I came across some blood relations / intra family marriages like first cousin marriages in some of my family history books that I have. They are all documented as text in a family history book, not as a pedigree. I tried  to draw such a tree, but no luck. I don't think I can loop back a child node to an ancestor and create a marriage relation, but has to create another duplicate tree.  Reading about , I came across such a . Is this the right way to show a family tree which has first cousin marriages or is there a better way? Is there a software or website where I can do something like this?
Deep in my families history (1600's or there abouts) our family split in two. About three or four generations later two distant cousins got married creating a split / rejoin.                G.G.G.Parents A        +---------+---------------------------+     G.G.Grand Parent                      G.G.Grand Parent        |                                     |     G.Grand Parent                        G.Grand Parent        |                                     |     Grand Parent                          Grand Parent        |                                     | +------+-------+                     +-------+-------+ Aunt       Parent A - - -+- - - Parent B         Uncle                          |                   +------+------+                Child A        Child B                  ...           ...   So in this small example, the family splits in two at G.G.Grandparents and then rejoins later when Parent A and Parent B marry.  About 8 years ago I tried to find a software package which could model this and failed. Has anything happened in the intervening time?  Sorry I'm just asking in SE without doing much research, but I spent a lot of effort last time without any success and I am sure there is someone out there who can point me to an excellent package!    @ColeValleyGirl: I'm looking for a piece of software that is able to print out such a tree/DAG (thanks @ACProctor) in high enough quality to display/frame. All software I tried before didn't seem to be able to display this as they seemed to support mainly variations of Ancestors / Descendants rather than an output of all the people that had been inputed.  @AdrianB38: Essentially, I want to see "everyone". The tree I have was put together by my grandfather, who probably had a lot more data/people, but I've only got the hand written tree which highlights this split. It's essentially a tree of my grandparents ancestors (including this split which is joined at a common ancestor) and descendants (me + my family). I'd like to reproduce this in the computer (there is about 400 years - hundreds of people).  @AdrianB38: Re your point about generations, yes, I have that issue. I think it's only one generation, might be two - i've not looked at the tree in a while. The split between families happened over about 150-200 years iirc.  I can write an SVG generator if I really need to (I'm a Software Engineer) albeit I'm aware such a "loop"/"dependency" is painful to program for, but I was hoping that there was something which could handle this.
How to get into Walker in the Wastes as a level 3 Wizard I am building a Wizard character that focuses on using Greater Drought from the Walker in the Wastes prestige class.  The campaign is starting at level 12, so I need to figure out a way to build a Wizard 3/Walker in the Wastes 9.  I am planning on using Southern Magician and Extra Spell to get around the spell requirement, but I'm having trouble qualifying for Heat Endurance by level 3.  We are using a variant rule where, at every level divisible by 3, we get 3 feats instead of 1. At level 3, I'll have 1 feat from level 1, and 3 feats from level 3.  How can I build a character with 11 total levels of Wizard spellcasting and the Greater Drought Walker in the Wastes ability by level 12?  My current character sheet can be found . How to find historical airfares? Is there a way to find out how much it would have cost to buy a particular airplane ticket at some point in the past?    For example, how could I find out how much it would have cost to buy a one-way itinerary from airport A to airport B on October 1, 2011 for travel on November 1, 2011? Inverting Polygons using QGIS? I have a Shapefile with Polygon features  representing the world's land areas (continents, islands).   Is it possible to invert these, and get a geometry that represents the world's oceans and seas?   So the original land Polygons need to become rings in a single global Polygon that covers the planet.  Basically, I'm looking for something like Select > Inverse in Photoshop.   I am using QGIS. Insert Login IP Ranges using apex in salesforce Is it possible to insert to Login IP ranges via apex? If the series $\sum_0^\infty a_n$ converges, then so does $\sum_1^\infty \frac{\sqrt{a_n}}{n} $ Problem:      Suppose that for every $n\in\mathbb{N}$, $a_n\in\mathbb{R}$ and $a_n\ge 0$. Given that   $$\sum_0^\infty a_n$$   converges, show that    $$\sum_1^\infty \frac{\sqrt{a_n}}{n} $$   converges.   Source: Rudin, Principles of Mathematical Analysis, Chapter 3, Exercise 7. What to do with cross-site duplicates? What's the right course of action for cross-site duplicates?  There are two flavors:   A question is posted which belongs on another site and ends up already having been asked there. I can't find an example right now, but it's bound to happen soon if it hasn't already. The same question is posted in two places at the same time. Take  for example, which is a duplicate of , posted within a half hour of each other by the same user.   Possible actions:   Move it to the proper site and close it once it gets there as a duplicate. Provide a way to close it right away as a cross-site duplicate, without moving it first. Flag it and let a moderator merge them. Close it as "no longer relevant" or something else.   Additionally, flavor 2 is a bit of a special case; perhaps the question really spans both sites in terms of content and intended audience. Should multiple-postings in this case be allowed? If so, should they somehow be linked to each other? If not, how do we avoid a migration war? As much as I have tried, it doesn't seem possible to use separate labels when using a casesconstruction (from the amsmath package).  Ideally, I would like to be able to write something like  \documentclass{article} \usepackage{amsmath} \begin{document} \begin{equation} f(x)=\begin{cases}   1&amp;x\geq0\label{positive}\\   0&amp;x&lt;0\label{negative} \end{cases} \end{equation} \end{document}   and later refer to both cases at different places. What would be the best way to achieve this result? Oddly wide spaces in subsection title I have a problem, this is what it looks like:     And this is the code:  \subsection{Bakterienst\"amme und Anzuchtbedingungen}   Where does the huge whitespace come from? If $p,q,r$ are all primes,and $p|qr-1$,$q|pr-1$ and $r|pq-1$,find all possible values of $pqr$. If $p,q,r$ are all primes,and $p|qr-1$$~~~~~~~~~~~~~$$q|pr-1$$~~~~~~~~~~$ and $~r|pq-1$. Find all possible values of $pqr$.    My work: $qr-1=pk_1$ $pr-1=qk_2$ $pq-1=rk_3$ From the above equations, we can conclude that either $k_1,k_2,k_3$ are all even or one of the primes is $2$. I can also get that, $p^2q^2r^2=(pk_1+1)(qk_2+1)(rk_3+1)$ Now, I cannot proceed. Please help! Parallel website running a copy of my original website We have been working on a gaming website. Recently while making note of the major traffic sources, I noticed a website that I found to be a carbon-copy of our website. It uses our logo, and everything else the same as ours, but with a different domain name.   Their domain name is not however pointing to our site because at several places the links are like: carbonccopy-website/our-links. This website even has links to some images as: carbonccopy-website/our-images.   How could they have done that, and what can I do to stop it? $H_1 ,H_2 \unlhd \, G$ with $H_1 \cap H_2 = \{1_G\} $. Prove every two elements in $H_1, H_2$ commute How does Router know where to forward packet What is the simplest SQL Query to find the second largest value? How to run updmap-sys after installing cm-super? My original question was:   The answer that seems suitable to my cause is to install cm-super. I did that (using package manager [winxp 32 bit, MikTex installation 2.9 recently updated]). But still the command  \usepackage{cm-super}    yields an error.  User H Cavendish suggested to run updmap-sys, but I am not sure about how to do that on WinXP.   2011 November 04 edit: I made it sure that I have installed 'cm-super' - but still get the same error:   I have also tried updating the file name databases - but no avail. Prove that a limit doesn't exist In my assignment I have to prove that the following function doesn't have a limit:  $$f(x)=\frac{x}{x-\lfloor{\sin x}\rfloor}$$ when $${x \to 0}$$  In other words, I have to prove that for every $\delta$ such that $0&lt;|x-{x_0}|&lt;\delta,$ $|f(x)-L|&gt;\epsilon$.  In fact, I don't even know how to start. Do I choose my $\delta$? I know that the sin function has certain values that's supposed to help me. How do I use it?  I have to prove this by definition, so I can't use limit arithmetic for example  Thanks. How can I prevent data theft from a company?  Are there any solutions to this problem?  Is there any software that encrypts important data (.doc, .xls, etc.) and prevents it from copying?  I need a solution where employees can read/write documents but can not copy then to a USB drive or e-mail them. I've been reading , and I would like to know why the Lasso provides variable selection and ridge regression doesn't.  Both methods minimize the residual sum of squares and have a constraint on the possible values of the parameters $\beta$. For the Lasso, the constraint is $||\beta||_1 \le t$, whereas for ridge it is $||\beta||_2 \le t$, for some $t$.  I've seen the diamond vs ellipse picture in the book and I have some intuition as for why the Lasso can hit the corners of the constrained region, which implies that one of the coefficients is set to zero. However, my intuition is rather weak, and I'm not convinced. It should be easy to see, but I don't know why this is true.  So I guess I'm looking for a mathematical justification, or an intuitive explanation of why the contours of the residual sum of squares are likely to hit the corners of the  $||\beta||_1$ constrained region (whereas this situation is unlikely if the constraint is $||\beta||_2$). When you attempt to modify a file without having write permissions on it, you get an error:  &gt; touch /tmp/foo &amp;&amp; sudo chown root /tmp/foo &gt; echo test &gt; /tmp/foo zsh: permission denied: /tmp/foo   Sudoing doesn't help, because it runs the command as root, but the shell handles redirecting stdout and opens the file as you anyway:  &gt; sudo echo test &gt; /tmp/foo zsh: permission denied: /tmp/foo   Is there an easy way to redirect stdout to a file you don't have permission to write to, besides opening a shell as root and manipulating the file that way?  &gt; sudo su # echo test &gt; /tmp/foo How to programmatically send SMS on the iPhone? Does anybody know if it's possible, and how, to programmatically send a SMS from the iPhone, with the official SDK / Cocoa Touch? Each site got a &quot;hot&quot; tab, where its contents are calculated based on . However take a look on the screenshots below and see for yourself that &quot;hot&quot; got nothing to do with many of the questions listed there. :    :    As you can see, there are questions with negative score, no answers, and even closed. I won't be surprised to see spam in there as well. This can't be any worse. What I suggest, instead of fixing the formula or patching it, simply have the hot tab show the same questions as the Hot Network Questions sidebar. (from the specific site only, of course.) Since the hot questions &quot;pool&quot; (as seen ) is limited to 100 for the whole network, either expand it or have the per-site list show questions with less hotness points - it would still be better than what we have now.