Does Luton Airport have a blanket ban on unaccompanied minors?

Question: I was told by a member of staff at Luton airport during an emergency redirect of my daughter's flight from Heathrow during heavy snow that children (Unaccompanied minors - UMs) cannot normally fly out of Luton. But I don't know if the staff member was speaking for the airport as a whole, or for their specific airline. Nothing on the Airport website, search or FAQs. The airline I want to use does allow them to fly alone at her age. No mention of Luton in their FAQ either.
Comment: Normally UMs flight is an airline's policy and responsibility.  Not sure how an airport plays into this at all.
Answer: I checked london-lutons FAQ's the closest I could find was special-asistance / wheelchairs where they recommend you contact your carrier.


Intersection of 2 spheres and a cube

Question: In the Cartesian coordinate system, given 3 geometrical solid objects (interior plus boundary): spheres S1(x1,y1,z1, R1), S2(x2,y2,z2, R2) and a cube (which is orthogonal with coordinate system) at the center C (x3,y3,z3)  with size L x L x L. The question is  "Whether the 3 objects have any common volumetric intersection (Yes or No) " ?
I need a math solution or computing algorithm for this problem.
Comment: "Sphere" and "cube" could refer to either the solid object (interior plus boundary) or the surface (boundary only).  Which specific type of intersection are you looking for?
Comment: It depends on the values of your parameters.
Answer: At first we need to check whether 2 spheres intersect or not.
 if (x1-x2)^2+ (y1-y2)^2+ (z1-y2)^2 > (R1+R2)^2  ---> flag of intersection=FALSE.
else
 (
 (i) Define
x4=(x1*R2+x2*R1)/(R1+R2)
y4=(y1*R2+y2*R1)/(R1+R2)
z4=(z1*R2+z2*R1)/(R1+R2)
(ii)
  if (
(abs(x4-x3)<=L/2) & ( abs(y4-y3)<=L/2) & ( abs(z4-z3)<=L/2) &  ---->flag of intersection=TRUE )
    else ( // they have intersection if and only if the volumetric intersection of the 2 spheres intersects with at least one of 6 faces of the cube ( e.g. bottom face z= x3-L/2, x3-L/2<= x <= x3+L/2 &  y3-L/2<= y <= y3+L/2)
        // this criteria is quite straightforward to check since it is only in the plane ( e.g. bottom face z= x3-L/2)
        )
  )
Answer: Probably the easiest way to solve this problem is to reduce it to linear programming.  Note that this formulation would work for checking if the intersection of any number of spheres/convex polytopes is non-empty.  To begin with, we would first rewrite the cube as an intersection of halfspaces.
Next we need to replace the spheres with linear halfspaces as well.  This is done by lifting them along the map from $\mathbb{R}^3$ to $\mathbb{R}^{4,1}$ where,
$ (x, y, z) \mapsto (1, x, y, z, \frac{1}{2} ( x^2 + y^2 + z^2 ) )$
Where we fix the metric that,
$ \langle (o_1, x_1, y_1, z_1, n_1), (o_2, x_2, y_2, z_2, n_2) \rangle = x_1 x_2 + y_1 y_2 + z_1 z_2 - o_1 n_2 - n_1 o_2$
So, a linear halfspace of the form,
$a x + b y + c z \leq d$
Can be written as:
$ \langle (0, a, b, c, d), (1, x, y, z, \frac{1}{2}(x^2 + y^2 + z^2) ) \rangle \leq 0 $
And a spherical halfspace,
$ (x - a)^2 + (y - b)^2 + (z - c)^2 \leq r^2 $
Becomes:
$ \langle (1, a, b, c, \frac{1}{2} (a^2 + b^2 + c^2 - r^2) ), (1, x, y, z, \frac{1}{2}(x^2 + y^2 + z^2) ) \rangle \leq 0$
As a result, our problem is now to determine if a system of linear inequalities has a solution.  This is of course linear programming, and you can resolve it either by a brute-force determinant test (aka apply Helly's theorem), or use whatever efficient algorithm you would prefer.  In this instance, since it is so small, brute force may be preferrable.  For larger numbers of primitives, Seidel's algorithm should perform better.
Comment: Hi Mikola, thank you your answer, however I need only an algorithm in this particular case ( 2 spheres and 1 cube) and easy to be implemented for computer code.

Intersection of 2 spheres and a cube


What's the correct technique for strumming a guitar?

Question: By correct I mean from a biomechanical perspective to minimize the risk of injury.  I have seen some advice saying that strumming should be controlled by the big muscles such as the shoulder.  My teacher says it is simply a rotation of the wrist i.e.  A small muscle movement. What's the safest technique for avoiding RSI, carpal tunnel and similar?
Answer: Actually both parts are correct - you have different kinds of strum, and different sizes of movement.
Often, on an un-mic'ed acoustic playing to a large room, you would use a large movement from the elbow, with a little shoulder movement added in, to ensure you get significant power to the strings - translating to volume.
A strum with partial string coverage (think a basic D or C shape where you are only playing 4 or 5 strings) it can give you much more control to keep the arm relatively still and rotate at the wrist.
Safest is probably to make sure you vary things, sometimes use the wrist, sometimes the elbow, sometimes a bit of the shoulder - this helps spread the load on your joints, muscles etc.
Of course the extreme version is the windmill (but be aware it can hurt a lot if you get it wrong :-)

(from musicradar.com)
Answer: while playing accompaniment for traditional Irish music i found that strumming with the elbow can cause a lot of problems, me and a few local fellow guitar players have had issues with "tennis elbow" like injuries causing the muscles in my upper forearm to become knotted and extremely painful, one friend even developed tendinitis and had to stop playing until he built his muscles up again.
this can be avoided by performing the correct stretches before picking up a guitar. also with that style of music the guitar turns into quite a percussive instrument with similarities to the bodhrán (an Irish percussion instrument). these similarities mean that players often play a lot harder than is needed. great influences in the world of Irish music include Steve Cooney (an Australian man), another great musician who really plays hard is Donal Lunny (bouzouki player) and a great overall player is a guy called Arty McGlynn.
i was always taught to use my wrist and forearm instead of my elbow to strum the guitar and was always told to be careful not to play too hard while at the same time, not being afraid to "hit" the thing to get a bit of sound out of it.
Answer: I use a combination of a rotation of the forearm and movement of the forearm (up and down) with just a little of the upper arm. You probably should avoid bending the wrist too much. Overall you want to be relaxed, loose and natural feeling - this last part can be misleading because whatever you get in the habit of doing will start to feel natural to you.
Hold your arm up, bend your wrist forward maybe 20 degrees, certainly not as much as 45. This is about the amount of play you need to do the work mainly with the rotation of the forearm and a little up and down.
Answer: I'd like to throw something out there from a physiological perspective. In your wrist there are 8 carpal bones, two forearm bones, several major tendons, a couple veins and 3 nerves. The more structures in a smaller space means that that space is easier to injure. More different surfaces of bones are rubbing together, therefore more wear and tear. Your elbow is a larger stronger structure. THere are 3 larger bones joining together vs the 10 of the wrist. Therefore, its more of a wear and tear resistant structure.
Thus, it matters what you are doing musically when you ask whether to strum from wrist or elbow.  Say you are strumming Gordon Lightfoot's Canadian Railroad Trilogy. I would say that your wrist is going to get very tired doing that. However if you hold your wrist still and strum from you elbow, you should probably be able to do the same song without getting tired. But, if you are playing some finicky and detailed picking, or maybe some light strumming, use your wrist.
Most importantly, you need to do exercises other than guitar to keep the area and your body in shape. Also, muscular trigger points in the neck, upper arm, and lower arm can refer pain into your wrist, so a good chiropractor or massage therapist is ideal.


Where can I download the Google Road network as shapefile?

Question: Is there any site from where I can get Google Road network as shapefile? As per my knowledge It is not distributed by google. So anybody can suggest how can I create this road network for a custom use?
Answer: No, Google's road data is proprietary and is not distributed in a GIS capable format. This is because Google spends a lot of money keeping their GIS accurate and current, and distributing it for free would allow Google's competitors (e.g. Microsoft, MapQuest, Apple, ESRI) to download it. This would forfeit Google's competitive advantage in the web mapping world.
OpenStreetMap does offer downloads of their entire road dataset. The "Downloading data" Wiki page has some more information. The data download page is here. If you only need data for a single region or country, I recommend using the prepackaged downloads from geofabrik.de.
Answer: Options
Buy a commercial product- TeleAtlas or Navteq (Google now use TeleAtlas - originally it was a mix of both)
Google do provide Downloadable data but only for MapMaker Countries
https://services.google.com/fb/forms/mapmakerdatadownload/
shapefile or KML format:
(Mapperz did a blog about this in April 2009 http://mapperz.blogspot.ca/2009/04/google-maps-map-maker-vector-data.html)
Or use OpenStreetMap [Recommended]
http://wiki.openstreetmap.org/wiki/Planet.osm
(for commercial use allowed)
Answer: I would not recommend doing copy of those data. It is not FREE. The license did not allow you to use it outside of google maps.
You could try extract some data using the google maps webservices but this would be allowed only for use with your client map.
You can buy street information from some companies or use free available data published.
Answer: You can download Road data without digitize but not in bulk you have to select which road you have to download.
https://youtu.be/OsGBjHikAqs


Why does 腰抜け mean coward?

Question: Why does 腰抜け mean coward?
I see 腰 (waist) + 抜 (missing/losing) = 腰抜け (coward), but I fail to see how they add up.
Comment: 腰抜け{こしめけ} ... just wanted to add the furigana.
Comment: In English we say people who are cowards "have no backbone", or "have no spine". Just pointing out that certain concepts have a kind of universality among humans.
Answer: Looking at the Daijisen definition, it seems to mean in the first definition "losing the strength of the back/waist and becoming unable to stand", and probably from that in the second definition "lacking guts"/"coward".
I would say from this that 腰抜け might be very close to the English expressions "spineless", "no spine", "lacking spine" etc for a similar reason.
Comment: I guess if forgot to look there.  腰の力が抜けて立てなくなること。explains it for me. thanks
Comment: Also probably worth mentioning: 腰があるうどん is udon which is not overboiled, still has some chewiness to it (dang, I suck at describing food).
Answer: An upright posture is symbolic of strength and bravery. Being able to resist being forced into other postures such as being forced to bow or kneel to another requires 腰.
Answer: I see two possible meanings for this character combination:
It's gonna sound a little gross, but the two ideographs tell me exactly what a coward is doing. When scared, most people have the fight or flight response. The body's natural reaction, to make flight (read: running away) easier is to make itself lighter. This is done by emptying itself. that's as detailed as I'll get, you can read more on what this means on the wiki article I linked.
Most people who are seen as cowards will run away from their problems, or from scary things. This might be a reason why these two characters might go together to give the compound idea of a coward. As in "A coward is someone whose waist extracts (the contents of itself) when trouble is around" <- I made that up, it's not a quote from anything (that I know of).
The other possible reason for these two characters being used together might be less likely, but it's still possible.
What used to happen to cowards and people who betrayed their masters/superiors/lords? They would be forced to commit Seppuku. Seppuku requires that the belly (just above the waist) of the coward/betrayer be opened (or emptied) and their head removed, then the head is severed. Maybe the first act of Seppuku is referenced in this character combination.
I seem to remember reading somewhere that the removal of the head during the act of committing Seppuku is to save the person from too much pain, and bring a swift death. I can't remember where I read it, though. I'm sure it was either in one of my Japanese history texts or in Book of Five Rings/Bushido, but I could be wrong. anyway, that's a side  note.
Again, this is just conjecture and guess work on my part. Mainly, these guesses are based on what I think the though process behind the creation/first use of the phrase may have been.
I'm sorry that I can't link to any definitive proof. I just thought that I would share my two cents on the OP.

Why does 腰抜け mean coward?


How to calculate a firing location from point of impact data?

Question: I would like to know how to calculate the point at which a bullet is fired from a gun given information from the scene where the bullet falls.  The scene would contain the point of impact (GPS location data), the angle at which the bullet decended (taken from the ceiling to the actual point of impact), and the height of the point of impact.  As you can see, I am trying to determine weather a person who fires a bullet into the air and it impacts someone, can be located via some physics and mathematical formulas.  From the crime scene we would also have the specific bullet type and its dimensions and manufacturers ballistics trajectory information.  I've checked some sites for ballistics and there are many tables calculating the ranges of specific bullets and guns.  I hope to use this data somehow.  If someone has already done this, please let me know.
Answer: The velocity of the bullet $\vec{v}$ changes during the flight according to the second Newton's law:
$$
\frac{d \vec{v}}{d t} = \frac{\vec{F}_a(\vec{v})}{m} + \vec{g}; \qquad (1)
$$
where
$m$ is the mass of the bullet
$\vec{F}_a$ is the force of the air resistance
$\vec{g}$ is the free fall acceleration.
The air resistance force is always directed against the velocity (if the bullet has no wings).
Let's select $x$ and $y$ axes as it shown on the picture:

Then equation (1) leads to the following ODE system for the velocity projections:
$$
\left\{
\begin{aligned}
\frac{d v_x}{d t} + \frac{F_a(v)}{m v} v_x & = 0 \\
\frac{d v_y}{d t} + \frac{F_a(v)}{m v} v_y & = -g
\end{aligned}
\right. \qquad (2)
$$
where $v = \sqrt{v_x^2 + v_y^2}$.
The formula for $F_a(v)$ should be known for any kind of bullet. If we know the velocity at the end of the trajectory $\vec{v}_0$ then the system (2) is a Cauchy problem and can be solved numerically. It can be solved analytically if the air resistance force fits Stokes' law (for bullet it is usually not true).
So, if we know the velocity at the end (both direction and absolute value) we can find it at any moment in the past, calculate the trajectory and find the position of the shooter on it. The solution will not be very stable though. Small uncertainty in $\vec{v}_0$ will lead to substantial uncertainty in the shooter's position that will grow with the distance.
Edit:
If the flight of the bullet takes much time the vertical component of the velocity can reach the terminal value. The gravity force will be compensated by the air resistance and $v_y$ will remain constant until the end of the flight.
In that case it will be impossible to calculate the position of the shooter. The condition to distinguish this case is
$$
F_a(v_0)\frac{v_{0y}}{v_0} \simeq mg
$$
Comment: But if it went through the ceiling at any sort of arc it's probably falling at terminal velocity so difficult to get a good solution
Comment: it works pretty well for a ballistic trajectory, like an artillery shell from only two points - especially if you know the muzzle velocity from the calibre
Answer: An interesting problem, it's sort of "reverse aiming" - start at the impact point, aim through the hole in the ceiling, then figure out where the bullet came from, right?
I don't think a general solution is possible, because the problem is underspecified - the only data we have to work with are the location of impact, direction of the last portion of the trajectory, and the drag characteristics of the bullet.  We don't know speed the bullet came in at, nor do we know what speed it left the rifle; the combination of these two parameters will affect the path length of the trajectory.
Consider that you have a hole in a roof and a splash in the floor that indicates the bullet entered at (say) 20 degrees from vertical, from a particular azimuth.  I could have stood three kilometres away and fired a rifle at a very high angle, and had the bullet drop in like that.  Or I could have stood on the roof and fired down through the roof.  How could you tell which happened?
In principle you would have to also know the muzzle velocity and the arrival speed of the bullet - then there would be enough information to do the calculation.  But as a practical matter this would not be accurate enough to be useful; the biggest single error source that I can see is that when the bullet enters the roof, it will almost certainly be deflected by at least a small amount (and not a predictable amount).  This in itself will introduce enough error in the arrival angle and direction to make the calculation meaningless.
So I think that what you are looking for ("here's the impact, find where the shooter was") isn't solvable.  A much easier problem is "we have this persons/location as a suspect, who fired a shot from this rifle; could his shot have caused the observed impact" - in comparison this is much more straightforward.
Comment: Two obvious missing pieces of data which would impact a calculation are: an unusual path after passing through ceiling, and the lack of knowledge about windage (other than air resistance).


Are 3.5 Bards mechanically weak?

Question: People frequently seem to think that Bards are mechanically weaker than other classes, and I was wondering if this was true?
Answer: Not at all; Bards are a very flexible and potent class
At least not if you allow an admittedly-large number of supplements. Even in straight Core, Bards are fairly middle-of-the-road (decidedly better than Fighter, Monk, or Paladin, decidedly worse than Cleric, Druid, or Wizard), though they are quite limited. But if you have a lot of books available, then they have a ton of options out there, many of them quite good.
Inspire Courage is great
Inspire Courage, by default, gives +1 to attack and +1 to damage to all allies who can hear it. Not particularly glamorous, but that's a pretty sizable bonus. It does, unfortunately, grow very slowly, at +⅛ per level.
Take the Song of the Heart feat (Eberron Campaign Setting), cast inspirational boost (Spell Compendium), activate a Badge of Valor (Magic Item Compendium), and you're at +4+⅛/level attack & damage. If you're willing to allow it, Words of Creation (Book of Exalted Deeds) doubles this.
Dragonfire Inspiration (Dragon Magic) allows you to play a separate song that gives +1d6 Fire damage for each +1 to attack/damage your Inspire Courage would normally grant, again to all allies who can hear it. Note that this stacks with Inspire Courage; they're two separate songs. Now we're looking at +4 attack, +4d6+4 damage, or twice that with Words of Creation.
Bardic Music can make you a melee powerhouse
Snowflake Wardancing (Frostburn) allows you to add your Charisma to damage rolls, Gauntlet of Heartfelt Blows (Dragon vol. 314) adds Fire damage equal to your Charisma (that's Charisma×2), and a Crystal Echoblade (Magic Item Compendium) gains bonus Sonic damage if you're using Bardic Music. The harmonizing magic weapon enhancement (Magic Item Compendium) allows you to attack and use your music together more easily. In combination these can turn a Bard into a very potent melee character, while still distributing considerable bonuses (through the above stuff) to the rest of his party. Use Song of the White Raven (Tome of Battle) to multiclass Bard with Crusader or Warblade for even more martial prowess.
Diplomancy, or just Suggestion
Diplomacy, if you use the rules straight from the book, is absurd. It's not very hard to make the check necessary to make even your most heated rival fanatical to you (DC 50). Most DMs don't run Diplomacy this way, and even if you do, a real "diplomancer" quickly becomes dull since everyone is supposed to always do what he wants. Still, never underestimate the power of convincing someone to do what you want.
If you don't want to rely on Diplomacy, which are probably governed by ill-defined houserules, fascinate and then later suggestion are extremely potent abilities whenever you've got to convince a crowd of anything. If you haven't, read Julius Caesar, Act 3, Scene II ("Friends, Romans, countrymen, lend me your ears") for just how amazingly awesome this can be. Sure, he used Diplomacy, but the Bard doesn't even have to.
Spellcasting
Don't underestimate the Bard's spells: they aren't a Cleric's or a Wizard's, but they're really quite good. They make a Bard flexible and adaptable.
Some great choices include summon instrument and the aforementioned inspirational boost, as well as grease (see why), glitterdust, heroism, phantom steed, freedom of movement, etc. etc. The various image spells are amazing. Invisibility is never bad. And so on.
Glibness
Glibness gets its own section. Hell, for that matter, glibness got its very own Order of the Stick comic! This spell is stupid-amazing. +30 to Bluff, on a high-Charisma, high-skill class, means almost nothing that isn't actively using magical truth-detection abilities is going to fall hook, line, and sinker for even the most preposterous lies. If you cannot think of awesome ways to use this, you're not trying hard enough.
Prestige Classes
There are more awesome Bard-related prestige classes than you can shake a stick at. Lyric Thaumaturge (magic+songs), Virtuoso (magic+better songs), Urban Savant (lots of really nice city-themed abilities), Sublime Chord (9th-level spellcasting as a Bard), Warchanter (powerful new songs) etc. etc. The list really does go on. You've even got weird things like the Battle Howler of Gruumsh (faster Inspire Courage progression).
Comment: @lisardggY: I not only notice that, I pointed it out in the very beginning of the answer. Core-only Bards are at a disadvantage, true, but then so are everyone who isn't Cleric, Druid, Sorcerer, or Wizard. The Core spell lists for those classes are incredibly powerful; the Core options for every other class are decidedly mediocre. Bards are doing *better* than most thanks to their spells. Mostly, though, balance in a Core-only game in the face of competent optimization is impossible. The PHB is *by far* the most imbalanced book WotC published for 3.5.
Comment: @DanB If a wizard doesn't use spells, he's weak too. If a fighter doesn't have a weapon, he needs to hide too. I didn't say being a bard automatically makes you powerful: I said there are plenty of options to make a bard powerful. As for having many books, that's acknowledged, but also applies to **everyone** except full-casters. And high level? Inspire Courage is at 1st. *Inspirational boost* is at 2nd, Song of the Heart 3rd. *Suggestion* too. Where is high-level coming into this?
Comment: @Miniman Yes, so you perform Dragonfire Inspiration first, stop playing that (and get 5 rounds of it lingering), then play Inspire Courage.
Comment: Yes, but in practice my bard players don't *do* that stuff.  The last bard player I had was in a campaign that started at third level.  She wasn't casting *inspirational boost* or using *snowflake wardancing* or *suggestion*.  What she was doing was hiding behind the fighter, because she had no weapon and no combat-useful spells, because she'd assumed that wouldn't be necessary for a Diplomacy-focused character.  In the meantime the fighter was being effective and useful, even though you've dismissed fighters as being "decidedly worse" than bards.  After two sessions she quit the game.
Comment: I think the advice you are giving is well-suited for high-level games played by very experienced players (with, as you say, lots of books allowed).  I don't think this advice is useful in campaigns which don't meet those criteria.
Comment: Have you noticed that most of the cool feats and powers you describe come from splatbooks, obscure Dragon articles and the like? Doesn't that leave base-rulebook-only bards at a disadvantage, which would explain the lack of love they usually get?
Comment: @KRyan Ah, right. Clever.
Answer: A single, lone, non-multiclassed bard, is nowhere nearly as powerful as a Wizard, Cleric or Druid, especially in Core (but see below). Still, he is much more versatile than a fighter and it is a property of individual game and individual player if a character/class suffers more from a lack of raw power or from a lack of versatility.
Bard's roles are social, versatility and force multiplier. The first and the second of these are very strong, but depend on the game. The last depends on the composition of allied force - he can add a lot to a field battle, with lots of knights, henchmen, and mounts (more than plus-minus several knights), but not so much to a small band of magic-users who do not rely on melee to fight.
Answer: The real answer is that a core bard depends on the nature of the campaign. The fascinate ability is extraordinarily powerful because it used a skill check as a save DC. And bards can pump their skill check through the roof. Fascinate, however, works BEFORE combat, not once it has started. So if you are playing in a hack and slash campaign, the bard is going to be a generalist and at best a nice 5th wheel for the party. But if your DM encourages role playing and intrigue, then the bard can be horribly overpowered when tossing suggestions on top of the fascinate.
I personally like bards as a choice for a cohort with my Leadership feat, since you want a cohort to kind of be able to do a little of everything.
Comment: Hey, welcome to the site! It's a solid answer (and mine does not spend enough time on the core-only bard, I'll admit), so have an upvote! When you get a chance, you should take a look at our [Tour](http://rpg.stackexchange.com/tour), and when you've got yourself 20 Rep (and you're halfway there with my vote), you should feel free to join us in the [Chat](http://chat.stackexchange.com/rooms/11/rpg-general-chat)!
Answer: Yes and no.
Bards are designed to be flexible; they're a jack-of-all-trades, with an emphasis in being The Face.  They have magic - but they're weaker than wizards and clerics.  They can have rogue skills - but they're weaker than thieves, because they have multiple important stats and can't just max out dexterity. They can fight - but not as well as fighters or even rogues. And as the bard levels up, those party-wide bonuses start to pale in comparison to having the bard do something other than sing in combat. You can focus in one aspect or another, and get a bard who is great at, say, magic, but they still won't be as powerful in that aspect as, say, a wizard who focuses on magic. But the fact that bards can take almost any role is their prime strength.
If your party lacks a role, then bards can do it - just not quite as well as a character dedicated to filling that role. The trouble with bards in D&D is that the system rewards specialization more than generalization, and bards are generalists. If they're on their own, then they're less likely to be stuck because they can't do something, though they may have problems doing it well.
Bards are The Face
Between bardic knowledge, high social-interaction skills, bardic music, and their sheer reputation, bards are good at persuading people to go their way. People want to be remembered well in bardic songs, and don't want to be vilified by a bard's next original song. Bardic knowledge lets you know what tack to take with people: is the duke insecure about his title? Are those ruins just ruins, or do they have a long history? Bardic knowledge can also short-cut some puzzles or clues, though it won't hand you the quest objective.
Of course, this makes a bard's powers dependent on the GM: if they ignore the (somewhat broken) Diplomacy rules, and don't include any situations where talking will help, and run roughshod over the players' attempts to get information out of an enemy, then all of those bardic powers won't do much; bards won't be very effective in a pure dungeon crawl.
But if your GM likes to include intrigue, skulduggery, persuasion, and talking in the campaign, then a bard far outshines what its mechanical numbers say on the character sheet. A few well-turned phrases at the right moment can end a war or topple a kingdom, and bards are the kings of well-turned phrases.
Answer: I think a lot of people seriously underestimate the aforementioned "force multiplier" effect.
Plus one to hit and damage, for example (or higher for higher levels), on every single one of your characters using a weapon definitely can add up over the course of a combat.  A mass buff, so to speak.  The ability to fill any breach at least adequately can be tremendous.  Having played several bards, when the cleric goes down ... The bard can heal him, get him back up and running.   Not as well as the cleric, but well enough.  There is a breach in the frontline?  A bard can plug the hole.  Not as well as the fighters, but well enough.  And so on.  A bard is also a good skill monkey, and especially as the levels accumulate, a potential source of information in just about any field that another player isn't already covering.
Answer: In a high-level campaign, with access to lots of expansion books, bards can be an effective class.  (If nothing else, they are a spellcasting class, and spellcasting classes become very powerful at high levels.)
However, when a player is new to the game, if they build a low-level bard character it is likely to be a flat-out non-combat character.  (Reading the bard character description, they can get the impression that a bard's role in combat is to spend the whole time singing Inspire Courage while the rest of the party does the actual fighting.)
This might be a good fit for some campaigns (those that contain no combat or very little combat) but in other campaigns it can be unplayably bad.  The character might get less unplayable at higher levels, once it starts getting good spells, but many players will get frustrated and quit the game before that happens.
The stereotype of bards being weak probably comes from observation of low-level high-Charisma bards in combat-centric adventures.

Let me offer a specific example.
I had a player who played a paladin character; it was an effective and useful character and she had fun in my game.  In the next campaign she played a druid; it was an effective and useful character and she had fun in my game.  In the campaign after that she played a bard.
We started at third-level, as is usual.  We got into combat and she didn't have anything to do; she didn't have any useful spells, she didn't have a weapon, and she hadn't thought that would be a problem for a Charisma-based character focused on the Diplomacy skill.  She spent the whole time hiding behind the fighter.  After two sessions she stopped showing up and I never heard from her again.
When I say "the bard class is too weak", this sort of experience is what I am talking about.
Answer: The question is problematic, because "weak" is arbitrary and dependent upon situation.  Spellthieves are "weak" when fighting fighters but "strong" when fighting spellcasters, especially those that depend on buffstacks.  A so-called "Tier 1" wizard is useless and more or less helpless in an antimagic field.  Its not a linear spectrum progressing from weak to strong.
Bards are largely dependent on the teammates that they make stronger.  The more allies the bard has, the more pronounced an effect he has.   This is also true of "aura" users like marshals or dragon shamans. A solo bard is relatively ineffective; in a party with a Conjurer who focuses on summoning and a druid with animal companions he is terrifying.
In combat, bards lack damage-dealing benefits other than the buffs they share with teammates, most of whom can exploit them better than the bard can.  But they have a decent BAB, light armor and proficiency in the exotic weapon the whip, which is the best tripping weapon in the game; a bard who goes with Combat Expertise and Improved Trip can be an effective defensive fighter to protect soft arcanists from melee, and an use healing magic to patch them up in an emergency.
Conversely, bards are surprisingly effective as anti-casters as well: the bard spell list is full of great anti caster spells like glitterdust and dissonant chant.  They have the stealth skills Hide and Move Silently and the points to make them work, although they lack the Evasion ability that makes other stealthers so deadly.  They can also counterspell pretty well and use a variety of spell trigger items for specialized uses, courtesy of being the best Use Magic Device skill of any class.
Even more than his buffs, the information spells a bard can use are invaluable.  Know Vulnerabilities and Know Opponent are amazing.
As a PC, bards are often considered unfun, but I disagree.  A bard always has something to do.  Specialists inevitably end up in situations outside their forte where they can't contribute much; this never happens to bards.  They always have something they can do that moves the party forward; even if someone else can do that thing better.
Comment: " Its not a linear spectrum progressing from weak to strong." That much you got right: it's an **exponential** spectrum, not linear. For a given op level and level of strategic/tactical play, effectiveness at achieving objectives is reasonably approximated as being proportional to the second or third power of the highest level of spell the character is capable of accessing.

Are 3.5 Bards mechanically weak?


Does Ubuntu only work on Desktop PCs?

Question: On the download page for Ubuntu it says "Download Ubuntu for your desktop". Is ubuntu 12.10 only compatible with desktops? Or does it work with notebooks as well?
Comment: No.  I run it on my laptop (with a Wacom Digitizer screen), and in a virtual machine just fine :-)
Comment: In addition to the helpful answers, Ubuntu also works (with the right hardware) on touch-screen tablets. There are even Ubuntu TV and Ubuntu for Android in development.
Comment: Laptops have more individual hardware that can throw up problems in my experience. Desktop/towers have more generic thus better supported hardware.  I stand to be corrected...
Answer: You can use it on a desktop.
The "desktop" is actually a misnomer. It will work on laptops quite well. In fact, I'm using it on a laptop right now.
The term "desktop" is only to distinguish it from "server" edition where it has no GUI and only a terminal. That will work but it is not useful for a non-server-class user.
You can look in the official resources to know if your hardware is fully supported and avoid any surprises. Look in the wiki page or the certified hardware page. You should note graphics cards, and wireless, especially.
After this, download the file, burn it, and boot it!
I hope you'll enjoy Ubuntu.
Remember that if your processor is 32-bit, you'll need the i386 (32-bit) edition of Ubuntu.
I also want to note that Ubuntu will work on tablets, thanks to Paddy Landau's comment:

In addition to the helpful answers, Ubuntu also works (with the right hardware) on touch-screen tablets. There are even Ubuntu TV and Ubuntu for Android[to install on Android devices, not referring to what kernel and system libraries power the OS] but  in development.
Answer: No.
The reason that edition of Ubuntu is called "desktop" is because it comes with a graphical desktop (by default).  A "graphical desktop" is what you are familiar with if you have used most modern operating systems such as Windows or Mac OS.  It means that there are windows, icons, menus, buttons etc all sitting in a virtual "desktop" on the screen, and that you use a mouse or other pointing device:

This is to distinguish it from the "server" edition which does not come with a graphical desktop by default.  Instead, on a server you typically interact with it via a text console:

So the "desktop" refers to the desktop you see on-screen when you boot the OS, not to the fact that it runs on a desktop computer.  The desktop edition is the same edition you should use for desktop computers, laptop computers, notebooks, netbooks, and so on as long as they're compatible (and if they run Windows 7, they probably are).
I can see how this confusion occurred, and possibly Ubuntu might need to think about how they convey this to people new to Ubuntu, and whether they need to reconsider the names for their editions.  For example, if instead of calling their editions "desktop" and "server", they could call them "Ubuntu for users" and "Ubuntu for servers".
Comment: Or how about just calling it "Ubuntu"?  You don't see windows specifying it's for "Desktops".  The Server edition can just have the extra title tacked on.
Comment: That is also a possibility.  While I'm sure Canonical would not want Ubuntu's server edition to be seen as secondary to its desktop edition, I'm sure that practically, those using Ubuntu on a server would be capable of finding the non-graphical installer.
Answer: It works for both laptops and desktops.
Answer: Desktop here is a synonym for GUI that you can see in your laptop or pc.Unlike desktop there is a another version which primarily can be used for server,it does not contain any GUI.
p.s: rightly explained by @neon_overload
Answer: Desktop is basically a computer with a display, keyboard, and mouse (or equivalent).  This is the same paradigm that
I use the same distribution on my desktop and laptops.
The server edition is the same but it has different tools installed.  The netbook version is also the same but with fewer installed goodies.
Tablets are a bit different, but Ubuntu interface seems to be moving toward tablet/surface type interface and away from focus on supporting the legacy desktop paradigm, but that is just my opinion.
Comment: I think you accidentally forgot to
Answer: No, Ubuntu can work on a desktop, laptop, and netbook. If you have a netbook it may run a bit slower, and you must be up to date with your netbook. But, any laptop or desktop should work.
Answer: Ubuntu work on any IBM PC (anything that is called PC whether "Desktop", "Notebook", "Netbook", with Intel CPU or with ARM CPU's).
There are Ubuntu versions prepared for running on Android phones too.
And if you have know-how you can run Ubuntu on some tablets too.
There are also Ubuntu version for servers and for cloud too.

Does Ubuntu only work on Desktop PCs?


Looking for web and desktop tools with GML support

Question: I am a graduate student and a novice in GIS field. I have few GML files that contain vector polygon data and I want to see them in a map format. The problem is that I do not have access to ArcGIS/Grass GIS software installed in my machine. I am wondering if there are online GIS website where I can upload my file and visualize it. Also is there any simple and small size free/open source software that I can install on my computer?
Answer: A great GIS that has a huge amount of functionality is QGIS.  It is very easy to install especially if you use the osgeo4w installer (Windows).  You can use it to view your GML file too.
OSGeo is the place you want to look for OpenSource (free) GIS tools and libraries: http://www.osgeo.org/.  You will find a ton of stuff here plus links to QGIS and other desktop mapping tools (scroll down to the links on the bottom right of the page).
Answer: Look into using ogr2ogr to convert your files to another format. There's a lot more support for KML and GeoJSON in the general open-source GIS world than GML.
Answer: If you're a programmer, there are lots of ways to visualize GML files with Google Maps and other Map APIs. Here's an example library for Google Maps JavaScript.
Answer: I can recommend Gaia 3.4 (The Carbon Project). It is free, and it supports a lot of different formats including gml. I use it, whenever I have trouble with WMS or WFS because of Gaia's great compatibility with these formats.
Reagards from Steen


What type of information can I get from the waveform and the spectrum of audio?

Question: If I have the spectrogram and waveform of a clip of audio what sort of information can I gather by looking at those two things?
Answer: I'll start from the very beginning: sine signals.

Also known as pure tones, these kind of signals are periodic (i.e. repeat the same pattern over and over again). Anything that is periodic can be said to have a frequency, which is in fact f=1/T, being T the period. If you look at the image, you can see that the period is 2*pi and therefore frequency is 1/(2*pi) Hertz (Hz).
This one is, in fact, a time domain signal. A waveform. In this examples it's pretty easy to compute the frequency, but it isn't always like that. So the only real information you can extract out of it is the amplitude at each moment.
Sine waves contain a single frequency and, in fact, sound like this. If we apply the Fourier transform to a 200 Hz, we would get the following spectrum:

This means, roughly, that the signal's whole power is at 200 Hz. I will get more deeply into that later.
Speech, or music, are far from featuring just one frequency. You can easily distinguish a note played by an electric guitar from that very same note played by a trombone. Same musical note means same fundamental frequency, so there must be more frequency components. That would not be a pure tone, but a some of some of them. Look at what the signal looks like when you sum to sines (first row, a is time domain and c is its spectrum):

So now we have a time signal that seems periodic, yet more complicated. If we look at its spectrum, we now see two frequency components.
So let's generalize. According to Fourier's theories, any signal can be decomposed into infinite a sum of sine signals. If a sine signal had one component and its spectrum had one impulse, two sines had two impulses... infinite sines means a real spectrum, showing the most powerful frequencies as higher components. Infinite vertical bars mean "so many that you can't distinguish one from the other", so the plot appears to be a single one.

Now, let's get to practice. You can open any song in Audacity to have it plotted in time domain. If you select the whole song and plot its spectrum (Analyze > Plot spectrum...), what do you see? Well, you will probably see some sort of plot that means almost nothing. What would you hear if you played all the notes of a song at once? In the bottom row of the previous image, the two distinct sine signals happen at different moments but, as the spectrum of the whole signal was taken, it seems that it happened at the same time. So the same happened here: it's like printing a book in a single page.
So the real interest is taking a small sample of the audio (let's say, 0.1 s) and plotting its spectrum. Now we will see what's happening in that time lapse. You can, for example, see if low frequencies (bass) are too loud.
An interesting experiment is to take a brass instrument and plot its spectrum. You have samples here. As you are analyzing a single undistorted instrument playing a single note, you can see its harmonic structure: if you have taken a Tuba playing F2 (87 Hz), its harmonics would be 87*2=174, 87*3=272, etc.
But, in general, as I said, the most interesting information appears when you take a little time lapse. Wouldn't it be great if some sort of software looked into every little fragment and plotted it to you? That's the spectrogram, which shows how much power is into every frequency at every moment.

An example: this is the spectrogram of someone saying "Rice University". The spectrogram has a bunch of info impossible to obtain just looking at the waveform, i.e. the frequency components contained in each phoneme.

"R" sounds bassy, so has strong low frequency components.
"i" is a vowel. Those have an harmonic structure similar to the tuba's previous example.
"c" sounds like "s" which contain pretty high frequencies.

etc. This is this way up to a point that if an experienced phoneticist looks at an spectrogram can indeed "read" what the person said.
Comment: this answer is absolutely amazing. I had great pleasure when reading it! Thanks a lot!
Answer: Here below is an image of a waveform (top part) and a spectogram (lower part).

Waveform
This is a two-dimensional graph where the amplitude of the signal (your audio) is shown over time. The amplitude is interpreted as the volume, so you see your total volume progression over time.
Spectogram
This graph has three dimensions. X-axis is the time, Y-axis is the frequency and the colour represents the amplitude of the signal.
Here below is a simple example to show you how the spectogram works.
First a 400Hz tone over the duration of 8 seconds:

You see that the lightest colour (highest intensity) is on the 400Hz line of the Y-axis. Some other frequencies slightly higher and lower than 400Hz also exist in the tone, but those have a lower intensity (darker colour) and are not the main tone.
Now a 200Hz tone shows the same behaviour. Highest intensity at the 200Hz frequency:

If I play the 400Hz and 200Hz tone simultaneously I see on the spectogram that both the 400 and 200Hz have a high intensity.
Comment: I am a bit puzzled by this one - a pure 400Hz tone should not show other frequencies above and below the 400Hz line at all. Your spectrogram output shows frequencies of up to 100Hz either side of that midpoint - this is not normal!
Comment: This might be caused by the way I produced the 400Hz tone. It was through Ableton Live (with which I'm not very familiar). But it was more to show an example of what a spectogram would look like and how to read it, and I think that is achieved in this answer.
Comment: @DrMayhem I've looked into it and apparently the other frequencies are not there at all, my spectral resolution was just to low. I've changed it now from 512 to 8192 in Adobe Audacity and this gives me more precise spectograms. I will update the answer, thanks for pointing out the error.
Comment: Lovely - the graphs look like I'd expect now :-)


Is there any level design copyright?

Question: I am planing to develop a game, in fact a puzzle game, I have changed the graphics but the level design is all the same. For example, the original puzzle game have five aliens as the obstacle in the human way to airship, the aliens spit fire on human. So here I have changed the alien to chameleon, with same positions(the aliens position never change so as the chameleon's ) and exact strike range(stick its tongue out to catch) and exact measurement(tile) and also converted the human to honey bee. So my doubt is that will there be any issue on this, for I am rendering the exact level design? ( I have searched, but didn't get a precise answer for my doubt)
Comment: It sounds like you're trying to rip-off their game... That would favor them in court.
Comment: I suppose the bigger question is why are you copying another game like this anyway.
Comment: Why don't you just make your own levels? Why bother copying theirs?
Answer: First: I AM NOT A LAWYER, THIS IS NOT LEGAL ADVICE.
Second: I recommend checking out this question:
I think it is important to note here that 'They' can sue you for really whatever they want in terms of Copyright. Of course, you can get a frivolous case thrown out, but all they need is reasonable belief that you infringed upon their intellectual property to file suit at that point it becomes your legal department against theirs.
When you copyright something, you copyright the execution. Either way, it seems that you would be straddling nicely on the bounds of a lawsuit.
Of course, there is also the Copyright and Trademark office's new-ish stand on being able to copyright game mechanics. So like all legal questions, the best advice I can give is that you GET A LAWYER.
Oh and remember, even if the game mechanics can't be copyrighted, they may still be patented. Likewise, they could also have a design patent on how stages are set up.
Links:

How closely can a game legally resemble another?
http://www.sloperama.com/advice/faq61.htm
http://www.sloperama.com/advice/lesson39.htm
Comment: Just a note about the "if you change 25%" part; that is incorrect. If you change any part of an existing asset set it is a derivative work and still infringing. You would have to remake everything from scratch no matter what.
Comment: @Coderanger thanks for clearing that up, I'll remove that part.
Comment: I think the "they can sue you for whatever" is very good advice. Even if you are in the right, getting sued will cost you in lawyer fees, time and stress. I would just avoid things that might have a chance of inviting a lawsuit :)
Answer: You may possibly. I am not entirely sure, but to be completely safe it could be good to alter the positions as well.
Then there is no way there can be any legal doubts, since you're just developing a game similar. ;)
Comment: It could still be argued to be a derivative work. http://en.wikipedia.org/wiki/Derivative_work
Comment: That he's developing a game that happens to have enemies that have ranged attacks, with the same ranges as an existing game?
I can see how it would be derivative if it were the same positions. But if they were changed, then surely there would be no issue?
Answer: I don't think they can sue you over positions. They don't own those pixels and as long as you're not using any of their code/assets/names etc you are fine.
Answer: While the other answers support the idea that the legal issues are a bit vague and you're probably fine, there's another issue here.  Ethically, this may be plagiarism.  If you're doing this as an exercise to improve your skills, or replicating a game that is no longer available, it might be fine.  But if you're making a game for general release for love or money, this is a bad idea.
The players who would like your game are likely to have played the original, and if they liked the original, they're probably going to think badly of you for having copied it.  If they didn't like the original, they won't like your game anyway.  It's far better, in my opinion, to expand on the original game with your own level designs and maybe some new gameplay elements.  From an ethical perspective, it's also a better idea not to lift so directly from another person's work.
Answer: Any good answer would require discussing the precise nature of the existing work as well as your intended use.  The three types of legal protection you should consider in the US are copyrights, patents, and trademarks.  Trade secrets should not worry you unless you are truly a badguy and have stolen inside info, for instance by hiring away a former employee / consultant of your competitor and pumping them for it.
Game graphics, text, music, and the like are subject to copyright in most jurisdictions, including the US.  Original computer code is always copyrighted, without any further action on the author's part.  Affixing an original work to a medium is all it takes to create a copyright in the US -- registration is helpful for various purposes (such as to document a security interest for a loan, or to fix a date for litigation purposes) but not necessary.  A game design may be patentable if it is sufficiently novel and non-obvious, but a game design or mechanic is not automatically self-protecting as such without a patent application.  Very few computer game makers seek specific patents on individual game designs, although an increasing number of major companies are patenting generally useful game-related mechanisms (wiimote-related stuff; gesture controls; etc.).  Interestingly enough, board games are quite frequently patented, and in fact it is easier to patent a board game design than it is a more free-form computer game.  Trademark protection could apply to distinctive characters (Mario & Luigi) and the game's packaging itself (the look of the "box" or website delivery and advertising scheme).
You can avoid running afoul of copyright protection by making sure to, among other practices: never use code from another game without a license, and always vet your third-party / outsourced code with a plagiarism detector; always write your own music or license it officially; create your own art assets or license them; if you are including referential material, make sure it is clearly a satire/parody or otherwise fits within a legal exception.  For patents, unless you know of a patent that reads into your area, you should probably use your instinct as to whether your game mechanic is ripping off another developer.  For instance, just b/c Donkey Kong pioneered the platformer mechanic does not mean that all future platformers had to license the idea; it is safe to assume that game design involving jumping and dodging is not in fact patented or patentable.  The reason that most people do not conduct an exhaustive search for infringed patents before building something is that there is a huge sea of patented material out there, and if you knowingly infringe on another's IP, you can be subject to a claim for treble damages, whereas if you unknowingly happen to infringe a patent that you were not aware existed, you are only liable for 1X damages and therefore a license negotiation will be much more favorable to you.  Finally trademark -- avoid using art assets in the game, and external marketing / packaging, that is confusingly similar to your competitors'.
I see a lot of amateur legal advice in response to these kinds of questions in forums, and it is usually hit or miss.  At the end of the day, if you are really concerned (and it sounds like perhaps you should be) you ought to discuss the specifics of your case with a knowledgeable lawyer.  If you can change a few things so you are not so closely mimicking another game, then perhaps that will be easier and cheaper than hiring a lawyer to analyze a close call scenario.
Hope that was helpful.
Zeke Vermillion
Comment: Please edit your answer to look like an answer.  Currently your answer looks more like an editorial in the opinions page.  Just drop the salutation and the closing.
Comment: Especially the Dear Anon part.

Is there any level design copyright?


Problems with WSP Deployment

Question: We have a server farm that is having issues deploying WSPs. The odd thing is that the server goes through all the motions of deploying the WSPs with no errors. That is, the job is scheduled appropriately. I can see the status change on the Solution Management page from deploying to deployed. There are no errors in the trace logs or event viewers. However, the 12 hive only contains files that existed prior to the upgrade. This is also the case in a retract,delete,add,deploy scenario.
Note: Our server topology has changed over time. Our Central Admin machine reached its End of Life, so we added another server to the farm, moved the central admin with the stsadm tool, and removed the old server from the farm.
Here is what I have tried:

Deployed to two other farms:
successfully deployed new files
(rules out WSP as the problem).
Restarted OWS Timers on both WFE
Restarted both Machines
Verbose Logging

The one difference here is that on the server farms that work, you see individual files being deployed. On the server farm that doesn't work, the logs show that the system checks to see if it is deployed and that is it.

Ran preupgradecheck to check on server farm health with no errors
Checked the databases (namely config) to see if there are quota/growth/space issues. There were no errors.

What else can I check? Typically, we can use the errors in the logs as a basis for research, but without something to go on, I'm striking out.
UPDATE:
I tried two more debugging steps that might be helpful in the future but did not produce results in this case:

Retract, Delete, Add, Deploy Solution - left with the same files as I started
Run ProcessMon while upgrading the solution - I could see where the cab was unpacked in the temp directory, then promptly deleted.

Finally, we were lucky enough to still have the soon to be decommisioned server that previously ran Central Admin (Server1). So, I added the server to the farm. Removed the Central Admin from the new Server (Server2). Added it to the old server (Server1). Deployed the WSP. On the Solution Management page, two of the three front ends deployed successfully (Server1+Server3). I ended up having to remove and re-add Server2 from the farm. Then move the CA back and remove Server1 from the farm.
All is now well.
Comment: @MBSurf: It would be great if you could move your solution into answer. Otherwise the system will forever think it is unanswered!
Answer: Have you tried removing the files in the hive and redeploying the wsp? Just to make sure nothing is wrong with the files themselves.
Do you get any warning in central admin that your frontends are not in sync?
Comment: I re-ran the deployment using ProcessMon and did not see any attempts (failed or otherwise) to write to any directories in the 12 hive.
Comment: Judging from the updated question (with the answer) his WFE or Central Admin servers were out of sync, so I think this is a good answer.
Answer: To roll the dice...
Are you able to deploy any WSPs at all now?
Alternatively, can you manually install a feature without wrapping it in a WSP?
Comment: No, I was not able to install any WSPs at the time.

Problems with WSP Deployment


On bent combining functions

Question: Bent functions are Boolean functions with maximum nonlinearity and are widely studied for their potential applications in cryptography. Let's say you want to use a simple $2$-input AND gate as a nonlinear combiner for the outputs of two linear feedback shift registers. Because a $2$-input AND gate is a bent function, is it technically correct to call the output sequence of this combination generator a bent sequence? I need to know this for a paper I am writing.
Answer: No.  As far as I can tell, this does not appear to produce a bent sequence.  (Or, if it does, that fact requires proof/justification.)
According to Wikipedia, a "bent sequence" is a sequence of the form $(-1)^{f(x_0)}, \dots, (-1)^{f(x_{2^n-1})}$ where $x_0,\dots,x_{2^n-1}$ is the sequence of $n$-bit values in lexicographic order and $f$ is some bent function.  That's different from what you are mentioning.  If what you're mentioning happens to fit this definition, that fact is far from obvious.
I don't know if this is the same definition of "bent sequence" you are using.  If it isn't, I suggest editing your question to include the definition you are using.
Answer: Bent functions can be obtained from linear feedback shift registers but not by the method that you propose. In fact, the method you propose (using an AND gate to combine the output
of two linear feedback shift registers) will not give you a bent function.
Bent functions (though not by that name) were studied for use as signature sequences
in direct-sequence spread-spectrum communications. In the literature on this topic,
such sequences are called the small set of Kasami sequences.  The sequences are
of length (or period) $2^{2m}-1$ and can be obtained as the (XOR) sum of the outputs
of two maximal-length linear feedback shift registers (LFSRs) of lengths $2m$ and $m$ respectively. The feedback polynomials of the LFSRs thus are primitive polynomials of degrees $2m$ and $m$ respectively, and they produce maximal-length LFSR sequences
($m$-sequences) of periods $2^{2m-1}$ and $2^m-1$ respectively. Thus, $2^m+1$ copies
of one period of the shorter sequence get added into one period
of the longer sequence, and the result is of
period $2^{2m}-1$. A total of $2^m-1$ distinct sequences can generated by using
a fixed nonzero initial loading of the longer LFSR and $2^m-1$ nonzero initial
loadings of the shorter LFSR.
Note that one cannot choose both feedback polynomials arbitrarily.
If the longer polynomial is chosen as a specific primitive polynomial of degree
$2m$, then only one primitive polynomial of degree $m$ will give you a small set
of Kasami sequences.  If the shorter polynomial is chosen first, then the longer
one must be chosen from a subset of the  set of all
primitive polynomial of degree $2m$.  For more details, see the paper
D. V. Sarwate and M. B. Pursley, "Cross-correlation properties of pseudorandom and
related sets of sequences," Proc. IEEE, May 1980.
The set of sequences thus generated are of period or length $2^{2m}-1$ whereas
the description of bent functions says they are of length $2^{2m}$.
To relate this to Wikipedia's version, consider the Boolean function
$$f(\mathbf x) = f(x_1, x_2, \ldots, x_2m)
= x_1x_2 \oplus x_3x_4 \oplus \cdots \oplus x_{2m-1}x_{2m}.$$
Wikipedia'a definition says that the bent function is the sequence
of values of $(-1)^{f(\mathbf x)}$ as we cycle through the $2^{2m}$
values of $\mathbf x$ in lexicographic order. A sequence from the
small set of Kasami sequences cycles through all the nonzero
values of $\mathbf x$ in a different order, usually in what might
be called shift-register order (successive contents of a
length-$2m$ maximal-length LFSR) or Galois-field order
(polynomial representation of successive powers of a primitive
element of $\mathbb F_{2^{2m}}$.  So, if you need the
symbols in Wikipedia order, you are going to have to do
a permutation of the $2^{2m}-1$ bits from the output
of the XOR gate that adds the two seqeuences and prepend
a $+1$ to get the missing $(-1)^{f(\mathbf 0)}$.

On bent combining functions


Is the connector the only difference between a Cinema Display and a Thunderbolt Display?

Question: Is the connector the only difference between a Cinema Display and a Thunderbolt Display, or are there other features that changed between the two models as well?
Answer: The Thunderbolt monitor includes a number of integrated peripherals as well as being a monitor:

Three powered USB 2.0 ports
FireWire 800 port
Gigabit Ethernet port
Thunderbolt port

The actual connector for MiniDisplayPort and Thunderbolt is the same, but Thunderbolt can pass many protocols over the same cable, not just A/V signals.
Comment: It should also be noted that the Thunderbolt display is not backwards-compatible with Mini DisplayPort Macs.
Comment: @KyleCronin: +1 That is a big caveat. Forget about trying to use your older Macs (or PC) with your new display. http://apple.stackexchange.com/questions/17960/are-there-adapters-to-use-thunderbolt-display-with-non-thunderbolt-computers
Answer: The panel, power and general design of the two screens are the same, however as Stuffe said above there are additional ports which are powered by the Thunderbolt connector.
There is also an integrated power lead for Macbook (Air/Pro) and I believe it's active power consumption is a little higher.
The Thunderbolt connector is not backwards compatible with a Mini Displayport 'port' - but of course a mMini Displayport is compatible with the thunderbolt 'port'.
Last point - you can daisychain the Thunderbolt display with an additional thunderbolt (or cinema or any other) display using the Thunderbolt output port.


Is it possible to remember a wifi network in iOS 6 without automatically connecting to it?

Question: Once in a while I need to use my iPhone 4 for work related tasks that require a lot of bandwidth. When doing this I will connect to the wireless network at work, do what I need to do, and then disconnect so that any personal activity goes over 3g. Currently my choices are to either leave wifi off while at work, only turning it on when I need to do work tasks, or join the work network every time I need to do work tasks, then forget the network. Turning wifi off is annoying since I have to remember to turn it off before I get to work, and then turn it back on after I leave work. Constantly joining the network is also annoying since I need to enter my username, password, and proxy information. Is there a way to have my iPhone remember my work network so I can manually join it without entering all my information, but not connect to the work network unless I force it to? I haven't found anything obvious on either the phone or the iPhone configuration assistant so I'm pretty sure the answer is no but it can't hurt to ask.
Comment: At least not without jailbreaking, you can't.
Comment: Still can't do this as of iOS 8, lame.
Answer:
As you can see from this screenshot, iOS will automatically join any available known network based on signal strength. As of right now, it is not possible to do what you are asking with iOS.
Answer: Yes...

Add the network to your phone.
Then touch the "i" next to the network and change "Auto-Join" to off.
Turn off wifi and then turn it back on.

You will notice that you are now on the cell network.  However, if you touch the wifi network that you just updated (in settings), you will then log into it.
Then can repeat...to return to the cell network and turn off the work wifi network (while not forgetting it)...simply turn off wifi and turn it on again and then you will notice that once again you are utilizing the cell network and not your work network...and the wifi network is not forgotten and can be used again simply by touching it (in settings).
Comment: What iOS version is this? I don't see this in iOS 7.12.


How was the UK involved in Yugoslavia during WW2?

Question: What was the role and the level of involvement of the United Kingdom in Yugoslavia during World War II?
Comment: [Documenting preliminary research will improve both the probability of an answer and the quality of the answer(s)](https://history.meta.stackexchange.com/a/785/26786)
Comment: Check out the book *Eastern Approaches* by Fitzroy MacLean. It's by a British officer who worked with the Partisans.
Answer: Yugoslavia was established before WW2 (on 3 October 1929 the Kingdom of SHS was renamed to Kingdom of Yugoslavia), but it is true that after the WW2 the entire regime changed. (During and) after WW2 there was communist republic with president Tito, named Democratic Federal Yugoslavia (1943), renamed to the Federal People's Republic of Yugoslavia in 1946.
On 25 March 1941 Hitler made Yugoslavian government to sign the Triparte Treaty. That was followed by huge protests throughout the whole country. Senior military officers were also opposed to the treaty and launched a coup d'état when the king returned on 27 March. Army General Dušan Simović seized power, arrested the Vienna delegation, exiled Paul, and ended the regency, giving 17-year-old King Peter full powers. The new government decided to stay in Triparte Treaty, but at the same time they secretly connected with GB for help in military material (GB was encouraged by events from 27 March). This government also tried to connect with Soviet Union (a pact was made to help each other).
Hitler then decided to attack Yugoslavia on 6 April 1941, followed immediately by an invasion of Greece.
The Axis Powers occupied Yugoslavia and split it up. The Independent State of Croatia was established as a Nazi satellite state, ruled by the fascist militia known as the Ustaše that came into existence in 1929, but was relatively limited in its activities until 1941. German troops occupied Bosnia and Herzegovina as well as part of Serbia and Slovenia, while other parts of the country were occupied by Bulgaria, Hungary, and Italy.
The government went to exile in London. The Yugoslav resistance forces consisted of two factions: the communist-led Yugoslav Partisans and the royalist Chetniks, with the former receiving Allied recognition only at the Tehran conference (1943). The heavily pro-Serbian Chetniks were led by Draža Mihajlović, while the pan-Yugoslav oriented Partisans were led by Josip Broz Tito. The Chetniks were initially supported by the exiled royal government and the Allies (before 1943), but soon they focused increasingly on combating the Partisans rather than the occupying Axis forces. From 1941 to June 1944 there was a British representative in Chetniks' staff. Axis helped them with material and propaganda system. By the end of the war, the Chetnik movement transformed into a collaborationist Serb nationalist militia completely dependent on Axis supplies.
In May 1943 the Partisans army connected with Axis. They got help in food, munition, medicine and so on.
The Teheran Conference (1943): The Partisans of Yugoslavia should be supported by supplies and equipment and also by commando operations.
There was some role and involvement of GB in Yugoslavia. The involvement was much bigger after the war for borders, mostly about the question of Trieste.
Sources for part of the answer:
Invasion of Yugoslavia
Teheran conference
Answer: Yugoslavia was created after WW1 (initially as the Kingdom of Serbs, Croats, and Slovenes), and as such had no reason to try and change the balance of power created in Europe as a result of post-WW1 peace treaties. Many members of the country's ruling circles were pro-British, and in March of 1941 they organised a coup d'etat. Hitler's response was to declare war on Yugoslavia. In barely two weeks, the country was overrun by Axis forces, and its government fled to exile in London.
The Communist partisans put up more effective resistance against the occupiers than the royalist/nationalist Chetniks, so the British and their allies gradually shifted their support to the partisans, even though they were communists.  The British and the Western Allies assisted with this resistance  with support in logistics, equipment, training, and air power. The decision to help the Partisans of Yugoslavia was made at a summit in Tehran attended by Churchill, Roosevelt and Stalin in December 1943


There are linear and rotary molecular motors in the cells. Do any of them have a fixed or stable frequency or speed?

Question: Are there any linear, rotary or oscillatory molecular motors in the cells which can have fixed frequeny and which can be used as a reference for elapsed time timer? This question is with relevence to my earlier question 'Is there a realtime molecular clock within the genome to co-ordinate the developmental sequences in an embryo?'
Answer: There are molecular motors but the frequency is a function of energy input (ATP); similar to the angular velocity dependence on amount of current in electrical motors.
The concept of molecular motor may not be suitable for a clock like device. There are clocks based on genetic circuits, which produce stable oscillations. Examples include the circadian clock, cell division, menstrual cycle etc.
Developmental events involve checkpoints and the timing is regulated by several factors such as number of cells, concentration of some protein etc. However, I haven't come across a master clock that integrates and synchronizes all these signals for precise developmental timing. That makes it an interesting area of research.
Answer: These molecular motors' response maybe dynamic and nonlinear. But it entirely dependent on the external influence and also the characteristics of the motor itself including number of active motors involved in operation. As it is microscopic, it will not possible to analyse by assumptions and say they have some random frequency. They do have certain frequency of operation (I do not know whether they are controlled by biological clock or some master clock but they are controlled by nucleus of the cell) and "Modeling molecular motors" explains how motors act on the filament inside the cell. It mainly talks about the influence of external force on the operation of motor and also speed(v) of the motor. The following excerpt from that paper talks about the external force on motor.

The action  of  the  motor is induced by generalized forces, which for
  the motor/filament system may be identified  as the mechanical force
  fext  applied  to the  motor, and  the chemical potential difference
  Dm, which measures the free-energy change per consumed ''fuel''
  molecule. The force fext describes external forces, for example of
  optical tweezers,  microneedles, or the viscous load of an object that
  is carried. fext could also include viscous friction forces between
  the motor and the surrounding solvent if the latter  is considered as
  ''external.'' The chemical  potential  difference Dm is for the
  process of the hydrolysis of Adenosinetriphosphate (ATP) to
  Adenosinediphosphate(ADP) and phosphate (P).

The frequency of molecular motor according to "Biophysics of Molecular Motor" has been classified into two categories:

Density controlled: In the density-controlled model, it is assumed that the depolymerization rate is proportional to the motor density at the terminal site of the microtubule. Here the frequency of motor is dependent on density of the motor.
Flux controlled: Filament depolymerization is determined by the flux of motors
to the end. Here the frequency is dependent on the flux of the motor.

In both the above cases the length of the filament on which motor is acting is also important. These models have been analysed and plotted on a graph to give a clear picture of it.

The paper explains the catastrophe frequency, the frequency at which the filament shrinks. Shrinking of of a filament is due to motor. So the paper concludes saying the catastrophe frequency is 0.5 per min for a 8um length of filament.

(Catastrophe = the transition from growing to shrinking of dynamic microtubules).
To summarize, these motors do have speed and frequency of operation but they are not fixed. They vary in a non linear fashion due dynamic environment. But the motor tries to be as much stable and resistant as possible.


SQL Server Management Studio Show last executed query

Question: I am looking for a way for SQL Server Management studio to show me the last SQL query that was run. For example, when I make modifications to a table in the designer mode, I will eventually want to make the same changes to the production DB without recreating the entire table. I'm looking for functionality similar to PHPMyAdmin for MySQL which tells you the last query ran and the results of the query at the top of the page after the modifications are complete.
Answer: If you want to know what is the query corresponding to the change you've done to a table (or other object) in designer mode, use Generate Change Script (Table Designer → Generate Change Script... or the very first icon, with a diskette and a script, in Table Designer toolbar) command.
Note that actually you don't need to commit the changes, which makes it a good medium to learn things. For example, if you've forgotten how to create a primary key which spans on multiple columns, one way is to Google it; another one is to create such key and see the change script.
If you rather want to track all the queries, not just the ones made by the designer, use the profiler (Tools → Sql Server Profiler).
Comment: In 2008 there is also a checkbox to Automatically generage change script on every save.
Answer: If you have more than one developer making changes to your schema, then you might need a tool like Redgate SQL Compare or similar create change scripts between environments.
Although more of an admin tool than a developer tool, dbcc inputbuffer({spid}) will get the current / last executed sql statement on a per connection level. It won't however return anything useful on the current connection (dbcc inputbuffer(@@SPID) returns dbcc inputbuffer(@@SPID) :P))
At a server / audit level, SQL Server Audit can assist with tracking changes to your schema.
Answer: SQL Audit could definitely catch the changes but the audit events can be a little cryptic.  LOGbinder SQL translates them into readable English.  I think the Audit Action Group you'd want to enable is SCHEMA_OBJECT_CHANGE_GROUP
Answer: WHy are you not making the changes through scripts and committing them to source control like any other code? Then you know what is supposed to be pushed to prod.


End of Tron Legacy

Question: At the end of Tron Legacy, Sam Flynn and Quorra escape with his father's ID disk.  Why are they so reluctant to leave Kevin Flynn behind when it is clear that Sam could simply get out, leave Quorra there, and come back in to rescue his father? The portal only closes from the inside, not the outside.
Answer: The whole trip would cost Sam some time and there's no telling what might happen during his absence. CLU could capture Quorra and his father or even kill them. The risk of CLU getting the upper hand and escaping to the real world is too big.
Answer: You can only exit with Flynn's disc. Sam's disc doesn't contain the information necessary to exit the Grid. We know that because when CLU examines Sam's disc he says he was expecting more and gives Sam back his disc. If Sam's disc had the ability to let him exit CLU would have kept it.
Also Sam didn't have a disc when he entered the Grid. It was only given to him after he was captured as a rogue program.
Answer: The portal is open only from the outside, and for only a limited amount of time. Once it closes no one inside the grid can open it again. Only someone from the outside can open it. That is why Flynn was trapped inside the grid for so many years.
Sam doesn't know about the portal until he finds his father. At that time they realize there is very limit time left to escape the grid. They all must travel across the bad lands to get to the portal before it closes.
A disk is not required to exit the grid. Any human can exit via the portal and ISO's are more like humans then programs so they could also exit, but I assume they didn't know that until Quorra actually tried to leave.
CLU is a program and can't exit via the portal, but there was something on Kevin Flynn's disk that solved that problem. Not only for CLU but for all programs to exit.
The key to stopping CLU was to get Kevin Flynn out of the grid. As long as Kevin was in the grid CLU would be hunting for him. Sam could have left the grid to come back later, but that wouldn't have solved anything. CLU would still have been hunting down his father's disk. Getting his father out of the grid was the only solution to stopping CLU.
The only other option was for Kevin and CLU to merge again. That would have stopped/destroyed CLU, but also kill Kevin in the process.
Had Sam left the grid he would be abandoning his father to his fate at the hands of CLU. Sam had already exposed where his father was hiding. His father had no where else to go, but for them all to try and to escape.

End of Tron Legacy


How to forward a domain on IIS on windows 7

Question: Briefly my question is about combining my registered domain with the websites listening on port 80/8080 on my server.
I have a web server IIS on windows 7 and two web sites listening on port 80 and 8080.
I have successfully forwarded any incoming request to port 80 and 8080 to my web server.
So everything works like a charm when I try to access these websites entering http://myglobalip:80/Index.aspx or http://myglobalip:8080/Index.aspx from a computer outside of the local network.
So I have a domain registered, lets say www.mydomain.com. What steps should I follow in which sequence? What should I consider to do? I need a step by step guide to follow.
I have registered my domain on Godaddy's website and only configured forwarding so the domain forward to my webserver but when I attempt to access the web page, It always try and try until It times out.
Answer: I think the best thing to do is add an A Record through the Go Daddy interface:
http://help.godaddy.com/article/680#arecs
Once you have the A record you can bind it in IIS (Right click the website, edit bindings)
and then hopefully it should work!


Can I publish a Bing map from OpenLayers Plugin in my thesis?

Question: I have QuantumGIS 1.8.0. I made a map that I'd like to use in my thesis. I made it using Bing road layer map. I found it in OpenLayers plugin. Do I have the rights to publish the map as a part of my thesis?
Answer: Here is an interesting site from MIT that discusses copyright of figures and fair use policy.  I would be inclined to accept their assertions given their status as a premier institution.
See the answer from @tmcw for a link to the Bing ToS.  Reading that, I believe that you can utilize the map in a not-for-profit academic setting.
Comment: the interesting link does not work anymore
Answer: Bing terms of use: http://www.microsoft.com/maps/product/terms.html
You cannot:

Save, download, print, distribute, transmit or manipulate the bird's eye imagery, or offer others that ability, through your Company Application.
Comment: That quote is not valid for academic use: "If you are using the Services only for Education or Non-Profit Organization Use (as defined in Section 2), Sections 1, 2, 5 and 8 apply."  It comes from section 3.
Answer: The license agreements of those "Open" layers usually only allow a private, noncommercial use. Publishing data in an academic context is somewhat disputeable as to whether the terms of conditions are violated or not.
I'd advise you to simply use the Openstreetmap (OCM) layers since they are under Fair Use and can be used in any context as long as the origin is mentioned.


May a woman freeze her ova?

Question: Is a woman allowed to freeze her own ova if she is coming to the later years of her life and is afraid she will miss her opportunity to have her own children naturally or otherwise, or is that frowned upon in Halacha?
Comment: As in all cases, I strongly encourage you to [CYLOR](http://en.wiktionary.org/wiki/CYLOR) for practical guidance rather than relying on what you may read on this site.
Answer: The worldwide experts in fertility and halacha are Machon Pu'ah.  They have a questions & answers section on their website.
According to Rabbi Elhanan Lewis (link) it is permissible with halachic supervision.
I second the opinion to ask your local rabbi, and I think it is relevant to draw your rabbi's attention to Machon Pu'ah.
Answer: I'd assume it's permitted if the woman wanted it.
Extracting and freezing the cells
I know the similar question was asked regarding taking a man's sperm and freezing it so he might still be able to father a child after, say, treatment for testicular cancer.
Philosophically it's permitted, though not required (nor particularly advocated; patient's own decision). The mitzva of Pru Urvu covers only marrying someone believed to be fertile, and going about normal life.
The concerns for a man have to do with some halachically objectionable methods of extraction.
In a woman's case, the extraction isn't halachically prohibited other than that the process can be taxing on the individual and, as it involves some surgery, contains a small amount of risk. My strong sense is that the need here far outweighs the costs, if that's the patient's choice.
What about faith?
The last question is a philosophical one: it's one thing to bank reproductive cells if, say,  the patient is about to have cancer treatment that could be sterilizing. We know there's a problem, so G-d gives us permission to use medical technology to treat it. In the case of a woman who just can't find a decent husband, should we say she should have faith rather than go through long and arduous processes?* My guess here is that the process isn't that bad, and the risk of not finding a husband in time are (sadly) non-trivial enough that it would be justified, if that's what this woman wanted to do. Again it would be wise for her to discuss the idea with a counselor and spiritual advisor, to see if this would really improve her life.
*If genetic testing was a long and arduous process, and its outcome useful only in rare cases, Rabbi Moshe Feinstein wrote that people of faith shouldn't do it (however that's not the case; go get tested for Tay Sachs and the like!)
Comment: A source for your conclusions or is it your opinion?
Comment: @Chalutzhanal That would be my conclusion, based on the halachic literature I've read on sperm banking; Rabbi Feinstein's responsum on faith vs. medical tests; and the observation that halachic questions of IVF tend not to concern themselves much with the egg-harvesting portion of it.

May a woman freeze her ova?


Does anyone know how to use TRIKE?

Question: TRIKE  is an open source threat modeling methodology and tool, as presented by the authors. After i tried several threat modeling tools and methodologies, I have the feeling that it is the only real "DATA FLOW" threat modeling as the Microsoft STRIDE is not considering the behavior data flow. Now my problem is i found no documentation on how to use trike! does anyone try it before and have some docs? or at least can give some hints on how to fill in the tool?
Comment: i found this pdf maybe help you http://homepages.feis.herts.ac.uk/~comqjs1/SSPTM2.pdf
Answer: The most current documentation already posted (by the Trike team, anyway) is in the Help spreadsheet, which you can find here:
http://sourceforge.net/apps/trac/trike/browser/spreadsheet/trunk/docs/help/TrikeHelp.xlsx
I also have a very rough draft of the documentation for how to actually do the first half of the methodology using the spreadsheet.  I am running it by some of the people who use the tools already & expect to post it somewhere on http://www.octotrike.org/ sometime next week.  I will post/update here when I post there.
If you are in the San Francisco or Seattle area and are willing to take notes for more documentation, I am willing to show you how to do it.

Does anyone know how to use TRIKE?


Determining the spin of wavefunction

Question: We all know that by uncertainty principle, location of a wave-particle is perfectly determined when uncertainty of momentum becomes infinite. (I also heard that in reality, it is almost impossible to determine the location of a wave-particle perfectly and the location has some uncertainty.)
So, what happens to spin? Spin can be superpositioned, so I am wondering what happens to spin.
Answer: Much like position is the operator $\hat x$ that has a continuous spectrum and whose predicted value has some uncertainty, the spin is the triplet of operators $(\hat J_x,\hat J_y,\hat J_z)$ that have a discrete spectrum (each of them) and they don't commute with other components, for example
$$ [J_x,J_y] = i\hbar J_z $$
which means that two (or three components) of $\hat J$ cannot be measured at the same moment (unless the whole vector is zero) and we may derive the inequality:
$$\Delta J_x \cdot \Delta J_y \geq \frac\hbar 2 \langle  J_z \rangle$$
Moreover, the eigenvalues of $\hat J_z$ or any other components are discrete numbers from $-j\hbar$ through $+j\hbar$ where $j$ is an integer or half-integer multiple of $\hat J^2$ and the spacing is $\hbar$.
In the units of $\hbar$, each component is guaranteed to be measured as integer-valued or half-integer-valued but when one component is measured, the other components are completely uncertain.
Spin is a basic part of elementary quantum mechanics so see a textbook or e.g.

Spin at Wikipedia

Determining the spin of wavefunction


What should I do when I see a non-programming question on SO?

Question: I don't have enough rep to vote to close.  Should I...

vote it down?
ignore it?
tag it notprogrammingrelated?
or something else?
Answer: Don't tag not-programming-related or similar. That's a useless tag. Either

vote down
ignore and let users that can, close it
flag for moderator attention
Comment: @sth: That's a moot point. Not programming related posts are not allowed on SO by definition.
Comment: I disagree that the tag is useless: It makes it easy for people to ignore not-programming-related posts.
Answer: I don't know how this question got bumped, but it's due for a new answer. The flag system has been extended to let you flag as 'off-topic' as a way of attracting the attention of people with enough rep to vote to close. So that's preferable.
Answer: A nicely worded message pointing to the FAQ about what is considered to be an on-topic question usually doesn't hurt.   Don't encourage a user to repost to the another site.
A nice comment will both inform the user, may discourage other people from needless down-voting, miss-tagging, and possibly help other 3k+ people decide to click close or not if they are on the fence about the question.
Comment: yes, polite comments pointing out *specifics* are always welcome, I think
Answer: The right thing to do is to vote for closing, but I realize you do not have the necessary 3000 rep to do so. I would not even flag for moderator attention, as usually a question is viewed and voted on for closing pretty fast. Flag it if it is blatantly offensive.
As Martinho points out, please do not add a useless tag. Nobody searches for it.
Answer: Call the stack overflow police!


Longest Element of an Affine Weyl Group

Question: I know that the Weyl groups of affine Lie algebras don't have a longest element, but are there any good substitutes for w_0. In particular, is there any good substitute for a reduced decomposition of the longest element?
Answer: If you look at section 4 of Thomas Lam and Pavlo Pylyavskyy's recent preprint, they study infinite reduced words in W, modulo braid and commutation relations. This is a good substitute for a reduced word for the long word in the context of total positivity, as they explain. I think it should also be useful in the context of canonical bases.
Answer: If you consider just a Weyl group, then I guess there is nothing replacing the longest element (of course, every element also has a reduced decomposition, though).
However, as pointed by Greg Muller, there are some situations when there is a good analogue, namely in the theory of twin buildings. For example, if you consider a semisimple algebraic group G defined over a field K, then G(K[t,t^(-1)]) acts on two affine buildings, which are the buildings associated to G(K((t)) ) and  G( K((t^(-1))) ). Then there is something called "codistance" between chambers of these two buildings. Two chambers at codistance 1 are called "opposite". This opposition relation shares the same kind of property, and should really be thought as an analogue of, the opposition relation in finite buildings and Coxeter complexes.
Answer: Here is another notion of a reduced decomposition for the long word, as used for example in a recent preprint of Baumann, Kamnitzer and Tingley.
Recall the theorem from the finite type case that reduced decompositions of w0 are in bijection with convex orderings on the set of positive roots. The latter notion is easier to generalise, and can be considered an appropriate analogue.
Definition: A convex order on the set of all positive roots Φ+ is a preorder ≤ such that
i) For all α, β in Φ+, we have α ≤ β or β ≤ α (OR not XOR).
ii) If α ≤ β and α+β is a root, then α ≤ β+α ≤ β.
iii) If α ≤ β and β ≤ α then α and β are proportional.
Voila.
Comment: Tigley -> Tingley
Comment: apologies to Peter if he is reading this for forgetting his 'n'.
Answer: I don't know very much about this, but I have heard that in the theory of 'buildings' (nice simplicial complexes on which Coexeter groups act), the affine Weyl groups act naturally on 'twin buildings', a pair of spaces with a notion of distance between them.  I'm under the impression a map which switches the two buildings makes a good analog of the longest word.

Longest Element of an Affine Weyl Group


Move a Trello card in iOS?

Question: It's simple to create lists and cards but I have not found a way to move a card from one list to another.
How do I move a card to another list in Trello on the iPad?
Answer: I can't tell for sure if you're using the Trello website or the the Trello iPhone app, though I'm assuming it's the web site, given the context.
I recommend you use the app, however. It allows you to tap and drag cards left and right, to different lists, and that works well.
Note that when you click on a card to open it, you can click on the list name, to open up a couple of spinners, to move to a different list, and a different position. However, in my experience, that bit of the user interface is annoyingly buggy, and I gave up using it.
(I just tried it again, and in one of my three attempts, the item I was moving disappeared completely!)

Move a Trello card in iOS?


what are the best techniques for getting back into shape

Question: i had an injury recently that prohibited me from working over for several months.  Now that i am healed, i am having a hard time motivating to get back into the gym to work out (as its not a habit,etc).  i wanted to get recommendations for the best way of getting motivated to get back in shape.
Answer: My suggestion is to start slow and don't overdo it.  Set very small, achievable goals that you can measure every week.
For instance, you could start by going for a walk every day during your break time at work and also supplement the walk with some stretching.  Stick with this for more than three weeks (so that it becomes a habit) and then add something else to the list, such as a run or some weight lifting.
You could also sign up for a class at your local gym or community center.  The regular schedule and social/group aspects of the class environment may help keep you motivated and also give you a place where you have to be.
My local gym runs a bootcamp in the Spring, Summer, and Fall, and I am seriously considering taking it myself because I'm having trouble staying consistent at my gym.
Comment: Being with like-minded people is definitely a motivator.  Esp. if they challenge you when you slack off.  They aren't doing it to be mean, it's usually coming from a good place.
Answer: I'd like to use this opportunity to warn a fellow man about what happened to me when I was in a similar situation.
As you said, I have had a big pause and when I got back to working out, I did a huge mistake. the thing is: my muscles were still 'strong', capable of lifting great weights, but my joints weren't capable of holding those weights.
So what happened? After a 30 minute exercise, when I got to biceps, I started with almost the same weight I was working out with before the gap. My biceps was strong, so it was pretty easy, but after about 8 reps, my wrist "exploded with pain" and I couldn't work out for another 2 months after that. It hurts till today and I think I'll never really get it back to its normal state.
Hope this helps. Take care, learn from mistakes of others!
Comment: Yes! (Been there done that too!!) When going back to the gym, it's perfectly ok to start at a lower weight than when you started. Don't worry though, you will be back to your normal weight soon enough :)
Answer: Motivation is tough.....what motivated you prior to stopping? and has that goal(s) changed?  Everyone gets/is motivated differently, I like to write my goals down and visualize what it is I'm going for.  Some people get motivated by being in groups (social), others by watching movies (try a Rocky movie).  What it comes down to is that it's easy not to do something or coming up with a reason why - twist it around, just do it and unless you can come up with 5 good reasons not to, continue.  Make it a routine and over time you won't even think about it.
Answer: Motivation?  Determine 3 reasons short term and long term why you want to spend your time in the gym instead of munching potato chips on the couch.
Write those reasons on paper.
Put copies of that paper everywhere - mirror in your bathroom, on your bedroom door, in your car.
Read it everytime you see it and GO TO THE GYM.
In the gym, start slow and progressively build intensity.
Here are some great motivational quotes.