zsync vs. jigdo

Question: What's the difference between zsync and jigdo? Their core functionality seems the same, so I'm curious on things like performance, file size, and ease-of-use. Would also be interesting to know why one got created when one already existed.
Answer:
zsync is being actively developed
jigdo is 'now in "maintenance mode", development has stopped.'

For a new project, using actively developed software will have many advantages over frozen software. What will your project need in a year, and will Jigdo provide that new functionality?
Now, I couldn't find evidence to back this up so someone please correct me. I believe that:

jigdo allows clients to download chunks from multiple, different mirrors, similar to bittorrent. This greatly reduces the load on the central mirror.
zsync is designed for a single, central mirror.
Comment: So in a way, you could state that bittorrent supersedes jigdo.
Comment: @Gert: Bittorrent will download an entire ISO. As I understand it, Zsync and jigdo will only download the parts of the ISO which have changed between releases. This can be a significant difference between download times. However, jigdo and zync have only been implemented for a handful of projects, while bittorrent is more widely used.
Comment: I don't think ur edit is accurate. jigdo is much closer to zsync that it is to bittorrent. Both rely on some central server (or it's mirrors), while bittorrent is decentralised.
Answer: IIRC, Jigdo allows you to break out the files within an ISO and pull the individual files from other servers.
Case in point: Jigdo used to be the preferred way to get Debian ISO files.  The Jigdo config file you downloaded would direct the Jigdo client to download all of the files from the regular distribution servers/mirrors, using FTP or HTTP protocols.  Then, it would build the ISO client-side.  It could start with an existing ISO and "update" it or add stuff which you didn't have time to download and add in, earlier.  However, if one of the .deb files (which are compressed) in the ISO changed, you had to download the entire .deb file to rebuild the ISO.
RSync looks at what you have downloaded and what is "current" on the server, downloads the diffs and patches the file(s).  Consequently, if you have 650 MB ISO file downloaded, running RSync against it and a server-side version of the ISO file will only download what changed.  That allows you to "maintain" a folder or file, relative to another server.  That server, however, needs to support the RSync protocol and it will have a pretty high CPU load anytime someone wants to sync with it.  Finally, it doesn't work so well for compressed files, because a small change to the uncompressed version can cascade to some VERY significant changes to the compressed version.  Consequently, changing a couple files within a .deb file in the ISO will result in downloading the entire new .deb file, not unlike with Jigdo.
ZSync works over HTTP, so no special protocol support is needed.  ZSync pushes the CPU load down to the client, instead of the server, so it works better when you have large numbers of users syncing against a centralized server.  Finally, small changes to the uncompressed versions of files will result in very small downloads over ZSync, even if the resulting, compressed file has significant changes.  If you have an ISO containing thousands of .deb files and you change a few files within one of the .deb files, ZSync would a download just enough information to patch the out-of-date .deb file and re-compress it as needed, then verify the CRC or MD5 signatures, and be done with it.  Less bandwidth used, less server-side CPU used, no special protocols needed.
When they can merge all of this with BitTorrent, they've got a winner.  When that happens:

syncing with the server will tell you what changes you need
peers will provide all of the data, served up in parallel, ensuring maximum speed on the total download
checksums and hashes from the server will ensure that no peers provide bogus data

That would use even less bandwidth on the server and result in even faster updating.  Does anyone know of a protcol/system like that? Last I checked, BitTorrent doesn't allow you to "update" an existing copy of a file.
Comment: That last bit is worthy of being asked separately, perhaps on a larger site like Stack Overflow.
Answer: jigdo can be difficult to use.  In today's world, if you need distributed file distribution (boy, doesn't that sound just plain odd) it is probably best to use BitTorrent.  It may not do all that great for updates, or incremental improvements, but it's a helluva way to distribute the load across the entire Internet, of course given enough participation.
If what you need is a means by which to do incremental updates, perhaps as a central mirror to fan-out sites, or even from a collection of mirrors to end-users, I'd recommend using rsync's daemon mode to expose modules that can be synchronized.
Honestly, what tool to use depends on your audience, though I can say that if your audience are not a patient bunch, jigdo is most likely out of the question entirely.
Comment: I thought jigdo was hard, until I used it again: **(1)** select jigdo file from web; **(2)** on CLI, run jigdo with that jigdo file as argument; **(3)** jigdo will prompt you if there is an iso mount you want to add the new iso.

zsync vs. jigdo


Does AndEngine have a way to manage scenes?

Question: Does AndEngine have a way to manage scenes (for example, main splash, menu, options, main game), and should I use a different scene per activity?
Answer: Yes, you can separate your game per screen. In fact, usually only the game itself needs to use a specific 2D/3D rendering, but classic splash screen, menu, options can be done with the classic android layout and some tweaking on the appearance and animations.
Besides this let you change each screen independently, and just create different intents to play the game, with specific information (like which level to load, the saved states etc..) in the intent data
Answer: Personally I found it extremely easier to simplify the process with different "scenes". I created one for the menu-system, and one for the game itself. This allowed me to do some cool stuff (rendering/animation) in the menu. Just create one scene, throw some buttons/text on it. When you hit a button, remove those buttons from scene and add new ones. Just create a static management class to help your flow. Then just remove that scene, and give the gameScene to the engine, and you're good to play, and vice-versa when you're ready to exit game into menu.
Answer: AndEngine provieds specific classes to satisfy the game requirement.
You can have a single activity with different scenes for specific purpose:
Firstly, You can use Scene with TimerHandler to have asplash screen.
Secondly,You can use MenuScene from andengine.entity.scene.menu.MenuScene to manage MainMenu scene.
Third,on Click of a particular menu of the game u can either launch different activity say to show 'HighScore' or 'How To Play' or you can have scenes to do the same. Its your choice. But managing scenes this way is much better.
You can also refer this.


Wort aeration on a budget

Question: To aerate my wort I have been using a whisk, but i am worried about contamination. What are other more effective ways to aerate wort without spending too much money?
Comment: Shake it like a Polaroid picture.
Answer: Pour the wort from the kettle into the primary through a colander. The hops get caught in the colander, and the wort dripping through this aerates it.
Answer: Sloppy Pouring.
When my boil's done and cooled, I pour it between the carboy and my bottling bucket a few times, making sure it gets well-splashed.
If you're doing a partial boil, you can often ignore aerating the wort, and just pour the extra water around to aerate, then add that to the wort in the fermenter.
According to Palmer, this will get you to about 8 ppm oxygen, which is on the lower end of the ideal range for most yeast (8-16ppm).  That said, I haven't had any problem with it, and got a great fermentation on a 1.074 OG stout doing that just two days ago.
Answer: If you rack from your brew kettle to your fermentor with some tubing and racking cane you can get a wort disperser.
These are little cone like things that go on the end of the tubbing and create a spray of wort as it enters the fermentor.
Here is a link to one at NortherBrewer
One of these combined with good ole' shaking in the carboy works pretty well for the cheap route.
Answer: I use MixStir wine degasser attached to a cordless drill.  Based on the results, it's remarkably effective and costs under $20.  It's the preferred method of 2 time Ninkasi winner Gordon Strong, also.
Comment: It's used as a degasser in wine since it forces out accumulated CO2 when you use it on fermented wine.  But when you use it on unfermented beer, it whips O2 into the beer.  I had the same reservation as you before I tried it, but it's remarkably effective.
Comment: This sounds like an attractive solution. I have to admin, my gut reaction on reading this is that it sounds like degassing is the opposite effect. Can you explain the difference?
Comment: @DennyConn How long do you whip it for?
Comment: Until the fermenter is full of foam....usually about 2-3 min.
Answer: If you want to do it cheap, with a canister of Bernz-O-Matic oxygen, a small regulator, and some aquarium stones from Wal-Mart you can do home oxygenation yourself.
Couple of caveats:

You must sanitize the aquarium stones. They will break down if left in One Step more than five minutes.
Throw out the aquarium stones when you are done.  They are 1-batch use, no way to get them clean again after submersion in wort.

I invested in a stainless steel stone and oxygenate with it, it can be cleaned and boiled if necessary. A kit for this kind of think is usually around $35.00.  I would skip the whole aquarium stone thing and just buy this kit.  The little oxygen cylinders are cheap and last nearly forever, especially if you take the regulator off between uses. The whole kit is really not very expensive and I have found it helps fermentation more than our old splash method.
Answer: The whisk is fine. I've heard of using a collander before. All I do is dump the wort straight into the fermenter then repeat dumping water into it until filled enough. Ive been fine with it. Sometimes I'll whisk or shake if I don't feel it's enough. I typically stand by observing if bubbles seem to float in and on top of the beer then quickly pitch and seal up.

Wort aeration on a budget


How do I get a young toddler to walk holding my hand?

Question: Baby boy is just 12 months, but walks really well and prefers to walk.  When we are at the grocery store or somewhere we need to go from Point A to Point B, sometimes he doesn't want to go where I want to go.  If I try to lead him by the hand, he throws himself to the ground.  If I try to carry him, he screams and throws a fit.  I usually either let him wander around a bit, if the situation permits, or carry him screaming through the store ignoring his fit until he stops.  Since I can't usually let him lead the way, any advice on how to get him to walk happily by my side?  Sometimes letting him push the cart in the store works for a while.  Is this expecting too much from a 12 month old?
Answer: At twelve months we put ours in the trolley seat - in fact even up to about 3 or 4 years old, as you really don't want the little ones tripping up shoppers with heavy bags etc.
That said, when we did walk with them we would just say "holding hands or we need to carry you" and positively reinforcing that meant that pretty early on they would come to us to hold hands without being asked.
It is a very good thing to encourage in all busy spaces or near roads, steps etc.
Comment: This is exactly what we do.  C sits in the cart and A rides around on the front (I don't know what age it happened, but suddenly riding in the cart went from being this big exciting thing to being this huge punishment.  I was so sad when that happened.).
Comment: Additionally, some stores have carts with cars (or some other "riding toy" designed for little kids), I've found that to work better than the cart's standard seat. It might be worth trying if your store has them.
Answer: If you absolutely must hold his hand (like crossing the street, or in the parking lot).  Give him a choice, "Would you like to hold my hand, or be carried?".  It gives him the sense of control and determination he is looking for but still gives you the peace of mind that you need that he is safe.  If he says hands, but then still tries to get loose, he looses his choice and you carry him or harness him into a stroller.
Comment: This has seemed to be the approach that works best for us.  He gets a choice, but only the 2 acceptable choices.  I think giving it a little more time and practice has helped as well.
Answer: The way we have been handling it is that we don't present him with a choice in the matter.
If we're not in a hurry, we let him walk while holding his hand.  However, if he starts heading in a direction that isn't where we want/need to go, we limit ourselves to very light tugs on his hand to indicate without pressuring him if he resists, coupled with verbal encouragement (e.g. a light tug or two while we say "come on, we need to go this way... over here!" in a positive and encouraging tone).  Sometimes he will stand there for a minute or two before he heads the right way.  Sometimes he will head in a different direction, which we will allow as long as it is somewhere safe.  However, he has to hold our hand at all times.
If he pulls his hand away from ours, we take his hand again.  If he insists on pulling his hand away repeatedly, we simply pick him up without saying anything.
If he refuses to go in the direction we want him to, we simply pick him up without saying anything.
If we're in a hurry, we either pick him up, or put him in a stroller (whichever is more appropriate).
I think the trick to this is to make sure he has plenty of opportunities for wandering at his own pace, in the directions he wants to go, without making a big deal of the times when you need to go somewhere specific and have to pick him up.
Answer: You need to communicate to him that he has 2 choices. The first choice is to hold your hand. The second will depend on the situation and your own feelings, but something like: sit in the cart; sit on a naughty step; be carried (kicking and screaming!).
If you get a tantrum then you need to ignore him or you'll encourage the behaviour. Additionally you can offer that when he behaves he'll get something (i.e. sweets?). In order to combine these two you must only make the offer at the beginning and then ignore the bad behaviour. You need to be strong if in a public place!
Let him have free-choice of what to do when he's playing - this he may particularly enjoy if you're playing with him and following his lead. In a public place isn't really the place for him to be taking the lead.
Good luck!
Comment: Two choices are good, but examples like the naughty step aren't helpful.  The objective of giving choices is to make sure the child HAS a choice.  Telling him to choose between sitting on the naughty step and holding hands is really just giving a threat.  I suggest Reading Parenting with Love and Logic.
Answer: At 12 months, even if he is a proficient walker (our son certainly was), expecting him to understand he needs to hold hands and go where you are going is a bit much. They want to explore the world and what fascinates them, they are too young to understand where you are going and why it's so important to go there directly or quickly or ever get there for that matter. Whether the child will contentedly hold your hand and walk is partly a matter of personality and partly a matter of age. At 18 months or so, my son started being more cooperative about being willing to hold hands while walking compared to at 12 months. Other personalities may cooperate younger or older. But even at almost 2, I still frequently have to pick him up and carry him (or buckle him in a cart or stroller), sometimes kicking and screaming, when he is refusing to cooperate about holding hands and walking in the prescribed direction.
Balancing freedom and directed travel is about the only thing I've found that seems to increase the ability to cooperate for the directed parts. There's a lot they have the inclination to explore, and having had that satisfied it's easier to sit still or follow without wandering off.
Answer: First of all, you need to deal with the tantrums. They are a separate issue, and should be dealt with with strength and courage. There are good answers to some tantrum questions here and here and here.
To the issue of getting the child to hold your hand, the idea is compliance. Getting the child to hold your hand is no different than getting the child to listen to any other direction from you. Give the command, and apply consequences if it isn't obeyed. It is SIMPLE in concept, but often very difficult in practice.
That said, I would get a harness. In crowded areas holding the hand is not good enough, as it is too easy for the child to slip away. When my 19 year old was a toddler we used one in amusement parks, baseball games, swap meets and other crowded areas. The peace of mind was priceless.
Take heart, be strong, and good luck!


If my server was compromised, is my database safe?

Question: I have an AWS instance running a rails app that I don't actively maintain. Since I didn't keep track of what was going on with this app, I didn't update it promptly when all the rails vulnerabilities were being discovered, so I think there's a good chance that it's been compromised. I want to save some of the data on it by ftp'ing a copy of the database (SQLite, if it matters) before I wipe it. Is it safe to do that, and to put the database back once everything's been wiped? Is there a way I can check the database to see if it's safe?
Answer: There are a couple of ways to check the validity of your data. Not finding signs of tampering doesn't mean your data was not compromised because the logs could be compromised as well. Logs should be kept in a different security container.

Check for changes against a backup. Even if the backup is old you could still identify changes to old data.
Check HTTP server logs for requests that would have touched the data.
Check DB server logs for queries that change data in a different way than the web application does. You can eliminate valid queries and identify malicious ones by sorting the queries by type and count.
Answer: Your database cannot be trusted.  At the very least, reset all administrative passwords stored in the database -- if you have a small set of users reset all passwords.  You should also not trust that fake accounts weren't arbitrarily created or email addresses of admin accounts changed.  I'd also make sure that the account running your webserver does not have a password set and cannot login.  (Assuming a linux setup where apache/nginx typically runs as user www-data).
The recent rails vulnerability gave skilled attackers ability to run arbitrary remote commands on your server through embedding a YAML-encoded object in an XML HTTP request.  It would be difficult to rule out that you were attacked; normally your best guess would be to consult your webserver logs -- however a skilled attacker could alter these logs (as your webserver user has permission to update these logs) -- and as these attacks could have been exploited any time in the past 6 years (even before it became public knowledge) your logs likely do not go back far enough.
Answer: You might also want to look at SQLite's built in integrity check, which will give you some confidence that the underlying structure of the DB hasn't been corrupted.
This won't tell you if any data has been modified though; see Cristian's answer for that.


Stop Facebook from showing the pictures you like

Question: The photos I like are showed on my friends' news feed. How do I stop that?
Answer: Sharing is the core nature of Facebook and I don't think you can hide it partially, the way you intend to. I don't remember having an option not to show all or some of the likes, or comments, etc. But there is a workaround possible now: with the new version of the privacy settings, you can share only with a subset of friends while hiding your activity from others. But it's all your activity, not just parts of it.
See this question for details of how to exclude some friends from viewing your activity.
Otherwise, just like x3ja said, you would have to stop liking the photos.
Answer: I think a "Like" is just like a post/comment, so it's controlled via the Privacy Setting for Posts (not tested this). So I think the only way around this is to stop clicking "Like" on the photos...
Answer: It shows if your friend has a public profile. If you like a photo of their's or their status it shows on all of your friend's newsfeeds. A way to tell if it is something your friend posts, is there is an icon that looks like a globe meaning it is public.
I always look for this before "liking" anything and encourage others to do the same.
Answer: Just like the picture, and then post a pic to show more attivity to help hide liking the picutre. Update your status, anything to kinda hide that.


Flavor extracts - add to secondary or add during bottling?

Question: What are the pros and cons of adding flavor extracts (fruit, chocolate, what have you) at bottling time versus adding them to the secondary?  Does it make a difference?  Is there a trade-off between one versus the other?
Answer: I have always added to the bucket durring bottling. I have never tried in secondary. By doing it at bottling it has allowed for me to add the correct amount to get the flavor I was looking for. Adding at bottling seems to give the most control over your final results.
Answer: Extracts can be added at either secondary or bottling to get the same results. I don't see any trade offs or benefits between them regarding the final beers flavor.
The pro at bottling time is to add a little at a time and sample the beer as you go to dial in the flavor.  Once you have a set amount that works for your recipe, you can jsut add that amount all at once.
The only time you'd add an extract in secondary is because you need it to sit an age or condition a bit.  But extracts don't really need that sort of development, so you're just better off adding at bottling.  In the bucket with your priming agent, the rack the beer on top getting a good mix.  No need to add the stuff at secondary ever, IMO.
Answer: Adding something like fruit introduces additional fermentable sugar to the process. If you do that at bottling time, you may run a risk of creating "bottle bombs". So the sources i've read suggest doing that in a secondary, with the same controls as for a primary fermentation (an airlock or something equivalent).


Renekton vs Teemo

Question: How do you avoid getting completely zoned by a teemo as renekton ?
His ranged pokes outrange anything you have in your arsenal as renekton, and even if you go in with e for a w-q combo you end up getting forced out because of his blind and his e damage.
Answer: Stay in the bush and only come out to CS.
If he moves close E to him and stun him with W followed by Q and E again back into the bush. Depending on his reaction time he might/might not get his blind off. If you manage to stun this combo should deal quite a bit of damage to him.
Buy an early MR item since his blind and poison as well as his shrroms are both magic damage.
Ganks help before lvl 6 but after that a good teemo will be pretty much impossible to gank thanks to his mushrooms and his high movespeed.
The match up itself is pretty hard for Renekton or most melee top lanes since Teemo counters them.
Comment: Note that Renekton's stun is applied even if you are blinded by Te emo.
Answer: get ganks, buy maw of malmortius first. Basically counterbuild the teemo and get ganks to shut him down. If you cant do that just farm safely at tower.
Answer: Get magic resist so that his poison does not do as much damage and keep harassing him wen you can.
Answer: If you're a decent Renekton, then you will buy magic res. I find shoes and 3(4) hp pots to be a good start though; followed by magic res and Maw of Malmortius. Tenacity boots with magic res also helps a bunch. After that, it's all about waiting for him to come too close, then e-w-q-e. After level 6 you can chose to keep fighting if you want, just make sure you get your important areas warded!
Answer: Renekton
Early game

Stay in the brush as much as you can (try avoid to lose last hits on the creepers) and attack him. You'll fall behind in the start of the duel, but then you'll get ahead. save your cooldowns for this moment (or to escape if something goes wrong).
Mid Game

Passing level 6 you will be able to do some extra damage and have extra survivability thanks to your ultimate. Try at all costs hit a mushroom if you are engaging into a fight versus Teemo. When you get close to him, he'll probably drop a mushroom at your feet (in front of him). use Slice to go to Teemo's back, Don't use dice unless you are sure you'll be able to avoid mushrooms. Wait for him to use blind, then you can stun him (so he'll be unable to hit you while you can't hit him. Keeping the fight at your favor) and use all your cooldowns, including your ultimate (when the blind is about to go off).
General Tips

Renekton builds usually starts with atk dmg and/or arm pen. So your early game will be one of the most fearsome from all the champions, use it at your favor to keep teemo from getting last hits as much as possible.
After level 6, avoid the brush and keep an eye where he's putting his mushrooms, try keep him busy so he can't mine field your lane.
If he's building Ap or Hybrid Teemo, get some MR items. Be always aware of what your opponent is building.

Renekton vs Teemo


Buying a SIM card at Heathrow

Question: I'm flying to London and would like to get a UK SIM card as soon as I can. Is it possible to buy those at Heathrow airport? Should I buy one from there, or should I order it in advance instead and try to get it delivered to my hotel? Or should I just walk out to the nearest cellular store when I get to the hotel and buy one there?
Answer: There are two types of mobile operators in the UK, network operators and virtual operators. Last time I landed at Heathrow terminal 1 there was a stand selling sim cards from one of the virtual operators between passport control and baggage claim though in central London you shouldn't have a problem finding a store of one of the network operators or the likes of phones4u or the carphone warehouse. There is normally at least one network operator store and one general mobile store per high street. If you know what you want and it's only a pay as you go sim you can normally be sorted in 10min.
If you're going to be in a city for a while its important to think about what you need your cellphone for, local/international calls, text and data and choose an operator accordingly. Other things to consider, ease of top up for pay as you go, rolling monthly contracts(depending on the length of your stay) and Coverage.
Central London has good coverage from all providers the rest of London is adequately covered again if your staying long term make sure you accommodation isn't in a blind spot on the providers coverage map. Outside of London and the main centers coverage varies form network to network so choose accordingly.
The network providers are O2, Vodafone, Orange(t-mobile) and Three and. Each of these four own their own networks, there are also countless virtual operators who use part of, one, or more than one of the four networks.
O2 and Vodafone have the low frequency ranges, However Vodafone does not offer 3G(Data) on their 900mhz network. The low frequency means you're more likely to get a signal in a confined space. However you typically pay a little more with these two providers.
Three won't let a non 3G capable phone connect to its network so if you have an older phone it might not connect. Because 3G is designed for data and not voice the call quality on Three isn't the best.
Comment: Very good tips, thanks! I'll be staying in London for a few months so I was thinking about a rolling monthly contract. Regarding your technical comment, I'll be using my own 3G phone and I want data, so it sounds like O2 and Three are the two candidates.
Comment: Not sure whether "Because 3G is designed for data and not voice the call quality on Three isn't the best" is true - this shouldn't make a difference! +1 for good answer otherwise.
Comment: To clear things up, Orange and Vodafone also offer 3G as well. Three only offers 3G, and O2 has 3G on their low frequency spectrum.
Comment: Sorry I didn't want to go into a wealth of technical detail, sufficed to say three has good data but very average call quality.
Answer: O2 have vending machines in the airport (well, they did in Manchester last year and I doubt that was a one off). 10 pounds for a sim with 10 pounds credit and you can phone for more credit/data/SMS/whatever.
Answer: The last option is the best in my opinion. I did exactly that in 2007. The nice thing is that you might compare different operators. Some of the operators even offer very interesting sim cards to call abroad. Finally I ended up using a sim card where calling home was cheaper then calling within the UK. Unfortunately for you I forgot the name of the operator :(
But really there is so much choice, and most of the sim cards are immediately available. You might be able to buy one at heathrow, but I am not sure you have the same choice as on the street.
Your best bet is to go to a shopping center with multiple phone stores to compare.
Comment: [O2 International Sim - UK calls to international mobiles and landlines starting from 1p per minute.](http://www.o2.co.uk/international/intsim)
Answer: I have heard that some of the £10 SIMs from vending machines at Heathrow do not contain any call credit. Carphone Warehouse, and Phones4U are big multiple phone retailers that offer all the major networks; there are also lots of independent phone shops that offer SIMs from networks like Lebara which specialise in cheap overseas calls.
Answer: From your use of the word "cellular", I presume you're from the USA. Make sure your phone is a GSM phone. CDMA phones are mostly found in the USA and won't work in EU.
If not, you can probably buy a really cheap phone, along with the SIM card, in a phone shop in the UK.
Comment: I'm not from the states, but thanks for the tip anyway, can be useful for other viewers!
Answer: A friend suggested 3 as useful if you are travelling in some EU countries eg Italy France Switzerland Scandanavia, Ireland... due to them not having any roamihg charges with the Feel at Home
http://www.three.co.uk/Discover/Phones/Feel_At_Home

Buying a SIM card at Heathrow


Where are deployed solutions being used?

Question: I'm in a MOSS 2007 environment and am looking to find a way to see where solutions listed in the stsamd -o enumsolutions are activated in site collections.  How would I go aout finding out where these solutions/features are activated down to the site level?
Answer: Preupgradecheck tells you what's wrong, but it doesn't say where the issue lies.  I used the enumallweb stsadm command in conjunction with the -includewebparts and -includesetupfiles switches to enum through all the site collections and subsites to find the offending features and setup files.
For the borken web parts, I could just go to the site listed and append contents=1 to the URL to delete the erred web part.  The output also told me where the missing files were located.  This appears to be a bug from the meeting templates as described here.  I'm still tracing down a couple web parts and will resort to querying a backup copy of the database if I have to.
Answer: Solution management in Operations tab of Central Administration can show you which site collections a particular solution has been deployed to, good for one-off queries. Do you need something more "ad-hoc" callable, perhaps by a user without access to Central Admin?
Comment: The solutions in CA are deployed farm wide.  What I'd like to know is where webpart.wsp is actually being utilized at the site level.  So like webpart.wsp is being used at http://domain/mgpath/sitecoll/site1 and http://domain/mgpath/sitecoll/site2/pages/mywebpartpage.aspx for example.
Comment: I think this might actually be a feature of the SharePoint 2007 to 2010 Pre Upgrade Check tool available in STSADM. It's designed to help you scope out your farm before you upgrade to 2010, but it might provide you with the info you need...
Comment: I'll have to take a closer look at that information and see.


How do I print professional-looking labels?

Question: I'm brewing some beer for a wedding present. Going to bottle half the batch and serve the other half at a party.  I have a full-color PDF with a label design, and would like the nicest-looking labels possible.  I'm probably only going to do about a dozen bottles. What are my options?
Comment: Most inkjet printers are going to be just fine with resolution. What are you most concerned with for "professional" labels?
Answer: Beerlabelizer.com is great.
Comment: came across the site today, and it's an awesome way to get started. I plan to try it first with regular printer paper and glue to get a rough idea of how they look before I upgrade to a more professional look
Answer: I make my labels in business card format using Microsoft Publisher.
Print them on perforated business card stock, spray both sides with clear lacquer (to make them waterproof so they don't run in the cooler) punch a single hole in the corner and tie them to your bottles using string.
The main advantage to this method is that you don't have to scrape the labels off when you're done - just cut the strings.
Comment: The lacquer idea is awesome.
Answer: For my wine I use a place called Landmark Label in Fremont.  You have to order 500 labels minimum and they come on a roll (of 500), but you could do something that has a logo or whatnot and then an area where you could write in the details so you could use the same roll for years to come.
You just contact them and send over the PDF, pick out your paper and rock and roll.
Answer: Rather than buying expensive sticker labels, a great (and surprising) trick you can use to adhere paper labels is to just put a little bit of milk on them. Get them slightly wet and stick them on, and as the milk dries it will stick to the bottle (it won't turn sour and start to smell).
Answer: Well, it's not -easy- but I've seen a method unrelated to beer used on a bottle.  Looked quite nice, actually.  As a simple art project, friend of mine used photo paper in a plain inkjet printer to make a "label".  Which was then scissor cut by hand and adhered using clear packing tape, also scissor cut to make a clean back edge.
Don't know if this is the sort of thing you're looking for, but the clear tape layer did a good job protecting the photo paper and would do well to protect a bottle label - so long as it wasn't doused in a cooler full of ice water.
A bonus would be that cleaning off the bottle for re-use would be as easy as pulling off some clear packing tape.  Or using "goo-gone" if it's stubborn.  ;)
Comment: We actually tried clear packing tape and photo paper, but it didn't work for us. The paper was too thick.
Answer: You could always make a template with 3-4 copies in an 8.5"*11" PDF file and take it to a professional printer.
The number of copies would be dependent upon the size of the labels.
Post an update in the future with the picture of the label in the original post, just for fun.
Answer: I got some label paper from midwest supplies, they have a word document that you can download and put your PDF into each slot, I think it's nine per sheet, and then print them out on the label paper, they're self adhesive and look really nice.  I would order them again if needed.  I never put them in a cooler though, I don't know how well they stay on in an ice bath.
Answer: Just go to kinkos or some place like that and print them on a color laser printer, cut them out and stick them on with milk. I've done this with a number of labels for beer and wine. They look pretty darn professional and they don't run if they get wet.
Answer: I use Microsoft Visio at work, which can add graphics, jpegs, photos etc and also you can add text in various fonts colours etc, then sneakliy print on a colour laserjet printer at work ;-) the laser colour ink is fast and doesn't run. I then use a glue stick to put them on the bottles, however thinking of trying milk as the glue-stick glue is quite sticky and takes a bit of effort to remove.
Comment: Unless you print on quality paper or stickers, it will look ok but not really professional.
Comment: Spray Mount/Display Mount is best way if you want easy of application and removal.
Answer: I use a similar method to PunkyBrewster to adhere my printed labels however I find that adding milk isn't enough. I use a mix of 1:1 water and milk with a teaspoon of gelatine. This method means the labels won't come off when condensation builds up!
Also if you can get your hands on a Laser printer (I use one at work) you don't have to worry about the ink running when adhering labels. So to answer your main question I just use powerpoint to design and make 4 labels per A4 piece of paper, I keep to a simple rectangular design.
For a simple label design idea take a look at some of the craft beers on my brewing website The Small Brewing Company.


Teaching K and G sounds

Question: K and G are the consonants in most western languages that are hardest to learn how to say. What ways can I help my kid(s) to learn how to pronounce these sounds?
Answer: The way we taught our three was the same as with other sounds - sitting with them and showing them how the mouth and tongue move when making these sounds.
Best bet is repetition of sounds like ke ke ke ke ki ki ki and words like kicking, get, give etc as they got older.
They actually got K and G really quickly. We actually had much more difficulty getting them to distinguish between Th and F, even though the tongue position is obvious.
Comment: I make gingerbread cookies yesterday. Will try with Swedish "kaka" a lot over the next day and see if she gets how to say "k". :-)
Comment: We are native English speakers (obviously since we're American) and my son still has difficulty with the "Th" versus the "F" sound.  It's tricky!  Even for us natives.
Answer: Depends on the age. It's most easily done when they are young (1-4 years old) and their phonem maps are still forming. In this case they just need to hear it (frequently and correctly) and need to regularly interact with native speakers. When we moved to an English speaking country, my kids often listen to a tape of "Thomas the tank engine". They happily listened to it without initially understanding a single word. In conjunction with play-mates and pre-school they quickly spoke fluently and accent free including the sounds that are tricky for Germans (e.g. "th" or "v" vs. "w" sounds).
More formal training is probably only useful for older kids.
Answer: Very important to make sure they have  normal hearing. If there is any doubt, get a hearing test to test all the frequencies of speech.
Then make sure they have lots of examples to listen to. You can make them tapes of words that have the sounds at the beginning, middle, and end, as well as words that have the sounds before and after different vowel sounds. Check out   http://www.soundsofenglish.org/pronunciation/gk.html to learn more.
Songs are another way to help them learn. Choose some songs they already know and point out the sounds. If you don't know any, try: http://www.songsforteaching.com/earlychildhoodelementarypreschoolkindergarten/funnyrhymes.php
Comment: Those are good links!

Teaching K and G sounds


Model-implied yield spread on corporate bonds

Question: While using Merton (or any other) model, is the model-implied yield spread on bonds greater than actual yield spread? And is it possible to estimate actual probablities of default?
Answer: First some remarks in a model agnostic sense. Credit spread is actually thought to be significantly smaller than the actual one (some even say about 1/3 only, for corporates Longstaff 2005 reports the range 5%-25% for the default component), as there are many other factors such as liquidity. For PDs it might be slightly better to use CDS spreads. In any case what you'll get are risk neutral implied PDs, not objective ones; disentangling the "actuarial" credit spread from the proper credit premium is not easy (and beware that many improperly call "premium" the full risk neutral credit spread).
If a model returns a higher spread than the actual one, something has probably gone wrong. What are you calibrating to?


Group Velocity and Phase Velocity of Matter Wave?

Question: In quantum mechanics, what is the difference between group velocity and phase velocity of matter wave? How can it also be that phase velocity of matter wave always exceeds the speed of light?
Comment: Related: https://physics.stackexchange.com/q/16063/2451 , https://physics.stackexchange.com/q/34214/2451 and links therein.
Comment: 'How can it also be that phase velocity of matter wave always exceeds the speed of light?'- Not always
Answer: I will not go into math (because many already did ) but will try to explain physics.
Wave function describes the wave of probability (this of course rough analogy) it means when it travels in space, information of probability (probability of finding the particle) travels with it, thus this is phase velocity (which can have higher speed than speed of light) and it is not a real "physical matter" wave, but just a flow of information on probability, but it still a special kind of waves, in sense it can't have additional cargo of informations that may enable us to pass any additional useful information, thus it will not violet relativity in any way, while group velocity describes wave packages speed (also very rough and not very true analogy, but very helpful to build intuition) and this package can be imagined as your particle, thus it has the same speed of your particle.
Answer: Actually matter wave describes the probability of finding a particle at any time at any point of space. It is not exactly a sine wave, it is an wave packet. So it contains lots of component of single frequency wave. These the velocity of the single component is called phase velocity. And the overall velocity of composite wave is called the group velocity.
The phase velocity actually don't carry any meaningful physical information for matter wave. All the meaningful information (like, momentum, velocity etc) contains in the group wave. So the velocity of the particle is determined by the group velocity, not phase velocity.
Now since phase velocity does not carry any physical signal, so it can have speed greater than light. It does not violet the theory of relativity. Only the group velocity should be less than speed of light.
Hope this will help you understand


When are Hilbert schemes smooth?

Question: I know that Hilbert schemes can be very singular. But are there any interesting and nontrivial Hilbert schemes that are smooth? Are there any necessary conditions or sufficient conditions for a Hilbert scheme to be smooth?
Answer: A very well-known condition is that the Hilbert scheme of a smooth surface is smooth.  As David pointed out below, the Hilbert scheme of a smooth curve is smooth and equal to the symmetric product (since k[t] has only one finite dimension quotient of each dimension).
I don't know of any other examples, but one of the versions of Murphy's Law in algebraic geometry is roughly "if you don't have a good reason for a Hilbert scheme to not be horrible, it will be as horrible as you can possibly imagine."
Comment: Yes, the Hilbert scheme of n points on a smooth curve is also smooth (and it equals the n-fold symmetric product of the curve).
Answer: I don't know of many global conditions for a Hilbert scheme to be smooth/singular.  Ben's answer probably gives the most interesting example of a smooth Hilbert scheme, namely the Hilbert scheme of n points on a smooth surface.
Here are two more examples of smooth Hilbert schemes.
1)  The Hilbert scheme of hypersurfaces of degree d in PP^n.  Such hypersurfaces are parametrized by homogeneous degree d polynomials in n+1 variables, and hence this Hilbert scheme is a projective space of dimension n+d choose d.
2)  The Hilbert scheme of linear subpsace of dimension d of PP^n.  This is just the Grassmanian Gr(d+1,n+1).
Comment: in the same line as example (1): if $X$ is a projective surface and $\rm{H}^1(\mathcal{O}_X = 0$ then its Hilbert schemes of curves are smooth. So, the family of surfaces with $b_1(X) = 0$ yields examples of smooth Hilbert schemes.
Answer: Here is yet another example of a smooth Hilbert scheme.  Let $X$ be a smooth degree 3 hypersurface in projective space of dimension $n \geq 3$ (say, over an algebraically closed field), and let $H$ be the Hilbert scheme of lines on $X$ (i.e., corresponding to Hilbert polynomial $t + 1$).
The tangent space to $H$ at a point $[L]$ (corresponding to a line $L$ in $X$) is $H^0(L, N)$ where $N$ is the normal bundle of $L$ in $X$.  The rank of $N$ is $n - 2$ and the degree of $N$ is $2n - 6$ (you can see this by looking at the standard tangent bundle and normal bundle sequences).  Every vector bundle on $L = \mathbb{P}^1$ splits into the direct sum of line bundles.  Then the degree of each rank 1 summand of $N$ is at most 1 ($N$ injects into the normal bundle of $L$ in $\mathbb P^n$) and then you can show that no piece can have degree less than $-1$.  This allows us to conclude that $H^1(L, N) = 0$.  This means that $H$ is smooth at the point $[L]$ (see for example Kollár's book Rational Curves on Algebraic Varieties, Chapter 1, where he explains the infinitesimal behavior of the Hilbert scheme).  Since this is true for any line $L$ in $X$, the Hilbert scheme is smooth.
The same argument works for lines on a smooth Quadric.  In the same book, Kollár proves that for a general degree $d$ hypersurface $X$ in $\mathbb P^n$, the Hilbert scheme of lines on $X$ is smooth.
Comment: Another reference, arguably more readable, is *Higher-Dimensional Algebraic Geometry*, by Olivier Debarre.
Answer: For some more examples of smooth HS see A.P.Staal: The ubiquity of smooth Hilbert schemes, arxiv AG 31.Jan. 2017.
Answer: The Hilbert scheme of n points on a 3-fold is not smooth for n sufficiently large, but the exact value of sufficiently large is unknown. See the chapter on Hilbert schemes in "Combinatorial Commutative Algebra", by Miller and Sturmfels.
Comment: I think that David's answer is not correct.  The Hilbert scheme of 4 points on a 3-fold is not smooth.  The singular point is defined by the ideal (x,y,z)^2.  Most likely, David is alluding to the fact that the Hilbert shceme of n points on a 3-fold is REDUCIBLE for n>>0, and the precise value of n is unknown.
Comment: 3-folds shouldn't be smooth, you can compute tangent space I think.

When are Hilbert schemes smooth?


Conditional Probability

Question: I have a question on conditional probability, which goes as follows:
In London, half of the days have some rain. The weather forecaster is correct 2/3 of the time, i.e., the probability that it rains, given that she has predicted rain, and the probability that it does not rain, given that she has predicted that it won't rain, are both equal to 2/3. When rain is forecast, Mr. Pickwick takes his umbrella. When rain is not forecast, he takes it with probability 1/3.
Find
(b) the probability that he brings his umbrella, given that it doesn't rain.
I cannot seem to understand why the probability that he brings his umbrella is $\frac{5}{12}$. I seem to get $\frac{5}{9}$ Using the total probability theorem given that we are told it rains.
Please help and thanks in advance.
Answer: Let $p_{ab}$ be the probability for $a,b\in\{r,n\}$ (for "rain" and "no rain"), with $a$ the forecast and $b$ the actual outcome. Then $p_{rr}=p_{nn}=\frac13$ and $p_{rn}=p_{nr}=\frac16$. Given that it doesn't rain, we're left with $p_{nn}=\frac13$ and $p_{rn}=\frac16$, so with probability $\frac23$ no rain is forecast and with probability $\frac13$ rain is forecast. In the former case Mr. Pickwick brings his umbrella with probability $\frac13$, and in the latter case with probability $1$. Thus he brings it with probability
$$
\frac23\cdot\frac13+\frac13\cdot1=\frac59\;,
$$
as you correctly calculated.
A simpler way to derive the probabilities $\frac13$ and $\frac23$ for the prediction is to use the symmetry between the prediction and the outcome: We can consider the actual outcome to be a "prediction" of the prediction, which is "correct" precisely if the actual prediction is correct, and thus with the same probabilities.
Answer: The answer 5/12 is for another question: the probability P(It does not rains, given the he brings his umbrella). Some books edition puts answers for changed exercises. Then P(not rain|brings umbrella) = (5/9 * 1/2) / (12/18) = 5/12 !!!

Conditional Probability


Templar follower equipment

Question: My templar is level 20 and I have unlocked (at 18) the slot for relics. Where do I find these? Do I have to purchase them from a merchant? Crafting? I haven't been able to find anything. I guess another question is what do the relics exactly do?
Answer: They are random drops in the game world just like other items. I seem to have found them dropping more frequently as the game wears on.
If you want one earlier, I suggest hitting the auction house. There are plenty available for very cheap.
The relics are just another way to increase the stats on your followers. It works just like an item slot that only the followers have access to.
Another thing you should know about equipping followers is that they receiver a 2.5x multiplier to any of the base stats (STR, VIT, INT, DEX), so it is advantageous to seek out gear for them that maximizes that.
Answer: Relics are just another stat increasing gear.  They can only be found as a drop from defeated enemies.
Here's a list of some of the different types to be found.
Relics

Templar follower equipment


Apache and Tomcat integration

Question: I am trying to integrate apache and tomcat. I thus want apache to forward requests to tomcat.
I am using the mod_jk module for apache to achieve this.
So far I am trying to get tomcat to auto-gen the configuration files for the mod_jk - I add the relevant to my server.xml
<code><Listener className="org.apache.jk.config.ApacheConfig" modJk="/usr/lib/apache2/modules/mod_jk.so" />
</code>
This does not however work.
Please could someone that has done this recently give me some direction? I suspect that a lot of the documentation is for old versions of apache and tomcat.
Answer: Okay, I got it. You have to include the worker.properties before it will generate the mod_jk.conf

Apache and Tomcat integration


How do I know the position of some mass in space (starting at rest) over time when applying earth's gravitational force to it?

Question: I know how to use Newton's law of universal gravitation.  But I'm not sure where to go from there.
This is for my understanding while working on a game.  I'm not trying to do anything fancy here.
Comment: The way you would want to implement this is going to depend on your game engine.  Are you doing things in time steps?  Are you tracking velocity and position?
Answer: I will assume that the mass of the mass you are concerned with is very small as compared to Earth's mass, hence, the gravitational potential is only due to Earth's mass.
Furthermore, you said that the mass is initially at rest, I will assume that the same goes for Earth (no orbiting around the sun). The motion of the mass $m$ in Earth's gravitational field $\Phi$ is then governed by the following Hamiltonian:
$$ H = \frac{p^2}{2m} - G \frac{M m}{q} $$
where I defined the impulse $p$ of the particle, it's position relative to Earth's core $q$ and the gravitational constant $G$. $M$ is the mass of Earth.
This Hamiltonian leads to the following Hamilton's Equations:
$$ \dot p = - \frac{\partial H}{\partial q} = - G \frac{M m}{q^2} $$
$$ \dot q = \frac{\partial H}{\partial q} = \frac{p}{m} $$
You can solve these equations, but this is a rather cumbersome business. A nicer approach is the conservation of energy: As the $m$ falls in the gravitationa potential, it loses potential energy. This energy has to go somewhere: the velocity of the particle. We hence have (by setting the overall energy to $0$):
$$ m \dot q^2 = 2 G \frac{m M}{q} $$
$$ \frac{\textrm{d}q}{\textrm{d}t} = \sqrt{\frac{2 G M}{q}} $$
$$ \sqrt{q} dq = \sqrt{2 G M} dt $$
$$ q^{\frac{3}{2}} = \frac{3}{2} \sqrt{2 G M} t + C $$
$$ q(t) = \left( \frac{3}{2} \sqrt{2 G M} t + C\right)^{\frac{3}{2}} $$
with some integration constant $C$ equal to the initial position of $m$ to the power of $\frac{2}{3}$ (note that I already set $\dot q(0) = 0$). Furthermore, note that the first equation also gives you a relation between the velocity and position of a particle.
This also solves Hamilton's equations somewhere up there.
If you want to include rotations (that is, either Earth moves orthe mass moves initially), things get slightly more difficult.
Answer: $F=ma$ so if you know the force due to gravity, you need to divide it by the mass $m$ of the object to get the acceleration.
You'll probably be doing discrete timeslices, so it makes sense to use an approximation known as Euler's step-by-step method:
At any point in time, you'll be storing the position and the current velocity of the object. As you say you're aware how to calculate the gravitational force I'll skip that, but then divide by $m$ to get $a$. You need to divide $a$ by number of time intervals per second (for example 100ms is 10 frames per second, so divide $a$ by 10) to get the change in velocity for that time chunk, and add this to your velocity. Similarly, divide your velocity by the frames per second, and add that to the position.


ssh public keys instead of SASL for authenticated SMTP sending?

Question: I'm currently using postfix and SASL on my personal server for authenticated SMTP.
The server is purely for my personal use and my personal domains, so I'd much rather have something simpler based on ssh public keys. Does any such solution exist?
Answer: While it isn't SSH's pubkey authentication (which is something that only exists in the SSH protocol, not SMTP), you could set up TLS Client certificates.  This will require a valid SSL certificate on the client side.
Also, if you must use SSH's pubkeys, you could simply allow all mail connections from localhost on your personal SMTP server, and set up an SSH tunnel over SSH to port 25 on the SMTP server.
Answer: Nothing prevents networked application to use ssh keys for authentication/encryption, except these applications have to be written to support this (i.e. by using libssh). You don't say what mail user agent you use, nor what SMTP server it connects to, but it is not very likely they support ssh natively.
But of course, you can use a normal ssh connection to your server to make a tunnel for SMTP sessions.This of course authenticates the users to your machine, not to your SMTP server, which may not be what you want.
Answer: SMTP servers usually don't check the SSL certificates when connecting, but do use them to encrypt the channel.  This makes them easy to configure with self-signed certificates, or certificates from a private authority.  (Self-signed certificates are equivalent to ssh certificates.)  I use tinyCA to create my own certificate authority.  You can use key sizes up to 4096.  You should use a size of at least 2048.
MUAs (Mail User Agents: Firefox, Outlook, etc) work well with self signed certificates.  You do need to accect them the first time.  I suggest using the submission port with startTLS and authentication.  This will give you a secure authenticated channel.
I use Dovecot IMAP with startTLS using self-signed certificates for reading email.  Using IMAP gives extra options like using a WebMail interface in addition to the one or more clients.
Answer: Configure your mail server to allow unauthenticated relay from localhost and set up an ssh tunnel for sending mail.
ssh yourserver -L 8587:localhost:587

This will forward the local port 8587 through ssh to yourserver on yourserver's port 587. Then configure your mail client to use localhost port 8587.
Although I would still encourage you to leave SASL authentication on.


How can I repair a tyre with a deep cut?

Question: I have some foldable racing tyres, still with plenty of tread but with some small cuts through the tread & cloth.  Can I do anything to them or are they destined for the bin?
Comment: How small are the gashes?
Comment: No more than 2mm across, but they just manage to get through the tread & casing; Inside they are less than 1mm.
Answer: You should be able to patch the tire with a tire boot, which you should be able to pick up at your LBS. It's basically a rubber patch that you apply to the inside of the tire, where a gash is. Similar to a tube patch, but thicker. There's all sorts of things that people use for makeshift boots, too, such as a $1 bill. The important thing with a boot is that it prevents the tube from herniating through the gash.
Park Tools Emergency Tire Boot
Comment: I'm in Oz - would a $1 coin do, since we no longer have $1 bills? (& the $5 notes and up are plastic ;-)
Comment: Those are all good solutions to get you home, but not permanent fixes for salvaging a cut tire.
Comment: @Anthony K, It's a pity about the $5 note.  I find I need to deflate my tire after the ride to buy the burger!
Comment: I think a Pound note (or other banknote) will work just as well as American currency.
Comment: Duct tape is good to have in the saddle bag.
Comment: I used a power bar wrapper once, it held for a few hours' riding until I could get to a shop for a new tire. I wasn't aware they made more permanent ones, but I'm not surprised.
Comment: The Aussie $5 actually works very well.
Answer: If the cuts are very small (1mm as you posted above) then there's not need to do anything.  Normal punctures -- especially from glass -- are liable to leave that size of cut.  I've used a tire this season for at least 3000km which accumulated many such minor cuts -- I only replaced it last week because it was getting far too thin.
You'll want to watch out for larger cuts though -- anything that the tube might bulge out through.  The sidewalls are especially susceptible to this since they're thinner and gashes squeeze open wider where the tire meets the ground.  My rule of thumb is if you can see the tube through the tire, even if you have to pinch it open, then it's probably done.  Put a tire boot in to limp home but replace the tire as soon as possible.
Answer: If tire is heavily cut, it should not be used for racing anymore. It can be repaired, but give it to someone who rides on pavement only.
Answer: If you can see cloth, I'd be seriously considering replacing the tyre.
While it might have lots of tread, a deep cut is going to be an area of weakness and while you might be able to back it with tape, notes or similar padding, the tyre will not cope well with high pressure - and will be much more susceptible to rupturing at that point.
And make the next set of tyres you buy Kevlar-lined, it really does make a serious difference to longevity.


How does ITIL training benefit my software testing career

Question: I have just been offered an opportunity to do ITIL certification. How will this benefit my career as a QA Tester? I have read about the course but I still dont get how important it will be for me.
Comment: Welcom to SQA, lbexy. Do you mean ITIL Foundation or some [further level](http://www.peoplecert.org/en/ITIL_V3/ITIL_Certifications/Pages/ITIL_Certifications.aspx) in the ITIL framework?
Answer: Your title mentions ITIL training, while your question talks about ITIL certification.
Training and certification are not the same thing. You may find some benefit from the training, while the certification may provide little to no value.
To examine the training aspect, look at what you will learn during any classes, look at the syllabus, etc. Decide if these are things you want to learn, and consider if it will help you on your current career path.
To examine the certification aspect, look on job boards and see how many software testing jobs (if any) require ITIL Certification.
This might help:
https://strazzere.blogspot.com/2010/04/software-qa-certifications-aid-to.html
Comment: @manu - fixed it. Thanks for the heads up!
Comment: The link you provided is no longer valid
Answer: The following thread includes discussions regarding the value of certifications in the software testing profession in general: Do ISTQB/ISEB Testing Certificates prove that someone can test?
It doesn't answer your specific question regarding ITIL certification, but should be pretty informative.
Answer: The worth of the certification depends totally on your environment. It's definitely possible to do good quality assurance or testing without the certificate. On the otherhand, knowing more about IT services doesn't hurt, but if taking the course means that you can't participate in some other course, I think you can find better choices. Finally, when looking for a job it's up to the recruiter how much they value such certificates and up to you how much you want to work in an environment that would value the certificate.


Conditional Probability

Question: Suppose the following are true:
$\bullet$ The probability of a random kindergartener having chicken pox at any given time is $2\%$.
$\bullet$ Among kindergarteners who have chicken pox, $75\%$ have red spots.
$\bullet$ Among kindergarteners who do not have chicken pox, $1\%$ have red spots.
Given that David, a kindergartener, has red spots, what is the probability that David has chicken pox?

My reasoning so far is from 1000 kids, 20 have chicken pox and 15 of those children have red spots. So then the answer would be 15/1000 = 3/200. I'm not sure that this address the third bullet point though.
Comment: Try drawing a tree diagram, it makes things much more obvious. Your first branch will be "Has chickenpox/Doesn't have chicken pox" and the second branch will be "Has red spots/Doesn't have red spots".
Answer:
My reasoning so far is from 1000 kids, 20 have chicken pox and 15 of those children have red spots. So then the answer would be 15/1000 = 3/200. I'm not sure that this address the third bullet point though.

Your reasoning is correct that: of $1000$ kids, $20$ kids are expected to have the pox and $15$ of these to show spots.
To address the third bullet point, you also need to note that we expect $980$ kids not to have the pox and $9.8$ of these to have spots (on average).
So of the $15+9.8$ kids who have red spots only $15$ have the pox.   Thus the probability of having the chicken pox given red spots is:$$\frac{15}{24.8} = \frac{75}{124}$$

More formally: $$\begin{align}
\mathsf P(C\mid R) & = \frac{\mathsf P(C\cap R)}{\mathsf P(C\cap R)+\mathsf P(\neg C \cap R)}
\\[1ex] & = \frac{2\%\times 75\%}{2\%\times 75\% + 98\%\times 1\%}
\\[1ex] & = \frac{75}{124}
\\[1ex] & \approx 60.5\%
\end{align}$$
Answer: P(pox) = 0.02
P(spots|pox) = 0.75
P(spots|no pox) = 0.01
P(spots,pox) = P(pox)P(spots|pox) = 0.015
P(spots, no pox) =  P(no pox)P(spots|no pox) = 0.0098
P(spots) = P(spots,pox) + P(spots,no pox) = 0.0248
P(pox|spots) = P(spots,pox)/p(spots) = 0.6048

Conditional Probability


Notes about pdf file in file browser

Question: I have some folders where I have many pdf files, and it is inconvenient for me to open every file and see the contents, while searching for a particular document. Is there some way or any file browser, which will open a preview/side pane on the right side when I just select it and the pane should contain the details the pdf file including some notes which I can write to identify the file?
Answer: I could use a feature like this myself (and now I have it thanks to your asking this question!)
I did some Googling and here are some pieces of the puzzle.
Thumbnails:
This is a bit awkward, but it would work.
http://blog.prashanthellina.com/2008/02/03/create-pdf-thumbnails-using-imagemagick-on-linux/
With this, you could write a script to generate thumbnails in the same directory as the pdfs.  If you name them the same as the pdf, except changing the extension, they would sort right next to the originals and hovering over them would show the thumbnail.  You could rerun the script periodically (possibly comparing modification dates on the pdf and thumbhnail) and regenerate thumbnails for those which have changed.
I'm not much of an imagemagick user, but I have seen posts on how to add annotations to an image that would allow you to add very limited captions/notes to the thumbnails.
Adding clutterflow to nautilus (This link also mentions a thing called gloobus, but the links didn't lead to anything about pdfs.)  I'm a kde user and don't run nautilus, so I haven't tried this.
https://superuser.com/questions/294765/quickly-view-pdf-files-in-directory
I found this and it works (but for dolphin/KDE)!  (no annotations though)
Enabling PDF preview in Dolphin
Here's one that says it works in nautilus (but no annotations):
https://apps.ubuntu.com/cat/applications/gnome-sushi/
Annotations:
Looks better than nothing.  The second (python) answer looks better.
They mention a limitation of zenity in the first answer.  If you pursue it, check out yad.  It's compatible, has way more features, and a developer who will often add things quickly if he's convinced of their merit.
File notes tab gone in Nautilus 3.2.1
HTH

Notes about pdf file in file browser


Is there any way to survive solarwinter like in Sunshine - movie?

Question: Is there any way to survive solarwinter like in Sunshine - movie?
Solar winter is where for some reason sun looses its capasity to produce radiation( heat etc.). It doesn't loose everything but some of its radiation energy( say 50 %) That causes earth to cool down causing next "ice age"
Answer: Currently all life lives off of the sun's energy, at least indirectly. One possible exception is some types of bacteria that need only heat energy plus some inorganic chemicals that abound in the ocean - those would be fine as long as the Earth is geologically active.
For us, however, it would be curtains, within months or several years at best. You could watch the movie The Road for at least one potential scenario where this happens (in the form of nuclear winter, where cloud cover never lets the sun through) - not good.
Energy would remain available for a long time to come - fossil fuels, nuclear fission fuels, and then even more if we figure out fusion. But a big question would be where do we get our food. Currently, science does not know how to keep humans alive without at least some input from the biosphere in the form of calories and minerals. Food is chemically complex, and we haven't fully characterized it yet, and don't know how to synthesize it. Because of that reason mostly, we would be doomed if the sun took a several-years nap. Since there's a lot of food stored around the earth, a lot of people would find ways to survive for a while - but the inevitable would be that once those thermophilic bacteria are the only other living creatures, and we've eaten up all canned food - we would be finished.
Interesting question! Whenever the answer to this becomes "yes we could survive" it would mean we are capable of surviving in the dead of space - which for me would mean a new level of evolution for our species.
Answer: Food could be grown using UV lights, powered by nuclear fission.
We could probably do it.
But it would be the spece equivalent of a human being on a life support machine - all our time and energy would be consumed just with survival, so while humans as a species might survive, our society, culture and science would probably slow down to a crawl, or disappear completely. Most other species would die off, so it would be a pretty dismal future.


Should I insulate a finished basement if there is only 3 degrees difference?

Question: We are finishing our basement and I'm wondering if it is worth putting in insulation if there is only a 3 degrees temperature difference from my upper floors to my basement. This is during the winter months. The temperature in my basement stands at 66 degrees in the winter.
Comment: I am assuming you are talking about insulating the exterior walls of the basement? Some of the answers seem to assume you're asking about insulating between the basement and upper floors, can you just clarify that?
Comment: Yes I intent to insulate only the exterior walls and not the ceiling.
Answer: A couple things to consider.   If you have heat ducts in the floor of the upper level (i.e., the basement ceiling), you may be losing heat into the basement; insulating them (and especially sealing any leaks) may prevent heat from being "wasted" by warming the basement.    Depending on the floor surface above, insulation may make them a bit more comfortable (although I would not expect a dramatic difference with the basement that close to room temperature), and may provide some sound insulation if that matters.
If you don't have warm-air ducts in the ceiling, and sound isn't an issue, the payback on saved heating costs would probably be pretty long.
Comment: You are correct. We do have heat ducks on the basement ceiling. Sound is not an issue.
Answer: If there is currently no insulation, the basement is being heated from above. Putting in insulation would thus make the basement somewhat colder, and reduce the heating-costs upstairs. How much depends on how well the basement is insulated from outside.
Insulation also helps with soundproofing, if this matters to you or now, depends on what you use the basement for, so can only be answered by you.
If air moves freely between basement and house (i.e. no plastic-membrane or other air-tight barrier) then insulating it may make the basement moister. What happens is that warm are (which can carry more moisture) gets into the basement where it's colder, which leads to higher moisture (or in extreme cases even condensation - you've surely seen that warm air with moisture that hits a cold surface sometimes causes condensation) If this is a concern, it might be an argument against insulation.
Comment: Your answer sounds like you are talking about insulation between the basement and floor above, while the OP seems to imply the basement is not insulated at all.
Comment: The basement currently has no insulation.
Answer: For me, a 66F (18C) space is a bit cold. I am okay with that temperature at night while sleeping, but not while I'm working in my office or just sitting watching TV. Retrofitting for insulation after the basement is finished is a major task, and basically involves tearing down all the exterior drywall and hoping you've done the studs correctly. Depending on your finish, it's at least half the work it would take if the basement was totally unfinished to start with, and more work if you have bathrooms or tile work or lots of interior walls touching.
Consider not just your use, but future use. If I was purchasing the house from you, my offer price would not only reflect my thinking that the basement is effectively unfinished (because I have to redo it), but that I also have to spend a day tearing out and disposing of half the work you've done.

The other aspect to this is that your basement is currently being heated, so of course there is not a huge temperature difference. You are likely losing a large amount of heat through the walls. The change you'll see when you insulate is that your furnace will run much less often and your utility bills will be lower as a result. One way you can see this is by using an infrared thermometer. Compare the temperature of your basement walls to your upstairs walls. I would suspect your upstairs walls will be very close to room temperature, and your basement walls will be more in the 10C / 50F range.

To me, this is a no-brainer. Insulate the walls and put in a vapour barrier (or use closed-cell spray foam, which is WAY better insulation and doubles as vapour barrier, but is more expensive). You should also consider insulating the floor or putting in a raised sub-floor. I did this in my basement and it feels basically the same as an upstairs floor (both in the temperature, and the "feel" of walking on it) instead of cold, hard concrete with carpet on top.


How should I angle my foot throughout a pedal stroke?

Question: When I say "angle my foot," I mean in relation to the ground. Is it best to keep your foot level throughout the stroke? Should I point my toes downward or upward at any point? I'm wondering what's best for power transfer, and for your feet and ankles.
Answer: For most people the advice goes that you keep your foot as flat as possible. There are some riders that ride toes down (even some famous ones in the Tour) but they've had a coach determine that in their specific case there is benefit to riding toes down.
It's unlikely that you can keep your foot entirely level as it comes over the top of your pedal stroke but it should be level through the power stroke and around the bottom as you pull back on the pedal to spin.
As a response to one of the other posters, be very careful about ankling. While it is touted as a great thing many coaches feel that it does nothing and is an old wives tale. Some even feel it's harmful to you. I've attached some links for futher reading on the subject.

http://www.sheldonbrown.com/gloss_an-z.html#ankling
http://www.sheldonbrown.com/brandt/ankling.html
http://www.pezcyclingnews.com/?pg=fullstory&id=4812
http://www.roberts-1.com/b/pt/ankling/discuss/index.htm (good links in post)
http://triandrunsports.com/triforum/index.php?topic=2362.0
http://www.bicycling.com/training-nutrition/training-fitness/perfect-pedal-stroke

From the reading above, and other articles on the subject, I'm inclined to recommend against it. At the very least talk to a medical professional who can look at your pedaling technique and biomechanics and advise properly.
Comment: Ankling was exactly the concept I was wondering about. Thanks!
Answer: Most hard-soled cycling shoes position your heel slightly above the ball of your foot (so a slight toes-down angle).
That's probably the angle I maintain throughout each pedal stroke, but to be honest I don't think about it much, nor do I know what's "correct".  I focus on trying to make smooth circles and let my ankles do what comes naturally.
Focusing on pointing my toes down seems to help on tough spinning climbs, but it's probably just a psychological trick.


How can I login iChat with my Apple ID?

Question: I have 2 apple ID. All of them are not mac.com or me.com account. I didn't know about them hone making the accounts. However, now I can't login with my apple ID on iChat. I have been used Google Talk account, but it has too many features not supported. I want full featured iChat experience (support all iChat features including file transfer, group chat, video chat...). What should I do?
Answer: If both people are using iChat, all the features will work over Jabber, but you are out of luck if both people are not using iChat.
The MobileMe/.Mac sign in, when I used it anyway, used AOL's OSCAR protocol used for AIM and ICQ (you should still be able to sign in with an ICQ account by treating it as an AIM account) due to an old and separate deal between Apple and AOL, so MobileMe users can talk to AIM and ICQ users without a gateway and vice versa. Still, even talking to them, the feature ratio between AIM clients and iChat is not 1:1, so some things would probably still break, iChat Theater if nothing else anyway, unless the other party was also using iChat.
So for a full featured iChat experience, send free Macs to all of your friends. Instant Messaging clients have shaky interoperability at best beyond basic text messages, which is unfortunate. As an alternative, I can recommend Skype which works on multiple platforms, and I find it also has better audio quality than iChat (both are quite crashy for me with audio chats and screen sharing though). There is also FaceTime which IIRC does use your Apple ID, but will only work for people using Macs, iPhones and iPads.
Comment: Of course all of my friends are using Mac and iChat. The problem is there is no IM service provider supports group chat and file transferring on iChat.
Answer: You cannot use a apple id for logging into iChat. You nee to have one of MobileMe, AIM (AOL Instant Messenger), Google Talk, or [any] Jabber account. And as toy have already found out, you cannot use all features of iChat with jabber accounts. I think this is more because of the Jabber/XMPP protocol than iChat.
From http://support.apple.com/kb/ht2515:

To use iChat, all you need is access to the Internet and one of the
  following accounts: MobileMe, AIM (AOL Instant Messenger), Google
  Talk, or Jabber. Here's how to set up and use iChat

How can I login iChat with my Apple ID?


Reference request for type theory

Question: I am interested in learning the theory of types, especially in how they can provide a foundation to mathematics different to sets and how they can avoid self-referential paradoxes by stipulating that a collection of objects of type n has type n+1. As for my background knowledge, I only know a little of propositional and predicate logic and Zermelo-Fraenkel set theory.
Answer: I would suggest you look at Martin-Löf's work, such as the following reprint of his earlier unpublished manuscript (from 1972?):

Per Martin-L: An Intuitionistic Theory of Types. In: Twenty-Five Years of Constructive Type Theory Proceedings of a Congress held in Venice, October 1995. Editors: Giovanni Sambin and Jan M. Smith. Oxford University Press, 1998.

I belive a fairly good approximation of this paper is available online. If you are looking for other online references, have a look at this lecture by Martin-Löf.
This should give you some idea for type theory as foundation of mathematics.
Comment: I found https://github.com/michaelt/martin-lof to be a helpful collection of Martin-Löf's papers including An Intuitionistic Theory of Types.
Answer: The kind of type theory you're asking about, Russell's simple theory of types, is from about the early 1900's. Here's a reference:

Russell, Bertrand: Mathematical Logic as Based on the Theory of Types. Amer. J. Math. 30 (1908), no. 3, 222--262.

Recent work in type theory is somewhat different, continuing the tradition of Per Martin-Löf. In addition to his work (referenced by Andrej), I would also recommend the following book by Luo:

Luo, Zhaohui: Computation and reasoning. A type theory for computer science. International Series of Monographs on Computer Science, 11. The Clarendon Press, Oxford University Press, New York, 1994. xii+228 pp. ISBN: 0-19-853835-9.

For the relation between set theory, type theory, and category theory, you might want to have a look at this preprint by Steve Awodey.
There's also an n-lab page, and the type theory page at Stanford Encyclopedia of Philosophy has a reference section.
Answer: In terms of modern type theory, you might be best off playing around with Coq; this will give you instant feedback on any misconceptions you might have about how things work.  The book Coq'Art (linked from the Coq website) is quite good and the system hasn't changed too much since the book was written.
Answer: I found this a valuable and concise introduction:

The Seven Virtues of Simple Type Theory by William M. Farmer.

Reference request for type theory


What in the meaning of "schematic support"?

Question: In the book FGA of AMS page 109 said, "the schematic suppor of F is... " (F is a sheaf)
What that means? Thank you for help.
Comment: That supp(F) is proper means that the topological space supp(F) together with an arbitrary subscheme structure is a proper scheme.
Answer: Assume $\mathcal{F}$ is coherent on $X$. To complement the answers you have already got, there are two useful definitions of its schematic support: either use the annihilator ideal or the Fitting ideal. They have the same underlying reduced scheme, but in general different scheme structures. The annihilator is usually (always, I think) meant if nothing else is said.
The annihilator support $Z = V(\mathrm{Ann}(\mathcal{F}))$ can be viewed as the minimal closed subscheme $i\colon Z \subset X$ such that the natural map $\mathcal{F} \to i_*i^*\mathcal{F}$ is an isomorphism (more or less a tautology).
The Fitting ideal (locally the maximal minors of a free presentation) gives a subscheme that contains $V(\mathrm{Ann}(\mathcal{F}))$, but with a possibly thicker scheme structure. A feature is that it is compatible with pullback; the annihilator construction is not.
Example: a rank $r$ vector bundle $i_*E$ on a divisor $i\colon D\subset X$ has $D$ as annihilator support, and $rD$ as Fitting support.
Answer: The scheme structure on the support of the coherent sheaf of $\mathcal{O}_X$-modules $\mathcal{F}$ is defined by the sheaf of ideals $Ann(\mathcal{F}) \subset \mathcal{O}_X$.
It is easy to see that the (topological space underlying the) locus defined by this sheaf of ideals is the same as the locus supporting $\mathcal{F}$. Indeed this is a local assertion, which we prove as follows.
Let $A$ be a ring, $M$ a finitely generated $A$-module, $P \subset A$ a prime. Then we must check that $M_P \neq 0$ if and only if $Ann(M) \subset P$.
Note that an element $m/1 \in M_P$ is $0$ if and only if there exists $a \notin P$ such that $a m = 0$, that is $Ann(m) \not \subset P$, and $M_P$ will be trivial if and only if $m/1 = 0$ for all $m$. Now use the fact that $$Ann(M) = \bigcap_{m \in M} Ann(m),$$ which can be written as a finite intersection, taking only the generators. Since $P$ is prime, it contains this intersection if and only if if contains at least one term $Ann(m)$, which means exactly that $M_P \neq 0$.
Comment: More generally, the closure of $supp(F)$ is $V(Ann(F))$ (also if $F$ is not coherent).
Answer: A sheaf $\mathcal{F}$ doesn't just come with topological support on a scheme.  If you look at the definition of support (Which should be available in any good book, none of which I have at hand at the moment) it should describe to you that the support is a subscheme of the ambient scheme, not just a subspace, and may really have non-variety structure on it.


Does the Battlestar Galactica game spoil the TV series?

Question: I've watched the first few episodes of Battlestar Galactica, and a friend recently got the game. We love The Resistance, and I'm eager to try a similarly deceptive game with more going on than just deception. But, I don't want to spoil the suspense of the TV show. Do I need to watch more before I play the game?
Comment: There's a [Penny Arcade comic](http://www.penny-arcade.com/comic/2013/10/11) showing what happens when you play the game without having watched the show at all!
Answer: Absolutely
(Very) broadly speaking, the base game spoils Season 1, Pegasus spoils Season 2 (and the start of Season 3) and Exodus spoils Seasons 3 and 4.
At least one exception to this that I can remember is that one Pegasus character's card spoils an event in Season 4. (Spoiler follows)

 Dualla's disadvantage

Having said that, I've played with multiple people who were watching the series at the same time. As long as you're roughly half-way through the first season, you should be (mostly) fine for the base set (as long as you don't read too much flavour text!). I'd hold off on the expansions until you've seen a lot more though.
Answer: The base game contains several spoilers that are not completely revealed until you finish the first season, and a couple of episodes into Season 2. If you have watched the mini series, and the first disk of Season 2.0 you will be.fine.
The Battlestar Galactica expansions contain spoilers that go well into the 4th season.
As for some specifics (SPOILERS)

 Cylon Sympathizer card image, Helo character card, Adama is an Admiral....
Answer: Yes. I will not link to specific examples because that would defeat the purpose of not spoiling, but the the Crises cards encountered, character abilities,and still-frames chosen to illustrate the cards contain major spoilers as to events, identities, and loyalties of various characters.
Once you have seen all of Season 1, you are clear to play the base game. I don't remember how far in the series the Pegasus and Exodus expansions span.
Answer: The best you can do is to say that a game will be "minimal spoilers" as opposed to "no spoilers".  Problem is, someone who's more perceptive in observation and putting two and two together will notice things that give away plot points, personalities, and situations from the various cards.  Hell, many of the crisis cards depict struggles in the TV show, with some of them the actual names or the main plot of the episodes themselves.  Even just looking at the box front, backs, and reading the game description will do that too!
If you want to reduce the # of spoilers, have everyone watch at least the miniseries before playing the base game.  Otherwise:
mini-series = decent chunk of the base game
season one = roughly base game.  Do NOT read flavor text in this case!
Season 2 = Pegasus
season 3 = Exodus
Season 4 = Daybreak
Note though that some of the stuff does spill over, hence the "roughly".  For example, there was probably a crisis cards in Pegasus that was actually a season 3 occurrence.


The role of writing in understanding concepts

Question: I am an engineer student from Norway who is not that fascinated with "engineering maths", so I am trying to work through Spivak's Calculus book on my own. I know that there is no "how to" manual for grokking concepts. But I wonder if anyone has used writing as a tool to understand complex concepts. The reason I ask is i bumped into this essay about writing, and I was wondering how that relates to my epic battle with Spivak's book. Any thoughts?
Comment: [This thread is somewhat related](http://math.stackexchange.com/questions/53175/should-i-write-out-stuff).
Comment: I always use writing when I want to understand or learn something complicated in math.
Answer: If a deeper understanding of mathematical concepts is what you're after, then writing is essential.  I'd argue that if you can't explain a concept in words, then you don't really understand it.
You don't have to look far for your answer, either.  Take a look at the profiles of some of the users with a huge reputation scores and peruse their answers to questions.  You'll see a lot of nice, thorough, (and often clever) explanations in words.  This comes from being able to write about mathematical concepts (along with ability to write in general).
As Beni commented, write!  And don't just write an equation.  If it's hard or unnatural at first, start by writing in purely mathematical terms/symbols, but then step back, look at what you have on the paper/screen, and start asking 'What..', 'Why...', 'How...' questions.
'What do I learn from this equation?'
'What happens if I change this one parameter?'
'Why is it of this form?'
'How can I prove this?'
It can be laborious at times, but (I claim) it's necessary.
Answer: (answer I gave in MathOverflow yesterday, for those who didn't see it)
During the late 1980s to mid 1990s (roughly), there was a strong push in the U.S. for "writing across the curriculum" in high school and college mathematics courses. A lot was written about this in various MAA and NCTM publications, but I don't have a list of references to offer. However, the following google searches appear to bring up much that may be of interest:
http://www.google.com/search?q=writing-across-the-curriculum+math
http://scholar.google.com/scholar?q=writing-across-the-curriculum+math


How does taking lower-resolution pictures with a higher-resolution sensor affect image quality?

Question: Does taking a picture with 8 megapixel resolution with my Canon IXUS with a 1/2.3" sensor and 12M max resolution provides the same or worse image quality (particular, noise) as if the picture was taken by another camera of the same sensor size and but with 8 megapixels maximum resolution?
Comment: This probably depends entirely on your camera, and how good a job it does at down-sampling. To answer for a specific camera model, you'll probably just have to try it and see the results for yourself.
Comment: Related: http://photo.stackexchange.com/questions/11074/does-it-give-higher-quality-to-shoot-in-low-res-mode-in-camera-or-to-downsize-h
Comment: Also related: http://photo.stackexchange.com/q/3419/1356.
Comment: I do not find any 8 Mpixel mode for the 12Mpixel IXUS (SX 230).  There is a *cropped* view mode that delivers 9 Mpixel (http://usa.canon.com/cusa/consumer/products/cameras/digital_cameras/powershot_sx230_hs#Specifications).  This brings up an important point that needs clarification: does the question ask about changes in image quality when taking *lower resolution* pictures or is it really concerned about *cropping* to change the picture aspect ratio?
Answer: I believe Flimzy replied to exactly what you're asking:

This probably depends entirely on your camera, and how good a job it
  does at down-sampling. To answer for a specific camera model, you'll
  probably just have to try it and see the results for yourself.
  Flimzy

Additionally, fyi: when you select a lesser megapixel count mode (16:9 or something), that usually just crops the image, you get the same image quality "per pixel". When you select some of the modes with less megapixels within the same proportions, down-sampling comes in, and "per pixel quality" may vary.
I refer you to Flimzy's answer again, downsampling is entirely camera-dependent.
That being said, i bet photoshop or lightroom probably downsample as well or even better than in-camera algorithms.
Answer: When you reduce a noisy picture from its original sensor size to a smaller size you will always find that some of the noise disappears. This is not a defect in the camera, you will see the same thing if you shoot 12MP and then reduce the picture in Photoshop.
The reduction algorithm takes a bunch of noisy hi-res pixels and averages them down into less pixels in the reduced image. You can define noise as pixels that have a higher or lower value than the correct value. When you average a few pixels together some of the noise will cancel out, since you will be mixing pixels that are too high with pixels that are too low. The end result is that the smaller image has less noise.
If you want less noisy 12MP pixels, then switch to P mode (or any other manual or semi-manual modes) and use as low ISO as you can.
Another option to get less noisy images is to mount the camera on a tripod and shoot 2 or 3 or as many pictures as you want at 12MP, all identical. Take all those pictures into Photoshop or GIMP and average them out. This averaging has the same effect on noise that a size reduction has without actually reducing the picture.
Answer: Image quality (especially noise, especially when not using max resolution) is so affected by the camera technology (noise reduction algorithm, down sampling algorithm, low ISO performance) and the lens (aperture) that the effect of the number of pixels is negligible.
If you could swap your camera's sensor with a sensor with similar technology but fewer pixels you would have gotten better quality — but since you can't, the camera with better optics and technology would always perform better regardless of megapixels.
That means that, if you are using good P&S cameras, the newer model (that is likely to have more pixels) will produce better pictures.
This is not always true for DSLRs, but is still usually true for cameras in the same "family" with the same lens. For example the 550D 18MP sensor performs better in low light than the 500D 15MP sensor because it handles high ISO better even with the smaller pixels.
Answer: In a general way, a higher-resolution sensor, with the same lens, is more sensitive to optical problems like chromatic aberrations. So if you have a lens that makes those aberrations, they should be more visible on the higher-resolution sensor, even after downsampling.
You should also care about the dynamic range: the higher the resolution is, the lower the dynamic range should be (for the same sensor size).
For noise, it cannot be compared theoretically between 2 cameras. The noise reduction depends on the camera itself, most of all if pictures are taken in JPG.
Answer: Yes, you can trade off spacial resolution for signal to noise ratio.  Each camera will have its own tradeoff between sensitivity and noise.  One way to look at sensitivity is the point at which you get a certain level of noise.
Since spacial resolution and noise can be traded off, that leaves the question of how to compare sensitivity between cameras with different resolutions.  To be fair, it would have to be done at the same resolution.  For example, what is better, a 12.5 Mpix camera with good sensitivity or a 25 Mpix camera with less sensitivity.  The 25 Mpix image may have more random noise on each pixel than the 12.5 Mpix image with all else held equal.  But the 25 Mpix image can be shrunk to 12.5 Mpix and some of the noise reduced in the result.  So the real question is which one makes the better 12.5 Mpix picture, and how in general should the noise (or sensitivity) of cameras with different resolutions be compared.
This was one of the things I was wondering when I made some tests with my camera (Nikon D3S, reputed to have top notch sensitivity).  I don't have other cameras to compare it to, so published the result of my tests at www.embedinc.com/d32s.  I did this mostly to see what the tradeoffs were with my camera, but it would be interesting to see similar tests done with other cameras, especially higher resolution cameras (like the D3X) and what the results would look like filtered down to the same resolution.  Anyone with a D3X or other high end hi-res camera want to try and show the results?