above, $\tau\sigma\tau^{-1}=\rho$. (Note. As Gerry Myerson notes, if we aren't working in all of $S_n$, we may not have $\tau$ in whatever subgroup we happen to be working in; so there is an implicit assumption for the "if" part that we are working in $S_n$).
Comment: @William: Yes; in the standard setting, $\sigma$ acts on $\{1,2,\ldots,n\}$, and you want to act on $\{\tau(1),\tau(2),\ldots,\tau(n)\}$.
Comment: I see that you've used $\rho = \tau \sigma \tau^{-1}$ over what the other answer (by Alon Amit) has used $\rho = \tau^{-1} \sigma \tau$. I'm confused. The latter notation ($\tau^{-1} \sigma \tau$) intuitively means, relabel > shuffle > un-relabel, but how do I read your notation $\tau \sigma \tau^{-1}$? Un-relabel > shuffle > relabel? I know both are equivalent by setting $\tau^{-1}= \alpha$ but still how does one read and understand it intuitively?
Comment: @William: Amit is actually using $f$ as the *inverse* of the relabeling, if you read his answer carefully, so though his notation seems to clash with mine, it is actually *exactly the same*, both now and 10 years ago when I wrote that. If $\tau$ relabels, then you first need to *un-relabel* so you can apply $\sigma$ (which doesn't understand the re-labeled things), then permute, *then* relabel.
Comment: @William: Think of it this way: $\sigma$ understands English. $\tau$ translates from English to Russian. You want to understand russian using $\sigma$. So first you translate Russian to English ($\tau^{-1}$), then you understand it ($\sigma$), then you translate it back to Russian ($\tau$). The result of $\tau\sigma\tau^{-1}$ is in the new labeling, so it should be the latter of your sequences, not the former.
Comment: Thanks for the response! Let me see if I understand you correctly. $\sigma$ and $\rho$ are defined on same sets but just for distinction, say $\sigma : X_1 \to X_1$ and $\rho: X_2 \to X_2$ where $X_1=X_2$. So $\tau$ is relabelling set of $\sigma$ ie $X_1$ with set of $\rho$ ie $X_2$ (again $X_1$ and $X_2$ are same) so $\tau : X_1 \to X_2$ and so $\tau^{-1}: X_2 \to X_1$ hence, $\tau \sigma \tau^{-1}$ first relabels $X_2$ back using $X_1$ then $\sigma$ permutes $X_1$ then $\tau$ labels $X_1$ using $X_2$ so in a way, $\sigma$ of $X_1$ is the same as $\rho$ of $X_2$ under $\tau$. Is this correct?
Answer: Warning: the permutations are conjugate $\bf in\ S_n$ if they have the same cycle structure. This may not be true in subgroups of $S_n$. For example, $A_4$ is the alternating group on 4 symbols, it consists of the even permutations in $S_4$. The elements $(1\ 2\ 3)$ and $(1\ 3\ 2)$ of $A_4$ have the same cycle structure, but they are not conjugate in $A_4$. That is, there are elements $g$ in $S_4$ such that $g^{-1}(1\ 2\ 3)g=(1\ 3\ 2)$, but there is no such element in $A_4$.
Comment: Why don't you post that as a question, instead of hiding it in a comment on an old answer?
Comment: Thank you for your answer, sir. How can we see that for a cycle we have the equation $r(i_1,i_2,\dots,i_k)r^{−1}=(r(i_1),r(i_2),\dots,r(i_k))$?
Comment: Very well, I'll ask my question in a separate post. I "hid" it in a comment becouse of [this thread](http://meta.math.stackexchange.com/a/4110/34371).
Comment: @Student - where did you asked the question? I can't find it! I had to asked again in http://math.stackexchange.com/questions/1700180/why-c%E2%88%921a-1-a-2-dots-a-kc-ca-1-ca-2-ca-k?noredirect=1#comment3469997_1700180 but no answer yet (for such a widely used formula no proof!).
Comment: I don't remember, but you can look through my questions, @Liebe.
Answer: The intuitive way to see this is to realize that "conjugation" in a permutation group is the same as "renaming". Take some permutation; conjugate it by (1 2), the permutation that swaps 1 and 2; what's the result? Calculate a few examples, and you'll see that the result is the same as the original permutation with 1 and 2 changing roles.
Another good way to understand this is to separate the domains of the permutation and the conjugation. If $A$ is a set and $\sigma$ is some permutation of the objects of $A$ (take $A=\{1,2,\ldots, n\}$ for example), imagine there's a new set $Z$ of the same cardinality as $A$ and a one-to-one, onto mapping $f:Z\to A$. What is $f^{-1} \sigma f$? It's a function on $Z$ which first maps everything to $A$, permutes according to $\sigma$, and maps back along the same "mapping lines" as $f$. It should be relatively obvious that the result "does to $Z$ exactly what $\sigma$ does to $A$". Again, working out a few small examples should help.
So, conjugation in $S_n$ is the same thing only when $Z$ happens to be the same set as $A$; the "names" and the "objects" are one and the same.
Answer: Suppose $\rho=\pi\sigma\pi^{-1}$, for any $m\in Z$,
we have $\rho^m=\pi\sigma^m\pi^{-1}$, i.e. $\rho^m\pi=\pi\sigma^m$.
For a cycle $(i,\sigma(i),\ldots,\sigma^{r-1}(i))$, we have
$$(\pi(i),\pi\sigma(i),\ldots,\pi\sigma^{r-1}(i))
=(j,\rho(j),\ldots,\rho^{r-1}(j))$$
where $j=\pi(i)$.  This is intuitive, isn't it?
Comment: +1 for succinctness!


The Difference Between ACL and FPM

Question: What's the difference between ACL and FPM? In detail, please, but in a simple, easy-to-understand way.
Answer: I assume you're asking to compare Cisco Access Control Lists (ACL) and Cisco Flexible Packet Matching (FPM).
Packets contain a number of fields, such as:

IP source address
IP destination address
TCP Source Port
TCP Destination Port
UDP Source Port
UDP Destination Port

ACLs
Traditional ACLs can only permit or deny based on a limited number of fields (some of most commonly used fields are listed above); these fields are well-known throughout the internet.  However, traditional ACLs cannot filter inside the payload of an IP packet, for instance if someone wanted to block certain kinds of Tibco RV UDP Multicast payloads, it's impossible to do so with traditional ACLs.  Traditional ACLs look like this...
! Note: this ACL is only granular to a TCP port
access-list 102 permit tcp any any eq 80
access-list 102 permit tcp any any eq 443
access-list 102 permit tcp any any eq 23
access-list 102 permit tcp any any eq 25
access-list 102 permit tcp any any eq 110
access-list 102 deny ip any any log
!
interface FastEthernet0/0
 ip access-group 102 in

FPM
However, FPM can block / allow on any bit inside a single packet header or payload1, as long as there is a valid PHDL file loaded for the field that needs to be blocked or allowed.  FPM can define a hierarchy of classes and policies to implement very granular control over the packets that are allowed or denied.
This is an example policy, taken from the FPM docs, which matches a UDP packets sent by the Slammer Worm.  It would be impossible to block the hosts infected with the Slammer Worm using ACLs unless you block both good and bad SQL traffic by individual IP source addresses.
load protocol disk2:ip.phdf
load protocol disk2:udp.phdf
!
class-map type stack match-all ip-udp
 description "match UDP over IP packets"
 match field ip protocol eq 0x11 next udp
!
class-map type access-control match-all slammer
 description "match on slammer packets"
 match field udp dest-port eq 0x59A
 match field ip length eq 0x194
 match start l3-start offset 224 size 4 eq 0x4011010
!
policy-map type access-control fpm-udp-policy
 description "policy for UDP based attacks"
 class slammer
  drop
!
policy-map type access-control fpm-policy
 description "drop worms and malicious attacks"
 class ip-udp
  service-policy fpm-udp-policy
!
interface GigabitEthernet0/1
 service-policy type access-control input fpm-policy

End Notes:
1 FPM's limitation of inspecting a single IP packet is non-trivial, since that means it's possible to circumvent FPM if an attack manages to split the attack signatures across multiple IP fragments, or TCP packets (since the TCP stream is reassembled at the receiver).  That said, it's a still very powerful tool as long as you understand the limitations of the technology.
Answer: Access Control Lists (ACL) are network statements that permit or deny access to a given set of conditions based on the first match.
Standard ACLs are the oldest forms of ACLs and operate in an incredibly broad manner.  They only match based on a single IP address, and because of this limited functionality, they operate much faster other types under most circumstances; this is not taking into account hardware-based acceleration.
Suppose we want to limit access to a single host, below is what we would do.
rtr(config)# access-list 1 permit 10.1.1.100 0.0.0.0

This ACL functionality is refined even further with the introduction of Extended ACLs.  This allows you to specify source and destination IP addresses, as well as port numbers and a few other parameters (e.g., tos, precedence, etc.).  The added functionality this provides also comes with a downside: increase overhead and packet inspection.
Suppose we wanted to refine the scenario above even further to limit this host to a single IP and allow HTTP access.
rtr(config)# access-list 199 permit tcp host 10.1.1.100 host 192.168.1.1 eq 80

Flexible Packet Matching (FPM) is really the newest ACL that's available.  The primary focus is for intrusion prevention/detection because of its extensive matching characteristics.  You can seemingly define any parameter inside a packet for inspection.  Like anything with additional features though, this comes with a significant performance toll.  I grabbed this next example from Cisco's documentation on FPM and modified it to match the relevant fields.
Suppose we want to refine the above restriction even further.  We want to allow access from that single host, and prevent any of those 'trusted' users from passing malicious queries (specifically "GET \%") to the single host.
rtr(config)# load protocol flash:ip.phdf
rtr(config)# load protocol flash:tcp.phdf
rtr(config)# class-map type stack match-all ip_tcp
rtr(config-cmap)# description "match TCP over IP packets"
rtr(config-cmap)# match field ip protocol eq 0x6 next tcp
rtr(config-cmap) # description "Match HTTP Exploit Packets"
rtr(config-cmap)# match field tcp dest-port eq 80
rtr(config-cmap)# match field ip source-addr eq 10.1.1.100
rtr(config-cmap)# match start tcp payload-start offset 0 size 32 regex ".*GET \%"
rtr(config)# policy-map type access-control fpm_tcp_policy
rtr(config-pmap)# description "policy for TCP packets"
rtr(config-pmap)# class http_psirt_class
rtr(config-pmap-c)# drop
rtr(config)# policy-map type access-control fpm_policy
rtr(config-pmap)# description "policy HTTP Get exploitation"
rtr(config-pmap)# class ip_tcp
rtr(config-pmap-c)# service-policy fpm_tcp_policy

The Difference Between ACL and FPM


Select largest subset, subject to a separate weighting constraint

Question: Given an unsorted set of tuples $(c, w)$ and a threshold value $W$, I want to select $k$ tuples such that:
$$
maximize\sum_{i=1}^k c_i \\
\sum_{i=1}^k w_i \ge W
$$
It seems pretty simple at first. Without the weighting constraint, you can use any selection algorithm to select the $k$ elements with largest $c$. But with the weighting, it seems there's no special structure to exploit. Seems like you'd have to search all subsets?
Answer: Use dynamic programming.
Let the $(c,w)$ pairs be $(c_1,w_1),\dots,(c_n,w_n)$.  Define $A[k^*,n^*,W^*]$ to be the largest possible sum of $c$-values obtainable by selecting $k^*$ pairs from $(c_1,w_1),\dots,(c_{n^*},w_{n^*})$ such that the sum of their $w$-values is at least $W^*$.  Then you can write down a recursive definition of $A[k^*,n^*,W^*]$:
$$A[k^*,n^*,W^*] = \max(A[k^*,n^*-1,W^*], A[k^*-1,n^*-1,W^*-w_{n^*}]+c_{n^*}).$$
Now fill in this table using dynamic programming.  The running time will be $O(nkW)$, where $n$ is the number of $(c,w)$-pairs in the input.
This is basically an adaptation of the dynamic programming algorithm for the knapsack problem: https://en.wikipedia.org/wiki/Knapsack_problem#0.2F1_knapsack_problem
Comment: Eh I totally forgot about the $k$ limit in my answer, oops.


Can sound travel in the form of transverse waves?

Question: We all know that sound travels in longitudinal waves but in some books, I have found that sound travels in the form of both longitudinal and transverse waves while passing through rocks. Can anybody explain this to me?
Comment: @ Anil, can you share the name of those books?
Comment: Yes, they can. Depends on the intermolecular forces between molecules of the medium. In air, these forces are low, so one particle has to to collide with another to actually get the disturbance to get transferred. In mediums like solids, which are more rigid, sound waves can transfer as transverse waves, but remember, there should be a way, to shake your ear drum, if you're to listen anything.
Comment: In solid state physics, there are "transverse acoustic modes", but that is not really the sound that one can hear. Here "acoustic" is in contrast with "optical modes".
Answer: The difference between a fluid and a solid is the following: fluid's have zero shear modulus, so they cannot carry a shear force, but solids have non-zero shear modulus, so they can carry shear force.
Fun little way to visualize this: let's say we line up a bunch of second graders on rectangular grid. Now we push one of the students along one row. That student will push the next student in the same row and so the push will move through the row. However, the students in the other rows are unaffected. That's how a fluid behaves.
Now we ask the students to hold hands with their neighbors in the adjacent rows. If we push one student, not only will the push travel through the same row, but since the student are holding hands with their neighbors, these kids will move as well, so the the push will also travel laterally along the columns through the other rows. That's how a solid behaves.
In a solid, molecules are "holding hands" with their neighbors, in fluid they do not. This enables transversal waves in a solid.
Of course, in reality all the second graders would fall over each other giggling hysterically. The branch of physics dealing with kids is neither solid mechanics nor fluid mechanics, but probably chaos theory.
Answer: According to this website:

Sound is transmitted through gases, plasma, and liquids as longitudinal waves, also called compression waves...Through solids, however, it can be transmitted as both longitudinal waves and transverse waves.

This means that through most forms of matter (gases, plasma, liquids), such as water, or the air, sound travels as longitudinal waves. Through solids (such as rock), though, it can be transmitted as both longitudinal and transverse waves. A diagram that compares a transverse wave to a longitudinal wave is shown below:

The reason sound can travel as a transverse wave through a solid is because, as this website says:

Say that you hit a big steel block on top with a hammer. Just picturing how the atoms are displaced by the blow, you can see that there should be a compressional (longitudinal) wave going downward. Out to the sides, there should be transverse waves.

Since liquids are non-compressible, sound can't travel as a transverse wave through liquid. Also, the compression/rarefaction of gases facilitates longitudinal waves as opposed to transverse waves. According to this website:

An example of rarefaction is as a phase in a sound wave...Half of a sound wave is made up of the compression of the medium, and the other half is the decompression or rarefaction of the medium.

Since this is true, the rarefaction of gases clearly makes longitudinal waves a better choice in gases.
Hope this helps!
(Picture from http://msascienceonline.weebly.com/waves.html)
Answer: Treating a medium as continuous (which works for our purposes), for sound to travel through the medium the motion of one unit of it has to affect the motion of the next unit, and so on and so on. Sound in a gas or liquid does this by varying pressure: the air pressure next to a speaker suddenly increases, pushing a unit of air outwards towards the adjacent lower-pressure unit. That unit's pressure increases, pushing it out towards the next unit along, and so forth. Bingo: longitudinal sound wave.
But, if you move the air side to side without varying the pressure, the next unit along will feel no force, and so will not in turn move, so the incipient transverse sound wave dies aborning.
(This is not completely true, as viscosity and turbulence can pass force between adjacent sliding units of gas. However, the effects of these are dissipative rather than elastic, so there will be no recoil and thus no continuing vibrations.)
In a solid, however, transverse motion can be passed along through the elasticity of the medium. For example, if you take a long fiberglass rod and shake one end side to side, the displacement will travel down the rod in a wave. Even if you stop shaking, the existing waves will continue until they reach the end of the rod.
So, fluids cannot propagate transverse sound waves, but elastic solids can.


How to avoid an English accent in Hebrew

Question: I speak fairly fluent Hebrew as a second language, and I have a UK English accent. I want to know what pronunciation issues generally would be an issue for English speakers and would sound strange/be obvious to a native speaker aside from the guttural r and kh sounds which I have a fairly good grip on.
Answer: I'm no expert in Hebrew, but I did find this extremely helpful YouTube playlist of 6 videos that directly addresses difficult pronunciation sounds in Hebrew for native English speakers. The videos are also very recent, as the last one was posted in September 2015.
Answer: I have exactly the same problem, except that I've got an American accent.
Besides for the r and kh (which I still can't nail the difference between Israelis' pronunciation and us American Jews' pronunciation), there's the obvious difference of vowels - if you start pronouncing the patach (short a) sound like a Brit, the taxi drivers are going to rip you off by at least 50 shekel. Beyond that, just remember that most places in Israel read the Taf and Saf the same way, and you should be fine. :)
Answer: There are two big issues outside of 'r' and 'kh' sounds:

Vowel length. English speakers tend to have much longer vowel sounds than Hebrew speakers. Shorten your vowels.
Another aspect of pronunciation that many don't think about is the speed at which you speak. You could have perfect ר and ח, but if you speak at a snail's space, then you will still stick out as a foreigner.
Answer: A few more tips:

Your vowels should sound the same whether in an accented or unaccented syllable. In English, unaccented vowels all turn to shwa.  So don't do that in Hebrew.  The first word in "good morning" should not rhyme with "poker"!

Don't "swallow" the final consonant of a word.  The final 't' in "tachat" should sound every bit as t-like as the first one.


Worldgaurd not working

Question: In my main world where the spawn is, regions are working with worldgaurd. I made another  world for warps with mutliverse and when I try to do regions in that world it won't work. I have no current regions set in the world now that I made. No even "pvp deny" will work.
Answer: Easy, update your world edit to latest ver, world gaurd also. And if you can to the latest build that your in(if needed).

Worldgaurd not working


Views Menu Tabs and Ajax?

Question: Is it possible to use menu tabs/default menu tabs available in Views, along with ajax, so that hitting a tab does not load a new page?
Answer: If you want to user tabs and have blocks inside them coming from then, then one very beautiful module which you can use is Drupal Quick tabs: http://drupal.org/project/quicktabs
This module works amazingly. It also takes arguments and allow you to do a lot of advanced modifications like Ajax call to the tabs or directly load them etc. You can check the Techtree website for an example of quick tabs that we have used in the side bar.

Views Menu Tabs and Ajax?


The Integration Constant in the Formula for a Catenary

Question: This question may be overly simple, but why does the integration constant appear in some versions for the catenary equation, while in others, not so. What is the mathematical significance of the integration constant, i.e. what does the $C$ in $y = a\cosh(x/a) + C$ denote?
Comment: Consider the difference between the graphs of $f(x)$ and $f(x)+C$ for any function $f$.
Answer: In a nutshell, $C$ is not so much the constant of integration, but more or less determines the depth or placement of the catenary.
If $C>0$, the catenary extends further up from the origin up the $y$-axis, while if $C<0$, the catenary extends further down from the origin down the $y$-axis.  If $C=0$, the inflection point of the catenary will be at $(a,0), a \neq 0$.
Comment: Gratitude. Never did it occur to me how intuitive such a matter could be.


Team Foundation server project template

Question: When we create a project in TFS, we always follow these steps:
1) Create new team project
2) Create workspace, assocate to source control folder and local folder
3) Create three folders under team project (Main, Dev, Release)
4) Check in source to Main
5) Convert Main to branch
6) Create Dev/Dev and Release/Release branches from Main branch
These 6 steps are pretty much stock for every project we build, but it is possible for developers to get it wrong or stray from this design.  Is there something available for TFS that we can use to automate this process?
Answer: You can create a new team project with the "tfpt createteamproject" (from the power tools). You can also execute all your tasks from the command line to (use the tf and the tfpt commands).
In your case, creating a batch file that executes all these commands could be your solution

Team Foundation server project template


Discovering important topics in corpus of text using metadata and text content

Question: I am working on a system to classify documents into important/non-important. I have a large (200,000) sample set of documents which have been pre-labelled and using Naive-Bayes I have achieved 95% accuracy in classifying documents using an 80:20 split of training:test data. This result is amazing and I am confident I can tune the system to achieve better results.
However, the system must be able to be used for an indefinite amount of time. This raises the issue that the content of the documents being classified, or what constitutes important/non-important will change over time, so the model must evolve. Thus I need to find a way to train the model without using pre-labeled data. I have only been able to come up with one potential method for this and it didn't work.
The first method I have tried is using LDA topic modelling to create a set of topics from the corpus. I then attempted to find a subset of topics which fit the important documents and a subset which fit the non-important topics. Unfortunately this method did not work as the content of the important/non-important documents is too similar to create obviously distinct topics.
Does anyone have a suggestion for how I could achieve this or any resources that could point me in the right direction?
Answer: There is no way to keep a supervised model update as the data distribution changes over time without labeling new instances.


Understanding Test functions

Question: Now I'm studying distributions and I have a quesition. One of conditions of function $\varphi$ to be a test function is that it has to be in $C^{\infty}(\mathbb{R})$. So, what are the methods to prove it? For example,
$$
\varphi = \begin{cases}
e^{\frac{1}{x^2-1}}, \text{if} \, |x|< 1, \\
0, \text{if} \, |x| \geq 1.
\end{cases}
$$
Comment: [Related](https://math.stackexchange.com/questions/476195/infinitely-differentiable-functions-how-to-prove-that-e-frac1x2-1-has-d).
Answer: There are two parts of the proof. Second part is to prove that it's infinitely differentiable at $\pm 1$ and on the first is to prove it to be everywhere else.
The first part we see obviously it's true for $|x|>1$. For $|x|<1$ we use properties of rational functions under derivation. We have that if we have a class of functions on the form $r(x)e^{q(x)}$ where $r$ and $q$ are rational and continuous in $(-1,1)$ we have it's derivative $(r'(x)+r(x)q'(x))e^{r(x)}$ is also in that class and it will be indefinitely differentiable. Note that the derivative $r'(x)$ of a rational does not add any poles/discontinuitis as $D_x f(x)/g(x) = (f'(x)g(x)-g'(x)f(x))/(g(x))^2$ so it's only discontinuous when $g(x)=0$ which was the poles of the original rational function.
Now for the point $\pm 1$ we have to consider limits of $r(x)e^{-1/({x^2-1})}/(x-1)$ as $x\to 1$ which are $0$. So this will lead it to be indefinitely differentiable at $\pm 1$ as well. The limit is the "in"-side limit and the "out"-side limit is obviously $0$ as well. The important point here is that $e^{-1/(x^2-1)}$ approaches $0$ so fast it will dominate any pole of any rational function (ie that $e^{-1/(x^2-1)}/(1-x)^n \to 0$ for any $n$).
Comment: Sounds pretty convincing. Thanks!
Answer: You need to prove that $\varphi$ and all its derivatives are continuous.
So first check that $\lim_{x \nearrow 1} \varphi(x) = \varphi(1)=0$ and $\lim_{x \searrow -1} \varphi(x) = \varphi(-1)=0$.
Afterwards prove that the derivatives are continuous.
For $|x|>1$, we have $\varphi'(x)=0$ and for $|x|<1$, we have $\varphi'(x)=\frac d {dx} e^{\frac 1 {x^2-1}}$.  Thus we need to check
$$\ \lim_{x \nearrow 1} \frac d {dx} e^{\frac 1 {x^2-1}}= \lim_{x \nearrow 1} \varphi'(x) = \lim_{x \searrow 1} \varphi'(x)=0,$$ and the corresponding statement for $x\to -1$.
Then continue for the derivatives of higher (arbitrary) order.  Here you need to use the fact that the exponential function grows faster than any polynomial.
Comment: Not sure that this is correct proof. I think we need Taylor series, or may be someting more sophisticated.
Comment: I saw that i didnt write down that $\varphi$ is smooth smooth on $\mathbb R \setminus \{-1,1\}$, but this is obviously true.
The rest of the prooof works, but misses some details which need to be filled in by the op. It is the same idea as skyking uses.

Understanding Test functions


Why we should use REST?

Question: Why should I use REST if I can get my job done with only post and get requests?
Comment: see also [What is the advantage of using REST instead of non-REST HTTP?](http://stackoverflow.com/q/2191049/211232)
Answer: Roy Fielding blogged with some frustration about RPCs masquerading as REST.
REST demands the use of hypertext, which scales very well since the client and server are very loosely coupled.  With REST, the server is free to change the exposed resources at will.  There is no fixed API above and beyond what REST itself defines.  The client needs only know the initial URI, and subsequently chooses from server-supplied choices to navigate or perform actions.  A server may download code to the client which aids in navigation and state representation.
All of this is in stark contrast with the various remote procedure call (RPC) schemes in which the client and server must agree upon a detailed protocol that typically needs to be compiled into both ends (e.g. URIs of a particular form accessed in a particular order at one extreme, SOAP/WSDL/WS* at the other).  This approach is brittle, because any changes need to implemented on both the server and client sides at the same time.  It rapidly becomes untenable as the number of servers and/or clients grows.  Servers in particular suffer because evolution of the published API becomes progressively more difficult as popularity increases.
In light of these factors, REST is always the better choice when possible.  It allows for rapid evolution of servers and allows an astronomical number of applications to interact freely on an ad hoc basis (e.g. the whole Internet).
But what about the "when possible" part?  REST works best when there is a human in the loop.  After all, a human has a good chance of being able to make a rational choice when presented with a previously unknown set of options.  Machines aren't there yet.  Web RPC protocols were born precisely to handcuff both sides to a fixed protocol.  This makes it easier for automated processes to communicate when the human is removed from the picture.  An RPC is a valid design choice when purely automated operation is more important than evolution and scalability (in Internet time and on an Internet scale).
Scale and Coupling?
"Scale" here is meant in a broad sense.  It includes numbers of users and sessions, yes, but also application size and development process.  Tight coupling presents a severe impediment to application size.  It is hard to imagine the existence of the largest known application, the World-Wide Web, without the extremely loose coupling afforded by the REST architecture.  Millions of developers around the globe have collaborated to build this application that supports billions of users.  Yet the developers do this while remaining blissfully unaware of each other (or at least they would be unaware of each other if it weren't for StackOverflow ;).
The primary enabling principle of REST is hypertext.  The other elements of the architecture exist to support that principle in very large scale (in every sense).  Is REST the only conceivable way that the Web could have been built?  No.  But it happens to be the wildly successful de facto standard.  It should be the default choice for any new entry into the ecosystem, discarded only after careful and explicit design consideration.
Comment: How are scale and coupling related?  REST architectures scale because of the layered architecture and caching.  The loose coupling allows components to evolve.  REST is not always the better choice.  If I have two servers in a data center where I control both and they need to do distributed transactions between them, then REST is not the best approach.  Apart from those issues, you make some good points.
Comment: Even when there is a human in the loop, how are clients supposed to redesign themselves on the fly when the API changes? Is it unusual to have a REST client that has any hard-coded forms and buttons? Are all REST clients generating their entire UI dynamically?
Comment: @Darrel Thanks for the helpful comment.  I added the **Scale and Coupling?** section in an attempt at clarification.
Comment: @AlexanderTaylor A typical user agent has little hard-coded UI: address bar, back button, refresh, etc.  Everything else is generated dynamically from the server-provided representation.  See, for example, the _Uniform Interface_ and _Code On Demand_ constraints in section 5.1 of Fielding's REST dissertation.  In a machine-to-machine interaction, these constraints are often too onerous (AI anyone?).  Humans are better at adapting to unexpected interface changes.  Nothing stops us from ignoring REST and tunnelling an API across HTTP (so-called "RESTful API", perhaps better styled "RESTless" :)
Comment: Thanks @WReach. I'm not sure I understand that... for the client, my feeling is that you would still require either navigating the restful resource or reading the docs to figure out what to request. And I don't know what you mean by `there is no public API to break`. Are you saying that the public API is actually a layer that corresponds to your resources? What do you mean by code served on demand to the user agent
Comment: @WReach, then in this case the argument for REST is from the perspective of the server? I.e. a Restful API would require less maintenance from the serverside devs when updating resources, since theoretically those resources' endpoints would update automatically if a RESTful architecture was strictly adhered to?
Comment: @ZachSmith I think the benefit is for the entire ecosystem.  As a user, I can (to a good approximation) sit in front of any browser on any machine anywhere on the planet and get the same application experience.  As a server dev, I do not need to worry about making any breaking API changes because there is no _public_ API to break (and I am in control of both ends of any _private_ API between my server and code served on demand to the user agent).
Comment: @ZachSmith Let's continue this discussion in [chat](http://chat.stackoverflow.com/rooms/143819/why-we-should-use-rest).
Answer: Using REST correctly can help your system components remain properly decoupled and can be evolved more easily in the future than if you had tied them directly together in a typical RPC-like fashion. It's an architectural choice that you must make based on your application's needs. Others have noted some of the technical benefits, and they should be taken into account too.
Answer: REST allows easy evolution of an API design. And that's the key with REST - you're creating an API. Some of the comments have touched on aspects of this thought, but have not actually brought the core issue to life. When you are dealing with REST, you are creating an API that would be used by clients (or yourself). The HTTP actions on the resources give a clear indication to the clients of the API design and functionality. Therefore, when we use the correct HTTP verbs properly, we are declaring an API that is standardised and understandable from a client perspective.
Answer: Why do you think only using POST and GET means it's not REST?
The point to REST is that each "resource" has a resource identifier, a URI.  Each URI potentially has GET, POST, PUT, DELETE.

GET is read
POST is update
PUT is create
DELETE is delete

If you're not doing some of those things -- like PUT is kind of rare and a potential security hole -- then you don't.
Comment: I think it would be more correct to say that POST is create and PUT is update.
Comment: Nobody agrees on which way round POST and PUT go, which is a good reason not to abuse HTTP in this way IMO.
Comment: Trying to map POST and PUT to update and create really does not work.  I do agree though that REST does not require the use of all methods, it just says if you do use one, make sure you use it correctly.
Answer: If your GET requests are not idempotent then HTTP caching between your server and clients would break your application. POST requests are by definition not idempotent, so HTTP caches will not cache these requests and results: you still get the benefits of caching GET requests, without breaking your application's protocol. Great success.
And, if you ever need to delete objects, DELETE will be much easier to read on the wire and logs than a POST request that does the deletion. But web browsers cannot easily make HTTP requests with the DELETE verb, so it's really more for clients you've programmed yourself.
Answer: Discovery is far easier in REST. We have WADL documents (similar to WSDL in traditional webservices) that will help you to advertise your service to the world. You can use UDDI discoveries as well. With traditional HTTP POST and GET people may not know your message request and response schemas to call you.
Answer: You should use REST because of below features and advantages:

Features

Stateless client/server protocol: Each HTTP contains all the necessary information to run it, which means that neither the client nor the server need to remember any previous state to satisfy it. Be that as it may, some HTTP applications incorporate a cache memory. This configures what is known as the stateless client-cache-server protocol: it is possible to define some of the responses to specific HTTP requests as cachable, so the client can run the same response for identical requests in the future. However, the fact that the option exists doesn't mean it is the most recommended.
There are four very important data transactions in any REST system and HTTP specification: POST (create), GET (read and consult), PUT (edit) and DELETE.
Objects in REST are always manipulated from the URI. It is the URI and no other element that is the sole identifier of each resource in this REST system. The URI allows us to access the information in order to change or delete it, or for example to share its exact location with third parties.
Uniform interface: to transfer data, the REST system applies specific actions (POST, GET, PUT and DELETE) on the resources, provided they are identified with a URI. This makes it easier to obtain a uniform interface that systematizes the process with the information.
Layer system: hierarchical architecture between the components. Each layer has a functionality within the REST system.
Use of hypermedia: hypermedia is a term coined by Ted Nelson in 1965 and is an extension of the concept of hypertext. This concept, taken to web page development, is what allows the user to browse the set of objects through HTML links. In the case of a REST API, the concept of hypermedia explains the capacity of an app development interface to provide the client and the user with the adequate links to run specific actions on the data.

Advantages

Separation between the client and the server: the REST protocol totally separates the user interface from the server and the data storage. This has some advantages when making developments. For example, it improves the portability of the interface to other types of platforms, it increases the scalability of the projects, and allows the different components of the developments to be evolved independently.
Visibility, reliability and scalability. The separation between client and server has one evident advantage, and that is that each development team can scale the product without too much problem. They can migrate to other servers or make all kinds of changes in the database, provided the data from each request is sent correctly. The separation makes it easier to have the front and the back on different servers, and this makes the apps more flexible to work with.
The REST API is always independent of the type of platform or languages: the REST API always adapts to the type of syntax or platforms being used, which gives considerable freedom when changing or testing new environments within the development. With a REST API you can have PHP, Java, Python or Node.js servers. The only thing is that it is indispensable that the responses to the requests should always take place in the language used for the information exchange, normally XML or JSON.

Source
Answer: You should use REST because it really encompasses all the potential actions you want to do on a resource/object.

GET - Retrieve a resource based on given conditions
POST - create a resource
PUT - update a resource with the given updated attributes
DELETE - delete a resource

Another reason is that it is a standard that everyone can implement and use. To read up on why standardization is important, I would suggest reading this and this (it is rather funny, but really helps people grasp the concept of REST).
Comment: It is NOT a W3C standard.
Comment: POST and PUT does not map to Create and Update. Sometimes it does. But there is nothing wrong with creating new resources with a PUT if that suits the problem best. However the request must be safe to repeat (idempotent), and if it is you should use PUT, not POST. Conversely, if your updating request is not safe to repeat, you should use POST, not PUT.

Why we should use REST?


How to pass dynamic pcollection as sideinput in python?

Question: I have use case in which I need to append a file_path (as a new element) with another pcollection which is a dictionary of elements.
So I decided to take pcollection as input to my next transform and file_path (which is generated from pardo function) as a sideinput.
As generated file_path is a pCollection so I am using it as :
beam.pvalue.AsSingelton(file_path)
but strangely it's not executing this statement hence no output from this and not even any error.
But when I create a pcollection using :
file_path = beam.Create(['some_path_value']) and than pass as above
beam.pvalue.AsSingleton(file_path)  it works perfectly.
but I don't want to create a pcollection explicitly .i need to use above transform output as it is as sideinput.
I tried each form for my "file_path" like made it List, dictionary, tuple.
I tried different beam functions as well.
def collect(pcoll, path):
   print(pcoll, "-----------")
   print(path,"-------------")
   return path

class Extract(beam.DoFn):
   def process(self, element, *args, **kwargs):
       pub_sub_json= json.loads(element)
       gcs_url = "gs://" + pub_sub_json["bucket"] + "/" + pub_sub_json["name"]
       yield gcs_url

file_path = (p |"Read" >> beam.io.ReadFromPubSub(
                           subscription=options.session_subscription,
                           with_attributes=False)
             | "Extract" >> beam.ParDo(Extract()))

result = (some_other_pcollection |"display" >> beam.FlatMap(collect, path=beam.pvalue.AsList(file_path)))

Expect: It should go inside a collect function and print whatever Extract method will return as file_path.
No Errors and warnings are coming but it's not even going inside the collect method. It mostly happens when the data won't come from the above transforms. But I checked it many times file_name has data.
but no output, it only shows output when I use beam.Create(["pass_some_file_path"]) and use its result as sideinput
Answer: Output from a Transform should be in the 2-tuple ( (key,value) ) format in order to accept it as a side input with pvalue.AsDict(). It works well with value.AsList() too.
def collect(pcoll, path):
   print(pcoll, "-----------")
   print(path,"-------------")
   return path

class Extract(beam.DoFn):
   def process(self, element, *args, **kwargs):
       pub_sub_json= json.loads(element)
       gcs_url = "gs://" + pub_sub_json["bucket"] + "/" + pub_sub_json["name"]
       yield pvalue.TaggedOutput("url",("url" :gcs_url))

file_path = (p |"Read" >> beam.io.ReadFromPubSub(
                           subscription=options.session_subscription,
                           with_attributes=False)
             | "Extract" >> beam.ParDo(Extract()))
file_path_new= (file_path["url"] | "Group by key" >> beam.GroupByKey())

result = (some_other_pcollection |"display" >> beam.FlatMap(collect, path=beam.pvalue.AsList(file_path_new)))

Were you able to solve it in a better way?


Creating a 3d illusion pattern

Question: I want to make a pattern to etch on a table with a laser. What I want to do is start by generating a repeating pattern and then bend it in a way that makes it look like it's going in and out of the page. Something like the background of this pic but 100% original. If you can tell me what software to use and give me the steps I'd appreciate it.
Answer: If you have a repeating pattern, then you could use the Liquify filter in Photoshop and use its Pucker tool, or you could use the Warp Transform Tool in GIMP, and in the Tool Options set it to "Shrink Area".
Here's an example made using GIMP's Warp Transform tool. The same is possible in Photoshop using the Liquify filter.
Comment: fantastic! that's exactly what i was looking for! thanx. any file type is fine, no vectoring needed. i can etch raster images. So the one last thing is figuring out how to generate a repeating pattern from scratch. Is there a tool you know for that?
Comment: @DrorSapir You can use GIMP or Photoshop to make seamless patterns. Perhaps search for some tutorials. There are some on youtube.

Creating a 3d illusion pattern


In The Wheel of Time, how were Aes Sedai able to be used as damane while under the Three Oaths?

Question: That is, those Aes Sedai who were captured but were not part of the Black Ajah. If the Three Oaths bind them to not use the One Power to harm another except for Darkfriends and shadowspawn, how could they be compelled to do so even under the influence of an A'dam?
Answer: Robert Jordan has answered a question similar to this. It can be found on Theoryland when searching for Third Oath

INTERVIEW: Jan 25th, 2005
TOR Questions of the Week Part II (Verbatim)
WEEK 21 QUESTION: Just how can an Aes Sedai be a damane? Aren't they bound by the Third Oath: to not use the One Power as a weapon except to defend their lives, their Warder's life, or another sister's life? Wouldn't they be useless as damane to the Seanchan?
Robert Jordan: The Aes Sedai captured by the Seanchan are indeed useless as weapons, except against Shadowspawn or Darkfriends, because they are bound by the Three Oaths, and that limits their value considerably since being weapons is a major use for damane. Damane are used for other tasks, however, including finding ores for mining (Egwene was tested for this, remember; it's a very valuable, and fairly rare, ability), for some mining operations where it would be too dangerous or uneconomical to use human miners (bringing ores out of the ground and refining them using the Power), and in some construction projects, especially where something very large or with a need for added strength is envisioned. The first two both require a high ability in Earth, which has faded considerably on "this" side of the Aryth Ocean and to a smaller degree of the other side, but construction projects and others things, such as producing Sky Lights, are well within the abilities of collared Aes Sedai. The Three Oaths don't inhibit them there at all.

In short, the Aes Sedai damane were not used as weapons, but instead they were used as tools to find ore, heal the injured, build buildings.
An excerpt from Knife of Dreams -

He had considered using another damane than Mylen. The tiny woman with the face he could never put an age to almost bounced in her saddle with eagerness to lay eyes on the High Lady again. She was not properly composed. Still, she could do nothing without Melitene, and she was useless as a weapon, a fact that had made her hang her head when he pointed it out to the der'sul'dam. She had needed consoling, her sul'dam petting her and telling her what beautiful Sky Lights she made, how wonderful her Healing was.
Karede's Point of View - Knife of Dreams (Chapter 36)

Even though Mylen (Sheraine Caminelle) wants to please the der'sul'dam very badly, she still cannot use the One Power as a weapon.
I finally found the quote referencing an Aes Sedai damane, Pura (originally known as Ryma Galfrey), who could not be forced to lie about the colour of a scarf:

Her agents reported that the women from the White Tower could not lie. It had not been possible to force Pura to tell even a simple lie, to say that a white scarf was black, yet that was not enough to be conclusive.
Seeds of Shadow - The Shadow Rising (Chapter 1)
Comment: There's also another quote about some of The Blood trying to force an Aes Sedai damane to lie about the colour of a scarf but I can't find it anywhere
Comment: +1; that KoD quote is exactly the one I thought of when I saw this question.
Comment: There were actually comments in the books to this effect too, which would strengthen your answer
Comment: Good answer, thanks. I'm rereading the series for the first time in years right now and I didn't remember this point ever being addressed (I'm only on The Dragon Reborn right now).
Answer: This may work better as a comment on the word of god answer however IIRC the oaths only bind an Aes Sedai dependent on their perception IE an Aes Sedai could tell a lie if she believed what she said to be true
If the Seanchan managed to brainwash an Aes Sedai into believing that their enemies were darkfriends the power could be used as a weapon.


What makes a weight-controlled microlight tumble, and can it recover?

Question: As shown in this video, what causes a weight-controlled microlight to tumble, and is it possible to stop it from tumbling once it starts?
Comment: Looks like stall.
Comment: The tricky thing about this type of aircraft is that wing camber is influenced by the pressure distribution over the wing. This means the pitching moment of the wing is changed by the pitching motion, causing a lock-in. Also, centrifugal acceleration makes it hard for the pilot to shift his weight any more once the motion has started.
Answer:
what causes a weight-controlled microlight to tumble

There seem to be several mechanisms. One is an excessively sharp nose-down control input after entering or approaching a stall.

and is it possible to stop it from tumbling once it starts?

Not without an external safety device (presumably a throwable parachute or something similar)

The tumble mode is a little known mode of departure from controlled flight experienced by weightshift controlled microlight aeroplanes. It has been a very significant factor in fatal accident records, being non-recoverable without the use of external safety devices. The mode consists of a nose-down autorotation at a rate of up to 400°/s. The tumble entry mechanism is explained, and advice to operators developed which should prevent tumble entry. Evidence is shown of the nature of the developed tumble – both modelled and through wind tunnel results, which explain how the autorotation occurs. It is also shown how this theory may be applied during testing of an aircraft to develop a tumble resistant aircraft.

See A theoretical and experimental appraisal of airworthiness evaluation techniques for small light aeroplanes

This seems to be an excellent paper 255-page dissertation which contains far far far more than the average reader of this website could ever want to know about this phenomenon.
You should note that this contains stills from the Youtube video in the question. It is therefore directly relevant. If you can find a better analysis I will print out my answer and eat it.
Comment: With a 255 pages count, I find it difficult do describe it as a "paper" but rather a book. EDIT: and in fact is a Doctoral dissertation.
Comment: @Federico: Good point, amended.
Comment: Stall itself causes down pitch moment and weight-controlled aircraft have limited control authority.


Bus from San Pedro de Atacama to Antofagasta, Chile?

Question: I'm looking for a bus from San Pedro de Atacama to Antofagasta, Chile in September 2013
I found a bus company but looks like there are no buses in September. Do you know any other bus companies who operates in September on my route?
Comment: What makes you think that do not offer buses in September? It seems to me only the reservation system does not reach that far. Did you try to call them?
Answer: There are buses.  At the very least, you can get a bus 1.5 hours west to Calama, which has a bigger exchange. A member of our party did that in August (winter) and got to Antofagasta, Iquique and more.
The bus companies in Chile/Bolivia don't have much online presence - it's far easier to just get one in the town - but go as early as possible when you know when you want to leave, gives you more options.
Indeed, as per Wikivoyage, there are many daily arrivals into Antofagasta from both San Pedro and Calama.
If you are arriving in San Pedro after a Salar De Uyuni tour, ask your tour company as they can often book ahead for you. Members of my party did that with Tierra Mistica - the company we used for the salt flats.
In general, after 4 months travel in South America from July to November, the only place I could really book online was in Argentina - everywhere else I just did it at the bus terminal in each city, and never had a problem finding some sort of bus.
Answer: My English is not so good but you can seek for Turbus buses. The bus company covers all Chile ;-)
Bon voyage
Comment: Unfortunately they do not sell tickets outside the country (i.e. you cannot buy it online unless you're chilean resident) Do you know any other ways to buy the tickets?
Answer: The ease of searching and booking bus schedules in Chile online has improved since this question was posted; you can look at recorrido.cl to check schedules and book. Searching that website for an arbitrarily-selected date a few weeks from now shows three services per day offered by Pullman Bus, though of course things may vary. Travelers who do not have a Chilean debit or credit card can pay by PayPal.
Particularly outside of peak season, though, it is probably also completely fine to just stop by the bus station in San Pedro and ask around; the bus station is easy to find and an easy walking distance from the main tourist center of town. As other posters have mentioned, you may have more options for travel time if you are willing to connect in Calama, and it is easy to ask about this if you talk to the bus companies in person.