J1 visa followed by ESTA

Question: My daughter will be studying in the United States on a J1 visa. After her course finishes she has 30 days left on her J1. Can she then stay for a while longer to travel using ESTA?
Comment: No. She has to leave first then enter on ESTA IF they allow her in so soon.
Comment: Are you asking if she can stay *longer* than the 30 day grace period? The answer you've received so far assumes that you want to know if she can spend the 30 day grace period as a tourist but your question reads as though she wants to some some more time in addition.
Answer: Yes, your daughter can travel within the United States for 30 days after completion of her program. This is not "using ESTA", this is a grace period granted by USCIS for people who have completed their J1 program. From Adjustments and Extensions:

Travel Grace Period
Following the completion of their program, the period defined on the Form DS-2019, the United States Citizenship and Immigration Services (USCIS) allows participants a 30-day travel period commonly referred to as the "Grace Period." During this 30-day grace period, participants are no longer in J-visa status, and are under the jurisdiction of the USCIS. The USCIS grants this period to allow participants to settle their affairs and to prepare to return to their home countries. Program participants may no longer continue and/or complete exchange activities, nor may they work. Although participants may travel in the United States, it is recommended that they do not travel beyond the borders of the United States as they may not be permitted reentry.
Comment: @NickAtherden: I would not recommend leaving the US for a short while during the grace period. As the quoted page says, she may not be let back in.
Comment: Thanks Greg. Is it unlikely they will let her back in if she leaves to go to Mexico for a few days?

J1 visa followed by ESTA


Is certification required to conduct runways repairs?

Question: I know that you need a certain certification to fix a plane, but are you required to have a certification to fix a runway?  Or can anyone with the proper equipment be paid to do it?
Answer: To the best of my knowledge, you do not require any certification to fix a runway/taxiway, and anyone with a proper equipment can do that. But to facilitate the process, the FAA has published a few checklists which have to be filled while doing this repair job. These checklists can be found Here. FAA also provides assistance in guiding the construction jobs and identifying risks, the link to which is in the same website as mentioned above.
Comment: Indeed no formal certification, but with the amount of problems I have the feeling you could run into with that checklist I would imagine the companies willing to take on this type of job would probably have experience with it. It seems pretty well defined.


Calculating Euclidean distance in ArcGIS

Question: I am willing to model the distribution of an amphibian species in relation to climate and land cover in MaxEnt. For this I have downloaded the WorldClim data and the Global Consensus Land Cover (https://www.earthenv.org/landcover). The latter data consists of a raster file for each land cover class (open water, cultivated and managed vegetation,...etc.). However, I will not be using directly the raster of each land cover class, but instead a raster of the Euclidean distance of the XY coordiantes (longitude, latitude) where the species occurs from the nearest open water, cultivated and managed vegetation,...etc. I tried to calculate the Euclidean distance in ArcGIS 10.7.1 with the following: input raster (shapefile deature class of my occurrence data) and input barrier raster (open water raster). The Euclidean distance is calculated without errors but I get a blank raster with only one value (!) and I can not find where the problem is. Any thoughts?
Answer: I assume this is because you use degree as your unit, perhaps WGS1984 default projection? doing the euclidean distance in degree unit can produce raster with very little values, depending on your scale of analysis. I usually project them to UTM for small scale analysis:

Project all of your features, especially your occurrence, into UTM projection so that the units of your features are in meter. (using Project tool, or Project Raster tool)
change your dataframe coordinate system (View -> Data Frame Properties -> Coordinate system -> select the same projection that you used with the previous project tool
do Euclidean distance and set the environment setting (there should be environment setting on the bottom of your Euclidean Process window')
be sure to set snap raster the same with your landcover data.
you should also check your landcover data (after you do project raster) cell size, and set your euclidean distance output cell size the same.

This way it should be less risky for errors because you can make sure you have the same projections for each of your features. I hope this solves your problem.


How can I spawn Wither Skeletons in the Overworld?

Question: I would like to spawn Wither Skeletons without being in the Nether. Is this possible without the use of mods?
Comment: short answer is 'no'
Comment: Outside mods and Dinopet123's answer, no.
Answer: Are you asking how to make a Wither Boss? If not:

You can teleport a Wither Skeleton through a Nether Portal.
I think you can use a skeleton spawn egg.

Hope this helps!
Answer: You can spawn any mob in the overworld without the use of mods in two different ways:

Bringing a mob through a portal. Hard, but possible.
Going into creative mode and use spawn eggs. Easy but can't be used in survival.

Otherwise, you will have to rely on mobs or travel through the Portal to get them.
Answer: You can spawn wither skeletons by using the player commands.
 Press / to bring up player commands and type: summon WitherBoss.
  Once you do that a wither skeleton will spawn.
 You can summon many other things such as giants, skeleton horses, zombie horses and much more. Use this website to generate the commands to bring up whatever you want. You can choose it's health its armor strength and you can enchant its armor. Play around and you can summon pretty cool things.
Answer: Make sure you are OP if playing on a multiplayer server or cheats enabled if on Singleplayer (if not Open to LAN > Enable Cheats).
/summon Skeleton ~ ~ ~ {SkeletonType:1}
Note: This is for Minecraft 1.9


2d cellular automata Wolfram binary codes

Question: This is a similar question to How 2d cellular automata rules works?
However, the answer there did not provide me what I am looking for. Specifically, I want to be able to render these 2d cellular automata forms: https://www.wolframscience.com/nks/p173--cellular-automata/
I cannot find any reference anywhere that explains how to change between a real number and a growth rule. In 1d, the situation is well documented, such as here: https://mathworld.wolfram.com/ElementaryCellularAutomaton.html but in 2d the exact mapping of bits is nowhere to be found. I'd really like to make a program, so that I can for instance enter the number 465 and it will draw the pattern 465 from the Wolfram book. The other stack exchange answer I linked to above provides a possible binary mapping, however the method given there does not produce the same numbers as in the Wolfram reference. The binary value of 465 is 111010001 which does not help me at all. This particular shape is based on adding a cell when exactly one neighbor is currently occupied, so shouldn't we expect to have 4 1's in a row, one for each of the four neighbors? And to make this even more confusing, the last two digits seem to be swapped from the description given on the Wolfram page itself... It seems clear from the other Stack Overflow answer that there is not just one possible binary mapping but many, however given that there already exists a guide with pictures referenced by rule numbers I would really like to actually be able to use those specific rule numbers. Thanks.
Comment: There is explanation on the bottom of the Wolfram page you link to. The bits indeed code the number of cells set in the neighbourhood and the value of the central cell itself, starting from the last bit for central=white, all white neighbours. So your binary value is then read as (all 4 neighbours;black,white) 01. (3) 11. (2) 01. (1) 00. (0) 01. Unfortunately that does not comply with your assumption, when one neighbour is occupied the cell well be empty afterwards.
Answer: The description given on the page you linked to is correct:

"In each case the base 2 digit sequence for the code number specifies the rule as follows. The last digit specifies what color the center cell should be if all its neighbors were white on the previous step, and it too was white. The second-to-last digit specifies what happens if all the neighbors are white, but the center cell itself is black. And each earlier digit then specifies what should happen if progressively more neighbors are black. (Compare page 60.)"

What you might be missing is that, if the rule number is odd, the empty lattice is unstable since white cells surrounded by other white cells will spontaneously turn black.  Specifically, any rules whose number is congruent to 1 modulo 4 (i.e. whose binary form ends in 01), like 465, are "strobing", i.e. the empty lattice will alternate between all white and all black in each successive generation.
In particular, this means that rule 465 cannot correspond to "adding a cell when exactly one neighbor is currently occupied".  (That would presumably be rule 686, or 1010101110 in binary.)
Instead, as you correctly note, 465 equals 111010001 in binary.  Written in five groups of two bits each, that gives 01-11-01-00-01.  In each of these groups the rightmost bit in group $k$ (numbered right-to-left from 0 to 4) is 1 if a white cell with $k$ black neighbors will turn black in the next generation, and the leftmost bit is 1 if a black cells with $k$ black neighbors will stay black.
This means that, under this rule, a white cell will turn black if it has 0, 2, 3 or 4 black neighbors (since the rightmost bit is 1 in groups 0, 2, 3 and 4 counting from the right) and a black cell will stay black if it has exactly 3 black neighbors (since the leftmost bit is 1 only in group 3).
And indeed, simulating this rule for 22 generations, starting from one black pixel on a white background, produces an image matching the one on the linked page.

Ps. It turns out that rule 465 is the "strobing equivalent" of the state-symmetric rule 558 = 010001011102, which differs from rule 686 by exactly one bit and can be described as "add a cell when exactly one neighbor is occupied, remove a cell when exactly one neighbor is empty".
Started from a single cell, it seems that rules 558 and 686 evolve identically, since from this starting point they apparently never generate a live cell with exactly three live neighbors.  Thus, on even-numbered generations, the strobing rule 465 also looks identical to both of them.
Comment: thank you for clearing that up! I had seen the construction of that specific form described elsewhere and I didn't realize that 465 was actually different and what had been described was actually 686. Also, the grouping of the the bits makes plenty of sense the way you describe it. Thanks!


Libreoffice document recovery automatization

Question: I am wondering if there is a way I can launch libreoffice so it does document recovery or exits. I want this so when my computer boots up and I log in I am immediately prompted with document recovery. I want libreoffice to exit if there are no documents to recover. Is there a command line argument that will achieve this I can add to my gnome session?
Answer:
I want libreoffice to exit if there are no documents to recover.

Isn't that superfluous ?
Here's one possible solution. It will only start LibreOffice (LO) if there's actually any document to recover. Otherwise nothing will happen.
LO saves the information needed to restore all open documents in case of a crash in so called "Temporary files". The default location (in linux) is /tmp and LO saves the data in some directories under /tmp.

Change that location to a dedicated directory for temporary files, preferable under $HOME:

Create new dir:
mkdir -p ~/.cache/lo

Start LO and go to Tools - Options - LibreOffice - Paths
Select Temporary files and click Edit (or double click the entry)
Select (navigate to) the newly created directory:
/home/YOURUSERNAME/.cache/lo

save, close LO. So from now on LO will place the temporary files (with names like lu2s2clv.tmp, lu2s2clx.tmp, lu2s2cly.tmp etc) in a directory with a similar name, e.g. lu2s2ckt.tmp under ~/.cache/lo. It's only a matter of checking if there's anything to recover and fire up LO.

Create a script:

#!/bin/sh

sleep 2
[ -e ~/.cache/lo/*.tmp ] && libreoffice

save it somewhere in your $PATH e.g. /usr/local/bin/odrecover, make it executable.
Then fire up gnome-session-properties and add /usr/local/bin/odrecover to your start-up programs. Next time you log in, if there's any document to recover LO will automatically prompt you with document recovery.

Note: sleep 2 in the above script is needed on my system so that LO starts after gpasted (clipboard manager daemon) otherwise, for some unknown reason, gpasted goes crazy.


Edit character requirement

Question: Can we get rid of the requirement that edits have to be at least six characters? Often a post is missing a letter or punctuation and that's all I want to change. I don't want to have to start editing an otherwise very well written post.
Answer: Note that it's only suggested edits that have this technical limit. And once you've earned 2000 reputation points, you can edit without suggesting. Here's what Jeff Atwood had to say back in 2011:

As a < 2k rep user, you should make reasonably substantive edits. The approval cost for your edit is not free, as it costs the attention of one or more users who have to look at your edit and think about it. This cost is high for extremely trivial edits.
This will not be changing.
If you want to make single-character trivial edits, earn 2k rep.
Comment: Sorry, I mistyped. Suggested edits, not suggested posts. I've edited the answer to link to an explanation of suggested edits. Anyway, that it will be peer reviewed is the very problem, according to Mr. Atwood: by putting such a slight change before your peers, you're wasting their time.
Comment: I don't know what suggested posts are. All I know is that whenever I try to fix a missing letter or the like it doesn't let me. I don't have 2000 reputation and I don't see why it should be necessary for me to add a missing letter or missing punctuation that will be perfect reviewed anyway.

Edit character requirement


What does "can freeze hell over with a glance" mean?

Question: I read on a post, "The kindest people alive but can freeze hell over with a glance" squad. Is it a kind of English idioms. What does it mean?
Comment: Is the source something related to Astrology and Horoscope ?
Comment: It is related to Horoscope.
Answer: I've dug over the internet and I've found out that

"The kindest people alive but can freeze hell over with a glance" squad.

is something that is used to describe the group of people who are born under the zodiac signs of Aquarius, Virgo, Gemini, Taurus, Cancer. The sentence tries to sum up the characteristics of this group of people using a single sentence. So what does it mean ?
People born under the signs of Aquarius, Virgo, Gemini, Taurus, Cancer are very kind people, perhaps the kindest people among all their counterpart in the other zodiac signs. Even with such a warm-heart, they can become cold and heartless, when  circumstances force them to be. This is symbolic, rather than idiomatic. Hell is always referred to as the hottest place (with all the fires, or so they say). Now to freeze hell is a herculean task (hypothetically). If someone can be as cold as that, it means that they can become very heartless, given the unfavorable situations. So in plain words, these people are generally very nice and warm-hearted, but can become cold and heartless when they are angry or annoyed or sad.
NOTE:
As far as idioms go, when Hell freezes is an idiom used to describe something that is highly unlikely to happen. But I don't think that has to do anything with the phrase used in your context.
Answer: Your sentence

The kindest people alive but can freeze hell over with a glance

is describing a group of people as having a warm and generous nature

The kindest (possible) people alive

but also potentially very emotionally cold (hearted), since they can

freeze hell over

Hell is thought of as being the hottest possible place in human imagination.
To freeze it, something would need to be very cold, and to freeze it

with (just) a glance

something would need to be extraordinarily cold since a glance is an infinitesimally small period of time.  Think Elsa in Frozen.  It also has the connotation that the emotion from hot to cold can happen fairly quickly.
The idiom in your sentence is

(with) at a glance

meaning very quickly.


Image of an Immersion

Question: I cannot prove any conclusion of this problem. Can anyone please help me?
Let $f:M\to N$ be an immersion of $M$ into $N$ and dim $M=\dim N$.Prove or disprove that $f(M)$ is a submanifold.
Thanks for any help.
Comment: http://math.stackexchange.com/questions/568160/submanifold-given-by-an-open-immersion?rq=1 .Have a look at this.By this result I think it will be a submanifold,because in this case we have a local diffeomorphism.
Comment: I missed the assumption in the question that the dimension of $M$ was equal to the dimension of $N$ and this certainly changes the relevancy of my comment above.
Comment: The image $f(M)$ need not be a submanifold as there might be self-intersections.  Consider Boy's surface for example
http://en.wikipedia.org/wiki/Boy%27s_surface (which gives an immersion of the real projective plane into $\mathbb{R}^3$), or something even less exotic such as the surface parametrized by
$$
\mathbf{x}(u, v) = \left(\cos\left(u\right), \sin\left(2 u\right), v\right),
$$
where $ -\pi < u < \pi$ and $0 < v < 3$. (I would add a figure for the second example, but comments don't seem to allow for that).

If you think more locally in $M$, then you can draw some conclusions.
Answer: $f(M)$ is an open subset of $N$ and thus  a submanifold. Proof by unwrapping of definitions: say $y=f(x)\in f(M)$. Since $f$ is an immersion $df(x)$ is injective, and since $\dim(M)=\dim(N)$ $df(x)$ is in fact an isomorphism. By the inverse function theorem $f$ restricted to some  neighborhood of $x$ is a diffeomorphism onto a neighborhood of $y$. In particular, $f(M)$ contains a neighborhood of $y$.
Answer:
Use this. An immersion is an open map if (and only if, I think) $\dim M = \dim N$. This is because for $\dim M = \dim N$, we have that immersion, submersion are local diffeomorphism are equivalent.
Images of open maps are open subsets. (Conversely, image open subset implies open map, I think.)
Open subsets can always be made into submanifolds of codimension zero. (Conversely, underlying sets of submanifolds of codimension zero are open subsets, I think.)

Image of an Immersion


will i lose my photos, voice recordings, videos and notes if i reset my samsung galaxy s1

Question: If I reset my Samsung Galaxy S1 to factory reset mode will i lose my photos my voice recordings and my notes?
Because i really need those, but its been so long since i've used this phone and i forgot my password to the account and the only way to delete the account is to reset the phone to factory mode i have another account but it wont let me use it. Can someone help me?
Answer: Depends if you have used memory card and saved it there, in which case they are safe and won't be deleted. it could be the reason why Ramzy Shah didn't lose his data, if he had external memory to save all private data on, or used some backup cloud service like Aravindan said.  I'd rather focus on either recalling your password or looking for a way to recover password, because once reset, it will erase all the data.

With that said, I think you'll find this guide very useful and recover your password :)https://www.howtogeek.com/226942/what-to-do-if-you-forget-your-android-phone's-pin-pattern-or-password/
Good luck!
Answer: Yes. Surely you will lost your personal data, contacts and everything. To avoid this, you should Backup your files and everything to your SD Card. You can Restore it again to your mobile.
This following site will help you how to take backup and reset your mobile and then restore it back.
http://www.wikihow.com/Reset-a-Galaxy-S
Thats all.. :-)
Answer:
Usually you shouldn't lose any of those, only the settings you've made on the phone and applications you've installed on it. I've reset a phone to the default settings, but it was really long time ago so right now I can't remember in detail what exactly got deleted. However I would suggest you connect your phone to a computer and make a backup of the files you don't want to lose, just in case, but usually you really shouldn't lose any of this files, by resetting it.


Whom is a player bankrupt to if a Chance card tells him to pay $50 to each player and he can't pay?

Question: If a player draws the Chance card (US standard edition) that tells him "You have been elected Chairman of the Board. Pay each player $50", and his cash is insufficient (even after he sells hotels/houses and/or trade/mortgages properties), then whom is he bankrupt to? To whom must he hand over his remaining assets?
Answer: There are indeed no instructions in the official rules on how to resolve multiple payments. A common mechanism in game design to handle such cases is to pay your debts in turn order. You go bankrupt to the player who you cannot pay.
Example: turn order is Alice, Bob, Charlie, Daniel and Eve. It's Alice's turn and she is instructed to pay $50 to each player. Her entire liquid assets are $149. She pays $50 to Bob and Charlie, respectively, but since she's $1 short of paying the debt to Daniel, she goes immediately bankrupt and turns all her assets to Daniel. Eve gets nothing.
Turn order is clockwise, as indicated by the rules:

THE PLAY... [...] After you have completed your play, the turn passes to the left.
Comment: Well, an interesting solution. But the distributuon of assets is not equal to every player, whereas the original debt is equal to each player.
Answer: The assets are sold off and divided equally among the other players
This actually situation occurred in a Monopoly Tournement
"Phil Orbanes, who wrote The MONOPOLY Companion and is the official Judge at the World Championships provided me with this answer when it came up in tournament play a few months ago:

If you cannot pay a debt to ONE player due to a card, you go bankrupt to that player and turn over all asset  (std. procedure here).
If you cannot pay a debt to TWO or MORE players (after calculating any money you could get from the bank by mortgaging and selling houses) due to a card, you go bankrupt to them all.  The issue then becomes: fairness. How do you divide your assets as evenly as possible?
Procedure: after selling any houses for 1/2 price to the bank, the bank then rebuys your properties at face value if unmortaged, or for 1/2 value if mortgaged.   You divide the resulting cash as evenly as possible, with the player(s) to your left collecting any odd dollar(s). The bank then auctions all properties it purchased to the highest bidders."

Source : Quora.com : Kevin Tostado, Director of "Under the Boardwalk: The MONOPOLY Story." MonopolyDocumentary.com
Conclusion.
The players may get a lot more than the 50$ that they were originally owed.
Comment: It seems unlikely that players would get much more than the original debt of $50, as if a player has $500 worth of property, and owes $200, he should be able to raise $200 by selling the property to other players, rather than to the bank. In fact, if I was handling this situation, I'd cap the amount players could receive at $50 each anyway, and have the bank keep the surplus.
Comment: @Pelotas : Assume that all of the player's properties are mortgaged. Then, it is to the other players' advantage to let that player go bankrupt and leave the game - that's the only objective of the game. All the  mortgaged properties will be bought at half-price by the bank and that money will be redistributed to the creditors; that sale would probably represent more than 150$. Also, the repossessed properties will auctioned off by the bank.
Answer: My play group treat this as being bankrupt while owing the Bank.
The reason for this is that the player collectively owes every player $50. If the whole collective cannot be payed then the player is bankrupt owing everyone.  There is no way to equally distribute the assets so handle the redistribution by Auction.
We don't pay the other players the $50.  The only effect is that the Bankrupt player is removed and the new auction occurs.
Comment: 1. Why "owing the bank" if the debt is to the players? 2. This doesn't answer the question "to whom must he hands over his remaining assets?"
Comment: This seems to be a reasonable interpretation where the rules are not clear.  Each other player gets M$50 from the bank, and the player is [bankrupt](https://hasbro-new.custhelp.com/app/answers/detail/a_id/83/~/what-happens-if-a-player-owes-more-than-he-can-pay-in-monopoly%3F) to the bank, so all of their properties are auctioned off.  This seems the fairest solution to me.
Comment: It seems silly to have whom you go bankrupt to be dependent on the order in which you pay out the $50.  The rule described in this answer makes good sense: You go bankrupt to the bank; the bank pays out the $50 to each player; the bank takes your assets and does the auction.  Certainly it's within the spirit of Monopoly for a player to go bankrupt over a few bucks, but not to go bankrupt to one particular person when owing several players money simultaneously.
Comment: @JBentley It does answer it indeed.  You are not owing a single player therefore you can't distribute assets to a single player.  Handle the redistribution by auction, same as if the player had gone bankrupt owing the bank.
Comment: How if the Bank takes over both the assets and the debts? The assets are handed over to the Bank, but the Bank has to pay each player the $50.
Comment: You didn't put that in the answer...
Comment: @FerdinandLiem We don't pay it out.
Answer: Like Leppy, I would play this situation as "the player goes bankrupt to the bank." That way, you don't have one player getting all the property just because of his/her position in the turn order when debt is "collective."
My answer differs from Leppy's insofar as I would have the bank pay $50 to each player (in this example) or otherwise satisfy the debt, so that all the players get what is owed them. In return, the bankrupt player forfeits all property to the bank (rather than to another player) and leaves. A real banker would usually be pleased with such an arrangement, to get someone's property back for small payments. A variation of the answer is that the property goes back to the bank, and the liquid assets (cash) are divided evenly between the other players (each gets more than $0, less than $50).
What goes on from here depends on what role you assign to the banker at this point. If you want a shorter, more "deterministic" game (based on the existing situation), the bank auctions off the properties one by one (although there are issues about the order of the auctions).* If you want "house rules" for a longer, more luck based game, the bank, having repossessed the bankrupt's properties, will sell them as the other players land on and buy them (or put them up for auction).
*Using the "auction" method, I would have an "order rule," either auction the properties alphabetically (Atlantic Ave. comes first, then Baltic and Boardwalk), or else from cheapest to most expensive.


Need more memory in micromax Canvas colors 2

Question: I have my one year old model of  micromax Canvas colors 2. As many of you may know, it has limited internal memory, So I cannot install app which are only stores in phone memory. I have to install so limited apps on my phones due to this drawback. Can anyone tell me how can I solve this issue?
Comment: I suggest starting with our [insufficient-memory tag-wiki](http://android.stackexchange.com/tags/insufficient-memory/info), which contains several hints/links on exactly this topic. Then come back here and either [answer your own question](http://meta.stackexchange.com/questions/17845/etiquette-for-answering-your-own-question) (if you found a solution), or [edit] your question with what you've tried and where you're stuck. Note that not all hardware limitations can be overcome, so the only real solution might be buying a "better device".
Comment: Right Izzy, agreed with you about hardware limitation , but I thought there may be some 'tricky' tools which can be helpful.
Comment: Those you might find using the mentioned tag-wiki as starting point :)
Answer: Is your device rooted ? If it is you can use link2sd it can increase internal memory by adding an SD card.
If it's not there are many apps that you can move to SD without any program in settings.
Comment: I will try your first solution, For 2nd, It is only useful if app can be installed in SDcard, Where I am blocked.


Use Webdav on Linux to get a file from SkyDrive *without* mounting

Question: I want to download a file from SkyDrive programmatically using Python on Linux.
I can't use the API as it's a OneNote file and the API can't be used to download these.
My understanding is that SD supports Webdav and there are plenty of examples where people have mounted an SD folder using davfs2 but I just want to be able to grab a specific file without mounting.
I can use the API to get the document owner's cid so don't need to jump through any windows based hoops but my - probably lame, have not really researched webdav - efforts to download the file always resort in an error.
For example using easywebdav:
<code>import easywebdav
webdav = easywebdav.connect("d.docs.live.net/mycid")

webdav.download('me/skydrive/Documents/Getting\ Started', '/tmp/foo')
#this gives the 302 error mentioned in the comments at the end of the the 'jumping through windows hoops' link I posted above.
</code>
Is there any workaround for the redirection problem I've seen mentioned?
Do I have this wrong and when accessing files on a webdav share it makes sense, and indeed it's essential, to mount it as a file system?
Answer: If you are downloading a specific file, and already know the exact path/URL to that file (as per your example), I'm not sure that you really need to worry about the DAV extensions. Have you tried downloading the file using a simple HTTP GET, through something like urllib2?
Comment: Useful, thanks.

Using the link that one can read from the document metadata using the API urllib2 did actually download something. Unfortunately it's not the file (but that's a different problem related to how Skydrive handles Skydrive documents).

I was hoping that using Webdav it might actually give me the target file not the placeholder for the file.

I think I'll tinker with Cadaver to see if I can get it using the CLI.


Are these white bits mold?

Question: I bought some coffee beans today. When I poured them into a jar, I found some white bits. Are they mold? Thanks
Comment: Hard to tell, especially as the photo is rather blurry. (Any chance you can get a better one? ) Off the cuff, I'd check for what could be webbing from pantry moths. But I can't see it well enough for an answer. Do you still have the packaging and could check that too?
Comment: Dear @Stephie. Thanks for your reply. They are dissolvable in water, it seems to me they are coffeemate powder since there were some in the next box in the shop, however, I was not sure about it.
Comment: good to hear - feel free to self-answer ;-)
Answer: Based on the picture I believe that these white spots are something form when he beans have been harvested or they have been sugar and sprinkled when the manufacture was selling this product.
Comment: "something form when he beans have been harvested", Impossible, these white dots looks easily removable, which means during the process of shipping, roasting, and packing, it definitely would have fallen off.

Are these white bits mold?


Can I power a security camera from a ceiling fan junction box?

Question: I have a ceiling fan in a screened in porch. I would like to install a security camera on the outside of the porch's soffit. Can I connect either a USB cable or a 110 electrical wire from the ceiling fan box to the security camera? The ceiling fan is not on a switch.
Comment: How about a picture? Some ceiling fan boxes have knockouts and you could others maybe not.
Comment: I do not see what you have but they make pull chain socket adapter that have an outlets, one on each of two sides and a socket for a bulb. they screw in a normal lamp socket and are not very expensive. Your local box or mail order store would have them.
Answer: A little unusual (but not impossible) to have a ceiling fan not on a switch at all. But if that is the case then you definitely have always hot in the fan box. If there really is a switch somewhere then you may have always hot in the fan box, or you may only have switched hot. Of course, if there is a switch and only switched hot in the fan box, but that switch never gets turned off because nobody knows where it is, then you have a practical always hot anyway.
You can't run USB or any low voltage into the fan box. You can splice into hot and neutral in the box and run that to another box and install a receptacle in that box, either with a USB port built in (costs a little more, but one less exposed gadget) or plug in a standard USB adapter.
Depending on the type of ceiling and how far away the camera will be from the fan, you can either run non-metallic cable (a.k.a. Romex) through the ceiling or you can use conduit, Legrand Wiremold or similar products on the surface.


Can the following sum be counted or expressed in terms of special functions?

Question: Let us define this sum as a function of $z \in \mathbb{C}$ with some positive parameter $a$
$$
f(z; a) = \sum\limits_{n = 0}^{\infty}\frac{|z|^{2n}}{n!}e^{-ian^2}.
$$
Probably, it can be expressed (or somehow related) in terms of theta-function.
Comment: It's really $f(|z|;a)$.  That aside,
if $a$ is a rational multiple of $\pi$ then $f(z;a)$ is a linear combination of
terms $\exp 2c|z|$ for some roots of unity $c$ (because $e^{-ian^2}$ is periodic
and can be written as a discrete Fourier series).  Irrational multiples of $\pi$
seem much harder.
Comment: There is [a question here on MO](https://mathoverflow.net/q/101191/41291) about this same series (up to substitution)
Comment: Yeh, here $a$ - some real parameter.
Comment: @მამუკაჯიბლაძე Thank you!
Answer: Probably the answer is negative. Your series is a restriction of the analytic function in two complex variables:
$$F(\zeta,q)=\sum_{n=0}^\infty\frac{q^{n^2}}{n!}\zeta^n,\quad |q|\leq1,$$
obtained by setting $q=\exp(-ia)$ and $\zeta=|z|^2>0$. Function $F$ is continuous, entire with respect to $\zeta$ and analytic for $|q|<1$.
This important function has been studied much recently, see
lectures of Alan Sokal for a survey of known results; as Sokal says himself, there are many conjectures and almost no theorems, and there is no indication of its expression in terms of standard special functions.  (Except the trivial observation that it is the "Hadamard product" of the "partial theta-function'' with the exponential, or Borel's transform of the partial theta function, but this partial theta-function is itself outside of the set of
common special functions, and its properties make a current research subject.)
The case when your $a$ is real, that is $|q|=1$ is especially difficult and mysterious; all these points are singular for $q\mapsto F(\zeta,q)$.
Comment: I see. Thank you for your answer! And especially for the link.


Tags should have types

Question: It would be nice if tags had types.
This way we could create a class type for all tags designating some library class like QStateMachine (from Qt framework). We could create another type of tag, let's say programming-language and make all tags designating some programing language of this type.
This way we could allow users to search only in specific types of tags if they wish.
Comment: Programmers would understand that. But users?
Comment: Perhaps useful in a few scanarios, but I still disagree because it would add a lot of unnecessary complexity to a feature that basically works well as it is now.
Answer: It's an interesting idea, but it has some complexity considerations.

Who categorizes existing tags?
Who can re-categorize?  What's the process?  How many people does it take?
What's UI for (any of) it look like?
When you create a new tag, do you have to categorize it?
Can a tag be in more than 1 category?  Frankly, it's gotta be.  There's gonna end up being a "microsoft" category, and a ".net" category.  Categories aren't idempotent.
Can categories be in categories?  Cause sql-server would be a reasonable category, but it'd also fall under Microsoft which would be another category.
(steve yegge link here)

Then you have to think of the "wins" of it:

Essentially gives all questions a "broader" tag implicitly: all .net tags get microsoft, all t-sql tags get sql-server, all sql-server tags get sql.  This lets you follow a much broader stream of information. (and drink from a larger firehose)
Search would get "better" (for some definition of better) because you could search within a category.  Don't show me anything from any category from mac because I'm a snob (I kid).
I know there's more but I'm getting hungry

Do the wins justify the cost?  I think this falls into the following feature-request type

Feature requests which are good but unlikely due to the cost/benefit

It's not a bad idea, it does get you wins in certain areas but it also has a deceptively high development cost for the few wins.
Comment: ad. 1-4 The same or similar as with tags themselves.
ad. 5-6 These are the interesting questions. The idea is called meta tags. See this http://meta.stackexchange.com/questions/1620/meta-tags
Answer: The cost vs. benefit of this would be pretty monumental in my own opinion. If I have to start tagging my tags, my head may pop off.
This also sounds eerily similar to hierarchical tagging, which Jeff has said in absolute terms would never be showing up.
Comment: taggin tags, poppin heads... hmm sounds like some retarded rap song.

Tags should have types


Is there an intuitive geometric view of the effects of Lorentz transformations?

Question: Is there a time + two spatial dimension representation of a Minkowski-space surface which could be constructed within our own (assumed Euclidean) 3D space such that geometric movement within the surface would intuitively demonstrate the "strange" effects of the Lorentz transformation (length contraction, time dilation)? Perhaps by making manifest the idea of a hyperbolic rotation (the rapidity)?
Comment: Huh? The metric on manifold embedded in some other manifold is just a pullback of the bigger manifold's metric. Obviously this can't change signature of that metric. So either I don't understand what you are asking or you don't :)
Comment: Yes, the obvious fact that the Minkowski metric is not the same as the Euclidean metric is certainly a problem. I just wondered whether someone, somewhere had a neat model which just did the best it could. Something better than those hyperboloids of revolution.
Answer: I think what you are looking for is given in the first chapter of the epic text "Spinors and Spacetime" by Wolfgang Rindler and Roger Penrose. Or at least it is if what you're asking for is a simple and clear geometric construction that illustrates the effects of Lorentz transformations on the bulk (3+1) geometry.

[Fingers crossed .... IMHO the use of this image and the ones below is covered under "fair use". If it is deleted blame the copyright regime.]
To cut a long story short, you identify points on the celestial sphere $\mathcal{S}^-$ with a light ray as seen by an observer at the center of the sphere. A stereographic projection allows to map points on $\mathcal{S}^-$ to the complex plane $\mathbb{C}$. The action of Lorentz boosts on the observer translates into the action of an $SL(2,\mathbb{C})$ element on the points of $\mathcal{S}^-$. The result is shown in the figure below:

I do not know of any other constructions which so vividly illustrates the geometrical effects of Lorentz transformations. I have left out many details for which I once again recommend the amazing text by Penrose and Rindler.
All hail the copyright gods.

Edit: In response to the comments, I answered the question the best I could understand it. I've emphasized the relevant sentence in the first para.
Comment: Glad you like it @Nigel. Do you mean the pdf of the book? Maybe it is djvu you're looking for. Cheers!
Comment: Wow! If we can only download the PDF!
Comment: Hm, sure, there is also the obvious $Spin(1,3) \cong SL(2, {\mathbb C})$ isomorphism and isomorphism of four-vectors and $2 \times 2$ hermitian matrices with norm given by determinant but I fail to see how these facts even remotely relate to the question (which asked for the 2+1 case, by the way) :)
Comment: @Marek from the OP's question I gather that he's asking for something that *would intuitively demonstrate the "strange" effects of the Lorentz transformation ... Perhaps by making manifest the idea of a hyperbolic rotation (the rapidity)?* This construction does exactly that. Also note @Nigel's clear approval in his comment ;)
Comment: Yes, a quick approval of your ingenuity before going to bed!
Comment: @space_cadet: all right. But you'll note that the title of the question has nothing to do with your answer whatsoever. I am going to change it to something more appropriate.
Answer: Since this question is about learning Special Relativity with an alternative to the Minkowski Diagram to aid understanding (and dropping one - even two - dimensions shouldnt cause much harm for that purpose), might I recommend consideration of the Bondi K-Calculus?
Here the "K" is introduced into the geometry, which represents the relativistic Doppler term: it is additive and cancels out much of the hyperbolic weirdness in basic Minkowski accounts.
A quick G-search found this simple Tutorial: http://www.math.ku.edu/~lerner/m291/SR_Lecture2.pdf with drawings.
Wikipedia links to another Tutorial (without diagrams as far as I can tell).


When I try to connect to work wifi I am asked to sign in

Question: My work wifi runs netgear routers via a lan.
when I try to connect with my Samsung galaxy s5 I am asked to sign in but these are open routers no security. When I try to sign in I am redirected to google home page. Connection only stays active for a short period of time then drops the connection. Everyone with a Samsung device is having the same problem but iPhones are ok.
I have no problems with my home wifi. This started after the latest android update.
Answer: WiFi "sign in" now includes dealing with landing pages asking you to accept terms & conditions. I've noticed more and more public routers throwing these out, and then terminating connections if you don't hit the right web page quickly enough. I've seen iOS and Android respond differently to these things, depending on when the device finds the connection, how tolerant the router is, and so forth.
The solution I've found that works for me on any device is to shut off WiFi, give it a few seconds to "calm down," then start it up again and watch your notifications. If you get a "Sign in to ..." notification, tap on it as quickly as possible. If you don't, and you know it's an access point that exhibits this behavior (like at your place of work), tap the browser icon to open it up, then go to some page that's likely not cached (like SE here), or force a refresh. You should get to the sign-in landing page. Accept, and you should be good at least until your phone goes to sleep (which, sometimes, will cause a disconnect and make the access point whine at you to sign in again).
Yep, it stinks, but the issue seems to be on the access points, not Android.


How to test with different versions of PHP in a GitHub Action

Question: I have some PHP code with tests which run using PHPUnit and wanted to test it on GitHub Actions. I could not find a method in their documentation for testing PHP packages.
I want to test using different versions of PHP, but they only have the latest one 7.3 installed.
Answer: You can add the setup-php action in your workflow. If not present, it installs the PHP version(s) you specify with required extensions and various tools like composer. It supports all the virtual environments supported by GitHub Actions and PHP versions >= 5.3.
For example you can have a workflow like this
jobs:
  run:
    runs-on: ${{ matrix.operating-system }}
    strategy:
      matrix:
        operating-system: [ubuntu-latest, windows-latest, macOS-latest]
        php-versions: ['7.2', '7.3']
    name: PHP ${{ matrix.php-versions }} Test on ${{ matrix.operating-system }}
    steps:
    - name: Checkout
      uses: actions/checkout@v2
    - name: Install PHP
      uses: shivammathur/setup-php@v2
      with:
        php-version: ${{ matrix.php-versions }}
        extensions: intl #optional
        ini-values: "post_max_size=256M" #optional
    - name: Check PHP Version
      run: php -v

Note: This will setup PHP, you need to add steps to install your dependencies using composer and another step to run your tests using PHPUnit
You can specify the required extensions in the extensions and the php.ini configuration you want in ini-values. Both these inputs are optional and take a CSV as an input. The php-version input is required. In above example it will run the workflow and setup the PHP environment with the versions specified in matrix.php-versions i.e 7.2 and 7.3, you can adjust these as per your requirements.
Comment: @simonw16
Are you using another action to install composer dependencies.
If yes, it might be a docker based action while setup-php runs on the host container. I would suggest calling the composer command directly.

If not, please create an issue here specifying your workflow.
https://github.com/shivammathur/setup-php/issues
Comment: Thanks, I was looking for something exactly like this.
Comment: Thats exactly what the issue was! Took me hours to figure this out. I thought the actions were on the host container, but turns out they're mostly in their own. Running manually solved it. Thanks!
Comment: @Shivam Mathur I've used your package setup-php@v2 and specified `7.3`, and then checked the version afterwards. Confirmed is running `7.3`, but my composer install step directly afterwards fails and tells me I am on `7.4.10`. How is this possible if the previous step `php -v` tells me `7.3.10`?
Comment: @simonw16 same for your test suite. For example, if you use PHPunit, call that directly as well.


HP iLO xmldata modification

Question: I've just installed a HP Microserver Gen8 and I would like to monitor it (using Rainmeter).
Unfortunately I have restricted internet access (80/443) so I would like to use XML for this. I can get some basic information using:
https://myserver/xmldata?item=All
How could I modify this xml to have some more details (like temperature/memory/cpu etc.)?
Answer: I think you will not get this information. This interface is only for discovering.
Maybe this will help to get a little more data, but do you really what all information about the server without authentication?
Read
http://h20565.www2.hpe.com/hpsc/doc/public/display?docId=c03334058
If configured to do so, the iLO device returns identifying information in
response to an
unauthenticated XML query. By default, the iLO device is configured to
return this information.
To disable this feature, set the CIM_SECURITY_MASK in the
MOD_SNMP_IM_SETTINGS
command to disable unauthenticated XML query return information.

and
CIM_SECURITY_MASK accepts the integers 0–4. The possible values are:
• 0—No change
• 1—None (no data is returned)
• 2, 3, 4—Enabled (medium — 3)

Answer: A little late but may help others.
*HPE Redfish, and hperest was implemented on Gen 8 (gen8's may need an updated ilo firmware to access this functionality) and Newer ProLiants
This allows Collection of things like, CPU , POWER, Thermal etc over a Secure HTTPS connection**

'@humans374 Your url indicated you have https access which allows you
the ability to collect a Ton of information when utilizing various
tools Take a look at'

https://www.hpe.com/us/en/product-catalog/detail/pip.scripting-tools-for-windows-powershell.5440657.html
There are powershell cmdlets for HPEREST, HPEREDFISh, HPEilo HPEOA, etc.
There are also extensive python and curl samples available.

HP iLO xmldata modification


Xcode 4.2 does not commit files?

Question: I have Xcode 4.2 and I was working ona a project, that was commited previously with - let;s call it - place A. Then I copied it on my disk to another place, made modifications and now I imported via Xcode Organizer whole new project into place B. But when I checked out project from place B I cannot commit any file. I select a file, choose commit, write comment and go. It looks ok, but in fact the status of this file is not changing, so I can without any warning make commits on and on... Is it problem with some project setting or what? I remember that in previous Xcode in project settings you could set svn location, but here I don't see anything like it.
Answer: I think you have not copied a folder .svn in the root of your Project - there are the meta-informations of SVN, without this infos SVN can not work. Just find and copy this folder from A to B and the issue will gone!

Xcode 4.2 does not commit files?


Printing from a .NET Service

Question: I am working on a project right now that involves receiving a message from another application, formatting the contents of that message, and sending it to a printer.  The technology of choice is C# windows service.  The output could be called a report, I suppose, but a reporting engine is not necessary.  A simple templating engine, like StringTemplate, or even XSLT outputting HTML would be fine.  The problem I'm having is finding a free way to print this kind of output from a service.  Since it seems that it will work, I'm working on a prototype using Microsoft's RDLC, populating a local report and then rendering it as an image to a memory stream, which I will then print.  Issues with that are:

Multi-page printing will be a big headache.
Still have to use PrintDocument to print the memory stream, which is unsupported in a Windows Service (though it may work - haven't gotten that far with the prototype yet)
If the data coming across changes, I have to change the dataset and the class that the data is being deserialized into.  bad bad bad.

Has anyone had to do anything remotely like this?  Any advice?  I already posted a question about printing HTML without user input, and after wasting about 3 days on that, I have come to the conclusion that it cannot be done, at least not with any freely available tool.
All help is appreciated.
EDIT: We are on version 2.0 of the .NET framework.
Answer: Trust me, you will spend more money trying to search/develop a solution for this as compared to buying a third party component. Do not reinvent the wheel and go for the paid solution.
Printing is a complex problem and I would love to see the day when better framework support is added for this.
Answer: Printing from a Windows service is really painful. It seems to work... sometimes... but finally it craches or throws an exception from time to time, without any clear reason. It's really hopeless. Officially, it's even not supported, without any explanation, nor any proposal for an alternate solution.
Recently, I have been confronted to the problem and after several unsuccessful trials and experimentations, I came finally with two viable solutions:

Write your own printing DLL using the Win32 API (in C/C++ for instance), then use it from your service with P/Invoke (works fine)
Write your own printing COM+ component, then uses it from your service. I have chosen this solution with success recently (but it was third party COM+ component, not own written) It works absolutely fine too.
Comment: GDI+ was never designed/tested to work in service context.  Thats why it does not work.  You should use GDI and it function to draw.  Refer to this document to find equivalent Win32 calls : http://msdn.microsoft.com/en-us/library/aa302340.aspx#win32map_printingfunctions
Comment: @Yann Trevin, I am working on a similar requirement, Could you please suggest which third party COM+ component you have used. It would be great
Answer: I've done it.  It's a pain in the A*s.  The problem is that printing requires that GDI engine to be in place, which normally means that you have to have the desktop, which only loads when you're logged in.  If you're attempting to do this from a Service on a Server, then you normally aren't logged in.
So first you can't run as the normal service user, but instead as a real user that has interactive login rights. Then you have to tweak the service registry entries (I forget how at the moment, would have to find the code which I can do tonight if you're really interested).  Finally, you have to pray.
Your biggest long term headache will be with print drivers.  If you are running as a service without a logged in user, some print drivers like to pop up dialogs from time to time.  What happens when your printer is out of toner?  Or out of paper?  The driver may pop up a dialog that will never be seen, and hold up the printer queue because nobody is logged in!
Answer: To answer your first question, this can be fairly straight forward depending on the data.  We have a variety of Service-based applications that do exactly what you are asking.  Typically, we parse the incoming file and wrap our own Postscript or PCL around it.  If you layout is fairly simple, then there are some very basic PCL codes you can wrap it with to provide the font/print layup you want (I'd be more then happy to give you some guidance here offline).
One you have a print ready file you can send it to a UNC printer that is shared, directly to a locally installed printer, or even to the IP of the device (RAW or LPR type data).
If, however, you are going down the PDF path, the simplest method is to send the PDF output to a printer that supports direct PDF printing (many do now). In this case you just send the PDF to the device and away it prints.
The other option is to launch Ghostscript which should be free for your needs (check the licensing as they have a few different version, some GNU, some GPL etc.) and either use it's built in print function or simply convert to Postscript and send to the device.  I've used Ghostscript many times in Service apps but not a huge fan as you will basically be shelling out and executing a command line app to do the conversion.  That being said, it's a stable app that does tend to fail gracefully
Answer: Printing from a service is a bad idea. Network printers are connected "per-user". You can mark the service to be run as a particular user, but I'd consider that a bad security practice. You might be able to connect to a local printer, but I'd still hesitate before going this route.
The best option is to have the service store the data and have a user-launched application do the printing by asking the service for the data. Or a common location that the data is stored, like a database.
If you need to have the data printed as regular intervals, setup a Task event thru the Task Scheduler. Launching a process from a service will require knowing the user name and password, which again is bad security practice.
As for the printing itself, use a third-party tool to generate the report will be the easiest.
Answer: This may not be what you're looking for, but if I needed to do this quick&dirty, I would:

Create a separate WPF application (so I could use the built-in document handling)
Give the service the ability to interact with the desktop (note that you don't actually have to show anything on the desktop, or be logged in for this to work)
Have the service run the application, and give it the data to print.

You could probably also jigger this to print from a web browser that you run from the service (though I'd recommend building your own shell IE, rather than using a full browser).
For a more detailed (also free) solution, your best bet is probably to manually format the document yourself (using GDI+ to do the layout for you). This is tedious, error prone, time consuming, and wastes a lot of paper during development, but also gives you the most control over what's going to the printer.
Answer: If you can output to post script some printers will print anything that gets FTPed to a certain directory on them.
We used this to get past the print credits that our university exposed on us, but if your service outputs to a ps then you can just ftp the ps file to the printer.
Answer: We are using DevExpress' XtraReports to print from a service without any problems.  Their report model is similar to that of Windows Forms, so you could dynamically insert text elements and then issue the print command.
Answer: I think we are going to go the third party route.  I like the XSL -> HTML -> PDF -> Printer flow... Winnovative's HTML to PDF looks good for the first part, but I'm running into a block finding a good PDF printing solution... any suggestions?  Ideally the license would be on a developer basis, not on a deployed runtime basis.
Answer: In answer to your question about PDF printing, I have not found an elegant solution. I was "shell" ing out to Adobe which was unreliable and required a user to be logged in at all times. To fix this specific problem, I requested that the files we process (invoices) be formatted as multi-page Tiff files instead which can be split apart and printed using native .NET printing functions. Adobe's position seems to be "get the user to view the file in Adobe Reader and they can click print". Useless.
I am still keen to find a good way of producing quality reports which can be output from the web server...
Answer: Printing using System.Drawing.Printing is not supported by MS, as per Yann Trevin's response.  However, you might be able to use the new, WPF-based, System.Printing (I think)

Printing from a .NET Service


Does the norm of an operator on a $w^{*}$ dense subspace determine its norm?

Question: Let $X$ be a (separable) Banach space, $T:X^{*}\to X^{*}$ a bounded operator, and $Y\subset X^{*}$ a norm closed, $w^{*}$ dense subspace of $X^{*}$. Is it true that $\|T\|=\|T_{|Y}\|$?
Answer: No, this is not true. For example, let $X=\ell_1$, $X^*=\ell_\infty$, and $Y=c_0\subset \ell_\infty$. Then $Y$ is a weak* dense subspace, but not norm-dense. Fix a nonzero vector $v\in \ell_\infty$ and define $T:\ell_\infty\to\ell_\infty$ as $T(x) = \phi(x)v$ where $\phi$ is a Banach limit. Then $T$ is identically zero on $Y$, but not on $X^*$.
Comment: Thank you. do you have a quick counterexample when $X^{*}$ is separable?


Combinatorial binomial

Question: Calculate the sum value:
$$ \sum_ {k = 0} ^ {n} k \cdot 3 ^ {k} \cdot \binom {n} {k} $$
Tip:
$$ \binom {n} {k} = \binom {n-1} {k-1} \cdot \frac {n} {k} $$
I can get here:
$$\sum_ {k = 0} ^ {n} 3 ^ {k} \cdot \binom {n-1} {k-1} \cdot n $$
After that, the original resolution takes 'n' out of the sum and places it outside in the '3n' form. I have no idea where this three came from. Then they rewrite the expression this way:
$$3n \cdot \sum_ {k = 1} ^ {n} 3 ^ {k} \binom {n-1} {k-1} $$$$ 3n \cdot (3 + 1) ^ {n-1} $$$$ 3n \cdot 4 ^ {n-1} $$ Could someone simply elude the above steps or develop a workaround?
Original source of the problem: https://portaldosaber.obmep.org.br/uploads/material/dgr8vm27u08os.pdf
Comment: Which steps don't you understand ?
Comment: You seem to have a typo going to the step you don't understand.  The summation should have been $\sum\limits_{k=1}^n3^{\color{red}{k-1}}\binom{n-1}{k-1}$.  You incorrectly had $3^k$ instead of $3^{k-1}$.  The $3$ came from factoring out a common factor of $3$ from every summand.  Now, let's rename the indexing variable $j$ instead, letting $j=k-1$ and we have $\sum\limits_{j=0}^{n-1}3^j\binom{n-1}{j}$
Comment: @user "and so the starting value of the sum is adjusted", no, this adjustment comes from different reasons, namely that $\binom{n-1}{-1}=0$ in this context, and so we don't need to include a term which we know to be zero in our summation, or alternatively worded, we skip over this term and handle it separately so as to avoid the division by zero errors.
Comment: @DonaldSplutterwit After my comment in part two
Answer:
We obtain
  \begin{align*}
\color{blue}{\sum_{k=0}^nk\,3^k\binom{n}{k}}&=\sum_{k=1}^nk\,3^k\binom{n}{k}\tag{1}\\
&=\sum_{k=1}^nk\,3^k\frac{n}{k}\binom{n-1}{k-1}\tag{2}\\
&=n\sum_{k=1}^n3^k\binom{n-1}{k-1}\tag{3}\\
&=n\sum_{k=0}^{n-1}3^{k+1}\binom{n-1}{k}\tag{4}\\
&=3n\sum_{k=0}^{n-1}3^{k}\binom{n-1}{k}\tag{5}\\
&\,\,\color{blue}{=3n4^{n-1}}\tag{6}\\
\end{align*}
  and the claim follows.
Comment:

In (1) we skip the index $k=0$ which does not contribute anything.
In (2) we apply the binomial identity $\binom{n}{k}=\frac{n}{k}\binom{n-1}{k-1}$.
In (3) we cancel $k$ and factor out $n$.
In (4) we shift the index and start with $k=0$. We compensate the shift of the index $k$ by replacing in the summand each occurrence of $k$ with $k+1$.
In (5) we factor out $3$.
In (6) we apply the binomial theorem to $4^{n-1}=(1+3)^{n-1}$.
Answer: You are right, but another way is:
$$(1+x)^{n}=\sum_{k=0}^{n}  {n \choose k} x^k$$, D.w.r.t.x we get
$$n(1+x)^{n-1}=\sum_{k=0}^{n} k {n \choose k} x^{k-1}$$
By putting $x=3$, we get the sum as $3n 4^{n-1}$
Comment: Where did n and k come from?

Combinatorial binomial


Short story "trash" in SF or Fantasy Anthology

Question: A long time ago I bought a Sci-Fi or Fantasy book that was one of those collections of short stories by various writers - this was probably 10 years ago at a used book store, so no idea how old it was.  One of the last stories in the collection was called "trash".  In it a guy was using a worm hole to put his trash in, and whoever was on the other side of the wormhole was not pleased. I've been trying to find it again, but so far no luck.  Does anyone know the author or which book it was in?
Comment: I recall a story like that, but the one I remember it was the whole neighbourhood and eventually people from further afield that used it as a dump.
Answer: This is a provisional answer because I can't remember what anthology I read it in so I can't check the details. However I think this is a story called Litterbug, and some Googling suggests it was written by Tony Morphett and published in The Magazine of Fantasy and Science Fiction July 1969.
I have a somewhat fuzzy memory of reading this as a teenager (forty years ago!). I'm certain I didn't read it in the magazine so I would have read it in an anthology. Possibly in Beyond Tomorrow as that would have been about the right date.
My recollection is that an Earth scientist invents a garbage disposal device based on a portal/wormhole and everyone starts using it. All is well until some very annoyed aliens turn up!
Answer: There is a story about a worm hole garbage disposal in "The Best from Fantasy and Science Fiction 19
by Edward L. Ferman (editor)"
The story is called Litterbug by Tony Morphett.
The anthology was published in 1971, so it might make sense for you to have found it in a used book store.
Good luck!
Answer: If the story was from the perspective of the person on the trash-receiving end of the wormhole, it might have been Singularity by William Sleator. Some teenage twins discover that their eccentric distant uncle has died, and go to his house to see what he left them. There is a reinforced shed in the backyard.
The narrating character (one of the twins) figures out from his uncle's correspondence and an accident where one of them was locked in the shed for seconds outside/hours inside that the output from a singularity (everything is sucked into a singularity, but the matter has to go somewhere) is in that shed, so his uncle had been collecting alien trash and some unusual dead bodies from it.
Later, the narrator spends extended time in that shed, and one of the major plot points is that something big (or maybe it was "still alive" - I don't remember exactly) is about to come through and he's not sure what will happen when it does.
Singularity was a fairly short story, but I don't know if it has ever been published in an anthology. On the other hand Sleator is prolific enough it wouldn't surprise me if his stories were included in one.


Icon suggestion for items/accessories that are personalised

Question: Trying to think of an icon for a page that has heavy feelings of personalisation. Ideally, users see the icon and they understand that the space it links to is like their private area. But not something so simple as the typical user profile icon of a silhouette head.
Looking for something that might be related to a brainstorm of the feels and places this space would invoke:
privacy, individuality, art, quiet, ambience, tools, buttons, power, share, edit, studyroom, desks, collections, clarity, creativity, abundance
I am hoping for ideas to do with an item/accessory/scene that would get across these feels.
Answer: What about an icon representing a diary? It fits most of the feelings you're trying to evoke. It might be hard making it look like a diary rather than just a book, but it's a starting point at least!
Answer: Paper Plane font from 'Entypo' Picto gram Suite.


how to array with 2 group objects

Question: Im making a ring with diamond attached. I have 2 object diamond made a group and i want to array that to object in a circular manner. I have the 2 object with 2 different color and i dont want to join them and array. I want that 2 separate object to be just group and array. i have made it parent and array but only one object array not the both.
Answer: Unfortunately groups (even instanced) can not have an array modifier.
Your best bet will be to add the array to one object, then select the other, shift select the object with the array and press Ctrl + C and select Copy Modifiers.
Make sure you use Constant Offset or Object Offset and not Relative Offset.

By request, I will add an explanation how to create the target for the array with circular symmetry

Snap an empty to the object, which has the array modifier: arrayTarget
Snap an empty to the center of the circle: circlePivot
Set the object Array Offset to: arrayTarget
Parent arrayTarget to circlePivot
Rotate the circlePivot the desired amount.
Comment: I believe you meant to say "groups... *cannot* have an array modifier."
Comment: i want to know u  have selected the object offset array target what is that and how it bend and shape in to arc or circle shape. can u plz help me
Comment: I added this, to the explanation, but next time open a new question.

how to array with 2 group objects


Bounties offered.by me

Question: Can bounties offered  by me can turn out to be disadvantageous for me?
Answer: Help clearly states that offering a bounty always costs you

All bounties are paid for up front and non-refundable under any circumstances.

If your new reputation brings you below the requirement for any privileges, you will lose access to those privileges.

You may not cancel a bounty once it has been started.

The utility of bounties on martial arts for question visibility is very low. The volume of questions on martial arts is low enough that most everyone will see any question you post.
Comment: ^_^ And, because volume is low, it can make one a bit less inclined to give a big bounty just as a reward. On an active site, I can make a 200+ bounty back up in a day or two. Here... I maybe get an upvote every day or two on average.

Bounties offered.by me


Would a circlet be acceptable to hold an arcane focus?

Question: I'm currently in a homebrew campaign and the DM has stated he doesn't mind my character using a circlet (what would essentially be her crown since she's a royal type) but it has to have some sort of symbolism. I read that an arcane focus could be a crystal so could I just have her still have her crown but the crystal as the focus and be embedded?
Comment: What do you mean by "using a circlet"? Using to do what?
Answer: Yes, but...
The character will need to hold the circlet in their hand when using it as a focus. From the section on Material Components in Chapter 10 of the PHB:

A spellcaster must have a hand free to access a spell's material components - or to hold a spellcasting focus - but it can be the same hand that he or she uses to perform somatic components.

The exception to this rule would be a holy symbol, which a cleric can have displayed on a shield, for example.
Comment: You can of course hold the circlet in your hand without taking it off your head
Comment: Somatic components are described as "forceful gesticulation or an intricate set of gestures" and that "free use of at least one hand" is required to perform them. If the circlet/focus is on the head and the caster grabs it without removing to cast, that is not free use of the hand.
Comment: True, but then she would probably have to perform the somatic components with her other hand.
Comment: Not at all, the rules say you must hold it in your hand and can use that hand for the somatic components- there is no restriction on where you can hold your hand
Comment: @Orvir You can perform the somatic components with a free right hand while holding the material components/spellcasting focus in the left hand.


Should instant yeast be room temperature when used?

Question: Should instant yeast be at room temperature when used to make bread? I store mine in the freezer but I was wondering if it should be allowed to warm up a little before use.
Answer: It probably doesn't matter too much.  By the time you mix it with other ingredients, and then add the friction of kneading it will be the temperature of other ingredients.  I keep mine in the refrigerator and just pull it out and add it to the mix.
Comment: I also keep it in the fridge, and have never had a problem… but don't leave it out of the fridge for extended periods or you risk condensation
Comment: I buy yeast by the pound (I make about 5 loaves of bread a week).  I use a no-kneed recipe that takes a 1/4 teaspoon of yeast per loaf - so the yeast lasts a _long_ time.  I keep the bulk of the yeast in a sealed thermos bottle in the fridge, occasionally transferring it to a 113g Fleishman's jar for daily use (filling the jar about 2/3).  Each day, I pull out the little jar, add my yeast and put it back in the fridge.  It works like a charm, whether with at the start of a new bag of yeast or as I'm finishing it up.


How should outliers be dealt with in linear regression analysis?

Question: Often times a statistical analyst is handed a set dataset and asked to fit a model using a technique such as linear regression.  Very frequently the dataset is accompanied with a disclaimer similar to "Oh yeah, we messed up collecting some of these data points -- do what you can".
This situation leads to regression fits that are heavily impacted by the presence of outliers that may be erroneous data. Given the following:

It is dangerous from both a scientific and moral standpoint to throw out data for no reason other than it "makes the fit look bad".
In real life, the people who collected the data are frequently not available to answer questions such as "when generating this data set, which of the points did you mess up, exactly?"

What statistical tests or rules of thumb can be used as a basis for excluding outliers in linear regression analysis?
Are there any special considerations for multilinear regression?
Comment: Related: possible dupe of this: https://stats.stackexchange.com/questions/37865/is-there-a-simple-way-of-detecting-outliers | R howto: https://stats.stackexchange.com/questions/53227/test-for-bivariate-outliers
Comment: Does this answer your question? [Is it OK to remove outliers from data?](https://stats.stackexchange.com/questions/200534/is-it-ok-to-remove-outliers-from-data)
Answer: Rather than exclude outliers, you can use a robust method of regression. In R, for example, the rlm() function from the MASS package can be used instead of the lm() function. The method of estimation can be tuned to be more or less robust to outliers.
Comment: For a robust regression, the assumptions behind an F test are no longer satisfied, and R^2 can be defined in several ways which are no longer equivalent. See http://stats.idre.ucla.edu/stata/faq/how-can-i-get-an-r2-with-robust-regression-rreg/ for some discussion on this for Stata.
Comment: If using rlm() function, I see the coefficients and their t-tests are produced. But how can I get the f-test, R-square values from here? I suppose I cannot simply bring these f-test and R square values from the simple 'lm' summary results if I am correct.
Comment: See also https://stats.stackexchange.com/a/68367/159
Comment: But I find the command called f.robftest from the sfsmisc package which gives out the f-test result. Can I use this result to define the f-test statistics for rlm? Also, I seem to get R square by simply inputting the values into the R square mathematical formula like 1 - sum(residuals(rlm(y~x))^2)/sum((y-mean(y))^2). For t-test values to check the significance of the coefficients, I get the t-test values from summary(rlm(y~x)) that I compare with the t-values from 95% confidence levels or so. Can I use these methods?
Comment: @RobHyndman why would the usual $1-SSE/TSS$ (sum of squares errors, total sum of squares) not apply? We've not changed the model, just the estimation method. Is it something to do with $SSE$ and $TSS$ being particularly sensitive to outliers and other extreme values?
Answer: Sometimes outliers are bad data, and should be excluded, such as typos. Sometimes they are Wayne Gretzky or Michael Jordan, and should be kept.
Outlier detection methods include:
Univariate -> boxplot. outside of 1.5 times inter-quartile range is an outlier.
Bivariate -> scatterplot with confidence ellipse. outside of, say, 95% confidence ellipse is an outlier.
Multivariate -> Mahalanobis D2 distance
Mark those observations as outliers.
Run a logistic regression (on Y=IsOutlier) to see if there are any systematic patterns.
Remove ones that you can demonstrate they are not representative of any sub-population.
Comment: Agree with most of what is said here, but I'd like to add the additional caution that "*outside of 1.5 times inter-quartile range is an outlier*" is a *convention*, not a rule with any theoretical foundation. It should not be used as a justification for excluding data points.
Comment: And if you still have outliers, consider using a different model than linear. For example, if you use a model with power-law like behaviour, Michael Jordan is no longer an outlier (in terms of the models ability to accommodate him).
Answer: I do think there is something to be said for just excluding the outliers. A regression line is supposed to summarise the data. Because of leverage you can have a situation where 1% of your data points affects the slope by 50%.
It's only dangerous from a moral and scientific point of view if you don't tell anybody that you excluded the outliers. As long as you point them out you can say:
"This regression line fits pretty well for most of the data. 1% of the time a value will come along that doesn't fit this trend, but hey, it's a crazy world, no system is perfect"
Comment: "hey, it's a crazy world, no system is perfect" +1 for that my friend! :)
Comment: Do consider other models though. The world if full of removed "outliers" that were real data, resulting in failing to predict something really important. Many natural processes have power-law like behaviour with rare extreme events. Linear models may seem to fit such data (albeit not too well), but using one and deleting the "outliers" means missing those extreme events, which are usually important to know about!
Comment: (-1) Summarising data with extreme values does not imply removing data that is not easily summarised by a simple model. Improve your model, don't throw out (valid) data.
Comment: I like how it was serious until the " but hey, it's a crazy world, no system is perfect"
Answer: Sharpie,
Taking your question literally, I would argue that there are no statistical tests or rules of thumb can be used as a basis for excluding outliers in linear regression analysis (as opposed to determining whether or not a given observation is an outlier). This must come from subject-area knowledge.
I think the best way to start is to ask whether the outliers even make sense, especially given the other variables you've collected. For example, is it really reasonable that you have a 600 pound woman in your study, which recruited from various sports injury clinics? Or, isn't it strange that a person is listing 55 years or professional experience when they're only 60 years old? And so forth. Hopefully, you then have a reasonable basis for either throwing them out or getting the data compilers to double-check the records for you.
I would also suggest robust regression methods and the transparent reporting of dropped observations, as suggested by Rob and Chris respectively.
Hope this helps,
Brenden
Answer: I've published a method for identifying outliers in nonlinear regression, and it can be also used when fitting a linear model.
HJ Motulsky and RE Brown. Detecting outliers when fitting data with nonlinear regression – a new method based on robust nonlinear regression and the false discovery rate. BMC Bioinformatics 2006, 7:123
Answer: There are two statistical distance measures that are specifically catered to detecting outliers and then considering whether such outliers should be removed from your linear regression.
The first one is Cook's distance.  You can find a pretty good explanation of it at Wikipedia: http://en.wikipedia.org/wiki/Cook%27s_distance.
The higher the Cook's distance is the more influential (impact on regression coefficient) the observation is.  The typical cut-off point to consider removing the observation is a Cook's distance = 4/n (n is sample size).
The second one is DFFITS which is also well covered by Wikipedia: http://en.wikipedia.org/wiki/DFFITS.
The typical cut-off point to consider removing an observation is a DFFITS value of 2 times sqrt(k/n) where k is number of variables and n is the sample size.
Both measures usually give you similar results leading to similar observation selection.
Answer: Garbage in, garbage out....
Implicit in getting the full benefit of linear regression is that the noise follows a normal distribution.  Ideally you have mostly data and a little noise.... not mostly noise and a little data.  You can test for normality of residuals after the linear fit by looking at the residuals.  You can also filter input data before the linear fit for obvious, glaring errors.
Here are some types of noise in garbage input data that do not typically fit a normal distribution:

Digits missing or added with hand-entered data (off by a factor of 10 or more)
Wrong or incorrectly converted units (grams vs kilos vs pounds; meters, feet, miles, km), possibly from merging multiple data sets (Note: The Mars Orbiter was thought to be lost in this way, so even NASA rocket scientists can make this mistake)
Use of codes like 0, -1, -99999 or 99999 to mean something non-numeric like "not applicable" or "column unavailable" and just dumping this into a linear model along with valid data

Writing a spec for what is "valid data" for each column can help you tag invalid data. For instance, a person's height in cm should be in a range, say, 100-300 cm.  If you find 1.8 for height that's a typo, and while you can assume it was 1.8 m and alter it to 180 -- I'd say it is usually safer to throw it out and best to document as much of the filtering as possible.
Answer: For a linear regression you could use a repeated median straight line fit.
Comment: This description sounds similar to the [Theil-Sen estimator](https://en.wikipedia.org/wiki/Theil%E2%80%93Sen_estimator), which is illustrated [here](https://gist.github.com/galenseilis/d2ffb4cfe4e05c6789870c4a676d8f98) with a Python gist. In what sense are you considering "repeated" medians?
Comment: @Galen My repeated median fit is very similar to Thell-Sen. I coded it up and posted on my blog at https://dekalogblog.blogspot.com/search?q=repeated+median. Please note that some of the links in the above post no longer seem to work.
Answer: Statistical tests to be used as a basis for exclusion:

standardised residuals
leverage statistics
Cook's distance, which is a combination of the two above.

From experience, exclusion should be limited to instances of incorrect data entry. Reweighting outliers in the linear regression model is a very good compromise method. The application of this in R is offered by Rob. A great example is here.
If exclusion is necessary, 'one rule of thumb' relates to Dfbeta statistics (measures change in the estimate when the outlier is deleted), such that if the absolute value of the DfBeta statistic exceeds 2/sqrt(n) then that substantiates removal of the outlier.


How to avoid e-mail spoofing

Question: My website e-mail is getting 'spoofed' and I would like to put things in place to avoid that happening.
As some background, I have a shared hosting account with a dozen domains added to my hosting account. I do not receive many e-mails but recently (twice in the past 2 months) have had an e-mail address locked by my host due to this spoofing activity.
I use a PHP form for the Contact Us page and it uses mail() and has an autoresponder.
I have read that there are ways to mitigate spoofing with using DMARC in a DNS setting.
Do you have any tips for preventing spoofing or links to good articles? Thank you in advance.
Answer: There is no way to prevent someone to spoof your address. The sender information shown in e-mails (the From: field) can be spoofed easily. But usually, mail clients (like gmail) have logic to detect which email is spoofed or not.
Maybe your email account hosting been locked because you detected as a spoofer, to prevent this just use the email from field with your authenticated email address. Or you should not set the from field(just make it as default).
Another way just use different mail hosting than from your shared hosting. Shared hosting has very restricted and limited email. It's not recommended for sending emails except for testing or rarely usage.
Comment: My understanding is that if you use SPF/DMARC/DKIM DNS options available, then when someone spoofs your domain's email addresses, the receiver's email system if they have verification lookups enabled, will flag the email as potentially false/spam. If you have all that setup, and someone is complaining that they're received authenticated spoofed emails from your domain, then likely your email system is compromised and you need to work with your provider to tighten security, as the spoofed emails should never be verifiable if you have the DNS setup correctly is my understanding.
Comment: So that's not 'spoofed' but it's 'hacked'. Just change the password, or the last option is using different mail hosting.
Comment: Email spoofing is the creation of email messages with a forged sender address.

The core email protocols do not have any mechanism for authentication, making it common for spam and phishing emails to use such spoofing to mislead or even prank the recipient about the origin of the message.
Comment: Spoofer can not use your email hosting if they don't know your password/credential, but they can easily spoof your address with another hosting(and this will never affect your hosting). Maybe you are detected as the spoofer because you are sending a massive email that not allowed by your provider, or your website form is spammed by someone.
Comment: The issue at my host is that these spoofed e-mails are failing to be delivered. Whoever is sending them has an automated system that keeps re-trying and my host receives notification of the failed delivery. This failure is triggering my host to send me notifications by e-mail. I notice this excessive amount of e-mails at what is otherwise a quiet e-mail address and have to contact my host to stop them.My host told me I was being spoofed.
Comment: I would like to explore ways to mitigate this and it looks like there are means in place. Looks like I can set things up at my domain registrar as I have access to the DNS settings. It is a little cryptic so I thought I would reach out to get some advice and help.
Answer: I am surprised by the accepted answer (which is largely incorrect. I'd downvote it, but I don't downvote where I answer as well).   You can and should largely prevent spoofing by setting up SPF - ie DNS records what servers can send emails with your domain associated with the sender.   This is fairly easy to do - just Google "Creating an SPF record".
Even better would be to enable DMARC and DKIM which are additional DNS based mechanism (DKIM requires server support) to sign your emails.  This is a lot harder to do.
Its worth pointing out that not all servers check SPF, DKIM, DMARC, but the vast majority of credible ones - including Microsoft and GMAIL do.

How to avoid e-mail spoofing


Why do diesel engines tend to have larger engine displacements?

Question: There are cars with petrol engines having 1,0 l or even less engine displacement but I have never seen a car with diesel engine having less than 1,5 l. Are there technical reasons that diesel engine cannot have less than about 1,5 l?
Comment: And did you miss the Renault 1461cc diesel?
Comment: @SolarMike Obviuosly, yes. But even 1,4-1,5 is still far from 1,0.
Comment: You specifically ask for less than 1.6l.... not less than 1L so perhaps you should correct the question...
Comment: How about a 1396cc turbo diesel : https://www.autocarindia.com/car-reviews/hyundai-creta-14-diesel-review-test-drive-402464
Comment: So, 1,0l diesel engine is possible, the manufacturers just don't develop it. Right? (saying _possible_ I mean that such an engine would be able to push a normal consumer car without any noticable flaws).
Comment: you keep moving your limit down, now each time do some research ....
Comment: "Are there technical reasons that diesel engine cannot have less"  ?  You can buy diesel model airplane motors less than 10 cc.. so no there is no technical limitation.
Comment: There are a lot 1,2L and even more 1.4 diesels around, at least in europe. They don't often get to 1.0L as some petrol engines do, but it's no big difference. Biggest reason I think is that ultra small cars which can do with 1.0L engines, just don't get equipped with diesel engines for other reasons. But it'd be perfectly possible.
Comment: @agentp Are you absolutely sure?  Glow engines are nitro-methane or kerosene mixes, not Asda diesel.
Answer: Diesel engines use compression to ignite fuel. Compression ignition requires higher compression ratios than Otto cycle engines. This results in parts that have to tolerate higher stresses, which means heavier parts.
If you try to shrink a diesel engine down, you'll have small cylinders and everything else will be heavy (even the engine block). It's just not an efficient setup—lots of work goes into moving those heavy parts!
Also, the main benefit of diesel is higher torque at low RPMs. A small engine is probably in a small vehicle. You don't need lots of torque to get a small vehicle going.
Answer: There are model diesel engines, so technically it is possible. My guess in the case of car engines would be that it is about economics. Diesel engines are more expensive to manufacture (because they need to be stronger to withstand higher compression), but you earn that back in their better fuel efficiency and lower fuel taxes if you make enough kilometers. People who buy small cars are more likely to not make a lot of kilometers per year, and more likely to care more about the car's initial sale price compared to fuel costs.
Answer: Ignition lag in diesels makes it difficult to run them over a range of rpms that peak out above about 4500 rpm. You can tinker with them to run just at higher rpms, but not to run over the wide range of rpms required of a vehicle diesel. The little 1 liter gas jobs can be perfectly driveable at 7000 rpms or more. Hence they don't need to have as large a displacement.
Honda's new little aluminum diesel apparently tops out at 4000 rpm.
Comment: I knew of a 6cyl 3 litre inline diesel built and tuned to 6500rpm - the person who did it owned the machine shop and applied all sorts of trucks and this was before the fancy ecu's we have now. It was fitted into a Jensen interceptor to replace the original V8 and it developed more power with a better  fuel consumption...


Would the time dilation from being in low orbit around a black hole delay/slow the effects of quantum tunneling?

Question: If quantum tunneling will cause rigid objects like rocks to rearrange their atoms into a slow-moving liquid-like state in ~10^65 years, could an object delay this fate through time dilation in a low, stable orbit around a black hole?
Answer: 10^65 years aren't enough for you?*
Yes, for time as experienced by an observer distant from the black hole. An object always experiences its own proper time, however. For another exercise in time dilation, see The Twin Paradox.
*When you start talking about ridiculously long periods of time like that, you have to take into account a lot of things we normally would neglect. Your black hole might emit non-negligible Hawking radiation in that time, protons might be unstable, etc.
Comment: on a much shorter time, the gravitational wave losses would cause the rock to spiral into the black hole.
Comment: Precisely... you have to take *everything* into account when you extrapolate that far out, because even processes that normally get totally blown off and ignored can become dominant after long enough times.


Is it possible to make an infinite directed acyclic graph with all vertices having a indegree of at least one

Question: Is it possible to make an infinite directed acyclic graph with all vertices having a indegree of at least one. Since the graph is infinite and all vertices have a indgree of at least one, that would create cycles. Would that make a directed acyclic graph impossible to be infinite, and would always have to be finite to work?
Comment: What about $\mathbb{Z}$ as a vertex set of a directed graph, with $(m,m+1)$ an edge for every $m\in \mathbb{N}$? Is that not an example?
Comment: I wonder if you're saying "finite" when you mean "infinite" and vice versa? Because it's actually not possible to create a *finite* DAG where every vertex's indegree is at least one.
Answer: Consider the graph that has one vertex $v_i$ for each natural number $i \in \mathbb N$ and an edge $v_i \to v_j$ if and only if $i = j + 1$.
It is false that being infinite with all vertexes having in degree at least one implies the existence of a cycle.
Comment: Don't you mean "for each integer $i \in \mathbb{Z}$" instead of "for each natural number $i \in \mathbb{N}$"?
Comment: Arrows go down, so vertex $0$ doesn't have an arrow out, but everyone has an arrow in.
Comment: Ah yes, of course. I should have read your answer more carefully. Thanks!
Answer: Let $G=(V,E)$ where $V=\mathbb Z$, and $E=\{(a,b)\mid a+1 = b\}$.
This graph is obviously infinite, with in and out degree equal to $1$
Comment: You can extend this to $V=\mathbb R$ for an uncountable example
Answer: It is possible to make a directed acyclic graph with all vertices having a countably infinite indegree: start with a single vertex at Stage $0$; and at Stage $n+1$, for each vertex created in Stage $n$ you simply add countably infinite vertices that point to it.
This probably works for higher infinities as well, but there might be set-theoretic subtleties involved, and it's getting late here...


The continuity of the the stable and unstable in definition of hyperbolic sets for flows

Question: I would like to know whether the continuity of the stable and unstable subbundles $E^{s}$ and $E^{u}$ follows from the growth conditions as in the discrete case, or must be hypothesized, in the definitions of hyperbolic sets for flows.
Answer: Yes, it follows from the growth conditions. It should be done in standard texts (e.g. Katok-Hasselblatt) but I have not checked. Indeed, it is a general fact about dominated splittings.
In fact, the growth conditions provide a gap in the singular values of the map and this forces the existence of a continuous splitting. See for example this paper by Bochi and Gourmelon (see also section 2 of this paper where it is explicitly stated for flows).


Does cache hit time include both time to read a cache and time to write a cache?

Question: For example, if it takes 1 cycle to read the cache and 3 cycles to write the cache, is the hit time equal to 4 cycles? Also, does this vary based on whether the cache is an instruction cache or a data cache?
Comment: Define "cache hit time".
Comment: a "hit" occurs when either a read or a write (or both) occurs and the associated address range is inside of a cache line in cache already. A "cache hit" takes no time. A cache *miss* takes time. I believe it to be the case that a miss for a read or a write will be very close to the same on modern cores since either way they both move data from one layer up to one layer down.
Answer: I would say, it depends.
Overall there are several strategies how a cache could be incorporated into a process. Few of these options are:

read through: a client reads from cache, and if the cache does not have a value, then the cache itself reads the data from the store. And the cache saves the value before being returned to a customer. In this case the cost will be vary, depending if the value is already in cache.
cache aside is another option - the client checks the cache - the cache either gives back the value or returns nothing. If the value was not found, it's the client who goes to datastore to read and also write to the cache.

There are few more strategies, and all of them will have a different cost.
Also, it is important to understand what "cache hit" and "cache miss" is. These are term unrelated to the way how cache is integrated. By definition, a cache hit happens when a client requests a key, and the key is already in the cache, regardless how that key got there. "Cache miss" is opposite - a client asks for the key, and the key is not there.


Wordpress Themes Directory: Template which hits the standards?

Question: Is there a template which I can use for themes which I want to submit to the wordpress themes directory? A naked template which hits the standards of the Wordpress Themes Directory and which I could use as base for developping new themes would be great. Is there maybe an official "naked" theme which can be used for that?
Answer: If you're looking for standards, you want to make sure you look at TwentyTen and TwentyEleven - those are included with Wordpress and written by the core developers.
It doesn't get anymore "standard" :-)
But in terms of guidelines - this is the best place to look for official rules:
http://codex.wordpress.org/Theme_Development
Frameworks are there to help speed things up and get your project done. But none of theme will cover all of your needs.
Try a few out - see if one works for you. If not then just grab the html5boiler plate and start from there.
Comment: The point is that I'd like to create some themes for the wp themes directory. In the past I had some problems to get my themes into the directory because they didn't "hit" the "standards". So I hoped that there is something which I could use as a model so I could concentrate at the design without thinking about any other things which a theme for the wp themes directory must have.
Answer: I think what you are looking for is a Framework.
Here are a couple of good ones:
"Hybrid"
"Thematic"
If you are looking for something a bit simpler check out this post:
http://speckyboy.com/2010/03/22/10-blanknaked-wordpress-themes-perfect-for-development/


Use of data on a website

Question: I wanted to use some data for statistical analysis available on a company's website. The data is in the form of a time series. Am I allowed to publish my results and conclusions?
Comment: Is the data published as a data set or did you "scrape" it off the site? If the latter, what do their TOS say about use of the site, e.g., are the use of "robots" restricted or otherwise discouraged? Have you considered simply contacting the site to obtain explicit permission?
Comment: Its published as a data set in csv format. I have written to them seeking their permission. They will probably answer on Monday. I cannot find their TOS that explicitly talks about use of data.
Answer: Anything published on a website is automatically copyright, whether or not the property of the poster.  Unless explicitly stated otherwise (for example, copyleft), it does require permission to reproduce. though not to analyse.  However, if you want to publish the result of the analysis, it would at the very least be courteous to ask and offer to provide a copy of the analysis.  Some websites, particularly governments and those to which one has to subscribe for a fee and agree to a confidentiality clause, may be able to impose further restrictions.  Regards, Robert - P.S.  I am not a lawyer and if you are in any doubt, then that is the best source of advice, but see the Wikpedia article for more information.
Comment: Can websites sue the person analysing the data (available for download) and publishing the results?

Use of data on a website