A critically wounded soldier who recovers gets a permanent Will penalty due to the psychological trauma. Does this stack for each time the soldier has to recover? If so, what's the limit on how low a soldier's Will can go? Does the penalty eventually stop stacking? Do low-Will soldiers always die instead of getting critically wounded? Or can I eventually deploy negative-Will panicky messes?
How much willpower do gravely wounded soldiers lose? The text says they suffer a permanent reduction?
Totally ordering the power set of a well ordered set. Let's say I take a set $S$, where $S$ can be well ordered. From what I understand, one can use that well ordering to totally order $\mathscr{P}(S)$.  How does a body actually use the well ordering of $S$ to construct a total ordering of $\mathscr{P}(S)$?  Perhaps construct is too strong a word. Is there a way to prove that a total ordering of $\mathscr{P}(S)$ just exists, no need to explicitly state what it is, since that might be very difficult. If you run a code snippet, a hat still appears (hats are above snippets in the Z-order) Suppose $f(x)$ is an irreducible polynomial over $\mathbb Z$ of degree $n$. Is it always the case that there exist distinct $x_1,\ldots,x_{2n+1}\in \mathbb Z$ such that $f(x_1),\ldots,f(x_{2n+1})$ are all prime?  So far I've tested a few irreducible polynomials using mathematica, and this has held. The motivation is to use this as a test for irreducibility, as if $f(x)$ is not irreducible then it takes on at most $2n$ prime values, as either factor takes on $1$ or $-1$ at most $2n$ times. (I'd also be interested in learning if this bound can be improved).  This could potentially be expended to other rings of integers, i.e. $\mathbb Z[i]$, but in that case the minimal number of primes needed to certify that $f(x)$ is irreducible would increase as more units appear. Give each site a parallel site for polling, recommendations and subjective-ish stuff Stuff like polls, recommendations based on subjective constraints, puzzles, webcomics etc. do not belong on the serious main SE sites, where professionals should be considered at work and having just a few spare minutes ("code's compiling") to answer questions, so they should not be distracted by such things. However, I'd also like to have a home for these things still using the SE engine. For the reason I mentioned before, this needs to be a separate place though. Let's call it four.[sitename-here].com. Why is a ConcurrentModificationException thrown and how to debug it What exactly are the spikes, or peaks and valleys, caused by in pictures such as these    Wikipedia states that "From the point of view of magnetic energy, peaks and valleys are energetically favorable", but I'm not exactly sure what that means, or how it works. Why isn't the fluid just happy being attracted to the magnet in a semi-sphere shape? Could it be that it gains a magnetic charge, so it attempts to repel itself at the same time? Just pulling at straws here. Local polynomial regression: Why does the variance increase monotonically in the degree? How can I show that the variance of local polynomial regression is increasing with the degree of the polynomial (Exercise 6.3 in Elements of Statistical Learning, second edition)?  This question has been asked  but the answer just states it follows easliy.  More precisely, we consider $y_{i}=f(x_{i})+\epsilon_{i}$ with $\epsilon_{i}$ being independent with standard deviation $\sigma.$  The estimator is given by  $$ \hat{f}(x_{0})=\left(\begin{array}{ccccc} 1 &amp; x_{0} &amp; x_{0}^{2} &amp; \dots &amp; x_{0}^{d}\end{array}\right)\left(\begin{array}{c} \alpha\\ \beta_{1}\\ \vdots\\ \beta_{d} \end{array}\right) $$ for $\alpha,\beta_{1},\dots,\beta_{d}$ solving the following weighted least squares problem $$ \min\left(y_{d}-\underbrace{\left(\begin{array}{ccccc} 1 &amp; x_{1} &amp; x_{1}^{2} &amp; \dots &amp; x_{1}^{d}\\ \vdots\\ 1 &amp;  &amp;  &amp;  &amp; x_{n}^{d} \end{array}\right)}_{X}\left(\begin{array}{c} \alpha\\ \beta_{1}\\ \vdots\\ \beta_{d} \end{array}\right)\right)^{t}W\left(y-\left(\begin{array}{ccccc} 1 &amp; x_{1} &amp; x_{1}^{2} &amp; \dots &amp; x_{1}^{d}\\ \vdots\\ 1 &amp;  &amp;  &amp;  &amp; x_{n}^{d} \end{array}\right)\left(\begin{array}{c} \alpha\\ \beta_{1}\\ \vdots\\ \beta_{d} \end{array}\right)\right) $$ for $W=\text{diag}\left(K(x_{0},x_{i})\right)_{i=1\dots n}$ with $K$ being the regression kernel. The solution to the weighted least squares problem can be written as $$ \left(\begin{array}{cccc} \alpha &amp; \beta_{1} &amp; \dots &amp; \beta_{d}\end{array}\right)=\left(X^{t}WX\right)^{-1}X^{t}WY. $$ Thus, for $l(x_{0})=\left(\begin{array}{ccccc} 1 &amp; x_{0} &amp; x_{0}^{2} &amp; \dots &amp; x_{0}^{d}\end{array}\right)\left(X^{t}WX\right)^{-1}X^{t}W$ we obtain $$ \hat{f}(x_{0})=l(x_{0})Y $$ implying that  $$ \text{Var }\hat{f}(x_{0})=\sigma^{2}\left\Vert l(x_{0})\right\Vert ^{2}=\left(\begin{array}{ccccc} 1 &amp; x_{0} &amp; x_{0}^{2} &amp; \dots &amp; x_{0}^{d}\end{array}\right)\left(X^{t}WX\right)^{-1}X^{t}W^{2}X\left(X^{t}WX\right)^{-1}\left(\begin{array}{ccccc} 1 &amp; x_{0} &amp; x_{0}^{2} &amp; \dots &amp; x_{0}^{d}\end{array}\right)^{t}. $$ My approach: An induction using the formula for the inverse of a block matrix but I did not succeed.  The paper  by D. Ruppert and M. P. Wand derives an asymptotic expression for the variance for $n\rightarrow\infty$ in Theorem 4.1 but it is not clear that is increasing in the degree. Method defined as testMethod do not support web service callouts, test skipped What purpose does downvoting questions serve? Conditional Expectation of Composite Function Preliminaries  Let $(\Omega, \mathcal{G}, \mathbb{P})$ be a complete probability space.  Let $D$ be a complete, separable, metrizable topological space with Borel $\sigma$-algebra $\mathcal{B}(D)$ (such as $D = \mathbb{R}^q$ with $\sigma$-algebra $\mathcal{B}(D) = \mathcal{B}(\mathbb{R}^d)$).  Let $\mathbb{R}$ be equipped with its canonical Borel $\sigma$-algebra $\mathcal{B}(\mathbb{R})$.  Let $g: \Omega \times D \rightarrow \mathbb{R}$ be a bounded $(\mathcal{G} \otimes \mathcal{B}(D) ) / \mathcal{B}(\mathbb{R})$-measurable function.  Let $\Pi: \Omega \rightarrow D$ be a $\mathcal{G}/\mathcal{B}(D)$-measurable random variable.  Let $H : \Omega \rightarrow \mathbb{R}$ be a $\mathcal{G}/\mathcal{B}(\mathbb{R})$-measurable random variable, defined by $$ H(\omega) := g(\omega, \Pi(\omega)).$$ Note, that, since $g$ is bounded, we have $H \in \mathcal{L}^2(\Omega, \mathcal{G}, \mathbb{P})$.  Let $j: D \rightarrow \mathcal{L}^2(\Omega, \mathcal{G}, \mathbb{P}) $ be defined by $$ j(\pi)(\omega) := g(\omega, \pi)  $$  For all $\pi \in D$, let $j(\pi)$ be independent of $\Pi$.  Question  I am interested in the conditional expectation $$\mathbb{E}[H \mid \Pi] :\Omega \rightarrow \mathbb{R}$$ of $H$ with respect to $\Pi$. More specifically, I suspect that (a $\mathbb{P}$-unique version of) this condititional expectation is given by  $$ \mathbb{E}[H \mid \Pi] (\omega) = \mathbb{E}[j(\Pi(\omega))], \quad (\dagger)  $$ whereby $\mathbb{E}[j(\Pi(\omega))]$ can of course also be written as $$\mathbb{E}[j(\Pi(\omega))] = \int_{\Omega} j(\Pi(\omega))(\tilde{\omega}) d\mathbb{P}(\tilde{\omega}) . $$  How can I prove, that $(\dagger)$ is the case? I have tried, tracking the definition of conditional expectation and using Fubini, but with little success so far.  Thanks for any advice! Adding HTML entities using CSS content Drop rates for set / legendary items Just wondering what the drop rates were for Set / Legendary items, or is it totally random? I imagine they would increase for later acts in Inferno. My monk is comfortable in Act 3 in Inferno, but I've only found one set item, so MF will increase chances for them? Path-connected and locally connected space that is not locally path-connected How do you force constructor signatures and static methods? Is there a way of forcing a (child) class to have constructors with particular signatures or particular static methods in C# or Java?  You can't obviously use interfaces for this, and I know that it will have a limited usage. One instance in which I do find it useful is when you want to enforce some design guideline, for example:  Exceptions They should all have the four canonical constructors, but there is no way to enforce it. You have to rely on a tool like FxCop (C# case) to catch these.  Operators There is no contract that specifies that two classes can be summed (with operator+ in C#)  Is there any design pattern to work around this limitation? What construct could be added to the language to overcome this limitation in future versions of C# or Java? I get the following error when trying to ls *.txt | wc -l a directory that contains many files:  -bash: /bin/ls: Argument list too long   Does the threshold of this "Argument list" dependent on distro or computer's spec?  Usually, I'd pipe the result of such big result to some other commands (wc -l for example), so I'm not concerned with limits of the terminal. How do I share a folder on SAMBA? Re-number a list when a new entry is inserted I have a text file of numbered entries:  1. foo 2. bar 100% 3. kittens 4. eat cake 5. unicorns 6. rainbows   and so on up to some large number. Then after an empty line, a new block starts from 1.  I insert a new entry, replacing, say, 4. and I need to renumber all the subsequent entries in the block:  1. foo 2. bar 100% 3. kittens 4. sunshine &lt; 5. eat cake 6. unicorns 7. rainbows Double vs. BigDecimal? Using Gnome 3.18. I share files between other family members, but the default umask on my distro (archlinux) is 0022. So every file/directory created is not writable for our common group.  I tried to put umask 0002 in /etc/profile but the gnome session is still using 0022. It's working for a login bash shell, though.  I also tried to add this line in /etc/pam.d/system-auth:  session   required  pam_umask.so umask=0002  It has the same effect as the one in /etc/profile. I tried  If I change the umask manually in a gnome-terminal shell, then I launch an application from it, say gedit, then the files created by it have the wanted permissions. If I launch gedit from the gnome menus, it doesn't. So my matter is really to set the umask for the gnome session, and I can't find where to do it.  EDIT (to answer Gilles' comment): I'm using gdm 3.18 as the DM. I also tried to add the pam_umask line into /etc/pam.d/gdm-launch-environment. All other gdm-* files contains includes of session from the system-auth file, so they should not need more. It doesn't change anything.  /etc/login.defs contains UMASK 077 but also USERGROUPS_ENAB yes which should set the umask to either 0077 or 0007 for users whose primary group is the username.  The only file that contains 022 for umask in /etc is /etc/profile but that was my first try.  As for /etc/Xsession.d, I don't have this directory. Besides, as wayland is now the default display server, I'm not sure the umask should be set as part of X initialisation, even if I'm still using it myself. Adding dynamic text to layout from attribute table with Data Driven Pages I was trying to figure out how to use dynamic text from an attribute table in a collection of Data Driven Pages in ArcGIS 10.   I've looked in the help files, but can't find anything on dynamic text from attribute tables.