Does pure math have an application in communications engineering?

Question: I am a communications engineering undergraduate, and I was thinking of studying pure math courses will this help me later on in graduate school, and if it will help what courses of pure math will be related to my major?
Comment: The "pure math" label is very, very silly, ... especially as usually put in opposition to "applied math", ... when we're asking about applications to signals engineering, say. But, certainly, as in the work of C. Shannon (as @WillieWong noted), in the work of N. Wiener, and many others: yes, certainly mathematics is useful to communications engineers. Linear algebra over finite fields, Fourier transforms, and so on. So, abstract algebra, real analysis, complex analysis, functional analysis. And these have prerequisites.
Comment: You may get a better range of responses to this question if you ask it on http://math.stackexchange.com/
Comment: You mean, like the stuff that [this guy did](https://en.wikipedia.org/wiki/Claude_Shannon)?
Comment: If so, then it will be called "applied math". ;-)
Comment: @Willie Wong yes
Comment: Group theory has applications for error control codes.
Answer: I'm in a similar situation to you. I'm finishing my masters in digital communications and doing my thesis right now. Math is an issue for me definitely.
In my experience, a bit more complicated math is helpful if you're going to be developing systems that do statistical signal processing (which seems to be very popular now) and anything that has "smart" in its name.
What exactly do you need depends on what you want to study in detail. It might be a good idea to first dip your toes in the fields you want to be working with first and the pick math courses you want to take. You could try looking at some books or papers about say adaptive filters or modern receivers or estimation theory. This should give you an idea what's usually needed. If you're lucky enough to have approchable professors, do ask them about what will be useful to you.
Answer: I find Paul Garrett's recommended courses rather ambitious for a non-math major undergrad, if the context is the U.S.
You would be well served by covering most of the basic math classes needed for a physics or engineering major:

the calculus, including multi-variate
an intro to ordinary differential equations -- this is a classic course and will prepare you for the Fourier transform
linear algebra -- will make a lot of things easier once you've had this; also, as long as your course is rigorous and not too cookbook, you will gain mathematical maturity by doing lots of proofs
if you enjoy it, you could have some fun with a numerical methods class (although this is not a pure math course)
intro to probability or graph theory (for something totally different)
if you want more pure math, then take "advanced calculus" (but not without a rigorous linear algebra class under your belt)
Comment: If you like math, and want to take advanced math courses, it is quite likely that they will help you later in your career. Especially if you choose topics related to communications engineering. For example, the amount of probability taught in an intro to probability course is  insufficient for a lot of real applications. On the other hand, if you don't like math, I wouldn't advise taking extra math courses. You'll struggle to get through them and possibly forget everything you learned before you have a chance to use it.


Can I use Amiibo as a playable character in Smash?

Question: I recall seeing an ad of bunch of teenagers playing Smash as their Amiibo characters, but I can't seem to find a way to actually do it.
I know I can play in a team with Amiibo and have it be controller by the CPU, but is it possible to control it myself?
Answer: It is impossible to control the Amiibo character.
I checked the electronic manual and it specifically mentions that Amiibo can be used as a Figurine Player and cannot be controlled.
Comment: Unfortunately I couldn't find the electronic manual online, so I can't link it.
Answer: I checked Nintendo's FAQ on amiibo, and confirm you can't play as your amiibo.  I felt so let down when I saw that you cannot use your them as a player.  It's like you have your own Poke'mon but for Smash Bros.
Answer: Unfortunately, no you can't. Trust me, I just figured this out as well. They're like a pet, you can train them and battle other pets. I bought 5 today. It's like a Pokemon I can train it and everything. Until I log on and find out all I do is watch it fight and level up. You can't play as them, but you can fight beside them. But still, I just spent about $60, and the commercial on TV showed teens playing as their Amiibo, which is apparently wrong. So you can not be them.


By what authority can Wonder Woman perform a marriage?

Question: Apparently, in a new issue Wonder Woman officiates a marriage. However as a foreign diplomat under what authority does Wonder Woman have to do so?
Comment: She's Wonder Woman. Are you going to argue?
Comment: She took an online course and paid $20 for a license.
Comment: Even Dwayne "The Rock" Johnson performed marriage. It can't be that difficult for Wonder Woman.
Comment: Wonder woman would not legally be recognized as a valid wedding officiater in NYC. She is not a minster or clergy (wo)man as far as the new 52 had shown. Diplomats and Ambassadors do not have special marriage privileges in NYC. And as can clearly be seen, she is performing the ceremony in line of sight of NYC, putting her in the 5 boroughs, so the line about "By the Power vested in me by the ***State*** of NY" is bs since NY state registered ministers have no standing in NYC which has its own rules/laws. Anyone married within nyc limits must follow NYC code.
Answer: She says it right there, the State Of New York.  Wonder Woman got licensed to perform marriage in New York state.  She tells Clark after...

I'm licensed in every state and country that would allow me.

It's not difficult in New York, there are just some hoops.
To perform marriage in New York state (see Solemnization Of Marriage) the person performing the marriage must register with the appropriate clerk and be any one of...

Clergy or minister of any religion.
The leaders of one of several Societies For Ethical Culture.
Various judges.
Various clerks.
Various mayors.

One does not need to be a resident of New York.
As a Goddess, Wonder Woman could be considered clergy by New York State. It's Wonder Woman, so the clerk would probably give her some leeway. Or she's a minister in the Universal Life Church or similar religion who will ordain you and give you the necessary paperwork.
In New York City it's a bit harder.  Simply being ordained a minister isn't enough, you need to show you have a congregation.  I don't know her lore enough to know if she has worshipers and performs ceremonies for them.  If she did, that would be enough.
Answer: Keeping it in the USA (since she says it's in New York):
Let's skip Las Vegas, which has a few gazillion wedding chapels with Elvis impersonators and many other unusual wedding officiants, since that basically proves that, in Nevada, it's not but so difficult to get a license to perform weddings.
Wonder Woman's ability or authority to perform a wedding has nothing to do with her diplomatic status or lack thereof.  Each state has its own laws about what is required for a person to be able to officiate at a wedding.  Quite often it comes down to having some kind of certificate of ordination and paying a small fee, swearing an oath (or something like that) and then being certified by a court clerk.  (Sometimes this may need to be done in each county or city where one wishes to officiate at a marriage.)
The most specific part of the process is gaining a certificate of ordination, but this can be obtained through the mail or online from many sources, even at least one Church of the Flying Spaghetti Monster.  All one needs to do is find a group with beliefs they are comfortable with, fill out the forms, and become ordained in their unique little religion.
In New York (since that's the state she's in), requirements don't appear to be too difficult, but she might have to use some paperwork to show she's authorized by a church.
Essentially anyone can gain the qualifications to marry a couple in most states in the USA.

For those requiring more detail or an example, In Virginia (good, simple example, plus I live there and know people who have gone through this process), an officiant simply needs to go to a court clerk (I presume for the locality in which the officiant wishes to perform marriages), present the certificate of ordination and $16 and answer some questions.  Then, poof, it's official and the person is a able to officiate marriages.  Also note that, in Virginia, one must be a resident of the state to qualify.  (Again, this is just an example, but maybe Wonder Woman could provide some proof of residency if needed.  But non-residents and non-ordained can obtain certificates for one-time-only officiations, so that would mean Wonder Woman could do this.)
Other states, of course, have different laws.  Some will have different residency requirements for the couple getting married, as well.
A certificate of ordination is a tricky thing.  I have friends who can officiate at weddings and have their own faith and, basically, their own church.  I know some who have basically sent in a few dollars to various "churches" and have received the papers that are considered legal.
I know of one example that doesn't fit most "normal" definitions.  I belong to a local Quaker Meeting.  Quakers don't handle many things like other faiths do.  For instance we (at least unprogrammed Quakers) do not believe in ordination and we do not have a specified minister or preacher.  The closest we have to any recognized leader is the Clerk of the Meeting, and that changes every two years.  The Clerk's job is to facilitate and coordinate and handle administrative issues, but not to be a preacher or a leader in the traditional sense.  So every two years we have a new Clerk, and they have to get certified to perform weddings.  I don't know the details, but I know it's a simple process and one done every time we get a new Clerk of Meeting.  They're not ordained (and Quakers do not swear oaths, either).  I don't know what exception is made, but that's proof one does not have to be any kind of local, state, or federal official to perform a wedding, at least in this state, and that even someone without ordination is able to do this.
Comment: Yeah, well, when you finish filling out the forms, the power is vested in you, whether you're a state official or not.
Comment: Can of worms eh? Howzabout this ? By Amazonian laws she can officiate nearly anything she wants but as to who will recognize it...
Comment: I'm not sure, but can't you do a quick civil wedding in NY State for $100.00 bucks? Almost the same as Vegas?
Comment: Speaking of being married by Elvis impersonators, I see a great opportunity for Vegas wedding chapels here.
Comment: Some states also require a letter of good standing in the religion you are ordained in. So for the universal life church, you simply pay a fee and they send you the required letter.
Answer: Knowing that Themiscyra has it's own Amazonian laws; and that Diana served as Ambassador, it seems feasible. In reality most of the Commonwealth has revoked that privilege.

Until DC's New 52 relaunch, there were a few other aspects of the origin story that remained consistent. Her mother, Hippolyta, created her out of clay, and the Greek gods bestowed her with life, making her the only Amazon who was not conceived by a man. She grows up among the Amazons who teach her the skills of a warrior as well as the lessons of peace and love. When Steve Trevor, an American pilot, crash lands on Paradise Island, the Amazons have a contest to determine who should receive the honor of taking him back to man's world and acting as an ambassador of all that the Amazons represent.

Source

In January 1995 the Australian Attorney General revoked all appointments of marriage officers at Australian overseas missions. Therefore consular officers can no longer marry Australians.

Source
Comment: Australian law would not apply to New York state.
Comment: She says "by the power vested in me by the State of New York", not "by the power of the Amazons" or even "by the power of Greyskull". An ambassador on foreign soil performing a wedding under their own laws would invoke their own country, not the location they're currently standing in. The clincher is the next panel where she tells Clark Kent ["I'm licensed in every state and country that would allow me."](http://funagram.com/wonder-woman-speaks-out-for-marriage-equality-and-educates-clark-kent-in-the-process/)
Comment: Why would an Amazonian ambassador invoke the power of the State of New York?
Comment: True, but it would be a U.S. Federal decision whether a foreign marriage is recognized. Most Commonwealth countries have gay marriage rights; but they would not be recognized in some American states. Simply saying that as an Amazonian Ambassador she feasibly could officiate a wedding. As to who would recognize it, well depending upon definition there would be 200 different countries laws to run through.
Comment: Hence my point, Diana can officiate the wedding but there will be plenty of jurisdictions that would not recognize the ceremony; Amazonian or not. I'm touching on the ambasssador role; if done the ceremony was exercised on a consular property then it would be legal under set country's laws. Go Battlecat!!
Comment: Sorry forgot something. Every state...that would allow me. Obviously, a great many would not.
Comment: Which countries does NY recognize Ambassodor foreign weddings? Just curious. We've had one in Canada; Dutch princess; escaping the Nazis. Birth ward of the hospital was declared Dutch territory for the birth of a royal. If I'm wrong please feel free to enlighten me.


Why is Ubuntu 16.04 so slow to boot on my Dell Inspiron 6000?

Question: Ubuntu takes roughly 3.5 to 4 minutes to boot on my old Dell Inspiron 6000 (2GB Ram).
Removing powerd solved the problem for someone else's device, but powerd is not loaded on my installation.
Answer: Ubuntu 16.04 comes with systemd as the start-up manager.
The following command can show you all the startup services of your system from longest to shortest to help you determine what can be causing your slow boot:
systemd-analyze blame

Here is an example output of that command:
terrance@terrance-ubuntu:~$ systemd-analyze blame
          5.077s NetworkManager-wait-online.service
          3.921s postfix.service
          1.806s winbind.service
          1.789s nmbd.service
          1.540s samba-ad-dc.service
          1.405s dev-sde1.device
          1.393s fail2ban.service
          1.222s upower.service
          1.210s accounts-daemon.service
          1.169s vmware.service
          1.034s smbd.service
           895ms apt-daily.service
           797ms media-500GB.mount
           768ms media-250GB_SHARE.mount
           762ms ModemManager.service
           758ms networking.service
           683ms media-Seagate.mount
           639ms NetworkManager.service
           592ms vboxdrv.service
           578ms media-320GB.mount
           453ms grub-common.service
           450ms gpu-manager.service
           420ms vmware-USBArbitrator.service

Hope this helps!
Answer: Why so slow?
Ubuntu is a heavy operating system with a lot of demanding resources. It has a lot of "eye-candy" that can slow down the system, too.
Try a different Ubuntu flavor
Other Ubuntu flavors, like Xubuntu or Lubuntu, keep all of the features in Ubuntu but with a lighter and faster interface.


Increasing font/typeface size in Windows Live Mail (Windows 7)

Question: I am a handicapped user. As my handicap progresses, I find the font/typeface size used in the read panel is progressively harder to read. I already have the font size set to "largest". Is there a way to increase the size of the font/typeface used in the read panel?
Answer: Before I tell you how to change all your settings, You need to know about 1 trick, that works in the browser (usually) and In the Live e-mail programs. ZOOMING.
Hold down the CTRL button and press the + & - Keys on the keyboard or number pad.
This method could be superior to making any other changes, it is fast, adjustable, and less things break when you use this method.
To use that method in the e-mail , double click on an eamil to open it first.
To change the Read and compose fonts in WLM Windows live e-mail.
There is a very poorly marked blue button on the same line as the menus

Clicking on that button can get you to the Options for Mail.

Once you get into the options, there will be 2 tabs you will want to access.
1) Read , click on the read tab in options.

To adjust the font size for reading e-mails , select Font in that tab as shown.
Then adjust the font sizes to larger.  (see notes)

2) Compose, for making an e-mail on your end.

Click on Font Settings, and adjust the Mail font here in the compose tab.
Notes: This is based on Windows Live Mail 2013 version.
Some people indicate that these changes are not enough. This is becuse many of the e-mails we are observing are created in HTML, the fonts are set in the html.  Look back in the 2nd picture and you can see [X] Read All Messages in Plain Text This has ramifications of reading the actual HTML code items itself, but returns control of the font rendering to the settings.
When all else fails, the magnifyer has 2 methods of operation, zooming the whole screen >200%, and being used to zoom up parts of the screen. Refer to the Help in the magnifyer, or ask about it in another question.
Comment: Ctrl-+ didn't zoom for me but Ctrl+ scrolling the mouse wheel did. Works great on HTML.


Term for "something that pursues goals"

Question: Is there a word for "something that pursues goals"?
Animals pursue goals, but so do humans, and we can even say that bacteria pursue goals, or even governments and companies.
Comment: **Never** consult a thesaurus when writing your résumé, especially not our local elugameosaurus here.
Comment: Is this comment in the right place? I'm wondering because there's no reference to a résumé in the question.
Answer: An important concept here is that of teleology and telos:

Teleology or finality is a reason or explanation for something as a function of its end, purpose, or goal.

  A telos (from the Greek τέλος for "end", "purpose", or "goal") is an end or purpose, in a fairly constrained sense used by philosophers such as Aristotle.

Per Merriam-Webster, the adjective form is telic:

Tending toward an end or outcome
Characterizing an action that moves toward a goal

So you could describe the telos of animals, humans and bacteria, or describe them as telic. Or you could be studying the teleology of them.
Comment: I actually thought of that too, but double checked with the Wiki article and figured it's a bit too broad here. It's original meaning is to describe how everthing has some ultimate purpose. Wiki: "Aristotle claimed that an acorn's intrinsic telos is to become a fully grown oak tree."
Answer: I agree with Jason Bassford's 'goal-oriented'.
Purposive is an alternative synonym; in your context you could speak of purposive organisms.
Dictionary

having, showing, or acting with a purpose, intention, or design.

There is a branch of psychology called purposive behaviourism which includes humans and animals. Here a quote from the Wikipedia article:

This approach of Tolman's was first introduced in his book, Purposive
  Behavior in Animals and Men, published in 1932. To Tolman, it was
  obvious that all actions of behavior are goal-oriented, including
  those for animals.The main difference between behaviorism and Tolman's
  purposive behaviorism is that behavior is goal oriented.
Answer: I can't think of a noun that means that, but the adjective, appropriately enough, is simply goal-directed:

[Merriam-Webster]
  : aimed toward a goal or toward completion of a task
  // goal-directed behavior

In short:

They are goal-directed.

A less specific, but perhaps more common, adjective is purposeful:

[Merriam-Webster]
1 : having a purpose: such as
a : MEANINGFUL
  // purposeful activities
b : INTENTIONAL
  // purposeful ambiguity
Comment: Related: _goal-oriented_
Answer: seeker
Use cases:

the Doppler frequency difference's fomulas are given based on its relationship with the flight altitude, relative velocity and range between target and seeker.
  (Effect of target parameters on pulse Doppler radar seeker … in Sys Engg & Elec.,2012. Abstract)

See also:

…R denotes the spatial distance between target and seeker; …
  (Gaoxiang Zou, A Modified Four Path Method for Calculating Coupling Field of Super-Low Altitude Aircraft Target, J. Comp. & Comm. VI 12, 2018. Abstract)

and

Minor plane differences between target and seeker will be corrected during boost flight by the Titan 2.
  (Aviation Week & Space Technology, Vol. 79, 1963, p.195. Extract, Google Books)

Term for "something that pursues goals"


Is it possible to mark all articles in a group as "unread" in Feedly?

Question: I have added several interesting blogs to my feedly RSS feed, but I would like to mark all the articles there as unread. Is there a way to do that in feedly?
Answer: You can now on a item-by-item basis. The quickest way is using the keyboard shortcuts n to select the next article in the current feed and then m to toogle read status to unread.
Comment: That's at least something, thanks, however some RSSs are hundreds of articles long. Upvote, but no answer yet
Answer: Scroll down to load all articles inside the feed you want to mark as unread,
press F12 to open the Developer Tools Console, paste the following code in the console, and hit enter (source):
document
 .querySelectorAll('.mark-as-read')
 .forEach(markAsReadButton => {
   if (markAsReadButton.title === 'Mark as unread') {
     markAsReadButton.click()
   }
 })

It works, but you have to remember that Feedly, at least on the free program, only saves articles 30 days old, so only these will be saved as unread.
Answer: Go to https://feedly.com/i/label/feedly.history and log in. open console and write in:
document.querySelectorAll('.EntryMarkAsReadButton.rounded.EntryToolbar__button.button-icon-only').forEach(div => {div.click()})
this works for have loaded and read news, so you shoul reload website and run this command in console again until all news will be marked as unread.
Answer: Building on HeyJude's answer, slightly less tedious than scrolling with the mouse-view.
Open the Developer Tools Console.
Spam these lines a few times to scroll to the bottom of the page and trigger more articles to be loaded on the page:
headings = document.querySelectorAll('.EntryList__heading');
headings[headings.length-1].scrollIntoView();

Then, once you've loaded a month's worth of articles:
document.
  querySelectorAll('.EntryMarkAsReadButton').
  forEach(buttonElement => {
    buttonElement.click()
  })

Answer: Still couldn't find this feature today. A workaround I recently found is as follow (I tested it on Chrome browser)

Click the 'check' button, then select "Older than one day"
Immediately click "undo" on the bottom right corner.

by now, all the articles older than one day are marked as unread. You'll have to mark today's articles as unread one by one, though.


How to skip verification of .dmg file located on a network filesystem?

Question: I have a file server (SMB/Samba 4.5.16) in the local network. If I put a .dmg file on it (anywhere) and try to mount it, MacOs will ALWAYS verify it first, which means reading through the whole thing, which takes almost 30 minutes for a 200GB file over GBit Ethernet.
So again, the scenario is: An SMB server exports a share, I mount that normally on the Mac (which works fine), the share contains a .dmg file, I try to mount that, the .dmg file gets verified. Every time. After that, the mount succeeds and I can use the dmg's filesystem without issue, but the 30 minute verification is a total show stopper.
I tried the following things, none of which help (all from How do I skip verification of a .dmg file?):
# Disable the "Are you sure you want to open this application?" dialog
defaults write com.apple.LaunchServices LSQuarantine -bool false

# Disable Disk Image Verification: Verifying ...
defaults write com.apple.frameworks.diskimages skip-verify -bool true
defaults write com.apple.frameworks.diskimages skip-verify-locked -bool true
defaults write com.apple.frameworks.diskimages skip-verify-remote -bool true

Mounting the thing with hdiutil attach -noverify mounts the filesystem read-only -- useless.
This is an M1 Mac running Big Sur. I had an Intel Mac running Catalina before, and I didn't have this problem with that. The file mounted almost instantly (i.e. no verification), from the same file server.
If I copy the file to the local disk and mount it from there, it works without verification.
How do I fix this? Is anyone doing this successfully, and if so, which file server and MacOs version are you using?
Answer: Update: I just updated to Monterey, and it looks like they fixed this. Whatever. Miracles do happen.


Sort Tablesort by Computed Field?

Question: I am using an EntityFieldQuery with ->tableSort() and then adding a few columns to each row programatically. Is there a way to have tableSort() sort by my computed fields instead of only raw db fields? (Note: I don't mean the module Computed Field - which I now realize is probably the solution.)
Answer: Unfortunately not; an EntityFieldQuery is just an interface to a normal SQL query.
All values for computed fields are determined after the data has been loaded from the database (in the _computed_field_compute_value() function) so this won't be possible using the TableSort extender.
Comment: Two possible options for providing this functionality: 1. Add fields to the db table that are computed as the entity values change. Then use those as properties in a conventional EFQ. 2. Subclass EntityFieldQuery and override tableSort() with a function that could accept headers with type 'computed' and a callback function in the specifier that builds the computed field. Then modify tableSort() to make mysql sort if by db fields or load all rows and sort/limit by computed field in php. Thoughts?
Comment: Personally I wouldn't go with option 1; modifying core database tables is not considered good practice (even if you do it in a non-intrusive manner). I'm pretty sure you'd still need to subclass `EntityFieldQuery` to do that anyway so I'd go for option 2. It's a much more scalable (and pleasing) solution
Comment: For option 1, I was actually talking about adding properties to custom entities (not core). With option 2, performance would quickly become an issue since all rows would have to be loaded and computed fields would be computed on every query. What about an API that would use its own table to store the results of computed fields and provide an EFQ subclass that joined that table into the query? Actually, that would be very similar to just using Computed Field.
Comment: Ah if you're using custom entities that makes things a lot easier. Id go for option 1; I'm pretty sure all you'd need to do is implement `hook_entity_presave()` to loop through the fields on the entity, get the computed values, and assign them to the properties. Then they'd be persisted to the db and you can use them with a bog standard `EntityFieldQuery`

Sort Tablesort by Computed Field?


Replacement water shut off valve stem is too short to protrude past the wall board

Question: In my condo, I replaced my old, crusty, main shutoff gate valve with a brand new ball valve.  The only problem is that the distance from the base of the gate valve to the end of its stem is about two inches longer than the distance from the base of the ball valve to the tip of its stem.  So, while the gate valve's stem protruded through the sheet rock wall that covers it, the tip of the stem on the new ball valve is below the sheet rock's surface.  I've seen some valve extenders on-line but they appear to be for a specific brand of valve--I got mine at Lowes, it's an "Everbilt"--and I cannot tell if the one on-line will fit my valve.  Does anyone have a solution?
Answer: Make the drywall hole a lot bigger or just big enough for your hand to operate the valve & put one of these Access Panels (left) over the drywall hole. Preferably glued or caulked & drywall anchor screwed, since you need to pry these open with a flathead screwdriver. Or, 1 or 2 (hot & cold) of these 2-gang electrical outlet covers (right). These just need 2 screws in the drywall at opposing corners to then just slide up & off...a shot of spray paint to camouflage.


Rivals For Catan - Riots

Question: My daughter and I have been playing this game, and disagree on what happens if riots occur and you can't pay. Yes, you have to put a card back under the stack. BUT, can the person who returned the card immediately pay to exchange a card and look through the stack and get that card back (assuming the riots occurred on their turn)?
Answer: If you discard a card at the start of your turn, you can pick it back up at the end of your turn.
There's nothing that would prevent this from happening. As the last part of your turn, you are allowed to exchange one card from your hand, and you may pay to look through a draw stack and pick any card you want. The game doesn't place any restrictions on what card you can take, nor does it have any "memory" about where the card has been in the past. You can even do this to pick up the card that the other player discarded. Note that this can't happen "immediately" as you suggest, since you don't exchange cards until the end of the turn, so Riots will take your unit out of commission for at least one round. But it's perfectly legal to discard a unit due to Riots at the start of the turn, pick it back up at the end of the turn, and then play it again on the following turn.
Also note that with expansions, there are non-unique units, so it'd be pretty impractical to disallow a player from picking up the same unit they just discarded - after the fact, it would be impossible to prove if you exchanged for the Chief Cannoneer on the bottom that you just discarded, or the one that's second from the bottom that you didn't discard.

Rivals For Catan - Riots


What modifications need to be made on an engine that normally uses AVGAS to utilize it with MOGAS?

Question: Asking just out of curiosity. What modifications need to be made on an engine, e.g. Lycoming O-360, that normally uses AVGAS to utilize it with MOGAS?
Comment: I think you need to narrow this question down some, there are many, many engines out there and they aren't all the same. Some will require no modifications whatsoever, other may not be able to use it at all.
Comment: Just to confirm you mean just the engine itself, not the fuel delivery system, fuel tanks, or anything else on the airplane?
Comment: Yes, mean the engine itself.
Comment: Might depend on the particular engine, but in the only example I'm familiar with (Lycoming O-360 in a Piper Cherokee) no engine modifications were needed, just the installation of dual electric fuel pumps replacing the OEM one.
Answer: For any certificated aircraft engine, the type certificate will specify the required fuel. If the TC specifies AVGAS, using MOGAS will require an STC for that engine.
Developing a MOGAS STC for an engine is a complicated and expensive effort, so you're realistically limited to purchasing the rights to an existing STC. If there isn't an STC for your engine, you're likely out of luck.
The two most common STCs for GA piston engines are available from EAA and Petersen Aviation. Check their web sites for a list of engines covered by their STC.
Once you purchase the STC, it will include the installation instructions outlining the necessary modifications for your engine. In many cases, it's nothing more than placards and a flight manual supplement.
Comment: This doesn't really answer the question, the OP asked what modifications are necessary, not if they need an STC or how to get one...
Comment: I don't think it would be impossible to answer "what is needed to change from avgas to mogas" without being specific to a model. You can generalize things like re-jetting the carb, may require a new pump, valve seat issues, etc.
Comment: The question is quite broad as the solution is dependent on the specific engine model. The STC is what defines the necessary modifications. And installing an STC is a modification to the engine.
Comment: 'Off the top' (with the usual risks associated with human memory): A few years ago, the engines of a couple of DC-3s based in Switzerland and flown for sightseeing tours were modified for leadfree 95 octane gasoline. The main modification was fitting specially designed cylinder heads...
Answer: STC aside, no physical modifications are required to an engine to run on Mogas (except possibly the fuel system - see below).  My Lycoming O-290 has been using it for 9 years with no issues, and in fact the engine is FAR happier on Mogas than 100 LL, which low compression engines are unable to lead scavenge adequately and require frequent plug cleaning and are prone to exhaust valve sticking from lead buildup on valve stems (on engines meant for 80 octane).
The only benefit to running an 80 octane engine on avgas is a lubrication benefit to valve seats due to oxidized compounds that form with leaded fuel, and I will put some avgas in from time to time (there is a sliding action on the valve seat as the valve centers itself when closing - the lubrication effect reduces seat wear from this sliding).
One interesting effect is when I borescope my cylinders at annual, the exhaust valves are uniform off-white like they are in car engines, from the ash deposits unique to Mogas (on avgas, exhaust valves have a reddish bullseye pattern from the heating of the valve).  You also get more soot in the exhaust instead of grey lead deposits.
The main potential issue is with the fuel system related to temperature and Mogas's higher vapour pressure (lower boiling point).  If your plane has a fuel pump and it gets really hot under your cowling, it's strongly recommended to add a cooling shroud for the fuel pump (I recently added one to my plane to alleviate problems in really hot weather, where I could tell I was getting fuel pressure fluctuations after landing). It's a bigger problem for fuel pump systems than gravity feed because the pump's suction is effectively raising the altitude, as far as the fuel being pulled into the pump is concerned, and the fuel will boil more readily at the pump inlet. Gravity feed doesn't have this problem.
You can actually run high compression 100 Octane non-turbo Lycs like the O-360 on Mogas (I was in a glider club with thousands of hour operation on it with O-360s) and there is no issue with detonation, and in Canada you can even run engines like the supercharged R-985 on Mogas, on commercial operations even (some bush operators use it).
The above assumes the fuel is alcohol free. You can't legally use car gas with ethanol under the STC anyway, and if you have a homebuilt where you can use whatever you want, and want to use fuel with ethanol, then you have to make sure that all the rubber components in the fuel system, including the carburetor float valve seal, are alcohol compatible. This is possible to do.
Finally, if you are getting Mogas yourself from a gas station, make sure it is alcohol free and test it yourself (a simple test using water) to confirm it is alcohol free.  If you're buying it from an airport, that's not a problem.


Is there a word for general envy for the rich?

Question: In the past few months, I've observed that there is actually a thing like general envy for the rich. They tend to be blamed for the slightest bad events that is connected to them in anyway even if it is completely out of context or insignificantly related.
Comment: "General envy for the rich?" Actually that's a pretty big assumption that opens up many reasonable questions from several points of view. Sociologists would have something to say about this claim in terms of *social norms* (https://en.wikipedia.org/wiki/Social_norm). Economists such as Thomas Piketty, whose 2013 book *Capital in the 21st Century* was a best-seller for months, would view that claim through the corrosive lens of trends in wealth and income inequality. In other words, finding a single, all-purpose *word for general envy for the rich* is not a simple task.
Comment: Are you looking for "resentment"?  (But note that the rich resent the poor probably even more than the poor resent the rich.)
Comment: If you do not insist on a single word, please make that clear.

If you do insist then no, there isn't.

"Plutophobia" would be a great start and I'd suggest "plutinvidia" but that's first invented and then pompous…

Beneath which, adding "general" could complicate it out of useful recognition…
Comment: The rich resent the poor? Would like to see data on that. Still trying to analyze the situation but usually, it seems they have no problems by default until the name of any rich person/organization pops into the news, and then they become irrational and instantly condemning. This is a behavior which I think is responsible for a lot of triving conspiracies amongst others.
Comment: It's actually very interesting. It actually seems higher in areas with higher wealth inequalities. And what's funny is the more I read, the more it seems like an accepted norm. In fact, the definition of grudge from Google provides "she resented the fact that I had children" as an example. Suggesting that envy which may be apparently what is behind it all is completely normal. It seems to be a difficult topic. Maybe survival instinct is the real word I'm looking for.
Comment: @ChibuezeOpata - Yes, the rich resent the poor.  They feel the poor are getting "free ride" and want everything handed to them.  (Or at least they realize that if they can make the "working class" think this way then they can control that voting bloc.)
Comment: Is there any word to distinguish envy from general envy? Now, there's a thought.
Answer: There's a difference between envy (wanting to be like someone or have what they have) and blaming someone for something.
Going with the second - and completely opposite to the first - "Plutophobia" has been used to describe a fear of wealthy people, though the term is more general than that, and can also relate to a fear of wealth itself.
However, it's probably not the word you're looking for, since a sufferer of plutophobia might blame and try to avoid the wealthy but would have no feelings of envy for anyone rich.
Comment: I agree - envy of something is different than blaming that something for your ills.   One may be envious of something AND blame that same something for your troubles, but those are separate emotions.


binomial option pricing model - problem with risk-neutral probability

Question: I have a little problem:
in the binomial option pricing model, the price of a european derivative security $V_{n}$ satisfies:
$V_{n}=[1/(1+r)]*[\tilde{p}*optionUp +\tilde{q}*optionDown]$
where:
$\tilde{p}=\frac{e^{r*\Delta T} -d}{u-d}$
But when I read the article "option pricing model" on Wikipedia(http://en.wikipedia.org/wiki/Binomial_options_pricing_model), the $\tilde{p}$ of Wikipedia's $\textbf{algorithm}$ is slightly different:
$\tilde{p}=\frac{(ue^{-r*\Delta T} -1)*u}{u^2-1}$ (I take q=0)
I try to compare these 2 forms but they are not equal... why ???
Thanks !
:)
Answer: In the link you provided, by noting the construction of array p[], p0 and p1 are respectively the discounted $\texttt{down}$ and $\texttt{up}$ probabilities. Since $d=\frac{1}{u}$, then
\begin{align*}
p0 &= e^{-r \Delta T}\, \frac{u-e^{(r-q)\Delta T}}{u-d}\\
&= \frac{\big(u\,e^{-r \Delta T} -e^{-q\Delta T}\big)u }{u^2-1},
\end{align*}
and
\begin{align*}
p1 &= e^{-r \Delta T}\,\big(1-p0\, e^{r \Delta T}\big)\\
&=e^{-r \Delta T} - p0.
\end{align*}
Note that $p1\, e^{r \Delta T}$ and $p0\, e^{r \Delta T}$ are respectively the $\texttt{up}$ and $\texttt{down}$ probabilities.
Comment: God bless you !  I'm a bit embarred actually it was very simple one(but I'm a beginner)... Thank you !


how to identify what is causing the CPU Wait status ORACLE

Question: I'm new to oracle and I have a problem because CPU Wait rises and I can't identify what is causing it
Comment: It might be useful to indicate what query or tool is computing these values.
Comment: I would hazard a guess it's Oracle Enterprise Manager.
If so, there should be sections that give information at the host server level which might give an indication of what [else] the host was doing at the time.
Answer: "CPU Wait" is caused by Oracle processes having to wait to get CPU time from the operating system. This can be caused by several things, not all of which are internal to the database.
From How to reduce "CPU + Wait for CPU" or "CPU + CPU wait":

For your SQL statements experiencing high CPU utilization, look at the
total number of executions and the average elapsed time per execution.
If the average time is high, see if the SQL statement can be tuned to
reduce the number read operations (logical and/or physical). If the
number of executions is high, then look at the application code that
is calling that SQL statement to see if there is a more efficient way
of handling it. For example, performing the SQL iteratively in a loop
can increase the total number of executions. Maybe we can rewrite the
code to get the data in bulk instead of row by row.

From "Finding the Root Cause of CPU Waits Using Stack Profiling"

... the database is spending a lot of time somewhere, and this time is
not accounted for by known database waits or time running on CPU. It
could be an uninstrumented wait (the database process sleeping while
e.g. waiting for some sort of resource occupied by a different
process), or wait for the CPU time.

A scenario like this may require - as described in the article - troubleshooting at the user stack or OS kernel level to get to the bottom of things.


Why use some cracks a patch and a keygen?

Question: A lot of cracked software in the internet looks like it's liberated with a patched executable and an additional key generator. Why so complicated? If the executable is patched why isn't the necessity for a key completely removed?
Answer: One of the possible reasons for this is assymetric encryption used in newer protections. The software vendor has the private key, the public key is embedded in the software. This means you just can't write a key generator from the information that's publicly available. If the key checking itself is heavily protected against modification, it may be easier to roll your own private/public key pair, have your keygen use the private part of this pair, and replace the original public key in the software with yours.
Comment: If we're already patching the binary AND we've figured out the mechanism to check keys for validity, why couldn't we simply make the key verification function always return true?
Answer: Sometimes, it's better to do so because the target has a powerful protection against trivial patches; therefore, the cracker would make some changes to make the target accepts a generated key (that might not be fully correct) so the target protection would simply collapse because it's (kind of) registered.


What does it mean bipolar or unipolar junction in a transistor?

Question: I can't find the definition of unipolar and bipolar junction in a transistor, for example BJTs has a bipolar junction and MOS-FET has a unipolar junction, what does it mean unipolar and bipolar junction?
Comment: @Janka A standard MOSFET has 2 PN junctions as well.
Comment: NPN and PNP transistors each have two PN junctions. That's why they are **bipolar**. A FET in contrary only has a N or P doted channel, and one gate or body diode. That's only one junction.
Comment: Way back when dinosaurs roamed the Earth there was another kind of semiconductor device called a point-junction or more accurately [point-contact transistor.](https://en.wikipedia.org/wiki/Point-contact_transistor) This is possibly the only kind of transistor one could fabricate with hand tools.
Answer: No, you're reading it wrong. Both 'Bipolar' and 'junction' are not "connected"... I mean to say it is not like junction is bipolar or unipolar. Actually 'Bipolar' means current conduction in device is due to both polarity charge carriers, electrons and holes. In NPN BJT, electrons are majority charge carriers and holes are minority charge carriers but holes still play their (small) part in conduction hence called bipolar transistor. FETs in which only one, either electrons or hole plays part in current conduction are called 'Unipolar' transistors
I haven't heard "Unipolar junction" term but if you are referring to UJTs then
'UniJunction' word signifies that the device has only one P-N junction and not that the current conduction is due to only one type of charge carriers, however that's true.
Answer: It doesn't have anything to do with the junction. The terminology stems from the charge carriers involving current flow in the device. BJT is called bipolar because the current in a BJT flows due to both electron and hole carriers, whereas the current in a Field Effect Transistor (FET) flows due to either electron carriers for N-type FET or hole carriers for P-type FET, hence they're called unipolar transistors.
Comment: I had the impression that etymology of *bipolar* was invented after FETs had become more widespread. The old difference was about bipolar transistor vs. unijunction Transistor.


"아, 예뻐라!" - can 아/어라 be used as an expression of surprise?

Question: I thought 아/어라 normally meant an imperative, but in "아, 예뻐라!"
that wouldn't make sense. Is it more like an expression of surprise or admiration? Is it a general pattern that can be used with other descriptive verbs?
Answer: Yes, when "-아라/-어라" attaches to descriptive verbs (a.k.a. adjectives / 형용사), they make the sentence an exclamation (감탄문), in the same way as "-구나".  Examples include "어머 예뻐라", "아이 추워라", "참 착하기도 해라", etc.

Note that in the last example, "하다" is an auxiliary adjective (보조 형용사), not an auxiliary verb (보조 동사).  Contrast with "빨리 오기나 해라 (Just come fast!)" where it is 보조 동사.

In fact, in prescriptive grammar (i.e., school grammar 학교 문법), this is the only accepted meaning of "-아라/-어라" combined with adjectives, because adjectives are not allowed to take a command form.
In other words, commonly used expressions like "행복해라" (Be happy) or "건강하세요" (Stay healthy) are considered wrong by prescriptivist grammarians.  See, for example, these posts by 국립국어원: 평생불행해라 / 건강하세요, 행복하세요

If you ask my opinion, I think expressions like "행복해라" or "건강하세요" are perfectly fine, and I think the majority of Koreans will have the same judgement.
Comment: As an aside: I recently watched an episode of drama 미생 (which aired a few years ago), where one guy was agonizing how to avoid a certain task at work because he was morally opposed to it.  In the end he exclaims "우리, 아프자!" (Let's get sick!) and proceeds to drink a carton of rotten milk, so that he can claim sick leave.  Another nice example of a perfectly normal Korean sentence which is considered wrong by the standard.  ("아프다" is an adjective, so according to the standard, it can't have "-자" ending.)


ArcGIS API for Javascript - InfoTemplate on a polyline

Question: I have a web map with a few points and a single polyline. I have infoTemplate(s) attached to the points and tried to replicate this to the polyline however, I can't get it to work. I looked on the ArcGIS API for JavaScript site and found an example against a polygon (hover) which is close but I need an example based on a polyline. Does anyone have a code sample that works for this request? Thanks!
Answer: The following code should work to attach an infoTemplate to a polyline.
<code>        var infoTemplate = new InfoTemplate();
        infoTemplate.setTitle("Your Title");
        infoTemplate.setContent("field1 label: w ${field1}<br/>" +
            "field2 label: ${field1}");

        polyline = new FeatureLayer("[Your Rest Endpoint URL]", {
            mode: FeatureLayer.MODE_ONDEMAND,
            infoTemplate: infoTemplate,
            outFields: ["field1", "field2"]
        });

        map.addLayer(polyline);
</code>


Linking back to table of contents in word document

Question: I am editing a word document (on Mac) which includes a table of contents.  The TOC is linked to appropriate places in the document.  Great!   Links to return to the TOC have been inserted in headers.  However, the only time the link works is if I open the header.  Therefore, I've tried to bookmark the Table of Contents and create links to it,  but when I attempt to add a link elsewhere, no bookmarks appear in the dialogue box.  The bookmarks are there, but I can't link to them.   ( I did not create the document, but need to finish it, so would appreciate some guidance.  Where am I going wrong?  Thanks!
Comment: You may be able to use the arrow keys to go back. On Windows, this is 'Alt`+`<--`. It is the same as the go-back keyboard shortcut in most browsers. You may be overwriting your bookmark when you update your TOC. Try placing the bookmark before the TOC and its heading/title. Links in headers footers do work when you publish a document as pdf.
Answer: The easiest way to allow jumping back to the TOC is to use a bookmark.
Select something near the beginning of the TOC (perhaps the TOC's header)
and bookmark it.
You may now create hyperlinks in the document that jump to the bookmark,
that could be placed anywhere, perhaps at the end of each section of the
document, or in the footer of each page.
You can also use "Go To" to jump to the bookmark.
Another method is to use a small VBA macro to jump to the TOC,
where the bookmark is named MyTOC in the example below:
Sub JumpTOC()
    Selection.GoTo What:=wdGoToBookmark, Name:="MyTOC"
End Sub

This macro could be assigned to a keyboard shortcut or even put up on
a toolbar.
Answer: You can add a bookmark in Word, and then insert a link to the bookmark wherever you want to return back to the table of contents.
See: https://support.microsoft.com/en-us/office/add-or-delete-bookmarks-in-a-word-document-or-outlook-message-f68d781f-0150-4583-a90e-a4009d99c2a0
Bookmark the location of the Table of Contents:

Select text, a picture, or a place in your document where you want to insert a bookmark.
Click Insert > Bookmark.
The Bookmark icon is highlighted on the Insert tab
Under Bookmark name, type a name and click Add. (for example: TOC)

Note:  Bookmark names need to begin with a letter. They can include both numbers and letters, but not spaces. If you need to separate words, you can use an underscore ( _ )—for example, First_heading.
Link to a bookmark:

You can also add hyperlinks that will take you to a bookmarked location in the same document.
Select the text or object you want to use as a hyperlink.
Right-click and then click Hyperlink Hyperlink button.
Under Link to, click Place in This Document.
In the list, select the heading or bookmark that you want to link to.

Note:  To customize the Screen Tip that appears when you rest the pointer over the hyperlink, click ScreenTip, and then type the text that you want.

Click OK.
Comment: Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers [in the help center](/help/how-to-answer).


EEA family permit application location requirements

Question: I'm French, my wife is Chilean. I'll keep my questions brief. Can my non-EU wife apply for an EEA family permit from within any country (apart from the UK, obviously) even if it is not her country of origin? It's next to impossible to apply in Chile because of the pandemic and I doubt it'll get better soon. Would she be able to apply for one in France while we are there? If so, what is the estimated application processing time for a married spouse?
Answer:
Can my non-EU wife apply for an EEA family permit from within any country (apart from the UK, obviously) even if it is not her country of origin?

Yes.  The consulate or embassy may ask her to show that she is legally present in the country; I am not certain whether this is a requirement, but I suppose it won't be difficult to show.
However, because Chilean citizens do not need visas to visit the UK,  your wife does not need an EEA family permit.

Would she be able to apply for one in France while we are there?

She ought to be able to, but do check whether the relevant offices are open in France.

If so, what is the estimated application processing time for a married spouse?

It shouldn't take more than a week or two.
Comment: @mjm questions about moving somewhere and working there belong on [Expatriates.SE], but the purpose of your entry into the UK does not matter. What does matter, of course, is the timing, since the UK will be withdrawing from the free movement system at the end of the year (subject to possible extension). This answer will cease to be correct when the UK withdraws. There are several relevant questions and answers on Expatriates, and several permutations of the process, but the simplest is that once you're both there you apply for a registration certificate and she applies for a residence card.
Comment: @mjm I take that back -- the simplest is that once you're both there you both apply for the [EU Settlement Scheme](https://www.gov.uk/settled-status-eu-citizens-families) -- the registration certificate and residence card cease to be useful when the UK leaves the free movement system.
Comment: @mjm you should be prepared to prove your wife's entitlement to entry under free movement at the border.  If they get wind of her intention to remain in the UK for more than six months then she won't qualify to enter as a visitor.  You'll want to have the documents whe would present in an EEA family permit application, namely your marriage certificate with an English translation (in addition to your French passport and her Chilean passport).
Comment: @phoog That's great news! What if it's to live and eventually work rather than just visit? Does that change things? I'm due to start working in September.
Comment: That we we were planning to do from the very first month in the UK anyway. It's comparatively easier as we can do it from within the UK. I wanted to make sure my wife didn't need an EEA family permit first from outside the UK, but from what you've told me this is not the case. Thank you, you have been tremendously helpful!
Comment: Ok, we will have all that on hand at the border.


Linux Bridge Won't Forward Packets?

Question: I am trying to share my Wifi internet connection on my laptop with a desktop computer temporarily. I have set up a bridge between wlan0 and eth0 (called br0), got an address on br0 from dhcp, and even got an address from the wireless router to the (Windows) pc using dhcp. The pc can ping the laptop, but not ping the router or get on the internet. is there a step i'm missing?
Comment: The PC got an IP from the router via DHCP, so we know in principle that they can communicate.  The laptop is the most likely culprit.  Can you run ```sudo tcpdump -ei br0``` on the laptop and then ping the router from the Windows box?  You may need to install tcpdump.
Answer: Unfortunately, some wireless cards do not support bridging. In order to forward packets from the wired side of the bridge, the wireless interface needs to 'spoof' the MAC address of the source host. If the card (or driver) is unable to spoof packets, the bridge won't work.
You may want to use NAT instead, or find a different wifi device.
See http://www.linuxfoundation.org/collaborate/workgroups/networking/bridge#It_doesn.27t_work_with_my_Wireless_card.21 for a full explanation.
Comment: Wow! there's an old question answered. This is correct, it turns out to be a hardware/driver issue.
Comment: Yeah, I was trying to debug my (non-wireless) bridge, and some googling lead me here, so I thought I'd answer :)
Answer: Maybe the routes tables need some adjusting.
http://www.cyberciti.biz/faq/linux-route-add/
Every machine needs to
a) know how to reach other machines in the same network
b) know how to reach everythng else (the internet) through a so called "gateway"
As Paul pointed out, the routing tables should have been set correctly because you are using DHCP but you could check.
Comment: The laptop is a bridge, so not a gateway, and the PC got its IP address from the router via dhcp so would have been provided a default gateway
Answer: I tried something similar with a bridge too, but then I decided to use a 2nd NAT to connect an USB device, so my setting looks like

router with NAT - desktop-PC with NAT - USB device

and this is simply done with some iptables rules on the PC.
Answer: Try clearing your iptables rules.
iptables -F
iptables -X
iptables -t nat -F
iptables -t nat -X
iptables -t mangle -F
iptables -t mangle -X
iptables -P INPUT ACCEPT
iptables -P FORWARD ACCEPT
iptables -P OUTPUT ACCEPT

Also clear your arp table: arp -d *

Linux Bridge Won't Forward Packets?


Suggestions on Postpartum exercises

Question: I know that everyone is different and you should be getting cleared by your MD, but once they do clear you, what are some good exercises to do to help your body recover? Specifically to help with strengthening your abdominal muscles and strengthening your pelvic floor muscles.
Answer: After you give birth, it is incredibly important to approach your recovery just as that—recovery. Your body has gone through trauma and needs to heal with time and therapy
What happened to your core?
When we are pregnant, our belly grows, and as our belly grows our abdominal wall thins to allow for enough space for the baby. This creates a weaker core and the muscles begin to drift and separate, known as Diastasis Recti (DR). Everyone has a different experience and a different degree of DR that presents after child birth.
Your pelvic floor is also affected after childbirth. It has been holding the weight of a child for ~9 months and needs to be cared for and strengthened
Rebuilding the Core
It is important to first repair the mind muscle connection with your core. This can be done by practicing 360 breathing. Locating a neutral spine, finding your pelvic floor, and making your body build back the previously natural habit of how and when to engage your core when breathing.
Next you can start to work on your deep core. Start to engage your pelvic floor with your 360 breathing. From there you'll work to engage more of your body. Think of engaging one more item as a time, starting close to your pelvic floor. So, glutes, then lower abs. At this point, all work should be done on your back with your extremities on the ground (like heel slides). Hold your core as you perform your exercises. Make sure your lower back is connected with the floor, your core is engaged, and you have no coning. If all of these aren't happening, take a break and try and later. After you have mastered this, you will start to engage legs, arms (think dead bug), and eventually be able to move off your back and into a quadruped position.
Please do plenty of research. There are a lot of great programs such as Get Mom Strong online if you wish to work on this in your own home. You can also get a referral to a Physical Therapist who specializes in the pelvic floor and DR and will build a program based on your evaluation.
Finally
This is a LONG process. Do not rush. Back pain, incontinence, and prolapsed uterus are NOT normal and typically symptoms of a weak deep core. Once your core is strong, this is when you can start to add more full body training such as running, sports, weightlifting, etc.
Answer: While I have not been pregnant I would assume exercises such a hip thrusts and RDLs (Romanian Deadlifts) would be most beneficial to strengthen your abdominal muscles as well as your pelvic floor during the postpartum. I would recommend easing into them by using light weights and a bar pad/yoga mat wrapped around the bar just so the bar itself isn't putting pressure on your hips. Take these exercises slowly and focus on your breathing, breathing out as you perform the exercise. I hope this helps.
Comment: Please do not do oblique twists. This will put too much pressure on your core for a first postpartum workout. If you had a c-section this will likely be one of the LAST workouts you will perform while rebuilding your core.
Comment: Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers [in the help center](/help/how-to-answer).

Suggestions on Postpartum exercises


When to use Cucumber and when to use RSpec?

Question: I am new to Cucumber testing and I am trying to understand when to use Cucumber and when to use RSpec. For my models, I know I should be testing them with RSpec, and I know that I don't need to write RSpec request specs if I write Cucumber stories instead. The thing I don't know when to use what is with views and controllers. Should I be using RSpec to test my views and controllers, or can I just skip them because I am using Cucumber for my higher level testing? Any advice would be greatly appreciated! Thanks!
Answer: I use RSpec to drive the development and testing of my models and to some extent my controllers, and Cucumber to drive the development and testing of my views (and subsequently their integration with the controllers).
I don't feel writing Cucumber tests allows me to "skip" writing RSpec tests because a lot of development takes place in the model layer before any views are created.
Comment: To what extent do you text your controllers with RSpec?
Comment: Nowadays very little as I try to keep as much logic at the model layer, but if for some reason there's a fair bit of logic in a controller action I like to write a spec to cover it (for my own sanity really).
Answer: If you keep writing Cucumber scenarios instead of unit tests, then you will probably find that your tests become very slow to run. If the tests are slow, you probably won't run them very often, so your development pace will slow down.
You can use RSpec for integration tests operating at the same level as Cucumber. If you need to share and discuss features with non-developers, then Cucumber is a huge help. But even if you're a solo developer, Cucumber helps by acting as a 'mental guard' between the behaviour you need and the underlying implementation.
The standard practice most people follow is to write extensive unit tests for the model, minimal tests for the controller, and very rarely any unit tests for the view. Then you would use Cucumber to check everything is interacting properly (be sure that you scenarios cover any loops/conditions in the controllers and views).
Answer: I'm not sure if it's OK to recommend a book here, but The RSpec Book by David Chelimsky (ISBN 9781934356371) does provide a nice practical example of how Cucumber and RSpec can be interleaved to behaviour-drive the development of a small command-line game in Ruby.
In a nutshell: writing your Cucumber features adopting the point of view of your end-user, and your RSpec specs using your own point of view as a developer is a good balance between execution speed of the test suite, testing granularity (how precise are the error messages when your tests fail) and documentation coverage (the Cucumber features can be seen as an always up-to-date documentation - the very own RSpec documentation is a great example of that).
Comment: _The Rspec Book_ by David Chelimsky was published in 2010, so a lot of the specifics are certainly out of date. However, with that caveat, as an example of working with Cucumber and RSpec together, I believe it still would be a good reference. (Syntax details change, but not the principles.) You can find it in multiple shops by ISBN 9781934356371.
Comment: Sadly the link to that Rspec book isn't working any more, do you have an updated link for where I can find it?
Answer: Just a small addition that might be helpful to you. Many people think (i also do) that cucumber is more of a hassle than a practical test framework for the programmer. As long as you do not have to cooperate by discussing scenarios with clients that do not know much about programming, i would highly recommend that you do not use cucumber. I'm with DHH on this one. But RSpec, use and even abuse :)


Is it ethical to consume pirated content for understanding references rather than direct enjoyment?

Question: E.g. a guy watching torrented Fifty Shades of Gray to understand what are the people on the internet fussed/excited about.
Comment: As written, this seems largely-opinion based, can you clarify by giving us some basic moral bearings that you're operating under or a theoretical framework, like Kantianism or utilitiarianism, or virtue ethics? Without that, we're either just going to share our own views on the matter or guess what views you might have and extend from there.
Answer: You might make arguments why pirating content instead of paying is always or often ethical (I would likely disagree), but the reason why you are watching the movie doesn't make a difference (with few exceptions; if it turned out that somewhere in the background shot out of a window we can see a car being stolen, then it would be ethical for a police officer to watch that scene without paying).
Comment: What if the movie itself is a crime (not necessarily punishable by the host country's laws)? E.g. some sort of commercial nazi propaganda movies?
Answer: That would depend on your ethical principles. Some people have no objections to theft of physical property; there are those who have no truck with the concept of intellectual property (so it would be wrong to take an artist's physical painting, but okay to make a copy). I assume you generally accept the general moral principle that a person owns the intellectual "content" that he creates and this has the same property rights as he would have to his vegetables and house.
Moral philosophy also admits "exceptions", for example killing a person is immoral, but there are contexts where it is not -- for instance, if the person is attempting to kill you, then you may kill him if it is necessary to preserve your life. Such an "exception" follow, at least in an egoist framework, from the purpose of a moral code which is to prescribe how to live your life – being killed obviously contradicts that purpose.
So: what could possibly justify an exception for the purpose of understanding the fuss? Well, it would be something like, "The wish to understand a popular internet trend justifies ignoring the property rights of others". But this is obviously not a general principle, it's a post-hoc rationalization. I can't conceive of any reasonable principle that would lead to such an exception.


Unknown Accounts suddenly appearing in MetaMask wallet....?

Question: My MetaMask wallet has multiple accounts which I did not create. I have no idea how they there.
Is my MetaMask wallet compromised? Or is this normal that MetaMask creates new wallet addresses when needed for certain transactions or webpages?
The unknown addresses are only visible in "Transfer between my accounts" which of course suggests that they are mine, but I cannot even access them or see the complete addresses.
I have attached a screenshot below the above account that is blurred out is mine, the other accounts below the blue line are the ones unknown and unaccessible to me. I cannot edit/delete them.
If any is familiar whit this please advice me on what to do.
Thanks guys
Comment: Created an Avalanche account and there were already transactions from a few months back. I am not sure why it is there.
Answer: In that dialog Metamask is showing addresses that were used as recipients in previous transactions.
If you previously interacted with a dapp or contract they will appear there.
It seems bad that Metamask doesn't allow to see the full address.
Comment: Thank you Ismael you're right that must be it since I mostly interacted with dapps and contracts.

MetaMask should fix the not seeing the full address issue. It causes unnecessary panic.
Answer: That definitely looks like a problem, have you given your priv key to anyone? left it on github?
Or, those are people you have sent eth or token to.
Comment: Nope I haven't given anyone my private key. I also haven't visited GitHub since creating the account so that can't be it either. These are people I have sent ETH or Token to??? Very strange shouldn't the addresses in this case be in the recent section as well? I have only sent it tokens to 4 addresses and those are not these. Strangely I am not missing any ETH or Tokens. But I will clear out the account to be safe. I was just wondering if this was normal. Thanks
Answer: me also happen but in different way. i created a new adding account in metamask but suddenly that new account have some small amount of 0.002eth. I checked in etherscan and found that it was transferred 4 month ago by somebody account. what going on i dont know.


Sources of chlorophyll fluorescence

Question: I have been reading this article recently, which claims that photoinhibition of photosystem II can have measurable impacts of chlorophyll fluorescence. This confused me, however, because photoinhibition (at least as the article describes it) occurs mainly in the PSII reaction center, and I had thought that the majority of chlorophyll fluorescence was caused by excitations that form in the antenna and don't reach the reaction center in time before they decay (after all, there are many more antenna chlorophylls than reaction center chlorophylls). With this in mind, how can it be that photoinhibition of the RC modifies the F0 value of chlorophyll fluorescence data?
Answer: Not an expert in this field, but a dig through the literature seems to indicate that the chlorophyll fluorescence that is generally referred to for measuring photoinhibition is indeed localized to or associated with the PSII reaction center. In case it is in question, there are estimated to be ~100 chlorophylls directly positioned within the PSII.
I don't know the basis of your supposition about the excitations that never reach the reaction center, so I'm not really sure how to address it. This paper writes that the efficiency of excitation reaching the reaction center is actually quite high in realistic physical simulations. A quantity of interest here is $L_D$, the parameter controlling how far an excitation can travel readily through a photosystem before being lost; I was not able to readily find their estimates for this value though:

Most of the LHCIIs in the mixed membrane are surrounded by PSII-S within a radius of $L_D$, which led to the 82% maximum quantum efficiency of the membrane upon uniform chlorophyll a (ChlA) excitation.

This review links chlorophyll fluorescence to PSII phenomenologically and theoretically but does not directly address the mechanism:

Changes in the yield of chlorophyll fluorescence were first observed as early as 1960 by Kautsky and co‐workers (Kautsky et al., 1960). They found that, upon transferring photosynthetic material from the dark into the light, an increase in the yield of chlorophyll fluorescence occurred over a time period of around 1 s. This rise has subsequently been explained as a consequence of reduction of electron acceptors in the photosynthetic pathway, downstream of PSII, notably plastoquinone and in particular, QA. Once PSII absorbs light and QA has accepted an electron, it is not able to accept another until it has passed the first onto a subsequent electron carrier (QB). During this period, the reaction centre is said to be 'closed'. At any point in time, the presence of a proportion of closed reaction centres leads to an overall reduction in the efficiency of photochemistry and so to a corresponding increase in the yield of fluorescence.

In one rather blithe review, it is suggested that other sources of fluorescence are close to zero at relevant wavelengths, though they only mention PSI as a source:

At room temperature, we assume the variations in the fluorescence signal arise from PSII only and we ignore emission from PSI largely because the signal does not make a significant contribution below 700nm (Butler, 1978; Pfündel, 1998; Baker, 2008)

Looking into the Pfündel paper, they write in turn:

At room temperature, a small fraction of the absorbed light energy is re-emitted as chlorophyll a fluorescence. It is usually assumed that most of this
fluorescence is emanated by PSII, and that the PSI contribution is negligibly small (Krause and Weis 1991; Govindjee 1995)

Without following the citation trail any further, it seems that the general assumption in the field is that excitation "lost" to fluorescence of ChlA without a reaction center accepting the energy is pretty negligible. No one seems to be interested in distinguishing the total PSII fluorescence from the PSII fluorescence actually associated with reaction centers. This probably indicates that the two amounts are pretty close to identical.
For some validation of your intuition, this paper writes:

FV/FM works well for plants with Chl a/b antenna systems in which in vivo fluorescence is dominated by emission from Chl a associated with PSII. In phytoplankton, with their diverse antenna systems and thylakoid configurations, FV/FM must be interpreted with more caution [36], [52]. Taxonomic differences in FV/FM can result from contributions to the minimum fluorescence (F0) from pigments outside PSII (see e.g. [53]). Due to the fluorescence from such pigments, the measured values of FV/FM may depend on the excitation and emission wavelengths (unpublished data).

In other words, you need to be careful to account for fluorescence from non-reaction center-associated pigments but it's quantitatively not a large amount (though I haven't yet found a direct estimate despite a lot of looking!).

Sources of chlorophyll fluorescence


Can you obtain classification thresholds for specific features in a Random Forest?

Question: Say I've created a random forest model for binary-classification prediction target of either "Pass" or "Fail" for a group of students based upon numerical features "Hours Studied" and "Amount of Sleep obtained." Is there a way to tell what SPECIFIC number of hours studied or amount of sleep obtained is the classification threshold for the model's prediction? For example, <6 hours studied = Fail while >6 hours of studied = Pass. Is there a way to determine this with a random forest model? Is this even possible or is my understanding off?
Comment: You can from an heuristic point of view, i.e. trial and error; probably not what you are looking for.
Answer: I think this is not possible since a RF is an ensemble of potentially many decision trees (DTs).
Basically, each DT has its own "decisional path" which is kind of "averaged" in the RF. So you loose the interpretability of DTs, which may haved allowed you to understand at which value of a given feature the decision, at a given point, is made. Anyway, what you still get by a RF is an estimate of the importance of each feature which can help you understand which of them is more important (impactful) in the decision process.
Answer: You can try using partial dependence plots. I give you an example for binary classification problem:
<code>from sklearn.inspection import PartialDependenceDisplay
from sklearn.ensemble import RandomForestClassifier
import matplotlib.pyplot as plt

# Create some samples and behavior
samples = 1000

X = [[i, i*2] for i in range(0, samples)]
y = []

for x0, x1 in X:
    if x0 > 700:
        y.append(1)
        continue
    elif x0 > 300 and x1 > 700:
        y. append(1)
        continue
    else:
        y.append(0)

rf = RandomForestClassifier()
rf.fit(X, y)

# Make partial dependence plots for features 0 and 1
features = [0, 1]
PartialDependenceDisplay.from_estimator(rf, X, features)

plt.show()
</code>
The plot is:

where you can see the value at which the change is produced. Hope it helps.


Select a random subset of objects

Question: In Inkscape I have a large number of objects.
I would like to select a random subset of these objects and change their width en masse.
Is it possible to do this in Inkscape?
Comment: Hi. Welcome to GDSE. The software has no ability to automatically select objects randomly. I suppose it could be scripted, but I'm no coder. Scaling on one axis can be done using the Trasform dialog, Scale tab, and the option "apply to each separately".
Comment: Hello, Richard, can you tell us something more and perhaps add an example? What do you expect to achieve? What efforts have you made?
Answer: Currently, it's not possible to randomly select objects using the main GUI of Inkscape. I have created this inkscape extension to randomly select a subset of objects and change their width or height attributes:

Download the extension and install it.
Select all the objects (Make sure to convert them to paths).
Extensions > Modify Path > Batch property random selection

Below is a demonstration:

More features could be added later.
Answer: I'd been interested in generating a star field with randomly-sized stars.
It's easy to generate nicely-distributed circles using Poisson Disc Sampling and to find SVGs where people have already done this via Google Image Search. With such an SVG in hand the question then becomes: how do I resize some of the "stars" to be larger than others. Choosing these randomly seems reasonable.

However, I didn't end up using the above approach. The stars were too uniformly distributed.
Instead, I downloaded bsc5.dat.gz from the Yale Bright Star Catalog.
I then passed it through the script at the bottom of this post.
This produced an image similar to this

which I can then clip as needed.
Star Generation Script
#!/usr/bin/env python3

import math
from typing import List, Optional, Tuple

class Star():
  """
  A class representing a star, with name, magnitude, right ascension (ra),
  declination (dec) and projected co-ordinates x,y calculated by a class
  method.

  """
  def __init__(self, name: str, constellation: str, mag: float, ra: float, dec: float) -> None:
    """
    Initializes the star object with its name and magnitude, and position
    as right ascension (ra) and declination (dec), both in radians.

    """
    self.name = name
    self.constellation = constellation
    self.mag = mag
    self.ra = ra
    self.dec = dec
    self.visible = True
    self.x: Optional[float] = None
    self.y: Optional[float] = None

  def project_orthographic(self, ra0: float, dec0: float) -> Tuple[float, float]:
    """
    Calculates, stores and returns the projected co-ordinates (x, y) of
    this star's position using an orthographic projection about the
    angular position (ra0, dec0).
    """

    delta_ra = self.ra - ra0
    self.x = math.cos(self.dec) * math.sin(delta_ra)
    self.y = math.sin(self.dec) * math.cos(dec0)\
          - math.cos(self.dec) * math.cos(delta_ra) * math.sin(dec0)
    return self.x, self.y

# Read in the star data
star_data = open('bsc5.dat', 'r').readlines()

# Parse all the stars into Star objects
stars: List[Star] = []
for line in star_data:
  constellation = line[11:14]
  name = line[4:14]
  try:
      mag = float(line[102:107])
  except ValueError:
      # some stars do not have magnitudes: ignore these entries
      continue
  # Right ascension (hrs, mins, secs), equinox J2000, epoch 2000.0
  ra_hrs, ra_min, ra_sec = [float(x) for x in (line[75:77], line[77:79], line[79:83])]
  # Declination (hrs, mins, secs), equinox J2000, epoch 2000.0
  dec_deg, dec_min, dec_sec = [float(x) for x in (line[83:86], line[86:88], line[88:90])]
  # Convert both RA and declination to radians
  ra = math.radians((ra_hrs + ra_min/60 + ra_sec/3600) * 15.)
  dec = math.radians(dec_deg + dec_min/60 + dec_sec/3600)
  # Create a new Star object and add it to the list of stars
  stars.append(Star(name, constellation, mag, ra, dec))

# Now find the number of stars in the Orion constellation and use this to find
# the center (average position) of the constellation
n = sum([1 for star in stars if star.constellation == "Ori"])
ra0 = sum([star.ra for star in stars if star.constellation == "Ori"]) / n
dec0 = sum([star.dec for star in stars if star.constellation == "Ori"]) / n

# Now get the projections of all of the stars when projected to an orthographic
# projection centered on the constellation
coords: List[Tuple[float, float]] = []
for star in stars:
  # Orthographic projection (ra, dec) -> (x1, y1)
  coords.append(star.project_orthographic(ra0, dec0))

# Get dimensions and aspect ratio of image
xmin = min(coords, key=lambda x: x[0])[0]
xmax = max(coords, key=lambda x: x[0])[0]
ymin = min(coords, key=lambda x: x[1])[1]
ymax = max(coords, key=lambda x: x[1])[1]
aspect_ratio = (xmax-xmin)/(ymax-ymin)

# The stars will be output on a canvas of dimensions width x height, with
# some extra padding around the outside of the "paintable" area.
padding = 50
height = 2500
width = int(height * aspect_ratio)

# Write the SVG image file for the constellation
with open('{:s}.svg'.format("/z/test.svg"), 'w') as f:
    print('<?xml version="1.0" encoding="utf-8"?>', file=f)
    print('<svg xmlns="http://www.w3.org/2000/svg"', file=f)
    print('     xmlns:xlink="http://www.w3.org/1999/xlink"', file=f)
    print('     width="{:d}" height="{:d}">' # style="background: #000000">'
            .format(width + 2*padding, height + 2*padding), file=f)
    for star in stars:
        if not star.visible:
          continue
        # Enable to filter stars by magnitude (brightness)
        # if star.mag > 4.5:
          # continue
        # Enable to filter stars by constellation
        # if star.constellation != "Ori":
          # continue
        rx = (star.x - xmin) / (xmax - xmin)
        ry = (star.y - ymin) / (ymax - ymin)
        cx = padding + (1-rx) * (width - 2*padding)
        cy = padding + (1-ry) * (height - 2*padding)
        radius = max(1, 6-star.mag) if star.constellation == "Ori" else max(1, 5-star.mag)
        print('<circle cx="{cx:.1f}" cy="{cy:.1f}" r="{r:.1f}"'
              ' stroke="none" fill="#000000" name="{name:s}"/>'.format(
              cx=cx, cy=cy, r=radius, name=star.name), file=f)
    print('</svg>', file=f)

Select a random subset of objects


Stability of Time Series Hierarchical Clustering

Question: We have a dataset with six time points and three biological replicates each. Therefore, we have a vector of 18 measurements for each feature, and used hierarchical clustering with Euclidean distance to cluster by the features and cut the tree at a certain point to propose groups of features. This is a simple and sufficient approach for the problem we are addressing. It has been suggested to do bootstrap resampling of the six time points to determine the stability of the feature clustering. Is that valid, because it breaks the relationship between consecutive time points ? Is there a suitable method for this small experiment ?
Answer: Indeed, it breaks the 'time series' aspect. Maybe your time series are more or less random walks? In my opinion, 6 time points is too few... Besides bootstrapping, you can define your own perturbations based on your expertise of the time series. For instance, in finance you can study "multiscale" perturbations (but 6 points is too few for that). You can have a look at this paper for some perturbation ideas.
Actually, you can try to play with your "features" vector (or the population) instead of the 'time'.


Limit of discontinuous function

Question: This question is from my calculus 1 worksheet about limits. I am given the function
$$f:[0,1]\cup\{2\}\to\mathbb{R}:x\mapsto\begin{cases}
\arctan(x),  &x\in[0,1] \\
8, & x=2
\end{cases}$$
I am supposed to use the $\epsilon$-$\delta$-definition of a limit to show that the limit of $f$ when $x\to2$ is equal to any real number $b$. In other words
$$\lim_{x\to 2}f(x)=b$$
$$b\in\mathbb{R}$$
I know that the $\epsilon$-$\delta$-definition of that limit is
$$\forall\epsilon>0,\exists\delta>0,\forall x\in \operatorname{dom}(f):0<\vert x-2\vert<\delta \Rightarrow \vert f(x)-b \vert<\epsilon$$
And I am inclined to say that the limit of $f$ as $x\to2$ does not exist. Still, I am very confused by this question. My question is how to prove that the limit of $f$ as $x\to2$ is equal to any real number.
Comment: Recall that any universally quantified statement over an empty domain is trivially true.
Comment: It depends on your definition, but it is vacuous. If you take $\delta = 1$ then the set of $x$ in the domain that satisfy $0<|x-2|< \delta$ is empty, so the conclusion is (vacuously) true.
Answer: Take any $\varepsilon>0$ and take $\delta=1$. Then there is no element $x\in\operatorname{Dom}(f)$ such that $0<|x-2|<\delta$, and therefore is indeed true (actually, vacuously true) that$$\bigl(\forall x\in\operatorname{Dom}(f)\bigr):0<|x-2|<\delta\implies\bigl|f(x)-b\bigr|<\varepsilon.$$

Limit of discontinuous function


Are US states bound by the US constitution when it comes to gun rights?

Question: I am confused by a basic feature of US constitutional law.    Does the US constitution restrict state laws as well as federal ones? Specifically, can a state law (or even a city law) ban the possession of guns or, say, the sale of pornography?
Comment: Related (and pretty much the same answer, substituting 1st Amendment for 2nd Amendment): https://law.stackexchange.com/q/6097/3209
Answer: No.  The Fourteenth Amendment prevents this (it was originally implemented to enforce the 13th Amendment on the States, when the Confederate states returned to the Union after the Civil War.).
The idea here is that if the Constitution says it is a right of the People, all citizens of the Federal Nation must be afforded the right.  Now, the Constitution does allow for regulation by states and lower levels of government.  All Federal Level Gun regulation is based on the Interstate Commerce Clause for justification.  The States may further regulate so long as that regulation does not ban the sale of fire arms (Though some states will try to make effective bans.).
SCOTUS case Heller v. D.C. effectively confirmed this by overturning a Washington D.C. law banning the use of Fire Arms for self-defense in private property.
Comment: Actually, the 14th Amendment does not prevent this nor does Heller confirm this. The 14th Amendment actually does bind the states to the provisions outlined in the Bill of Rights. Heller actually applied to DC, which is not a state and so did not address the question of whether the Second Amendment's protections are incorporated by the Due Process Clause of the 14th Amendment against the states. Rather, McDonald v. Chicago addressed that and found that it did.
Comment: Yes.  However, D.C. being part of the U.S.'s territorial control, is subject to Federal Law which is bound by the Constitution.   The Constitution has several provisions that can be summed up:  If the Constition says the feds can do it, the feds can do it.  If it does not say the feds can do, than the feds definately cannot do it BUT The states may (Amendments 9 and 10).  If it explicitly says the Feds can't do something, then the states cannot do it either!


Can all conservative vector fields from $\mathbb{R}^2 \to \mathbb{R}^2$ be represented as complex functions?

Question: Considering that such a vector field $(M,N)$ is conservative iff for $M,N$ differentiable, $\frac{\partial{N}}{\partial{x}} = \frac{\partial{M}}{\partial{y}}$, we only have one of the two Cauchy-Riemann equations satisfied. Are there then examples of conservative vector fields $\mathbb{R}^2 \to \mathbb{R}^2$ that are not complex-differentiable?
Comment: Whenever $M$ depends only on $x$ and $N$ only on $y$, you have $\frac{\partial N}{\partial x} = \frac{\partial M}{\partial y}$. That is rarely holomorphic.
Comment: @LebronJames Generally, if you associate the field $(u,v)$ to the function $f = u+iv$, holomorphic functions don't give conservative fields. The line integrals you consider for the Cauchy theorem are different from the line integrals for vector fields on $\mathbb{R}^2$. In the Cauchy theorem, you consider $f\,dz$, which becomes $(u+iv)(dx+idy) = (u\,dx - v\,dy) + i(v\,dx + u\,dy)$. For vector fields $(a,b)$ on $\mathbb{R}^2$, you consider $a\,dx + b\,dy$ or $a\,dy - b\,dx$, so you have a sign-flip in the second component. Roughly, for vector fields you look at $f\,d\overline{z}$.
Comment: Right, of course.  This answers my question nicely.
Comment: Hi @DanielFischer, I'm trying to show that this is true in the other direction:  that all holomorphic functions on a simply connected domain are curl-free and conservative, and integrate to zero on any closed curve that is contained in the domain -- which agrees with the Cauchy-Goursat theorem.  However, I can only verify that the *conjugate* of f is conservative, using the C-R equations.  What can we say about f itself?  Thanks,
Comment: Awesome explanation, @DanielFischer - thanks so much and have a great night :-)
Answer: If a scalar function $\phi(x,y)$ on $\mathbb{R}^{2}$ is twice continuously differentiable, then $\nabla \phi = (\frac{\partial\phi}{\partial x},\frac{\partial\phi}{\partial y})$ is a conservative vector field because $\frac{\partial^{2}\phi}{\partial x\partial y} =\frac{\partial^{2}\phi}{\partial y \partial x}$. (That's not much of a restriction on $\phi$, and certainly not enough to guarantee that $\phi$ is the real part of a holomorphic function, for example.)
Conversely, given $(M,N)$ as you describe and continuously differentiable, then you can integrate
$$
       \phi(x,y) = \int_{(0,0)}^{(x,y)}M(x',y')dx' + N(x',y')dy'.
$$
The above is well-defined because the smooth path you choose from $(0,0)$ to $(x,y)$ doesn't matter, which follows from Green's Theorem:
$$
        \oint_{C}Mdx+Ndy = \int\int_{R} \frac{\partial N}{\partial x}-\frac{\partial M}{\partial y}\,dx dy = 0,
$$
where $C$ is a simple closed positively oriented curve enclosing a region $R$. Because you can choose any smooth path from $(0,0)$ to $(x,y)$, it is not hard to show that $\nabla \phi = (M,N)$.


Books on Abstract Algebra and its applications to solve puzzles

Question: I am currently reading some introductory textbooks on abstract algebra ("Contemporary Abstract Algebra" by Gallian and "A book on Abstract Algebra" by Pinter). I am learning the concepts from these books but I am not yet confident about using them in solving real-world problems. I know that Abstract Algebra can be used to solve a lot of interesting puzzles( For example, 15-puzzle, Rubik's cube, etc). Are there any books or websites that includes usage of abstract algebra framework to solve some puzzles?
Comment: [Related](https://math.stackexchange.com/q/2739098/104041).
Comment: *Are there any books or websites that* . I stopped reading here because the answer to your question is to use a search engine. Any search engine.  Why do you need to try to fire up a bunch of meat-search-engines to get highly incomplete and limited responses?
Answer: How about Adventures in Group Theory by David Joyner?
He outlines how you might set up the problems of describing the configuration space of the Rubik's cube and other puzzles. However, I suspect more thorough discussions might be open.
Wikipedia has the Rubik's cube group as $ G=(\mathbb{Z}_2^7\times \mathbb{Z}_3^{11})\ltimes ((A_8 \times A_{12})\ltimes \mathbb{Z}_2)$. Can you think of an element of order $3$ in that group? All the twists, $\{F,B,U,L,D,R\}$ have order $4$. Perhaps there's a sequence where when you repreat it three times, preserves the identity?
Look at any speed-cubing page. The algorithms are slow much less than God's number of 20. What local features could allow you to speed up?
Rubiks.com's own solution page. Can you build your own sequence that preserves the top row? Top two rows? Corner swapping?
These kinds of questions may still have not been attacked theoretically.
Comment: Thank you! "Adventures in Group Theory" sounds like the book I am looking for :)
Answer: In this forum thread, several links to books (or PDFs) about twisty puzzles are provided.  In the first few posts are papers (or books) which most people who searched for this genre know about.  However in later posts (specifically, mine), I provided links to other works.  For example, one of the best ones is Permutation Puzzles: A Mathematical Perspective written by Dr. Jamie Mulholland from SFU university.


Do Ideal spring go on oscillating after given a push?

Question: One end of an ideal spring is attached to the wall and other free end to a particle sized block (no friction). If a push is given to the block, will it go on oscillating about the equilibrium position?
I am thinking of this considering Law of conservation of energy.
Comment: From wikipedia "Ideal Spring – a notional spring used in physics—it has no weight, mass, or damping losses. The force exerted by the spring is proportional to the distance the spring is stretched or compressed from its relaxed position.[9]" So since it has no damping losses you might lean towards yes. But maybe the block has friction
Comment: @pentene no friction, Thanks for the answer. Am editing question to mention it.
Answer: Yes, in an ideal condition, where no energy dissipation and no damping occurs, the spring would go on oscillating for ever. This comes as a direct result of law of conservation of energy (because no energy is lost from the system).
Answer: Friction acts as a "damping force" for a harmonic oscillator. It is usually assumed proportional to the instantaneous velocity, and contributes to the instantaneous force as such. If one solves the differential equation for the displacement of the particle about the equilibrium position after adding a term proportional to the velocity to the usual equation for a harmonic oscillator, one gets a sinusoidal function of time, whose amplitude decreases exponentially with time- i.e. the amplitude goes ever closer to zero, reaching zero at infinite time. Realistically, this means that it has to stop after some finite time. Why? Because our capabilities for measurement are limited by some resolution; that is, we cannot measure distances lesser than some very small length measurable by the most powerful length-measuring instrument in the world. And so, for all intents and purposes, the block becomes stationary at the time its amplitude dips below this small distance. Interestingly, quantum mechanics tells us that the constituent particles are never stationary, and keep oscillating even at zero kinetic energy- but this oscillation is different.


Globally loading packages while using a CellGroup as the default context

Question: I have a notebook I wish to set up where the sections are conceptually related to each other. But, I wish to isolate them from each other programmatically, so that they do not interfere with one another. A built-in method of doing this is to set the default context to CellGroup so that each group of cells has its own context. However, each section relies on the same set packages, and because one of them is quite large, I do not wish to reload the packages for each section.  An option is to put each section in its own context manually using Begin and End, but I would rather avoid that if possible. Ideally, though, I would like to be able to load the packages in their own separate section and elevate them to the Global` (or equivalent) context. Any thoughts on how this can be accomplished?
Answer: One possibility would be to modify the notebook's stylesheet so that Input cells (or a clone) have something like:
CellProlog -> ($ContextPath = DeleteDuplicates[Prepend[$ContextPath,"abc`"]])

Then your package's context should be available to all the code:
Comment: Ah, brilliant. That should have occurred to me, +1. What about loading in packages though? ;)
Comment: Possibly the `Prolog` could be a `Needs` statement, though I haven't checked to see if it would actually create symbols in the package context correctly.
Answer: Below Brett's answer:

Ah, brilliant. That should have occurred to me, +1. What about loading in packages though? ;) – rcollyer

Perhaps you know this but Packages are already loaded to a shared context in the sense that doing Get["package`"]</code> loads the definitions into (typically) the context <code>package`, and the definitions are available from any other Cell Group by using the fully qualified name.
What remains is getting e.g. package` into the $ContextPath.  Brett's method works if you know the package contexts ahead of time, but we may want to adapt it to use a (true) global list of shared contexts.  For example we could use Global`$sharedContexts to store any contexts to be shared across Cell Groups and then set CellProlog to:
($ContextPath = DeleteDuplicates @ Join[Global`$sharedContexts, $ContextPath])

Starting with Global`$sharedContexts = {}; we could then load a package with:
<< "Combinatorica`"
AppendTo[Global`$sharedContexts, "Combinatorica`"];

Or we could use a custom Needs-type function stored in the System` context (to make it easily accessible), or we could perhaps modify BeginPackage like this:
Unprotect[BeginPackage]

BeginPackage[con_, x___] /; ! TrueQ[$shrCntxtMod] :=
     Block[{$shrCntxtMod = True},
       BeginPackage[con, x];
       If[
         ValueQ @ $sharedContexts,
     AppendTo[$sharedContexts, con],
         $sharedContexts = {con}
   ]
 ]

Which will add any context created with BeginPackage to Global`$sharedContexts.
Comment: Hmm, two years and I haven't upvoted this? Bad user. +1
Comment: @rcollyer Thanks for acknowledging. :-)  Sometimes I wonder if anybody read an answer like this with few or no votes.
Comment: I had read it, but I wanted to go through it before I voted on it, and then I forgot about it. :)