Conditional Probability

Question: Suppose that you are trying to buy a car, and a car is either in good condition (with $80\%$ probability) or in bad bad condition (with $20\%$ probability). You can inspect the car first, and this inspection has an accuracy of $80\%$, i.e. if the inspector says the car is in good condition, then the car is in good condition $80\%$ of the time, and so is if the inspector says the car is in bad condition.
I would like to know what the probability of the inspector saying the car is good is (I'm not actually sure if this is possible with the information given).
My attempt at solving the problem is as follows. Let

$A:=$ the car is good and
$B:=$ the inspector says the car is good.

Our premises tell us that $\Pr(A)=0.8$, $\Pr(A\mid B)=0.8$ and $\Pr(A^c\mid B^c)=0.8$. By the law of total probability we have:
\begin{align}
\Pr(A)&=\Pr(A\mid B)\Pr(B)+\Pr(A\mid B^c)\Pr(B^c)\\[0.2cm]
0.8&=0.8\Pr(B)+0.2(1-\Pr(B))\\[0.2cm]
1&=\Pr(B)
\end{align}
But intuitively this doesn't seem right to me... and I can't for the life of me figure out where I'm making an incorrect assumption.
Answer: Think of a sample space of 100 cars. There will be 80 good and 20 bad. The inspector is wrong 20% of the time. He/she will say 20% good cars are bad, and 20% bad cars are good. Thus the inspector says there are 64 good and 16 bad for the 80 actually good cars; and says there are 16 bad and 4 are good for the 20 actually bad cars. The inspector will say 64+4 good cars and 16+16 bad cars, giving a probability of 68/100.

Conditional Probability


How do I draft proof a "drop down" loft hatch

Question: I am trying to draft proof our drop down loft hatch, however I can't see how to get a good seal as its "push to release" click does not hold it tightly enough against the draft proofing strips.
Are there any good solutions?
Answer: I've seen solutions that go over top of the drop down-stairs.  You can find them by searching for 'attic stair insulation kit'.
If you were to go completely home-made, you can get sheets of rigid styrofoam, then make a box that you can drop over the hole before you put the stairs back up.  If the floor is flat and smooth, that might be enough on its own, otherwise you can put down some weather stripping and find a way to secure it down.  (maybe eye hooks?)
Answer: It sounds like you want to create a firm seal around the hatch.
I would start with something like adhesive foam tape or strip gasket tape. See if you can measure the depth of any present gaps, and try to get a tape thick enough to compensate for that.
(If that doesn't do the trick, posting pictures of the hatch from different angles will help a lot.)

How do I draft proof a “drop down” loft hatch


Strange Digital Assets Library Behaviour

Question: I am having a bit of an issue with a Digital Assets library.
When I view the page, everything seems as it should, with the pictures located in the library, and the thumbnails being stored in _t.
The issue is, for some users (and only some not all) the thumbnails show correctly, but when trying to actually view the files they get a Red X (which I am assuming means that the file can't be found).
I would think it would be a right issue, but they can see the library and all its contents and can even see the thumbnails, so this has me kind of stumped.
Has anyone seen this and know why it is happening/how to to fix or has seen something similar to this before?
Thanks,
Mike
Answer: Usually that means the user doesn't have the correct permission to the picture


Do I need to make a separate partition when installing via Wubi?

Question: I am using Wubi. Do I need to make a separate partition for Ubuntu? The last time I tried this, it made a folder called root on my drive and I could not access any files on that drive within Ubuntu.
Comment: "a separate partition for ubuntu?"- No." I could not access any files on that drive within ubuntu."- You can access the Windows files by going to the /host folder once you booted into Ubuntu.
Answer: No, if you are using Wubi (the Windows installer) to install Ubuntu in Windows, you don't need to do any repartitioning. Partitioning your drive is only required if you plan on installing Ubuntu alongside Windows via the LiveCD/USB method. Wubi installs Ubuntu in such a way that it is more like a Windows program instead of a standalone OS with its own space.
If you need to access your Windows files in Ubuntu if you installed it using Wubi, see Accessing Windows partition inside Wubi.
For more information on Wubi in general, see here.
Answer: I believe you can access it. However, I'd recommend installing it on a small partition of about 20GB.
It will be relatively hassle free (unless you like tinkering with the system).
Answer: you should do it in windows . if you will do it in linux , maybe can be a problem. Disk Manage Windows . after that you can install ubuntu . and you should mount windows disk to ubuntu


How can I debug sharepoint app attaching to IIS?

Question: I built a HTTP Module, insert the DLL into the GAC, changed the webConfig
Now , if on visual studio , I Attach to process W3WP , Open the web page where the module must work,   I notice that breakpoints has warning and they don't hit!
There are more than one w3wp.exe process. Which one should I Catch?
I don't if I'm attaching to the wrong process.
Answer: Usually you can discover which one to attach to by the user name. It is usually the same as the application pool identity you're running your SharePoint Web Application with.
It's no problem to attach to all, but for god sakes, do not attach to processes on a production environment, because hitting breakpoint, pauses sharepoint processes.
It is also important to at least recycle the application pool after adding the DLL to Gac.
Comment: Just what I was going to say. If you are on a dev machine, attach to all w3wp processes that you find.
Answer: To find more information about the w3wp processes to figure out which one to attach to, you can use this command (I have it saved to a batch file).
<code>%windir%\system32\inetsrv\appcmd.exe list wp</code>
I've got one for SecurityTokenService, one with a GUID-ish name that is the search service, and one called "Sharepoint - Port#" for each web app.
Answer: The rule of thumb for me was always to pick the worker process with the highest number as ID.


block changing IP addresses on port 25 SMTP

Question: A script is currently being run against my exchange server attempting to access resources on port 25 SMTP. This is generating event 4776 within Windows event logs. How can I stop this? Would I need to block this at the firewall or at the exchange server? Do I block incoming or outgoing on port 25 (I don't want users to lose their email capability)? What if I block a specific IP address and it keeps changing? How exactly do I block these attempts and prevent this from happening in the future? As of now, the script being run against port 25 might contain some valid usernames as they are coming up in the event logs, which is preventing some users from logging in. Note: blackberry services are running on the exchange server as well.
Answer: Try to block the IP at firewall level, use DROP not REJECT. Monitor, if he does it again, add that IP too.
They are probably scanning for an open relay or a way to use your mailserver as a relay for spam. Don't panic because these scans are quite common. You can try to look for IDS solutions to automatically block this behavior if it bothers you too much.
Should it be that it is not a break in attempt with spoofed IP's then it is probably a DDoS and you will need to contact your ISP. (If they want to get into your system they will be using real IP's since they want a response)


SQL Server memory issue

Question: As soon as I start SQL Server with no application querying, in the task manager it starts to consume memory very fast till it consumes around 15GB.
How can I resolve this issue?
Comment: You have queries on the server, you just don't know you do.
Comment: It's doing what it should, for best performance.  What *issue* are you referring to?  Is this causing any other effects?  Or are you just concerned about the amount of memory used?
Comment: This [post](http://stackoverflow.com/questions/1289558/how-much-ram-is-sql-server-actually-using) may be of some use.
Answer: To determine which queries are pulling objects into the buffer, use a server side trace or a tool like SQL Server Profiler. This will capture each query that is being ran on the database server, as it is being executed.
You didn't say which version of SQL Server, but if 2005 or higher, I'd strongly recommend reading Aaron Bertrands Determine SQL Server memory use by database and object post. The first query returns the databases which have objects in the buffer, and the number of pages and space they are consuming. Find the top database, and use the second query to determine which of the databases objects are taking up most of the buffer.
If you are on SQL Server 2008 or higher AND CPU is not a bottleneck AND you have memory pressure and can't get more memory added, I'd also review Edwin Sarmiento's Implementing Data Compression in SQL Server 2008. You may try data compression on a few of the top objects from the memory by object query. Compressed data takes up less space on both the storage substem and in the memory buffer, so you can fit more data pages in memory. When more data pages fit in memory, it reduces the number of reads from / writes to disk. As Edwin describes: "Data compression reduces the storage costs and increases query performance by reducing I/O and increasing buffer-hit rates." The tradeoff is a slightly higher CPU Utilization.
Answer: Yes SQL Server will consume as much memory it can get, right click on the server instance in SSMS and select properties.  Then click on the memory page and put a value in for the maximum server memory to restrict how much memory the server will take.
Comment: But with the same settings for memory in my personal computer it does not take all the memory unless query is being run.
Comment: Are you using the AWE option that existed prior to 2012 on any of them ?
Comment: Neoafter is right. Sql server uses memory and for other application like SSAS, where in properties is some percent which shows how many memory Analysis services can take. Probably and Users if there are any, then they connect to database or Analysis services are using memory. Sometimes then I work there is lag on server then I minimize the memory usage, but after work I set it almost to the maximum.

SQL Server memory issue


Pot / kettle sizing

Question: Apologies if this seems like a rather basic question, but I've been researching various sites and can't seem to get a decent answer. I've been homebrewing for about 2 years (infrequently), and I want to start doing all-grain recipes with full wort boils. Eventually, I'd like to move to 10 or possibly 15 gallon batches. Do I want to get brew pots (HLT, mash tun, boil pot) and a fermenter that can handle a 15 gallon batch and use them for 5 gallon batches, or should I get smaller equipment and upgrade equipment when I'm ready to increase the batch size?
Answer: The main thing you need to consider is the boil-kettle in terms of size, because of boil off. For example, you want a 9 or 10+ gallon boil kettle for 5 gallon all-grain batches if you're doing a full boil, because you will have boil-off and generally want to start with around 7 gallons of water, and will want some room in the pot above the water line. 7 gallons of water is fine in a 15 gallon pot also. It would be awkward to have say 3 gallons in a 15 gallon pot, but for boiling you should be fine with the largest size you'll think you'll want. For the other kettles (HLT), you don't need to worry about boil-off, so they don't need to be too much bigger than the batch size (1-2 gallons larger to give you some space and avoid spillage). They can be a bit smaller. People tend to do them all the same size probably more for aesthetics and convenience than necessity.
Answer: So long as you have the additional up front money to put down on larger equipment, there should not too much of an issue. Most things should scale down well enough. An oversized fermentor would be fine for primaries, since the yeast will be throwing out CO2 to fill the head space. Boil kettle shouldn't make too much of a difference, although depending on the diameter, you might get more boil off.
The main thing to keep in mind is when you mash in the larger mash tun, you'll have more dead air above the mash, more surface in the tun to initially heat up, and more surface on the outside to lose heat to. So, you'll want to try to compensate for that when you do your first batch.

Pot / kettle sizing


Toggle visibility of only one of a group of layers?

Question: I have 5 layers in a group in Photoshop that represent five states of an app screen. Only one would be shown at a time. Is there a way to get Photoshop so that it only solo's one of the five in the group, but leave unchanged other layers outside the group? In other words, if I try to solo one of them, any other ones currently visible go invisible, but other layers outside the group remain visible.
Answer: Nope.
You can option-click a layer's visibility icon in the layers panel to solo it, but I don't believe that can be done while keeping layers in another group enabled. I usually structure things so that each app state is a group itself. It can mean there's some duplication, but makes viewing an entire state easy.
You could use Layer Comps, but I find them more trouble than they're worth, for documents that are still being actively worked on (and therefore having layers added and removed).


What are the chances to get a child to a state school in the area you are moving to, like London?

Question: I have a fairly specific question about primary school admissions in England. Suppose that we move to a new area with child that is already school age (e.g. move from one part to another or move into England from abroad). What are the rules/chances to get him/her to a state school in that area? Assume that there are many primary schools nearby (e.g. in London).
Answer: In our area of London (Southwest) it depends a bit on the age of the child. The entering classes are over-subscribed (ages 4-6), so it's difficult to get a place, but the local authority will offer you something. It may not be in your first choice school and you may end up with a commute. Above the age of 8 or 9, families tend to move to where the secondary schools are good, which means that there are often extra places available in the good local primary schools. Our local population is rather international and mobile, so there are a couple of leavers and new children each year.
The new allocations start in January for the following September. The entering class places are offered around April, but there is often a lot of change before school starts in September. You might have better luck getting a place if you can apply in the spring.
Answer: I believe that your local authority is under an obligation to provide a school place -- and that's all.
Everything else depends on the local authority. For instance, our local village schools are way oversubscribed so even if someone moved next door they would need to travel four or five miles to the only school that has places available.
Some local authorities will provide free transport if the school place is beyond a certain distance from home - typically three miles.
Comment: In addition you are likely to find that the only school with any places is the one that nobody else wants to send their children to.


Which oil grade and kind should I use on a sport car that does amateur drag?

Question: The car is a Dodge Neon SRT-4 with about 81,000 miles that is used for amateur occasional drag.
What grade and type of oil would be the best to improve my performance while still preserving the engine for daily drive during the summer period?
Answer: If you are looking to improve your cars performance, then I suggest you try something different. Your gains from using a different viscosity oil will be laughable (if there will be any), especially compared to any proper performance-oriented change. Unless, of course, if what you can do with the engine is limited by regulations and you are exploring the last remaining possibilities to get those extra split seconds.
You should always use engine oil with the viscosity specified by your car's manufacturer (unless you have been doing something with the engine and/or oil pump), definitely NOT with higher viscosity.
Using synthetic oil instead of semi-synthetic might be a good idea, if you want to prolong your engine's life. It usually has better properties and retains them for longer.
It probably should also be noted that semi-synthetic oil actually is mineral oil mixed with synthetic in unspecified proportions. So you really never know what you are paying for unless you really trust the manufacturer for some reason, or you have a mobile lab handy.
Answer: I know some Honda guys that run 0W-20, but that is much too thin for the 2.4L SRT motor. People in the Neon community run 5w-30 or 10w-30 (pretty much the standard for turbo 4bangers nowadays).
There is risk of cars that have been running non-synthetic leaking through seals after switching to synthetic oils with higher detergent content.  However, I have done this on many 100k+ mile cars and have never witnessed this.  Turbocharged cars should always run synthetic, as standard oil has the tendency to coke up the oil lines near the exhaust end of the turbo.
Personally I would make the switch to full synthetic - Royal Purple or Amsoil.  If you burn a little, no big deal - add some more.


pH for oatmeal stout and how to get it

Question: I am planning an oatmeal stout and read that the mash pH is really important for stouts in general. Which pH should I go for in my oatmeal stout and how can I get to it?
Answer: You want to make sure that your MASH pH stays in the proper range of 5.2-5.5. THis is important for proper enzymatic activity in the mash.  Dark roasted malts and drop the pH as they tend to be more acidic than lighter malts.  That drop of pH can effect the enzymes responsible for starch to sugar conversion.
pH is not something that is a concern for flavor of an oatmeal stout specifically.
If you suspect you are going to have pH issues (due to some weird brewing water chemistry) then you need to adjust your mash process.  The easiest thing to do would be to mash the grist minus the dark malts.  Then during the sparge mix the crushed malts into the surface gently to get them wet.  Then sparging over the top of the grain bed will pull the color and flavors through the mash.  At that point the pH is less of a concern because the conversion is done.
Answer: Mash pH should be 5.2-5.5 measured at room temperature. Room temp is the standard reference for pH.  You can adjust pH with mineral additions.  Dark grains have a tendency to drive down the pH and the darker the grain the more that will happen.  Chalk (CaCO3) is often used to raise pH for dark beers.  The problem with that is that it's only partially soluble so you may not be able to add enough to get the pH where you need it without adversely affecting the flavor.  A better choice is pickling lime (Calcium hydroxide-Ca(OH)2).  It has much better solubility and is much more effective at raising pH.

pH for oatmeal stout and how to get it


Did tactics training improve your chess significantly?

Question: There are quite a few sites for training in chess tactics. For those having experience with using any of these, how did these affect your rating? Is there a strong correlation between e.g. http://chess.emrald.net rating and ELO? Has the use of these sites made a significant change to your ELO?
Comment: The best one I know of is http://chesstempo.com, which does a good job of rating its users.  And yes, tactics training is the best way to get better at chess.
Answer: As BlueRaja said, chesstempo is good, but you can train tactics @ FICS, chess.com, gameknot.com, chesscube.com...etc
Famous quote "1 problem a day keeps the patzer away"
Indeed when you start doing tactics regularly you immediately see results.
You tend to do a lot less blunders (which obviously takes you a rank up), remember some positions and tactics.
There's also some tactics training that I will describe as an answer to your other question.
Answer: Tactics are the most important part of the game, so training in tactics will improve your game the fastest.
Other parts (opening, endgame etc.) are helpful, but they take more effort to learn well. Tactics gives you the biggest "bang for the buck."
Answer: I haven't seen a site that offers the right kind of tactics training for beginners, including emrald.net.  While I think strong players do well on sites like emrald.net, I do not believe the converse is necessarily true: that players who only do well on sites like emrald.net do well in playing real games.   Strong players certainly have excellent tactical vision, and high ratings on emrald.net will reflect this.  But strong players also possess other qualities which make them strong, including a consistent and thorough thought process, which emrald.net does not measure.
For beginners and improving players, it's very important to start tactics study with a set (on the order of several hundred) of fairly simple tactical positions, and to go through them repeatedly, over and over, until you can instantly recognize them, spending only up to a minute or so on each position, then looking at the answer (and decreasing this time each pass through the set), and moving on to the next problem.   Recognition is the goal in the beginning, not building tactical analysis skills.
I think the best way to do this is to use randomized "flash cards" with the only instruction being "white/black to move."  One excellent source of suitable positions is John Bain's book: "Chess Tactics for Students"  (as recommended by Dan Heisman, http://danheisman.com, the top guru of beginning/improving chess instruction).   I copied, cut, and laminated all the positions in that book, making flash cards out of them, and studied them in randomized order repeatedly until I knew the entire set on sight instantly.   This gave a huge boost to my playing performance and to my further tactics studies of more involved problems.
Tactical ability is certainly right at the top of importance, but along with it is developing a proper "thought process."  One thing a proper thought process includes (among many others, this is just a simple example) is a safety check for all candidate moves (moves you're thinking about making when it's your turn to play): "will this move lose material or allow a mating attack against me?"    Without a consistent thought process, all tactics, strategy, endgames, opening knowledge is basically useless.   It takes just one bad move to lose a game!
There are many techniques to help reinforce a good thought process, but again, sites like emrald.net do not assist in that sort of training when used in the typical fashion.   When I was using emrald.net actively, I worked only for accuracy, never for speed.    Used in such a way I think the site can be useful as a training aid.
Answer: Chess is all about tactics!
Some people will argue that positional thinking is part of chess.  In fact positional play is just very advance tactic position.  So at the end it is just tactics!


Recommended arm and hand position for neck side

Question: I was wondering if there are some really clear sites, videos or texts explaining the best practices regarding the way to hold your guitar, both to be efficient and to avoid straining your fingers/arm.
Answer: In my own personal experience its a good idea to think about economy of movement; don't worry about hand or wrist position too much; worry about finger position; that in mind i recommend practising with a 'finger per fret' where possible; what I mean by this is if you are playing in a specific area of the neck; position your hand over four frets so that each finger is responsible for fretting notes on its fret.   Many scales and chords naturally fall into a four fret block of the fretboard, as deviations are often only a note or two outside of this, its a good place to start.
It is necessary to deviate from this pattern for a lot of things, however if you stick to this and move your hand around the neck with this in mind you will find it less stressful on your body; and your hand and wrist will settle into a position naturally instead of being forced into a position.
Answer: You always want to have as little bend in your wrist as possible, if that helps. Less bend also contributes to better efficiency. The height of your guitar contributes to this as well. The lower on your body your guitar is the more you will have to bend your wrist.
Here is a site explaining a couple of hand positions, focusing on the "Classical" position: Left Hand Technique
Comment: @Matthew Read - Updated my response.
Comment: I can't even bend my wrist 90 degrees, and I'm very flexible ...
Answer: Here are some images from Fernando Sor's Méthode Complète pour la Guitare, illustrating the standard opposite the fingers thumb position as well as the Hendrix thumb over the top style.

So, it's Classically Approved! Somebody tells you don't use your thumb like that, you say: "Go Read The Sor Method and School Yo-self!"
Answer: Any beginner's guitar book or web site will begin with a picture of the right way to hold a guitar.
For the left hand, the important thing is that you can fret notes on every string, with your finger coming down vertically, and without straining your wrist.
For this to happen (for most people) you need your thumb on the back of the neck, and you need the neck facing away from you so that you can do this without bending the wrist too much.
In this position, you can't really see the fretboard, so you need to get in the habit of tilting it towards you when you need a peek, but remembering to tilt it away again afterwards.
There are plenty of people who flaunt convention in this respect though; Hendrix had big enough hands he didn't need to, and would use his thumb to fret the bottom E.


Top cohomology of resolution of singularities

Question: Let $X$ be a projective variety over $\mathbb C$ of dimension $n$.  Let $\tilde{X} \to X$ be a resolution of singularities.  Suppose that $H^n(\tilde{X}, \mathcal O_{\tilde{X}}) = 0$.  What can we say about $H^n(X, \mathcal O_X)$?  When is it $0$?
Answer: First, let me point out that $H^i(\tilde{X}, O_{\tilde{X}}) \cong H^i(X, O_X)$ if $X$ has rational singularities for all $i > 0$.
Indeed, if $X$ has rational singularities if and only if

$R^j \pi_* O_{\tilde X} = 0$ for $j > 0$ and
$\pi_* O_{\tilde X} = O_X$.

It immediately follows from the Leray spectral sequence that
$$H^i(\tilde{X}, O_{\tilde{X}}) \cong H^i(X, O_X)$$
for all $i \geq 0$.
In fact, for any Cartier divisor $D$ on $X$, the same argument implies that
$$
H^i(\tilde{X}, O_{\tilde{X}}(\pi^* D) ) = H^i(X, O_X(D))
$$
for any $i \geq 0$ since the projection formula can be applied in the cases of 1. and 2. above.

Now, without rational singularities, you can run into trouble.  For example, suppose that $X$ is a normal Cohen-Macaulay variety with an isolated singularity $x \in X$ that is not rational.  Consider the exact triangle in the derived category:
$$O_X \to R \pi_* O_{\tilde X} \to C \xrightarrow{+1}$$
Because $X$ is a normal Cohen-Macaulay, and has an isolated non-rational singularity, we know $C = M[-n+1]$ is a nonzero module supported at $x \in X$ (shifted over by $n-1$).  See Lemma 3.3 in Rational, Log Canonical, Du Bois Singularities:
On the Conjectures of Kollár and Steenbrink by Sándor Kovács.
Then we have the following exact sequence by taking (hyper)cohomology
$$
0 \to H^{n-1}(X, O_X) \to {{H}}^{n-1}(\tilde{X}, O_{\tilde{X}}) \to {\mathbb{H}^{n-1}}(X, C) \to H^n(X, O_X) \to H^n(\tilde{X}, O_{\tilde{X}}) \to 0
$$
where the two end points are zero since $C = M[-n+1]$ an Artinian module with a shift.  On the other hand, $\mathbb{H}^{n-1}(X, C) = H^0(X, M) \neq 0$ for the same reason.
Now, if $\tilde{X}$ is for example Fano and we are in characteristic zero, then
$$H^i(\tilde{X}, O_{\tilde{X}}) = H^i(\tilde{X}, O_{\tilde{X}}(K_X-K_X)) = 0$$
by Kodaira vanishing for $i > 0$.  But then $H^n(X, O_X) \neq 0$ from the exact sequence.
Beyond the Fano case, you might luck out of course, but I don't see any reason why it would hold in general.
Answer: A very easy counterexample: let $X$ be a nodal cubic in $\mathbb{P}^3$. Then the resolution of singularities of $X$ is $\bar X = \mathbb{P}^1$, so $H^1(\bar X, \mathcal{O}_{\bar X}) = 0$. On the other hand, the exact sequence of sheaves on $\mathbb{P}^2$
$$ 0\to \mathcal{O}(-3)\to \mathcal{O} \to \mathcal{O}_X \to 0 $$
shows that $H^1(X, \mathcal{O}_X)$ is one-dimensional.


Does removing a Facebook app delete your account in the app?

Question: If I remove an app in Application Settings, does it remove my account and any of my progress / information in that app?
Answer: From what I understand, developers do not have to remove  any data from the database unless specifically asked by the user or Facebook. So it really depends on the application and you should follow up with the application in question.
http://www.facebook.com/help/?faq=12892
Answer: Not necessarily. Unless the app developer has designed his app to automatically remove your account information based on your removal from within Facebook, the app may still contain any information you already put into it. You might want to read the app's policy (if this even exists) on that as each will have their own way of handling it.
Regarding Facebook's policy on the matter, they are only required to remove the information which was provided from Facebook (your profile info, your pictures, your related info). Data you provided directly to the application is free to use how the developer chooses.
An article by ReadWriteWeb details some additional info to be concerned about when dealing with Facebook Apps.


Getting up to speed on Forgotten Realms

Question: What one single resource should I read before playing in my first ever 4e Forgotten Realms campaign?
Answer: The D&D 4e forgotten realms handbook was very well laid out. It describes the more recent changes that make it fit into the 4e world.
Answer: The 4e Forgotten Realms Players Guide is all you need, even if you are completely new to the Realms. It's entire reason for being is so that there is just one book to go to that gives you an overview of the setting.
Answer: For 4e, as Scott notes, the Forgotten Realms Player's Guide is pretty good. Since there've only been two 4e Forgotten Realms books so far, it's kind of the default choice. WotC has announced the Neverwinter Campaign Guide as a 2011 release, but that won't come out until fall of 2011.
If you're wanting game mechanics as well as lore, then the FRPG may be more important. You can get them from the Character Builder as well, but you may be the kind of person who likes to have them on paper for easy browsing.
For 3e, I think the 2002 Forgotten Realms Campaign Setting is superb. It does have a lot of GM material in it, so check with your GM before you read it if you haven't already. Since there have been so many changes in the Realms in 4e, it won't be as useful to a 4e player, unfortunately: otherwise I'd recommend it over the 4e version. What it would do is give you a really solid grounding in the history of the Realms.
If your campaign focuses on a specific area, it's possible that one of the 1st, 2nd, or 3rd edition books about that area might be more useful to you. Again, this is something to ask your GM about.
As a supplement to most of the above, Candlekeep is the best Forgotten Realms fansite on the Internet. It won't help much at all with the 4e time period, but for anything else it's a great alternative or add-on to any book you could read, and it's very good for getting a picture of the history of the Realms.

Getting up to speed on Forgotten Realms


Character Limit w/ Excerpt removes Images Why?

Question: So I limited the amount of characters per post via the_excerpt('50') but it removes the image that I added to my post. How can I bring that image back so it shows up above the post then limits the characters?
Answer: The problem is that the_excerpt() strips all HTML. There's a good reason for this: what if the 49th word of a 50 word excerpt was the first word of a bulleted list? Or the second word in an
?
The way I would work around this is by using post thumbnails. These allow you to have an image you can choose to display at different sizes (or not at all) depending on the situation. I've often used them as small image queues above excepts which link to a full post. I would then insert a larger version of the image inside the post.
If your theme doesn't currently support post thumbnails, you can activate them by adding:
add_theme_support('post-thumbnails');

to your functions.php. You can also add custom image sizes in functions.php like so:
add_image_size('sideFeature', 252, 999, false);

where the arguments are: name, width, height, and crop. Here's the reference. I've made the height "999" here because I only really care about the width being a certain amount. Afterward, you can then call:
the_post_thumbnail('sideFeature');

inside of your theme to display it when you're in the loop.
If you need more than one thumbnail, you can use something like the Multiple Post Thumbnail plugin. I've used it a few times, and it's worked quite well for me.
Answer: Gavin is totally right about the excerpt needing to strip html, but sometimes you really do want to keep some of that html. Then what?
I wrote an excerpter that preserves key html tags. You can find it here: https://wordpress.stackexchange.com/questions/42989/limit-to-a-certain-number-of-characters-in-excerpt-but-keep-html-tags-and-only
And maybe you have some suggestions to make it better?


Fewer big servers or more smaller ones?

Question: For servers that serve only PHP (memcache+MySQL) is it better to have fewer big servers (8-core) or more smaller servers (4-core).
Comment: You plan the server around the app, not the app around the server
Comment: 4-core and 8-core are both pretty small nowadays. You can get 1U 48-core AMDs with 64GB ram for around $8k per server.
Answer: There is no one correct answer and the popular opinion on this swings back and forth constantly. My personal view takes into consideration what happens when a server dies. For everything I've ever worked with multiple smaller servers make recovery simpler. In a pinch I could use a workstation to fill the void while waiting for a replacement server to arrive. Others have their own reasons for favouring fewer and more powerful servers, with virtualization being a common(try replacing that one with a workstation!). The truth is, neither answer is going to apply everywhere.
Answer: The best thing you can do is having a server for MySQL only and one for PHP+Memcached. Then, depending on the load you put on these, you can load balance them with some more server... The database server should always be the most powerful as is must serve many request at the same time.
That said, I must remember you that it always depend on the load websites on these server generate... For a small site, let's say 4000 visitors a day, you can easily put everything on the same server, but if you're talking of a website with more then let's say 10k visitors per day, then you gonna have a major advantage by splitting your service (mysql, apache, etc) on more then one server. It's also very depending of what kind of website you're talking about.
Hope this help you a bit.
Answer: Everything you need to know about Scaling Up (Big Iron servers) or Scaling Out (Lots of little servers) can be read on Jeff Atwood's post here: http://www.codinghorror.com/blog/archives/001279.html. Follow the links in his post to "My Scaling Hero", which also gives you a good story.
There are no answers in those posts, but it will give you clear direction on how to reach your own answers, because everyone's answers will be different.
And if you've no idea who Jeff Atwood is, he's one of the founding fathers of the Stack Overflow/Server Fault/Super User sites, and a world renowned blogger in the programming/IT field, and whilst you should never take any personal opinions on the intertubes as gospel, the hard numbers in that post really do provoke some thought.
Answer: Could I suggest a alternate setup - one that involves 'light-weight' virtualisation like OpenVZ/VServer (or even Xen). You could feasibly get a single powerful machine and break it up into multiple lesser virtual machines in order to gain the benefits of both worlds.
Answer: The dilemna is always the same :
"Many servers" cost less, but they are generally less stable : so the maintenance time increases. (I know THAT IS NOT something always true...)
"Few servers" costs more, but there are generally more stable (due to the high quality components) BUT that also means that you will host more services, if you have any issue, more services will be impacted.
you should consider the virtualization, it combines the both questions : you'll have a high quality - rox stable server and inside your "many servers" If there is any issue, only the concerned server will be impacted.
From what i've experienced (small experience thouhg :p ) it's always better to put the price in order to avoid pains later. In production, people don't care about our issues, they only want to see the thing working at anytime
Answer: Probably some questions that if you can answer will help you...
A few big servers:
Can you get a server big enough?
Does your load scale out on this server?
What happens when it fails?  Can you buy two of them or pay company XXX enough to fix it fast enough?
Many small servers:
Does you load scale out with this model?  Some loads do, some don't.
What happens when one fails?  Can the remaining N-1 deal with the load until you fix the broken one?
How fast can you get a new copy of the server you need?
If you go with the many small server model, I would go for configuring them as close as possible so that you can substitute one for another.
We use puppet for this so that servers can be swapped, and, renamed, and volia, the system is up.  Well, the new system is up modulo the debugging that you have to do because you forgot something..

Fewer big servers or more smaller ones?


Is it possible to assign sql logins into a group?

Question: This may be a bit too elementary question for this site but is it possible to control SQL Server authenticated logins using groups? So is it possible to assign sql logins under groups and give rigths for these groups? If so, are these groups only seen for an instance in question?
Answer: When working with SQL Logins you "group" them by using roles within SQL Server. Roles are created at the database-level but with SQL Server 2012 you will be able to create them at the server-level as well.
Once the role is created you can assign specific permissions to that group and it will be applied to the logins that are member of that role. The roles are localized to the instance you are under and are not visible or accessible to remote instances. You will only be able to add the logins in that instance of SQL Server to the roles.
Answer: If I understand your question, logins using SQL Server authentication, no; logins using Windows Authentication, yes.  The Windows logins are placed into a Windows group (or groups) eliminating the need to each user's Windows login set up under SQL Server.


SSIS: "The buffer manager cannot write 8 bytes to file"

Question: We have about 60 or more SSAS cubes on one server. All the cubes have the same structure. Each cube has a different size because each cube has a different underlying data warehouse. However the schema of the data warehouses are the same, the only difference is the data.
Each data warehouse is populated using the same ETL job in SSIS. A parameter is passed into the SSIS package that changes the source and destination.
To speed processing we created partitions in the cube. The cubes are processed and ETL ran individually throughout the day with some overlap.
I am looking for advice about how to debug the following error messages we get from SSIS:

The buffer manager cannot write 8 bytes to file
  "C:\Users\SQLSER~1\AppData\Local\Temp\DTS{A627C703-7524-4906-84D5-6D239B9745FF}.tmp".
  There was insufficient disk space or quota
Failed to load task "DFT Load Target Stage", type "SSIS.Pipeline.2".
  The contact information for this task is "Performs high-performance
  data extraction, transformation and loading;Microsoft Corporation;
  Microsoft SQL Server v10; (C) 2007 Microsoft Corporation; All Rights
  Reserved;http://www.microsoft.com/sql/support/default.asp;1".
Unable to load XML data into a local DOM for processing.
Error 0x800705AF while loading package file "D:\eTrigue
  Library\eTrigue\eTrigue Deploy\BETA\Exec
  Packages\PKG_EventActivity_Staging.dtsx". The paging file is too small
  for this operation to complete.

Why am I not getting the errors every time the SSIS packages are run?
How can I go about finding the root of the problem?
The errors started to happen after I added the partitions to the cube.  I use an SSIS script task to processes partitions that is called in the ETL.
Is there a way to find memory leaks in SSIS script tasks?
Anybody want to see the code?
Comment: How much free space is on the drive? Are you running a FS with a 2Gb file limit?
Answer: You don't have sufficient disk space to process everything you're trying to do concurrently.  Data flow operations that spill to disk and temp files that get created are just some of the many reasons you might run out of space.
You should be able to run Perfmon during one of these runs to see how disk space and activity play out.
It's next to impossible for us to recommend anything without intimate knowledge of your system.  The fact you're running several processes concurrently - where the actual speed and state of each process can vary widely from run to run - makes it impossible to know when or why the processes are encountering the "perfect storm" of starving each other of disk space.
You will have to understand the resource usage of each one of your processes independently then you'll be able to know if you should even try to run them concurrently.


How do I use MS Exchange 2003 with OS X?

Question: My company still relies on the antiquated Exchange 2003. Besides using Windows in a virtual machine, has anyone found any type of workaround to enable Exchange 2003 access with OS X apps (Calendar/Address Book/Mail)?
Answer: A little amplification of what "apps" you are specifically referring to would be helpful. Assuming your company is using Exchange 2003 SP2, you should be able to use Active Sync with Microsoft Outlook for Mac or Entourage. This should allow you to sync your contacts, email and calendar events. Beyond that an app would need to suport active sync to interact with an Exchange 2003 server natively.
Answer: The current Outlook for Mac does not support Exchange 2003 and below, it requires at least Exchange 2007.
Entourage will work if you have a copy of that.
If you don't have Entourage a program like DavMail may be the trick. I was never able to get it working properly with our Exchange server though so mileage may vary.
Personally I ended up using Windows Outlook in Parallels until we upgraded to Exchange 2010. That was the only stable option I could get working... Sorry.
Comment: "Current Outlook" -- is that Office for Mac 2011?
Comment: That is correct.


what is the difference between boot-sector virus and rootkits?

Question: I have read the definition for both and also read about a few examples for both the cases. I'm still not very sure what the difference is. Is the difference blurred or are there some specific characteristics that sets them apart from each other?
Answer: A rootkit works by changing the output of system actions. This could be by replacing standard commands such as ls with other tools. It can also be by modifying libraries or kernel code. Rootkits don't necessarily take advantage of an exploit, but rather the user. They may rely on another exploit to place them.
Boot sector viruses are a subset of rootkits, but the term is far older. It referred specifically to viruses that would alter to the boot sector of a hard drive to launch themselves on reboot. They have a connotation of harking from the era when MS DOS was still a substantial piece of the personal computing world. Being from simpler times, the viruses were often simpler and didn't always need booting to another OS instance to detect. Despite that, their launch early in the boot process could provide them with all the potential power that we associate with rootkits.
Even the technical difference between the terms is very muddled. It is possible that code could be considered just a rootkit, just a boot sector virus, or both. As far as colloquial speech goes, I think it is most common to refer to modern viruses that fit the definition of both as rootkits. I can't think of any notable contemporary malware that is considered to be merely a boot sector virus.
Comment: `Rootkits don't necessarily provide privilege escalation.` Really - I always thought that was the definition. A kit for becoming root.
Comment: I suppose I worded that poorly. Will edit.
Comment: I always read 'rootkit' as 'a kit, running as root, for hiding other code'.
Answer: A boot sector virus that runs from the boot sector and doesn't bother hiding itself is just a boot sector virus.
A boot sector virus that actively protects its storage in the boot sector, hides itself from detection and actively intercepts scans attempting to detect its operation is part of a root-kit.
Boot Sector viruses have been around since Brain, the first MS-DOS virus created, and was easily scanned and removed.
Answer: A boot sector virus loads himself from the boot record then executes the real boot sector, which is saved to somewhere else on the disk. It doesn't really take care of hiding himself. There were problems if the same boot sector virus came because it didn't check the presence of the previous instance, so overwrote the real boot sector on the disk with previous instance of himself - so no boot possible until reinstalling at least the systemfiles. This kind of malware belongs to DOS-era.
A rootkit mainly hides processes, so it could download and install other malwares, backdoors etc.


Can a video uploader block ads if he/she does not own all content?

Question: If my video contains a musical recording and the owner of the recording master rights authorizes YouTube to place ads on the video, do I have the right / capability to prevent ads from being displayed?
Answer: I assume you're talking about the music offerings from YouTube themselves - the ones they'll dub in for you automagically. If this is the case, no, you do not have the ability to block ads or monetize your own videos. This is how the providers of the music get paid for their offering.
If you'd like to dub in music and either have no ads or monetize your own content, you'll need to find a track that is explicitly licensed under creative commons (without a non-commercial clause) or similar license. YouTube will also ask that you provide a link to the location the file was downloaded including its licensing information. The audio will have to be dubbed in before upload and YouTube may still reject your video if the licensing isn't 100% kosher.


The product $\prod_{m=1}^{11} (x^m - m)$

Question: What would be the co-efficient of  $x^{60}$  in the expansion of $\space$  $\prod_{m=1}^{11} (x^m - m)$ ?
Answer: HINT: Imagine multiplying out that product without collecting like terms. Each uncollected term has the form $$u_1u_2u_3\dots u_{11}\;,\tag{1}$$
where $u_k$ is either $x^k$ or $-k$. Let $S=\{k:u_k=x^k\}$; then the term $(1)$ is an $x^{60}$ term iff $\sum S=60$, and its coefficient is the product of the $-k$ for $k\notin S$.
Now $\sum_{k=1}^{11}k=\frac{11\cdot12}2=66$, so there aren't really very many subsets of $\{1,\dots,11\}$ whose sum is $60$; just find all of them, calculate the corresponding terms of type $(1)$, and add them.
Answer: The product $\space$  $\prod_{m=1}^{11} (x^m - m)$  is
$$x^{66}-x^{65}-2x^{64}-x^{63}-x^{62}+5x^{61}+x^{60}+13x^{59}+4x^{58}+...$$
so the coefficient of $x^{60}$ is $1$. There may be a clever way to arrive at this, but since the coefficients seem to be a bit erratic, it seems perhaps it's just a coincidence that it comes out 1, due to some cancellations.
Answer: Note that $(a + b)(c + d) = ac + ad + bc + bd$. Each term in the expansion is the product of one of the two summands in the first bracket and one of the two summands in the second bracket (and every such product appears in the expansion). This is also true when more factors are included i.e. $(a + b)(c + d)(e + f)$, etc.
In the expansion of $\prod_{m=1}^{11}(x^m - m)$, before collecting like terms, each term in the expansion is the product of one of the two summands from each bracket. Which means we need to determine what possible choices could be made to come up with an $x^{60}$ term. As $x^a.x^b = x^{a+b}$ we are looking for all possible products $x^{a_1}\dots x^{a_n}$ with $a_1, \dots, a_n \in \{1, \dots, 11\}$, $a_i \neq a_j$ for $i\neq j$ and $a_1 + \dots + a_n = 60$. That is, we need to determine the ways to obtain $60$ as a sum using each of the numbers $1, \dots, 11$ at most once. As $1 + \dots + 11 = 66$, it isn't too hard to write out all the possible ways to obtain $60$ in this way.
One example is $1 + 2 + 3 + 4 + 5 + 7 + 8 + 9 + 10 +11 = 60$. Then in the expansion of the product, this decomposition of $60$ corresponds to the term which is obtained as the product of $x^1$ (from the first bracket), $x^2$ (from the second bracket), $\dots$, $x^5$ (from the fifth bracket), $-6$ (from the sixth bracket), $x^7$ (from the seventh bracket), $\dots$, $x^{10}$ (from the tenth bracket), and $x^{11}$ (from the eleventh bracket). This is the term
$$x^1.x^2.x^3.x^4.x^5.(-6).x^7.x^8.x^9.x^{10}.x^{11} = -6x^{60}.$$
If you can figure out all the decompositions of $60$ as outlined above, and then calculate the corresponding element of the expansion of $\prod_{m=1}^{11}(x^m - m)$, you will obtain (not many) $x^{60}$ terms. Adding them up will give you the $x^{60}$ term in the final expansion at which point you will be able to read off the desired coefficient.

You can actually take a short cut. It is equivalent (convince yourself why) to find all possible ways to write $6$ as a sum using the numbers $1, \dots, 6$ at most once, and then for each sum $a_1 + \dots + a_k$, calculate $(-1)^ka_1\dots a_k$. Adding up the resulting numbers for each decomposition gives you the desired coefficient.
Answer: The degree of the given polynomial is , $1+2+...+11=66$ . $66-60=6$ . We have to consider polynomials of degree $6$ ; $x^6-6$ , $(x^2-2)(x^4-4)$ , $(x-1)(x^5-5)$ , $(x-1)(x^2-2)(x^3-3)$ .
The coefficient of $x^{60}$ is the sum of the constant terms  i.e., without  $x$ , terms in these $4$ polynomials, that is $\space$ $-6+8+5-6=1$
$HAPPY$ $NEW$ $YEAR$$\space$ $!$
Comment: Why do polys of degree only 6 have to do with the degree 60 term? Are you using a symmetry of the polynomial? If so please add to your answer.


Find repositories without changes

Question: On GitHub, how can I find the repositories I have forked but are still identical to the parent repository (i.e. no changes were made in the fork)?
Comment: Maybe you can use the Updated before the date Repositories Option in [advanced search](https://github.com/search/advanced?q=oops&type=Issues).
Answer: Painstakingly and one by one.
There isn't anything to show you at a glance all your project forks which share the same commit revision history or are different in some way to the original repo.
For each of the original repos you want to compare against, click on their respective Network Graphs at the following URL type:
<code>https://github.com/{username}/{repo}/network
</code>
The original repo will be at the top (base reference point) and list a few other repos in timelines below it. All branches and commits are marked out in the first line. Any commits or branches that forked versions contain, but are not in the original, will show up as competing racing lines in the graph.
Example network graph

original-repo     |---*----*----*----*------------*--*-*----------***----*-
                                     |               |
toothygrinmeister |                  |--------*      |
                                                     |
cuddlebucketeer   |                                  |------*--*-*

In this example, both toothygrinmeister and cuddlebucketeer have commits that original-repo does not. Should either one of these users issue a pull request and their code is rolled back into original-repo, then the respective dots on the graph would disappear.
Similarly, if your fork does not appear on the network graph when viewing against the master as the zero point, then you can assume your fork is up to date and matches that repository's commit history.
Comment: Using the network graph is a good idea indeed. Thank you.

Find repositories without changes


Does Voice Dictation on the New iPad require a network connection?

Question: Does the the new iPad's voice dictation require a network connection? I ask because Siri does require an active network connection and I am wondering if voice dictation works in a similar manner.
Answer: Yes.
With many methods of voice dictation, what happens is that your voice is recorded and digitized, and your speech is broken up into phrases which are uploaded over the Internet to a powerful computer server which translates your speech into text and then transmits the text back to your device.
However, there is a long history of programs for Mac and PC which perform voice dictation and transcription entirely on your Mac or PC without using an Internet connection.
I don't know of any apps for iOS that perform voice transcription entirely on the device without using a connection to a server on the Internet.
Answer: Yes - if your device has no network connection, the Voice Dictation key will not appear on the keyboard.
If your network connection does not route properly to Apple's servers, then you can tap the button and speak, but the three magenta circles that pulse will remain on screen until the iPad can get a response from the servers or you cancel the input.

You also get the usual network circle spinner in the menu bar to the right of the Wifi / Data Connection icons to indicate a network wait status is ongoing.


Higher order fractional laplacian

Question: when consider the fractional laplacian $(-\triangle)^\alpha$,is there an essential difference between   $0<\alpha<1$ and $\alpha>1$ ? As far as I'm concern,the higer order laplacian ($\alpha>1$ ) ,unlike the lower case, has little connection with stochastic process.(lack of positivy.) Since most paper i have met is the case of  $0<\alpha<1$.And i wonder how things change when considering the higer order laplacian?
Answer: Well, the answer is in your question. When $0<\alpha<1$, and only then, $(-\Delta)^\alpha$ has a positive inverse. In particular, equations like
$$(-\Delta)^\alpha u=f$$
or
$$\partial_tu+(-\Delta)^\alpha u=0$$
satisfy a maximum principle. You get immediately an $L^p$ estimate for every $1\le p\le\infty$. If the equation is quasi-linear instead, it is likely that you have a $BV$-estimate for free. This helps a lot in proving well-posedness of the Boundary-value problem or the Cauchy problem.
Answer: The fractional Laplacian can be represented as a hypersingular integral operator, an integral operator with a singularity higher than the space dimension. Its convergence is provided by a regularization whose form depends on the order. From its form the difference in positivity properties is immediately clear. See S. G. Samko, Hypersingular Integrals and their applications, Taylor and Francis, London, 2002.
On the other hand, there exists a theory of parabolic equations with fractional Laplacians (and more general pseudodifferential operators) of any order. See S. D. Eidelman, S. D. Ivasyshen, and A. N. Kochubei, Analytic methods in the theory of differential and pseudo-differential equations of parabolic type, Birkhauser, Basel, 2004.
Comment: thanks for the useful reference.i'm considering the fractional shrodinger equation and it's $L^p$ estimate ,so i first want to know more about it'e kernel
Comment: i try to look for that book,but it's not available.. I'm really appreciated that if you can send me a copy of the pdf file of your book mentioned above .here is my adress: email@example.com. thank you very much!
Answer: I discovered a two-sided fractional derivative similar to the Grunwald-Letnikov derivative and defined for orders greater than -1. If the absolute value of the order is less than one, there is an inverse given by the same formulae. I proved that this derivative is equal to the Riesz potential, but does not have its problems. You can see the papers:
Ortigueira, M. D., "Riesz Potentials and Inverses via Centred Derivatives" International Journal of Mathematics and Mathematical Sciences, Volume 2006 (2006), Article ID 48391, pages 1-12.
Ortigueira, M. D., "Fractional Central Differences and Derivatives", Journal of Vibration and Control , 14(9–10): 1255–1266, 2008.
Prof. I. Podlubny made an implementation for this derivative that is in the site of Matlab.
If you need you can contact me firstname.lastname@example.com

Higher order fractional laplacian


Why does symplectic geometry have many applications in mathematics

Question: It is not quite intuitive , at least from its origin. Could any one can give me an intuitive explanation?Thank you!
Answer: Any two of (a) symplectic structure, (b) almost-complex structure, and (c) Riemannian structure determine the third.  This reflects the fact that $$ U(n) = O(2n) \cap GL(n,\mathbb{C}) \cap Sp(2n),$$ but the intersection of any two is already $U(n)$.  This gives rise to the theory of Kähler manifolds (cf. wikipedia), which are central to mirror symmetry (and the mirror symmetry conjecture).
Answer: I suppose a question to ask here is : what kinds of applications?
One of the areas where symplectic geometry is used is Hamiltonian dynamics, where the geometric framework allows one to generalize away from cotangent bundles, but this direction is directly related to the origins of the subject.
Another direction comes from algebraic geometry, where the fact that complex and Riemannian structure determine a symplectic one  (see Aaron's answer) makes all complex projective (and affine) algebraic varieties symplectic. Viewing them as such allows one to use differential-geometric methods, while the symplectic form provides some control (in the theory of holomorphic curves, symplectic form gives the crucial energy bounds without which things fall apart; this is why there is no Gromow-Witten theory of almost-complex manifolds). Add a bit of mirror symmetry to the mix and you have interaction with many other areas of math.
There is also the fact that the wedge product is anti-symmetric, which leads the space of connections on a principal bundle over 2-d Riemannian manifold to be an (infinite dimensional) symplectic manifold (the gauge group is Hamiltonian, and curvature is the moment map, leading to flat connections being the reduction!). This leads, for G=SO(3) and the surface coming from a Heegard splitting, to Atiyah-Floer conjecture and some related stuff leads to Heegard-Floer theory. Thus connections to low-dimensional topology. The "naive" connection here is the anti-symmetry underlying symplectic form and wedge product, but probably there is a deeper reason known to wise people...
Answer: Symplectic geometry is applicable in lot of areas such as Classical mechanics, Hamiltonian mechanics. While browsing through the web i have found a reason as to why SG is good for classical mechanics. You may read it here: http://research.microsoft.com/en-us/um/people/cohn/thoughts/symplectic.html
Comment: I think the question is more about why symplectic geometry has found applications beyond classical mechanics.
Comment: @Qiaochu Yuan: I answered the question, w.r.t my thinking.
Answer: There is a simple "philosophical" answer: Symplectic forms allow you to only measure two-dimensional quantities, not one-dimensional ones (you can measure area infinitesimally). That's the basic difference with Riemannian geometry, where you can measure length infinitesimally.
Furthermore symplectic geometry pops up in connection with the cotangent bundle. For instance if you have a (scalar) first order differential operator on a manifold, then the principal symbol transforms like a covector (when changing coordinates). Note that this does not require a metric.


Is it bad if I push my daughter into playing sports?

Question: I played sports growing up and learned many valuable lessons while on the field. I want my daughter to learn some of those same lessons. Is it wrong of me if at a young age I start to push sports on her? Enroll her in soccer, t-ball etc.
Comment: No, it's not wrong.
Answer: I think it's important to push your kids.  I also think it's important not to push too hard.  Balance in all things.
Encourage her.  Play with her yourself and make sure she enjoys it.  When she agrees, then sign her up.  Make sure she understands that she'll have to stay with it for at least some period of time -- it's a lot more fun once you've gotten past the initial awkwardness.
Comment: Agreed on _play with her_. You have to train and prepare her for what she is going to face on the field at least so she is average skill with the kids that will already be there. Otherwise she will be discouraged and disinterested.
Comment: It's also just an amazing way to bond with your kids.  Sports will always be a pleasant thing for them because they associate it with "Good Times With Dad" (or Mom).  Reading to/with your kids fits well here, too.
Comment: The play with only results in feelings of "good times" and enjoyment if it isn't pushed and they really do enjoy it.  Make sure to keep it fun and relaxed so that can happen.
Answer: No.  You should not push any recreational activity, no matter how rewarding you found it, on her.
However... it is perfectly appropriate to encourage her to try sports.
The difference between pushing and encouraging is kind of subjective and hazy, but my interpretation is that "pushing" occurs when the child has already formed their opinion, and you enforce behavior that is contrary to that opinion.
If you have your daughter try football, and she doesn't like football, continuing to pressure her into participating in football is pushing, and is not likely to result in a life-long passion for football.
If she doesn't like football, then you should encourage her to try something else, until she settles on one or more sports she does like.
Depending on the age and personality, it may be appropriate to make it a requirement for the child to give a sport that initial attempt.  Much like a policy of trying everything on your plate at dinner, enforcing "you must try a sport before deciding you don't want to do it" is perfectly reasonable.
What "try" means is something you should be very clear on ahead of time (i.e. is it one session?  One week?  A full season?).
It is also reasonable to establish an expectation that, while the child may have veto power over individual sport activities, they have to pick something, particularly if you are focused on the health and educational (teamwork, goals, strategies, etc.) benefits of sports.  Just be wary of budding lawyers... make sure that you address ahead of time whether you consider "NASCAR" a legitimate sport for your child to pursue, for example!
Answer: Let me tell you a story: My ex-wife's father, a military career person, forced her brother into riding bicycles from early childhood. The boy hated it, sucked at it, but was forced into doing it anyway. One of those times resulted in a nasty fall, a broken leg, and a broken relationship between him and his father that never healed. That boy turned into a man and never spoke a word with his father. His father's like dead to him.
Would you like to experience the same? Is it worth it?
Comment: And yet there are plenty of cases to the contrary, where kids didn't want to because "it's too hard" but later in life are thankful that their parents pushed/forced them to keep at it.  It's a difficult balance, to be sure, one that needs to be carefully evaluated for each kid and each activity.
Answer: While I totally agree with the idea that pushing or forcing your child to do extracurriculars they are not interested in in any way is wrong, I also think physical activity is super important too.  My rule with my own daughter has been that she must be doing one activity that involves physical training.  This encompasses a lot of things from the team sports you mention to individual sports such as many track and field events or even dance.  As it stands now, she has discovered she really enjoys tennis and Taekwondo so that is what she does.
For some kids, team sports are fairly intimidating.  If you are worried about exposure to lessons learned from "team" exposure, there are other ways for them to get exposure to these types of skills.  Debate teams need to work together for example, as do many other groups.  To address these types of skills, my daughter has chosen instead of a team sport, theater.  She is now involved with a community theater which gives her a lot of exposure to some of the same things "teams" have to learn in team sports such as awareness of others on the stage, knowing how to share the spotlight (or the ball) and even strategy with other actors and actresses about how to work together to depict the emotions aimed for most clearly and accurately.
Anyway, this plan has worked to give her enough choice not to feel "pushed", but still meets my need of wanting her to have the exposure to the lessons to be learned from such activities as well as the physical exercise.
It has worked really well for us.


How can PGP and openPGP be compatible?

Question: PGP and openPGP use different encryption algorithms. As I understand, PGP uses IDEA to encrypt a message, then RSA to encrypt the IDEA key. If openPGP doesn't use IDEA, how can it read PGP-encrypted messages?
Answer: PGP is the application which implements OpenPGP standard and adds some proprietary extensions. Consequently, as any other standard-compliant application it can interoperate with other applications which comply to the same standard.
Practically there exist old versions of PGP software which are limited in algorithms and features they support. Eg. PGP 2.6.3 used IDEA and RSA keys, while PGP 6.5 used CAST by default and Elgamal keys (if memory serves). But both these versions are outdated.
Modern versions of PGP and other OpenPGP-compatible software support probably everything the standard offers (i.e. all algorithms).
Your understanding is partially correct: if some implementation doesn't support the algorithm used in encrypted or signed message, it will fail to process this data. But as said, modern implementations (of PGP, GnuPG, our SecureBlackbox etc) handle all algorithms so problems happen only when it is old PGP used to process data encrypted or signed using modern implementations.
Comment: @user420 OpenPGP defines a set of algorithms which are expected to be supported by all compliant implementations. So yes, if the application finds that the data was encrypted using the supported algorithm, the application easily decrypts it. The algorithm itself is specified in OpenPGP packet (the wrapper around encrypted data).
Comment: Thanks for explaining. The book I'm reading seems to be quite old and I assumed PGP had not changed its main algorithms. When you say "support probably everything" and "handle all algorithms", does this mean that the algorithm used for encryption is known, and the software can detect it and use the same algorithm for decryption?
Answer: PGP (the commercial product) and GnuPG are implementations of the PGP concept: that asymmetric encryption can be efficiently implemented by symmetrically encrypting data and then asymmetrically encrypting the symmetric encryption key. OpenPGP is the published specification. The oldest versions of the PGP implementation supported RSA around IDEA and the specification was evolved from the implementation.
To interoperate and allow for updates to algorithms, the software is designed with abstraction and the message format with reserved header fields to tell software implementations what algorithms were used. You want to start looking at Section 5.1 of RFC 2440.
Eugene's answer mentions some historical algorithmic details and covers the version evolution details.
Short version: because of a shared specification, interoperability issues only exist between algorithms selected or backwards-compatibility issues. Modern versions of PGP and GnuPG support many overlapping protocols. Since generated keyfiles list supported algorithms, anything should interoperate with the receiver if your software was able to encrypt a message without error.
Answer: It seems to me one important question is whether you can open old PGP encrypted files. If the algorithm that was used to create it is no longer in the current PGP software it won't open.
I have a similar situation, using PGP on either Windows 3 or Windows 98. In addition I can't get PGP6 won't properly install in Windows 7.
It comes down to this. An old encrypted file can only be read if it is periodically decrypted, opened and re-encrypted with a current algorithm.

How can PGP and openPGP be compatible?


Learning more about racing

Question: I don't race and never will race. However, I am very interested in learning more about it. I read a number of cycling magazines, and I read about so many different racing terms, strategy etc. but they are never explained. Does any know of a good source (like a Bicycle Racing 101 course) where I can learn more about racing?
Answer: The best thing to do is to watch television coverage of races. For just learning, it is even better than actually being at a race because you can see what is going on and there's plenty of background stories.
Now is the BEST time for stage racing because the Giro has just started. Steephill.tv has bunch of links for online video coverage of the Giro. If you have sports cable channels check those too. The Tour de France in July is also fantastic because of the coverage, but the Giro is usually a more interesting and gritty spectacle, IMHO.
Answer: I learned a lot about racing when I had a roommate who was on a local team and raced full-time for a couple years (and then part-time since.)  You probably don't want to take on a roomie just to learn about racing, but you might be able to volunteer to help out a local team.
I also learned a lot reading my roommate's Velo News magazines.  I don't know if it's the same now, at the time it was a magazine for serious racers, not at all like the glossy newsstand magazines.
Answer: In addition to watching, there are lots of things to read, for instance the great autobiographies like Laurent Fignon's We Were Young and Carefree ("Nous étions jeunes et insouciants"), Bobet's Tommorow We Ride and David Millar's Riding Through The Dark - all of these have large sections devoted to races, racing and reacting to events.
The Rider by Tim Krabbe is fiction, but not really, giving wonderfully evocative descriptions of being a racing cyclist.
There are also some good bloggers, e.g. In The Saddle and Rouleur Magazine (which has some great articles if you can find it in your locale).
And then go to YouTube and search for Sunday in Hell. Probably the best movie ever made about cycling, not all about the strategies, but definitely a lot about how to race.
Comment: +1 for A Sunday in Hell. The entire movie is somewhere in Youtube. So awesome.

Learning more about racing


Natural law, accident

Question: When it comes to natural law (in Catholicism perspective), I understand that there is wrong to kill, also when it's suicide, but is it wrong with self defense? And what if there is an accident? Like you forget to turn off the oven at home and someone on the block gets hurt, is that the same as taking a life? On purpose?
Comment: If you are asking for a specifically Catholic perspective, could you make that clear in the question? And use the [catholicism] tag too? "Natural law" could have many interpretations amongst the different Christian traditions.
Comment: We need a doctrinal perspective such as Catholicism before we should try to answer this.
Comment: Natural law is simply consequences. Things with really bad consequences, we say violate natural law.
Answer: Generally speaking the intentions/motivations of the person make it right/wrong or allowable/forbidden.
Sin has always been rebellion against God—generally speaking, doing something that you believe to be wrong. The Jews had some mandates about accidental sins, but with the atonement that Jesus made, I don't see how there's a need for any form of repentance for things that you did not knowingly choose to do (or not do, in the case of something you ought to have done).
If someone dies due to my negligence or irresponsibility, then that might constitute a sin on my part, because I made that choice. Accidents that you could not have controlled do not constitute a choice. You're choices are what will condemn or exonerate you.
Comment: But wont that ruin the concept of natural law? Because God has given us the knowledge/conscience to choose right from wrong. As I see it, the problem is that we are too selfish or "destroyed" by the community, and this is where it comes in that some of us choose wrong, above right. But if it's not wrong, because we did mean it, what if you do something wrong to help someone? Or you subconscious has someting to win, but don't see that befor the actuall damage is done? I mean, if it is okey, because you didn't mean it or did a mistake, then want you allways be able to find a way to justify it?
Comment: @Anine, yes, I think there is no other way, before or after it be.
Answer: 2 question are asked here and 2 assumptions are made.
Assumption 1) Killing is wrong.  If this were true in all cases, then accidents, suicides, self defense, killing during armed combat, abortion and other forms of premeditated murder would have the same gravity.
Assumption 2) Suicide is wrong. This is true "suicide is always as morally objectionable as murder" pope John Paul II (Evangelium Vitae).  Even assisted suicide and euthanasia, but one needs to make a distinction in cases of euthanasia between withholding extraordinary means of keeping a person going and withholding the normal means (food and water).
Question 1.) Killing in self defense is not wrong, it's not the same as murder.  Reason dictates that man doesn't have to die just because someone else desires to kill him. Self preservation is in the Natural Law, not against it. Pope John Paul II applies to reason when he says the death penalty should never be used "except in cases of extreme necessity". One of those reasons is that society is unable to protect itself.
Question 2.) Accidents, a person is not morally culpable for something which they did not intend if they followed their consciences.  A person should seek to know the truth and not act with any doubt in their conscience.  If you forgot you left the oven on and had an inkling that you did that, then you owe it to your neighbors to check.  It is unlikely that any true accident could have the gravity of premeditated murder, but it could come close!
Answer: Biblically, there is no exception. By both word and deed, Christ taught that it is wrong to take a human life or hurt another person, even in self-defense. "But I tell you, do not resist an evil person. If anyone slaps you on the right cheek, turn to them the other cheek also." Matthew 5:39 (NIV).
But actions speak louder than words, and Christ did not resist his arrest and execution. When Peter picked up a sword and attempted to defend him (cutting off the ear of the high priest's servant/slave) Jesus forced him to put the sword down.  John 18:11-12
Catholicism and many other churches have made doctrinal exceptions, but these do not have any Biblical basis that I can find.
Even under the law of Moses, causing an accidental death was not treated as murder. "If anyone kills his neighbor unintentionally without having hated him in the past— as when someone goes into the forest with his neighbor to cut wood, and his hand swings the axe to cut down a tree, and the head slips from the handle and strikes his neighbor so that he dies—he may flee to one of these cities and live, . ." Deut. 19:4-13

Natural law, accident


Conditional Probability

Question:
In a $13$ card hand, given that a person has one ace, what is the
  probability that person has more than one ace?
In a $13$ card hand, given that a person has the ace of spades, what is
  the probability that person has more than one ace?
Comment: Those two probabilities will be the same.
Comment: Count the total number of hands in which a person has at least one ace, or, easier, count the number of ways the person can have exactly one ace.
Comment: @TMM: One is about 50% larger than the other.
Answer: This is just a matter of counting. Let's look first at the second question. How many hands contain the ace of spades? The other $12$ cards may be any of the $51$ other cards, so there must be $\binom{51}{12}$ such hands. How many of them contain no other ace? To form such a hand, you must pick all $12$ of the other cards from the $48$ cards that aren't aces, something that can be done in $\binom{48}{12}$ ways. Thus, $\binom{48}{12}$ of the $\binom{51}{12}$ hands that contain the ace of spades contain no other ace, and therefore $\binom{51}{12}-\binom{48}{12}$ of them do contain at least one other ace. Thus, the probability that the hand contains at least one other ace, given that it contains the ace of spades, is
$$\begin{align*}\frac{\binom{51}{12}-\binom{48}{12}}{\binom{51}{12}}&=1-\frac{\binom{48}{12}}{\binom{51}{12}}\\
&=1-\frac{48!}{12!\,36!}\cdot\frac{12!\,39!}{51!}\\
&=1-\frac{39\cdot38\cdot37}{51\cdot50\cdot49}\\
&=1-\frac{13\cdot19\cdot37}{17\cdot25\cdot49}\\
&=1-\frac{9139}{20825}\\
&=\frac{11686}{20825}\;,
\end{align*}$$
which is a little more than $0.56$.
Now we can tackle the first problem. There are $\binom{48}{13}$ hands that contain no ace, so there are $\binom{52}{13}-\binom{48}{13}$ hands that contain at least one ace. To build a hand with exactly one ace, you must choose one of the $4$ aces and any $12$ of the other $48$ cards; this can be done in $4\binom{48}{12}$ ways. Thus, $\binom{52}{13}-\binom{48}{13}-4\binom{48}{12}$ hands contain more than one ace. Given that you have at least one ace, therefore, the probability that you have more than one is
$$\begin{align*}
\frac{\binom{52}{13}-\binom{48}{13}-4\binom{48}{12}}{\binom{52}{13}-\binom{48}{13}}&=1-\frac{4\binom{48}{12}}{\binom{52}{13}-\binom{48}{13}}\\
&=1-\frac{\frac{4\cdot48!}{12!\,36!}}{\frac{52!}{13!\,39!}-\frac{48!}{13!\,35!}}\\
&=1-\frac{\frac4{12!\,36!}}{\frac{52\cdot51\cdot50\cdot49}{13!\,39!}-\frac1{13!\,35!}}\\
&=1-\frac{4\cdot13\cdot39\cdot38\cdot37}{52\cdot51\cdot50\cdot49-39\cdot38\cdot37\cdot36}\\
&=1-\frac{13\cdot19\cdot37}{17\cdot25\cdot49-19\cdot37\cdot9}\\
&=1-\frac{9139}{14498}\\
&=\frac{5359}{14498}\;,
\end{align*}$$
or a little under $0.37$.
Answer: You can argue indirectly for the first question, by finding the probability of having exactly one ace: after being given the first ace, throw away all the remaining aces, and then select the 12 cards from the non-aces. Then, if $X_n$ is the event of aving n aces,$ P(X_1)+P(X_2)+ P(X_3)+P(X_{4}) =1$ (I am assuming there are a total of four aces in the deck). Basically: the probability of having more than one ace, given that one already has one, is given by fixing one card to be the ace, and then seeing what the probability is that the remaining cards have exactly two, three, or four aces; for the event $X_2$, select a second card to be the ace, throw the two remaining aces; for $X_3$, select three aces, throw away the remaining ace, etc.

Conditional Probability


Why isn't there a server edition for Fedora like Ubuntu?

Question: I was looking for a server edition of Fedora to download, and just found that they don't have one. It's very strange to me. If Ubuntu has both desktop and server editions, why doesn't Fedora follow suit?
Comment: There's no difference between server and desktop, all just different kernel and package installations.
Comment: There is. It's called [Red Hat Enterprise Linux](http://www.redhat.com/products/enterprise-linux/), and you're expected to buy it.
Comment: RHEL is a paid version, CentOS and Scientific are free.
Comment: *What* prevents you from installing Fedora Core as a server?
Comment: Duplicate of http://unix.stackexchange.com/q/28647/11284
Answer: Fedora only has a Desktop editionhas Server edition.  In my experience, "server" distros have a longer support lifetime than desktop distros.  If you want something that has a longer support cycle, use Red Hat Enterprise Linux, or one of the RHEL clones like CentOS.  Fedora really isn't suited for a long-term support OS, because at best you'll get 13 months of support if you install a release the day it comes out (Unlike RHEL).
While Fedora is really only aimed at the desktop, the OS certainly supports being installed as a server, using the DVD or network installer.  RHEL6 is based on Fedora 12 (with backports from later Fedoras and security fixes) and uses the same installation software as Fedora, so there's nothing stopping you from using Fedora as a server OS, just don't expect to get updates or security fixes past the end of its support lifetime.
Answer: RedHat Enterprise Linux is Fedora server.
Fedora is where RedHat innovates and so it's bleeding edge by definition and not meant for servers. RedHat Enterprise is based on Fedora. Fedora provides a platform to develop and test new updates before they get pushed to RedHat Enterprise.
This is why Fedora gets the newest stuff before other distributions. This makes Fedora a great desktop OS for early adopters who like to get the new stuff first, but for servers, you want battle tested code, not bleeding edge.
Fedora is such an asset to RedHat because by the time something makes it into RedHat Enterprise, the code has been hardened after being battle tested in the wild by millions of users.
RedHat has been in the game for a long time pushing Linux development, and the Fedora model has proven effective. RedHat's first release was in 1995, Fedora was released in 2003, and in 2012 RedHat became the first billion dollar open-source company.
In essence, Fedora is RedHat Linux before the addition of RedHat Enterprise Linux. The name was changed to reduce confusion, but the project's importance was made clear when they renamed it after RedHat's iconic symbol -- its red fedora.
See the Red Hat/Fedora project announcement.
Running Fedora on your desktop keeps you at the forefront of Linux development world (it's what Linus uses), and it makes your life easier if you're running RedHat or CentOS servers because the environments are the same. In contrast, if you run RedHat on your servers and Ubuntu on your desktop, you have different package managers, file system layout, etc.
Answer: Fedora as a server does work fine, but its short lifetime make it a hassle (must upgrade due to end-of-life just in the middle of finals or such...).
Fedora isn't "aimed at the desktop", it's driving force is to get the newest bling out. That happens to be what the desktop users demand...


Can I trust on DropBox as a resource?

Question: After Ma.gnolia Major Data Loss in 2009, I believe only Google, Microsoft and Yahoo services. Can I trust DropBox as my resource host? I would like to use my website's static content in DropBox and use it in my website. Is it good for me?
Answer: What do you mean by 'trust'? I'll assume you're talking about data loss.
If you are talking about data backups and preventing loss of data, you need to take responsibility for backing up your data. You can count on the company you are paying to do their best, but you have no real idea what their best IS until the feces hits the fan, at which point it's a bit late to figure out that their backup strategy just doesn't work.
You MUST ALWAYS be responsible for your own data. You can certainly pay other vendors to help with the task of keeping it available, but if you don't have a copy where you have physical control of the copy, then you are COMPLETELY at the mercy of people who's only loyalty to you is $29.99 a month. And you need to keep in mind that $29.99 will only barely pay for someone to pick up the phone.
Can you trust Dropbox? Sure. You can trust them to try to keep your data safe. Especially if you have one of their paid plans - they like money and by keeping your data safe, you'll keep giving them money. But if that's your only off-site storage, then you have a problem, because you just can't tell how good they are.
Answer: I wouldn't use Dropbox to host content because it will stop serving the resource if it's used too much:

We watch carefully for any fraudulent use of Dropbox public links and will suspend suspicious links when they are detected. Links that use up more than 10GB/day for Basic (free) accounts and 250GB/day for Pro (paid) accounts are automatically suspended.

If you want to share images, I suggest you use something like imgur (with a paid account). It's reliable and fast.
For other types of content, Amazon S3 can help you if you serve a lot of content.
Answer: I would ask the question: can you trust your web host? I think unless you host your own servers on your own net connection (which you can't since it probably comes from some kind of telco company) etc etc.
You just have to trust them.
I don't know what their SLA is like, but if you're really concerned, I suggest using something like Amazon's S3 service which does have an SLA. (It's work noting that dropbox use S3 to store your files)

Can I trust on DropBox as a resource?


Will upgrade of iOS delete any of my videos or photos?

Question: I wanna upgrade to the latest iOS 5 and wonder if my existing photos and videos at Camera Roll will be still on device. Is that right? Or I have to backup them before upgrading? If so, how would I do that - iTunes doesn't seem to backup those things at sync.
Answer: The photos and videos in Camera Roll are not synced with iTunes - they are, instead, the "raw" photos meant to be synced to the photo-organization tool you use - whether that's a set of folders in your filesystem, or iPhoto.
In other words, when your iPhone is mounted as a "USB camera" (on Windows) or when iPhoto opens (when plugging it into your Mac), the contents of the Camera Roll are what you see.
That being said, iOS 5 will delete all of this data during the upgrade, so you absolutely should back them up before going forward! Assuming you're using a Mac, plug in the phone, open iPhoto, and import everything before doing the upgrade.
(And I recommend making a backup of your phone, transferring purchases, and then syncing everything you can with iTunes before going forward... the iOS 5 upgrade appears to be a very destructive procedure.)
Answer: The photos aren't synced but definitively are backup by iTunes.
I just upgraded to iOS 5 and my photos are still at my camera roll
Answer: You run the risk of losing your pictures if you don't have the "Sync Photos" switch turned on in iTunes.  The iOS 5 upgrade may completely wipe your iPad/iPhone so you have to do a resync to bring everything back.  But that will only work if you've already backed it up and have sync turned on.
Be safe, not sorry.


Server Client position information exchanging

Question: I am doing small game in xna client/server, there can be 50f per seconds, but i don't belive that each client has to sent 50 mesagges about only their position, and then get back from server, regular ping is 50ms so even if 20 messages per second then success, so how it is made that everyone see immediately that someone else changed its position?
Answer: i recommend to all who want to implement multi player this article http://gafferongames.com/networking-for-game-programmers/what-every-programmer-needs-to-know-about-game-networking/
Comment: +1 This is the bare minimum of research anyone should have done before coming here to look for answers.
Answer: Generally, you don't send 50 movement packet updates a second, normally it should be around 20. Quake 1 had 10 packets/second. What you would do is send say 20 movement packets a second, and have the other clients interpolate between the old position and the new position to stop the jitteryness.
That won't be immediate, but networking never is. Even over fast LAN connections, there would still be about 2-5 frames latency.
The client doesn't sent the position, and then move when the server lets him. That would introduce large amounts of delay that would make it unplayable. (Assuming real time here). What you would do is the client would tell the server that I am moving here, and the server would go off to tell all the other clients.
It would also be possible to have some form of anti-cheat system, where the server watches where the player is moving to, and figures out if it is valid. So it would verify that it is not inside a wall, not teleporting across the map, etc.


Inflating/Deflating diffeomorphism

Question: I'm interesting in find (if it exists) any manifold with volume form and any diffeomorphism on it such that for any ball B corresponding sequence of B-iterated volumes (just measures of $T^i(B)$, where T is diffeomorphism) may take values arbitrarily close to volume of all manifold. In compact manifold case this question are equivalent to arbitary close deflation of ball in such sequence. What for non-compact manifolds in this case? What for one-parametric group of diffeomorphisms? More generalized, how invariant measures far from initial category/conditions? What is degree of measure invariance or measure-preservation of our diffeomorphism (except divergence if it come from vector field; some global properties, please)?
Sorry for bad english.
Comment: Here is my understanding of the first question. Is it possible to find a manifold (M, vol) (of finite or infinite volume) and a diffeo T such that for any open ball B in M limsup of T^n(B) goes to vol(M) as n goes to infinity.
Comment: Your question isn't making sense to me.  Manifold volumes can be any positive real number so by "arbitrarily close to volume of all manifold" do you mean "any positive real number"?
Answer: Not sure if it is related, but in Lemma 1 of this paper (A.Avila, J. Bochi, A C1 generic map has no invariant absolutely continuous probability measure) it is proved that if a map has no invariant absolutely continuous probability measure, then, there exists a compact set $K$ of measure abitrarily close to $1$ which has an iterate with arbitrarily small measure.
Sorry if this has nothing to do, but from how I understood the question, at least this should be useful.
EDIT: Re-reading the question, I've noticed that you are maybe more concerned about iterates of balls.
For this, it depends on what you want. For example, if you want, for any $\varepsilon$ a ball of smaller radius that has iterates with volume close to the manifold, it is easy to get (say, for example a north-south map). I believe this should be not what you are looking for.
If you look for every ball at a time, this won't be true in general, and let me rephrase your question (or at least the one I am responding to): Is there a homeomorphism $f$ such that given a ball $B$ and $\varepsilon>0$ there exists an integer $n$ such that $f^n(B)$ has measure larger than $1-\varepsilon$.
If $f$ is not transitive (or at least, if it has at least two chain recurrence classes), then, there exists an open set such that $\overline{U} \subset f(U)$ so, if you consider a ball in $\overline{U}^c$ it will never reach measure bigger than the complement of $U$.
For $f$ transitive, there are also examples where this does not hold. For example, for conservative $f$, it trivially does not hold.
In other cases, I would presume that it is not true (at least for ``tipical'' diffeomorphisms), however, I don't know a proof nor an example.
Comment: Thanks for this paper, despite the simplicity of lemma 1 it is really useful. But now it hasn't very much to do with first question.
Answer: As far as |I understand your question, examples you want are provided by the so-called North-South dynamical systems, which are actions of $\mathbb Z$ (discrete time) or $\mathbb R$ (continuous time) with one repelling and one attractive fixed points such that everything else is contracted to the attractive point as time goes to $+\infty$ and to the repelling point as time goes to $-\infty$. For instance, any hyperbolic isometry of the hyperbolic plane generates this kind of action on the boundary circle.
Comment: It true and obvious, but only for ball's wich include repelling point
Answer: I would try to reanimate this thread and write pair of trivial views. first, on 1-dimensional manifold it's imposible just because any suitable diffeomorphisms comes from vector fields (such topic is rised on mathoverflow) and last have potential on universe cover - line, but if potential exist problem have no solution (on any dimensional manifold). On other hand it's not surprisingly and now my main goal is to illustrate that in other cases existence of such diffeo intuitively justified. Call diffeo of M to be s-transitive if his natural action on any self-products M ($M\times M\ldots\times M$) is topological transitive. In other words any number of pair-distinct points on M is to posible send arbitrarily close to any else set of such number points. So images by iterations of any fixed ball is arbitrarily dense in manifold. Intuitively speaking, obstruction to volume changes high lies in ability us diffeo change curvature of boundary strongly enough. I hope to get around this. Any ideas?
Answer: Maybe try to solve a little bit simpler problem: is there a manifold and a diffeomorphism such that any small enough ball will have its volume increased at least 100 times (or any constant big number) under diffeomorhism, iterated some times.

Inflating/Deflating diffeomorphism


What should we ask from a Usability Trainer to identify if he is right for Training us?

Question: This looks a bit odd but we have been identified to get training on Usability and we have to talk with some of the Usability trainers who could provide us  training. On the basis of meeting up with them we need to figure out who suits us best. What do you guys think we should be asking them?
Answer: If I were hiring a usability trainer, I'd want evidence that the trainer…

knows the appropriate material well;
has real experience in the field; and
is a good teacher: he or she can explain complex ideas clearly, has a good stage presence, and can engage and captivate the audience and provide a memorable experience.

A certification or a relevant academic degree can serve as a certain kind of proof of knowledge, but in reality, these credentials rarely guarantee actual competence.
I'd personally prefer to see "portfolio evidence": Do they have a resume showing real-world experience doing usability-related work?  Can they show software that they've designed?  Have they actually used usability techniques like card sorts and have they gained better insights into what works and what doesn't?  Can they show and discuss something like a usability analysis report and recommendations that they've written?
If they've written a book or if they have a decent blog, that's another form of proof, and it gives you insight into their communication style.
To judge teaching ability and classroom presence, ask whether they can provide snippets of video recordings from past training sessions.  If not, maybe they could give a short sample lesson as a preview.
Ask for the proposed course outline. Is the content appropriate and is it customized for your organization's specific needs?  Does it integrate any live activities or exercises to get the participants actually thinking and doing?
Ask for references, and also ask for the results of previous course evaluations, but be aware that a lot of course participants give the trainer high ratings just to be "nice". A lot of courses are enjoyable to sit through but the students don't really take away any practical skills. Ask what specific learning objectives the training will address and ask what the participants should be able to do afterwards.
Training is an interpersonal activity, a soft skill, and you have to be comfortable with and generally like the trainer. So in the end, even after considering all of the above, you might well just have to trust your gut feeling about who you like best.
Comment: Great answers.  I'd add samples of their past work, even if it's old.  If the work is still on a NDA, they still can supply the table of contents, which can be very helpful.  I'd ask not just for studies, but a heuristic example since it really highlights one/a few peoples work, or even a competitive analysis. This goes back to their experiences in the field, the basics before they started training.
Comment: Nice answer. But you'd get a +1 just for mentioning "learning objectives".
Comment: Thanks for your answer Kevin .. good descriptive answer :-)
Answer: You want someone who is going to leave deep memorable insights.
As a killer question: I'd ask them whether their presentation covers door handles.
The affordances of door handles issue gets the idea over better than anything else because its simple.
http://www.jnd.org/dn.mss/when_bugs_become_features.html
http://en.wikipedia.org/wiki/Affordance
Comment: "As a killer question: I'd ask them whether their presentation covers door handles." I think the question should not be a surprise to them, but I'd hardly make my decision on whether it's in the presentation or not.