can we fit a VAR model if we have a mixture of I(0) and I(1) variables?
I have 4 time series. One of them is stationary and rest of them are not. I need to find relation between them. I will use AIC to decide lag length.   Should I use VAR or VECM to find relation between them?  Will VAR or VECM give me relation in terms of equation which can be used for forecasting?  Do I need to perform Johansen's test of cointegration?  What good would it do?
I had this "almost bonus" question on the final in Group Theory recently: prove that there is no such group $G$ which would satisfy Aut$(G)\cong \mathbb{Z}_n$, where $n$ is an odd integer. I don't have much certainty if this proof is OK, and one's opinion would be appreciated.  Here's my attempt:     Suppose that there exists such a group $G$ that satisfies the above condition. Since $\mathbb{Z}_n$ is cyclic, Aut$(G)$ is also cyclic and $G$ is abelian, which implies that Inn$(G)\cong \{e\}$. Thus Aut$(G)=$Out$(G)$. (I don't think this fact is important here though). Now, since an automorphism sends a generator to a generator, and since each automorphism is completely determined by such mapping, |Aut($G$)| must be of factorial order. But an integer factorial is always even. However, $|\mathbb{Z}_n|$ is odd, which is a contradiction. Therefore, no such $G$ exists.   I'm afraid that my proof is not very nice, but at least a genuine attempt was made. When running 'screen ls' the screen stops with the text [screen is terminating]. I would like screen to keep the session alive and reattach to it to see the output of ls.  Of course the real thing is that I don't run screen ls, but rather a screen fsck ..., so I would like to ensure that the screen is not terminating when this command is finished.  I would love to have an answer that is useful for an already existing running screen session, so some interactive keys like C-a ... or C-a : (Enter command line mode) Removing intercept from GLM for multiple factorial predictors only works for first factor in model I am running a binomial logistic regression with a logit link function in R. My response is factorial [0/1] and I have two multilevel factorial predictors - let's call them $a$ and $b$ where $a$ has 4 factor levels  $(a_1,a_2,a_3,a_4)$ and $b$ has 9 factor levels $(b_1,b_2,\dotsc,b_9)$. Therefore:  mod &lt;- glm(y ~ a + b, family = binomial(logit), data=pretend) summary(mod)   The model output would then show all the information about the model as well as the coefficients.  There is a factor level for both a and b missing (a1 and b1) from the summary output. I understand that it is constrained in the "intercept" of the model. I have read that if I want to remove the intercept term and see the estimates for those factor levels I can just add -1 to the model formula, i.e.:  mod2 &lt;- glm(y ~ a + b - 1, family=binomial(logit), data=pretend) summary(mod2)   In the new model (mod2) the intercept term is then gone and variable a's factor-level a1 is given amongst the list of coefficients. But, variable b's factor-level b1 is still missing and given that there is no intercept term anymore, how can I interpret the odds-ratio for that factor level then?  Could someone please explain to me how to get the coefficient for b1 too and why this is happening? Generate four random words from a list for XKCD-like passwords For start, we know how can we output random lines from a txt file:   perl -MList::Util -e 'print List::Util::shuffle &lt;&gt;' words.txt   But we need a general solution (perl is usually installed on every unix-like OS) to output 4 random words from a txt file, how can we do it?    $ cat words.txt ... alpha beta gamma delta epsilon ... $   The "..." represents many other words.   Example output (without newline between them, but one unix newline is needed at the end, spaces should separate them):  $ perl SOMEMAGIC words.txt gamma alpha delta beta $   Using only perl, the shortest possible solution (oneliner).   It will be used as human memorable password generator:    Since afaik perl is enough good to be named "random generator".   Example common english wordlist with 32768 unique lines: How to change launcher icon Is there a way to customize a Lucid Lynx Launcher icon for various programs? There does not seem to be a way to do this using Create Launcher or Launcher properties. The application is not actually "installed" on the PC, the executable has just been copied. All I've been able to do so far is to add the command /home/t32/bin/pc_linux/t32marm -c /home/t32/config_usb.t32 to a generic Launcher icon using Create Launcher. Linux, find all files matching pattern and delete Looking to find all files (recursively) which have an underscore in their file name and then delete them via command line. tikz relative coordinates Let $a\in \mathbb{Z}$ be such that $a=b^2+c^2$ where, $b,c \in \mathbb{Z}-\{0\}$. Then $a$ cannot be written as    $pd^2$ where $d \in \mathbb{Z}$ and $p$ is prime with $p \equiv 1~(mod~4)$ $pd^2$ where $d \in \mathbb{Z}$ and $p$ is prime with $p \equiv 3~(mod~4)$ $pqd^2$ where $d \in \mathbb{Z}$ and $p,q$ are primes with $p \equiv 1~(mod~4)$ and $q \equiv 3~(mod~4)$ $pqd^2$ where $d \in \mathbb{Z}$ and $p,q$ are primes with $p,q \equiv 3~(mod~4)$   The similar question with some part missing is asked , but I want to discuss additional options too.  Here, I got 1) is false Since $13=3^2+2^2$ For other options What should I do How do we use drupal_add_library(), drupal_add_css() and drupal_add_js()? How do I use drupal_add_library(), drupal_add_css() and drupal_add_js() in Drupal 8?  I am porting a module that uses those functions. I am following what reported in , which says these functions have been removed in favor of #attached, but I am not able to attach these files to my configuration page.  The error I am getting is the following:     Uncaught PHP Exception LogicException: "You are not allowed to use js in #attached"   How do I attach CSS and JavaScript to a page? GridView sorting: SortDirection always Ascending I run windows 7. I run a Minecraft server, but I can only host around 9 players before lag appears.   I heard that Ubuntu can run a server with much better performance than Windows 7. I kind of like the whole idea of Ubuntu, but I don't want to change my OS to Unix or anything else.  Basically, my question is, does running a server (specifically and Minecraft server) run easier and faster on a Ubuntu server? On top of that, how would one set that up? Intuitive/direct proof that a rectangle partitioned into rectangles each with at least one integer side must itself have an integer side A challenge problem asked to show that if rectangle $R$ with axis-parallel sides is partitioned into finitely many subrectangles $R_1,R_2,\ldots,R_n$ (also with axis-parallel sides), such that each $R_i$ has at least one integer side length, then $R$ must also have at least one integer side length. The only proof I've seen, although simple, is quite unintuitive. Namely you look at the integral  $$ \int_R e^{2 \pi i (x+y)} dx dy $$ and note that the integral is $0$ if and only if $R$ has an integer side length, and then note that by assumption the integral is $0$ over all the $R_i$, hence summing the integral over all $R_i$ gives that the integral is also $0$ over $R$. Can someone give a more direct/intuitive argument that doesn't use voodoo like a complex-valued integral? What *is* an Artificial Neural Network? As we delve into  literature, we get to identify other methods with neuromorphic topologies ("Neural-Network"-like architectures). And I'm not talking about the . Examples are given below.  Then, it makes me wonder: what is the definition of an artificial Neural Network? Its topology appears to cover everything.    Examples:  One of the first identifications we make is between PCA and a linear Autoencoder with tied-weights in the encoder and decoder and thresholded activations in the bottleneck layer.  Also, a common identification is done between linear models (logistic regression in special) and a Neural Network with no hidden layer and a single output layer. This identification opens several doors.  . ? ANN. Gaussian Process? ANN (with single hidden layer with infinite hidden units).  And so, just as easily, we can incorporate arbitrary regularized versions with specialized loss functions of these algorithms into a Neural Network framework.  But the more we dig, the more similarities appear. I just stumbled into , which makes the identification of a specific ANN architecture with decision trees, allowing these to be learned by ANN methods (such as Gradient Descent backpropagation). From this we can construct Random Forests and Gradient Boosted Decision Trees from solely Neural Network topologies.  If everything can be expressed as an Artificial Neural Network, what defines an Artificial Neural Network? I tried to write out the aura if statement but I am getting stuck if someone can explain it to me in detail. thank you  &lt;aura:if isTrue=&quot;{!lessthan(v.Tl.time, v.Tl.End_Date_Time1__c)}&quot;&gt;                            &lt;/aura:if&gt; Are shell scripts sensitive to encoding and line endings? I want to start an Xorg server (which should only feature a minimal xterm terminal emulator from a newly created &quot;pristine&quot; tty). I have thought this to be as simple as issuing a xinit or maybe a startx however both have failed me. Therefore the question: How to manually run/init/start a Xorg server on a different VT/TTY? here the Longer background story to the question at hand: This is the backgroud and what I have tried already: Looking at man openvt I was able to run a shell on a newly created tty (or vt, cannot tell precisly the different vt&lt;&gt;tty) like this:  $&gt; sudo openvt -s /bin/bash  the -s of causes the direct switch to that new tty/vt on that new tty I wanted to manually start a Xorg server which according to man xinit should start with a minimal xterm application. On the new shell on the switched to tty I (created via openvt) I hence issues this command:  $&gt; su -c 'xinit xterm -display :4 -- :4' - mahr &amp;&gt;/tmp/output  and I receive this output $&gt; cat /tmp/output X.Org X Server 1.19.6 Release Date: 2017-12-20 X Protocol Version 11, Revision 0 Build Operating System: Linux 4.4.0-148-generic x86_64 Ubuntu Current Operating System: Linux scitech 4.15.0-70-generic #79-Ubuntu SMP Tue Nov 12 10:36:11 UTC 2019 x86_64 Kernel command line: BOOT_IMAGE=/vmlinuz-4.15.0-70-generic root=/dev/mapper/ubuntu--vg-root ro Build Date: 03 June 2019  08:10:35AM xorg-server 2:1.19.6-1ubuntu4.3 (For technical support please see http://www.ubuntu.com/support)  Current version of pixman: 0.34.0     Before reporting problems, check http://wiki.x.org     to make sure that you have the latest version. Markers: (--) probed, (**) from config file, (==) default setting,     (++) from command line, (!!) notice, (II) informational,     (WW) warning, (EE) error, (NI) not implemented, (??) unknown. (==) Log file: &quot;/home/mahr/.local/share/xorg/Xorg.4.log&quot;, Time: Thu Nov 28 10:57:53 2019 (==) Using system config directory &quot;/usr/share/X11/xorg.conf.d&quot; (EE)  Fatal server error: (EE) parse_vt_settings: Cannot open /dev/tty0 (Permission denied) (EE)  (EE)  Please consult the The X.Org Foundation support       at http://wiki.x.org  for help.  (EE) Please also check the log file at &quot;/home/mahr/.local/share/xorg/Xorg.4.log&quot; for additional information. (EE)  (EE) Server terminated with error (1). Closing log file.  Session terminated, terminating shell...xinit: giving up xinit: unable to connect to X server: Connection refused xinit: unexpected signal 2  ...terminated. Old usernames stick to Community Wiki posts On a whim the other day, I changed my meta name from Lord Torgamus to Popular Demand.  I just noticed that the old name has "stuck" to the author tag of ; everywhere else on meta, my new name displays as expected.  Is this a feature?  Is it a bug?  Mostly I'm just curious, as I can't think of a strong reason in favor of keeping this behavior or a strong reason for changing it.  A question somewhat like this has been raised before as , but the previous poster implied that the issue had something to do with migration, which my situation shows is not the case. I want to know where the Metro applications (Mail, People, Messages, ...) executable file path is.  Also, how can I run Mail application when my PC starts? This is a very basic query I can't figure out....  Let's say I have a two column table like this:  userid  |  roleid --------|--------    1    |    1    1    |    2    1    |    3    2    |    1   I want to get all distinct userids that have roleids 1, 2 AND 3.  Using the above example, the only result I want returned is userid 1.  How do I do this? Finding an item in a List using C#